ggeo5manual

User’s Guide

Version 5.6

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Geo 5 - User's Guide © Fine Ltd. 2008

Content

Using function Find 12User defined environment 12 Window for application 12 Control menu 13 Horizontal tool bars 14 Tool bar Files 14 Tool bar Scale and shift 15 Tool bar Plot setting 16 Tool bar Stage of construction 16 Tool bar 3D visualization 17 Tool bar Selections 18 Vertical tool bars 18 Setting visualization style 19 Style manager 20 Frames 21 Tables 22 Dialogue windows 24 Active dimensions and objects 25 Unit metric / imperial 26 Copy to clipboard 26 Options 26 Options – copy to clipboard 27 Options – print picture 28 Options - input 29Common input 29 Project – Earth pressures 29 Inputting and editing soils 30 Soil classification 32 Soil and rock labels 33 Manual classification of soil 33 Interfaces in 2D environment 34 Adding interface 35 Editing interface 36 Corrector of inputted interface 36 World coordinates 38 Assigning soils 38 Design coefficients 39 Running more analyses / verifications 40 Connecting programs 41 Selecting and storing views 42 Setting results visualization 43 Setting color range 44 Scale color definition 45 Import - export DXF 46 Reading data into template 47 Inputting data using template 47 Modifying template during data input 48 Export DXF 49Input regimes and analysis 50 Program Earth Pressure 50 Project 50 Geometry 51 Profile 51 Soils 52 Assign 53 Terrain 54 Water 54 Surcharge 55 Earthquake 56 Setting 57 Analysis 57 Program Sheeting Design 58

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Project 58 Profile 59 Soils 59 Assign 60 Geometry 61 Anchors 61 Props 62 Supports 62 Pressure specification 63 Terrain 64 Water 65 Surcharge 66 Forces 67 Earthquake 67 Setting 68 Analysis 69 Program Sheeting Check 70 Project 70 Profile 71 Modulus of subsoil reaction 71 Soils 72 Geometry 73 Adding and editing section 73 User catalogue 74 Assign 75 Excavation 76 Terrain 77 Water 78 Surcharge 79 Forces 80 Anchors 80 Props 81 Supports 82 Earthquake 83 Setting 84 Analysis 84 Internal stability 86 External stability 87 Envelopes 88 Program Slope Stability 88 Project 88 Interface 89 Embankment 89 Earth cut 90 Soils 91 Rigid body 92 Assign 92 Anchors 93 Reinforcements 94 Surcharge 95 Water 96 Earthquake 97 Setting 98 Analysis 98 Constrains on the optimization procedure 100 Height multiplier 101 Program Cantilever Wall 102 Project 102 Geometry 103 Material 103 Profile 104 Soils 105 Assign 106 Terrain 106 Water 107

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Surcharge 108 Front face resistance 109 Inputted forces 110 Earthquake 111 Base anchorage 111 Setting 112 Verification 113 Bearing capacity 114 Dimensioning 114 Stability 115 Program Masonry wall 116 Project 116 Geometry 117 Material 117 Profile 118 Soils 119 Assign 120 Terrain 120 Water 121 Surcharge 122 Front face resistance 123 Inputted forces 124 Earthquake 125 Base anchorage 125 Setting 126 Verification 127 Bearing capacity 128 Dimensioning 128 Stability 129 Program Gravity Wall 130 Project 130 Geometry 131 Material 131 Profile 132 Soils 133 Assign 134 Terrain 134 Water 135 Surcharge 136 Front face resistance 137 Inputted forces 138 Earthquake 139 Setting 139 Verification 140 Bearing capacity 140 Dimensioning 141 Stability 142 Program Block Wall 143 Project 143 Geometry 143 Profile 144 Soils 145 Assign 146 Terrain 146 Water 147 Surcharge 148 Front face resistance 149 Inputted forces 150 Earthquake 151 Setting 151 Verification 152 Bearing capacity 152 Dimensioning 153 Stability 154 Program RediRock Wall 155

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Project 155 Blocks 156 Setbacks 156 Geometry 157 Footing 158 Profile 159 Soils 160 Assign 161 Terrain 161 Water 162 Surcharge 163 Front face resistance 164 Inputted forces 165 Earthquake 166 Setting 166 Verification 167 Bearing capacity 168 Dimensioning 169 Stability 169 Program Gabion 170 Project 170 Material 170 Geometry 171 Profile 172 Soils 173 Assign 173 Terrain 174 Water 175 Surcharge 175 Front face resistance 176 Inputted forces 177 Earthquake 178 Setting 178 Verification 179 Bearing capacity 179 Dimensioning 180 Stability 181 Program Spread Footing 182 Project 182 Project - Analyses 182 Profile 183 Soils 184 Assign 185 Foundation 185 Load 186 Import of loading 187 Geometry 188 Sand-gravel cushion 189 Material 190 Surcharge 191 Water, incompressible subsoil 192 Setting 193 1.LS - bearing of a footing 194 2.LS - settlement and rotation of a footing 195 Dimensioning 196 Program Pile 197 Project 197 Profile 198 Modulus of subsoil reaction 198 Soils 199 Assign 200 Load 201 Geometry 201 Material 202 Water, incompressible subsoil 203

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Negative skin friction 204 Setting 205 Vertical bearing capacity 205 Vertical bearing capacity CSN 205 Vertical bearing capacity FEM 206 Horizontal bearing capacity 207 Program Settlement 208 Project 208 Interface 208 Embankment 209 Earth cut 210 Incompressible subsoil 211 Soils 212 Assign 212 Surcharge 213 Water 214 Setting 215 Analysis 215 Program Abutment 216 Project 216 Geometry cut 217 Wings 218 Geometry plane view 219 Foundation steps 220 Material 220 Profile 221 Soils 222 Loading - LC 223 Assign 223 Terrain 224 Water 225 Surcharge 226 Front face resistance 227 Inputted forces 228 Earthquake 229 Setting 229 Verification 230 Bearing capacity 231 Dimensioning 231 Stability 233 Program Nailed slopes 233 Project 233 Geometry 234 Types of nails 234 Geometry of nails 235 Material 236 Profile 236 Soils 237 Assign 237 Terrain 238 Water 239 Surcharge 240 Earthquake 241 Setting 241 Internal stability 242 Verification 242 Bearing capacity 243 Dimensioning 244 External stability 245 Program Ground Loss 246 Project 246 Buildings 246 Profile 247 Soils 248 Assign 249

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Geometry 249 Measurement 250 Settings 251 Analysis 251 Damages 252 Program Rock slope 254 Project 254 Terrain 255 Rock 256 Slip surface – plane 256 Slip surface - polygonal 257 Parameters – polygonal slip surface 258 Water – plane slip surface 259 Surcharge – plane and polygonal slip surface 260 Anchors – plane and polygonal slip surface 260 Earthquake 261 Setting 262 Analysis – plane slip surface 262 Analysis – polygonal slip surface 263 Geometry 264 3D View 264 Slip surface – rock wedge 265 Parameters – rock wedge 266 Surcharge – rock wedge 266 Anchors – rock wedge 267 Water – rock wedge 268 Analysis – rock wedge 268 Program Terrain 269 Project 269 Basic data 269 Global coordinate system 270 Soils 271 Assign 272 Points 272 Import of points 274 Automatic calculation of height 274 Edges 275 Water 277 Bore holes 278 Earth grading 279 Generate 281 Modeling terrain on edges 282 Point constructions 283 Line constructions 284 Launching 285Outputs 287 Adding picture 287 Picture list 288 Print and export document 289 Print and export picture 290 Control menu Print and export 291 Tool bar Print and export 292 Setting header and footer 293 Page properties 294 Page numbering 295 About company 295Theory 297 Stress in a soil body 297 Geostatic stress, uplift pressure 297 Effective/total stress in soil 298 Increment of earth pressure due to surcharge 299 Increment of earth pressure under footing 300 Earth pressure 302 Sign convention 302

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Active earth pressure 303 Active earth pressure – the Mazindrani theory 303 Active earth pressure - the Coulomb theory 304 Active earth pressure - the Müller-Breslau theory 305 Active earth pressure - the Caqouot theory 306 Active earth pressure - the Absi theory 307 Active earth pressure – total stress 308 Passive earth pressure 308 Passive earth pressure - the Rankin and Mazindrani theory 309 Passive earth pressure - the Coulomb theory 310 Passive earth pressure - the Caquot – Kérisel theory 310 Coefficient of passive earth pressure Kp 312 Reduction coefficient of passive earth pressure 313 Passive earth pressure - the Müller – Breslau theory 313 Passive earth pressure - the Absi theory 314 Passive earth pressure - the Sokolovski theory 314 Passive earth pressure – total stress 316 Earth pressure at rest 316 Earth pressure at rest for inclined ground surface at the back of structure 317 Setting of analysis 318 Alternate angel of internal friction of soil 319 Distribution of earth pressures in case of broken terrain 320 Influence of water 321 Without ground water, water is not considered 321 Hydrostatic pressure, ground water behind structure 321 Hydrostatic pressure, ground water behind and in front of structure 322 Hydrodynamic pressure 323 Special distribution of water pressure 324 Uplift pressure in footing bottom 325 Influence of tensile cracks 326 Minimal dimensioning pressure 326 Earth - pressure wedge 327 Surcharge 329 Surface surcharge 329 Strip surcharge 330 Trapezoidal surcharge 331 Concentrated surcharge 331 Line surcharge 332 Surcharge in non-homogeneous soil 334 Surface surcharge 334 Strip surcharge 335 Trapezoidal surcharge 336 Concentrated surcharge 336 Surface surcharge 337 Influence of earthquake 337 Mononobe–Okabe theory 340 Arrango theory 340 Influence of water 341 Influence of friction between soil and back of structure 343 Table of ultimate friction factors for dissimilar materials 344 Table of recommended values DELTA/FÍ 345 Adhesion of soil 345 Parameters of rocks 346 Nailed slopes 347 Analysis of nails bearing capacity 347 Estimated bond strength 349 Analysis of internal stability 349 Force of transmitted by nails 350 Factor of safety 350 Theory of limit states 351 Verification of bearing capacity of nails 352 Dimensioning of concrete cover 352 Analysis of walls 353 Geo-reinforcements, mesh overhangs 354 Base anchorage 354

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Verification – limit states 356 Verification - factor of safety 357 Accounting for wall jump 358 Dimensioning of masonry wall 359 Bearing capacity of foundation soil 360 Wall dimensioning 361 Internal stability of gabion 362 Internal stability of gabion wall – limit states 364 Internal stability of gabion wall – factor of safety 365 Calculating abutment forces 366 Sheeting design 367 Analysis of sheet pile wall 367 Analysis of anchored wall fixed in heel 368 Analysis of anchored wall simply supported at heel 369 Sheeting check 370 Method of dependent pressures 372 Modulus of subsoil reaction 373 Modulus of subsoil reaction according to CUR 166 374 Modulus of subsoil reaction according to Schmitt 375 Modulus of subsoil reaction according to Ménard 375 Modulus of subsoil reaction according to Chadeisson 376 Modulus of subsoil reaction derived from iterations 376 Verification of internal stability of structure 378 Braced sheeting 379 Nonlinear modulus of subsoil reaction 380 Slope stability analysis 381 Soil body 381 Influence of water 382 Surcharge 383 Anchors 384 Georeinforcements 384 Earthquake effect 384 Analysis according to the theory of limit states / factor of safety 385 Polygonal slip surface - Sarma 386 Optimization of polygonal slip surface 388 Changing inclination of dividing planes 388 Foliation 389 Circular slip surface – Petterson, Bishop 389 Optimization of circular slip surface 390 Influence of tensile cracks 390 Analysis of bearing capacity of foundation 391 Bearing capacity on drained subsoil 391 Standard analysis 392 Bearing capacity on undrained subsoil 393 Standard analysis 394 Bearing capacity of foundation on bedrock 394 Standard analysis 395 Solution according to CSN 73 1001 395 Analysis according to EC 7-1 (EN 1997-1:2003) 395 Parameters to compute foundation bearing capacity 396 Horizontal bearing capacity of foundation 398 Homogenization of layered subsoil 400 Effective area 401 Determination of cross-sectional internal forces 402 Pile analysis 403 Vertical bearing capacity – analysis according to CSN 403 Vertical bearing capacity - FEM 404 Limit loading curve 405 Shear strength of skin 406 Coefficient of increase of limit skin friction 406 Depth of deformation zone 406 Incompressible subsoil 409 Negative skin friction 409 Influence of technology 410 Shear resistance on skin 410

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Stiffness of subsoil below the pile heel 411 Increments of vertical loading 412 Distributions of forces acting on pile 412 Dependence of shear on deformation 412 Horizontal bearing capacity 412 Constant distribution of modulus of subsoil reaction 413 Linear modulus of subsoil reaction 413 Modulus of subsoil reaction according to CSN 73 1004 414 Modulus of subsoil reaction after Matlock and Rees 414 Modulus of subsoil reaction after Vesic 415 Settlement analysis 415 Stress in the footing bottom 416 Overall settlement and rotation of foundation 417 Influence of foundation depth and incompressible subsoil 417 Influence of sand-gravel cushion 418 Analysis using the oedometric modulus 418 Analysis using the compression constant 419 Analysis using the compression index 419 Analysis according to NEN (Buismann, Ladd) 420 Analysis using the Soft soil model 421 Analysis according to the Janbu theory 422 Analysis for cohesionless soils after Janbu 422 Analysis for coarse-grained soils after Janbu 422 Analysis for sands and silts after Janbu 423 Analysis for overconsolidated sands and silts after Janbu 423 Analysis for cohesive soils after Janbu 424 Analysis for overconsolidated cohesive soils after Janbu 424 Settlement analysis using DMT (constrained modulus) 425 Theory of settlement 425 Primary settlement 426 Secondary settlement 428 Determination of the depth of influence zone 429 Theory of structural strength 429 Method of restriction of the magnitude of primary stress 430 Characteristics of settlement analyses 431 Compression index 431 Oedometric modulus 433 Compression constant 434 Compression constant 10 435 Void ratio 436 Recompression index 436 Janbu characteristics 437 Influence of loading history 438 Coefficient m 439 Modified compression index 439 Index of secondary compression 440 Overconsolidation index of secondary compression 441 Analyses in program Ground Loss 442 Analysis of subsidence trough 442 Volume loss 442 Recommended values of parameters for volume loss analysis 443 Classical theory 444 Analysis for layered subsoil 445 Shape of subsidence trough 446 Coefficient of calculation of inflection point 447 Subsidence trough with several excavations 447 Analysis of subsidence trough at a depth 447 Calculation of other variables 448 Analysis of failure of buildings 449 Tensile cracks 449 Gradient damage 450 Relative deflection 450 Failure of a section of building 451 Rock slope 451 Plane slip surface 452

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Stepped slip surface 453 Tensile strength of rock 454 Undulating slip surface 454 Anchorage of rock slope 455 Surcharge of rock slope 455 Influence of water acting on slip surface 456 GWT above toe of slope 456 GWT on tension crack 457 GWT on tension crack, max 458 Water acting on tension crack only 459 Own water force acting on slip surface only 460 Own water force behavior 461 Polygonal slip surface 461 Geometry of rock block 462 Anchor forces, surcharge 463 Influence of water 463 Solution procedure 464 Rock wedge 466 Geometry of rock wedge 466 Stereographic projection 467 Influence of ground water 467 Resolution of acting forces 469 Verification 469 Verification according to the factor of safety 470 Verification according to the theory of limit states 470 Rock - shear resistance criteria 471 Mohr - Coulomb 471 Parameters Mohr – Coulomb 471 Hoek - Brown 471 Parameters Hoek – Brown 472 Calculation of Hoek-Brown parameters 474 Barton - Bandis 476 Barton – Bandis parameters 476 Bulk weight of rocks 479 Influence of seismic effects 480 Dimensioning of concrete structures 481 CSN 73 1201 R 481 Materials, coefficients, notation 481 Verification of cross-sections made from plain concrete 482 RC rectangular cross-section under M 482 RC rectangular cross-section under the bending moment and normal compression force 483 Verification of spread footing for punching shear 484 Verification of circular RC cross-section 485 EC2 (EN 1992 1-1) 485 Materials, coefficients, notation 486 Standard values of coefficients 486 RC rectangular cross-section under M 487 RC rectangular cross-section under the bending moment and normal compression force 487 Verification of spread footing for punching shear 488 Verification of cross-sections made from plain concrete 489 Verification of circular RC cross-section 490 PN-B-03264 491 Materials, coefficients, notation 491 RC rectangular cross-section under M 492 RC rectangular cross-section under the bending moment and normal compression force 492 Verification of spread footing for punching shear 493 Verification of cross-sections made from plain concrete 494 Verification of circular RC cross-section 495 BS 8110 495 Materials, coefficients, notation 496 RC rectangular cross-section under M 496 RC rectangular cross-section under the bending moment and normal compression force 497 Verification of spread footing for punching shear 497 Verification of cross-sections made from plain concrete 499 Verification of circular RC cross-section 499

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IS 456 500 Materials, coefficients, notation 500 RC rectangular cross-section under M 501 RC rectangular cross-section under the bending moment and normal compression force 501 Verification of spread footing for punching shear 502 Verification of cross-sections made from plain concrete 503 Verification of circular RC cross-section 504 IS Road Bridges 504 ACI 31802 504 Materials, coefficients, notation 505 Verification of cross-sections made from plain concrete 505 RC rectangular cross-section under M 506 RC rectangular cross-section under the bending moment and normal compression force 506 Verification of spread footing for punching shear 507 Verification of circular RC cross-section 508 AS 3600-2001 509 Materials, coefficients, notation 509 Verification of cross-sections made from plain concrete 510 RC rectangular cross-section under M 510 RC rectangular cross-section under the bending moment and normal compression force 511 Verification of circular RC cross-section 512 Verification of spread footing for punching shear 512 Verification according to CSN 73 6206 513

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Using function SearchFunction "Search" allows for finding an arbitrary text in the subject help. The searched text iswritten into the field "Input searched text" and button "List of topics" lunches the search.The list of found topics containing the searched text is displayed in the column under thebuttons. Clicking the mouse on the topic title and pressing the "Show" button displays thecorresponding topic in the right part of the window (the double-clicking option is alsoavailable).

The searched text is highlighted in blue color. Switching back to "Content" tab sheet showsthe topic location in the tree (help content).

Frame "Help" - tab sheet "Find"

User defined environmentThe programs GEO5 are standard windows applications. Managing the applicationenvironment (application window, dialogue windows, control menu, tables, frames, tool bars,copy to clipboard) applies to standard properties of the Windows environment. The programssupport operating systems WIN 98, WIN 2000, WIN NT and WIN XP.

The minimum hardware and software configuration corresponding to class of PC PENTIUM IIIwith 128 MB of operating memory and minimum resolution of graphic adapter and monitor of1024x768 pixels with 256 bit color range is required. Recommended configurationcorresponds to a class of PC computers of Pentium 4, 512 MB of operating memory.

Window for applicationThe program is launched in standard dialogue window containing all managing tools typicalfor the Windows environment (minimizing, maximizing and closing the application window…).The window header displays information on currently executed task (file name and location) –see figure:

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Managing tools of window for application

The desktop constitutes the window of application. It includes the control menu, horizontaltool bars, space for graphic visualization of the executed task and vertical tool bars to selectindividual inputting modes to specify the task. The bottom part of the desktop displays frames that allow the user to introduce various input parameters into the task. Location ofindividual elements on the desktop is evident from the following figure:

Managing tools of window for application

Control menuSelecting an item from the menu is performed by clicking the left mouse button, oralternatively using keyboard by pressing ALT + underlined letter in the selected menuitem.

As typical for the WINDOWS environment, some of the options in the menu can be replacedwith the buttons on individual tool bars, or with abbreviated commands entered through thekeyboard (providing it exists it is displayed next to the command in the menu – e.g., Savefile – CTRL+S).

Some of the options in the program can be set only with the help of menu – e.g., program "Options".

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Control menu of program

Horizontal tool barsThe program contains the following tool bars:

Tool bar "Files"

Tool bar "Scale and shift"

Tool bar "Plot setting"

Tool bar "Stage of construction"

Tool bar "Files"The tool bar contains the following buttons:

Tool bar "Files"

Individual buttons function as follows:

New file opens a new file – if there is an existing taskopened in the same window, the programprompts the user to save the unsaved data

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Open file opens an existing file - if there is an existing taskopened in the same window, the programprompts the user to save the unsaved data

Save data into file saves data of currently opened task – if no nameis assigned to the task, the program opens the "Save as" dialogue window

Undo returns the last performed step (the function isavailable only in programs with 2D environmentand must be allowed in dialogue window "Options")

Redo restores one returned step (the function isavailable only in programs with 2D environmentand must be allowed in dialogue window "Options")

Print and exportdocument

opens the dialogue window to create, edit andprint output documents

Print and export picture opens the dialogue window to create, edit andprint the current drawing displayed on thedesktop

Copy copies the current picture displayed on thedesktop or the inputted soil profile into clipboard

Insert inserts the soil profile stored in the clipboard (thisoption allows the user to copy the soil profilecreated in a different GEO program – e.g., fromprogram "Pressures" to program "Gravity wall"

Tool bar "Scale and shift"The tool bar buttons serve to manage all plots displayed on the desktop (zoom in/out,move…). The following figure shows locations of individual buttons:

Tool bar "Scale and shift"

Scale up scales up desktop view while keeping location of thepoint under the axis cross unchanged – this action isrepeated using the left mouse button, the right buttonleaves the zooming mode

Scale down scales down the desktop view while keeping location ofthe point under the axis cross unchanged – this actionis repeated using the left mouse button, the rightmouse button leaves the zooming mode

Shows marked region shows and scales up the marked region - the region isselected using the left mouse button

Move displayed region moves the current view in an arbitrary direction – toproceed move mouse in the desired location whilekeeping the left mouse button pressed

Scale up scales up the displayed region while keeping theregion centered

Scale down scales down the displayed region while keeping theregion centered

Modify scale scales the view such that all objects are visible

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Use previous scale modifies view scale - returns the original view scaleprior to the last applied scale action

Tool bar "Plot setting"The button on a tool bar serves to set the setting visualization style on the desktop (colors,thickness and style of lines, background….).

Toll bar "Plot setting"

Plot setting The button opens the "Setting visualization style" dialoguewindow that allows for setting all parameters of the picturedisplayed on the desktop.

Tool bar "Stage of construction"Tool bar buttons serve to work with stages of construction. Picture shows location ofindividual buttons:

Tool bar "Stage of construction"

Adds construction stage adds new stage of construction at the end oflist

Removes constructionstage

removes the last stage of construction from thelist

Construction stage 1,2 ... switches between individual stages of

construction – selection is performed using theleft mouse button

In all programs GEO5 this bar allows for defining stages of construction. Construction stagesserve to model gradual building of a construction (essential for programs Sheetingverification, Settlement, FEM). This function can be also used for parametric studies and ineach stage of construction assume different soil assignment or different design coefficients. Itis rather advantageous to model earthquake effects on a structure in a separate stage ofconstruction as it is then possible to assume different factors of safety or different designcoefficients.For individual types of input (soil assignment, anchors, supports…) there always existsrelationship over construction stages. There are two types:

Defined heredity – (anchors, supports, surcharges…) – these objects always remember thestage, in which they were created. This is also the stage where these objects can be edited.In all subsequent stages these objects can be either removed or it is possible to change someof their properties (post-stressing anchor, changing surcharge magnitude, translatingsupport…). When defining a new construction stage these objects are automatically carriedover to that stage.

Automatic heredity – (assigning soil, terrain profile, water impact, analysis setting…) – forsuch types of inputs the properties from the previous stage are carried over to a new one ifcreated. When changing properties in the current construction stage the program proceeds asfollows:

if the property in the next stage remains the same as in the previous stage italso receives the tag new – this change also applies to all subsequent stages

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if the property in the next stage differs from the one in the previous stage(this means that this property has been in the next stage already changed)then this change is not carried over to subsequent stages

Changes within stages of construction – automatic heredity

Tool bar "3D visualization"The following buttons are available in the tool bar:

Tool bar "3D visualization"

Individual buttons have the following functions:

Lighting direction Opens the dialogue window, which allows us to setthe lighting direction

Axonometric view Sets the axonometric view of drawing

Perspective view Sets the perspective view of drawing

3D view Sets the predefined 3D view of drawing

View along the X-axis Sets the view in the direction of the X-axis

View in opposite directionto X-axis

Sets the view in the direction opposite to the X-axis

View along the Y-axis Sets the view in the direction of the Y-axis

View in opposite directionto Y-axis

Sets the view in the direction opposite to the Y-axis

View along the Z-axis Sets the view in the direction of the Z-axis

View in opposite directionto Z-axis

Sets the view in the direction opposite to the Z-axis

Moves the displayed cut Moves the displayed cut in an arbitrary direction – tomove the drawing slide the mouse while pressing theleft mouse button

Rotates the scene Rotates the displayed drawing in an arbitrarydirection – to move the drawing slide the mousewhile pressing the left mouse button

Automatic scene rotation Turns on an automatic rotation of drawing accordingto the last used rotation (use the "Rotate scene"button)

Tool bar "Selections"The tool bar buttons allow for setting the way in which individual objects on the desktop areselected when adjusting the drawing. The picture shows positions of these buttons:

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Tool bar "Selections"

Selectionindividually

in a given mode each mouse click adds one object into theselection set (point, edge)

Selection bycrossing

in a given mode each mouse click adds all objects crossed bythe line into the selection set (point, edge)

Selection usingrectangle

in a given mode each mouse click adds all objects found insidethe rectangle into the selection set (point, edge)

Selection usingrhomboid

in a given mode each mouse click adds all objects found insidethe rhomboid into the selection set (point, edge)

Add to theselection set

adds additional objects to the overall list according to theassumed selection mode

Remove from theselection set

removes objects from the overall list according to the assumedselection mode

Invert selection inverts all selected objects depending on the assumed selectionmode

Vertical tool barsThe vertical tool bars serve to select the desired mode (regime) of inputting data (project,geometry, profile….) including analysis type and verification. Selecting the mode from this bardisplays in the bottom part of the desktop the corresponding frame for data input.

Tool bar for switching between input data regimes

Standalone vertical tool bar serves to manage pictures.

The "Add picture" button opens the "New picture" dialogue window. The next line in the barprovides the number of stored pictures in a given regime of data input. The "Total" lineshows the total number of stored pictures. The "Picture list" button opens the list of pictures.

Tool bar for controlling view manager editor

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Setting visualization styleThe "Setting visualization style" dialogue window serves to set the plot style (line type andcolor) for visualization on the desktop or for printout, respectively. It contains a group of tabsheets that correspond to individual data input regimes. The tab sheets serve to set the stylefor drawing objects, which are specified in the related input regime.

The "Global" tab sheet defines the settings common to all input regimes (background color,color of elements to be deleted or modification and style of drawing of inactive elements).

The program implicitly contains two standard settings of styles and colors, particularly forblack or white background. The setting can be modified in combo list on the tool bar. Usersetting can be defined, i.e. the user can specify its own style of drawing and store that stylewith the help of button on the tool bar into the "Style manager".

Dialogue window "Setting visualization style" – global setting

The following picture shows an example of a tab sheet for setting the plot in the regime "Water". Individual columns of the table contain (moving from the left):

Item list of items plotted in a given input rgime (here, e.g., water tables,dimensions, gradient, water pressure….)

Active shows / hides a given item in the active regime "Water". In case theoption cannot be turned off (the field has a gray base – in this caseitems "Tables" and "Water pressure") the visualization on thedesktop is mandatory!

Inactive shows / hides a given item in other input data regimes.Visualization color depends on the assumed setting in the tab sheet "Global"

Desktop determines the item color displayed on the desktop

Pictures determines the item color displayed in the "Picture list" or on printout("Print and export picture", "Print and export document")

Line type determines the line style

Thickness determines the line thickness

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Dialogue window "Setting visualization style" – setting for the input regime "Water"

Style managerThe red button on a tool bar of the "Setting visualization style" dialogue window opens the"New style" dialogue window. The window allows for setting the style name and itsdescription. The "OK" button saves the selected style.

Saving the user profile of visualization style

In such a way an arbitrary number of user profiles of visualization styles can be defined. Thelist of such profiles can be accessed from a combo list already containing implicitly predefinedprofiles (black and white background), or a view manager (can be opened by pressing thebutton on a tool bar) that allows for editing the profile. The buttons "Up" and "Down" serveto move within a list of the user defined profiles.

Dialogue window "Style manager"

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FramesThe frame is a permanently opened window in the bottom part of the application window.Frames are changed depending on the input data regime of a given task selected from thevertical control bar. The frame may contain the following items: table, combo list, fields forinputting data (h1, h2….) and command buttons.

The function key "Tab" together with cursor arrows for moving within the selected element(e.g., combo list) and in case of command buttons the corresponding underlined letter ("Add"– "A") are employed when selecting the data using keyboard.

Frame control elements

The frame can be minimized using the button in the left upper corner. In this case the framespace is taken by the drawing space. In some cases it is more advantageous to exploit theframe space for increasing the drawing space, which is possible owing to the fact that theprogram uses the system of active dimensions and active objects so that the frame does nothave to be displayed all the time.

Returning the frame to its original face is performed by pressing the button in left bottomcorner of the desktop showing the frame name. Providing the frame is minimized, e.g. in theregime "Soils" it remains hidden even when switching to other input data regime.

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Frame control elements

TablesThe table is a list of inputted data (for example a list of surcharges, soils, profile interfaces…).The table header contains a list of items (surcharge, name, width, size…) and in the upperleft corner control elements to manage the table rows:

"+" selects all table rows

"-" cancels selection

"*" inverts selection

The assumed selection can be also changed by pressing the desired row number. Buttonswith numbers are "pressed".

The "Add" button opens the corresponding dialogue window for inserting the table data. Ifthe list of data in the table is empty then all input fields in the dialogue window are empty. Ifthe table contains some already inputted elements then the input fields are filled with valuestaken from the current table row (an "arrow" is positioned next to the row number).Elements (rows) are inserted in the table by pressing the "Add" button in the dialoguewindow. New data are placed at the end of the table.

Individual rows are edited with the help of the "Edit" button. Only the row marked with anarrow (see figure) will be edited regardless of other selected rows in the table. Some of thedialogue windows allows for editing a group of selected items using the "Edit selected"button. It is therefore possible to modify values in more rows all at once. Always the selectedrows are edited.

The "Remove" button deletes all selected ("pressed") rows. More than one row can beremoved at the same time. If not item is selected the program deletes the current row(marked with an "arrow").

It there is among rows selected for deletion a row, which cannot be deleted (e.g. startingpoint of a structure), the program stops the deletion process!

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Table example

Selection state of individual table rows corresponds to visualization state of objects on thedesktop. An object on the desktop that corresponds to the current row in the table (an "arrow" is positioned next to the row number) is implicitly displayed extra bold. If the row isselected ("pressed") the corresponding object is displayed in green. Pressing the "Remove"button colors all objects selected for deletion red.

Visualization of selected objects

Marking objects using these colors is implicitly set. This setting, however, can be modified inthe "Setting visualization style" - tab sheet "Global".

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Setting color for selecting objects

Dialogue windowsA dialogue window is one of the elements that allows for inputting data into program. In allGEO programs the dialogue windows apply to conventional windows management typical forthe WINDOWS environment. A left mouse button is used when selecting objects in thewindow or alternatively the function key "Tab" when using keyboard. The cursor arrows, key"ENTER" or in case of command buttons the corresponding underlined letter ("Cancel" - "C","OK" – "O") are employed when moving within an object.

A dialogue window can contain the following items: table, combo list, fields for inputting data(number, text) and command buttons. The "OK" command button confirms the selection,while the "Cancel" button leaves the input mode.

Providing the window contains a certain non-typical control element (or this element hassome other rather then typical effect) its function is described in the corresponding data inputregime.

As an example consider the following picture showing the "Edit surcharge" dialogue windowthat contains the "OK+ " and "OK+ " buttons. These buttons allow the user to move withinthe list of inputted surcharges and at the same time to confirm changes made in the window.Pressing this button results in the same action as if closing the window with the "OK" buttonand opening it again for the next element in the list.

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Dialogue window example

Active dimensions and objectsThe system of active dimensions and objects allows for faster editing of the inputted data.

Active dimension is a dimension that can be edited directly on the desktop. The value ofactive dimension is labeled by frame (dashed line). Positioning the mouse cursor and theframe changes its mask into a "hand". Clicking the value than changes the frame view (isplotted in a solid line), to cursor starts to blink and the dimension can be edited. The "Enter"button closes the editing mode. The change is immediately displayed on the desktop.

Active object functions in a similar way. Changing the cursor mask into a "hand" andclicking the object (double click) than activates the editing mode. In this case, however, thevalues are not edited directly on the desktop, but rather in the dialogue window originallyused to create the object. The picture shows an example of an active object (trapezoidalsurcharge), when clicking on the desktop opens the "Edit surcharge" dialogue window.

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Example of using active dimensions and active objects

Unit - metric / imperialThe program allows for choosing either metric or imperial units. Use combo list to select thedesired type of units. A prompt message appears requesting to confirm the selection.

Dialogue window to confirm the change of units

Copy to clipboardThe program allows for using the Windows clipboard in two different ways:

it is possible to copy the current desktop view. The picture can be theninserted into an arbitrary editor (MS Word, Drawing, Adobe Photoshop, etc.)Individual parameters are set in the "Options" dialogue window, tab sheet "Copy to clipboard"

it is possible to copy the program input data (soil parameters, profile andinterfaces, surcharges, water impact, terrain, etc.). The copied data can bethen inserted into another GEO5 program

Copying to clipboard is available either from the control menu (items "Modifications", "Copypicture") or using the "Files" button on the tool bar.

OptionsThe "Options" dialogue window serves to set some of the special program functions (copy toclipboard, print view, grid and step, etc.).

This dialogue window is opened from a control menu (items "Setting", "Options").

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The window contains individual tab sheets (number and content may vary depending onindividual programs) that allow for specifying corresponding settings.

Dialogue window "Options"

Options - copy to clipboardThe "Copy to clipboard" tab sheet allows for setting the controlling parameters:

Picture size the setting defines the picture size. Either the picture width orheight can be assigned manually. The other dimension is alwaysset automatically

Picture format the setting defines the picture format (*.EMF, *.WMF, *.BMP), itsresolution and color. Recommended setting is displayed in thefigure (format: *.EMF, resolution: 600 dpi, color)

Options the setting defines the picture frame and header. If both optionsare checked, the picture contains both the frame and header

The "Default" button in the window sets original implicit values.

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Dialogue window "Options" – tab sheet "Copy to clipboard"

Options - print pictureThis dialogue window is opened from the control menu (items "Setting", "Options"). The "Print picture" tab sheet allows for setting the picture parameters assumed for printout orexport in the "Print and export picture" dialogue window.

Options the setting defines the picture frame and header. If both optionsare checked, the picture contains both the frame and header

The "Default" button in the window sets original implicit values.

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Dialogue window "Options" – tab sheet "Print picture"

Options - inputThe "Options" dialogue window, tab sheet "Input" allows for setting the "Grid" parametersand parameters of functions "Back" and "Repeat".

This tab sheet is implemented only in 2D programs (Slope stability, Settlement, Beam,etc.).

Grid sets the grid origin and step in the X and Z directions

Show grid shows / hides grid on the desktop

Snap to grid turns on / off the snap to grid option using mouse(when shifting the mouse the cursor jumps over thedefined grid – a point off the grid can be specified byholding the "CTRL" key)

Horizontal rule shows / hides horizontal rule with a scale of distanceson the desktop

Vertical rule shows / hides vertical rule with a scale of distances onthe desktop

Functions Back andRepeat

turns on / off the possibility of using these functions inthe program (on horizontal tool bar these buttons are "foggy"

Dialogue window "Options" - tab sheeet "Input"

Common inputThis chapter contains the hint sections that either provide details on the chapter "Data inputand analysis regimes" or are common to several GEO programs.

Project - Earth pressuresThe "Project" frame – tab sheet "Earth pressures" contains basic settings driving theanalysis of earth pressures. The program offers presetting for various countries (Czech

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Republic, Germany, France….) and "Standard setting" recommended by the authors forcountries stored in the list.

When the "User" option is selected it is possible choose from an arbitrary type of analysisoffered by the program:

Earth pressure analysis

Methods to compute active pressure Methods to compute passive pressure

Caqout-Kerisel Caqout-Kérisel (CSN 730037)

Coulomb (CSN 730037) Coulomb

Müller-Breslau (DIN 4085) Müller-Breslau

Mazindrani (Rankin) Sokolovski (DIN 4085)

Absi Mazindrani (Rankin)

Absi

Earthquake analysis

Mononobe-Okabe

Arrango

Frame "Project" - tab sheet "Earth pressures"

Inputting and editing soilsThe "Add new soil" dialogue window serves to input name soil parameters that should beobtained from laboratory measurements or geological survey.

All inputting fields in the window must be filled. The only exception is the value of sat (bulkweight of saturated soil) in the window section "Uplift". Should this filed remain empty theprogram autonatically adds the value of (bulk weight of soil).

Cliking the hint button " " provides information about the theory of analyses linked toindividual values being inputted.

Color and soil sample are selected in "Soil and rock symbols" dialogue window. To open thiswindow press the "Sample and color" button.

If no geological survey or laboratoray experiments are available, the soil can be specified withthe help of soil database containg approximate values of basic characteristics. The "Classify"button opens the "Soil classification" dialogue window with the values offered for insertinginto the window. The "Delete" button allows for removing the information about classifiedsoil from the catalogue. Soil parameters that do not appear in the catalogue ("Friction anglestruc-soil" in the picture) must be in any case assigned manually.

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The specified soil is inserted into the list of soils by pressing the "Add" button.

Dialogue window "Adding new soils"

Soil classificationApproximate values of soils can be obtained from the catalogue of soils according to CSN 731001 standard "Foundation soil below spread footings". The combo list serves to select thedesired soil and specify its consistency or compactness, respectively. The soil parametersobtained from the catalogue appear in the window.

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Dialogue window "Soil classification"

Pressing the "OK" button shows in the "Add new soil" recommended values next tocorresponding input fields (see Fig.). Pressing the "OK+Assign" button then assigns toindividual input fields the average values of soil parameters. The "Cancel" button leaves thewindow with no action.

The "Manual" button opens the "Manual soil classification" dialogue window that allows forclassifying the soil if its parameters are known, e.g., from laboratory measurements (grading,moisture, compactness….).

Soil classification – recommended range of values

Soil and rock labels

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The soil inputted either manually or inserted from the catalogue of soils can be assigned asample (type of hatching) and color to be shown in the profile on the desktop.

A color selected from the "Desktop" combo list is the color used to plot soils (rocks) on thedesktop. A color selected from the "Pictures" combo list is the color used to visualize soils(rocks) in pictures that are either stored in the "Picture list" or printed with the help of "Printand export pictures".

The sample color to be sufficiently visible should be chosen with respect to the desktopbackground or printout paper, respectively.

Dialogue window "Soil and rock symbols"

Manual classification of soilThis dialogue window allows for specifying the soil parameters, which serve to add the soilinto a catalogue of soils. The "OK" button switches back to the "Soil classification" dialoguewindow with setting and classified soil.

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Dialogue window "Manual classification of soil"

Interface in 2D environmentThe left part of the desktop contains a table with the list of interfaces. Interfaces are orderedin the table from top to bottom. For currently selected interface the program displays in themid section of the desktop another table listing individual interface points.

A tool bar in the top part of the desktop contains control buttons to manage interfaces.

Tool bar "Interface"

Margins opens the "World coordinates" dialogue window thatallows for setting the world dimensions (left and rightedge).

Add turns on the regime for inputting a new interface –individual interfaces can be added in an arbitrary order.Each interface is automatically stored in the list ofinterface when leaving the input mode

Modify turns on the regime for editing an interface – this regimeis also activated by clicking the desired interface on thedesktop

remove upon pressing the "Remove" button the program marksthe selected interface with a red color and opens thedialogue window to confirm this action

Every change made to a given interface can be put back using the "UNDO and REDO" buttonson the horizontal tool bar.

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Frame "Interface"

Adding interfaceThe "Add" button starts the regime for inputting points of a new interface. Other buttons onthe same tool bar assumed for inputting and editing interface points become active. The "OK"button (tinged green) closes the input regime and stores the inputted points. The "Cancel"button (tinged red) closes the input regime without accounting for changes.

Two options are available to specify coordinates of individual interface points:

Using table: interface points are introduced in the "New interface points" table. The "Add"button opens the "New point" dialogue window that allows for specifying coordinates of anew point. The "Add" button then inserts the point into the table. The "Cancel" button isserves to close the input mode when all interface points are introduced. The "Edit" and "Remove" buttons allow for either editing or deleting the inputted points. Each change ininterface geometry immediately appears on the desktop.

Using mouse: individual buttons on the vertical tool drive this inputting mode. The followingmodes are available:

Add point the point is inserted by clicking the left mouse button on thedesktop - the grid option can be exploited when inserting thepoint - the inputted point is automatically rounded to twodecimal digits – both mouse and keyboard input modes aretherefore identical

Edit point usingmouse

pressing the existing interface point using the left mousebutton allows for selecting this point and then moving it to anew position

Edit point indialogue point

clicking the existing interface point opens the dialogue windowthat allows for modifying the point coordinates

Remove point pressing the existing interface point using the left mousebutton opens the "Remove point" dialogue window – whenconfirming this action the point is deleted

When inputting points, it is possible to utilize the template obtained from import DXF.

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The program allows also for introducing vertical interfaces – in such a case the programrequests to insert the point either to the left or to the right. The buttons that serve toconfirm the action are colored – the same color is also used to visualize both input variantson the desktop.

The "OK" button (tinged green) is used to store the inputted interface when all interfacepoints are introduced.

The program also contains an automatic corrector of inputted interface that determines theinterface end points and then adds the interface to the list of interfaces.

Frame "Interface"

Editing interfaceThe "Modify" button turns on the regime of inputting points of a new interface. The programalso opens the currently selected interface (it is selected from the "List of interfaces" table;it is displayed as a solid thick line on the desktop). An interface can be selected also as an active object by clicking a point, line or interface using the left mouse button.

The actual editing procedure (adding, shifting, deleting points) is the same as for addinginterface input mode.

The "OK" button closes the editing regime and stores all performed changes. The "Cancel"button closes the regime without accounting for all previously made modifications.

After leaving the edit mode (similarly to adding interface), the program immediately runs the corrector of the inputted interface to check for the interface shape and if necessary to modifythe interface end points.

Corrector of inputted interfaceWhen the inputting or editing process is completed the program automatically modifies theinputted interface to comply with the program requirements, i.e. the end points touch theworld edges or other interfaces. The automatic corrector can be further used to simplify theinput process – e.g., if only one point is used to specify an interface the programautomatically creates a horizontal interface containing the inputted point.

If the interface touches another interface the corrector creates new end points of the currentinterface. These points then also become the points of the interface being touched. All lines ofindividual interfaces thus start and end in a point.

In case of an incorrect input (see the picture below) the interface cannot be stored. In this

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case the interface must be modified or the inputting process must be stopped using the "Cancel" button.

Here we present examples of interface corrector functions (correct and incorrect input):

Correct and incorrect interface shapes

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World coordinatesThe dialogue window serves to specify world coordinates (dimensions) for a given task – leftand right edges. The third data is auxiliary – it determines the depth of drawing earth profileson the desktop – it has no effect on the performed analysis.

The world coordinates can be changed at any time – when increasing dimensions all inputtedinterfaces are automatically prolonged, when reducing dimensions all points falling off thenew world coordinates are automatically removed.

Dialogue window "World coordinates"

Assigning soilsTwo options are available to assign soils into individual profile layers. Clicking the left musebutton on the tool bar button above the table selects the desired soil (positioning the mousecursors in the bar above the soil button displays a bubble hint with the soil name). The soil isinserted by moving the mouse cursor (the cursor mask changes into a "hand") first into aspecific layer and then by pressing the left mouse button.

The second option requires opening a combo list of a specific interface and then selecting thedesired soil to be assigned. All changes in the soil assignment are automatically displayed onthe desktop.

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Frame "Assigning"

Design coefficientsThe "Analysis" or "Verification" frames that display the list of computed forces allow forspecifying design coefficients. A design coefficient multiplies the corresponding force. Wheninputting the coefficient the results are automatically recomputed and the desktop showsmodified forces.

Design coefficients are advantageous for example for:

structure testing when a structure response to an increase of forcespecified directly in the analysis window can be visualized

excluding several forces from verification or their reduction

Specifying design combinations – e.g., different coefficients can beassigned in the sense of EC to main load variables and sidevariable loads

The following combinations can be for example specified when performing the wallverification:

Analysis 1 Analysis 2 Analysis 3

Wall 1,0 1,0 1,0

Active pressure 1,0 1,0 1,0

Surcharde 1 1,0 0,5 0,5

Surcharde 2 0,5 1,0 0,5

Surcharde 3 0,5 0,5 1,0

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Frame "Verification" – application of design coefficients

Running more analyses / verificationMost frames that display the analysis results allow for defining more than one analysis to berun. Several analyses within one construction stage are carried out for example for:

dimensioning structure in more locations

analyses of various slip surfaces

verification with various design coefficients

The bar in the top part of the frame serves to manage individual analyses.

Frame "Analysis" – tool bar "Running more analyses / verification"

Add adds additional analysis on the bar

Remove removes the currently selected analysis

Analysis 1,2,3...

switches between individual analyses

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Frame "Analysis" - "running more analyses / verification"

Connecting programsIn some cases it is possible to launch a new program from a currently running program. Forexample, the "Cantilever wall" program allows for running the "Slope stability" program toverify the external stability of a structure, or the "Spread footing" program to verify thebearing capacity of a footing of a structure.

The new program loads the data of structure and then it behaves as a stand alone program –closing the program, however, is different. Pressing the "OK" button (on the right below thetool bars) closes the program and the analysis data are passed to the original program. Thisis not the case if closing the program with the help of the "Cancel" button.

The program, when running it for the first time, creates the data of a structure andpasses on the structure dimensions, geology, loads, surcharges and other data. The programthen requires inputting some additional data, e.g. the analysis method, analysis setting,slip surfaces, stages of construction, etc.

When running it again (always necessary if some changes were made in the originalprogram) the program regenerates the data to be passed on, but keeps the data alreadyinputted in this program. For example, when connecting the original program with the "Spread footing" program the new program keeps the additionally inputted sand-gravelcushion together with inputted soil – the footing dimensions, foundation geometry, andgeological profile are, however, regenerated.

Some actions are not allowed in the new program – e.g. to change the basic setting of theproject, unit, etc. The generated task, however, can be saved into new data using the "Saveas" button and work with it as with any other independent task.

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Run the program "Spread footing" from program "Cantilever wall"

Selecting and storing viewsThe programs offers a number of ways of displaying results. A specific option can be selectedfrom the "View results" dialogue window. Quite often is necessary to go through a complexand tedious setting of views – for example, if we are interested in the distribution of internalforces developed in beams using FEM, it is necessary to turn off the color range, draw onlyundeformed structure, select a variable to be displayed, select a suitable magnification, etc.

To simplify the way of managing individual views the programs allow us, using the "Selectingand storing views" bar, to store the current view and also to go from one view to theother in a relatively simple way.

The stored view keeps:

all settings from the "View results"

drawn variables

color range

picture zoom

The view is stored for all stages of construction – if it is not possible in a certain constructionstage to perform such a setting (e.g. in the first construction stage the settlem ent anddepression are not defined) the programs displays the closest possible setting and the definedview is switched to <none>.

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Control units of a tool bar "Views"

The following control units are available to manage views:

Define view opens the "Setting results visualization"dialogue window, which serves to definedetails for displaying the results

Select view a combo list allows for selecting an alreadyspecified and stored view

Store current view opens the "New view" dialogue window tostore a new view

Open view manager opens the window with a list of views

Setting results visualizationThe "Settlement - results visualization setting " dialogue window provides tools for a lucidway of displaying the results both on the screen and in the printed format:

parameters to draw depression line and influence zone

setting surface views and color scale drawing

setting and drawing tilted sections

The programs based on the finite element method further allow for setting:

parameters to draw the finite element mesh

parameters to draw construction – deformed /undeformed (note that undeformed option must beselected when displaying beam internal forces)

distribution of internal forces along interfaces and onbeam elements

All information specified in this window (including the setting of current magnification) can bestored using the selecting and storing views bar.

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Dialogue window "Settlement – results visualization setting"

Setting color rangeThe color range is an important tool providing a lucid way of visualization of results. Theprogram offers two predefined types of color ranges – "Uniform" and "Across zero". Bothranges have a moving minimum and maximum value and predefined colors. The minimumand maximum values are automatically regenerated whenever the variable or a stage ofconstruction is changed. The "Uniform" range means that colors are uniformly spread fromthe minimum to the maximum value. The " Across zero" range draws the positive valuesusing warm colors (yellow, red), while cold colors (green, blue) are used to representnegative values.

The program allows for introduction of user-defined ranges with both the fixed minimumand maximum and the moving minimum and maximum. A user-defined range is spec ified inthe "Scale color definition" dialogue window. The range is always defined for the current unit(e.g. kPa, m) – when switching the units the program always adjusts the range particular fora given unit.

Control units of a tool bar "Ranges"

The following control units are available to manage ranges:

Select range a combo list allows for selecting analready specified and stored range

Define color ranges opens the "Scale color definition" dialoguewindow to create a user-defined range

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Store current range opens the "New range" dialogue windowto store a new range

Open range manager opens the window with a list of automatic

and user-defined ranges

Scale color definitionThe "Scale color definition " dialogue window serves to cerate a user-defined color scale.

The "Floating minimum and maximum " check box determines the basic type of a scale. Ifchecked, the minimum and maximum values of a scale are automatically adjusted wheneverthe corresponding variable or a construction stage is changed. In such a case it possible toadjust the following:

scale refinement (the minimum number of levels isfour and the maximum is 100)

scale color

uniform scale / across zero

The number of scale levels and scale type are specified in the "Scale generation"dialogue window, which opens after pressing the "Generate values" button. It is possible toadjust both values and colors in the table in the left part of the dialogue window. The rangevalues can be easily changed in the table. If the box in the "Control color" column ischecked, it is possible to choose an arbitrary color from the combo box. The color onintermediate not checked rows are automatically blended from the inputted colors in checkedrows. The default values can be recalled anytime after pressing the "Predefined colors "button.

An important property of the program is a definition of ranges with the fixed minimum andmaximum. If the "Floating minimum and maximum " check box is not checked, the colorrange is fixed and its minimum and maximum values are inputted. As oppose to the movingrange it is further possible to specify:

range end points (in the "Scale generation" dialoguewindow)

colors to display values out of the range

When changing a variable or a construction stage the color range remains still the same ,keeping the same end ranges. The values found outside the range (below the minimum orabove the maximum value) are drawn using colors specified in the right part of the window. The minimum and maximum range values are inputted in the "Scale generation"dialogue window. The inputted minimum and maximum values are linked to the same unit– e.g. when specifying the rage of 0-200 kPa , this range is kept the same for all variablesbeing specified in kPa – when changing the currently displayed variable to the variablesettlement, the current range is switched to that corresponding to the unit of settlement.

For both the fixed and floating scale it is possible to choose whether the colors in the rangesare distributed uniformly or across zero. The "Uniform" scale means that colors aresmoothly spread from the minimum to the maximum value of the scale. The " Across zero"scale draws the colors above the selected value using warm colors (yellow, red), while coldcolors (green, blue) are used to represent the colors below the selected value.

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Dialogue window "Scale color definition"

Import - export DXFPrograms 2D (Slope stability, Settlement, FEM) allow for importing and exporting data in DXFformat. The program main menu (item "File") contains items "Import" and "Export" – "Format DXF". These items are accessible in the menu even if the module "Import-exportDXF" has not been purchased. If the module is not implemented, the program displays awarning message.

Warning message for missing module

If the module is purchased, the desktop contains a tool bar for handling the imported data.

Menu and tool bar for module "Export-import DFX"

Data import proceeds in two steps:

- Reading data into template- Inputting data using template

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- Modifying template during data input

The data inputted in the program can be exported in DXF format anytime.

Reading data into templateTo proceed, use the program menu (item "File") and choose the item "Import", "FormatDXF". Next, select the file intended for import. The loaded data are displayed in the dialoguewindow, which allows for selecting individual layers to be subsequently read into atemplate. All data are always loaded into the program so that the layer selection can be modified anytime.

When importing data it is possible adjust the world margins based on the imported data –this is particularly useful when defining a new task.

Imported data are not transferred directly into the program. Instead, they are read into atemplate, which is used to transfer data into program later on. When the data are loaded thetemplate is displayed on the desktop and the buttons on a horizontal tool bare, which areused to manage the template, are made available.

Reading data into a template

Modifying world margins

Inputting data using templateInputting data using a template is essentially the same as a standard input of data in theprogram. The main difference appears in the possibility of adding a point from a template intothe data being inputted. During input the mouse cursor appears as an axial cross – whenapproaching the template it turns into a small cross and long axes disappear. When a point

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is now inputted (using the left mouse button) the point from the template is inserted (theinputted point has now the same coordinates as the point in the template). To accelerate theinput of individual lines it appears useful to employ the zooming tools. After interfaces areinputted, the procedure can be applied to input other entities. During input it is possible to modify template anytime .

Inputting data using a template

Modifying template during data inputWhen inputting data, the template can be modified anytime. In particular, pressing the "Modify" button on the "Template DXF" tool bar opens a dialogue window with individuallayers of the template. For example, when inputting anchors, it is possible to turn off alllayers except for anchors – inputting anchors then becomes simple and lucid.

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Turning on/off layers in a template

Display after modifying layers in a template

Export DXFTo proceed, use the program menu (item "File") and choose the item "Export", "FormatDXF". Next, select the file name intended for export. Using a dialogue window the programthen provides information regarding the performed data export.

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Information regarding the performed data export

The exported data can be verified by importing them back into the program GEO5.

Check of exported data

Input regimes and analysisThis capture contains basic description of individual regimes of inputting data into theprogram:

Program Earth Pressure

ProjectThe "Project" frame is used to input the basic project data and to specify the overall settingof the analysis run. The "Project" tab sheet contains an input form to introduce the basicdata about the analyzed task, i.e. project information, project description, date, etc.

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The "Project" tab sheet also allows the user to switch analysis units (metric / imperial).

The "Earth pressures" tab sheet serves to choose the basic theory or standards to be followedin the solution of a given problem.

Frame "Project" - tab sheet "Project"

GeometryThe "Geometry" frame contains table listing the points of a structure. Adding (editing) pointsis performed in the "Add (edit) point" dialog window.

The existing geometry points can be further edited on the desktop with the help of activeobjects – double clicking on a selected point opens a dialog window to edit the point.

Frame "Geometry"

ProfileThe "Profile" frame contains a table with a list of inputted interfaces. After specifyinginterfaces it is possible to edit thicknesses of individual layers with the help of activedimensions.

Adding (editing) layer is performed in the "Add (edit) interface" dialogue window. The

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z-coordinate measured from the top point of a structure is specified.

The program allows for raising or lowering the top point of a structure in the "Changeterrain elevation" dialogue window so that the whole interface can be translated whilekeeping the thicknesses of individual layers. This function is important when copying theprofile from program "Terrain".

Frame "Profile"

SoilsThe "Soils" frame contains a table with a list of inputted soils. The table also providesinformation about currently selected soil displayed in the right part of the frame.

Adding (editing) a soil is performed in the "Add (edit) soil" dialogue window.

The soil characteristics are specified in the program "Earth Pressure". These characteristicsare further specified in chapters: "Basic data", "Earth pressure at rest" and "Uplift pressure".

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Frame "Soils"

AssignThe "Assign" frame contains a list of layers of profile and associated soils. The list of soils isgraphically represented using buttons in the bar above the table, or is accessible from acombo list for each layer of the profile.

Procedure to assign soil into a layer is described in details herein.

Frame "Assign"

Terrain

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The "Terrain" frame allows, by pressing the button, for specifying the terrain shape. Theselected shape with graphic hint ("Parameter chart") of inputted values is displayed in theleft part of the frame. The terrain shape can be edited either in the frame by inserting valuesinto input fields, or on the desktop with the help of active dimensions.

The last option to choose from is a general shape of a terrain. In this case the frame containsa table with a list of terrain points. The first point with coordinates [0, 0] coincides with thetop point of a structure.

Analysis of earth pressures in case of inclined terrain is described in the theoretical part of thehelp "Distribution of earth pressures for broken terrain".

Frame "Terrain"

WaterThe "Water" allows, by pressing the button, for selecting the type of water. The selected typetogether with a graphic hint (“Parameter chart”) of inputted values is displayed in the leftpart of the frame. Water parameters (h1, h2...) can be edited either in the frame by insertingvalues into input fields, or on the desktop with the help of active dimensions.

The last option is a manual input of pore pressure both in front and behind the structure. Twotab sheets "In front of structure" and "Behind structure" appear with tables. The table isfilled with values of pore pressure in front, or behind the structure at a depth of “z” (z-axis).

The ground water table can also be specified above the structure or earth profile,respectively – in such a case the depth of water is inputted with negative value.

Analysis of earth pressures with influence of water is described in the theoretical part of thehint chapter "Influence of water".

The program further allows for specifying a depth of tensile cracks filled with water.

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Frame "Water"

SurchargeThe "Surcharge" frame contains a table with a list of inputted surcharges. Adding (editing)surcharge is performed in the "New (edit) surcharge" dialogue window. The inputtedsurchages can be edited on the desktop with the help of active dimensions or active objects,respectively.

The z-coordinate measured from the top point of a structure is specified (positive directiondownwards) when inputting the surcharge at a certain depth. Providing the surcharge isfound off the terrain the computer prompts an error message.

Analysis of earth pressures due to surcharges is described in the theoretical part of the hint,chapter "Influence of surcharge".

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Frame "Surcharge"

EarthquakeThe "Earthquake" frame serves to input earthquake parameters. Directions of inputtedearthquake effects are displayed on the desktop.

Analysis of earth pressures while accounting for earthquake is described in the theoreticalpart of the hint in chapter "Influence earthquake".

Frame "Earthquake"

Setting

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The "Setting" frame contains basic settings for the analysis of earth pressures. The programoffers pre-setting for different countries (Czech Republic, Germany, France,...) and "Standard setting" recommended by the authors of the program for countries no included inthe list. While changing settings in the combo list the values of coefficients of reduction of soilparameters in corresponding windows are changed.

An arbitrary analysis setting is available with the option "User setting". Selecting the option"Reduce soil parameters" allows for specifying in input fields individual values of thecoefficients of reduction of soil parameters (e.g., recommended values according to EC7).

Frame "Setting"

AnalysisThe "Analysis" frame displays the analysis results. The frame serves to select type ofcomputed earth pressure (active pressure, pressure at rest, passive pressure). Two options "Create soil wedge" and "Minimum dimensioning pressure" are available when computing theactive earth pressure.

Several analyses can be performed for a single task by varying design coefficients ofindividual components of earth pressure.

The analysis results are displayed on the desktop and are updated immediately for anarbitrary change in input data or setting. Visualization of results can be adjusted in the "Setting visualization style" dialogue window.

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Frame "Analysis"

Program Sheeting Design





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Adding (editing) layer is performed in the "Add (edit) interface" dialogue window. Thez-coordinate measured from the top point of a structure is specified.


Frame "Profile"



The soil characteristics are specified in the program "Sheeting design". These characteristicsare further specified in chapters: "Basic data" and "Uplift pressure".

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Frame "Soils"



Frame "Assign"

Geometry

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The "Geometry" frame is used to specify the depth of a construction ditch and by pressingthe button to choose the shape of a bottom. The selected shape with a graphic hint ("Parameter chart") appears in the left part of the frame. The dimensions of a structure canbe edited either in the frame by inserting values into input fields, or on the desktop with thehelp of active dimensions.

The frame can be further used to input surcharge of a construction ditch bottom andcoefficient of reduction of earth pressure below the ditch bottom (this coefficient serves toanalyze braced sheeting).

Frame "Geometry"

AnchorsThe "Anchors" frame contains a table with a list of inputted anchors. Adding (editng)anchors is performed in the "New anchor (Edit anchor)" dialogue window. The inputtedanchors can be edited on the desktop with the help of active objects.

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Frame "Anchors"

PropsThe "Props" frame contains a table with a list inputted props. Adding (editing) props isperformed in the "New prop (Edit prop)" dialogue window. The inputted props can also beedited on the desktop with the help of active dimensions or active objects, respectively.

Frame "Props"

SupportsThe "Supports" frame contains a table with a list of inputted supports. Adding (editing)

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supports is performed in the "New support (Edit support)" dialogue window. The inputtedsupports can also be edited on the desktop with the help of active dimensions or activeobjects, respectively.

Frame "Supports"

Pressure determinationThe "Pressure specification" frame allows by pressing the button "Analyze" ("Input",respectively) for selecting a method for the calculation of active earth pressure. Chooseoption "Analyze" if you wish the active earth pressure to be computed automatically basedon specified earth profile.

In some special cases (redistribution of earth pressures due to presence of anchors,nonstandard rotation of a structure) it advisable to specify the distribution of earth pressureon a structure manually. Selecting the option "Input" opens a table in the frame with a list ofinputted points and the corresponding pressure value. The pressure is specified up to thedepth of structure increased by the depth of zero point (the depth of zero point is introducedin the top part of the frame). The depth of zero point equal to zero is selected if we wish tospecify the pressure values only up to the depth of construction ditch. Below the ditch theprograms computes the pressure values based on the specified geological profile. Providingthe earth pressure is specified manually the program does not account for the influence ofterrain profile, surcharge and water.

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Frame "Pressure determination"

TerrainThe "Terrain" frame allows, by pressing the button, for specifying the terrain shape. Theselected shape with graphic hint ("Parameter chart") of inputted values is displayed in theleft part of the frame. The terrain shape can be edited either in the frame by inserting valuesinto input fields, or on the desktop with the help of active dimensions.


Analysis of earth pressures in case of inclined terrain is described in the theoretical part of thehint, chapter "Distribution of earth pressures for broken terrain".

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Frame "Terrain"

WaterThe "Water" allows, by pressing the button, for selecting the type of water. The selected typetogether with a graphic hint ("Parameter chart") of inputted values is displayed in the leftpart of the frame. Water parameters h1, h2 can be edited either in the frame by insertingvalues into input fields, or on the desktop with the help of active dimensions.




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Frame "Water"




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Frame "Surcharge"

ForcesThe "Forces" frame contains a table with a list of forces acting on a structure. Adding(editing) forces is performed in the "New force (edit force)" dialogue window. The inputtedforces can also be edited on the desktop with the help of active objects.

Frame "Forces"

EarthquakeThe "Earthquake" frame serves to input earthquake parameters. Directions of inputted

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earthquake effects are displayed on the desktop.


Frame "Earthquake"

SettingThe "Setting" frame contains basic settings for the analysis of earth pressures. The programoffers pre-setting for different countries (Czech Republic, Germany, France,...) and "Standard setting" recommended by the authors of the program for countries no included inthe list. While changing settings in the combo list the values of coefficients of reduction of soilparameters in corresponding windows are changed.

An arbitrary analysis setting is available with the option "User setting". Selecting the option"Reduce soil parameters" allows for specifying in input fields individual values of thecoefficients of reduction of soil parameters (e.g., recommended values according to EC7-1).

Frame "Setting"

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AnalysisThe "Analysis" frame displays the analysis results. The analysis is carried out by pressing the"Analyze" button in the right part of the frame. The frame has two variants. The first variantapplies to a wall free of anchors (sheet pile) and the second one to an anchored (strutted)wall.

A coefficient of reduction of passive earth pressure (or factor of safety) together with a choicewhether to consider a minimum dimensioning pressure behind the structure is specified for anon-anchored wall.

A type of heel support (fixed, free) and analysis parameters (coefficient of reduction ofpassive pressure, minimum dimensioning pressure) are specified for an anchored wall.

The analysis results are displayed on the desktop. Visualization of results can be adjusted inthe "Setting visualization style" dialogue window.

Frame "Analysis" - non-anchored wall

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Frame "Analysis" - anchored wall

Program Sheeting Check




The "Other" tab sheet allows the user to specify subdivision of a wall in to finite elements (bydefault the number of elements equals to 30).


Profile

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The "Profile" frame contains a table with a list of inputted interfaces. After specifyinginterfaces it is possible to edit thicknesses of individual layers with the help of activedimensions . Adding (editing) layer is performed in the "Add (edit) interface" dialogue window. Thez-coordinate measured from the top point of a structure is specified.


The frame "Profile"

Modulus of subsoil reactionThis frame serves to specify a type of analysis for computation of the modulus of subsoilreaction, which is an important input parameter when analyzing a structure using the methodof dependent pressures.

The program makes possible to input the distribution of the modulus of subsoil reaction(along the length of a structure, as a soil parameter), iterate from soil material parameters,or to compute it. The modulus of subsoil reaction can be either linear or nonlinear.

Selecting the option "Input by distribution" opens a table in the frame that allows forspecifying the values of the modulus of subsoil reaction both in front and behind thestructure. When selecting other options the required information needed to compute themodulus value are inputted as soil parameters in the frame "Soils".

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Frame "Modulus of subsoil reaction"



The soil characteristics are specified in the program "Sheeting check". These characteristicsare further specified in chapters: "Basic data", "Earth pressure at rest", "Uplift pressure" and "Modulus of subsoil reaction".

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Frame "Soils"

GeometryThe "Geometry" frame contains a table with a list of inputted structural sections forming thesheeting wall. For each section the table stores its cross-sectional characteristics (A – area, I– Moment of inertia) and material characteristics (E – Modulus of elasticity, G – Shearmodulus – these variables are always expressed with respect to 1m of a construction length).Adding (editing) sections is performed in the "New section (Edit section)" dialogue window.

The program allows for adding (inserting) another section in between two already existingsections of a structure. Inserting a new section is performed in the "Insert section" dialoguewindow that complies with the "New section" dialogue window. The inserted section isordered such as to precede the currently selected section of a structure.

The inputted sections can be further edited on the desktop with the help of active objects –double clicking on a structure opens a dialog window with a given section.

Frame "Geometry"

Adding and editing sectionThe "New section (Edit, section, Insert section)" dialog window contains the followingitems:

Type of wall combo list containing individual types of walls to create asheeting (pile wall, reinforced concrete rectangular wall,sheet pile wall, steel I cross-section, or own generation ofdesired cross-sectional characteristics

Section length use input field to specify length of sheeting wall or lengthof a given section of a structure, respectively

Coeff. of reduc. ofearth press. belowditch bottom

coefficient allowing for computation of braced sheeting (forclassical sheeting is set equal to one)

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Geometry contains information about geometry for a given structuralvariant (e.g., for pile wall it contains pile cross-section andspacing of piles, for reinforced concrete wall its thickness,etc.)

Profile contains information about profile for the selectedstructural variant "steel I cross-section" (buttons "Catalogue" and "Edit" open the "Rolled section steelprofiles", which contains a list of these cross-sections)

Material contains information about material of a given structuralvariant (e.g., for pile wall it contains a catalogue ofmaterials to select the type of concrete, for sheet pile wallthe elastic modulus, etc.)

Information contains overview of cross-sectional characteristics of theinputted cross-section – area and moment of inertia arealways evaluated for 1m of length in out of plane direction

The "User catalogue" button in the bottom part of the window opens the "User catalogue"dialogue window.

Dialogue window "New section"

User catalogueThe user catalogue allows the user to define and store own cross-sections and theircharacteristics that appear in the construction of a wall. At first use of the catalogue (has notbeen yet created) the program prompts a warning message that no catalogue was found.Then, pressing the button "OK" opens the "Save as" dialogue window that allows for entering

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the catalogue name and saving it into a specified location by pressing the "Save" button (bydefault a folder used for saving the project data is assumed).

The program allows the user to create more than one catalogue. The next catalogue iscreated by pressing the "New" button – the program asks, whether the current catalogueshould be replaced (the currently loaded catalogue is not deleted!) and saves the newcatalogue under a new name. The "Open" button allows for loading an arbitrary usercatalogue and by pressing the "Save as" button for saving it under a different name.

Dialogue window at first use user catalogue of cross-sections

The "User catalogue" dialogue window contains a table listing the user definedcross-sections. The “Add item” button opens the “New catalogue item” dialogue windowthat allows for specifying and subsequent saving of characteristics of a new cross-section intothe catalogue. Buttons “Edit item” and “Remove item” serve to edit individual items in thetable.

The "Accept current" button accepts the current cross-sectional characteristics of across-section specified in the "New section" dialogue window and opens the "New catalogueitem" dialogue window that allows for modifying and saving the current cross-section.

Dialogue windows "User catalogue" and "New catalogue item"



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Frame "Assign"

ExcavationThe "Excavation" frame serves to input the depth of a construction ditch and by pressing thebutton to select the shape of the ditch base. The selected shape with a graphic hint "Parameter chart" appears in the left part of the frame. The dimensions of a structure can beedited either in the frame by inserting values into input fields, or on the desktop with the helpof active dimensions.

The frame also allows for specifying surcharge acting on the ditch base or a thickness ofmade-up ground of new soil below the ditch base (the soil can be selected from a combo listcontaining soils inputted in the regime "Soils"). When introducing the made-up ground withbrace sheeting it is assumed that there is a sheeted structure in the location of made-upground, i.e., all pressures are acting on the entire width of a structure as above theconstruction ditch base.

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Frame "Excavation"




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Frame "Terrain"

WaterThe "Water" allows, by pressing the button, for selecting the type of water. The selected typetogether with a graphic hint (“Parameter chart”) of inputted values is displayed in the leftpart of the frame. Water parameters (h1, h2...) can be edited either in the frame by insertingvalues into input fields, or on the desktop with the help of active dimensions.

The last option is a manual input of pore pressure both in front and behind the structure. Twotab sheets "In front of structure" and "Behind structure" appear with tables. The table isfilled with values of pore pressure in front, or behind the structure at a depth of “z” (z-axis).




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Frame "Water"




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Frame "Surcharge"

ForcesThe "Forces" frame contains a table with a list of forces acting on a structure. Adding(editing) forces is performed in the "New force (edit force)" dialogue window. The inputtedforces can also be edited on the desktop with the help of active objects.

Frame "Forces"

AnchorsThe "Anchors" frame contains a table with a list of inputted anchors. Adding (editng)

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anchors is performed in the "New anchor (Edit anchor)" dialogue window. The inpuutedanchors can be edited on the desktop with the help of active objects.

You are asked to input the anchor location, its length and inclination, pre-stress force andparameters needed to determine the anchor stiffness (cross-sectional area, modulus ofelasticity). The anchor is introduced automatically on already deformed structure (obtainedfrom the previous stage of construction).

The anchor stiffness becomes effective in subsequent stages of construction. In subsequentstages the anchor can no longer be edited. The only action available is the change of anchorpre-stress force.

Note: The program does not check the anchor bearing capacity against breakage.

Frame "Anchors"

PropsThe "Props" frame contains a table with a list inputted props. Adding (editing) props isperformed in the "New prop (Edit prop)" dialogue window. The inputted props can also beedited on the desktop with the help of active dimensions or active objects, respectively.

You are asked to input the prop location, its length and parameters needed to determine theprop stiffness (cross-sectional area, modulus of elasticity).

The prop is introduced automatically on already deformed structure (obtained from theprevious stage of construction). In subsequent stages the props can no longer be edited. Theonly action available is the change of prop stiffness.

Note: The program does not check the prop bearing capacity neither for compression nor forbuckling.

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Frame "Props"

SupportsThe "Supports" frame contains a table with a list of inputted supports. Adding (editing)supports is performed in the "New support (Edit support)" dialogue window. The inputtedsupports can also be edited on the desktop with the help of active dimensions or activeobjects, respectively.

You are asked to specify the support type (free, fixed, and spring) and its location. Thesupport is inputted automatically on already deformed structure (obtained from the previous stage of construction). In subsequent stages the supports can no longer be edited. The onlyaction available is the introduction of prescribed (forced) displacement in a support.

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Frame "Support"



Frame "Earthquake"

Setting

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The "Setting" frame contains basic settings for the analysis of earth pressures. The programoffers pre-setting for different countries (Czech Republic, Germany, France,...) and "Standard setting" recommended by the authors of the program for countries no included inthe list. While changing settings in the combo list the values of coefficients of reduction of soilparameters in corresponding windows are changed.


The "Other" tab sheet contains setting for minimum dimensioning pressure and setting ofparameters of internal stability of a structure.

The program "Sheeting check" is useful particularly when modeling real behavior of astructure – consequently we recommend the analysis to be performed without reduction ofinput characteristics of soils ("Standard setting").

Frame "Setting" - tab sheet "Pressure calculation"

Frame "Setting" - tab sheet "Other"

AnalysisThe frame "Analysis" displays the analysis results. Switching to this regime automaticallyruns the analysis. The frame contains three buttons to show the analysis results:

Kh + pressures

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Variation of the modulus of subsoil reaction is displayed in the left part of the desktop(by default a blue color with hatching) is assumed. Referring to the method ofdepending pressures some of the springs (values of modules of subsoil reaction) areremoved (spring stiffness set equal to zero) from the analysis. The analysis may fail toconverge providing the critical (limit) state developed both in front and behind thestructure and there is not enough constrains available (anchors, supports). Theprogram exists without finding a solution. An error message appears in the bottom partof the frame – such a case calls for modification in problem input – e.g., add ananchor, change a depth of excavation, improve soil parameters, etc.Some construction stages display (by default a yellow dotted line is assumed)deformation at the onset of mobilization of the earth pressure at rest – this is acomplementary information showing plastic deformation of a structure.

Distributions of limiting pressures (by default a green dashed line is assumed) arepresented in the right part of the window (passive pressure, pressure at rest and activepressure). The actual pressure acting on a structure is plotted in a solid blue line.

Both deformed (by default a solid red color is assumed) and undeformed structureappears in the right part of the desktop. Forces and displacements developed inanchors, supports and props are also shown.

Internal forces

Plot of a structure together with forces acting in anchors, reactions and deformations ofsupports and props appear in the left part of the desktop. Distributions of bendingmoment and shear force are then plotted on the right.

Deformations + Stresses

Plot of a structure together with forces acting in anchors, reactions and deformations ofsupports and props appear in the left part of the desktop. The deformed shape of astructure together with overall pressure acting on a structure is then plotted on theright.

Providing the modulus of subsoil reaction is found by iteration it is necessary to check thecourse of iteration in the dialogue window. Details are provided in the theoretical part of thehint "Modulus of subsoil reaction determined by iteration".

Frame "Analysis" - modulus of susoil reaction, earth pressures and deformations

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Frame "Analysis" - bending moment and shear force

Frame "Analysis" - deformation and pressure acting on structure

Internal stabilityThis frame serves to check the internal stability of anchors – the frame is therefore accessibleonly in stages, in which the anchors are introduced. For each row of anchors the table showsinputted anchor forces and the maximum allowable forces in each anchor. Overall check forthe most stressed row of anchors is displayed in the right part of the frame.

The verification procedure depends on "Setting" – either based factors of safety or according

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to the theory of limit states. The solution procedure is described herein.

Frame "Internal stability"

External stabilityPressing the "External stability" button launches the "Slope stability" program. Thisprogram then allows us to check the overall stability of the analyzed structure. The button isavailable only if the program "Slope stability" is installed.

After completing all analyses press the "OK" button to leave the program – all data are thencarried over to the analysis protocol of the "Sheeting verification" program.

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Frame "External stability"

EnvelopesThe frame "Envelopes" allows for displaying an envelope of internal forces anddisplacements from all analyses (stages of constructions). By default the envelope isconstructed from the results from all construction stages. It can, however, be created onlyfrom the selected stages (pressing buttons selects the constructions stages that are used togenerate the current envelope). The program makes possible to construct more envelopeswith various combinations.

The maximum internal forces and displacements are displayed in the right part of the frame.

Frame "Envelopes"

Program Slope Stability



The "Analysis" tab sheet is used to specify whether the analysis is performed in total oreffective parameters.

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InterfaceThe "Interface" frame serves to introduce individual soil interfaces into the soil body.Detailed description how to deal with interfaces id described herein.

Frame "Interface"

EmbankmentThe "Embankment" frame allows for inputting interfaces to create an embankment abovethe current terrain. The frame contains a table with a list of interfaces forming theembankment. A table listing the points of currently selected interface of the embankment isdisplayed in the mid section of the frame. Inputting an embankment interface follows thesame steps as used for standard interfaces.

An embankment cannot be specified in the first stage of construction. An embankment cannotbe built if there is an earth cut already specified in a given stage - in such a case either a newstage of construction must be introduced for embankment input or the existing open cut mustbe first removed.

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Frame "Embankment"

Earth cutThe "Earth cut" frame serves to specify the shape of an open cut. This function allows formodifying the terrain profile within a given stage of construction. Several earth cuts can beintroduced at the same time. In such a case some of the lines in the cut appear partiallyabove the terrain.

A table listing individual interface points is displayed in the left part of the frame. Inputtingan earth cut interface follows the same steps as used for standard interfaces.

An open cut cannot be specified in the first stage of construction. An earth cut cannot be builtif there is an embankment already specified in a given stage - in such a case either a newstage of construction must be introduced for earth cut input or the existing embankmentmust be first removed.

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Frame "Earth cut"



The soil characteristics are specified in the program "Slope stability". These characteristicsare further specified in chapters:"Uplift pressure" and "Foliation". An input of parametersfurther depends on the selected type of analysis (effective / total stress state), which is set inthe frame "Projekt", tab sheet "Analysis".

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Frame "Soils"

Rigid bodiesThe "Rigid bodies" frame contains a table with a list of inputted rigid bodies. The rigidbodies serve to model regions with a high stiffness – e.g., sheeting structures or rocksubgrade. This table also provides information about the currently selected rigid bodydisplayed in the right part of the frame.

Adding (editing) rigid bodies is performed in the "Add new rigid body" dialogue window.This window serves to input the unit weight of the rigid body material and to select color andpattern. The rigid bodies are in the frame "Assign" ordered after inputted soils.

Rigid bodies are introduced in the program as regions with high strength so they are notintersected by a potential slip surface. Providing we wish the slip surface to cross a rigidbody (e.g., pile wall) it is recommended to model the rigid body as a soil with a cohesioncorresponding to pile bearing capacity against slip.

Frame "Rigid bodies"

AssignThe “Assign” frame contains a list of layers of profile and associated soils. The list of soils isgraphically represented using buttons in the bar above the table, or is accessible from acombo list for each layer of the profile.


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Frame "Assign"

AnchorsThe "Anchors" frame contains a table with a list of inputted anchors. Adding (editing)anchors is performed in the "New anchor (Modify anchor parameters)" dialogue window.The inputted anchors can be edited on the desktop with the help of active objects.

You are asked to input the anchor location (starting point), its length and inclination, anchorspacing and pre-stress force. The anchor starting point is always attached to the terrain.All inputted parameters can be modified in the stage of construction, in which the anchor wasintroduced. In subsequent stages the program allows only for modifying the anchor pre-stressforce (option "Anchor post-stressing").

Anchors can also be introduced with help of a mouse click. Mouse input mode is determinedby pressing buttons on the horizontal bar "Anchor". The following modes are available:

Add clicking the left mouse button allows for specifying the starting andend point of an anchor. The grid function can be exploited in theinput mode. The starting point is always "attached" to the terrain.The coordinates of inputted points are automatically round up totwo digits – both input modes (manual, mouse) are thereforeidentical

Modify clicking the left mouse button on already existing anchor opens the"Modify anchor property" dialogue window, where the selectedanchor can be modified

Remove clicking the left mouse button on an anchor opens the dialoguewindow to confirm the reinforcement removal – confirming thisaction then removes the anchor

Effect of anchors on the analysis is described in more details in the theoretical part of thehint.

Note: The program does not check the anchor bearing capacity against breakage.

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Frame "Anchors"

ReinforcementsThe "Reinforcement" frame contains a table with a list of inputted reinforcements. Adding(editing) reinforcement is performed in the "New reinforcement (Modify interfaceproperties)" dialogoue window. The inputted reinforcements can be edited on the desktopwith the help of active objects.

Properties like reinforcement location, anchorage length from both left and right end andreinforcement strength must be specified. All inputted parameters can be modified only inthe stage of construction, in which the reinforcement was introduced. In subsequent stagesthe geo-reinforcement can only be removed.

Reinforcements can also be introduced with help of a mouse click. Mouse input mode isdetermined by pressing buttons on the horizontal bar "Reinforcement". The following modesare available:

Add clicking the left mouse button allows for specifying the startingand end point of a reinforcement. A predefined grid can be usedin the input mode. The starting point is always "attached" to theterrain. The coordinates of inputted points are automaticallyround up to two digits – both input modes (manual, mouse) aretherefore identical

Modify clicking the left mouse button on already existing reinforcementopens the "Modify reinforcement property" dialogue window,where the selected reinforcement can be modified

Remove clicking the left mouse button on reinforcement opens thedialogue window to confirm the reinforcement removal –confirming this action then removes the reinforcement

Reinforcements can be introduced only in the horizontal direction.

Including reinforcements in the analysis is described in more details in the theoretical part ofthe hint.

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Frame "Reinforcements"


All inputted parameters of a surcharge can be modified in the construction stage where thesurcharge was specified. Only the surcharge magnitude can be modified in all subsequentconstruction stages (option "Adjust surcharge").

Influence of surcharge on stability analysis of slopes is described in the theoretical part of thehint.

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Frame "Surcharge"

WaterThe "Water" frame serves to set the type of ground water table. Five options to specify thetype of water are available from the combo list.

Inputting the ground water table or isolines, respectively, is identical with the standard inputof interfaces.

A field for specifying a value of coefficient Ru or pore pressure appears next to the table ifintroducing water using isolines of Ru-interfaces or pore pressure, respectively. Pressingthe button with a blue arrow next to the input field opens the "Coefficient Ru" or "Porepressure" dialogue window to enter the desired value. It is advantageous to input all valuesat once using the "OK+ " and "OK+ ". The value of a given quantity found in a specificpoint between two isolines is approximated by linear interpolation of values pertinent togiven isolines. The first (the most top one) always coincides with terrain – it thereforecannot be deleted.

The ground water table or table of suction, respectively, is specified as continuousinterfaces, which can be located even above the terrain.

If the inputted data in individual stages are different, the program then allows for acceptingthe data from the previous stage of construction by pressing the "Accept" button.


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Frame "Water"


Slope stability analysis while accounting for earthquake is described in the theoretical part ofthe hint in chapter "Influence earthquake".

Frame "Earthquake"

Setting

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The "Settings" frame contains basic settings to assess the slope stability. The program offerspre-setting for different countries (Czech Republic, Germany, France,...) and "Standardsetting" recommended by the authors of the program for countries no included in the list.While changing settings in the combo list the values of coefficients of reduction of soilparameters in corresponding windows are changed. Changing settings in the combo listmodifies previously set values in corresponding windows.

An arbitrary analysis setting is available with the option "User setting".

Selecting the option "Safety factor" allows the user to specify in input field own value of thefactor of safety.

Selecting the option "Limit states" allows for specifying individual values of the coefficients ofreduction of soil parameters (e.g.,recommended values of coefficients according to EC7-1)and coefficient of overall stability.

Frame "Settings"

AnalysisThe "Analysis" frame displays the analysis results. Several analyses can be performed for asingle task.

The starting point in the slope stability analysis is the selection of the type of slip surface. Theinput is available from a combo list in the left top part of the frame containing two options –circular slip surface and polygonal slip surface. After introducing the slip surface theanalysis is started using the "Analysis" button. The analysis results appear in the right partof the frame.

The type of analysis is selected in the mid section of the frame – the circular slip surfaceallows two options – the Bishop or Petterson method, the polygonal slip surface is analyzedexploiting the Sarma method.

Based on the "Settig" in the frame the verification of the slope stability is performed usingeither the factor of safety concept or the theory of limit states.

Checking the box "Optimize slip surface" allows for optimizing either the circular orpolygonal slip surface. This step also activates the "Constrains" button – pressing this buttonchanges the frame appearance and makes possible to introduce constrains on optimizationprocedure.

It is also possible to specify how to deal with anchors in the analysis (box "Infinite anchorlengths assumed").

The slip surface (even the optimized one) must be introduced in the frame – severalpossibilities are available:

Circular slip surface

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using mouse – press the "Input" button to active the input regime and then byclicking the left mouse button enter three points to define a circular slip surface(the introduced slip surface can be further modified using the "Modify" button orspecified again with the help of the "Replace" button

using the dialogue window – pressing the "Input" button in the "Circular slipsurface" frame opens the "Circular slip surface" dialogue window that allows forspecifying the radius and coordinates of center

Polygonal slip surface

using mouse - press the "Input" button to active the input regime – entering thesurface points proceeds in the same steps as when specifying interfaces

using table – pressing the button "Input" actives several buttons that allow forfilling the adjacent table with the coordinates of slip surface points (buttons "Add","Modify", "Remove")

The analysis results appear in the left part of the frame and the optimized slip surface on thedesktop. Visualization of results can be adjusted in the "Setting visualization style" dialoguewindow.

Frame "Analysis" - circular slip surface

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Frame "Analysis" - polygonal slip surface

Constrains on the optimization procedureThe "Analysis" frame allows (after pressing the "Constrains") for specifying constrains onthe optimization process. Regardless of the assumed type of slip surface it is possible to introduce into the soilbody (with the help of mouse) segments, which should not be crossed by the optimized slipsurface. These segments also appear in the table in the left part of the frame.

Polygonal slip surface also allows for excluding some points from optimization, eitherentirely or partially only in specified direction. "Keeping the point fixed" duringoptimization process is achieved by checking the box in the table with corresponding point.This input mode is quitted by pressing the red button "Return to analysis regime".

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Frame "Analysis" - constrains on slip surface optimization by segments

Height multiplierProviding the analyzed slope is too long or has small height the plotted slip surface might notbe sufficiently visible. This problem can be solved by selected courser scale in the verticaldirection with the help of height multiplier. The value of this multiplier is set in the "Settingvisualization style" dialogue window, tab sheet "Global 2D". Using standard setting ("Heightmultiplier" equal to one) plots undistorted structure proportional to its dimensions.

Only polygonal slip surface can be inputted graphically when exploiting the height multiplieroption. The circular slip surface must be in such a case inputted manually in the "Circularslip surface" dialogue window using the "Input" button.

Setting height multiplier

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Visualization of the resulting slip surface when using height multiplier

Program Cantilever Wall



The "Project" tab sheet further serves to specify a standard for concrete structuresdimensioning. Referring to the selected standard the types of concrete and steel are theninputted in the "Material" frame. The dimensioning of cross-sections of the analyzed structureis then performed in the "Dimensioning" frame. Only ACI standard is available when selectingimperial units. While selecting standard it is also necessary to specify whether the stress inthe foundation joint used for verification of a wall front key is assumed uniform (CSN) ortrapezoidal (Eurocode).


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GeometryThe "Geometry" frame allows by pressing the button for selecting the wall shape. Theselected shape with a graphic hint "Wall geometry chart" appears in the left part of theframe. The shape of a wall can be edited either in the frame by inserting values into inputfields, or on the desktop with the help of active dimensions.

In case the structure is composed of inclined segments it is required to enter the ratio ofsides of an inclined segment 1:x. The straight structure is specified by entering the valuezero.

Frame "Geometry"

MaterialThe "Material" frame allows for the selection of material parameters for concrete andlongitudinal steel reinforcements.

Two options are available when selecting the material type:

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the "Catalogue" button opens the "Material catalogue" dialogue window (forconcrete or steel reinforcements), the list of materials then serves to select thedesired material

the "User" button opens the "Edit material – concrete" dialogue window (forconcrete) or the "Edit material – concrete steel" dialogue window (forlongitudinal steel reinforcements), which allows for manual specification ofmaterial parameters

The catalogues content depends on the selection of standard for the design of concretestructures set in the "Project" frame. The input field in the upper part of the frame serves tospecify the wall unit weight.

Frame "Material"




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Frame "Profile"



The soil characteristics are specified in the program "Cantilever wall". These characteristicsare further specified in chapters: "Basic data", "Earth pressure at rest" and "Uplift pressure".

Frame "Soils"

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Frame "Assign"




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Frame "Terrain"

WaterThe "Water" allows, by pressing the button, for selecting the type of water. The selected typetogether with a graphic hint ("Parameter chart") of inputted values is displayed in the leftpart of the frame. Water parameters (h1, h2...) can be edited either in the frame by insertingvalues into input fields, or on the desktop with the help of active dimensions.

The combo list serves to specify whether the influence of uplift pressure of water due todifferent tables at the foundation joint is considered. The uplift pressure can be assumed tobe linear, parabolic or it may not be considered at all. When verifying the wall, the upliftpressure in base of footing joint due to different water tables is introduced in terms of aspecial force.

The last option is a manual input of pore pressure both in front and behind the structure. Twotab sheets "In front of structure" and "Behind structure" appear with tables. The table isfilled with values of pore pressure in front, or behind the structure at a depth of "z" (z-axis).




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Frame "Water"




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Frame "Surcharge"

Front face resistanceThe "Front face resistance" frame allows by pressing the button for specifying the terrainshape and parameters of front face resistance. The selected shape with a graphic hint ("Parameter chart") of inputted values are displayed in the left part of the frame. The terrainshape can be edited either in the frame by inserting values into input fields, or on thedesktop with the help of active dimensions.

Combo lists in the frame allows the user to select the type of resistance and a soil (the combolist contains soils introduced in the regime "Soils"). The magnitude of terrain surcharge infront of the wall or soil thickness above the wall lowest points can also be specified in theframe.

The resistance on a structure front face can be specified as a pressure at rest, passivepressure or reduced passive pressure. The resulting force due to reduced passive pressureis found as a resultant force caused by passive pressure multiplied by a correspondingcoefficient, which follows from the inputted type of reduced passive pressure.

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Frame "Front face resistance"

Inputted forcesThe "Inputted forces" frame contains a table with a list of forces acting on a structure.Adding (editing) forces is performed in the "New force (edit force)" dialogue window. Theinputted forces can also be edited on the desktop with the help of active objects.

Frame "Inputted forces"

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Frame "Earthquake"

Base anchorageThe frame "Base anchorage" serves to input parameters (anchorage geometry, bearingcapacity against pulling-out and pulling-apart) specifying an anchorage of the wallfoundation. Geometry of footing anchorage can be edited either in the frame by insertingvalues in the inputting boxes or on the desktop with the help of active dimensions. Thebearing capacity values can be either inputted or computed by the program from the inputtedparameters.

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Frame "Base anchorage"


Evaluating the structure according to theory of limit states also calls for the input ofcoefficient of overall stability of a structure. When subjecting the wall to overallverification this coefficient is used to multiply the resisting moment Mres and the resistingshear force Hres.


The "Other" tab sheet serves to specify the type of pressure acting on a wall based on theallowable wall deformation. Providing the wall is free to move an active pressure is assumed,otherwise, a pressure at rest is used.

For wall with footing jump it is possible to choose in the tab sheet "Other" the way ofaccounting for the wall footing jump.

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Frame "Setting"

VerificationThe "Verification" frame shows the analysis results. Several computation with differentcoefficients of resultant force effects can be carried out for a single task.

The wall is loaded either by active pressure or pressure at rest depending on input in theframe "Setting".

Procedure for wall verification is described in the theoretical part of the hint.

The computed forced are displayed on the desktop and are automatically updated with everychange of input data and setting. The right part of the frame shows the result of verificationof a wall against overturning and translation. The "In detail" button opens the dialoguewindow, which contains detailed listing of the results of verification analysis.

Visualization of results can be adjusted in the "Setting visualization style" dialogue window.

Frame "Verification"

Bearing capacity

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The "Bearing capacity" frame displays the results from the analysis of foundation soilbearing capacity. The stress in the footing bottom (assumed constant) is derived from allverifications performed in the frame "Verification". The program "Spread footing" thenconsiders all verifications as loading cases.

Three basic analysis options are available in the frame:

Input the foundation soilbearing capacity

The input field serves to specify the foundation soilbearing capacity. The results of verification analysisof a soil for eccentricity and bearing capacity aredisplayed in the right part of the frame. The "Indetail" button opens the dialogue window thatdisplays detailed listing of the results of verificationanalysis of foundation soil bearing capacity.

Compute the foundationsoil bearing capacityusing the program"Spread footing"

Pressing the "Run "Spread footing" button startsthe program "Spread footing" that allows forcomputing the soil bearing capacity or settlement androtation of a footing. Pressing the "OK" button leavesthe analysis regime – the results and all plots arecopied to the program "Cantilever wall". Theprogram "Spread footing" must be installed for thebutton to be active.

Do not compute (pilefooting)

The foundation soil bearing capacity is not computed.


Frame "Bearing capacity"

DimensioningThe "Dimensioning" frame serves to design and verify the reinforcement of wallcross-section – the cross-section subjected to dimensioning is selected in the combo list.

Wall stem verification

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Construction jointverification

depth of construction joint from construction topedge is specified

Wall jump verification type of assumed stress acting in construction joint forverification (linear, constant) can be selected in theframe "Project"

Verification of heel ofwall

type of assumed stress acting in construction joint forverification (linear, constant) can be selected in theframe "Project"

Calculation of forces and their action on the analyzed cross-section is described here.

The wall stem and construction joint are always loaded by the pressure at rest. Whenverifying the front wall jump the wall is loaded either by the active pressure or the pressureat rest depending on input specified in the frame "Setting".

Procedure to derive distribution of internal forces in individual cross-sections is described inthe theoretical part of this hint.

Dimensioning of the steel-reinforced concrete structure is performed according to thestandard set in the frame "Project".

Several computations for various cross-sections can be carried out. Various designcoefficients of individual forces can also be specified. The resulting forces are displayed on thedesktop and are updated with an arbitrary change in data or setting specified in the frame.The "In detail" button opens the dialogue window that contains detailed listing of thedimensioning results.


Frame "Dimensioning"

StabilityPressing the "Stability" button launches the "Slope stability" program. This program thenallows us to check the overall stability of the analyzed structure. The button is available onlyif the program "Slope stability" is installed.

After completing all analyses press the "OK" button to leave the program – all data are then

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carried over to the analysis protocol of the "Cantilever wall" program.

Frame "Stability"

Program Masonry wall



The "Project" tab sheet further serves to specify a standard for concrete structuresdimensioning. Referring to the selected standard the types of concrete and steel are theninputted in the "Materiál" frame. The dimensioning of cross-sections of the analyzed structureis then performed in the "Dimensioning" frame. Only ACI standard is available when selectingimperial units. While selecting standard it is also necessary to specify whether the stress inthe foundation joint used for verification of a wall front key is assumed uniform (CSN) ortrapezoidal (Eurocode).


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GeometryThe "Geometry" frame allows by pressing the button for selecting the wall shape. Theselected shape with a graphic hint "Wall geometry chart" appears in the left part of theframe. The shape of a wall can be edited either in the frame by inserting values into inputfields, or on the desktop with the help of active dimensions.

Based on the selected shape of a wall, you specify in the frame "Geometry of masonry" thenumber and dimensions of masonry blocks in individual columns, or if applicable also thethickness of vertical joint between blocks. In addition it is necessary to input compressivestrength of masonry, which serves as the basic input parameter for the bearing capacityverification of reinforced masonry.

Frame "Geometry"


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The catalogues content depends on the selection of standard for the design of concretestructures set in the "Project" frame. The input field in the upper part of the frame serves tospecify the wall unit weight.

Frame "Material"




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Frame "Profile"




Frame "Soils"

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Frame "Assign"




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Frame "Terrain"







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Frame "Water"




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Frame "Surcharge"




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Frame "Earthquake"

Base anchorageThe frame "Base anchorage" serves to input parameters (anchorage geometry, bearingcapacity against pulling-out and pulling-apart) specifying an anchorage of the wallfoundation. Geometry of footing anchorage can be edited either in the frame by insertingvalues in the inputting boxes or on the desktop with the help of active dimensions. Thebearing capacity values can be either inputted or computed by the program from the inputtedparameters.

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Frame "Base anchorage"





For wall with footing jump it is possible to choose in the tab sheet "Other" the way ofaccounting for the wall footing jump.

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Frame "Setting"







Bearing capacity

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Pressing the "Run "Spread footing" button startsthe program "Spread footing" that allows forcomputing the soil bearing capacity or settlement androtation of a footing. Pressing the "OK" button leavesthe analysis regime – the results and all plots arecopied to the program "Cantilever wall". Theprogram "Spread footing" must be installed for thebutton to be active.







the number of a joint between masonry blocks isinputted

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Verification of heel ofwall

type of assumed stress acting in construction joint forverification (linear, constant) can be selected in theframe "Project"


The wall is loaded either by the active earth pressure or by the pressure at rest depending onthe setting in the frame "Setting".


Joints between masonry blocks are verified according to AS 3700 "Masonry structures"standard. The program verifies the bearing capacity for bending, shear and combination ofcompression and bending. Reinforcement can be specified on both front and back sides of astructure. An additional loading applied to a cross-section (bending moment, compressivenormal force and shear force) can also be specified. These additional forces are added to thecomputed ones.

Dimensioning of steel-reiforced concrete structure is performed according to the standard setin the frame "Project".




StabilityPressing the "Stability" button launches the "Slope stability" program. This program thenallows us to check the overall stability of the analyzed structure. The button is available only

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if the program "Slope stability" is installed.

After completing all analyses press the "OK" button to leave the program – all data are thencarried over to the analysis protocol of the "Masonry wall" program.

|Frame "Stability"

Program Gravity Wall


The “Project” tab sheet also allows the user to switch analysis units (metric / imperial).

The "Project" tab sheet further serves to specify a standard fornormy se concrete structuresdimensioning. Referring to the selected standard the types of concrete and steel are theninputted in the "Material" frame. The dimensioning of cross-sections of the analyzed structureis then performed in the "Dimensioning" frame. Only ACI standard is available when selectingimperial units. While selecting standard it is also necessary to specify whether the stress inthe foundation joint used for verification of a wall front key is assumed uniform (ČSN) ortrapezoidal (Eurocode).


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Frame Project - tab sheet "Project"

GeometryThe "Geometry" frame allows by pressing the button for selecting the wall shape. Theselected shape with a graphic hint ("Wall geometry chart") appears in the left part of theframe. The shape of a wall can be edited either in the frame by inserting values into inputfields, or on the desktop with the help of active dimensions.


Frame "Geometry"



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The catalogues content depends on the selection of standard for the design of concretestructures set in the "Project" frame. The input field in the upper part of the frame serves tospecify the wall bulk weight.

Frame "Material"




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The frame "Profile"



The soil characteristics are specified in the program "Gravity wall". These characteristics arefurther specified in chapters: "Basic data", "Earth pressure at rest" and "Uplift pressure".

Frame "Soils"

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AssignThe “Assign” frame contains a list of layers of profile and associated soils. The list of soils isgraphically represented using buttons in the bar above the table, or is accessible from acombo list for each layer of the profile.


Frame "Assign"




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Frame "Terrain"


The combo list serves to specify whether the influence of uplift pressure of water due todifferent tables at the foundation joint is considered. The uplift pressure can be assumed tobe linear, parabolic or it may not be considered at all. When verifying the wall, the upliftpressure in foundation joint due to different water tables is introduced in terms of a specialforce.





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Frame "Water"




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Frame "Surcharge"

Front face resistanceThe "Front face resistance" frame allows by pressing the button for specifying theterrainshape and parameters of front face resistance. The selected shape with a graphic hint ("Parameter chart") of inputted values are displayed in the left part of the frame. The terrainshape can be edited either in the frame by inserting values into input fields, or on thedesktop with the help of active dimensions.



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Frame "Earthquake"




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Frame "Setting"






Bearing capacityThe "Bearing capacity" frame displays the results from the analysis of foundation soilbearing capacity. The stress in the footing bottom (assumed constant) is derived from all

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verifications performed in the frame "Verification". The program "Spread footing" thenconsiders all verifications as loading cases.





Pressing the "Run "Spread footing" button startsthe program "Spread footing" that allows forcomputing the soil bearing capacity or settlement androtation of a footing. Pressing the "OK" button leavesthe analysis regime – the results and all plots arecopied to the program "Gravity wall". The program "Spread footing" must be installed for the button tobe active.








depth of construction joint from construction topedge is specifiedse

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The wall stem and construction joint are always loaded by the pressure at rest. Whenverifying the front wall jump the wall is loaded either by the active pressure or the pressureat rest depending on input specified in the frame "Setting".


Dimensioning of the steel-reinforced concrete structure is performed according to thestandard set in the frame "Project".





After completing all analyses press the "OK" button to leave the program – all data are thencarried over to the analysis protocol of the "Gravity wall" program.

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Frame "Stability"

Program Block wall





GeometryThe "Geometry" frame contains a table with a list of inputted structural precast units

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(blocks) of a wall (the lowest block is labeled as No. 1). Adding (editing) blocks is performedin the "New block (Edit block)" dialogue window.

This dialogue window serves to define the geometry of a block, parameters ofreinforcement (overhang length, anchorage length, bearing capacity against pull out,reinforcement strength) and material characteristics (self weight, shear resistance betweentwo blocks, cohesion).

The program allows for adding (inserting) another block in between two already existingblocks of a structure. Inserting a new block is performed in the "Insert block" dialog windowthat complies with the "New block" dialogue window. The inserted block is ordered such toproceed the currently selected block of a structure.

The inputted blocks can be further edited on the desktop with the help of active dimensionsor active objects - double clicking on a structure opens a dialog window with a given block.When using the regime of active objects the visualization of detailed dimensionsmust be turned off in the "Setting visualization style" dialogue window.

Frame "Geometry"




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Frame "Profile"



The soil characteristics are specified in the program "Block wall". These characteristics arefurther specified in chapters: "Basic data", "Earth pressure at rest" and "Uplift pressure".

Frame "Soils"

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Frame "Assign"




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Frame "Terrain"

WaterThe "Water" frame allows, by pressing the button, for selecting the type of water. Theselected type together with a graphic hint ("Parameter chart") of inputted values isdisplayed in the left part of the frame. Water parameters h1, h2 can be edited either in theframe by inserting values into input fields, or on the desktop with the help of activedimensions.






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Frame "Water"




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Frame "Surcharge"




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Frame "Earthquake"




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Frame "Setting"






Bearing capacityThe "Bearing capacity" frame displays the results from the analysis of foundation soilbearing capacity. The stress in the footing bottom (assumed constant) is derived from all

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verifications performed in the frame "Verification". The program "Spread footing" thenconsiders all verifications as loading cases.





Pressing the "Run "Spread footing" button startsthe program "Spread footing" that allows forcomputing the soil bearing capacity or settlement androtation of a footing. Pressing the "OK" button leavesthe analysis regime – the results and all plots arecopied to the program "Block wall". The program "Spread footing" must be installed for the button tobe active.





DimensioningThe "Dimensioning" frame allows for verifying joints between individual blocks of a wall. The"Joint above block No." field serves to select the desired joint subjected to verificationanalysis. The verification against overturning and translation is performed in the same wayas for the entire wall – friction between blocks and cohesion of a block material are inputtedin the frame "Geometry".

Several computations for various cross-sections can be carried out. Various designcoefficients of individual forces can also be specified. The resulting forces are displayed on the

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desktop and are updated with an arbitrary change in data or setting specified in the frame.The "In detail" button opens the dialogue window that contains detailed listing of thedimensioning results.




After completing all analyses press the "OK" button to leave the program – all data are thencarried over to the analysis protocol of the "Block wall" program.

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Frame "Stability"

Program RediRock Wall





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Frame "Project" - tab sheet "Earth pressure"

BlocksThe "Blocks" frame is used to input the parameters of blocks. This function is available onlyto the manufacturer. Editing and adding new types blocks in the freeware version is notallowed.

Frame "Blocks"

SetbacksThe "Setbacks" frame is used to input the allowable setbacks. This function is available onlyto the manufacturer. Editing and adding new distances of jumps of blocks in the freewareversion is not allowed.

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Frame "Setbacks"

GeometryThe "Geometry" frame contains a table with a list of inputted structural precast units(blocks) of a wall (the lowest block is labeled as No. 1). Adding (editing) blocks is performedin the "New block (Edit block)" dialogue window.

An group of blocks that is defined by a number of blocks and jumps between them is enteredat once.

The program allows for adding (inserting) another group in between two already existingblocks of a structure. Inserting a new group is performed in the "Insert" dialog window thatcomplies with the "Add" dialogue window. The inserted block is ordered such to proceed thecurrently selected block of a structure.

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Frame "Geometry"

FootingThe "Footing" frame is used to input the footing below the foundation. The footingdimensions and its material parameters are required. A soil footing requires the user tointroduce the footing bearing capacity, a concrete footing then requires its shear bearingcapacity and friction between a concrete footing and the first block.

The bearing pad is accounted for as specified by the user. A restriction according to Fig.4-4, page 73 of NCMA manual is neither automatically enforced nor checked by theprogram. The bearing pad must be introduced into the program such that it complies withthe design criteria.

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Frame "Footing"




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Frame "Profile"



The soil characteristics are specified in the program "Redi-rock wall". These characteristicsare further specified in chapters: "Basic data", "Earth pressure at rest" and "Uplift pressure".

Frame "Soils"

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Frame "Assign"




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Frame "Terrain"

WaterThe "Water" frame allows, by pressing the button, for selecting the type of water. Theselected type together with a graphic hint ("Parameter chart") of inputted values isdisplayed in the left part of the frame. Water parameters h1, h2 can be edited either in theframe by inserting values into input fields, or on the desktop with the help of activedimensions.






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Frame "Surcharge"




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Earthquake

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The "Earthquake" frame serves to input earthquake parameters. Directions of inputtedearthquake effects are displayed on the desktop.


Frame "Earthquake"

SettingThe "Setting" frame contains basic settings for the analysis of earth pressures. The programoffers pre-setting for different countries (USA, Czech Republic, Germany, France,...) and "Standard setting" recommended by the authors of the program for countries no included inthe list. While changing settings in the combo list the values of coefficients of reduction of soilparameters in corresponding windows are changed.

The tab sheet "Others" serves to specify the parameters for the Redi-Rock wall program.The check button "Hinge height concept" determines, whether the HInge height conceptdefined in the second addition of the NCMA manual will be used. Furthermore, the masonryfriction reduction factors, which reduce the bearing capacity of the joint between the soil andconcrete, are defined. Concrete-concrete or soil-soil joints do not account for the MRF in theprogram.



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Frame "Setting" - tab sheet "Wall check"

Frame "Setting" - tab sheet "Other"





To better understand the solution procedure it is possible to go through the sample handcalculation.


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Bearing capacityThe "Bearing capacity" frame displays the results from the analysis of foundation soilbearing capacity. The stress in the footing bottom (assumed constant) is derived from allverifications performed in the frame "Verification". The program "Spread footing" thenconsiders all verifications as loading cases.

The bearing pad is accounted for as specified by the user. A restriction according to Fig.4-4, page 73 of NCMA manual is neither automatically enforced nor checked by theprogram. The bearing pad must be introduced into the program such that it complies withthe design criteria.





Pressing the "Run "Spread footing" button startsthe program "Spread footing" that allows forcomputing the soil bearing capacity or settlement androtation of a footing. Pressing the "OK" button leavesthe analysis regime – the results and all plots arecopied to the program "Block wall". The program "Spread footing" must be installed for the button tobe active.





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DimensioningThe "Dimensioning" frame allows for verifying joints between individual blocks of a wall. The"Joint above block No." field serves to select the desired joint subjected to verificationanalysis. The verification against overturning and translation is performed in the same wayas for the entire wall – friction between blocks and cohesion of a block material are inputtedin the frame "Geometry".





After completing all analyses press the "OK" button to leave the program – all data are thencarried over to the analysis protocol of the "Block wall" program.

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Frame "Stability"

Program Gabion





MaterialThe "Material" frame contains a table with a list of inputted filling (aggregates) and material

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parameters of applied gabion wire netting. Adding (Editing) material and netting is performedin the "New material (Edit material)" dialogue window.

The material parameters of filling and netting of currently selected gabion block are displayedin the right part of the frame.

Frame "Material"

GeometryThe "Geometry" frame contains a table with a list of inputted blocks of a wall (the lowestblock is labeled as No. 1). Adding (editing) blocks is performed in the "New block (Editblock)" dialogue window.

This dialogue window serves to define the geometry of a block, and parameters of meshoverhang (overhang length, overhang anchorage, bearing capacity against pull out).

The program allows for adding (inserting) another block in between two already existingblocks of a structure. Inserting a new block is performed in the "Insert block" dialog windowthat complies with the "New block" dialogue window. The inserted block is ordered such toproceed the currently selected block of a structure.

The inputted blocks can be can be further edited on the desktop with the help of activedimensions or active objects - double clicking on a structure opens a dialog window with agiven block. When using the regime of active objects the visualization of detaileddimensions must be turned off in the "Setting visualization style" dialogue window.

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Frame "Geometry"




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Frame "Profile"



The soil characteristics are specified in the program "Gabion". These characteristics arefurther specified in chapters: "Basic data", "Earth pressure at rest" and "Uplift pressure".

Frame "Soils"



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Frame "Assign"




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Frame "Terrain"







Frame "Water"



Analysis of earth pressures due to surcharges is described in the theoretical part of the hint,

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chapter "Influence of surcharge".

Frame "Surcharge"

Front face resistanceThe "Front face resistance" frame allows by pressing the button for specifying theterrainshape and parameters of front face resistance. The selected shape with a graphic hint ("Parameter chart") of inputted values are displayed in the left part of the frame. The terrainshape can be edited either in the frame by inserting values into input fields, or on thedesktop with the help of active dimensions.



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Earthquake

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The "Earthquake" frame serves to input earthquake parameters. Directions of inputtedearthquake effects are displayed on the desktop.


Frame "Earthquake"



Pro An arbitrary analysis setting is available with the option "User setting". Selecting theoption "Reduce soil parameters" allows for specifying in input fields individual values of thecoefficients of reduction of soil parameters (e.g., recommended values according to EC7).

The "Other" tab sheet allows for specifying the coefficient of reduction of friction betweenblocks.

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Frame "Setting"

VerificationThe "Verification" frame shows the analysis results. Several computation with differentdesign coefficients of resultant force effects can be carried out for a single task.






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Pressing the "Run "Spread footing" button startsthe program "Spread footing" that allows forcomputing the soil bearing capacity or settlement androtation of a footing. Pressing the "OK" button leavesthe analysis regime – the results and all plots arecopied to the program "Gabion". The program "Spread footing" must be installed for the button tobe active.





DimensioningThe "Dimensioning" frame allows for verifying individual joints of gabion blocks. The "Jointabove block No." field serves to select the desired joint subjected to verification analysis.The verification against overturning, translation, for side pressure and joint between blocksis performed.


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After completing all analyses press the "OK" button to leave the program – all data are thencarried over to the analysis protocol of the "Gabion" program.

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Frame "Stability"

Program Spread Footing

ProjectThe "Project" frame is used to input the basic project data and to specify the overall settingof the analysis run.

The "Project" tab sheet contains an input form to introduce the basic data about theanalyzed task, i.e. project information, project description, date, etc.

The "Project" tab sheet further serves to specify a standard fornormy se concrete structuresdimensioning. Referring to the selected standard the types of concrete and steel are theninputted in the "Material" frame. The dimensioning of cross-sections of the analyzed structureis then performed in the "Dimensioning" frame. Only ACI standard is available when selectingimperial units. While selecting standard it is also necessary to specify whether the stress inthe foundation joint used for verification of a wall front key is assumed uniform (ČSN) ortrapezoidal (Eurocode).

The "Analysis" tab sheet serves to choose the basic theory or standards to be followed in thesolution of a given problem.


Project - AnalysesThe "Project" frame – "Analysis" tab sheet contains basic analysis settings. Three variants areavailable for the analysis of vertical bearing capacity of shallow foundation – foundation ondrained subsoil, foundation on undrained subsoil and foundation on rock subsoil.

The "Analysis method" tab sheet then serves to choose the analysis standard or solutionprocedure, respectively, based on the selected variant.

Options to determine the foundation vertical bearing capacity:

Analysis for drained conditions Analysis for undrained conditions Foudation on rock subsoilanalysis

Standard approach Standard approach Standardní approach

CSN 73 1001 CSN 73 1001 CSN 73 1001

PN PN EC7

IS IS

EC7 EC7

NCMA

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Options for settlement and foundation rotationanalysis

Options for determination of depth ofinfluence zone when computingsettlement

With the help of oedometric modulus Using structural strength

With the help of compression constant Using percentage of geostatic stress

With the help of compession index

NEN (Buissman, Ladd)

Soft soil model

Janbu theory

Analysis based on DMT

Frame "Project" - tab sheet "Analyses"




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Frame "Profile"



The soil characteristics are specified in the program "Spread footing". These characteristicsare further specified in chapters: "Uplift pressure", "Foundation bearing capacity" and "Settlement".

Frame "Soils"

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Frame "Assign"

FoundationThe "Foundation" frame allows for selecting a type of foundation. The selected type withgraphic hint ("Geometry chart") of inputted values is displayed in the left part of the frame.The values can be edited either in the frame by inserting values into input fields, or on thedesktop with the help of active dimensions. The frame also serves to specify the bulk weightof overburden.

The following types of foundations can be selected:

Centric spread footing Circular spread footing

Eccentric spread footing Circular stepped spread

Strip footing Centric spread footing withbatter

Stepped centric spread footing Eccentric spread footing withbatter

Stepped eccentric spreadfooting

The soil profile is specified from the original ground. The foundation bearing capacitydepends mainly on the depth of foundation measured from the finished grade. Providingthe finished grade is found above the original ground it required to assign the same depth toboth the finished grade and original ground and introduce into subsoil a layer with a newmade-up-ground. This frame also allows for inputting the foundation thickness.

When completed the foundation is usually filled up with a soil – its bulk weight must be

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specified (Overburden bulk weight). Providing the analysis follows the theory of limit statesits weight is multiplied by the coefficient inputted in the frame "Setting".

For foundations with an undrained subsoil (type of analysis is selected in the frame "Project"tab sheet "Analysis") it is possible to introduce an inclination of the finished grade andfooting bottom. In all other cases both the gound and footing bottom are horizontal.

Frame "Foundation"

LoadThe "Load" frame contains a table with a list of inputted loads. Adding (editing) loads isperformed in the "New (edit) load" dialogue window. Input of individual forces follows thesign convention displayed in the right part of the dialogue window.

The following types of loading can be specified:

- design load serves to verify the foundation bearing capacity

- service load serves to compute the foundation settlement and rotation

Dimensioning of reinforcements assumed for the foundation is carried out for both types ofloading.

The foundation is loaded always in the contact point between column and foundation. Theprogram automatically computes the foundation self weight and the weight ofoverburden.

When inputting loads the program allows by pressing the "Service" button for creating theservice loads by dividing the already inputted design loads by design coefficient.

The program also allows for import of loading using the "Import" button.

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Frame "Loading"

Import of loadingIt is possible to import values of loading into the program from text files. Import parametersare set in the "Import loading" dialogue window. In the "Column" input boxes you definethe column number in the text file, from which you wish to read data. The "Multiplier" boxallows for multiplying the original value by an arbitrary number (e.g. using the number onewith a minus sign changes the load direction). The "Import" button opens the "Open"dialogue window, which allows for loading the respective text file. The names of individualloadings if contained by the first column of the text file can loaded while importing the databy checking the "Name in the first column" box.

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Dialogue window "Import of loading"

The program allows for importing data from an arbitrary text file (*.TXT). All rows in the textfile marked at the beginning by a semicolon are ignored by the program. The figure shows alisting of imported data, where values of individual forces start in the fourth column.

Example of file "Import of loading"

GeometryThe "Geometry" frame allows for specifying the foundation shape. The selected shape withgraphic hint ("Geometry chart") of inputted values is displayed in the left part of the frame.The values can be edited either in the frame by inserting values into input fields, or on thedesktop with the help of active dimensions.

Foundation type and its thickness are specified in the "Foundation"frame.

The program automatically computes the self weight of both foundation and overburdenabove the foundation. The foundation self weight is specified in the "Material" frame.Providing the analysis is carried out employing the theory of limit states the footing selfweight is multiplied by coefficients specified in the "Settings" frame.

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Frame "Geometry"

The "Dimensions design" button opens the "Foundation dimensions design" that serveswith the help of program to compute dimensions of a foundation. The dialogue window allowsfor inputting the bearing capacity of foundation soil Rd or to select the option "Analyze". Insuch a case the program determines all dimensions of a foundation based on inputtedparameters (soils, profile, water impact, send-gravel-cushion, setting, etc.).

While leaving the dialogue window by pressing the "OK" button the specified dimensions areloaded into the "Geometry" frame.

Dialogue window "Foundation dimensions design"

Sand-gravel cushionThe "Sand-gravel cushion" frame allows for inputting parameters of the sand-gravelcushion below foundation. The cushion thickness and overhang over foundation edge arerequired. The values can be edited either in the frame by inserting values into input fields, oron the desktop with the help of active dimensions.

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The cushion filling can be selected from a combo list that contains soils specified in theregime "Soils".

The inputted sand-gravel cushion influences the analysis of both the foundation load bearingcapacity and settlement.

Frame "Sand - gravel cushion"

MaterialThe "Material" frame allows for the selection of material parameters for concrete andlongitudinal and transverse steel reinforcements.



the "User" button opens the "Edit material – concrete" dialogue window (forconcrete) or the "Edit material – concrete steel" dialogue window (forlongitudinal and transverse steel reinforcements), which allows for manualspecification of material parameters

The catalogues content depends on the selection of standard for the design of concretestructures set in the "Project" frame.

The input field in the upper part of the frame serves to specify the wall bulk weight.

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Frame"Material"

SurchargeThe "Surcharge" frame contains a table with a list of inputted surcharges. Adding (editing)surcharge is performed in the "New (edit) surcharge" dialogue window. The values arespecified according to "Geometry" chart displayed in the right part of the dialogue window.The inputted surchages can also be edited on the desktop with the help of active objects.

The z-coordinate measured from the foundation joint of a structure is specified (positivedirection downwards) when inputting the surcharge at a depth different from the depth offoundation joint.

The surcharge is considered only when computing settlement and rotation of a foundation,in which case it increases the stress in soil below foundation. When computing thefoundation bearing capacity, the surcharge is not considered – its presence would increasethe bearing capacity.

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Frame "Surcharge"

Water, incompressible subsoilThe "Water + IS" frame serves to specify the depth of ground water table and level ofincompressible subsoil.

The values can be edited either in the frame by inserting values into input fields, or on thedesktop with the help of active dimensions.

The influence of water is manifested by the change of ground water pressure belowfoundation.

The incompressible subsoil cuts off the influence zone below foundation and alsoinfluences reduction in settlement.

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Frame "Water, incompressible subsoil"

SettingThe "Setting" frame contains basic settings to assess the footings. The program offerspre-setting for different countries (Czech Republic, Germany, France,...) and "Standardsetting" recommended by the authors of the program for countries no included in the list.While changing settings in the combo list the values of coefficients of reduction of soilparameters in corresponding windows are changed.


Selecting the option "Safety factor" allows the user to specify in input fields own values ofthe factor of safety for vertical and horizontal bearing capacity.

Selecting the option "Limit sates" allows for specifying individual values of the coefficients of reduction of soil parameters (e.g., recommended values of coefficients according to EC7)and coefficients for computing the self weight of both foundation and overburden.

The frame further serves for inputting the design coefficients to determine the verticalbearing capacity and the horizontal bearing capacity of a foundation, respectively.

Frame "Setting" - safety factor

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Frame "Setting" - limit states

1.LS - bearing of a footingThe "1. LS" frame serves to verify the verital and horizontal bearing capacity of afooting. More computations can be performed in the frame. The verification can beperformed either for individual loads or the program finds the most critical one (can beselected from a combo list).

The analysis follows the theory approach selected in the frame "Project" – tab sheet "Analysis". The footing can be verified using either the theory of limit states or the factor ofsafety concept specified in the frame "Setting".

The vertical bearing capacity analysis requires selection of the type of contact pressure(general shape, rectangle). The shape of contact pressure is plotted in the left part of thedesktop.

The horizontal bearing capacity analysis requires selection of the type of earth resistance thatcan be assumed as the pressure at rest, passive pressure or the reduced passivepressure.

The soil parameters (friction angle structure-soil, cohesion structure-soil) can be furtherreduced when computing the horizontal bearing capacity.

Detailed listing of the results is displayed in the right part of the desktop. Visualization ofresults can be adjusted in the "Setting visualization style" dialogue window.

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Frame "1.LS - bearing of a footing"

2.LS - settlement and rotation of a footingThe "2.LS" frame serves to compute the foundation settlement and rotation. The frameallows for more analyses. The verification can be performed either for individual loads or theprogram finds the most critical one (can be selected from combo list).

The analysis of foundation settlement and rotation is carried out according to the theoryspecified in the frame "Project" tab sheet "Analysis".

The stress in the footing button can be subtracted from the geostatic stress given by:

original ground

finished grade

not specified

Distributions of the geostatic stress and the stress increment below foundation aredisplayed in the left part of the desktop. The label below footing represents the depth ofdeformation zone. The stress is drawn below footing at the point with a characteristicdeformation.

The frame also allows for specifying the coefficient of reduction of computation of settlement.

The detailed listing of the verification analysis results is displayed in the right part of thedesktop. It can be adjusted in the "Setting visualization style" dialogue window.

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Frame "2. LS - settlement and rotation of a footing"

DimensioningThe "Dimensioning" frame allows for designing and verifying the longitudinal reinforcementof a foundation and also for verifying the foundation against being pushed through. Theverification can be performed either for individual loads or the program finds the mostcritical one (can be selected from a combo list).

The program derives the stress in the construction joint (the stress diagram is inputted in theframe "Project") and determines the internal forces in individual cross-sections.Dimensioning of the steel-reinfoced concrete structure is performed according to the standardset in the frame "Project".

The resulting information are displayed on the desktop and are updated with an arbitrarychange in data or setting specified in the frame. The "In detail" button opens the dialoguewindow that contains detailed listing of the dimensioning results.


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Program Pile


The "Project" tab sheet contains an input form to introduce the basic data about theanalyzed task, i.e. project information, project description, date, etc.

The "Project" tab sheet further serves to specify a standard for concrete structuresdimensioning. Referring to the selected standard the types of concrete and steel are theninputted in the "Material" and the dimensioning is verified in the "Horizontal bearing capacity"frame.


The "Analysis" tab sheet serves to choose the analysis of vertical bearing capacity of a pile –analysis based on CSN 73 1002, or analysis using the finite element method.

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Frame "Project" - tab sheet "Analysis"




The frame "Profile"

Modulus of subsoil reactionThe combo list serves to select one of the methods for the evaluation of modulus ofsubsoil reaction – the required material parameters of soils are inutted in the frame "Soils"based on the selected method.

Selecting the option "Input by distribution" opens a table that allows for specifying thevalues of the modulus of subsoil reaction along the pile.

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Frame "Modulus of subsoil reaction"



The soil characteristics are specified in the program "Earth Pressure". These characteristicsare further specified in chapters: "Uplift pressure", "Oedometric modulus" and "Modulus ofsubsoil reaction". The specified soil parameters depend on the set up of modulus of subsoilrection and selected theory of analysis specified in the frame "Project", tab sheet "Analysis".

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Rám "Zeminy"



Frame "Assign"

Load

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The "Load" frame contains a table with a list inputted loads. Adding (editing) load isperformed in the "New (edit) load" dialogue window. The forces are inputted following thesign convention displayed in the upper part of the dialogue window.

The program also allows for import of loading using the "Import" button.

Frame "Load"

GeometryThe "Geometry" frame allows for specifying the pile cross-section (circular, circularvariable, rectangle, I-type cross-section) based on the theory of analysis (specified in the "Project" frame, tab sheet "Analyses"). The selected shape with graphic hint is displayed inthe central section of the frame. Input fields serve to specify dimensions of the selectedcross-section.

Cross-sectional characteristics (area and moment of inertia) are computed by default, butthey can also be specified (tubes, hollow cross-sections, steel I-profiles).

The bottom part of the frame serves to specify the pile location (pile lift out and the depth offinished grade). The pile lift out can also be negative – in such a case the pile is placed"in-ground".

Providing the pile is analyzed using the finite element method it is possible to account forinfluence of pile technology by selecting the specific type of pile or directly by inputtingcoefficients.

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Frame "Geometry"

MaterialThe "Material" frame allows for specifying the material parameters. The bulk weight of astructure and material of a pile (concrete, timber, steel) are introduced in the input fieldin the right part of the frame.

The elastic and shear moduli need to be specified when assuming timber or steel piles.

In case of a concrete pile the concrete material and parameters of transverse andlongitudinal steel reinforcements are required. Two options are available when selecting thetype of material:


the "User" button opens the "Edit material – concrete" dialogue window (forconcrete) or the "Edit material – concrete steel" dialogue window (forlongitudinal and transverse steel reinforcements), which allows for manualspecification of material parameters


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Frame "Material"

Water, incompressible subsoilThe "Water + IS" frame serves to specify the depth of ground water table and level ofincompressible subsoil.

The values can be edited either in the frame by inserting values into input fields, or on thedesktop with the help of active dimensions.

The influence of water is manifested by the change of ground water pressure.

The incompressible subsoil cuts off the influence zone below foundation and alsoinfluences reduction in settlement.

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Frame "Water, incompressible subsoil"

Negative skin frictionThe "Negative skin friction" frame serves to specify the settlement of surrounding terrainand the depth of influence zone. For more information on the influence of negative skinfriction the user is referred to theoretical section.

The setting option in the frame is active only when the finite element method is selectedfor the analysis in the frame "Project" – tab sheet "Analysis".

Frame "Negative skin friction"

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SettingThe "Setting" frame contains basic settings for footings verification. The program offerspre-setting for different countries (Czech Republic, Germany, France,...) and "Standardsetting" recommended by the authors of the program for countries no included in the list.While changing settings in the combo list the values of coefficients of reduction of soilparameters in corresponding windows are changed.


Selecting the option "Reduce soil parameters" allows for specifying individual values of thecoefficients of reduction of soil parameters (e.g., recommended values according to EC7).

The setting in the frame becomes available only if the type of analysis FEM is selected in theframe "Project" – tab sheet "Analysis".

Frame "Setting"

Vertical bearing capacityThe "Vertical bearing capacity" frame has two variants depending on the type of analysisof pile vertical bearing capacity:

according to ČSN 73 1002

using the finite element method

Vertical bearing capacity CSNThe "Vertical bearing capacity" frame serves to the vertical bearing capacity of a pile.Several analyses can be carried out in the frame. The verification can be performed forindividual loads, or the program locates the most critical one (can be selected from acombo list).

The analysis is carried out according to one of the method based on ČSN 73 1002.Parameters needed in individual methods are inputted in the lower part of the frame.

The "Loading limit curve" and "Point-bearing pile capacity" modes contain a table in thelower part of the frame, which allows for direct editing of inputted parameters using mouse.The "Edit" buttons open the dialogue windows that include hints for individual parameters. Agiven dialogue window allows for storing inputted parameters for a given layer in the tableby pressing the "OK" button.

Analysis results can be displayed in the right part of the desktop.

The "In detail" button opens the dialogue window containing detailed listing of theverification results.

The analysis results are displayed in the right part of the desktop. Visualization of the resultscan be adjusted in the "Setting visualization style" dialogue window.

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Frame "Vertical bearing capacity - analysis according CSN 73 1004"

Vertical bearing capacity FEMThe "Vertical bearing capacity" frame allows for verifying the pile vertical bearingcapacity. The analysis is performed automatically when swtiching to this frame. Morecomputations can be performed in the frame. The verification can be performed either forindividual loads or the program finds the most critical one (can be selected from a combolist)

The analysis is performed with the help of finite element method. The results areautomatically updated whenever one of the analysis parameters "Maximal deformation", "Coefficient increasing limit skin friction due to technology" or "Proceduredetermining influence zone bellow heel" is changed.

Two options are available to determine influence zone below the heel:

By default the analysis follows the procedure described in the theoretical part of the hint insecton "Depth of influence zone".

The second options assumes the depth influence zone to be set a k-th multiple of the pilediameter. During gradual increase of pile surcharge the depth of influence zone iscontinuously changed from zero at the onset of loading to the k-th multiple of the pilediameter when exceeding the total load.

The second method, originaly used in the old verision GEO4, with the value of k=2,5 offersless accurate results and usually underestimates the pile bearing capacity. Therefore a newoption that allows for specifying the depth of influnece zone through anlsysis is offered and isalso recommeded by default setting.

Switching between results is avaiable in the left part of the frame (limit loading curve,distributions of internal forces, dependence of shear on displacement). Theshear-displacement relationship is derived for a given depth measured from the pile head.The results are updated whenever the depth is changed.

The "In detail" button opens the dialogue window, which contains detailed listing of theresults of verification analysis.

VýsledkyVisualization of results can be adjusted in the "Setting visualization style" dialogue

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window.

Frame "Vertical bearing capacity - analysis according FEM"

Horizontal bearing capacityThe horizontal bearing capacity of a pile is verified in the "Horizontal bearing capacity"frame. Several analyses can be carried out. The verification analysis can be carried out forindividual loads, prescribed displacements, or the program finds the most critical load (canbe selected from a combo list). Assuming the prescribed displacement type of load requiresintroduction of boundary conditions in pile head (translation and rotation).

The fixed end type of boundary condition prescribed in the pile heel can be assumed for alltypes of loading.

For steel reinforced concrete pile the programs allow for verifying the reinforcement basedon the standard selected in the frame "Project".

The combo list serves to specify the direction of pile verification (x,y); for a circular pile theprogram allows for displaying the results in the most stressed direction.

The "In detail" button opens the dialogue window that contains detailed listing of theverification results.

The analysis results are displayed on the desktop. Visualization of results can be adjusted inthe "Setting visualization style" dialogue window.

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Frame "Horizontal bearing capacity"

Program Settlement



The frame "Analyses" serves to select the theoretical approach for the settlement analysisand the way of reducing the influence zone.


InterfaceThe "Interface" frame serves to introduce individual soil interfaces into the soil body.Detailed description how to deal with interfaces id described herein.

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Frame "Interface"

EmbankmentThe "Embankment" frame allows for inputting interfaces to create an embankment abovethe current terrain. The frame contains a table with a list of interfaces forming theembankment. A table listing the points of currently selected interface of the embankment isdisplayed in the mid section of the frame. Inputting an embankment interface follows thesame steps as used for standard interfaces.

An embankment cannot be specified in the first stage of construction. An embankment cannotbe built if there is an earth cut already specified in a given stage - in such a case either a newstage of construction must be introduced for embankment input or the existing open cut mustbe first removed.

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Frame "Embankment"

Earth cutThe "Earth cut" frame serves to specify the shape of an open cut. This function allows formodifying the terrain profile within a given stage of construction. Several earth cuts can beintroduced at the same time. In such a case some of the lines in the cut appear partiallyabove the terrain.

A table listing individual interface points is displayed in the left part of the frame. Inputtingan earth cut interface follows the same steps as used for standard interfaces.

An open cut cannot be specified in the first stage of construction. An earth cut cannot be builtif there is an embankment already specified in a given stage - in such a case either a newstage of construction must be introduced for earth cut input or the existing embankmentmust be first removed.

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Frame "Earth cut"

Incompressible subsoilThe frame "Incompressible subsoil" serves to input a depth of incompressible subsoil.

Inputting the depth of incompressible subsoil is the same as when inputting standardinterfaces.

Inputting an incompressible subsoil is one the options how to restrict an influence zone – ifinputted, then both ranges and tilted sections are drawn up to a depth of incompressiblesubsoil. No ground deformation appears below the incompressible subsoil.

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Frame "Incompressible subsoil"



The soil characteristics are specified in the program "Settlement". These characteristics arefurther specified in chapters:"Uplift pressure" and "Settlement analysis" - the inputparameters of soils are determined based on the selected theory of analysis in the frame "Project" tab sheet "Analyses".

Frame "Soils"



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Frame "Assign"


All inputted parameters of a surcharge can be modified in the construction stage where thesurcharge was specified. Only the surcharge magnitude can be modified in all subsequentconstruction stages (option "Adjust surcharge").

Influence of surcharge on the change of stress in the soil body is described in the theoreticalpart of the help section.

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Frame "Surcharge"

WaterThe "Water" frame serves to set the type of ground water table.

Inputting the ground water table or isolines, respectively, is identical with the standard inputof interfaces.

If the inputted data in individual stages are different, the program then allows for acceptingthe data from the previous stage of construction by pressing the "Accept" button.

Frame "Water"

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SettingThe frame "Setting" allows for specifying the position of control holes and thicknesses andlocations of layers where the stress values are calculated.

The program determines stresses at individual control holes. The terrain is alwayssubdivided into twenty holes with even spacing. Additional holes are automatically generatedin points specifying terrain, embankment, GWT, soil layer interfaces and end points ofsurcharge. The control (calculation) holes can be plotted in the frame "Analysis".

Individual holes are divided into layers according to the inputted values. The first layeralways coincides with the original ground. In addition, all points specifying interfaces, GWTand incompressible subsoil are included. The default setting of thicknesses of layers ensuresreasonable speed and accuracy of the analysis.

The layers are introduced up to depth of 250m. In actual analyses, however, the depth ofinfluence zone is restricted either by the inputted incompressible subsoil or by the reductionof magnitude of stress change or by the structural strength, respectively (depending on thesetting in the frame "Project").

The number and location of calculation holes can be adjusted when selecting the option "userdefined". In such a case it is possible to select both the location of doles and thicknesses andlocation of layers. The holes are then created according to the input – in addition, theprogram automatically includes all important points. When selecting the option exactdistribution, the holes are included into all terrain points, soil layer interfaces,embankments, GWP and into end points of surcharge. When selecting the option minimaldistribution, the holes are not included into points of interfaces of soil and embankmentlayers.

For standard analyses we recommend to keep the default setting of the analysis.

Frame "Setting"

AnalysisThe "Analysis" frame displays the analysis results. The analysis is carried out based onthe calculation theory selected in the frame "Project", tab sheet "Analyses". The depth ofinfluence zone is determined either by inputted incompressible subsoil, by the theoryrestriction of primary stress or by the theory of structural strength.

Information regarding the course of analysis, maximum settlement and the depth of influencezone are printed out in the bottom section of the frame. The results, as the main output, aredisplayed on the screen. To view the results, use the horizontal bar in the upper section ofthe screen, which allows for adjusting the way the resulting values are plotted. The barcontains the following control items:

- the button to display the "Settlement - results visualization setting" dialogue window.This dialogue window allows for specifying all drawing parameters: parameters to displaydepression line and influence zone, to set color range, to draw tilted sections, isosurfaces and

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isolines, etc.

- option to store individual views

- selecting values for visualization – either total values, or their change during the lastcalculation stage or their change in comparison with previous stages can be plotted.The setting is available only in problems where it makes sense. It is therefore possible todisplay the change of stress, settlement or deformation in comparison with previous stages –however, always the current depth of influence zone is plotted.

- selecting variables

SigmaZ,tot - overall vertical total stress [kPa,ksf]

SigmaZ,eff - overall vertical effective stress [kPa, ksf]

Pore pressure - stress due to water [kPa, ksf]

Settlement - settlement of a point [mm, feet]

Deformation - relative settlement of a layer [-]*1000

- plotting option (do not plot, isosurfaces, isolines)

The color range is visible on the right part of the desktop. The buttons for setting the colorrange are located below.


Frame "Analysis"

Program Abutment


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The "Project" tab sheet further serves to specify a standard for concrete structuresdimensioning. Referring to the selected standard the types of concrete and steel are theninputted in the"Material" frame. The dimensioning of cross-sections of the analyzed structureis then performed in the "Dimensioning" frame. Only ACI standard is available when selectingimperial units. While selecting standard it is also necessary to specify whether the stress inthe foundation joint used for verification of a wall front key is assumed uniform (CSN) ortrapezoidal (Eurocode).



Geometry cutThe frame "Geom. cut" allows for selecting the shape of bridge abutment. The selectedshape with a graphic hint "Wall geometry chart" appears in the left part of the frame. Theshape of a wall can be edited either in the frame by inserting values into input fields, or onthe desktop with the help of active dimensions.


The frame serves to specify the final shape of abutment including the closure wall. Theabutment can be verified also for the construction state (without the closure wall) based onthe choice in the frame "Loading - LC". The abutment length and the length of abutmentfoundation is specified in the frame "Geometry plane view ".

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Frame "Geometry cut"

WingsThe frame "Wings" allows for inputting the bridge wings dimensions. The wings can be eithersymmetrical or unsymmetrical. Assuming unsymmetrical wings requires inputting the rightand left wing dimensions separately. The screen always displays the currently inputted wing –only the left wing is then visualized in the remaining frames.

The frame "Geometry plane view" can also be used to input or edit the wing thicknesses andlengths.

The Wing-abutment joint cross-section can also be verified in the frame "Dimensioning". Theloading due to moment is considered. The whole wing is loaded by active pressuredeveloped behind the wall. The "Dimensioning" dialogue window serves to input themagnitude of surface surcharge to determine the wing pressure. The surcharge specified inthe frame "Surcharge" is then not taken into account and the terrain behind the wing isconsidered as flat. The resulting moment applied to the joint is obtained by multiplying theoverall magnitude of soil pressure acting on the wall surface and by the difference ofcentroids of the pressure resultant and the joint.

The length of cross-section used for dimensioning is considered by default as the wing height– a different length of wing-abutment joint can also be specified after selecting the option "Reduce for dimensioning".

When using prolonged wing walls it is possible to input dimensions of the foundation belowthe wall. Such foundation jumps are reflected in the analysis by computing a fictitious widthof the foundation as:

t o tf i c t

AdS

where: Atot - overall area of foundation including all jumps

S - length of abutment foundation

dfict - fictitious width of foundation for verification analysis

The foundation is then considered as being rectangular, which is simplified but rather

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conservative assumption.

Frame "Wings"

Geometry plane viewThe frame "Geometry plane view" allows for inputting the abutment length, length ofabutment foundation and also dimensions of abutment wings. Dimensions can be edited either in the frame by inserting values into input fields, or on thedesktop with the help of active dimensions.

For details on the effect of abutment dimensions on verification analysis we refer thereader to section "Calculating of abutment forces".

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Frame "Geometry plane view"

Foundation stepsThe frame "Foundation steps" serves to input the steps of foundation below abutment. Thisoption thus allows for specifying additional shapes of bridge abutment.

Adding (editing) foundation step is performed in the "New step" dialogue window. Inputtedfoundation steps can be edited on the desktop with the help of active dimensions or activeobjects, respectively.

Frame "Foundation steps"



the "Catalogue" button opens the "Material catalogue"dialogue window (for concrete or steel reinforcements), the list ofmaterials then serves to select the desired material

the "User" button opens the "Edit material – concrete"dialogue window (for concrete) or the "Edit material – concretesteel" dialogue window (for longitudinal steel reinforcements),which allows for manual specification of material parameters

The catalogues content depends on the selection of standard for the design of concretestructures set in the "Project" frame. The input field in the upper part of the frame serves tospecify the abutment unit weight.

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Frame "Material"




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Frame "Profile"




Frame "Soils"

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Loading - LCThe frame "Loading – LC" serves to specify individual loading cases (construction, service)and the loading caused by the bridge and approach slab. Verification and dimensioninganalyses of the whole bridge abutment or only its part are carried out according to thespecified type of LC.

No load specified in the case of construction state and the abutment is verified in a givenstage of construction without a closure wall and bridge wings.

In the case of service state the abutment is loaded by the bridge and approach slab, thewhole abutment is verified.

For abutment verification it appears advantageous to exploit the stage of construction andspecify in individual stages different load cases (e.g. construction state, service state withoutlive load, service state with all loads). Individual stages then allow inputting different loads,surcharges, terrain shapes, type of pressure analysis (active, at rest), design coefficients, etc.

Frame "Loading - LC"



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Frame "Assign"




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Frame "Terrain"







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Frame "Water"




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Frame "Surcharge"




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Frame "Earthquake"





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Frame "Setting"







Bearing capacity

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Pressing the "Run "Spread footing" button startsthe program "Spread footing" that allows forcomputing the soil bearing capacity or settlement androtation of a footing. Pressing the "OK" button leavesthe analysis regime – the results and all plots arecopied to the program "Abutment". The program "Spread footing" must be installed for the button tobe active.





DimensioningThe "Dimensioning" frame serves to design and verify the reinforcement of abutmentcross-section – the cross-section subjected to dimensioning is selected in the combo list. Thetable shows the abutment forces.

Offer of cross-sections that can be verified depands on the selected load case (construction,service). The following cross-sections are available for both the construction and servicestate:

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depth of construction joint fromconstruction top edge is specified

Wall jump verification type of assumed stress acting inconstruction joint for verification (linear,constant) can be selected in the frame "Project"

The service state makes also possible to verify:

Verification of closurewall

Verification wing -abutment

the surface surcharge due to terrain is inputted, foractual analysis we refer to section "Wings"

The abutment is loaded either by active pressure or pressure at rest depending on the inputspecified in the frame "Settting", an active earth pressure is used when analysing wing walls.


Dimensioning of the steel-reinforced concrete structure is performed according to thestandard set in the frame "Project". Verification analysis based on the standard CSN 73 6206"Design of concrete and steel reinforced concrete bridge structures" is describedherein.




Stability

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Pressing the "Stability" button launches the "Slope stability" program. This program thenallows us to check the overall stability of the analyzed structure. The button is available onlyif the program "Slope stability" is installed.

After completing all analyses press the "OK" button to leave the program – all data are thencarried over to the analysis protocol of the "Abutment" program.

Frame "Stability"

Program Nailed slopes



The "Project" tab sheet further serves to specify a standard for concrete structuresdimensioning. Referring to the selected standard the types of concrete and steel are theninputted in the "Material" frame. The dimensioning of cross-sections of the analyzed structureis then performed in the "Dimensioning" frame. Only ACI standard is available when selectingimperial units.


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GeometryThe frame "Geometry" contains a table with a list of inputted points of the structure frontface. Adding (editing) points is performed in the "Add (edit) point" dialogue window.

The inputted points can also be edited on the desktop with the help of active objects –double-clicking an already inputted point then opens a dialogue window for its editing.

Frame "Geometry"

Types of nailsThe frame "Types of nails" serves to specify a nail type in a specific table. The strengthparameters of nails can be either inputted by the user or directly determined by the programdepending on the inputted data.

The table lists the following input data, either inputted or computed – tensile strength, pull- out resistance, nail head strength per 1m (1ft).

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Frame "Types of nails"

Geometry of nailsThe frame "Geometry of nails" contains a table with a list of inputted nails. Adding (editing)nails is performed in the "New nail (Edit nail)" dialogue window. The inputted nails can alsobe edited on the desktop with the help of active objects.

The user is required to specify the nail depth, depth of a bench from a given nail (the nextnail must be introduced as deep as to be located below the bench of the upper nail), naillength, its diameter and distance.

Frame "Geometry of nails"

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the "Catalogue" button opens the "Material catalogue" dialoguewindow (for concrete or steel reinforcements), the list of materialsthen serves to select the desired material

the "User" button opens the "Edit material – concrete" dialoguewindow (for concrete) or the "Edit material – concrete steel"dialogue window (for longitudinal steel reinforcements), which allowsfor manual specification of material parameters


Frame "Material"




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Frame "Profile"



The soil characteristics are specified in the program "Nailed slopes". These characteristicsare further specified in chapters: "Basic data", "Earth pressure at rest" and "Uplift pressure".

Frame "Soils"

AssignThe "Assign" frame contains a list of layers of profile and associated soils. The list of soils is

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graphically represented using buttons in the bar above the table, or is accessible from acombo list for each layer of the profile.


Frame "Assign"




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Frame "Terrain"







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Frame "Water"




Frame "Surcharge"

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Frame "Earthquake"



The tab sheet "Other" is used to specify a procedure for the verification of internal stability ofa structure. When using factors of safety it is possible to input different factors of safety forthe plane and broken slip surfaces, respectively.

V The tab sheet "Other" further serves to introduce a coefficient of reduction of activepressure acting on a structure, which influences the calculation of nails bearing capacity. Bydefault the value of 0,85 is recommended.

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Frame "Setting"

Internal stabilityThe frame allows for the verification of internal stability of a structure assuming either planeor broken slip surface. The verification can be carried out depending on "Setting" usingeither factor of safety or the theory of limit states. Individual steps of the verificationprocedure are described herein.

This frame also allows for the verification of nails bearing capacity. This analysis must bechecked in the frame "Setting" tab sheet "Other".

Frame "Internal stability"


To verify the external stability a fictitious structure (wall) is created and further subjectedto the verification analysis. A fictitious wall consists of the structure front face, a lineconnecting end points of individual nails, a vertical line constructed from the end point of thefirst nail up to the terrain depth and from the end point of the last nail up to the structure

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depth (thus the bottom edge of a fictitious structure is always horizontal). The wall pointsthat cause a concave curvature of the structure back face are automatically excluded by theprogram. The structure is loaded by an active earth pressure.










Pressing the "Run "Spread footing" button startsthe program "Spread footing" that allows forcomputing the soil bearing capacity or settlement androtation of a footing. Pressing the "OK" button leavesthe analysis regime – the results and all plots arecopied to the program "Nailed slopes". The program"Spread footing" must be installed for the button tobe active.

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DimensioningThe frame "Dimensioning" allows for the design and verification of the reinforcement of thestructure concrete cover. The upper part of the frame serves to choose whether the verticalor horizontal reinforcement and its location will be verified. The program then determinesinternal forces developed on the selected section.

The table in the bottom part of the frame serves to specify locations for the verification of thedesigned reinforcement depending on the inputted standard for dimensioning ofsteel-reinforced concrete structures (the standard is specified in the frame "Project"). A cross-section is loaded by the bending moment in a given point. An amount of the tensilereinforcement in the cross-section is inputted. If the moment is negative, the designedreinforcement is placed at the structure front face and if it is negative, then at the structureback face.

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External stabilityPressing the "External stability" button launches the "Slope stability" program. Thisprogram then allows us to check the overall stability of the analyzed structure. The button isavailable only if the program "Slope stability" is installed.

After completing all analyses press the "OK" button to leave the program – all data are thencarried over to the analysis protocol of the "Nailed slopes" program.

Frame "External stability"

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Program Ground Loss


The "Project" tab sheet contains an input form to introduce the basic data about theanalyzed task, i.e. project information, project description, date, etc. The "Project" tab sheetalso allows the user to switch analysis units (metric / imperial).


The tab sheet "Analyses" allows for selecting the method for determining subsidence trough(Volume loss, Classical theories) and its shape (Gauss, Aversin). It also serves to input thecoefficient of calculation of inflection point, (for classical theories only), which influences theshape of subsidence trough.

Frame "Project" - tab sheet "Analyses"

BuildingsThe frame "Buildings" serves to input objects above excavation. An arbitrary number ofbuildings can be specified both on a ground surface and at a given depth.

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Frame "Buildings"

ProfileThe "Profile" frame contains a table with a list of inputted interfaces. After specifyinginterfaces it is possible to edit thicknesses of individual layers with the help of activedimensions. Adding (editing) layer is performed in the "Add (edit) interface" dialoguewindow. The z-coordinate measured from the top point of a structure is specified.


Inputting data in the frame is allowed providing the classical theory of analysis is selectedin the frame "Projekt".

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Frame "Profile"

SoilsThe "Soils" frame contains a table with a list of inputted soils. The table also providesinformation about currently selected soil displayed in the right part of the frame. Adding(editing) a soil is performed in the "Add (edit) soil" dialogue window.


Possible values of the angle of internal friction and cohesion are available in chapter "Rocksparameters".

Frame "Soils"

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Frame "Assign"

GeometryThe frame "Geometry" contains a table with a list of inputted excavations. The "Newexcavation (Edit excavation)" dialogue window serves to add (edit) excavations. Theinputted excavations can also be modified on the desktop with help of active objects.

Parameters of excavation differ depending on the analysis method selected in the frame "Project". Each excavation can be specified either by the radius or the area of excavation.Providing a sequential excavation is being inputted it is useful to specify the excavation areaand place a fictitious center of excavation to a center of gravity of this area.

Additional input parameters are explained in more details when describing individual analysismethods (Volume loss, Classical theories).

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Dialogue window "New excavation"

Frame "Geometry"

MeasurementThe frame "Measurement" contains a table with a list inputted measurements. The "Newmeasurement (Edit measurement)" dialogue window serves to add (edit) measurements.The inputted measurements can also be modified on the desktop with help of active objects.

Inputted measurements do not influence the actual analysis – their introduction into theprogram has resulted purely from designers needs. After excavating the first part of asequential tunnel it is useful to input the values measured in the construction site into theprogram and subsequently to add the excavation input parameters such that the calculatedand measured values are the same. Practical experience shows that the values of inputparameters acquired from this procedure (e.g. coefficient of volume loss) are valid also forsubsequent stages.

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Frame "Measurement"

SettingsThe frame "Settings" allows for introduction of boundaries of tensile and gradient damage.These values serve to verify the building damage in the frame "Damages". The programoffers a default pre-setting (default setting for masonry buildings) and a user-definedsetting – here it is possible to define arbitrary criteria recommended by standards or gainedfrom practical experience for arbitrary types of buildings.

The boundary values must be defined either in a descending or ascending order, respectively.Providing we wish to define fewer regions than specified in the program it is possible tocharacterize certain boundaries by the same value.

Frame "Settings"

AnalysisThe frame "Analysis" provides the results from the analysis of subsidence trough. More thanone analysis at different depths below the terrain surface can be performed for a single task.The computed values are displayed on a desktop and are continuously updated whenever acertain change in the inputted data or setting in the frame is introduced.

For a quick switch between different styles of graphical presentation of results (subsidence

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trough, distribution of values) the user may use the buttons in section "Visualization".Visualization of results can be adjusted in the "Setting visualization style" dialogue window.

Frame "Analysis" - "Settlement"

Frame "Analysis" - "Distributions"

DamagesThe frame "Failures" provides the results of failure analysis of buildings. The program offers

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four types of verifications

- verification of tensile cracks

- verification of gradient damage

- verification of relative deflection of buildings (Hogging, sagging)

- verification of the inputted section of a building

The program allows the user to perform an analysis for the current and all previous stages (envelope from all stages) or it is possible to input individual stages and evaluate theirinfluence. Such a procedure makes possible to find, e.g. an optimal process of excavation ofsequantial tunnels.

Several analyses can be carried out for a single task. Visualization of results can be adjustedin the "Setting visualization style" dialogue window.

Frame "Damages" - visualization of tensile cracks

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Frame "Damages" - visualization of gradient damage

Program Rock slope



Frame Project – tab sheet "Project"

The tab sheet "Analyses" serves to select the type of rock slope analysis. There are threeoptions available:

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- plane slip surface

- polygonal slip surface

- earth wedge

Content of the vertical tool bar depends on the selected type of analysis.

Frame Project – tab sheet "Analyses"

TerrainThe frame "Terrain" contains a table with a list of defined sections of a rock slope.

The coordinates of the origin – the first point of terrain followed by defined sections – areentered in the upper part of the frame. In the program the slope is always oriented from theleft to the right.

Adding (editing) section is performed in the "New section (Edit section)" dialogue window.These sections can also be edited on desktop with the help of active objects.

Each section can be defined by its dip, by the overall length of section, by the horizontallength and height of section of a rock slope. Only two selected values are used while theothers are determined by the program automatically (if more than two entry fields arechecked than the input and computation are not carried out). Both vertical and horizontalsections as well as overhangs can be represented.

In case of a proper input the program automatically plots the defined section on desktopusing dashed line, so that before accepting the defined section by pressing the "Add" buttonit is possible to check, whether the section is correctly defined.

Frame "Terrain"

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RockThe frame "Rock" allows for entering the material parameters of a rock slope (depending onthe type of shear strength) including the bulk weight of a rock. Three types of shear strengthson a slip surface are available in the program:

- Mohr - Coulomb

- Barton - Bandis

- Hoek - Brown

Material parameters of rock are then entered based on the selected method.

Frame "Rock"

Slip surface – planeThe frame "Slip surface" serves to specify the shape and parameters of a plane slip surface.The slip surface is defined by a point in the rock body and by its gradient. The programautomatically determines intersections of the slip surface with terrain.

The program also allows for defining a tension crack with an arbitrary gradient (notavailable for stepped slip surface). The crack is defined by a horizontal distance from the origin and by its gradient.

The plane slip surface can further be labeled as smooth, undulated or stepped.

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Frame "Slip surface - plane"

Slip surface - polygonalThe frame "Slip surface" contains a table with a list of defined sections of a slip surface.Adding (editing) section is performed in the "New section (Edit section)" dialogue window.These sections can also be edited on desktop with the help of active objects.

The coordinates of the slip surface origin – a point on the slip surface followed by othersections – are entered in the upper part of the frame. This point can be found even out of thesoil body – the program then automatically calculates the intersection of slip surface withterrain.

Individual sections of the slip surface can be defined by their dip, by the overall length ofsection, by the horizontal length and height of section of a rock slope. Only two selectedvalues are used while the others are determined by the program automatically (if more thantwo entry fields are checked than the input and computation are not carried out). Bothvertical and horizontal sections as well as overhangs can be represented.

In case of a proper input the program automatically plots the defined section on desktopusing dashed line, so that before accepting the defined section by pressing the "Add" buttonit is possible to check, whether the section is correctly defined.

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Frame "Slip surface - polygonal"

Parameters – polygonal slip surfaceThe frame "Parameters" contains a table with a list of blocks, which are created by enteringa polygonal slip surface. Parameters of individual blocks are edited in the "Edit block"dialogue window. Blocks can also be edited on desktop with the help of active objects.

The Mohr-Coulomb strength parameters on a slip surface and in the joints separatingindividual blocks icluding the bulk weight of a rock are specified here.

This window also serves to introduce forces due to water in rock blocks.

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Frame "Parameters" – polygonal slip surface

Dialogue window "Edit block" - vyměnit!!!!!

Water – plane slip surfaceThe "Water" allows, by pressing the button, for selecting the type of water. The selected typetogether with a graphic hint ("Parameter chart") of inputted values is displayed in the leftpart of the frame. Water parameters can be edited either in the frame by inserting values intoinput fields, or on the desktop with the help of active dimensions.

Solution procedure when accounting for water is described in the theoretical part of the help "Influence of water on slip surface"

Frame "Wster" - plane slip surface

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Surcharge – plane and polygonal slip surfaceThe "Surcharge" frame contains a table with a list of inputted surcharges. Adding (editing)surcharge is performed in the "New (edit) surcharge" dialogue window. The inputtedsurchages can be edited on the desktop with the help of active dimensions or active objects,respectively.

Introducing surcharge forces into the analysis differs for a plane and a polygonal slip surface.

Frame "Surcharge" - plane and polygonal slip surface

Anchors – plane and polygonal slip surfaceThe "Anchors" frame contains a table with a list of inputted anchors. Adding (editing)anchors is performed in the "New anchor (Modify anchor parameters)" dialogue window.The inputted anchors can be edited on the desktop with the help of active objects.

The following is specified – location (origin), depth, free length, anchor slope, spacingbetween anchors and anchor force. The anchor origin can automatically be positioned onterrain (by checking the particular entry field). All anchor parameters can be modified only inthe construction stage, where it was introduced. The subsequent stages allow only foradjusting the anchor force (option "Post-stressing anchor").

The plane slip surface allows for defining active and passive anchors. Only active anchors areallowed with the polygonal slip surface.

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Frame "Anchors" - plane and polygonal slip surface


Rock slope analysis while accounting for earthquake is described in the theoretical part of thehint in chapter "Influence earthquake".

Frame "Earthquake"

Setting

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The "Settings" frame contains basic settings to assess the slope stability. The program offerspre-setting for different countries (Czech Republic, Germany, France,...) and "Standardsetting" recommended by the authors of the program for countries no included in the list.While changing settings in the combo list the values of coefficients of reduction of soilparameters in corresponding windows are changed.


Selecting the option "Safety factor" allows the user to specify in input field own value of thefactor of safety.

Selecting the option "Limit states" allows for specifying individual values of the coefficients ofreduction of soil parameters and coefficient of overall stability.

Frame "Settings" – analysis according to factor of safety

Frame "Settings" – analysis according to limit states

Analysis – plane slip surfaceThe "Analysis" frame displays the analysis results. Several analyses can be performed for asingle task.

Verification of the rock slope can be carried out according to the factor of safety / theoryof limit states based on the input in the frame "Settingí". The analysis results are displayedin the frame in the bottom part of desktop.

In this frame the program makes possible to determine the anchor force needed forobtaining the required safety factor. In such a case the "Compute required anchor force"entry field must be checked and the slope of anchor force from horizontal must be entered.


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Frame "Analysis" – plane slip surface

Analysis – polygonal slip surfaceThe "Analysis" frame displays the analysis results. Several analyses can be performed for asingle task.

Verification of the rock slope can be carried out according to the factor of safety / theoryof limit states based on the input in the frame "Setting". The analysis results are displayedin the frame in the bottom part of desktop.


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Frame "Analysis" – polygonal slip surface

GeometryThe frame "Geometry" allows for entering the shape of a rock slope (earth wedge).

Geometry of earth wedge is defined by directions and gradients of fall lines of faces formingthe wedge. Geometry of earth wedge is displayed on desktop using a stereographic projection.

The "3D view" button opens the dialogue window for viewing an earth wedge in space.

Frame "Geometry" – input using directions and gradients of fall lines of faces

3D View3D view allows for graphical check of defined values. The picture can be rotated,translated, zoomed in and out and highlighted in a standard way. A direct print out of thepicture is not in this version allowed.

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Dialogue window "3D view"

Slip surface – rock wedgeThe frame "Slip surface" serves to enter the shape of a slip surface using directions andgradients of fall lines of faces forming the wedge. A tension crack can also be defined.Geometry of earth wedge is displayed on desktop using a stereographic projection.

The "3D view" button opens the dialogue window for viewing an earth wedge in space.

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Frame "Slip surface" - rock wedge

Parameters – rock wedgeThe frame "Parameters" serves to enter parameters of an earth wedge. The bulk weight of arock and the Mohr-Coulomb strength parameters of slip surfaces must be specified.

Frame "Parameters" - rock wedge

Surcharge – rock wedgeThe "Surcharge" frame contains a table with a list of inputted surcharges. Adding (editing)surcharge is performed in the "New (edit) surcharge" dialogue window.

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Surcharge forces are introduced into the stability analysis of earth wedge using resolution offorces.

Frame "Surcharge" - rock wedge

Anchors – rock wedgeThe "Anchors" frame contains a table with a list of inputted anchors. Adding (editing)anchors is performed in the "New anchor (Modify anchor parameters)" dialogue window.

Anchor forces are introduced into the stability analysis of earth wedge using resolution actingof forces.

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Frame "Anchors" - rock wedge

Water – rock wedgeThe frame "Water" allows for introducing water into analysis. If the influence of water istaken into account then checking the respective entry field opens the field for entering theheight of GWT above the lowest point of an earth wedge.

Solution procedure when accounting for water is described in the theoretical part of the help "Influence of ground water". The "3D view" button opens the dialogue window for viewing anearth wedge in space.

Frame "Water" - rock wedge

Analysis – rock wedgeThe "Analysis" frame displays the analysis results. Several analyses can be performed for asingle task.

Verification of the rock slope can be carried out according to the factor of safety / theoryof limit states based on the input in the frame "Setting". The analysis results are displayedin the frame in the bottom part of desktop.

In this frame the program makes possible to determine the anchor force needed forobtaining the required safety factor. In such a case the "Compute required anchor force "entry field must be checked and the slope of anchor force from horizontal and its directionmust be entered.


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Rám "Výpočet" - horninový klín

Program Terrain

ProjectThe "Project" frame is used to input the basic project data.


In this input regime the assumed setting can be modified only in the first construction stage.

Frame "Project"

Basic dataThe frame "Basic data" serves to input basic parameters of the task.

The frame contains a table with a list of specified layers. Layers can be added, inserted or

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removed using the buttons on the right from the table. The first layer can be neitherremoved, nor can another layer be inserted in front of it.

The frame section "Basic setting" serves to define world dimensions of the task. Whenincreasing or decreasing these dimensions the program prompts possible consequences ofthis action.

The section "Inputting grid" serves to define an origin and step of the grid in the X and Ydirections. The dialogue window, which allows for setting these parameters, is described inthe hint section "User-defined environment", chapter "Input".

Crossing the item "Input in the global coordinate system" opens the way for introducingthe data in the global coordinate system (JTSK, Gauss-Krüeger).

In this input regime the assumed setting can be modified only in the first construction stage.

Visualization of drawing on the desktop can be modified in any input regime based on thesetting adjusted in the "Setting visualization style" dialogue window and with the help ofbuttons on tool bars "3D visualization", "Scale and shift" and "Plot setting".

Frame "Basic data"

Global coordinate systemThe "Coordinate systems" dialogue window allows for definig the type of the globalcoordinate system.

Esential advantage is the possibility of specifying the coordinates of points and bore holesboth in the local and global coordinate systems and switching between the two systems.

Orientation of the global coordinate system with respect to the local one is defined using twopoints, where one point is always introduced in the local coordinate system and its image inthe global coordinate system.

Direction and sign convention is displayed for each type of the global coordinate system inthe legend chart.

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Dialogue window "Coordinate system"


Adding (editing) a soil is performed in the "Add (edit) soil" dialogue window. The programTerrain calls only for specification of the coefficient of bulkage to compute yardage ofexcavation pits or embankments. The remaining data are used only for possible export intoother GEO programs and have no effect on actual calculations performed in program Terrain.

Frame "Soils"

Assign

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The "Assign" frame contains a list of layers of profile and associated soils. The list of soils isgraphically represented using buttons in the bar above the table, or is accessible from acombo list for each layer of the profile.


In subsequent stages of construction the program automatically adds a new layer, to which asoil adjacent to terrain is automatically assigned. In many cases (excavation pits) this layermay have no volume – its introduction is necessary providing the new terrain is found abovethe terrain of the previous stage. The soil is always assigned, since it is not possible to apriory estimate, whether some part of the terrain in the new stage will be located above theoriginal one.

Frame "Assign"

PointsThe frame "Points" serves to define the coordinates of terrain points. There are two optionsavailable to define coordinates of individual points:

With the help of table : points are defined in the table. Pressing the "Add" button opens the"New point " dialogue window; coordinates of points are then specified and by pressing the "Add" button added to the table. An arbitrary number of points can be defined in this way.The "Cancel" button is used at last to close the window. These points can be further modified(in the dialogue window) using the " Edit" button or removed with the help of "Remove"button (more points can be marked in the table to remove them all at once – beforeremoving, the selected points are displayed on the desktop in red). Each change isimmediately reflected on the desktop.

With the help of mouse: this inputting mode is turned on by pressing a respective buttonon the horizontal bar. The following options are available:

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Add to input a point, click the left mouse button on the desktop (themouse cursor changes – see picture) – the program then opensthe "New point" dialogue window, which allows for modifying thepoint coordinates, or to input its Z-coordinate – after pressing the"OK" button the program adds this point into the table. Providingthe point cannot be added (e.g. duplicity of coordinates) theprogram prompts a warning message

grid functions can also be used when specifying a point

Edit clicking an already existing point (see active objects) using theleft mouse button opens the "Edit point" dialogue window, whichallows for editing the point coordinates - in the dialogue windowthe following buttons ("OK+ " a "OK+ ") can be used

Remove clicking the point using the left mouse button opens a dialoguewindow, which requests to confirm deletion of the selected point

Select actives the regime of graphical selection of points (type ofselection is set in the tool bar "Selections")

The selected points can also be imported from files in formats TXT, Atlas DNT, respectivelyDXF.

When defining points the program in some cases automatically calculates their Z-coordinates.Only one point can be assigned to a single coordinate X, Y.

Visualization of drawing on the desktop can be modified in any input regime based on thesetting adjusted in the "Setting visualization style" dialogue window and with the help ofbuttons on tool bars "3D visualization", "Scale and shift", "Selections" and "Plot setting".

Frame "Points"

Import of pointsThe program allows for data import in formats DXF, ATLAS DMT and TXT. When importing, all

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old data are deleted and replaced by the new ones. The world dimensions are automaticallydetermined according to minimal and maximal values of coordinates x and y – it is thereforedesirable to subsequently adjust the world dimensions in the frame " Basic data".

The program allows for importing TXT data from respective files . Each point is written on aseparate line of the file, coordinates are separated by comma. If the file contains for eachpoint first its name, it is necessary to check the item "Labeling of pints". In the dialoguewindow is then necessary to specify the order of coordinates. If the data have an oppositesign convention, it possible to multiply the corresponding line by the value -1. The dataimport is performed after pressing the " Import" button.

Dialogue window "Import" – format "TXT"

Dialogue window "Import" – format "Atlas"

Automatic calculation of heightWhen defining points, bore holes and points of ground water table the program in some casesautomatically calculates the point height (z-coordinate) and eventually the layer thickness.This function is particularly valuable when editing terrain or layers.

The possibility of height calculation depends on the status of generated terrain:

if no terrain is generated, the height is not calculated and the respective fieldremains empty (blank)

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if terrain is generated for the current data (displayed on the desktop in anon-transparent mode and in regimes Generation, Point constructions, Lineconstructions and Launching also in a color mode), the required values are thenautomatically calculated from the model of terrain – for a point it is theZ-coordinate, for a bore hole the program further determines the layer thicknessand possibly also the depth of the ground water table – when a point or a bore holeis specified the status of generated terrain is changed and the drawing is switchedto a transparent mode (the terrain is generated for the original input, not for thecurrent input)

when the terrain is generated, but it is not the current one, the Z-coordinates andlayers thicknesses are automatically calculated for the last generated terrain

Information regarding the terrain status (not generated, generated, generated for theoriginal data) are displayed on the vertical tool bar. The frame "Generate" allows for terraingenerating or removing the generated model.

Dialogue window – add new point and calculate the Z-coordinate

Dialogue window – add new bore hole and calculate the Z-coordinate, thickness of GWT andlayer thicknesses

EdgesThe frame "Edges" serves to input edges connecting the terrain points. Two options are

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available to define edges:

With the help of table : edges are defined in the table. Pressing the "Add" button opens the"New edge" dialogue window; sequence numbers of the starting and end points are thenspecified and by pressing the "Add" button added to the table. An arbitrary number of edgescan be defined in this way. The "Cancel" button is used at last to close the window. Theseedges can be further modified (in the dialogue window) using the " Edit" button or removedwith the help of "Remove" button (more edges can be marked in the table to remove themall at once – before removing, the selected edges are displayed on the desktop in red). Eachchange is immediately reflected on the desktop.


Add to input an edge, click the starting and end points using the leftmouse button (the mouse cursor changes – see picture) – afterclicking the end point the program adds the corresponding edgeinto the table and at the same time displays this edge on thedesktop. Providing the edge cannot be added (duplicity reason,crossing, etc.) the program prompts a warning message

Edit clicking an already existing edge (see active objects) using theleft mouse button opens the "Edit edge" dialogue window, whichallows for editing the sequence numbers of the starting and endpoints of the edge - in the dialogue window the following buttons("OK+ " a "OK+ ") can be used

Remove clicking the edge using the left mouse button opens a dialoguewindow, which requests to confirm deletion of the selected edge

Select actives the regime of graphical selection of edges (type ofselection is set in the bar "Selections")

Edges can intersect neither other edges nor earth grading. Only one edge can be definedbetween two points.

Visualization of drawing on the desktop can be modified in any input regime based on thesetting adjusted in the "Setting visualization style" dialogue window and with the help ofbuttons on tool bars "3D visualization", "Scale and shift", "Selections" and "Plot setting".

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Frame "Edges"

WaterThe frame "Water" serves to specify the ground water table (GWT). A combo list "Type ofwater" contains the following items:

No water – no water specified

Water specified by points – the GWT points are defined in the table in the same way aswhen defining terrain points. This approach is particularly suitable if having a horizontalwater table – then it is sufficient to define only one point of a given coordinate Z and theprogram automatically generates a horizontal line representing the GWT.

Water specified in bore holes – Ground water is defined within bore holes. A particulardepth of GWT measured from terrain surface is specified. This approach is suitable when boreholes with measured depths of GWT are available.


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Frame "Water"

Bore holesThe frame "Bore holes" serves to define bore holes (both real and fictitious), which allow forthe modeling individual geological layers (depending on the setting in the frame "Basic data") or ground water tables (depending on the setting in the frame "Water").

To input points that determine the location of individual bore holes proceed in the similar wayas when defining terrain points. Apart from coordinates it is necessary to enter the bore-holename and thicknesses of layers. The generated geological profile can be easily modifiedexploiting the option of automatic calculation of height z from the thicknesses of individuallayers.

Bore holes can be defined only in the first stage of construction. The program automaticallyassures that a lower layer always lies below an upper layer – "Crossing of layers" is notacceptable – the dominant layer is always the upper layer.


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Frame "Bore holes" – input, edit

Frame "Bore holes" – defined bore holes

Earth gradingThe frame "Earth grading" serves to define terrain earth grading. The earth grading cannotbe defined in the first stage of construction.

The earth grading should considerably simplify an input of excavation pits or embankments.The essential part of earth grading is the shape of bottom, form which the slopes ofexcavations or embankments are directed towards the original terrain. The original terrain

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points and edges, found in the region of earth grading, are during generation automaticallyremoved.

More than one earth grading can be defined within a single stage of constructions. Theymust not, however, cross each other . If that happens, they need to be combined into asingle earth grading. No part of earth grading can also exceed the world dimensions – in sucha case one should realize that faces of earth grading may exceed the world dimensions evenif the bottom is defined well inside.

The earth grading can be edited only in the stage, where it is defined. In to next stage ofconstruction, the earth grading is transferred in terms of terrain new points and edges.

With the help of table : earth grading is defined in the table. The "Add" button opens the "New earth grading " dialogue window, which allows for specifying the name of earth grading(by checking individual boxes it is possible to define a uniform depth of the bottom and auniform gradient of the slope). This dialogue window contains further a table to introducepoints, which define the ground plan (general polygon) of earth grading. To enter thesepoints, proceed in the similar way as when defining terrain points. Pressing the "Add" buttoncloses the dialogue window and the new earth grading is inserted into the table.

The earth grading can be further modified (in the dialogue window) using the " Edit" button orremoved with the help of "Remove" button (more than one earth grading can be marked inthe table to remove them all at once - before removing, the selected earth grading isdisplayed on the desktop in red). Each change is immediately reflected on the desktop.


Add earthgrading

To input an earth grading, click the left mouse button on the desktopto successively define individual points of the polygon, whichdetermines a ground plan of an earth grading – the polygon must beclosed (the last clicked point serves as the first point of the polygon) – after closing the polygon the program opens the "New earthgrading" dialogue window; to continue follow the same steps aswhen an input using the table is assumed - providing the earthgrading cannot be defined, or it overlays an already existing one, theprogram prompts a warning message

Edit earthgrading

clicking an already existing earth grading using the left mousebutton (see active objects) opens the "Edit earth grading" dialoguewindow, which allows for editing the respective grading (is possibleuse buttons in the dialogue window "OK+ " a "OK+ ")

Remove earthgrading

clicking an earth grading using the left mouse button opens adialogue window, which requests to confirm deletion of the selectedearth grading


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Frame "Earth grading" – input, edit

Frame "Earth grading" – defined earth grading

GenerateThe frame "Generate" serves to generate a model of the terrain.

Parameters to generate the model, which are valid for all subsequent stages, are specifiedin the first stage of construction.

These are model smoothing (none, medium, maximal)

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active edge – allows for modeling of terrain alongedges

The frame further serves to define drawing parameters (grid step, contour line step).

The actual model is generated by pressing the "Generate" button. The generated model canbe canceled by pressing the "Cancel model" button – this can be useful to enhance clarity ofinput.

Selecting the option "Compute yardage" allows for yardage calculation (in a combo list it ispossible input the construction stage number for which the calculation should be carriedout).


Frame "Generate"

Modeling terrain on edgesA special attention has to be given to boundary condition to correctly create a digital modelof terrain – heights of points in corners and boundaries (edges) of the world (worlddimensions).

The corner points can be either entered or they are inserted automatically during the firststage of construction. When automatically generated, the corner point receives the sameheight as has the closest point or bore hole already defined.

When generating terrain the corner points are connected by an edge . In some cases(slopes) we wish the edges to model the overall shape and inclination of terrain . In suchcases an active edge option can be used. An active edge is introduced as a percentagefraction of the world dimensions . All points found on an active edge are, duringgeneration, automatically projected in the normal direction on to an edge – new points arethen created at the same locations (on edge) having the same z-coordinate. The new pointsare stored in data associated with the next stage of construction.

Subsequent layers of the terrain model behave the same way. The thicknesses of these layerson edges are calculated according to thicknesses of layers of the closest bore holes.

The role of an active edge is evident from the following figure.

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Terrain generated without and with an active edge

Point constructionsThe frame "Line constructions" serves to introduce line constructions into the terrain.

To input points that determine the location of individual point constructions proceed in thesimilar way as when defining terrain points (using either table or mouse). The "New pointconstruction" ("Edit point construction") dialogue window allows also for specifying thename of the program to analyze the corresponding construction. The frame "Launch" is thenused to run the calculation program and to transfer thicknesses of layers and assignment ofsoils into the program.

Point constructions can be defined only if a correct model of the terrain is generated.


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Frame "Point constructions" – input, edit

Frame "Point constructions" – defined constructions

Line constructionsThe frame "Line constructions" serves to introduce line constructions into the terrain.

To input lines that determine the location of individual line constructions proceed in thesimilar way as when defining terrain edges (using either table or mouse). The "New lineconstruction" ("Edit line construction") dialogue window allows for specifying the nameand type of a construction line:

"Longitudinal line construction" is defined by coordinates of the starting and end points(the table is a part of the dialogue window). A combo list serves to select a particularcalculation program (Settlement, Slope stability, FEM…). To run the program, use the frame "Launch". Terrain shape and interfaces are transferred in the same way as when assigningsoils to layers.

"Line with points" is defined by coordinates of a broken line and can be used to specify newpoint construction. Point constructions are defined in the table "Point constructions on line", which is a part of the "New line construction" dialogue window. The frame "Launch" isthen used to run the calculation program and to transfer thicknesses of layers andassignment of soils into the program.

Line constructions can be defined only if a correct model of the terrain is generated.

Visualization of drawing on the desktop can be modified in any input regime based on thesetting adjusted in the "Setting visualization style" dialogue window and with the help ofbuttons on tool bars "3D visualization", "Scale and shift" "Plot setting".

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Frame "Line constructions" – input, edit

Frame "Line constructions" – defined constructions

LaunchingThe frame "Launching" contains a table with a list of defined point or line constructions.Based on the selection in the table and after pressing the "Launch" button the program

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associated with a particular task is launched (the corresponding calculation module must bepurchased). The required data are transferred into the program. The program then allows forperforming the specific calculations and verifications. If the program is not purchased, thelaunching button is not accessible.

When all calculations are completed the program is exited by pressing the "OK" button – theresults and defined pictures are transferred back into a corresponding calculation protocol inprogram "Terrain".

Frame "Launching"

Launching program "Spread footing" from program "Terrain"

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OutputsThe program contains three basic output options:

Print and export document

Print and export picture

Copy to clipboard

Adding pictureThe program allows for storing the current picture irrespectively of the program regime. Tothat end, press the "Add picture" button on the vertical tool bar. The button opens the "Newpicture" dialogue window and inserts the current view on the desktop view in the window.

The picture is always linked to a certain input regime or analysis. (The current regime isdisplayed next to the picture name). When printing document the picture is automaticallyadded to a specific regime in the tree.

The program allows for defining the picture either for a specific stage of construction (or forthe current analysis) or adjusting the setting such that the picture is added to the documentin all stages of construction (or all analyses). The latter option is assumed when selecting "all" in the "Stages" combo list (or "Analysis" list).

Warning: All inputted pictures are automatically regenerated whenever modifyingdata.

The picture view can be adjusted with the help of vertical tool bar in the left part of thewindow (edit size and location). See "Tool bar - scale and shift" section for more details onindividual buttons. The last button on the bar allows for adjusting the picture page ratio. The"Picture setting" frame in bottom part of the dialogue window further allows for adjustingcolors and style of line (object) drawing – see "Setting visualization style".

The "OK" button stores the picture into the "Picture list". It can be then opened and modifiedat any time.

The picture can be also printed out from this window – pressing the "Print" button opens thedialogue window for printing and exporting pictures. If the picture is active over all stages (orall analyses), then all possible combinations of pictures are printed all at once (each pictureon a separate page).

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Dialogue window "New picture"

Picture listPictures stored with the help of the "New picture" dialogue window are ordered in the table in"Picture list". The "Picture list" dialogue window is opened using the button on the verticaltool bar. The table of list of pictures contains the picture name and description, the regime inwhich it was created and stage of construction or the analysis number.

Individual pictures can be edited using the "Modify" button, which opens the "Picturemodification" dialogue window (this window corresponds to the "New picture" dialoguewindow both in the way it looks and in the way it functions).

These pictures can be printed out from the window by pressing the "Print" button that opensthe dialogue window for printing and exporting the picture. Providing the picture is activeover all stages of construction (over all analyses, respectively) then the program prints allpossible combinations of the picture (each picture on a separate page). Providing morepictures are selected then all selected pictures are printed out.

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Dialogue window "Picture list"

Print and export documentThe "Print and export document" dialogue window can be opened either from the controlmenu (items "Files", "Print document") or using the "Files" button on the horizontal toolbar. The page print preview with a generated text appears in the window.

This window generates output document including pictures stored in the "Picture list". Thiswindow allows either for printing the created protocol or exporting it for further use. The document is always up to date – the program creates the document again based oninputted data (even with regenerated pictures) whenever opening this window.

Only specific parts of the document including pictures can be generated by checking thecorresponding "tree" item in the left part of the window. Selecting or deselecting an arbitraryitem prompts the program to regenerate the document automatically.

The dialogue window contains its own "Control menu" and "Tool bar" for finalizing the pageface (header and footer definition, page size and edges definition and definition pagenumbering).

A mouse ball or scroll bar can be also used to view the document.

The button part of the dialogue window displays current information (defined page size,current document page and the total number of pages).

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Dialogue window "Print and export document"

Print and export pictureThis window serves to print or export one or more pictures. Three options are available toopen this window:

using the control menu (items "Files", "Print view") or the "Files" button on the tool bar to print data from the desktop.

using the "New picture" dialogue window by pressing the "Print" button

using the "Picture list" dialogue window by pressing the "Print" button

The window may contain more than one picture at the same time (when printing moreconstruction stages or analyses) when printing more pictures from the list. Each pictured isprinted on a separate page. The picture preview can be adjusted using buttons on the toolbar or a mouse ball.

The dialogue window contains its own "Control menu" and "Tool bar" for finalizing the pageface (header and footer definition, page size and edges definition and definition pagenumbering).

The button part of the dialogue window displays current information (defined page size,current document page and the total number of pages).

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Dialogue window "Documents" – print and export current picture (view)

Control menu - Print and exportThe control menu of the "Print and export document" and "Print and export pictures" dialoguewindows contains the following items:

Document

Save as opens the "Save as" dialogue window that allows forsaving the file in format *.PDF, or *.RTF

Send opens the dialogue window for mail client an adds thepicture as an attachement in format *.PDF

Open for edit opens text editor (associated in the Windows systemwith *.RTF extenison) that allows for editing the pagemanulally

Page properties opens the "Page properties" dialogue window thatallows for specifying the page style (size, edges,layout)

Header and footer opens the "Header and footer" dialogue window thatallows for inputting the document headers and footers

Print opens the system window for "Print"

Close closes the dialogue window

Edit

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Copy copies the selected picture (text) to clipboard –parameters are set in the "Options" dialogue window –tab sheet "Copy to clipboard"

Sellect all marks all on page (on document) into block

Unsellect all cancels entire selection (picture, text)

View

Full page modifies the page size such that the entire page in thedialogue window is visible

Page width fits the page to a maximum width of the documentdialogue window

Page (this item appers in the menu only if the document has more than one page)

First page shows the document first page

Previous page shows the previous page

Following page shows the following page

Last page shows the document last page

Tool bar "Print and export"The tool bar of the "Print and export document" and "Print and export picture" dialoguewindows contains the following buttons:

Tool bar "Print and export"

Individual buttons function as follows:

Save as opens the "Save as" dialogue window thatallows for saving the file in format *.PDF, or*.RTF

Print opens the system window for "Print"

Page properties opens the "Page properties" dialogue windowthat allows for specifying the page style (size,edges, orientation)

Header andfooter

opens the "Header and footer" dialogue windowthat allows for inputting the document headersand footers

Color style determines the style of picture view (color,gray scale, black & white)

Copy copies the selected picture (text) to clipboard –parameters are set in the "Options" dialoguewindow – tab sheet "Copy to clipboard"

First page shows the document first page

Previous page shows the previous page

Next page shows the following page

Last page shows the document last page

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Move moves the current view in an arbitrarydirection – to proceed move mouse in thedesired location while keeping the left mousebutton pressed

Zoom in scales up the desktop view while keepinglocation of the point under the axis crossunchanged – this action is repeated using theleft mouse button, the right button leaves thezooming mode

Zoom out scales down the desktop view while keepinglocation of the point under the axis crossunchanged – this action is repeated using theleft mouse button, the right mouse buttonleaves the zooming mode

Text selection allows for selecting the text under the axiscross - to proceed move mouse over thedesired text while keeping the left mousebutton pressed

Full page modifies the page size such that the entirepage in the dialogue window is visible

Page width fits the page to maximum width of thedocument dialogue window

Setting header and footerThe dialogue window serves to define properties of the document header and footer. The "print header (footer)" check box determines whether to print the document header(footer).

Header and footer lines may contain an arbitrary text and inserted objects implicitly definedby the program. These objects receive program information such as:

from the "Company data" dialogue window (company name, logo,address)

from the "Project" frame (name and task description, author)

from the document system data (date, time, page numbering)

Objects can be introduced using the "Insert" button (the button opens a list of objects). Thebutton is active only if the cursor is found in one of the line that allows for inserting text(object). Inserted objects are written in an internal format different from other text andplaced in curly brackets.

The program allows for defining various headers for the first page or odd and even pages,respectively. Individual headers are in such a case defined in separate tab sheets.

The "use as default" option sets the inputted header and footer parameters as default forthe newly created data. The assumed default setting is common for all GEO programs.Different computer users may use different settings.

Writing format and the resulting view are evident from the following pictures.

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Dialogue window "Header and footer"

View of document header and footer

Page propertiesThe dialogue window allows for setting the page layout (paper format, print orientation andedges).

The "use as default" option sets the inputted page properties as default for the newlycreated data. The assumed default setting is common for all GEO programs. Differentcomputer users may use different settings.

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Dialogue window "Page properties"

Page numberingThis dialogue window allows the user to set page numbering. The combo list serves to definethe numbering style (Arabic digits, roman digits, with the help of symbols). A constant textcan be placed both in front and behind the page number. The "Numbering from" optionallows for starting the page numbering from an arbitrary number. The "use as default"option sets the inputted page numbering properties as default for the newly created data. Theassumed default setting is common for all GEO programs. Different computer users may usedifferent settings.

Dialogue window "Page numbering"

About companyThe dialogue window is launched from the managing menu (items "Setting", "Company").

The "Basic data" tab sheet serves to specify the basic information about company. Theinputted data are used by the program when printing and exporting documents (pictures), inthe document header or footer.

The "Company logo" tab sheet allows the user to load the company logo. The "Load" buttonopens the dialogue window which allows for opening the picture in various formats (*.JPG,*.JPEG, *.JPE, *.BMP, *.ICO, *.EMF, *.WMF).

The "Employees" tab sheep allows for inputting the list of program users (employees). Whenfilling the name list it is no longer necessary fill the author's name in the frame "Project".

- 296 -


Dialogue window "About company" – tab sheet "Basic data"

Dialogue window "About company" – tab sheet "Company logo"

- 297 -


Dialogue window "About company" – tab sheet "Employees"

Theory

Stress in a soil body

Geostatic stress, uplift pressureStress analysis is based on existence of soil layers specified by the user during input. Theprogram further inserts fictitious layers at the locations where the stress and lateral pressure(GWT, points of construction, etc.) change. The normal stress in the ith layer is computedaccording to:

where: hi - thickness of the ith layer

i - unit weight of soil

If the layer is found below the ground water table, the unit weight of soil below the watertable is specified with the help of inputted parameters of the soil as follows:

- for option "Standard" from expression:

where: sat - saturated unit weight of soil

w - unit weight of water

- for option "Compute from porosity" from expression:

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where: n - porosity

s - specific weight of soil


where: V - volume of soil

Vp - volume of voids

d - dry unit weight of soil

Unit weight of water is assumed in the program equal to 10 kN/m3 or 0,00625 ksi.Assuming inclined ground behind the structure () and layered subsoil the angle , whencomputing the coefficient of earth pressure K, is reduced in the ith layer using the followingexpression:

where: - unit weight of the soil in the first layer under ground

i - unit weight of the soil in the ith layer under ground

- slope inclination behind the structure

Effective/total stress in soilVertical normal stress z is defined as:

where: z - vertical normal total stress

ef - submerged unit weight of soil

z - depth bellow the ground surface


This expression in its generalized form describes so called concept of effective stress:

where: - total stress (overall)

ef - effective stress (active)

u - neutral stress (pore water pressure)

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Total, effective and neutral stress in the soil

Effective stress concept is valid only for the normal stress , since the shear stress is nottransferred by the water so that it is effective. The total stress is determined using the basictools of theoretical mechanics, the effective stress is then determined as a difference betweenthe total stress and neutral (pore) pressure (i.e. always by calculation, it can never bemeasured). Pore pressures are determined using laboratory or in-situ testing or bycalculation. To decide whether to use the total or effective stresses is no simple. The followingtable may provide some general recommendations valid for majority of cases. We shouldrealize that the total stress depends on the way the soil is loaded by its self weight andexternal effects. As for the pore pressure we assume that for flowing pore water the poreequals to hydrodynamic pressure and to hydrostatic pressure otherwise. For partial saturatedsoils with higher degree of it is necessary to account for the fact that the pore pressureevolves both in water and air bubbles.

Assume conditions Drained layer Undrained layer

short – term effective stress total stress

long – term effective stress effective stress

In layered subsoil with different unit weight of soils in individual horizontal layers the verticaltotal stress is determined as a sum of weight of all layers above the investigated point andthe pore pressure:

where: z - vertical normal total stress

- unit weight of soil

- unit weight of soil in natural state for soils above the GWT and dry layers

- unit weight of soil below water in other cases

d - depth of the ground water table below the ground surface

z - depth bellow the ground surface


Increment of earth pressure due to surchargeEarth pressure increment in a soil or rock body due to surcharge is computed using thetheory of elastic subspace (Bousinesque).

Earth pressure increment in the point inside the soil or rock body due to an infinite strip

- 300 -


surcharge is obtained from the following scheme:

Computation of earth pressure due to infinite strip surcharge

A trapezoidal surcharge is automatically subdivided in the program into ten segments.Individual segments are treated as strip surcharges. The resulting earth pressure is a sum ofpartial surcharges from individual segments.Stress increment due to concentrated surcharge is computed as follows:

Surcharge related to point "O"

where:

Increment of earth pressure under footingIn the program "Spread footing" the stress distribution below foundation is determined by

- 301 -


combining the basic loading diagrams:

Chart of foundation loading

Chart of foudation loading

Chart of foudation loading

- 302 -


Earth pressureProgram system GEO5 considers the following earth pressures categories:

active earth pressure

passive earth pressure

earth pressure at rest

When computing earth pressures the program GEO5 allows for distinguishing between the effective and total stress state and for establishing several ways of calculation of upliftpressure. In addition it is possible to account for the following effects having on the earthpressure magnitude:

influence of loading

influence of water pressure

influence of broken terrain friction between soil and back of structure

wall adhesion

influence of earth wedge at cantilever jumps

influence of earthquake

The following sign convention is used in the program, text and presented expressions.

When specifying rocks it is also necessary to input both the cohesion of rock c and the angleof internal friction of rock . These values can be otained either from the geological survey orfrom the table of recommended values.

Sign conventionThe following sign convention is used in the program, text and presented expressions.

Sign convention for calculation of earth pressures

inclination of the ground surface is positive, when the ground rises upwards from thewall

inclination of the back of structure is possitive, when the toe of the wall (at the backface) is placed in the direction of the soil body when measured from the vertical lineconstructed from the upper point of the structure

friction between the soil and back of structure is positive, if the resultant of earth

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pressure (thus also earth pressure) and normal to the back of structure form an anglemeasured in the clockwise direction

Active earth pressureActive earth pressure is the smallest limiting lateral pressure developed at the onset of shearfailure by wall moving away from the soil in the direction of the acting earth pressure(minimal wall rotation necessary for the evolution of active earth pressure is about 2 mrad,i.e. 2 mm/m of the wall height).

The following theories and approaches are implemented for the computation of active earthpressure assuming effective stress state:

The Mazindrani theory

The Coulomb theory

The Müller-Breslau theory

The Caqouot theory

The Absi theory

For cohesive soils the tension cutoff condition is accepted, i.e. if due to cohesion the negativevalue of active earth pressure is developed or, according to more strict requirements, thevalue of "minimal dimension pressure" is exceeded, the value of active earth pressure dropsdown to zero or set equal to the "minimal dimensioning pressure". The program also allows for running the analysis in total stresses.

Active earth pressure – the Mazindrani theoryActive earth pressure is given by the following formula:

where: z - vertical geostatic stress

Ka - coefficient of active earth pressure due to Rankin

- slope inclination

- weight of soil

z - assumed depth

- coefficient of active earth pressure due to Mazindrani

where: - slope inclination

- angle of internal friction of soil

c - cohesion of soil

Assuming cohesionless soils (c = 0) and horizontal ground surface ( = 0) yields the Rankinsolution, for which the active earth pressure is provided by:

- 304 -


and the coefficient of active earth pressure becomes:

where: - angle of internal friction of soil

Horizontal and vertical components of the active earth pressure become:

where: a - active earth pressure

- angle of friction structure - soil

- back face inclination of the structure

Active earth pressure - the Coulomb theoryActive earth pressure is given by the following formula:


cef - effective cohesion of soil

Ka - coefficient of active earth pressure

Kac - coefficient of active earth pressure due to cohesion

The coefficient of active earth pressure Ka is given by:

The coefficient of active earth pressure Kac is given by:

for:

for:



- slope inclination



- 305 -





Active earth pressure - the Müller-Breslau theoryActive earth pressure is given by the following formula:





The coefficient of active earth pressure Ka is given by:



- slope inclination



for:

for:



- slope inclination


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Active earth pressure - the Caquot theoryActive earth pressure is given by the following formula:





The following analytical solution (Boussinesque, Caqouot) is implemented in GEO5 to

compute the coefficient of active earth pressure Ka:

where: Ka - coefficient of active earth pressure due to Caquot

KaCoulomb - coefficient of active earth pressure due to Coulomb

- conversion coefficient – see further

where: - slope inclination behind the structure




for:

- 307 -


for:



- slope inclination behind the structure






Active earth pressure - the Absi theoryActive earth pressure is given by the following formula:





The program takes values of the coefficient of active earth pressure Ka from a database, builtupon the values published in the book: Kérisel, Absi: Active and passive earth PressureTables, 3rd Ed. A.A. Balkema, 1990 ISBN 90 6191886 3. The coefficient of active earth pressure Kac is given by:

for:

for:

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- slope inclination






Active earth pressure – total stressWhen determining the active earth pressure in cohesive fully saturated soils, in which casethe consolidation is usually prevented (undrained conditions), the horizontal normal totalstress x receives the form:

where: x - horizontal total stress (normal)

z - vertical normal total stress

Kuc - coefficient of earth pressure

cu - total cohesion of soil

The coefficient of earth pressure Kuc is given by:

where: Kuc - coefficient of earth pressure


au - total adhesion of soil to the structure

Passive earth pressurePassive earth pressure is the highest limiting lateral pressure developed at the onset of shearfailure by wall moving (penetrating) in the direction opposite to the direction of acting earthpressure (minimal wall rotation necessary for the evolution of passive earth pressure is about 10 mrad, i.e. 10 mm/m of the wall height). In most expressions used to compute the passiveearth pressure the sign convention is assumed such that the usual values of correspondingto vertical direction of the friction resultant are negative. The program, however, assumesthese values to be positive. A seldom variant with friction acting upwards is not considered inthe program.

The following theories and approaches are implemented for the computation of passive earthpressure assuming effective stress state:

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The Rankin and Mazindrani theory

The Coulomb theory

The Caquot – Kérisel theory

The Müller – Breslau theory

The Absi theory

The Sokolovski theory

The program also allows for running the analysis in total stresses.

Passive earth pressure - the Rankin and Mazindrani theoryPassive earth pressure follows from the following formula:


Kp - coefficient of passive earth pressure due to Rankin

- slope inclination

- weight of soil

z - assumed depth

- coefficient of passive earth pressure due to Mazindrani

The coefficient of passive earth pressure Kp is given by:




If there is no friction ( = 0) between the structure and cohesionless soils (c = 0), the groundsurface is horizontal ( = 0) and the resulting slip surafce is also plane with the slope:

,

the Mazindrani theory then reduces to the Rankin theory. The coefficient of passive earthpressure is then provided by:


Passive earth pressure p by Rankin for cohesionless soils is given:

- 310 -


where: - unit weight of soil

z - assumed depth

Kp - coefficient of passive earth pressure due to Rankin

Passive earth pressure - the Coulomb theoryPassive earth pressure follows from the following formula:

where: z - effective vertical geostatic stress

Kp - coefficient of passive earth pressure due to Coulomb





- slope inclination


The vertical pv and horizontal ph components of passive earth pressure are given by:

where: - angle of friction structure - soil


Passive earth pressure - the Caquot – Kérisel theoryPassive earth pressure follows from the following formula:

where:

Kp - coefficient of passive earth pressure for = -see the table

- reduction coefficient for <, see the table


z - vertical geostatic stress


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Coefficient of passive earth pressure Kp

Coefficient of passive earth pressure Kp for = -

[°] [°] Kp when °

0 5 10 15 20 25 30 35 40 45

10 1,17 1,41 1,53

15 1,30 1,70 1,92 2,08

20 1,71 2,08 2,42 2,71 2,92

25 2,14 2,81 2,98 3,88 4,22 4,43

-30 30 2,78 3,42 4,18 5,01 5,98 8,94 7,40

35 3,75 4,73 5,87 7,21 8,78 10,80 12,50 13,80

40 5,31 8,87 8,77 11,00 13,70 17,20 24,80 25,40 28,4

0

45 8,05 10,70 14,20 18,40 23,80 90,60 38.90 49,10 60,7

0 69,10

10 1,36 1,58 1,70

15 1,68 1,97 2,20 2,38

20 2,13 2,52 2,92 3,22 3,51

25 2,78 3,34 3,99 4,80 5,29 5,57

-20 30 3,78 4,81 8,58 8,81 7,84 9,12 9,77

35 5,38 8,89 8,28 10,10 12,20 14,80 17,40 19,00

40 8,07 10,40 12,00 18,50 20,00 25,50 38,50 37,80 42,2

0

45 13,2 17,50 22,90 29,80 38,30 48,90 82,30 78,80 97,3

0111,04

10 1,52 1,72 1,83 .

15 1,95 2,23 2,57 2,88

20 2,57 2,98 3,42 3,75 4,09

25 3,50 4,14 4,90 5,82 8,45 8,81

-10 30 4,98 8,01 7,19 8,51 10,10 11,70 12,80

35 7,47 9,24 11,30 13,80 18,70 20,10 23,70 2ó,00

- 312 -


40 12,0 15,40 19,40 24,10 29,80 37,10 53,20 55,10 61,8

0

45 21,2 27,90 38,50 47,20 80,80 77,30

908,20 124,00 153,

00178,00

10 1,84 1,81 1,93

15 2,19 2,46 2,73 2,91

20 3,01 3,44 3,91 4,42 4,66

25 4,28 5,02 5,81 8,72 7,71 8,16

0 30 8,42 7,69 9,19 10,80 12,70 14,80 15,90

35 10,2 12,60 15,30 18,80 22,30 28,90 31,70 34,90

40 17,5 22,30 28,00 34,80 42,90 53,30 78,40 79,10 88,7

0

45 33,5 44,10 57,40 74,10 94,70 120,00

153,00 174,00 240,

00275,00

10 1,73 1,87 1,98

15 2,40 2,65 2,93 3,12

20 3,45 3,90 4,40 4,96 5,23

10 25 5,17 5,99 6,90 7,95 9,11 9,67

30 8,17 9,69 11,40 13,50 15,90 18,50

19,90

35 13,8 16,90 20,50 24,80 29,80 35,80

42,30 46,60

40 25,5 32,20 40,40 49,90 61,70 76,40

110,00

113,00 127,00

45 52,9 69,40 90,90 116,00

148,00 i88,00

239,00

303,00 375,00

431,00

10 1,78 1,89 I 2,01

15 2,58 2,821 3,11 3,30

20 3,90 4,38 4,92 5,53 5,83

20 25 6,18 7,12 8,17 9,39 10,70 11,40

30 10,4 12,30 14,40 16,90 20,00 23,20

25,00

35 18,7 22,80 27,60 33,30 40,00 48,00

56,80 62,50

40 37,2 46,90 58,60 72,50 89,30 111,00

158,00

164,00 185,00

45 84,0 110,00

143,00

184,00

234,00 297,00

378,00

478,00 592,00

680,00

- 313 -


Reduction coefficient of passive earth pressureReduction coefficient for <

[°] for <

1,0 0,8 0,6 0,4 0,2 0,0

10 1,00 0,999 0,962 0,929 0,898 0,864

15 1,00 0,979 0,934 0,881 0,830 0,775

20 1,00 0,968 0,901 0,824 0,752 0,678

25 1,00 0,954 0,860 0,759 0,666 0,574

30 1,00 0,937 0,811 0,686 0,574 0,467

35 1,00 0,916 0,752 0,603 0,475 0,362

40 1,00 0,886 0,682 0,512 0,375 0,262

45 1,00 0,848 0,600 0,414 0,276 0,174

Passive earth pressure - the Müller – Breslau theoryPassive earth pressure follows from the following formula:

where: Kp - coefficient of passive earth pressure






- slope inclination





- 314 -


Passive earth pressure - the Absi theoryPassive earth pressure follows from the following formula:

where: Kp - coefficient of passive earth pressure



The program takes values of the coefficient Kp from a database, built upon the tabulatedvalues published in the book: Kérisel, Absi: Active and passive earth Pressure Tables, 3rd Ed.A.A. Balkema, 1990 ISBN 90 6191886 3. The vertical pv and horizontal ph components of passive earth pressure are given by:



Passive earth pressure - the Sokolovski theoryPassive earth pressure follows from the following formula:

where: Kpg - passive earth pressure coefficient for cohesionless soils

Kpc - passive earth pressure coefficient due to cohesion

Kpg - passive earth pressure coefficient due to surcharge


Individual expressions for determining the magnitude of passive earth pressure and slipsurface are introduced in the sequel; the meaning of individual variables is evident from Fig.:

Passive eart pressure slip surface after SokolovskiAngles describing the slip surface:

- 315 -


,


p - angle of friction structure - soil

- slope inclination

Slip surafce radius vector:

Provided that < 0 the both straight edges of the zone r1 and r2 numerically overlap andresulting in the plane slip surface developed in the overlapping region. The coefficients ofpassive earth pressure Kpg, Kpp, Kpc then follow from:


p - angle of friction structure - soil


Auxiliary variables: ipg, ipp, ipc, gpg, gpp, gpc, tpg, tpp, tpcfor:

- 316 -


where:

For soils with zero value for the angle of internal friction the following expressions areemployed to determine the coefficients of passive earth pressure:

where:

Passive earth pressure – total stressWhen determining the passive earth pressure in cohesive fully saturated soils, in which casethe consolidation is usually prevented (undrained conditions), the horizontal normal totalstress x receives the form:

where: x - horizontal total stress (normal)


Kuc - coefficient of earth pressure


The coefficient of earth pressure Kuc is given by:

where: Kuc - coefficient of earth pressure


au - total adhesion of soil to the structure

Earth pressure at restEarth pressure at rest is the horizontal pressure acting on the rigid structure. It is usuallyassumed in cases, when it is necessary to minimize the lateral and horizontal deformation ofthe sheeted soil (e.g. when laterally supporting a structure in the excavation pit up to depthbelow the current foundation or in general when casing soil with structures sensitive tonon-uniform settlement), or when structures loaded by earth pressures are due to sometechnological reasons extremely rigid and do not allow for deformation in the direction ofloading necessary to mobilize the active earth pressure.

Earth pressure at rest is given by:

- 317 -


For cohesive soils the Terzaghi formula for computing Kr is implemented in the program:

where: - Poisson ratio

For cohesionless soils the Jáky expression is used:


When computing the pressure at rest for cohesive soils 0 using the Jáky formula for the

determination of coefficient of earth pressure at rest K0, it is recommended to use the

alternate angle of internal friction n. The way of computing the earth pressure at rest can be therefore influenced by the selectionof the type of soil (cohesive, cohesionless) when inputting its parameters. Even typicallycohesionless soil (sand, gravel) must be introduced as cohesive if we wish to compute thepressure at rest with the help of the Poisson ratio and vice versa.

For overconsolidated soils the expression proposed by Schmertmann to compute thecoefficient of earth pressure at rest Kr is used:

where: Kr - coefficient of earth pressure at rest

OCR

- overconsolidation ratio

The value of the coefficient of earth pressure at rest can be inputted also directly.

Influence of the inclined ground surface at the back of structure on earth pressureat rest is described here.

Earth pressure at rest for inclined ground surface at theback of structureFor inclined ground surface behind the structure (0° ) the earth pressure at restassumes the form:


- slope inclination


Kr - coefficient of earth pressure at rest

For inclined back of wall the values of earth pressure at rest are derived from:

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where: - back face inclination of the structure



Normal and tangential components are given by:




The deviation angle from the normal line to the wall reads:



Recommended design coefficients according to EC7-1

m - reduces the angle of internal friction (CSN) or its tangent (EC7-1) based on theselection from the last column of block of coefficients (in right bottom section ofsubform)

mc - reduces the cohesion of soil

m - reduces the Poisson ratio (for the calculation of horizontal pressure at rest fromthe theory of elasticity)

m - reduces the unit weight of soil both in front of and behind the structure. Whenperforming the analysis with the help of limit state theory the unit weight ofembankments and backfills with unfavorable influence is increased, and withfavorable influence decreased. For soils in natural deposit we have m= 1,00.In case of variable unit weight of soil it is more suitable to introduce a weightedaverage of the unit weight or to use a qualified estimate accounting for itseffects.

Recommended design coefficients for ultimate limit state of permanent or temporarydesign situations according to EC7-1

Case 1) Unfavorablepermanent

load

Favorablepermanent

load

Unfavorablelive load

tg cef i

A 1,0 0,95 1,5 1,1 1,3 1,2

B 1,35 1,0 1,5 1,0 1,0 1,0

C 1,0 1,0 1,3 1,25 1,6 1,4

1) The design must be checked for each of the three cases A, B, C separately.

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Alternate angel of internal friction of soilIn some cases it appears more suitable for the analysis of earth pressures to introduce forcohesive soils an alternate angle of internal friction n that also accounts for the influence ofcohesive soil in conjunction with the normal stress developed in the soil. The magnitude ofthe normal stress for determining the value of alternate angle of internal friction depends onthe type of geotechnical problem, foundation conditions, etc. For deep seated foundation pitsor constructions in homogeneous or relatively simple environment the normal stress isintroduced in the centroid of the loading mass. In case of shallow pits or complexenvironment the normal stress is assumed in the heel of the loading diagram – see figure:

Determination of normal stress for alternate angle of internal friction of soil n

The alternate angle of internal friction of soil is given by:




When computing the pressure at rest for cohesive soils r using the Jáky formula for the

determination of coefficient of earth pressure at rest K0, it is recommended to use the

alternate angel of internal friction n.

Determination of alternate angel of internal friction of cohesive soil

Distribution of earth pressures in case of broken terrainFigures show the procedure of earth pressure analysis in the case of sloping terrain. Theresulting shape of earth pressure distribution acting on the construction is obtained from the

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sum of triangular distributions developed by individual effects acting on the construction.

Principle of the earth pressure computation in the case of broken terrain

Principle of the earth pressure computation in the case of broken terrain for >

Influence of waterThe influence of ground water can be reflected using one of the following variants:

Without ground water, water is not considered

Hydrostatic pressure, ground water behind structure

Hydrostatic pressure, ground water behind and in front of structure

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Hydrodynamic pressure

Special distribution of water pressure



In this option the influence of ground water is not considered.

Complementary information:

If there are fine soils at and below the level of GWT, one should carefully assess an influenceof full saturation in the region of capillary attraction. The capillary attraction is in the analysisreflected only by increased degree of saturation, and therefore the value of sat is insertedinto parameters of soils.

To distinguish regions with different degree of saturation, one may insert several layers of thesame soil with different unit weights. Negative pore pressures are not considered. However,for layers with different degree of saturation it is possible to use different values of shearresistance influenced by suction (difference in pore pressure of water and gas ua - uw).



The heel of a structure is sunk into impermeable subsoil so that the water flow below thestructure is prevented. Water is found behind the back of structure only. There is no wateracting on the front face. Such a case may occur when water in front of structure flow freelydue to gravity or deep drainage is used. The back of structure is loaded by the hydrostaticpressure:

where: w - unit weight of water

hw - water tables difference

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Action of hydrostatic pressure

Hydrostatic pressure, ground water behind and in front ofstructure

Hydrostatic pressure, ground water behind and in front ofstructure

The heel of a structure is sunk into impermeable subsoil so that the water flow below thestructure is prevented. The loading due water is assumed both in front of and behind thestructure. The water in front of structure is removed either with the help of gravity effects oris shallowly lowered by pumping. Both the face and back of structure is loaded by hydrostaticpressure due to difference in water tables (h1 and h2). The dimension hw represents thedifference in water tables at the back and in front of structure - see figure:

Action of hydrostatic pressure

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The heel of a structure is sunk into permeable subsoil, which allows free water flow below thestructure – see figure. The unit weight of soil lifted by uplift pressure su is modified toaccount for flow pressure. These modifications then depend on the direction of water flow.

Action of hydrodynamic pressure

When computing the earth pressure in the area of descending flow the program introducesthe following value of the unit weight of soil:

and in the area of ascending flow the following value:

where: su - unit weight of submerged soil

- alteration of unit weight of soil

i - an average seepage gradient


An average hydraulic slope is given:

where: i - an average seepage gradient

hw - water tables difference

dd - seepage path downwards

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du - seepage path upwards

If the change of unit weight of soil provided by:

where: i - an average seepage gradient


is greater than the unit weight of saturated soil su, then the leaching appears in front ofstructure - as a consequence of water flow the soil behaves as weightless and thus cannottransmit any loading. The program then prompts a warning message and further assumes thevalue of = 0. The result therefore no longer corresponds to the original input – is safer.



This option allows an independent (manual) input of distribution of loading due to water atthe back and in front of structure using ordinates of pore pressure at different depths. Thevariation of pressure between individual values is linear. At the same time it is necessary toinput levels of tables of full saturation of a soil at the back h1 and in front h2 of structure

including possible decrease of unit weight y in front of structure due to water flow.

Example: Two separated horizon lines of ground water.

There are two permeable layers (sand or gravel) with one impermeable layer of clay inbetween, which causes separation of two hydraulic horizon lines – see figure:

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Example of pore pressure distribution

The variation of pore pressure above the clay layer is driven by free ground water table GWT1.The distribution of pore pressure below the clay layer results from ratio in the lowerseparated ground water table GWT2, where the ground water is stressed. The pore pressuredistribution in clay is approximately linear.

The capillary attraction is in the analysis reflected only by increased degree of saturation, andtherefore the value of sat is inserted into parameters of soils.

To distinguish regions with different degree of saturation, one may insert several layers of thesame soil with different unit weights. Negative pore pressures are not considered. However,for layers with different degree of saturation it is possible to introduce values of shearresistance influenced by suction.

Uplift pressure in footing bottomThe variation of uplift pressure in the footing bottom due to difference in water tables isassumed according to expected effect linear, parabolic or is not taken into account.

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Uplift pressure in footing bottom

Influence of tensile cracksThe program makes possible to account for the influence of tensile surface cracks filled withwater. The analysis procedure is evident from the figure. The depth of tensile cracks is theonly input parameter.

Influence of tensile cracks

Minimal dimensioning pressureWhen determining the magnitude and distribution of earth pressures it is very difficult toqualify proportions of individual effects. This situation leads to uncertainty in thedetermination of earth pressure loading diagram. In reality we have to use in the design themost adverse distribution in favor of the safety of structure. For example, in case of bracedstructures in cohesive soils when using reasonable values of strength parameters of soil alongthe entire structure we may encounter tensile stresses in the upper part of the structure – seefigure. Such tensile stresses, however, cannot be exerted on the sheeting structure(consequence of separation of soil due to technology of construction, isolation and drainagelayer). In favor of the safe design of sheeting structure particularly in subsurface regions,where tensile stresses are developed during computation of the active earth pressure, theprogram offers the possibility to call the option "Minimal dimensioning pressure" in theanalysis.

To determine the minimal dimensioning pressure the program employs for layers of cohesivesoils as the minimal value of the coefficient of active earth pressure an alternate coefficient Ka = 0,2. Therefore it is ensured that the value of the computed active earth pressure will not

drop below 20% of the vertical pressure (Ka 0,2) – see figure. Application of the minimaldimensioning pressure assumes for example the possibility of increasing the lateral pressuredue to filling of joint behind the sheeting structure with rain water. If the option of minimaldimensioning pressure is not selected the program simply assumes tension cutoff (Ka 0,0).

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Minimal dimensioning pressure

Earth - pressure wedge Providing a structure with a cantilever jump (foundation slab of cantilever wall, modificationfor reduction of earth pressures) is considered when computing earth pressures it is possibleto compute earth pressures acting either on the real back of structure with the inputted angleof friction 23 or on an alternate back of structure. The alternate back of sheetingstructure replaces the real broken one by a slip plane passing from the upper point of theback of wall towards the outer upper point of the jump and forms an earth wedge – seefigure. A fully mobilized angle of friction = is assumed along this plane. The weight ofearth wedge created under this alternate back further contributes to loading applied to thestructure. To introduce the alternate back of structure into the analysis it is necessary toselect in the program GEO5 Earth pressures the option "Consider developing ofearth-pressure wedge". In other programs the earth wedge is introduced automatically.

Calculation with and without earth–pressure wedge

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Determination of earth–pressure wedge in case of active earth pressure

The slip plane of the earth–pressure wedge is inclined from the horizontal line by angle a given by:


- slope inclination




h - height of earth wedge

The shape of the earth wedge in the layered subsoil is determined such that for individuallayers of soil above the wall foundation the program computes the angle a, which then

serves to determine the angle as. Next, the program determines an intersection of the line

drawn under the angle as from the upper right point of the foundation block with the nextlayer. The procedure continues by drawing another line starting from the previouslydetermined intersection and inclined by the angle as. The procedure is terminated when theline intersects the terrain or wall surface, respectively. The wedge shape is further assumedin the form of triangle (intersection with wall) or rectangle (intersection with terrain).

Influence of surcharge on earth pressuresThe following types of surcharges are implemented in the GEO5 program:

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Active earth pressure Surface surcharge

Strip surcharge

Trapezoidal surcharge

Concentrated surcharge

Line surcharge

Earth pressure at rest

Surface surcharge

Strip surcharge

Trapezoidal surcharge

Concentrated surcharge

Passive earth pressure Surface surcharge

Influence of surface surcharge on active earth pressureThe increment of active earth pressure at rest due to surface surcharge is given by:

where: p - vertical uniform loading


The vertical uniform loading p applied to the ground surface induces therefore over the entireheight of the structure a constant increment of active earth pressure – see figure:

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Increment of active earth pressure due to verticaluniform ground surface surcharge

Influence of strip surcharge on active earth pressureFor vertical strip loading fa acting parallel with structure on the ground surface along aninfinitely long strip the trapezoidal increment of active earth pressure applied to the structureover a given segment hf is assumed – see figure.

Diagram of increment of active earth pressure due to strip loading faThis segment is determined by intersection of the structure and lines drawn from the edgepoints of the strip loading having slopes associated with angles and a. The angle acorresponding to critical slip plane follows from:

The formula is described in details in section "Active earth pressure – line surcharge".

Variation of pressure increment is trapezoidal; the larger intensity of fs is applied at the

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upper end while the smaller intensity of fi at the bottom end. The two increments are givenby:

where: fa - magnitude of strip surcharge

b - width of the strip surcharge acting normal to the structure

hf - section loaded by active earth pressure increment

where: a - angle of critical slip plane



The resultant of the increment of active earth pressure due to strip loading fa is provided by:




fa - magnitude of strip surcharge

b - width of the strip surcharge

For non-homogeneous soils the program proceeds as follows.

Influence of trapezoidal surcharge on active earth pressureThe trapezoidal surcharge is subdivided in the program in ten segments. Individual segmentsare treated as strip loadings. The resulting earth pressure is a sum of partial surchargesderived from individual segments.

Influence of concentrated surcharge and limited surfaceloading on active earth pressureThe concentrated load (resultant F due to surface or concentrated load – see figure) istransformed into a line load with a limited length. If the width of surface loading b is smallerthan the distance a from the back of wall (see figure) the alternate line loading f havinglength 1+2(a+b) receives the form:

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where: F - resultant due to surface or concentrated load

a - distance of loading from the back of wall

l - length of load

b - width of surface loading

If the width b of surface loading is greater than the distance a from the back of wall (seefigure) the alternate line loading f having length 1+2(a+b) and width (a+b) reads:

where: F - resultant due to surface or concentrated load

a - distance of loading from the back of wall

l - length of load

b - width of surface loading

Alternate loading for calculation of increment of active earth pressure


Influence of line surcharge on active earth pressureVertical infinitely long line loading f acting on the ground surface parallel with structure leadsto a triangular increment of active earth pressure applied to the structure over a givensegment hf – see figure:

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Diagram of increment of active earth pressure due to vertical

line loading acting on ground surface

Action of the line surcharge is deterimened such that two lines are drawn from the point ofapplication following angles and a (corresponding to the critical slip surface), which isprovided by:


- angle derived from the following formulas







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h - assumed depth

For non-homogeneous soil and inclination of ground surface smaller than the angle ofinternal friction of the soil the value of the angle is given by:





The resultant of the increment of active earth pressure due to line loading f is provided by:




f - magnitude of line surcharge


Influence of surface surcharge in non-homogeneous soil onactive earth pressureFor non-homogeneous soil we proceed as follows:

compute the angle a for a given soil layer

determine the corresponding magnitude of force Sa and size of thecorresponding pressure diagram

determine the magnitude of earth pressure acting below the bottom edge of agiven layer, and its ratio with respect to the overall pressure magnitude

the surcharge is reduced using the above ratio, then the location of thissurcharge on the upper edge of the subsequent layer is determined

compute again the angle a for the next layer and repeat the previous stepsuntil the bottom of a structure is reached or the surcharge is completelyexhausted

Influence of surface surcharge on pressure at restAn increment of uniformly distributed earth pressure at rest r caused by the verticalsurface loading applied on the ground surface behind the structure is computed using thefollowing formula:

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where: f - magnitude of surface surcharge


Diagram of increment of earth pressure at rest due to vertical

uniform loading acting on ground surface

Influence of strip surcharge on pressure at restUniform strip loading fa acting on the ground surface behind the structure parallel with

vertical structure (see figure) creates an increment of earth pressure at rest r having themagnitude given by:

where: fa - vertical strip surcharge

,,, - evident from figure

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Increment of earth pressure due to vertical strip surcharge

Influence of trapezoidal surcharge on pressure at restThe trapezoidal surcharge is subdivided in the program in five segments. Individual segmentsare treated as strip loadings. The resulting earth pressure is a sum of partial surchargesderived from individual segments.

Influence of concentrated surcharge and limited surfaceloading on pressure at restApplication of concentrated load yields an increment of earth pressure at rest r acting onthe vertical structure and having the magnitude of:

where: F - concentrated force acting on ground surface

x,z - coordinates evident from figure

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Increment of earth pressure at rest due to vertical concentrated force

Influence of surface surcharge on passive earth pressureFor passive earth pressure only an increment due to vertical uniform loading fa is determinedusing the formula:

where: fa - vertical surface surcharge

Kp - coefficient of passive earth pressure

The vertical uniform loading q acting on the ground surface therefore results in a constantincrement of passive pressure applied over the whole length of wall - see figure.

Increment of the passive earth pressure

Influence of earthquake on earth pressuresEarthquake increases the effect of active pressure and reduces the effect of passive pressure.The theories used in GEO5 (Mononobe-Okabe, Arrango) are derived assuming cohesionlesssoils without influence of water. Therefore, all inputted soils are assumed cohesionless whenemploying these theories to address the earthquake effects. Earthquake effects due to

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surcharge are not considered in the program – the user may introduce these effects(depending on the type of surcharge) as "Inputted forces"

The coefficient kh is assumed always positive and such that its effect is always unfavorable.

The coefficient kv may receive both positive and negative value. If the equivalent acceleration

av acts downwards (from the ground surface) the inertia forces kvWs will be exerted on thesoil wedge in the opposite direction (lifting the wedge up). The values of equivalentacceleration av (and thus also the coefficient kv) and inertia forces kvWs are assumed aspositive. It is clearly evident that the inertia forces act in the direction opposite toacceleration (if the acceleration is assumed upwards – av = - kv*g then the inertia force presses

the soil wedge downwards: -kvWs. The direction with most unfavorable effects on a structureis assumed when examining the seismic effects.

For sheeting structures it is possible to neglect the effect of vertical equivalent acceleration kvWs and input kv = 0.

Sign convention

The seismic angle of inertia is determined from the coefficients kh and kv (i.e. angle between

the resultant of inertia forces and the vertical line) using the formula:

where: kv - seismic coefficient of vertical acceleration

kh - seismic coefficient of horizontal acceleration

Pressure from seismic effects

Increment of active earth pressure due to seismic effects (computed from the structurebottom) follows from:

where: i - unit weight of soil in the ith layer

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Kae,i

- coefficient of active earth pressure (static and seismic) in the ith layer

Ka - magnitude of earth pressure in the ith layer due to Coulomb

hi - thickness of the ith layer

kv - seismic coefficient of vertical acceleration

Reduction of passive pressure due to seismic loading (computed from the structure bottom) isprovided by:

where: i - unit weight of soil in the ith layer

Kpe,i

- coefficient of active earth pressure (static and seismic) in the ith layer

Kp - magnitude of earth pressure in the ith layer due to Coulomb



Active earth pressure coefficients Kae,i and Kpe,i are computed using the Mononobe-Okabe

theory or the Arrango theory. If there is ground water in the soil body the program takes thatinto account.

The basic assumption in the program when computing earthquake is a flat ground surfacebehind structure with inclination . If that is not the case the program approximates theshape of terrain by a flat surface as evident from figure:

Terrain shape approximation

Point of application of resultant force

The resultant force is automatically positioned by the program into the centre of the stressdiagram. Various theories recommend, however, different locations of the resultant force –owing to that it is possible to select the point of application of the resultant force in the rangeof 0,33 - 0,7 H (H is the structure height). Recommended (implicit) value is 0,66 H. Having theresultant force the program determines the trapezoidal shape of stress keeping both the

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inputted point of application of the resultant force and its magnitude.

Influence of earthquake – the Mononobe-Okabe theoryThe coefficient Kae for active earth pressure is given by:

The coefficient Kpe for passive earth pressure is given by:


H - height of the structure


- soil - structure angle of friction


- slope inclination



- seismic inertia angle

Deviation of seismic forces must be for active earth pressure always less or equal to thedifference of the angle of internal friction and the ground surface inclination (i.e. ). Ifthe values of is greater the program assumes the value = . In case of passive earthpressure the value of deviation of seismic forces must be always less or equal to the sum ofthe angle of internal friction and the ground surface inclination (i.e. ). The values ofcomputed and modified angle can be visualized in the output – in latter case the wordMODIFIED is also displayed.

Example of the program output

Influence of earthquake – the Arrango theoryThe program follows the Coulomb theory to compute the values of Ka and Kp while taking

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into account the dynamic values (*, *).For active earth pressure:

For passive earth pressure:



- seismic forces inclination

The coefficients of earth pressures Kae and Kpe are found by multiplying the coefficients Faeand Fpe by the values of Ka and Kp, respectively.


- seismic forces inclination

If the value of the angle * becomes larger than the program assumes the value (* = ).The values of computed and modified angle * can be visualized in the output – in latter casethe word MODIFIED is also displayed. It is the user's responsibility to check in such casewhether the obtained results are realistic.

Example of the program output

Influence of earthquake – water effectsWhen examining the influence of ground water on the magnitudes of earth pressure theprogram GEO5 differentiates between restricted water and free water.

Restricted water

This type is used in soils with lower permeability – app. below the value of k = 1x10-3 cm/s. Insuch soils the water flow is influenced, e.g. by actual grains (by their shape and roughness)or by resistance of fraction of adhesive water. General formulas proposed byMononobe-Okabe or Arrango are used to analyze seismic effects. The only difference appearsin substituting the value of the seismic angle by *:

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where: sat - unit weight of fully saturated soil

su - unit weight of submerged soil



Free water

This type is used in soils with lower permeability – app. above the value of k > 1x10-1 cm/s. Insuch soils it is assumed that water flow in pores is more or less independent of soil grains(e.g. turbulent flow in coarse grain soils). General formulas proposed by Mononobe-Okabe orArrango are used to analyze seismic effects. The only difference appears in substituting thevalue of the seismic angle e

by e+:

where: d - unit weight of dry soil

su - unit weight of submerged soil



GS - specific gravity of soil particles

where: S - density of the soil solids

w - density of water

Apart from dynamic pressure the structure is also loaded by hydrodynamic pressure causedby free water manifested by dynamic pressure applied to the structures. The actual parabolicdistribution is in the program approximated by the trapezoidal distribution.

The resultant of hydrodynamic pressure Pwd is distant by ywd from the heel of structure:

where: H - height of the structure

and its magnitude follows from:

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where: w - unit weight of water


H - height of the structure

Influence of friction between soil and back of structureThe magnitude of active or passive earth pressure, respectively, depends not only on theselected solution theory but also on friction between the soil and the back of wall and by theadhesion of soil to the structure face represented by the angle . If = 0 then the pressure acts in the direction normal to the back of wall and the resultant of earth pressure P is alsodirected in normal to the back of wall – see figure:

Distribution of earth pressure along structure for = 0

Providing the friction between the soil and the back of wall is considered in the analysis ofearth pressures, the earth pressure and also its resultant P are inclined from the back ofwall by the angle . Orientation of friction angles from normal to the back of wall must beintroduced in accord with the mutual movement of structure and soil. With increasing value of the value of active earth pressure decreases, i.e. the resultant force of active earthpressure deviates from the normal direction – see figure:

Distribution of earth pressure along structure for 0The magnitude can be usually found in the range of 13 to = 23 . The values of

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orientation of the friction angle between the soil and the structure are stored in table ofvalues of for various interfaces and in table of recommended values for . The value of 13 can be used if assuming smooth treatment of the back of sheeting structure (foiland coating against ground water). For untreated face it is not reasonable to exceed thevalue of = 23 . When selecting the value of it is necessary to reflect also otherconditions, particularly the force equation of equilibrium in the vertical direction. One shoulddecide whether the structure is capable of transmitting the vertical surcharge due to frictionon its back without excessive vertical deformation. Otherwise it is necessary to reduce thevalue of , since only partial mobilization of friction on the back of wall may occur. In case ofuncertainty it is always safer to assume smaller vale of .

Table of ultimate friction factors for dissimilar materialsValues of the angle for different interfaces (after NAVFAC)

Interface material Friction factortg ()

Friction angel °

Mass concrete on the following foundationmaterials:

Clean sound rock 0,7 35

Clean gravel, gravel-sand mixtures, coarse sand 0,55 to 0,6 29 to 31

Clean fine to medium sand, silty medium to coarse sand,silty or clayey gravel

0,45 to 0,55

Clean fine sand, silty or clayey fine to medium sand 0,35 to 0,45 19 to 24

Fine sandy silt, nonplastic silt 0,30 to 0,30 17 to 19

Very stiff and hard residual or preconsolidated clay 0,40 to 0,50 22 to26

Medium stiff and stiff clay and silty clay 0,30 to 0,35 17 to 19

Steel sheet piles against the following soils:

Clean gravel, gravel-sand mixtures, well-gradedrock fill with spalls

0,4 22

Clean sand, silty sand-gravel mixture, single sizehard rock fill

0,3 17

Silty sand, gravel or sand mixed with silt or clay 0,25 14

Fine sandy silt, nonplastic silt 0,20 11

Formed concrete or concrete sheet piling against thefollowing soils:

Clean gravel, gravel-sand mixture, well-gradedrock fill with spalls

0,40 to 0,50 22 to26

Clean sand, silty sand-gravel mixture, single sizehard rock fill

0,3 to 0,4 17 to 22

Silty sand, gravel or sand mixed with silt or clay 0,3 17

Fine sandy silt, nonplastic silt 0,25 14

Various structural materials:

Dressed soft rock on dressed soft rock 0,7 35

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Dressed hard rock on dressed soft rock 0,65 33

Dressed hard rock on dressed hard rock 0,55 29

Masonry on wood (Gross grain) 0,5 26

Steel on steel at sheet pile interlocks 0,3 17

Friction between soil and the back of constructionRecommended values Material Concrete Steel Wood

Surface Smooth Rough

Smooth Rough Smooth

Rough

Loose noncohesive soil 0,85 0,9 0,7 0,8 0,75 0,8

Firm noncohesive soil 0,8 0,8 0,6 0,7 0,7 0,7

Dense noncohesivesoil

0,7 0,7 0,5 0,7 0,65 0,65

Silt 0,8 0,9 0,6 0,8 0,8 0,9

Clayey soil 0,8 0,9 0,5 0,7 0,7 0,8

Clay 0,8 0,9 0,5 0,6 0,6 0,7

Adhesion of soilWhen performing the analysis in the total stress state it is necessary not only to use the totalshear strength parameters of soil u , cu but also to know the adhesion a of soil to the

structure face. The value of adhesion a is usually considered as a fraction of the soil cohesionc. The typical values of a for a given range of the cohesion c are listed in the following table.

Common values of the adhesion of soil aSoil Cohesion c [kPa] Adhesion a [kPa]Soft and very soft cohesivesoil

0 - 12 0 – 12

Cohesive soil with mediumconsistency

12 - 24 12 – 24

Stiff cohesive soil 24 - 48 24 - 36

Hard cohesive soil 48 - 96 36 – 46

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Parameters of rocksRock parameters of orientation with respect to strength of rock in pure compression

Compressivestrength ofrock

ci[MPa]

Strength parameter of rockafter Hoek

mi[-]

GSI[-]

Cohesion of rockc

[kPa]

Angle of internal frictionof rock

[°]

150 25 75 7000 - 13000 46 - 68

80 12 50 3000 - 4000 30 - 65

50 16 75 2000 - 4000 40 - 60

30 15 65 1000 - 2000 40 - 60

20 8 30 400 - 600 20 - 44

15 10 24 300 - 500 24 - 38

5 10 20 90 - 100 23 - 28

Unlike soils (both cohesive and cohesionless) the magnitude of the angle of internal friction(sometimes refer to as the angle of shear strength) varies and depends on the current stateof stress in the rock body. Graphically it is represented by the angle of the tangent to theenvelope of Mohr circles constructed for the ultimate stress state. The value of graduallydecreases with the increasing value of stress . If the elastic regime is exceeded (onset ofplastic deformation) we set = 0. As a representative value of the angle of internal friction we denote the value associated with the stress = 0. In practical applications the part of

the Mohr envelope between tensile Rt and compressive Rd circles is usually replaced by thetangent to both circles (see Fig.) The magnitude of the angle of internal friction then followsfrom:

Determination from Mohr circle

The angle of internal friction can be estimated by measuring angles of slip planes onremaining parts of tested specimens together with the following formula:

Some values of orientation:weathered sand conglomerate, lowly cracked 35 – 44°

unweathered clay slate, medium cracked 30 - 40°

unweathered tuff, medium cracked 33 – 42°

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unweathered diabase 39 – 50°

unweathered phantanite, lowly cracked 45 – 52°

Nailed slopesThe program "Nailed slopes" allows for the following verifications:- verification of structure internal stability- verification fictitious wall - the same as gravity wall - verification of structure concrete cover- verification nails bearing capacityverification of overall stability using the program "Slope stability"

Analysis of nails bearing capacityFor each nail the following bearing capacities are either computed or inputted:

Rf nail cap bearing capacity

Rt nail strength against breaking

Tp pull-out nail bearing capacity

Strength characteristics of a nail represent the basic parameters to compute the actualforce in a nail.

The tensile strength of the nail follows from:

where: Rt - strength against breaking

ds - nail diameter

fy - strength of nail material

SBT

- factor of safety against breaking

The pull-out resistance is provided by:

where: Tp - pull-out nail bearing capacity

d - hole diameter

a - ultimate bond strength

SBp - factor of safety against pull-out

The nail head strength is given by:

where: l - nail length

Smax - maximum spacing of nails in a structure

Rt - nail strength against breaking

Tp - pull-out nail bearing capacity

Providing the nail is not anchored to the structure cap, it is possible set the nail cap bearing

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capacity to zero.

Estimated bond strengthEstimated bond strength of soil nails in soil and rock (source: Elias a Juran, 1991) Material Construction

methodSoil / rock type Ultimate bond

strength qs [kPa]

Rock Rotary drilled Marl / limestone 300 - 400

Phyllite 100 - 300

Chalk 500 - 600

Soft dolomite 400 - 600

Fissured dolomite 600 - 1000

Weathered sandstone 200 - 300

Weathered shale 100 - 150

Weathered schist 100 - 175

Basalt 500 - 600

Slate / hard shale 300 - 400

Cohesionless soils Rotary drilled Sand / gravel 100 - 180

Silty sand 100 - 150

Silt 40 - 120

Piedmont residual 40 - 120

Fine colluvium 75 - 150

Driven casing Sand / gravel lowoverburden highoverburden

190 - 240280 - 430

Dense moraine 380 - 480

Colluvium 100 - 180

Augered Silty sand fill 20 - 40

Silty fine sand 55 - 90

Silty clayey sand 60 - 140

Jet grouted Sand 380

Sand gravel 700

Fine - grained soils Rotary drilled Silty clay 35 - 50

Driven casing Clayey silt 90 - 140

Augered Loess 25 - 75

Soft clay 20 - 30

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Stiff clay 40 - 60

Stiff clayey silt 40 - 100

Calcareous sandyclay

90 - 140

Note: Convert values in kPa to psf by multiplying by 20.9 Convert values in kPa to psi by multiplying by 0.145

Analysis of internal stabilityAn internal stability of a structure is checked assuming two types of a slip surface:- plane slip surface:

Plane slip surface- broken slip surface:

Broken slip surface

In both cases a specific slip surface is examined for a variation of angle υ.

When running an optimization analysis the calculation is carried out for all benches with avariation of the angle of slip surface ν changing from 1 up to 89 degrees with a one degreestep.

A verification analysis of internal stability can be performed using either the factor of safety ofthe theory of limit states depending on the setting in the frame "Setting".

The analysis checks whether a ratio of resisting and shear (driving) forces acting on a slipsurface is greater than the inputted factor of safety. The following forces are employed:

Shear forces:- component of gravity force parallel to slip surface

- in case of broken slip surface – component of active earth pressureacting on vertical part of structure and parallel to slip surface(pressure is determined without reduction of input parameters)

- horizontal forces due to earthquakeResisting forces:

- soil friction and cohesion along slip surface

- sum of forces of transmitted by nails

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Force of transmitted by nailsThe nail force is determined based on the location of its intersection with a slip surface. If anail is found completely in front of the slip surface, then it does not enter the calculation. If anail crosses the slip surface, then its force is determined as:

where: x - nail length behind slip surface in direction of soil body

y - nail length in front of slip surface

Rf - nail cap bearing capacity

Rt - strength of nail against breaking

Tp - pull-out nail bearing capacity

Distribution of tensile force along nail

Factor of safetyThe analysis checks whether a ratio of resisting and shear (driving) forces acting on a slipsurface is greater than the inputted factor of safety.

A factor of safety on the inputted slips forces is thus provided by:

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where: G - gravity force

Sa,sv - vertical component of active pressure

Sa,vod - horizontal component of active pressure

di - length of ith section slip surface

d - length of slip surface

Fh,n - bearing capacity of nth nail behind slip surface per 1m run

ci - cohesion of ith soil layer

i - angle o internal friction of ith layer

- inclination of slip surface

- inclination of nails from horizontal direction

Theory of limit statesThe analysis checks whether passive (resisting) forces Fp acting on a slip surface aregreater than the active (shear) forces Fa:

where: G - gravity force

Sa,sv - vertical component of active pressure

Sa,vod - horizontal component of active pressure

di - length of ith section slip surface

d - length of slip surface

Fh,n - bearing capacity of nth nail behind slip surface per 1m run

ci - cohesion of ith soil layer

i - angle o internal friction of ith layer

- inclination of slip surface

- inclination of nails from horizontal direction

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Verification of bearing capacity of nailsThis verification is required only in certain countries and is performed only when checked inthe frame "Setting". The magnitude of active earth pressure is reduced using a coefficientKn, which can also be introduced in the frame "Setting". The recommended (experimentallydetermined) value is Kn = 0,85.

Forces transmitted by individual nails are determined such that a particular portion of thecalculated earth pressure is assigned to a given bench. Each nail is then loaded by thecorresponding portion of the active earth pressure.

Forces transmitted by individual nails

The nail force is provided by:

where: b - nail spacing

- nail inclination

Kn - reduction coefficient

Ta,vod - active earth pressure acting on a given bench

Dimensioning of concrete coverThe concrete cover of a nailed slope is designed to sustain an active earth pressure. Tothat end, the structure is assumed to be subdivided into individual intermediate design strips.

In the vertical direction the nail cap is modeled as a support and joint between benches asan internal hinge.

In the horizontal direction the program generates (by default) a structure with fivesupports uniformly loaded by the magnitude of active pressure up to a depth of the nail cap.

The program further allows for the verification of concrete cover reinfocement of a structureloaded by the bending moment.

A scheme of constructing a design model including loading is evident from figure:

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Dimensioning of concrete cover

Analysis of wallsVerification analysis of walls can be performed with the help of: theory of limit states factor of safetyIn addition, the bearing capacity of foundation soil is examined for both cases.

Following forces are used in the verification: weight of wall – depends on the shape and unit weight of wall (for input use the "

Material" dialogue window) – uplift pressure is introduced for walls found below theground water table

resistance on front face – when inputting the resistance on front face the correspondingforce acts as the pressure at rest, or passive pressure or reduced passive pressure

gravity forces of earth wedges – an arbitrary number of these forces may occur dependingon the shape of structure

active earth pressure or pressure at rest acting on the structure – the basic loading ofstructure due earth pressures - depending on the selected option in the frame "Settings"the pressure is computed either with or without reduction of input soil parameters.

force due to water effects or pore pressure, respectively forces due to surcharge – a single force corresponds to each inputted surcharge. If the

magnitude of force due to surcharge is equal to zero (the surcharge has no effect on astructure) then it does not appear in the picture but only in the table listing.

inputted forces – forces entering the analysis are displayed forces due to earthquake – several forces enter the analysis due to earthquake –

increase of earth pressure acting on a structure, reduction of passive pressure on the frontface of a structure, or force due to free water behind structure

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mesh overhangs and geo-reinforcements are displayed and included providing theyappear in the analysis

base anchorage of wall

Geo-reinforcements, mesh overhangsIf mesh overhangs or geo-reinforcements are specified either for structure or blocks theanchor forces are introduced in the analysis. Graphical representation of anchorage system isevident from figure:

Scheme of application of mesh overhangs

Computation of the angle a is described in chapter earth wedge.

Forces due to anchorage assume the form:

where: li - length of mesh behind the slip surface to soil mass

Tpi - bearing capacity per one meter run of mesh against pulloutfrom the soil

The program also makes sure that the force Fi will not exceed the allowable tensilestrength of mesh (the default value for gabions is 40 kN/m) or tensile strength of

georeinforcement RT, respectively. Strength RT is specified per 1m run of a wall (kN/m).

Hint: If a georeinforcement is rigidly fixed to an anchorage block, then the pull-out strength Tp can be assumed as a large number – the georeinforcement bearing capacity is then

controled by the tensile strength RT.

Base anchorageAn anchorage of wall footing can be specified for cantilever walls. It is necessary to specify ananchor location, dimensions of a drill hole, and spacing of anchors.Two limit states of bearing capacity are defined for an anchor – bearing capacity againstpulling-out Re (kN/m) and strength of anchor Rt (kN). Final force is determine asminimum of these forces.

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Base anchorage

Bearing capacities can be either input or computed from the input values using the followingexpressions:

where: Tp - pull-out resistance

d - drill hole diameter

a - ultimate bond

FSp - safety factor against pulling-out

where: RT - strength of anchor

ds - anchor diameter

fy - yield strength of anchor

FST - safety factor against pulling-apart

Approximate values of bearing capacity against pulling-out

Material Ultimatebond

[N/mm2]

Ultimate strength for nominated hole dia [kN/m]

65 mm 75 mm 90 mm 100 mm 150 mm

Soft shale 0,21 - 0,83 42 - 169 49 - 195 59 - 234 65 - 260 98 - 391

Sandstone 0,83 - 1,73 169 - 350 195 - 407 234 - 486 260 - 543 391 - 562

Slate, HardShale

0,86 - 1,38 175 - 281 202 - 325 243 - 390 270 - 433 405 - 562

Soft Limestone 1,00 - 1,52 204 - 310 235 - 358 282 - 429 314 - 477 471 - 562

Granite, Basalt 1,72 - 3,10 351 - 562 405 - 562 486 - 562 540 - 562 562 - 562

Concrete 1,38 - 2,76 281 - 562 325 - 562 390 - 562 433 - 562 562 - 562

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Verification – limit statesAfter computing forces acting on the structure the program determines the overall verticaland horizontal forces Fv and Fh, computes the forces acting in the footing bottom (normal

force N and tangent force T):

Forces acting in the footing bottom

Next the program performs verification for overturning stability and translation. For walls witha flat footing bottom and specified jump it is possible to account for the wall jump either inthe form of pressure acting on the front face or by considering a wall with an inclined footingbottom. Check for overturning stability (the moment rotates around the point B of the wall - seepicture):

where: Movr - overturning moment

s - coefficient of overall stability of structure

Mres - resisting moment

Check for slip:

where: N - normal force acting in the footing bottom

d - design angle of friction structure-soil

cd - design cohesion structure-soil

d - width of wall heel

e - eccentricity


T - tangent force acting in the footing bottom

where eccentricity e:

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N - normal force acting in the footing bottom


Verification - factor of safetyAfter computing forces acting on the structure the program determines the overall verticaland horizontal forces Fv and Fh, computes the forces acting in the footing bottom (normal

force N and tangent force T):

Forces acting at the footing bottom

Next the program performs verification for overturning stability and translation. For walls witha flat footing bottom and specified jump it is possible to account for the wall jump either inthe form of pressure acting on the front facel or by considering a wall with an inclined footingbottom.

Check for overturning stability: (the moment rotates around the point B of the wall - seepicture)



FS - factor of safety against overturning

Check for slip:


- angle of friction soil - structure

c - cohesion structure-soil


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e - eccentricity

- coefficient of overall stability of structure

FS - factor of safety against translation

where eccentricity e:





The "Settings" dialogue window serves to assign the factors of safety FS (standard valuesare set to 1,5).

Accounting for wall jumpTwo options are available to account for the foundation wall jump in the analysis as shown inthe figure.

Options to account for wall jump

If the jump is assumed as an inclined footing bottom, then a new shape of the footingbottom is considered and the structure front face resistance is included only up to a depth ofthe wall front face.If the jump influence is considered as a front face resistance the analysis assumes a flatfooting bottom (as if there was no jump), but the structure front face resistance included upto a depth of jump. In such a case computation of the structure front face resistance mustalso be inputted – otherwise the jump influence is neglected. The jump introduced below the wall foundation is always considered as a structure front faceresistance.

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Assuming wall jump in the middle

Dimensioning of masonry wallReinforced masonry is verified for loading due to bending moment, shear force andcombination of compressive normal force and bending moment. When loading due normalforce is considered, it is necessary to specify also the slenderness ratio Sr.Design for members in compression and bending

where: Fd - the design compression force acting on the cross-section

- the capacity reduction factor - 0,75

ks - a reduction factor taken as 1,18 - 0,03 Sr but not greater than 1,0

f´uc - the characteristic uncofined compressive strength of masonry

f´m - the characteristic compressive strength of masonry

Ab - the bedded area of the masonry cross-section

fsy - the design yield strength of reinforcement

As - the total cross-sectional area of main reinforcement

Design for members in bending

where: Md - the design bending moment acting on the cross-section of member


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Asd - the portion of the cross-sectional area of the main tensilereinforcement used for design purposes in a reinforced masonrymember

the lesser of and Ast

f´m - the characteristic compressive strength of masonry

d - the effective depth of the reinforced masonry member

fuc - the characteristic uncofined compressive strength of masonry

Out-of-plane shear in wallA reinforced wall subject to out-of-plane shear shall be such that:

but not more than:

where: Vd - the design shear force acting on the cross-section of the masonrywall


f´vm - the characteristic shear strength of reinforced masonry - 0,35 Mpa

d - the effective depth of the reinforced masonry wall

fvs - the design shear strength of main reinforcement - 17,5 Mpa


Ast - the cross-sectional area of fully anchored longitudinal reinforcementin the tension zone of the cross-section

Bearing capacity of foundation soilVerification analysis of the bearing capacity of foundation soil takes into account forcesobtained from all already performed verifications of the overall stability of structure (limitstates, factor of safety). To that end, the following relationships are used:



Rd - bearing capacity of foundation soil

e - eccentricity

ealw

- allowable eccentricity

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Wall dimensioningAfter computing forces acting on the structure the program determines all internal forces inthe verified cross-section (normal force N, shear force Q and moment M) and then verifiesthe cross-section bearing capacity employing one of the standards selected in the Frame "Project". Only the forces found above the verified joint (see figure) are assumed for dimensioning.These forces are not multiplied by any design coefficients.

Forces entering the analysis

The front jump of wall as well as the back jusmp of wall is verified against the loadingcaused by the bending moment and shear force. Stress in the footing bottom can be assumedeither constant (CSN) or linear (EC).

Assuming linear variation of stress in the footing bottom the distribution of stress isprovided by:

or when excluding tension:

where: e - eccentricity of normal force N

d - width of wall foundation

N - normal force acting in the footing bottom (see verification accordingto limit states or factor of safety, respectively)

Bending moment and shear force are determined as reaction developed on the cantileverbeam as shown in figure:

Internal forces acting on wall jump

Internal forces corresponding to constant distribution of stress in the cross-section are

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provided by:

where: - maximum stress in the footing bottom

dv - jump length

e - eccentricity of normal force N


N - normal force acting in the footing bottom (see verification accordingto limit states or factor of safety, respectively)

Verification of the back jump of wall (top tensile reinforcement in the wall jump,respectively) is performed only in some countries and usually is not required. The programs"Cantilever wall" and "Reinforced wall" allow in version 5.5 for designing the reinforcement inthe back jump of wall. The cross-section is then assumed to be loaded by the self weight ofstructure, earth wedge, surcharge, anchorage force and the force associated with contactpressure in the soil. Forces due to pressure are accounted for only if having a negativeimpact. Forces introduced by the user are not reflected at all.

The cross-section is checked against the loading caused by the bending moment and shearforce.

Internal stability of gabionThe internal stability of gabion wall can be examined with the help of:

- the theory of limit states

- factor of safety

Verification of joints between individual blocks is performed in the "Dimensioning" dialoguewindow. The structure above the block is loaded by active pressure and corresponding forcesare determined in the same way as for the verification of the entire wall. A loose filling isused in the analysis – not hand-placed rockfill – but its effect can be simulated using a veryhigh angle of internal friction. It can be assumed that after some time due to action of fillingaggregate the stress in meshes will drop down. Individual sections of the gabion wall arechecked for the maximum normal and shear stress. With the help of these variables it ispossible to modify the slope of structure face by creating terraces or by increasing the slopeof face of wall .

Assuming loading applied to the bottom block is schematically represented as:

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Loading on the bottom block

Normal stress in the center of the bottom block is given by:

where: N - normal resultant of loading acting on the bottom block

B - width of upper block

e - eccentricity

M - moment acting on the bottom block

h - height of bottom block

- unit weight of the bottom block material

- gabion slope

Pressure acting on the wall of the bottom block is determined an increased activepressure:

where: d - design angle of internal friction of the bottom block material

cd - design cohesion of the bottom block material

- unit weight of material of the bottom block


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- gabion slope

T - average value of pressure acting on face of the bottom block

- maximal normal stress acting on the bottom block

Widths of meshes of the bottom block per one meter run of the gabion wall are:

where: Dhor - width of upper mesh between blocks loaded in tension

Dcelk - overall width of meshes loaded in compression T

v - spacing of vertical meshes


The program allows for analysis of gabions with both simple and double mesh placed betweenblocks. For double meshes the inputted tensile strength of mesh (the "Edit material"dialogue window) should be twice as large as the value assumed for simple meshes.

Geometry of gabions

Internal stability of gabion wall – limit statesReduced parameters of the gabion material, which depend on the coefficients set in the "Settings" dialogue window, are used in the verification analysis.

a) Check for overturning stability:


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b) Check for slip:

where: N - normal force acting on the upper joint of the bottom block

d - design angle of internal friction of the bottom block material


cd - design cohesion of the bottom block material

Q - shear force

c) Check for bearing capacity with respect to the lateral pressure:

where: T - average value of pressure acting on the face of bottom block

S - force per one meter run joint

Su - joint bearing capacity (for input use the "Material" dialogue window)

b - width = 1m

d) Check for bearing capacity of joint between blocks:

where: Nd - tensile force per one meter run of the upper joint of the bottom block

Nu - strength of mesh (for input use the "Material" dialogue window)

Qtr - shear force transmitted by friction and cohesion between blocks

Kt - coefficient of reduction of friction between blocks (for input use the "Setting" dialogue window – default value is 0,66)

Internal stability of gabion wall – factor of safetyThe following cases are assumed when examining the internal stability of the gabion wallusing the concept of factor of safety:

a) Check for overturning stability:



FSovr - factor of safety against overturning

b) Check for slip:

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c) Check for bearing capacity with respect to the lateral pressure:

where: T - average value of pressure acting on face of the bottom block

S - force per one meter run joint

Su - joint bearing capacity (for input use the "Material" dialogue window)

FSmesh - fac tor of safet y of st ressed mesh (for input use the "Settings"dialogue window – default value is 1.5)

b - width = 1m

d) Check for bearing capacity of joint between blocks:

. .t r tQ k N t g c B where: Nd - tensile force per one meter run of the upper joint

Nu - strength of mesh (for input use the "Material" dialogue window)

FSmesh

- fac tor of safet y of st ressed mesh (for input use the "Settings"dialogue window – default value is 1.5)

Qtr - shear force transmitted by friction and cohesion between blocks

kt - coefficient of reduction of friction between blocks (for input use the "Setting" dialogue window – default value is 0,66)

Calculating abutment forcesOpěraAn abutment is analyzed per 1m (1ft) run. All forces entering the analysis are thereforeadjusted in the program as follows:

the abutment self weight, assumed per 1m (1ft) run, is calculated from the inputtedtransverse cross-section

reactions inserted by the bridge and the approach slab are inputted in kN (kpi)using the values for the whole abutment, these values are in the analysis divided bythe abutment length

soil pressure is determined per 1m (1ft) run and then reduced by the ratio length ofload due to soil / abutment length,

weight of soil wedges is determined per 1m (1ft) run and then reduced by the ratiolength of load due to soil / abutment length,

surcharge is determined per 1m (1ft) run and then reduced by the ratio length ofload due to soil / abutment length,

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inputted forces and front face resistance are assumed per 1m run withoutreduction

wing walls – the wing walls self-weight is computed from their geometry; beforeintroduced in the stem design and foundation verification it is divided by theabutment length (it is the user responsibility to either include or exclude the effectof wing walls in from the analysis).

Computation of individual abutment forces is described in more details in chapter " Wallanalyses".

All forces acting in the foundation joint that are introduced in the verification analysis (exceptfor the front face resistance) are reduced by the ratio abutment length / foundationlength.

Geometriy of bridge abutment

Sheeting designAnalyses in the program "Sheeting design" can be divided into three groups:

- analysis of anchor free walls (e.g. sheet pile wall)

- analysis of anchored walls fixed in heel

- analysis of anchored walls simply supported at heel

Analysis of braced sheeting is also available in the program.

Analysis of sheet pile wallA sheet pile wall is analyzed using standard approach that account for effect of earthpressures (in general, the active earth pressure develops behind the structure while thepassive earth pressure appears in front of the structure).

Based on the theory of limit states the program searches in an iterative way a point on thewall to satisfy the moment equation of equilibrium in the form:

Moverturning = MresistingOnce this is accomplished, the program continues by determining the wall heel location forwhich the equilibrium of shear forces is fulfilled (computation of depth of fixed end). This wayis found the overall length of the analyzed structure.

When applying approach based on the factor of safety the program searches in an iterative

- 368 -


way a point to get:

It is obvious that the distribution of internal forces resulting from this approach is not veryrealistic. In some countries, however, this approach is required.

The computation can be driven either by choosing a minimal dimensioning pressure or byreduction of passive pressure. Assuming the actual magnitude of the passive earth pressureprovides deformations of the analyzed structure, which cannot usually occur. The actualpassive pressure can attain for walls free of deformation the value of pressure at rest as wellas all intermediate values up to the value of passive pressure for fully deformed wall (rotationapp. 10 mRad – i.e. deformation 10 mm per 1m of structure height). Therefore it isreasonable to consider reduced values of the passive earth pressure setting the value of the "Coefficient of reduction of passive pressure" to less than or equal to one. The followingvalues are recommended:

0,67 reduces deformations app. by one half,

0,5 approximately corresponds to deformation of structure loaded by increased active earthpressure,

0,33 approximately corresponds to deformation of structure loaded the pressure at rest,structure reaches app. 20 percent of its original deformations.

Analysis of anchored wall fixed in heelAnchored wall fixed in heel is analyzed as a continuous beam using the deformation variant ofthe finite element method such as to comply with the assumption of heel fixed in the soil. Theactual analysis is preceded by the determination of load due to earth pressure applied to thestructure. The pressure acting on the back of a structure is assumed as active pressure, whilethe front face is loaded by passive pressure.The passive pressure can be reduced with the help of the coefficient of reduction ofpassive pressure. Assuming the actual magnitude of the passive earth pressure providesdeformations of the analyzed structure, which cannot usually occur. The actual passivepressure can attain for walls free of deformation the value of pressure at rest as well as allintermediate values up to the value of passive pressure for fully deformed wall (rotation app. 10 mRad – i.e. deformation 10 mm per 1m of structure height). Therefore it is reasonable toconsider reduced values of the passive earth pressure setting the value of the "Coefficient ofreduction of passive pressure" to less than or equal to one. The following values arerecommended:0,67 reduces deformations app. by one half,

0,33 deformations attain approximately twenty percent of their original values.

The program offers two options to determine active pressure: calculation from inputted soil parameters, water, surcharge, terrain including introduction

of the minimal dimensioning pressure inputting an arbitrary distribution of earth pressure up to the depth of zero point (this way

it is possible to introduce an arbitrary redistribution of earth pressure)Zero-value point, i.e. the point at which the overall pressure equals zero is determined by thefollowing expression:

where: u - depth of zero-value point

a - magnitude of active pressure behind structure at the ditch bottom

K - coefficient of overall pressure

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- unit weight of soil below the ditch bottom

The analysis of structure fixed at heel assumes that the point of zero loading N (at depth u) isidentical with the point of zero moment. For the actual analysis the structure is divided intotwo parts – an upper part (upper beam) up to zero-value point and a lower beam:

Analysis of anchored wall fixed in heel

The upper beam is analyzed first together with evaluation of anchor forces F and the reactionforce R at the zero-value point. Then, the lower beam length x is determined such that themoment equilibrium condition with respect to the heel is satisfied (the beam is loaded by thereaction R and by the difference of earth pressures). To satisfy the shear force equilibrium thecomputed length of fixed end is extended by the value x as shown in figure:

Determination of the extension of the length of wall by x

Analysis of anchored wall simply supported at heelAnchored wall fixed in heel is analyzed as a continuous beam using the deformation variant ofthe finite element method such as to comply with the assumption of simply supportedstructure at heel. The actual analysis is preceded by the determination of load due to earthpressure applied to the structure. The pressure acting on the back of a structure is assumedas active presure, while the front face is loaded by passive pressure.The passive pressure can be reduced with the help of the coefficient of reduction ofpassive pressure. Assuming the actual magnitude of the passive earth pressure providesdeformations of the analyzed structure, which cannot usually occur. The actual passivepressure can attain for walls free of deformation the value of pressure at rest as well as allintermediate values up to the value of passive pressure for fully deformed wall (rotation app. 10 mRad – i.e. deformation 10 mm per 1m of structure height). Therefore it is reasonable to

- 370 -


consider reduced values of the passive earth pressure setting the value of the "Coefficient ofreduction of passive pressure" to less than or equal to one. The following values arerecommended:0,67 reduces deformations app. by one half,

0,33 deformations attain approximately twenty percent of their original values.

The program offers two options to determine active pressure:

- calculation from inputted soil parameters, water, surcharge, terrain including introduction ofthe minimal dimensioning pressure

- inputting an arbitrary distribution of earth pressure up to the depth of zero point (this way itis possible to introduce an arbitrary redistribution of earth pressure).

Zero-value point, i.e. the point at which the overall pressure equals zero is determined by thefollowing expression:

where: u - depth of zero-value point

a - magnitude of active pressure behind structure at the ditch bottom

K - coefficient of overall pressure

- unit weight of soil below the ditch bottom

For simply supported structures it is assumed that the moment and shear force are zero atthe heel. The program first places the end of a structure into the zero-value point, and then itlooks for the end beam location x, where the above condition is fulfilled (see Fig.). Solutionprocedure for multiplied anchored walls is identical.

Analysis of anchored wall simply supported at heel

Sheeting checkThe program evaluates the inputted structure using the method of dependent pressures. Theloading applied to the structure is derived from its deformation, which allows for realisticmodeling of its behavior and provides cost effective designs. The analysis correctly accountsfor the construction process such as individual stages of progressive construction of thewall (stages of constructions) including gradual evolution of deformations andpost-stressing of anchors, makes possible to model braced sheeting.

The use of the method of dependent pressures requires determination of the modulus ofsubsoil reaction, which is assumed either linear or nonlinear.

The program also allows the user to check internal stability of the anchorage system.

The actual analysis is carried out using the deformation variant of the finite element method.

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Displacements, internal forces and the modulus of subsoil reaction are evaluated at individualnodes.

The following procedure for dividing the structure into finite elements is assumed:

first, the nodes are inserted into all topological points of a structure (starting and endpoints, points of location of anchors, points of soil removal, points of changes ofcross-sectional parameters),

based on selected subdivision the program computes the remaining nodes such that allelements attain approximately the same size.

A value of the modulus of subsoil reaction is assigned to each element – it is considered asthe Winkler spring of the elastic subsoil. Supports are placed onto already deformed structure – each support then represents a forced displacement applied to the structure. Anchors, inthe load case at which they were introduced or post-stressed, are considered as forces(variant I in Fig). In other load cases, the anchors are modeled as forces and springs ofstiffness k (variant II. in Fig):

Braced sheeting

The change of anchor force due to deformation is provided by:

where: v - horizontal distance between anchors

w - increment of deformation at the point of anchor application

E - anchor Young’s modulus

A - anchor cross-sectional area

l - anchor length

k - anchor stiffness

- anchor inclination

Method of dependent pressuresThe basic assumption of the method is that the soil or rock in the vicinity of wall behaves asideally elastic-plastic Winkler material. This material is determined by the modulus of subsoil

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reaction kh, which characterizes the deformation in the elastic region and by additionallimiting deformations. When exceeding these deformations the material behaves as ideallyplastic.

The following assumptions are used:

• the pressure acting on a wall may attain an arbitrary value between active and passivepressure – but it cannot fall outside of these bounds,

• the pressure at rest acts on an undeformed structure (w=0).

The pressure acting on a deformed structure is given by:

where: r - pressure at rest

kh - modulus of subsoil reaction

w - deformation of structure

a - active earth pressure

p - passive earth pressure

The computational procedure is as follows:

the modulus of subsoil reaction kh is assigned to all elements and the structure is loadedby the pressure at rest – see figure:

Scheme of structure before first iteration

the analysis is carried out and the condition for allowable magnitudes of pressures actingon the wall is checked. In locations at which these conditions are violated the programassigns the value of kh=0 and the wall is loaded by active or passive pressure,respectively – see figure:

- 373 -


Scheme of structure during the process of iteration

The above iteration procedure continues until all required conditions are satisfied.

In analyses of subsequent stages of construction the program accounts for plasticdeformation of the wall. This is also the reason for specifying individual stages ofconstruction that comply with the actual construction process.

Modulus of subsoil reactionThe following options are available in the program to introduce the modulus of subsoilreactions:

- in the form of distribution (the assumed distribution of the modulus of subsoil reaction infront and behind the structure is inputted)

- as a soil parameter with a respective value (either linear or nonlinear)

- according to Schmitt

- according to CUR166

- according to Ménard

- according to Chadeisson

- iterate using deformation characteristics of soils

The modulus of horizontal reaction of a soil body generally corresponds to spring stiffness inthe Winkler model describing the relation between load applied to a rigid plate and theresulting soil deformation in the form:

where: p - load acting along plate-soil interface

k - stiffness of Winkler spring

y - translation of plate into subsoil

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Definition of the modulus of subsoil reaction

Modulus of subsoil reaction according to CUR 166The following table stores the values of the modulus of subsoil reaction derived fromexperimental measurements carried out in Nederland (described in CUR 166). The table offerssecant modules, which are in the program directly transformed into secant modules of subsoilreaction – see nonlinear modulus of subsoil reaction.

kh,1(kN/m3)p0 < ph< 0,5 ppas

kh,2 (kN/m3)0,5 ppas ≤ ph ≤0,8 ppas

kh,3 (kN/m3)0,5 ppas ≤ ph ≤ 1,0

Sand loosemedium densedense

12000 - 27000

20000 - 45000

40000 - 90000

6000 - 13500

10000 - 22500

20000 - 45000

3000 - 6750

5000 - 11250

10000 - 22500

Claysoftstiffvery stiff

2000 - 4500

4000 - 9000

6000 - 13500

800 - 1800

2000 - 4500

4000 - 9000

500 - 1125

800 - 1800

2000 - 4500

Peatsoftstiff

1000 - 2250

2000 - 4500500 - 1125

800 - 1800

250 - 560

500 - 1125

where: p0 - value of pore pressure at rest in kN/m2

ppas - passive pore pressure in kN/m2

ph - horizontal pressure in kN/m2 corresponding to a given shift of a structure

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Diagram of determination of the modulus of subsoil reaction

Modulus of subsoil reaction according to SchmittThis analysis draws on the relation between oedometric modulus and stiffness of the structureintroduced by Schmitt in Revue Francaise de Géotechnique no71 and 74:

where: EI - structure stiffness

Eoed - oedometric modulus

Modulus of subsoil reaction according to MénardBased on the results from experimental measurements (presiometer) of soil response loadedby rigid plate Ménard derived the following expression:

where: EM - presiometric modulus, if necessary it can be substituted by oedometricmodulus of soil

a - characteristic length depending on a depth of fixed-end structure,according to Ménard assumed at a depth of 2/3 of length of fixed-endstructure below final depth of sheeted ditch

- rheological coefficient of soil

Values of rheological coefficient of soil Clay Silt Sand Gravel

Overconsolidated 1 2/3 1/2 1/3

Normallyconsolidated

2/3 1/2 1/3 1/4

Non-consolidated 1/2 1/2 1/3 1/4

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Modulus of subsoil reaction according to ChadeissonBased on measurements on sheeting structures in different soils and computation of a shift ofstructure needed to mobilize the limit value of passive pressure R. Chadeisson derivedexpression for the determination of the modulus of subsoil reaction in the form:

where: EI - structure stiffness


Kp - coefficient of passive pressure

K0 - coefficient of soil pressure at rest

c´ - effective cohesion

Ap - coefficient of influence of cohesion (1 - 15)

Modulus of subsoil reaction derived from iterationsThe program allows for automatic calculation of the modulus of subsoil reaction fromdeformational characteristics of soil from iteration process. The procedure builds on theassumption that deformation of the elastic subspace characterized by the deformationmodulus Edef [MPa] when changing the stress state associated with the change of earthpressures is the same as deformation of the underground wall.

The goal therefore is to find such values of kh [MN/m3] so that the continuity of deformationsof wall and adjacent soil is maintained. Plastic deformation of structure is notconsidered when performing analysis with kh iteration. This approach is schematicallycleared by computing the modulus of subsoil reaction of the ith segment of wall free of anchor,see figure:

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Determination of modulus of subsoil reaction of ith segment

For change of stress r -the program determines uniform loading ol [MPa] of individual

segments of a structure. Next, the overall change of stress passing the ith segment (i*l [MPa*m]) is computed. This change is caused by additional loading of the soil body due tosegments 1 to n (ol,1 - ol,n). The overall change of stress i is reduced by structural

strength mior,i [MPa]. The new value of the spring stiffness then follows from:

where: Edef - deformation modulus of elastic subspace

ol - uniform load applied to segments of structure

i l - overall change of stress behind ith segment of structure

The change of stress inside the soil body is determined according to Boussinesque. Insertingthe new value of k directly into the next calculation would cause instable iteration – thereforethe value of k that is introduced into the next analysis of the wall is determined from theoriginal value of kp and the new value of kn of the modulus of subsoil reaction.

where: kp - original value of modulus of subsoil reaction

kn - new value of modulus of subsoil reaction

Maximum modulus of the subsoil reaction of the ith layer is limited by the value:

where: Edef,i

- deformation modulus of ith layer

The iterative procedure used when computing the modulus of subsoil reaction is as follows:

1) Determine the matrix of influence values for deriving change of stress in a depth of the soilbody passing the ith segment of a structure due to surcharge caused by the change of stressin other segments.

2) The first approximation of the modulus kh in front of the wall is introduced – a triangular

distribution of values at the wall heel kh = 10 MN/m3 is assumed.

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3) Perform analysis of the wall.

4) Compute new values of kh and determine new values for the next analysis.

5) The dialogue window to check iteration appears and the program resumes till the nextcommand. If the next n iterations are selected, the steps 3 and 4 are repeated n–times toarrive again at the step No. 5. The analysis is terminated in this dialogue window by pressingthe "Stop" button.

This iterative process is controlled by the user – her or she has to decide whether the resultsmake sense.

Verification of internal stability of structureThe internal stability of an anchorage system of sheeting is determined for each layerindependently. The verification analysis determines an anchor force, which equilibrates thesystem of forces acting on a block of soil. The block is outlined by sheeting, terrain, lineconnecting the heel of sheeting with anchor root and by a vertical line passing through thecenter of anchor root and terrain. The analysis is performed per one meter run of a sheetingstructure. Anchor forces are therefore computed with respect to their spacing in individuallayers.

Analysis of internal stability

Scheme for verification of the ith layer of anchors is shown in figure. The force equilibrium forthe block ABCD is being determined. The following forces enter the analysis:

EA - resultant of active earth pressure acting on sheeting (on line AD)

EAi - resultant of active earth pressure above the root of verified anchor (on line BC)

Gi - weight of the soil block ABCD; in addition, this value incorporates the surchargep applied on the ground surface providing the slope q of slip surface AB is greaterthan an average value of the angle of internal friction on this surface; in case of asmaller slope of slip surface AB the ground surchage is not considered

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Ci - resultant of soil cohesion on slip surface AB

Fj, Fk,

…

- forces developed in other anchors; only some of them enter the equilibriumanalysis of the ith layer, whether a given anchor (say the mth one) will enter theequilibrium of the ith block is determined as follows:

from two anchors m, i select the lower one, a plane slip surface, inclinedby 45o-n/2 from a vertical line, is placed in a body such that it passes

through the center of the selected anchor (lines ab and Bc in figure), n isan average value of the angle of internal friction above the root of loweranchor – location of the root of anchor found above the inserted slipsurface is then decisive, if the ith root is found above the mth one and the ith root is located outside the block cut by the slip surface, then the mth

anchor force is included into the analysis and vice versa, figure shows anexample in which the force Fj is included while the force Fk is excluded

from the stability analysis of the ith block

Qi - reaction on slip surface AB

Fi force in the analyzed anchor, the maximum allowable magnitude of this force isthe result of the equilibrium analysis carried out for the ith block

Solution of the equilibrium problem for a given block requires writing down vertical andhorizontal force equations of equilibrium. These represent a system of two equations to besolved for the unknown subsoil reaction Qi and the maximum allowable magnitude of the

anchor force Fi. The stability analysis then provides a factor of safety for each layer of

anchors. The factor of safety for the ith layer of anchors is found as a ratio of the allowableforce in the ith anchor (derived from the equilibrium condition written for the ith block) andthe actual force in the ith anchor.

Braced sheetingWhen analyzing braced sheeting the following approach is adopted to determine earthpressures:

Up to depth of ditch the pressures are determined with respect to one meter run of thestructure width. Below the ditch bottom the earth pressures are multiplied by the coefficientof reduction k (the "Coeff. of reduction of pressures below ditch bottom" – can beinputted in the frame "Geometry" as a parameter of the section of a structure) – thepressures are determined with respect to a reduced structure width k*b. In case of continuouswall the coefficient is set to one and no reduction of pressures is assumed. If "Landing ofsoil" above the ditch ("Excavation" dialog window) is inputted, then the pressures withinthis section are computed with respect to the whole width of wall (k=1).

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Braced sheeting

The coefficient k can be approximatelly determined (for safer design) according to:

where: m - longitudinal spacing of soldierbeams

t - width of soldier beam

Nonlinear modulus of subsoil reactionNonlinear model describes dependence of the modulus of subsoil reaction kh – i.e. change of kh in between the threshold values corresponding to failure due to passive earth pressure Tpand active earth pressure Ta – see figure (the modulus of subsoil reaction is given by slope ofthe curve; for pore pressure at rest acting on a structure it is possible to consider the valueof kh1). This model also accounts for spring supports and forced deflections of the structure,various boundary conditions, application of struts and anchors, etc.

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Interaction model to determine kh

The values of the modulus of subsoil reaction can be derived subsequently from the values ofsecant modules of subsoil reaction (CUR 166) – see figure:

Interaction model to determine kh - CUR 166

Slope stability analysisThe slope stability problem is solved in a two dimensional environment. The soil in a slopebody can be found below the ground water table, water can also exceed the slope ground,which can be either partially or completely flooded. The slope can be loaded by a surcharge ofa general shape either on the ground or inside the soil body. The analysis allows for includingthe effect of anchors expected to support the slope or for introduction of horizontal reinforcingelements – geo-reinforcements. An earthquake can also be accounted for in the analysis.

Two types of approaches to the stability analysis are implemented in the program – classicalanalysis according to the factor of safety and the analysis following the theory of limit states.The slip surface can be modeled in two different ways. Either as a circular one, then theuser may choose either from the Bishop or the Petterson method, or as a polygonal one, inwhich case the program exploits the Sarma method.

Soil bodyThe soil body is formed by a layered profile. An arbitrary number of layers can be used.

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Each layer is defined by its geometry and material. The material of a layer is usuallyrepresented by a soil with specified properties. The geostatic stress in a soil body isdetermined during the analysis.

A layer can be specified also as a rigid body. Such layer then represents bedrock or asheeting wall. The slip surface can never pass through the rigid body. When the Sarmamethod is employed, it is not possible to specify a point of a slip surface below the rigid body– in such a case the program prompts an error message.

Influence of waterGround water can be assigned to the slope plane section using one of the four options:1. Ground water tableThe ground water table is specified as a polygon. It can be arbitrarily curved, placed totallywithin the soil body or introduced partially above the ground surface.When using the circular slip surface the water influence is accounted for through the porepressure acting within a soil and reducing its shear bearing capacity. The pore pressure isconsidered as the hydrostatic pressure. Assuming inclined slip surface the pore pressure isdetermined by taking into account the actual shape of phreatic line. Below the ground watertable the analysis proceeds using the unit weight of saturated soil sat and uplift pressure;

above the ground water table the analysis assumes the inputted unit weight of soil . Theshear forces along the slip surface are provided by:

where: T - shear force along slip surface segment

N - normal force along slip surface segment

U - pore pressure resultant along slip surface segment

- angle of internal friction

c - cohesion

d - length of slip surface segment

When selecting the polygonal slip surface the unit weight of soil under water su is considered

and the corresponding equations of equilibrium are modified by adding the flow pressure Jwritten as:

where: A - block area


- inclination of section along given block

2. Ground water table including suctionSuction table can be introduced above the inputted ground water table. A negative value ofpore pressure U is then assumed with the region separated by the two tables. Suctionincreases as negative hydrostatic pressure from the ground water table towards the suctiontable.3. Coefficient of pore pressure ruThe coefficient of pore pressure ru represents the ratio between the pore pressure and

hydrostatic pressure in a soil body. The inputted unit weight of soil is used within the entireslope regardless of the magnitudes of inputted coefficients ru. ..

The values of ru are introduced with the help of isolines connecting points with the same

value of ru. Linear interpolation is assumed to obtain intermediate values. Computation ofshear forces is then influenced in the following way:

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where: T - shear force along slip surface segment

N - normal force along slip surface segment

G - resultant of geostatic stress along slip surface segment


c - cohesion

d - length of slip surface segment

4. Pore pressure valuesGround water can be introduced directly through the pore pressure values with the planesection of a soil body. The inputted unit weight of soil is used within the entire slope regardless of the magnitudesof inputted pore pressure values. The pore pressure values are introduced with the help of isolines connecting points with thesame value of pore pressure. Linear interpolation is assumed to obtain intermediate values.The magnitudes of resultants of pore pressure are then derived from the values of porepressure obtained in specific points within the slope plane section.

SurchargeThe slope stability analysis takes into account even the surcharge caused by neighboringstructures. The surcharge can be introduced either as a concentrated force or distributed loadacting either on the ground surface or inside the soil body.

Since it is usually assumed that the surcharge is caused by the weight of objects found on theslope body, the vertical component of surcharge having the direction of weight is added tothe weight of blocks (slices). It means that if the earthquake effects are included thiscomponent is also multiplied by the factor of horizontal acceleration or vertical earthquake.The components that do not act in the direction of weight are assumed in equations ofequilibrium written for a given block (slice) as weightless thus do not contribute to inertiaeffects of the earthquake.

The surcharge is always considered in the analysis with respect to one meter run. Providingthe surcharge, essentially acting over the area b x l, is introduced as a concentrated force it istransformed before running the analysis into a surface loading spread up to a depth of slipsurface along the slope 2:1 as displayed in figure.

Scheme of spreading the concentrated load on the slip surface

The analysis then proceeds with the resultant of surface load p having the value:

AnchorsAnchor is specified by two points and a force. The first point is always located on the ground

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surface; the force always acts in the direction of a soil body. The anchor force whencomputing equilibrium on a given block (slice) is added to the weightless surcharge of theslope.

Two options are available to account for anchors:

Compute anchor forces – analysis assumes infinite lengths of anchors (anchors arealways included in the analysis) and computes the required lengths of links anchors(distance between the anchor head and intersection of anchor with the slip surface)subsequently. The anchor root is then placed behind the slip surface. This approach isused whenever we wish the anchor to be always active and thus contribute to increasethe slope stability and we need to know its minimum distance.

Analysis with specified lengths of anchors – the analysis takes into account onlythose anchors that have their end points (center of roots) behind the slip surface. Thisapproach is used always whenever we wish to evaluate the current state of slope withalready existing anchors, since it may happen that some of the anchors may prove tobe short to intersect the critical slip surface so that they do not contribute to increasethe slope stability.

GeoreinforcementsGeoreinforcements are horizontal reinforcing elements placed in a soil body, which contributeto increase the slope stability through their tensile strength. They have their exact location,length and allowable tensile force. Providing a georeinforcement intersects the slip surfacethe equations of equilibrium written for a given slice are modified by including the forceacting in the georeinforcement. No action is taken otherwise.

Scheme to account for georeinforcements

Forces due to anchorage assume the form:

where: li - length of mesh behind the slip surface to soil mass

Tpi - strength of one meter run of georeinforcement againts pull-out

The program further ensures the condition that the force Fi cannot exceed the maximumstrength of the georeinforcement RT.

Earthquake effectThe program allows for computing the earthquake effects with the help of two variables –factor of horizontal acceleration Kh or the coefficient of vertical earthquake Kv.

Coefficient of vertical earthquake Kv

The coefficient of vertical earthquake either increases (Kv > 0) or decreases (Kv < 0) the unit

weight of a soil, water in a soil and surcharge by multiplying the respective values by 1+Kv. It

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is worth to note that the coefficient Kv may receive both positive and negative value and in

case of sufficiently large coefficient of horizontal acceleration the slope relieve (Kv < 0) ismore unfavorable than the surcharge.Factor of horizontal acceleration KhIn a general case the computation is carried out assuming a zero value of the factor Kh. Thisconstant, however, can be exploited to simulate the effect of earthquake by setting anon-zero value. This value represents a ratio between horizontal and gravity accelerations.Increasing the factor Kh results in a corresponding decrease of the factor of safety FS. Thecoefficient of horizontal acceleration introduces into the analysis an additional horizontal forceacting in the center of gravity of a respective slice with the magnitude Kh*Wi, where Wi is theslice overall weight including the gravity component of the slope surcharge.The following table lists the values of the factor Kh that correspond to different degrees ofearthquake based on M-C-S scale.

M-C-S degree Horizontal acceleration Factor of horizontalacceleration

(MSK-64) [mm/s2] Kh

1 0,0 - 2,5 0,0 - 0.00025

2 2,5 - 5,0 0,00025 - 0.0005

3 5,0 - 10,0 0,0005 - 0.001

4 10,0 - 25,0 0,001 - 0.0025

5 25,0 - 50,0 0,0025 - 0.005

6 50,0 - 100,0 0,005 - 0.01

7 100,0 - 250,0 0,01 - 0.025

8 250,0 - 500,0 0,025 - 0.05

9 500,0 - 1000,0 0,05 - 0.1

10 1000,0 - 2500,0 0,1 - 0.25

11 2500,0 - 5000,0 0,25 - 0.5

12 > 5000,0 > 0.5

Analysis according to the theory of limit states / factor ofsafetyThe verification analysis can be carried out according to the theory of limit states:




Soil parameteres (angle of internal friction, cohesion) are in this case reduced using thedesign coefficients introduced in the frame "Settings".When selecting the Sarma method (polygonal slip surface) the program computes the valueof utilization Vu, which is then compared with the value of 100%. The value of utilization isgiven by:

where: FS - factor of slope stability computed with reduced soil parameters

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The second option offers the verification analysis using the factor of safety:



FS - factor of safety for overturning

When using the Sarma method (polygonal slip surface) the factor of safety FS is computeddirectly. Verification formula than receives the form:

where: FS - computed factor of safety

FS - required factor of safety

Polygonal slip surface - SarmaThe Sarma method falls within a category of general sliced methods of limit states. It isbased on fulfilling the force and moment equilibrium conditions on individual slices. The slicesare created by dividing the soil region above the potential slip surface by planes, which mayin general experience a different inclination. Forces acting on individual slices are displayed infigure.

Static scheme – Sarma method

Here, Ei , Xi represent the normal and shear forces between slices. Ni ,Ti are normal and

shear forces on segments of a slip surface. Wi is the slice weight and K*Wi is the horizontalforce that is used to achieve in the Sarma method the limit state. Generally inclinedsurcharge can be introduced in each block. This surcharge is included in the analysis togetherwith the surcharge due to water having a free water table above the terrain, with forces inanchors. All these forces are projected along the horizontal and vertical directions, which arethen summed up into components Fxi and Fyi*K is a constant named the factor of horizontalacceleration and is introduced into the analysis in order to satisfy the equilibrium onindividual slices. There is a relationship between K and the factor of slope stability FS allowing for its computation. In ordinary cases the analysis proceeds with the value of K

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equal to zero. A non-zero value of K is used to simulate the horizontal surcharge, e.g. due toearthquake (see below).Analysis processComputation of limit equilibriumThe computation of limit equilibrium requires the solution of 6n-1 unknowns, where n standsfor the number of slices dividing the soil region above the potential slip surface. These are:

E - forces developed between slices

N - normal forces acting on slip surface

T - shear forces acting on a slip surface

X - shear forces developed between slices

z - locations of points of applications of forces

li - locations of points of applications of forces

K - factor of horizontal acceleration

5n-1 equations are available for the required unknowns. In particular, we have:a) horizontal force equations of equilibrium on slices:

b) vertical force equations of equilibrium on slices:

c) moment equations of equilibrium on slices:

where rxi and ryi are arms of forces Fxi and Fyd) relationship between the normal and shear forces according to the Mohr-Coulomb theory:

It is evident that n-1 must be selected (estimated) a priory. Relatively small error is receivedwhen estimating the points of application of forces Ei. The problem then becomes staticallydetermined. Solving the resulting system of equations finally provides the values of allremaining unknowns. The principal result of this analysis is the determination of the factor ofhorizontal acceleration K.Computation of factor of slope stability FSThe factor of slope stability FS is introduced in the analysis such as to reduce the soil strength

parameters c and tg. Equilibrium analysis is then performed for the reduced parameters toarrive at the factor of horizontal acceleration K pertinent to a given factor of slope stability FS. This iteration is repeated until the factor K reaches either zero or a specified value.Influence of external loadingThe analyzed slope can be loaded on its ground by inclined loading having general trapezoidalshape. This loading enters the analysis such that its vertical component (if having thedirection of weight) is added to the weight of a corresponding slice. This results in change ofboth the slice weight and its center of gravity. Providing the vertical component acts againstthe direction of gravity it is added to force Fyi. The horizontal component is added to force Fxi.The load centroid is always assumed on the ground.

Optimization of polygonal slip surfaceThe slip surface optimization proceeds such that the program changes subsequently locations

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of individual points of this surface and checks, which change of location of a given pointresults in the maximal reduction of the factor of slope stability FS. The end points of theoptimized slip surface are moved on the ground surface, internal points are moved in thevertical and horizontal directions. The step size is initially selected as one tenth of thesmallest distance of neighboring points along the slip surface. With every new run the stepsize is reduced by one half. Location of points of slip surface is optimized subsequently fromthe left to the right and it is completed when there was no point moved in the last run.

When optimizing the polygonal slip surface the iteration process may suffer from falling intothe local minimum (with respect to gradual evolution of locations of nodal points) so notalways the process is terminated by locating the critical slip surface. Especially in case ofcomplex slope profile it is therefore advantageous to introduce several locations of the initialslip surface. Combination with the approach used for circular slip surfaces is alsorecommended. Therefore, the critical slip surface assuming circular shape is found first andthe result is then used to define the initial polygonal slip surface.

The optimization process can be restricted by various constraints. This becomesadvantageous especially if we wish the searched slip to pass through a certain region or tobypass this region. The restriction on optimization process can be performed in two differentways:

1. Optimization constrains are specified as a set of segments in a soil body. Theoptimized slip surface is then forced to bypass these segments during optimization.

2. Another way of constraining the optimization process is to fix location of selectedpoints along the optimized slip surface or allow for moving these point only in oneof two directions, either vertically or horizontally.

Changing inclination of dividing planesIt is evident from figure that the planes dividing individual slices do not have to be verticaland not even mutually parallel. In the first stage of analysis when the optimization proceduremoves points along the slip surface assumes vertical alignment of dividing planes. To arriveat even smaller value of the slope stability it is possible to change the mutual alignment ofdividing planes. This process is again performed in several runs with limited value of rotationstep and this step is again reduced in the course of optimization. This stage of optimization isterminated once the rotation step drops below the value of 1o and no change of rotationoccurred during the last optimization run.

Static scheme – Sarma method

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FoliationSoils can be introduced with foliation. It means that along an angle specified in terms of acertain interval, which in turn is introduced as one of the soil parameters <Starting Slope ;End Slope> the soil experiences significantly different (usually worth) parameters (c a ).

If the slope of a slip surface segment or the slope of interface between blocks is assumedwithin the interval <Starting Slope ; End Slope>, the analysis proceeds with the modifiedparameters of c and .

Circular slip surface - Petterson, BishopThe Bishop method is one of the classical methods based on the theory of limit states. Itdraws on the assumption of circular slip surface. The method is based on fulfilling themoment equation of equilibrium and the force equation of equilibrium written in verticaldirection. Planes dividing the region above the circular slip surface are always vertical. Forcesacting on a given slice are plotted in figure.

Static scheme - Bishop method

Here, Xi are the shear forces acting between individual slices, Ni are normal forces on

individual segments the slip surface. Wi are weights of individual slices.

The Bishop method builds on the Petterson method, in which the factor of slope stability Fs isderived from:

where: ui - pore pressure within slice

ci,i - effective values of soil parameters

In addition, the Bishop method satisfies also the vertical equation of equilibrium.

It serves to determine the normal force acting on the slip surface:

Introducing this expression into equation due to Petterson provides more accurate expressionfor the determination of the factor of safety FS:

- 390 -


In the Bishop method the difference between forces Xi –Xi+1 is neglected as it does notsignificantly affect the result. The resulting expression for the evaluation of the factor ofsafety assumes the form:

Ground water specified within the slope body (using one of the four options) influences theanalysis in two different ways. First when computing the weight of a soil block and secondwhen determining the shear forces. Note that the effective soil parameters are used to relatethe normal and shear forces.

Introducing anchor forces and water above the ground surface into the analysis

Anchor forces are considered as external loading applied to the slope. They are taken withrespect to one meter run [kN/m] and introduced into the moment equation of equilibrium.These forces should contribute to additional stability, if that cannot be achieved in a differentway. There is no limitation to the magnitudes of anchor forces and therefore it is necessary towork with realistic values.

Influence of water above the ground surface is considered as a set forces acting on theground surface together with pore pressure along the slip surface, which is derived dependingon the depth of slip surface measured from the ground water table. The forces acting on theground surface enter the moment equation of equilibrium as forces acting on respective armsmeasured towards the center of the slip surface.

The factor of safety FS is determined through the already introduced iteration process.

Optimization of circular slip surfaceThe goal of the optimization process is to locate a slip surface with the smallest factor ofslope stability FS. The circular slip surface is specified in terms of 3 points: two points on theground surface and one inside the soil body. Each point on the surface has one degree offreedom while the internal point has two degrees of freedom. The slip surface is defined interms of four independent parameters. Searching for such a set of parameters that yields themost critical results requires sensitivity analysis resulting in a matrix of changes ofparameters that allows for fast and reliable optimization procedure. The slip surface thatgives the smallest factor of slope stability is taken as the critical one.

This approach usually succeeds in finding the critical slip surface without encountering theproblem of falling into a local minimum during iteration. It therefore appears as a suitablestarting point when optimizing general slip surfaces such as the polygonal slip surface.

The optimization process can be restricted by various constraints. This becomesadvantageous especially if we wish the searched slip surface to pass through a certain regionor to bypass this region. Optimization constrains are specified as a set of segments in a soilbody. The optimized slip surface is then forced to bypass these segments during optimization.

Influence of tensile cracksThe program makes possible to account for the influence of tensile that appear on terrainsurface and are filled with water h. The only input parameter is the depth of tensile cracks.The effect of cracks is incorporated when calculating normal and shear forces in sections of aslip surface containing cracks – in a section with tensile cracks the shear strength parametersare set to zero (c = 0, ϕ = 0). Next, a horizontal force F due to presence water in a tensile

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crack is introduced in the analysis (see figure):

Vliv tahových trhlin

Analysis of bearing capacity of foundationThe vertical bearing capacity of foundation soil is verified according to the theory of limitstates using the following inequality:

or based on the factor of safety as:

where: - extreme design contact stress in the footing bottom

Rd - design bearing capacity of foundation soil

RV - coefficient of vertical bearing capacity of foundation (for input use theframe "Settings")

FS - inputted factor of safety

Extreme design contact stress in the footing bottom is assumed the form:

where: Vde - extreme design vertical force

Aef - effective area of foundation

The vertical bearing capacity of foundation soil Rd is determined for three basic types offoundation conditions:- drained subsoil- undrained subsoil- bedrock

The above computations are applicable only for the homogeneous soil. If there is anon-homogeneous soil under the footing bottom (or there is ground water present), then theinserted profile is transformed into a homogeneous one.

Bearing capacity on drained subsoilOne of the following approaches is available to assess the horizontal bearing capacity of afoundation if drained conditions are assumed:- standard analysis

- according to CSN 731001 "Základová půda pod plošnými základy" approved 8.6. 1987

- according to Polish standard PN-81 B - 03020 "Grunty budowiane, Posudowienie

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bezpošrednie budowli, Obliczenia statyczne i projekktowanie" from year 1982

- according to Indian standard IS:6403-1981 "Code of Practice for Determination of BearingCapacity of Shallow Foundations" from year 1981

- according to EC 7-1 (EN 1997-1:2003) "Design of geotechnical structures – Part 1: Generalrules"

- according to NCMA Segmental retaining walls manual, second edition.

All approaches incorporate coefficients due to Brinch – Hansen (see standard analysis) toaccount for inclined ground surface and inclined footing bottom.

Assuming drained conditions during construction the soil below spread footing deformsincluding both shear and volumetric deformations. In such a case the strength of soil isassumed in terms of effective values of the angle of internal friction ef and the effective

cohesion cef. It is also assumed that there is an effective stress in the soil equal to the total

stress (consolidated state). Effective parameters ef , cef represent the peak strengthparameters.

Owing to the fact that the choice of drained conditions depends on a number of factors (rateof loading, soil permeability, degree of saturations and degree of overconsolidation) it is thedesigner's responsibility to decide, depending on the actual problem being solved, if theeffective parameters should be used.

Standard analysis of bearing capacity of foundation ondrained subsoilBy default the solution proposed by J. Brinch – Hansena is used, where the bearing capacityof foundation soil follows from:

where:

coefficients of bearing capacity:for: > 0

for: = 0

coefficients of shape of foundation:

coefficients of influence of depth of foundation:

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coefficients of slope of loading:

coefficients of slope of footing bottom:

coefficients of influence of slope of terrain:

Notation of angels and coefficients b,g

where: c - cohesion of soil

q0 - equivalent uniform loading accounting for the influence offoundation depth

d - depth of footing bottom

- unit weight of soil above the footing bottom

b - width of foundation

- objemová tíha zeminy

Nc,Nd,Nb - coefficient of bearing capacity

sc,sd,sb - coefficients of shape of foundation

dc,dd,db - coefficients of influence of depth of foundation

ic,id,ib - coefficients of influence of slope of loading

gc,gd,gb - coefficients of influence of slope of terrain


l - length of foundation

- angle of deviation of the resultant force from the verticaldirection

- slope of terrain

- slope of footing bottom

Bearing capacity on undrained subsoilOne of the following approaches is available to assess the horizontal bearing capacity of afoundation if undrained conditions are assumed:

- standard analysis

- according to CSN 731001 "Základová půda pod plošnými základy" approved 8.6. 1987

- according to Indian standard IS:6403-1981 "Code of Practice for Determination of Bearing

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Capacity of Shallow Foundations" from year 1981

- according to EC 7-1 (EN 1997-1:2003) "Design of geotechnical structures – Part 1: Generalrules"

In addition the coefficients due to Brinch – Hansen are used to account for inclined footingbottom (see standard analysis).

In case of undrained conditions it is assumed that during construction the spread footingundergoes an instantaneous settlement accompanied by shear deformations of soil in absenceof volumetric changes. When the structure is completed the soil experiences both primaryand secondary consolidation accompanied by volumetric changes. The influence of neutralstress appears in the reduction of soil strength. The strength of soil is then presented interms of total values of the angle of internal friction u and the total cohesion cu (theseparameters can be considered as the minimal ones). Depending on the degree ofconsolidation the value of the total angle of internal friction u ranges from 0 toef, the total

cohesion cu is greater than cef. Owing to the fact that the choice of undrained conditionsdepends on a number of factors (rate of loading, soil permeability, degree of saturations anddegree of overconsolidation) it is the designer's responsibility to decide, depending on theactual problem being solved, if the effective parameters should be used. Nevertheless, thetotal parameters are generally used for fine-grained soil.

Standard analysis of bearing capacity of foundation onundrained subsoilThe following formula is used by default:

with dimensionless coefficients:

where: cu - total cohesion of soil


l - length of foundation

d - depth of foundation

- angle of deviation of the resultant force from the verticaldirection

- slope of footing bottom from horizontal direction

Bearing capacity of foundation on bedrockThe following methods can be used to compute the design bearing capacity Rd of foundationwith a horizontal footing bottom providing the rock mass composed of rocks or weak rocks:

Standard approach

Solution according to CSN 73 1001

Solution according to EC7

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Standard analysis of bearing capacity of foundation onbedrockThe bearing capacity of foundation soil composed of rocks or weak rocks is found from the

expression proposed by Xiao-Li Yang and Jian-Hua Yin1:

where:

where: s - nonlinear parameter depending on rock properties (according toHoek and Brown)

GSI - Geological Strength Index

D - coefficient reflecting damage of a rock mass

Ns,Nq,N

- coefficients of bearing capacity depending on the angle of internalfriction

Ns - coefficient of strength of a rock depending on GSI and strengthparameter mi

- angle of internal friction of rock

c - uniaxial compressive strength of rock > 0,5 MPa

q0 - equivalent uniform loading accounting for the influence offoundation depth

- unit weight of soil above the footing bottom


1 Xiao-Li Yang, Jian-Hua Yin: Upper bound solution for ultimate bearing capacity with amodified Hoek–Brown failure criterion, International Journal of Rock Mechanics & MiningSciences 42 (2005),str. 550–560

Analysis of bearing capacity of foundation on bedrockaccording to CSN 73 1001The bearing capacity of foundation soil composed of rocks or weak rocks follows from articles97 – 99 of standard CSN 73 1001 "Foundation soil below spread footing" approved 8.6.1987.As input parameters the analysis requires the unit weight of soil , uniaxial compressionstrength c, Poisson's ratio and deformation modulus Edef.

Analysis of bearing capacity of foundation on bedrockaccording to EC 7-1The bearing capacity of the foundation Rd with a horizontal footing bottom is determined

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according to a design method for the derivation of expected bearing capacity of spreadfootings resting on a bedrock outlined in a supplement G (informative) EC 7-1 (EN1997-1:2003) "Design of geotechnical structures – Part 1: General rules". For low strength ordamaged rocks with closed discontinuities including chalks with low porosity less than 35%the derivation of expected bearing capacity follows classification of rocks into groups of rocksstored in the table below. The analysis further requires an input of discontinuity spacing Sd,

unit weight of rock , Poisson's ratio and uniaxial compressive strength c. It is assumed

that the structure is able to transmit a settlement equal to 0,5 % of the foundation width.The expected values of bearing capacity for other settlements can be estimated using directproportion. For weak and broken rocks with opened or filled discontinuities it is recommendedto use lower values than the expected ones.

Rock groups

Group Type of rock

1 Pure limestones and dolomites

Carbonate sandstones of low porosity

2 Igneous

Oolitic and marly limestones

Well cemented sandstones

Indurated carbonate mudstones

Metamorphic rocks, including slates and schist (flatcleavage / foliation)

3 Very marly limestones

Poorly cemented sandstones

Slates and schist (steep cleavage / foliation)

4 Uncemented mudstones and shales

Parameters to compute foundation bearing capacityParameters to compute vertical bearing capacity of a fondation resting on bedrock

The following parameters are used in program GEO5 to compute the foundation verticalbearing capacity:- values of coefficient D reflecting a state of damage of a rock mass- values of strength parameter mi

- strength of rocks in simple compression c- Poisson's ration of rocks - bulk weight of rocks Estimating disturbance coefficient D

Description of rock mass Suggested value of D

Rock mass, intact strong rock, excavation by blasting or by open TBM

0

Rock mass, poor quality rock, mechanicalexcavation with minimal disturbance

0

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Rock mass, poor rock, mechanical excavation,significant floor heave, temporary invert orhorizontal geometry of excavation sequence

0,5

Rock mass,very poor rock often very altered,rock very , local damage of surrounding rock(app. 3 m )

0,8

Rock slope or rock outcrop, modification with controled blasting

0,7

Rock slope or rock outcrop, modification withblasting results to the some disturbance

1,0

Open pit mines, excavatin with blasting 1,0

Open pit mines, mechanical excavation 0,7

Values of strength parameter mi

Type of rock Representatiiv rocks mi [-]

Carbonate rocks with welldeveloped cleavage

Dolomite, limestone andmarble

Lithified argillaceous rocks Mudstone, siltsone shale,slate

Arenaceous rock withstrong crystal and poorlydeveloped crystal cleavage

Sandstone and qurtzite

Fine grained polyminerallicigneous crystalline rocks

Andesite, dolerite, diabase,ryolite

Coarse grainedpolyminerallic igneous andmetamorphic rocks

Amphibolite, gabbro,gneiss, granite and quartzdiorite

Uniaxial compressive strength c , Poisson number and Unit weight of rock

Strengthof rocks

Types of rock (examples) Uniaxialcompr.

strength

c

[MPa]

Poissonnumber

Unit weight of rock

[kN/m3]0

Extremlyhardrock

Very hard, intact rock strongand solid quartzite, basaltand other extremely hardrock

>150 0,1 28,00 - 30,00

Veryhardrock

Very hard granite, quartzporphyry, quartz slate, veryhard sandstones andlimestones

100 -150

0,15 26,00 - 27,00

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Hardrock

Solid and compact granite,very hard sandstone andlimestone, silicious iron veis,hard pudding stones, veryhard iron ores hard calcite,not very hard granite, hardsandstone, marble,dolomite, pyrite

80 - 100 0,20 25,00 - 26,00

Fairlyhardrock

Normal sandstone, mediumhard iron ore, sandy shale,flagstone

50 - 80 0,25 24,00

Mediumhardrock

Hard mudstones, not veryhard sandstones and calcite,soft flagstone, not very hardshales, dense marl

20 - 50 0,25 –0,30

23 - 24,00

Fairlyweakrock

Soft schist, soft limestones,chalk, rock salt, frost soils,anthracite, normal marl,disturbed sandstones, softflagstones and soils withaggregates

5 - 20 0,3 –0,35

22,00 – 26,00

Weakrock

Compact clay, hard soil(eluvium with soil texture)

0,5 - 5 0,35 –0,40

22,00 - 18,0

Horizontal bearing capacity of foundationThe foundation horizontal bearing capacity is verified according to the theory of limit statesusing the following inequality:

or based on the factor of safety as:

where:

where: d - angle of internal friction between foundation and soil

ad - cohesion between foundation and soil

Aef - effective area of foundation

Spd - earth resistance

Hx,Hy - components of horizontal force

Q - extreme design vertical force

RH - coefficient of horizontal bearing capacity of foundation (for input usethe frame "Settings"

FS - factor of safety

The analysis depends on the design angle of internal friction below the footing bottom d, the

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design value of cohesion below the footing bottom cd and the design value of earth resistance

Spd. If the soil-footing frictional angle and the soil-footing cohesion are less than the valuesof soil below the footing bottom, then it is necessary to use those values.

The earth resistance is assumed as displayed in figure:

Earth resistance

The earth resistance Spd is found with the help of the reduction of passive earth pressure orpressure at rest employing influence coefficients:

where: Sp - passive earth pressure, pressure at rest or reduced passive pressure

mR - coefficient of reduction of earth resistance (for input used the frame "Settings") - for the analysis according to CSN it assumes the value mR

= 1,5 for passive pressure, mR = 1,3 for pressure at rest

Coefficients of earth pressures are found from the following formulas:for passive pressure:

for pressure at rest in drained soils:

for pressure at rest in other soils:

When determining the reduced passive pressure, the resultant force includes contributionsdue to the passive pressure and pressure at rest.The passive pressure can be considered, if the deformation needed for its activation do notcause unallowable stresses or deformations in upper structure.

Homogenization of layered subsoilIf the soil below the footing bottom is inhomogeneous (or if there is ground water present)then the inputted profile is transformed into a homogeneous soil based on the Prandtl slipsurface (see Fig.), which represents the type and location of failure of the foundation.

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The Prandtl slip surface

Determination of equivalent values of (angle of internal friction), c (cohesion of soil) (unitweight of soil below footing bottom) is evident from the following and subsequent formulas.The unit weight of soil above foundation is derived in the same way.

Procedure for computation of auxiliary values

Effective areaWhen solving the problem of eccentrically loaded foundations the program GEO5 offers twooptions to deal with an effective dimension of the foundation area:

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a rectangular shape of effective area is assumed

general shape of effective area is assumed

Rectangular shape

A simplified solution is used in such cases. In case of axial eccentricity (bending moment actsin one plane only) the analysis assumes a uniform distribution of contact stress appliedonly over a portion of the foundation l1, which is less by twice the eccentricity e compared to

the total length l.

Determination of effective area in case of axial eccentricity

An effective area (b * l1) is assumed to compute the contact stress, so that we have:

In case of a general eccentric loading (foundation is loaded by the vertical force V and bybending moments M1 and M2 the loading is replaced by a single force with giveneccentricities:

The size of effective area follows from the condition that the force V must act eccentrically:

General shape of contact stress

In case of an eccentric loading the effective area is determined from the assumption that theresultant force V must act in the center of gravity of the compressive area. The theoreticallycorrect solution appears in Fig.

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Determination of contact stress for general eccentricity – general shape

Owing to a considerable complexity in determining the exact location of the neutral axis,which in turn is decisive when computing the effective area, the program GEO 5 follows thesolution proposed by Highter a Anders1), where the effective areas are derived with help ofgraphs.

1)Highter, W.H. – Anders,J.C.: Dimensioning Footings Subjected to Eccentric Loads Journal ofGeotechnical Engineering. ASCE, Vol. 111, No GT5, pp 659 - 665

Determination of cross-sectional internal forcesLongitudinal reinforcement of a foundation is checked for the loading due to bendingmoment and shear force. The stress in the footing bottom is assumed either as uniform(CSN) or linear (EC). Stresses in individual directions x, y are determined independently.

When the linear distribution of stress in the footing bottom is considered the distributionof stress over the cross-section is provided by:

or when excluding tension:

where: e - eccentricity of normal force Nd - width of foundation


Bending moment and shear force are determined as reaction developed on the cantileverbeam as shown in figure:

Internal forces acting on wall jump

Internal forces in the cross-section corresponding to constant distribution of stress areprovided by:

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where: - maximal stress in the footing bottom

dv - length of jump

e - eccentricity of normal force N



Pile analysisAnalyses available in the program " Pile" can be divided into three main groups:

- analysis of vertical bearing capacity according to CSN- analysis of vertical bearing capacity using the finite element method- analysis of horizontal bearing capacity of a pile

Vertical bearing capacity – analysis according to CSNThere are three methods implemented in the program to compute the vertical bearingcapacity of a pile following the Commentary to the standard CSN 73 1002 "Pilotové základy":

- analysis according to the theory of the 1st group of limit states

The solution procedure is described in the Commentary to the standard CSN 73 1002"Pilotové základy" in Chapter 3 "Design" part B – general solution according to the theory ofthe 1st group of limit states (pp. 15). All computational approaches are based on formulaspresented therein. The original geostatic stress or is assumed from the finished grade. The

coefficient of conditions of the behavior of foundation soil is considered for the depth z(measured from the finished grade).

The effective pile length used for the computation of skin bearing capacity is reduced by asegment:

where: d - pile diameter

- analysis of pile driven into compressible subsoil – limit loading curve

The solution procedure for the computation of limit loading curve is based on part G –Analysis of vertical bearing capacity Uvd according to CSN 73 1004 - Commentary to CSN 731002 "Pilotové základy". The description begins in page 29 titled "Piles driven intocompressible subsoil". The procedure used in the program is identical. Coefficients I1, Rk, Rhare in the program interpolated from the built in values corresponding to Figs. 6-8. Table 17containing regression coefficients for various types of soils or rocks is also built in theprogram and appears as a help when introducing these parameters into individual layers ofsoils or rocks. The secant modulus Es is interpolated depending on the location of a layer anda width of the pile from the built in Tables 18-20.

- analysis of pile resting on incompressible subsoil

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Analysis of a pile resting on incompressible subsoil (rocks class R1, R2) is based on part G -Analysis of vertical bearing capacity Uvd according to CSN 73 1004 - Commentary to CSN 731002 "Pilotové základy". The description begins in page 27 titled "Piles resting onincompressible subsoil". The solution procedures used in the program are identical. Theinfluence coefficient of settlement Iwp is interpolated from Table 16, which is also built in theprogram.

Vertical bearing capacity - FEMThe program module "Pile FEM" is part of the program "Pile". It serves to compute thevertical bearing capacity of a pile placed in generally layered subsoil. As a result the analysisprovides the limit loading curve and distributions of forces and displacements developedalong the pile.

The main advantage of this module is availability of the required input parameters of soilsaround the pile – the user is asked to specify the angle of internal friction, cohesion, unitweight and deformation modulus of a given soil.

The solution procedure in the module "Pile FEM" is based on a semi-analytical approach. Thepile is represented by standard beam elements. The response of surrounding soil follows fromthe well known solution of layered subsoil as a generalization of the Winkler-Pasternak model.The elastic rigid plastic response in shear is assumed along the pile-soil interface in view ofthe Mohr-Coulomb failure criterion. The normal stress acting on the pile is determined fromthe geostatic stress and soil (concrete mixture) pressure at rest.

The influence of water in the vicinity of pile is not only introduced into the shear bearingcapacity of the pile skin, but also affects the depth of influence zone below the pile heel.

The pile may reach incompressible subsoil, which substantially influences its response. Thiseffect is also taken into account in the program. The pile settlement can also be influenced bythe settlement of the surrounding terrain. In particular, settlement of soil may reduce the pilebearing capacity. The pile settlement increases without increasing load. This phenomenon ismodeled in the program as so called negative skin friction. The analysis may also account for the influence of technological process of pile constructionon the stiffness of pile foundation.

The solution procedure consists of several steps:

1) The pile is represented as a member composed of several beams. Subdivisioninto individual element complies with the condition that the ratio between thepile length and its diameter should be approximately equal to 2,5. Theminimum number of beams, however, is 10.

2) Each element is supported at its bottom node by a spring. The spring stiffnessserves to model both the shear resistance of skin and at the pile heel thestiffness of soil below the pile heel.

3) For each element the limit value of shear force transmitted by skin Tlim isdetermined.

4) The pile is loaded at its top end by increments of the vertical load. For eachload increment the magnitude of spring force for each element is determined.This value is then compared with the value of Tlim for a given element. If a

certain spring force exceeds the value of Tlim its magnitude is set equal to Tlim.

Analysis for this load increment is then repeated so that the force isredistributed into other springs. Such an iteration within each load incrementproceeds as long as each currently active spring does not transmit force that isless than its corresponding Tlim. Gradual "softening" of individual springsresults in deviation of the limit loading curve from linear path. It is evident thatfor a certain load level all springs will no longer be capable of increasing itsforce and the bile begins to settle in a linear manner supported only by the heelspring that has no restrictions on the transmitted force.

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5) As a result the analysis provides the limit loading curve, forces developed inthe pile and a graph showing variation of shear as a function of deformation ata given location.

Limit loading curveThe limit loading curve describes the variation of vertical load Q as a function of the pilesettlement.

By default the program offers the construction of this curve for the maximal value ofsettlement equal to 25 mm. This magnitude, however, can be adjusted up to the value of 100 mm before running the calculation. An example showing a typical shape of the limit loadingcurve appears in the figure.

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Limit loading curve

Shear strength of skinFor each beam element of the analyzed pile the program determines the limiting value of theforce that can be transmitted by the pile skin at the location of a given element. Its valuedepends on the geostatic stress z found at a depth of a given element.


h - depth below the ground surface

Summation sign denotes that z is summed over individual layers of the soil.

The allowable shear stress is then given by:

where: c - cohesion of soil at the location of beam

- angle of internal friction of soil at the location of beam

k - coefficient of increase of allowable skin friction due to technology

If the beam is found below the ground water table, the allowable skin friction is then reducedto receive the form:

,

where: u - pore pressure below the ground water table

The allowable shear force then follows from:

,where: O - length of perimeter of pile skin

l - length of pile beam

Coefficient of increase of limit skin frictionA specific input parameter is the coefficient of increase of limit skin friction k due to appliedtechnology of construction. By default the value of this coefficient is set equal to one. There isno recommendation by standard for its specific value – its adjustment depends solely on thepractical experiences of the designer. It has been found from the in situ measurements onreal piles that the value of k is usually greater than 1 and may reach the value of 1.5.Theoretically, however, it may attain values even less than 1.

Depth of deformation zoneThe assumed depth of influence is a variable, which considerably influences the stiffness ofsoil below the pile heel. It is one of the input parameters for the determination of parametersC1 and C2 of the Winkler-Pasternak model. The deeper the influence zone the smaller thestiffness of subsoil. When the depth of influence zone approaches in the limit zero thestiffness of subsoil tends to infinity.

The depth of influence zone depends both on subsoil parameters and magnitude of theapplied surcharge, thus on stress below the pile heel. The program assumes that the depth ofinfluence zone is found in the location, where the stress below the heel equals the geostaticstress. Such an idea is depicted in the following figure:

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Determination of the depth of influence zone below the pile heel

For digital determination of the depth of influence zone H serves the function F(). Itsdistribution appears in figure. This function was derived using the above assumptions and inthe program appears in the form of table. Its application is evident from the following steps.The values of F() are determined for the current value of stress fz below the pile heel and for

the original geostatic stress h. For this value of F() we determine the parameter . This

value serves to determine for the actual value Poisson's number and pile diameter r thecorresponding depth of influence zone H.

Variation of function F()

The depth of influence zone can be affected by the presence of ground water. In such s caseits determination is outlined in following figure:

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Determination of the depth of influence zone below the pile heel including water

For digital determination of the depth of influence zone H is then used the function G(). Itsdistribution appears in figure. In the analysis this function is exploited in the similar way asfunction F(). The only difference when determining the values of G() appears in the use ofhydrostatic pressure whw.

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Variation of function G()

Incompressible subsoilAt a certain depth below the ground surface it is possible to specify incompressible subsoil. Ifthe pile exceeds this specified depth then all beam elements found below this value are fixedinstead of being spring supported. The pile then essentially experiences no settlement. Ifthere is incompressible subsoil below the pile heel but not deeper than the reach of influencezone below the heel, the depth of influence zone for the stiffness computation is then reducedsuch that the influence zone just reaches the incompressible subsoil. This way also theincompressible subsoil below the heel increases its stiffness and consequently also thebearing capacity of the pile heel. If the incompressible subsoil is found below the reach of theinfluence zone, then it does not influence the analyzed pile.

Negative skin frictionA negative skin friction is a phenomenon that arises from a settlement of soil in the vicinity ofa pile. The soil deforming around the pile tends to pull the pile downwards thus reducing itsbearing capacity for a given pile settlement.

The input parameters for assessing the influence of negative skin friction is the settlement ofground surface w and a depth of influence zone of this deformation h. For a uniformlydistributed load around the pile the value of w should be measured in the distance equal tothree times the pile diameter from its outer face. The value of then represents the depthinfluenced by the ground surface settlement and below which the soil is assumedincompressible with no deformation.

Computation of negative skin friction is carried out first while determining the limit shear

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forces transmitted by the pile skin Tlim. The solution procedure assumes that the soil

settlement decreases linearly with depth from the value of w on the ground surface up to 0 ata depth of h. The specific value of the soil settlement is therefore assumed for each levelbelow the ground surface till the depth of h. The forces developed in springs (springssupporting individual elements) due to their deformation are determined and then subtractedfrom Tlim to reduce the bearing capacity of the pile skin.

From the presented theory it is evident that for large settlement w or large depth h the valuesof Tlim may drop down to zero. In extreme cases the negative skin friction may completelyeliminate the skin bearing capacity so that the pile is then supported only by the elasticsubsoil below the pile heel.

Influence of technologyThe pile bearing capacity is considerably influenced by technological processes applied duringconstruction. The module Pile FEM allows for specifying the technology of pile construction.The mobilized skin friction and the resistance at the pile heel are then reduced with the helpof reduction coefficients depending on the selected technology. The values of thesecoefficients follow from the Dutch standard NEN 6743 Pile foundation.

Apart from technologies offered by the program and corresponding coefficients the users arefree to assign to these coefficients their own values. This way the users may introduce theirown practical experiences or information provided by other sources into the analysis.

Shear resistance on skinThe shear resistance on pile skin is in the analysis represented by stiffness of springssupporting individual beams of a pile. This stiffness is associated with material parameters ofthe Winkler-Pasternak model C1 and C2. The values of C1 and C2 are determined from

parameter Edef. They depend on the depth of influence zone, which varies with the pile

deformation (settlement). The variability of influence zone is in the analysis determined suchthat for zero deformation it receives the value of 1x the pile diameter and for deformation atthe onset of skin failure equals 2,5x the pile diameter.

The decisive parameter for the determination of magnitudes of C1 and C2 is the deformation

modulus. Caution must be taken when estimating the value of Edef from deformational

characteristics of soil using standards. In particular, in case of long piles we are essentiallydealing with deep seated foundations and the soil at the pile heel will certainly experienceshigher stiffness than that proposed by the standard for spread footings. This holdsparticularly for cohesive soils. The most reliable estimates are of course those obtaineddirectly from experimental measurements.

Formulas given below serve to determine the stiffness of springs representing the shearresistance of pile skin as a function computed parameters of the elastic subsoil. They dependon the shape of cross-section and for the implemented cross-sections they receive thefollowing forms:

Circle:

where: r - radius of pile cross-section

C1, C2 - subsoil parameters

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K1( r), K2(r)

- values of the modified Bessel functions

Parameter attains the value:

.

Rectangle:

,

where a,b are lengths of rectangle edges and C1, C2 are subsoil parameters and kred is thereduction coefficient, which reduces the stiffness with respect to slenderness of the rectangle.It receives the following values

for: ,

for: ,

where a is the length of a shorter edge of the rectangle and H is the depth of influence zone.

Croos, "I-section":For these cross-sections the stiffness is derived from the stiffness for rectangularcross-section reduced by subtracting the stiffness corresponding to four "removed" parts ofthe cross-section.

,a1, b1 - evident from the following figure

Stiffness of subsoil below the pile heelThe soil stiffness below the pile heel follows from the value of stiffness of the Winkler model C1. The value of C1 is determined for parameters Edef and of a soil at the location of pile

heel. The value of C1 further depends on the depth of influence zone beneath the heel. Thespring stiffness introduced into the support of the beam at the pile heel is then provided by:

,where: A - cross-sectional area at the pile heel

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Increments of vertical loadingThe analyzed pile is loaded gradually in ten increments. The magnitude of load increments inindividual steps is determined prior to the actual analysis. In particular, the program searchesfor such a magnitude of load that causes the pile to exceed the limiting value of settlementspecified for the computed limit loading curve. This value is then divided into 10 incrementssubsequently applied to the structure.

Distributions of forces acting on pileApart from the limit loading curve it is also possible to keep track of the distribution of normalforce in the pile and the distribution of shear force developed along the pile skin. The normalforces decreases from the top to the bottom as the load is gradually taken by the shear forcedeveloped along the pile skin. Unlike the normal force the shear force thus increases from thetop to the bottom. Both forces are evaluated in relative values related to the magnitude ofvertical load.

Dependence of shear on deformationAt an arbitrary (selected) depth it is possible to view the distribution of skin friction as afunction of deformation (settlement) of a given point of the pile. This graph shows theprocess of gradual reduction of shear stiffness of pile skin until zero with increasingdeformation. This dependency is initially linear, particularly in stage, where the spring forcedoes not exceed the value Tlim. When this value is exceeded the spring stiffness starts togradually decrease manifested by the flattening of the curve.

Horizontal bearing capacityHorizontal bearing capacity of a pile, dimensioning

The horizontally loaded pile is analyzed using the finite element method as a beam on elasticWinkler foundation. The soil parameters along the pile are represented by the modulus ofsubsoil reaction. By default the pile is subdivided into 30 segments. For each segment theprogram determines the values of the modulus of subsoil reaction, internal forces anddeformations. The program also allows for dimensioning of the steel-reinforced concrete pilebased on the standard specified in the frame "Project"

The program also enables to analyze a pile loaded by the prescribed displacements(translation or rotation of the pile head). In such a case the analysis is carried out only withthe prescribed displacement. The inputted mechanical loading is excluded.

The following options for inputting the modulus of subsoil reaction are available in theprogram:

- by distribution (distribution of the modulus of subsoil reaction along the pile is specified)

- constant distribution

- linear distribution (Bowles)

- according to CSN 73 1004

- according to Matlock and Rees

- according to Vesic

In general, the modulus of subsoil reaction corresponds to the spring stiffness in the Winklermodel. This model describes settlement of a rigid plate as a function of the applied load. Thecorresponding relationship is represented by the following formula:

where: p - load acting along plate-soil interface

k - stiffness of Winkler spring

y - translation of plate into subsoil

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Definition of the modulus of subsoil reaction

Constant distribution of modulus of subsoil reaction The modulus of subsoil reaction of the i-th layer is provided by:

where:Edef - deformation modulus of soil

r - reduced width of pile given by:

where: d - pile diameter - angle of dispersion – is inputted with respect to the angle of internal friction in the

range of /4-

Linear modulus of subsoil reactionThe modulus of subsoil reaction at a depth z follows from the formula:


l - length of pile

k - soil parameter after Bowles

r - reduced width of pile


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- angle of dispersion introduced by the user – is inputted with respect tothe angle of internal friction in the range of /4-

Possible values of modulus k after Bowles [MN/m3] :

dense sandy gravel 200 - 400

medium dense gravel 150 - 300

medium-graded sand 100 - 250

fine sand 80 - 200

stiff clay 60 - 180

saturated stiff clay 30 - 100

plastic clay 30 - 100

saturated plastic clay 10 - 80

soft clay 2 - 30

Modulus of subsoil reaction according to CSN 73 1004The modulus of subsoil reaction for cohesive soil assumes the form:

where: Edef - deformation modulus of soil

d - pile diameter

For cohesionless soils it is provided by:

where: nh - modulus of horizontal compressibility

d - pile diameter

z depth of a given section from finished grade

Soil nh [MN/m3]Relative density ID 0,33 0,50 0,90

Dry sand and gravelWet sand and gravel

1,5

2,5

7,0

4,5

18,011,0

Possible values of modulus nh for cohesionless soils

Modulus of subsoil reaction after Matlock and ReesThis method is applicable for cohesionless soils. The modulus of subsoil reaction thenfollows from the expression:

where: nh - modulus of horizontal compressibility

z depth of a given section from finished grade

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Soil nh [MN/m3]Dry sand and gravel- loose- medium densedense

1,8 – 2,25,5 – 7,0

15,0 - 18,0Wet sand and gravel- loose- medium densedense

1,0 – 1,43,5 – 4,59,0 - 12,0

Possible values of modulus nh for cohesionless soils

Modulus of subsoil reaction after VesicThe modulus of subsoil reaction is provided by:

where: Ep - modulus of elasticity of pile

lp - moment of inertia of pile

Es - modulus of elasticity of soil

d - pile diameter

- Poisson number

Settlement analysisOne of the following method is available to compute settlement:

- with the help of oedometric modulus- with the help of compression constant- with the help of compression index- according to NEN (Buismann, Ladde)- using the Soft soil model- employing Janbu theory - using DMT (constrained modulus)

The program offers two options to constrain the depth of influence zone:

- exploiting the theory of structural strength

- using the percentage of the magnitude of geostatic stress The theory of elasticity (Boussinesq theory) is employed to determine stress in a soil state inall methods available for the settlement analysis.

General theories of settlement analysis serve as bases in all the above methods.

When computing settlement below the footing bottom the programs first calculates the stressin the footing bottom and then determines the overall settlement and rotation of foundation.

The general approach in all theories draws on subdividing the subsoil into layers of a differentthickness based on the depth below the footing bottom or ground surface. Verticaldeformation of each layer is then computed – the overall settlement is then defined as a sumof partial settlements of individual layers within the influence zone (deformations below theinfluence zone are either zero or neglected):

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where: s - settlement

si - settlement of the ithlayer

Stress in the footing bottomThe stress in the footing bottom can be assumed as:

rectangular (uniform in the footing bottom)

general (trapezoidal) with different edge values

General distribution of stress follows from figure:

Stress in the footing bottom

where:

where: Q - vertical loading of footing

l,b - footing width and length

eb - loading eccenricity

M - moment acting on the footing

H - horizontal force

N - normal force at eccentric footing

p - column axis offset from the footing center

If in some points the stress becomes negative, the program continues with adjusteddimensions b*l while excluding tension from the analysis. Before computing the stressdistribution due to surcharge the stress in the footing bottom is reduced by the geostaticstress in the following way:

There are three options in the program to specify the geostatic stress in the footing bottom:

From the original ground

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It is therefore considered, whether the footing bottom in the open pit measured from theoriginal ground is free of stress for the time less than needed for soil bulkage andsubsequent loss of stress in the subsoil.

From the finished gradeThe same assumptions as above apply.

Not considered at all

Overall settlement and rotation of foundationThe foundation settlement is substantially influenced by the overall stiffness of the systemrepresented by foundation structure and foundation soil given by:

where: Ezakl - modulus of elasticity of footing

t - foundation thickness

Edef,prum - weighted average of the deformation modulus up to depth ofinfluence zone

l - footing dimension in the direction of searched stiffness

For k > 1 the foundation is assumed to be rigid and as a representative point for thedetermination of its settlement is assumed the characteristic point (distant by 0,37 timesthe foundation dimension from its axis).

For k < 1 the foundation structure is assumed to be rigid and as a representative point for thedetermination of foundation settlement is assumed the foundation center point.

The foundation rotation is determined from the difference of settlements of centers ofindividual edges.

Influence of foundation depth and incompressible subsoilWhen computing settlement it is possible to account for the influence of foundation depthby introducing the reduction coefficient 1:for strip footing:

for spread footing:

where: d - depth of footing bottom

z - depth under footing bottom

Influence of incompressible layer is introduced into the analysis by the reductioncoefficient 2:

where: zic - depth of rigid base under footing bottom


Incorporating the above coefficients allows transformation of the vertical component of

- 418 -


stress z such that the actual depth is replaced by a substitute value zr given by:

where: 1 - coefficient of footing bottom depth

2 - coefficient of rigid base


Influence of sand-gravel cushionIf the sand-gravel cushion is specified below the spread footing, the material parameters X inindividual layers are computed in the following way:

For layer ha,i :

where: Xi - material parameters at ith layer

Xc - material parameters of sand-gravel cushion

For layer hb,i :

where: Ac - area of sand-gravel cushion

Xc - material parameters of sand-gravel cushion

Xb,i - material parameters of b,i layer

bi - cushion widths in the ith layer

li - cushion length in the ith layer

Analysis Xi in the sand-gravel cushion

Settlement analysis using the oedometric modulusEquation to compute compression of an ith soil layer below foundation having a thickness h

- 419 -


arises from the definition of deformation modulus Eoed:

where: z,i - vertical component of incremetal stress in the middleof ith layer


Eoed,i - oedometric modulus of the ith layer

The oedometric modulus Eoed can be specified for each soil either as constant or with the help

of an oedometric curve (ef relation). When using the oedometric curve the program

assumes for each layer the value of Eoed corresponding to a given range of original and final

stress. If the value of oedometric modulus Eoed is not available, it is possible to input the

deformation modulus Edef and the program carries out the respective transformation.

where: - Poisson's number

Edef - deformation modulus

Settlement analysis using the compression constantEquation to compute compression of an ith soil layer below foundation having a thickness harises from the definition of compression constant C:

where: or,i - vertical component of original geostatic stress in the middle of ith layer

z,i - vertical component of incremental stress (e.g. stress due to structuresurcharge) inducing layer compression


Ci - compression constant in the ith layer

The program allows for inputting either the compression constant Ci or the compression

constant C10 (the program itself carries out the transformation).

Settlement analysis using the compression indexEquation for settlement when employing the compression index Cc of the i–th layer arisesfrom the formula:

- 420 -


where: or,i - vertical component of geostatic stress in the middle of ith layer


eo - initial void ratio


Cc,i - compression index in the ith layer

Settlement analysis according to NEN (Buismann, Ladd)This method computes both the primary and secondary settlement. When computing themethods accounts for overconsolidated soils and differentiates between two possible cases:

(1) sum of the current vertical effective stress in a soil and stress due to external surcharge isless than the preconsolidation pressure so that only additional surcharge is considered

(2) sum of the current vertical effective stress in a soil and stress due to external surcharge isgreater than the preconsolidation pressure so that the primary consolidation is set on again.The primary settlement is then larger when compared to the first case

Primary settlement

Primary settlement of the ith layer of overconsolidated soil (OCR > 1) is provided by: for: or + z ≤ p (sum of the current vertical stress and its increment is less than the

preconsolidation pressure)

for: or + z > p (sum of the current vertical stress and its increment is greater than the




p,i - preconsolidation pressure in the ith layer



Cc,i - compression index in the ith layer

Cr,i - recompression index in the ith layer

Primary settlement of the ith layer of normally consolidated soil (OCR = 1) reads:

- 421 -






Cc,i - compression index the ith layer

Secondary settlement

Primary settlement of the i–th layer assumes the form:

for: or + z ≤ p (sum of the current vertical stress and its increment is less than the


pro or + z > p (sum of the current vertical stress and its increment is greater than thepreconsolidation pressure)

where: hi - thickness of the ith layer

Cr,i - secondary compression index below preconsolidation pressure in the ithlayer

C - index of secondary compression in the ith layer

tp - time to terminate primary consolidation

ts - time required for secondary settlement

If we specify the value of preconsolidation index of secondary compression the same as forthe index of secondary compression, the program does not take into account in thecomputation of secondary settlement the effect of preconsolidation pressure.

Settlement analysis using the Soft soil modelThe analysis employs the modified compression index and is based on the Soft soilelastic-plastic model developed in university of Cambridge. The soil deformation assumes thevolumetric strain to be linearly dependent on the change of effective mean stress plotted innatural logarithmic scale. The settlement of the ith layer is then provided by:

kde: or,i - vertical component of geostatic stress in the middle of ith layer



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- modified compression index in the ith layer

The analysis requires inputting the modified compression index usually obtained fromtriaxial laboratory measurements.

If the modified compression index is not known, it is possible to specify the compressionindex CC together with an average value of the void ratio e (if that is also not know it is

sufficient to provide the initial void ratio eo) and the program then performs an approximatecomputation of the modified compression index using the available information.

Settlement analysis according to Janbu theoryIt is based on principles of nonlinear elastic deformation, where the stress-strain relationshipis described by a function of two dimensionless parameters unique for a given soil. Theparameters are the exponent j and the Janbu modulus m. Equations describing thesettlement are obtained by specifying from the definition of deformation modulus Et and bysubsequent integration. The program allows the user to compute settlement for the followingtypes of soil:

- noncohesive soils

- coarse - grained soil

- sands and silts

- overconsolidated sands and silts

- cohesive soils

- overconsolidated cohesive soils

Settlement analysis for cohesionless soils after JanbuFor cohesionless soils the stress exponent is not equal to zero. For layered subsoil theresulting settlement equals to the sum of partial settlements of individual layers:



ji - stress exponent in the ith layer

mi - Janbu modulus in the ith layer


Settlement analysis for coarse-grained soils after JanbuFor dense coarse-grained soils (e.g. ice soil) the stress-deformation (settlement) relationshipis usually assumed as "elastic", i.e. the stress exponent j is equal to one. Thus for j = 1 andthe reference stress r = 100 kPa the resulting settlement equals to the sum of partialsettlements of individual layers:

- 423 -


where: z,i

- vertical component of incremental stress (e.g. stress due to structuresurcharge) inducing layer compression - i.e. change of effective stress



Settlement analysis for sands and silts after JanbuFor sands and silts the stress exponent j receives the value around 0,5, for the referencestress r = 100 kPa the resulting settlement equals to the sum of partial settlements ofindividual layers. It can be derived from the following formula:

where: or,i vertical component of geostatic stress in the middle of ith layer

z,i vertical component of incremental stress (e.g. stress due to structuresurcharge) inducing layer compression

mi Janbu modulus in the ith layer

hi thickness of the ith layer

Settlement analysis for overconsolidated sands and siltsafter JanbuProviding the final stress in soil exceeds the preconsolidation pressure (or + z > p), the

settlement of layered subsoil is found from the following equation:





mr,i - Janbuův modul opětného stlačení v i-té vrstvě


If the stress due to surcharge does not cause the final stress to exceed the preconsolidationpressure (or + z ≤ p), it is possible to assume the following forms of equations for the

computation of settlement of layered sand or silt subsoil:




- 424 -


mr,i - Janbu modulus of recompression in the ith layer


Settlement analysis for cohesive soils after JanbuIn case of cohesive soils the stress exponent is equal to zero. For normally consolidated soilswe obtain from the definition of the tangent modulus of deformation (by modification andsubsequent integration) Et equation for the settlement of layered subsoil formed by cohesivesoils in the form:





Settlement analysis for overconsolidated cohesive soilsafter JanbuMost cohesive soils in the original order except very young or organic clays areoverconsolidated. If the final stress in the soil exceeds overconsolidation stress (or + z > p) than the settlement of the layered subsoil composites from cohesive soils is computed fromfollowing relation:for: or + z > p

for: or + z ≤ p





mr,i - Janbu modulus of recompression in the ith layer


- 425 -


Settlement analysis using DMT (constrained modulus)Constrained modulus MDMT [MPa] is defined as the vertical drained confined tangent

modulus at vo. MDMT is obtained from dilatometer test.

If the value of the constrained modulus MDMT is not available, it is possible to input the

coefficient of volume compressibility mV [m2/MN] (determined from the oedometer test) andthe program carries out the respective transformation:

where: MDMT - constrained modulus

mV - coefficient of volume compressibility

The analysis employs the constrained modulus MDMT or coefficient of volume compressibilitymV and is based on Marchetti method. This approach being based on linear elasticity,provides a settlement proportional to the load and is unable to provide non linear predictions.

The settlement of the ith layer is then provided by:

where: z,i - vertical component of incremental stress in the middle of ith layer


MDMT - constrained modulus

Theory of settlementIf the stress in a soil caused by ground surface surcharge, change in stress with the soil or inthe currently built earth structure is known, it is possible to determine the soil deformation.The soil deformation is generally inclined and its vertical component is termed the settlement.In general, the settlement is non-stationary dependent on time, which means that it does notoccur immediately after introducing the surcharge, but it rather depends on consolidationcharacteristics of a soil. Permeable, less compressible soils (sand, gravel) deform fast, whilesaturated low permeability clayey soils experience gradual deformation called consolidation.

Time dependent settlement of soil

Applied load yields settlement, which can be subdivided based on time dependent responseinto three separate components:

- 426 -


- instantaneous settlement (initial) - primary settlement (consolidation) - secondary settlement (creep)Instantaneous settlement

During instantaneous settlement the soil experiences only shear deformation resulting intochange in shape without volumetric deformation. The loss of pore pressure in the soil is zero.

Primary settlement

This stage of soil deformation is characterized by skeleton deformation due to motion andcompression of grains manifested by volume changes. If the pores are filled with water(particularly in case of low permeability soils), the water will be carried away from squeezedpores into locations with lower pressure (the soil will undergo consolidation). Theconsolidation primary settlement is therefore time dependent and is terminated by reachingzero pore pressure.

Secondary settlement

When the primary consolidation is over the skeleton deformation will no longer cause thechange in pore pressure (theoretically at infinite time). With increasing pressure the grainsmay become so closely packed that they will start to deform themselves and the volumetricchanges will continue – this is referred to as creep deformation of skeleton or secondaryconsolidation (settlement). Unlike the primary consolidation the secondary consolidationproceeds under constant effective stress. Particularly in case of soft plastic or squash soils thesecondary consolidation should not be neglected – in case of overconsolidated soils it mayrepresent app. 10% of the overall settlement, for normally consolidated soils even app. 20%.

Theory of primary settlementThe final primary settlement s is often is often substituted by the term settlement. Most ofthe computational approaches can be attached to one of the two groups:- linear elastic deformation- nonlinear elastic deformation

Linear elastic deformation

The linear stress-strain relationship follows the Hook law:

where: - induced deformation of the soil layer

ef - induced change of effective stress in the soil layer

E - Young modulus in the soil layer

- Poisson number

The applicability of Young's modulus E of elasticity is substantiated only in cases, in which thestressed soil is allowed to stretch in the horizontal direction. This, however, is acceptable onlyfor small spread foundations. When applying the load over a larger area, the stressed soilcannot, except for its edges, to deform sideways and experiences therefore only a vertical(one-dimensional) strain related to the oedometric modulus Eoed, that is larger than the

elastic modulus E.

The settlement of a soil layer s is determined by multiplying the deformation of a soil layer by the layer thickness (height) Ho:

where: - deformation of the soil layer

Ho - thickness of the soil layer

V In case of layered subsoil we get the total settlement by summing up settlements of

- 427 -


individual layers:

where: s - settlement of the layered subsoil

i - deformation of the ith soil layer

Hoi

- thickness of the ith soil layer

Nonlinear elastic deformationFor most soils the stress-strain relationship is nonlinear and often influenced by the loadinghistory. This nonlinearity cannot be neglected, particularly when computing the settlement offine-grained soils (silts, clays). Clearly, the procedure based on application of Young'smodulus of elasticity is not generally applicable. Even if employing the stress dependentoedometric modulus of deformation, it will not be possible to receive reasonable estimates ofthe behavior of certain overconsolidated soils. Nonlinear elastic deformation is generallymodeled using the void ratio and deformation characteristics derived from one-dimensionaldeformation of a soil sample (e.g. compression constant, compression index, etc.).

Procedure for the computation of settlement of a compressible saturated soil layer using thevoid e is described on the following soil element having the height Ho and the width B = 1 m:

Analysis of settlement from phase diagram

Owing to the fact that the soil is a three phase medium (it contains solid particles and porefilled with fluid and gas) it is possible to describe the solid particles (rock particles andmineral grains) by their volume Vs (and assumed to be equal to unity), while the porousphase can be described using the void ratio e.

The soil element is subjected on its upper surface to a uniform loading q causing the changein stress inside the sample and also the vertical displacement H, which in turn leads to thereduction of pores Vp and therefore also to the reduction of void ratio (from its original value

- 428 -


eo to a new value e). The vertical strain of a soil sample is given by the ratio of H to the

original sample height Ho, and can be expressed using the void ratio e:

where: - vertical relative compression

H - vertical deformation

Ho - origin height of the element

s - settlement

e - void ratio

e - change of void ratio

By modifying this equation we arrive at the formula describing the sample settlement withthe help of void ratio:

where: - vertical relative compression

Ho - origin height of the element

s - settlement

e - void ratio

e - change of void ratio

Secondary settlementTo describe a gradual creep of soil during secondary settlement the program employs theBuissman method (it incorporates the index of secondary compression Cderived by Lade).From observations suggesting that the soil deformation follows a linear path when plotted insemi-logarithmic scale against time Buissman proposed the variation of due to long-termstress in the form:

where: ε - total deformation

εp - deformation associated with primary consolidation

εs - deformation associated with secondary consolidation

t - time of consolidation

t0 - refereference time

- 429 -


Time dependent variation of strain (primary and secondary consolidation)

Determination of the depth of influence zoneFrom the theoretical point of view when applying a load on the ground surface we may expectthe change of stress in subsoil into an infinite depth. The soil, however, deforms only up to acertain depth – within so called influenced zone.The program offers two options to specify the influence zone:- using the theory of structural strength- by specifying a certain percentage of the primary geostatic stress

Determination of the depth of influence zone with the helpof structural strengthThe structural strength represents the resistance of soil against deformation for a loading atthe onset of failure of its internal structure. With decreasing coefficient m the soil respondstends to be linear.

If the structural strength is accounted for during settlement analysis, then:

a) the influence zone is characterized by the depth below the footing bottom at which theincrement of vertical stress z becomes equal to the structural strength of soil (determined by

multiplying the original geostatic stress or by the coefficient m):

where: m - coefficient of structural strength

or - original geostatic stress

b) when computing the settlement of a layer, the increment of vertical stress z due tosurcharge and reduced by the structural strength of soil is provided by:



- 430 -


z - incremetal stress in the middle layer

and the settlement s then follows from the stress denoted in figure by hatching and is givenby:



z - incremetal stress in the middle layer

Depth of influnece zone based on theory of structural strength

(area of effective surcharge is hatched)

Determination of influence zone by constraining themagnitude of primary stressPokud If we assume in the settlement analysis the constrains in terms of the percentage ofprimary geostatic stress, then:a) the influence zone is represented by a depth below the footing bottom where theincremental stress z reaches a certain percentage of the original geostatic stress:

where: x% - considered magnitude of the geostatic stress

or - geostatic stress

b) the settlement s is derived from stress value denoted in figure by hatching and it receivesthe form:

where: z - incremetal stress

- 431 -


or - geostatic stress

Depth of influence zone given by constraining the magnitude of primary stress

Characteristics of settlement analysesDepending on the selected solution method the program GEO5 employs for the computationof settlement the following characteristics that may differ by the type of experiment neededfor their determination or in the way of representation of measured variables:

- Compression index Cc- Oedometric modulus Eoed

- Compression constant C- Compression constant C10- Void ratio e- Recompression index Cr- Janbu characteristics- Correcting coefficient m- Modified compression index - Index of secondary compression C- Overconsolidation index of secondary compression Cr

Compression indexIt describes variation of the void ratio e as a function of the change of effective stress efplotted in the logarithmic scale:

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Void ratio e versus effective stress ef

It therefore represents a deformation characteristic of overconsolidated soil:

where: e - variation of void ratio

logef - variation of effective stress

Range of compression index Cc (Naval Facilities Engineering Command Soil MechanicsDESIGN

MANUAL 7.01)A typical range of the compression index is from 0,1 to 10. Approximate values forhomogeneous sand for the loading range from 95 kPa to 3926 kPa attain the values from0,05 to 0,06 for loose state and 0,02 to 0,03 for dense state. For silts this value is 0,20.

For lightly overconsolidated clays and silts tested in USA Louisiana Kaufmann and Shermann(1964) present the following values:

Soil Effectiveconsolidation

stress cef [kPa]

Final effectivestress in the soil

ef [kPa]

Compressionindex Cc [-]

CL soft clay 160 200 0,34

CL hard clay 170 250 0,44

ML silt of low plasticity 230 350 0,16

CH clay of high plasticity 280 350 0,84

CH soft clay with silt layers 340 290 0,52

Prof. Juan M.Pestana-Nascimento (University of California, Berkeley) offers the followingtypical values of the compression index Cc:

Soil Compression index Cc [-]

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Normal consolidated clays 0,20 – 0,50

Chicago clay with silt (CL) 0,15 - 0,30

Boston blue clay (CL) 0,3 – 0,5

Vickburgs clay - dray falls into lumps (CH) 0,3 – 0,6

Swedish clay (CL – CH) 1 – 3

Canada clay from Leda (CL – CH) 1 – 4

Mexico City clay (MH) 7 – 10

Organic clays (OH) 4 a více

Peats (Pt) 10 – 15

Organic silts and claye silts (ML – MH) 1,5 – 4,0

San Francisco sediments (CL) 0,4 – 1,2

Clay in the old San Francisco Bay 0,7 – 0,9

Bangkok clay (CH) 0,4

In addition, there are empirical expressions available to determine approximate values of Ccfor silts, clays and organic soils; their applicability, however, is more or less local:

Soil Equations Reference

Transformed clays Skempton 1944

Clays Nishida 1956

Brazilian claysSao Paulo clays

Cozzolino 1961

New York clays Terzaghi a Peck 1948

Clays of low plasticity Sowers 1970

Taipei clays and silts Moh a kol. 1989

Clays Pestana 1994

Oedometric modulusIf the results from oedometric test are represented in terms of oedometric curve ( = f(ef

- 434 -


)), it becomes evident that for each point on the curve we receive a different ratio ef /

Determination of oedometric modulus Eoed

If the stress-strain curve is replaced for a certain interval of two neighboring stresses 1ef -

2ef by a secant line, it is acceptable to assume a linear behavior of soil within this interval and

represent the soil compressibility by as ef – called the oedometric modulus of

deformation. The oedometric modulus of deformation is therefore a secant modulus linked toa certain stress interval 1ef - 2ef selected on the stress-strain diagram = (ef ):

In general, the oedometric modulus of deformation Eoed tends to decrease its value with the

increasing stress interval. Therefore we should consider for each layer a specific value of Eoedpertinent to a given stress interval (from original to final stress state). This is reflected in theprogram by the way of inputting Eoed, where it is possible to specify for each soil the

respective oedometric curve (ef diagram).

Practical experience, however, suggests (e.g. for clays) a several orders of magnitudedifference between the value of Eoed derived from the deformation modulus Edef and thatprovided by the in situ measured loading curve.

Approximate range of values of oedometric modulus of deformation Eoed for individualsoils and typical stress range (Vaníček: Mechanika zemin (soil mechanics)):

Soil Oedometric modulus Eoed [MPa]

gravels 60 – 600

medium dense sands to dense sands 7 – 130

cohesive 2 – 30

Compression constantWhen plotting the effective vertical stress against the vertical strain in the semi-logarithmicscale we often arrive at a linear dependency.

- 435 -


Detemination of compression constant C

Slope of this curve is one of the soil parameters particularly in case of one-dimensionaldeformation and is referred to as the compression constant C:

where: 1ef - initial effective stress of soil in oedometer

2ef - final effective stress of soil in oedometer

Margins of compression constant C (J.Šimek: Mechanika zemin)

Soil Compression constant C [-]

Loess silt 15 – 45

Clay 30 – 120

Silts 60 – 150

Medium dense and dense sands 150 – 200

Sand with gravel > 250

Compression constantIn engineering practice the natural logarithm with base is sometimes replaced by logarithmwith base 10 when plotting the stress ef. In this case it is common to denote the

compression constant with subscript 10: C10. Since it holds:

it is possible to derive a relationship between compression constant C and C10:

Arnold Verruijt (Soil Mechanics) offers the following values of compression constant:

Soil C C10

- 436 -


Sand 50 – 500 20 – 200

Silt 25 – 125 10 – 50

Clay 10 – 100 4 – 40

Peat 2 - 25 1 - 10

Void ratioThe void ratio e describes porosity of a soil and is provided by:

where: Vp - volume of voids

Vs - weight of soil solids

Ranges of void ratio e (Braja M. DAS: Principles of Foundation Engineering)

Soil Void ratio e [-]

Poorly graded sand with loose density 0,8

Well graded dense sand 0,45

Loose density sand with angular particles 0,65

Dense density sand with angular particles 0,4

Stiff clay 0,6

Soft clay 0,9 – 1,4

Loess 0,9

Soft organic clay 2,5 – 3,2

Glacial till 0,3

Recompression indexThe recompression index Cr is determined from the graph representing the variation of void

ratio e as a function of the effective stress ef plotted in the logarithmic scale for unloading –reloading sequence:

- 437 -


Determination of recompression index Cr

where: e - change of void ratio for the unloading-reloading curve

logef - change of effective stress for the unloading-reloading curve

If no results from either laboratory or in situ measurements are available, the recompressionindex Cr can be approximately derived from:

where: Cc - compression constant

Janbu characteristicsValues of the Janbu modulus m and of stress exponent j (according Canadian FoundationEngineering Manual 1992)

Soil Janbu modulus m Stress index j

Very dense to dense till, glacial till 1000 – 300 1

Gravel 400 – 40 0,5

Dense sand 400 – 250 0,5

Medium condition sand 250 – 150 0,5

Loose sand 150 – 100 0,5

Dense silt 200 – 80 0,5

Medium condition silt 80 60 0,5

Loose silt 60 – 40 0,5

- 438 -


Hard to very stiff clay 60 – 20 0

Medium to stiff clay 20 – 10 0

Soft claye silt 10 – 5 0

Soft marine clays 20 – 5 0

Organic clays 20 - 5 0

Peats 5 – 1 0

Influence of loading history on deformation characteristicsThe loading history has a substantial influence on the distribution of deformation curve andtherefore also on the values of deformation characteristics. The following figure displays thedeformation curve (e = f(ef) diagram) derived from oedometric loading testcorresponding, e.g. to natural dense sandy soil.

Loading historya) Deformation curve for clayey soils from oedometric test

b) Simplified interpretation of deformation curve

VzorekThe soil sample was gradually loaded to reach the stress level bef, the stress-strain

relationship (bef -)within the section a-b is linear and is denoted as primary or virgin (i.e.,

relative compression is encountered). Upon exceeding the stress level bef the sample waselastically unloaded and the soil moved up the b-c section of the deformation curve. Uponreloading the soil moved down the b-c section till reaching the original stress bef prior to

unloading. When loading beyond bef the deformation curve aproaches asymptotically withinthe d-e section the primary line accompanied by inelastic deformation of a soil sample. Sucha complex stress-strain curve is often simplified by the idealized deformation curve (fig. b).Such a curve characterizes so called overconsolidated soils, which were in the past subjectedlarge stresses and subsequamtly unloded. The overconsolidation ratio (OCR) then representsthe ratio between the maximum preconsolidation stress the soil has ever experienced and thecurrent vertical stress. Overconsolidated soils typicaly follow the deformation curve given bypoints c-d-e. The change in slope along this line (given app. by point d) corresponds either tothe vertical geostatic stress o (normally consolidated soils) or to preconsolidation pressure c (overconsolidated soils). This point influences the soil deformation, which is smaller withinthe c-d section when compared to the d-e section (where for the large degree ofoverconsolidation the soil deformation increases). Additional deformation characteristics suchas deformation modulus upon unloading Ee, one-dimensional swelling index Ce,

recompression index Cr, etc. were introduced to describe such a complex soil behavior.

Currently the most often used parameter is the recompression index Cr suitable for thecomputation of settlement of overconsolidated soils.

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Coefficient mCorrection coefficient of surcharge due to structural strength m determines the structuralstrength of soil.

Values of the correction coefficient of surcharge m

Type of fundamental soil m

Very compressible fine soils class F1 -F8

- with deformation modulus Edef < 4 MPa

- nonoverconsoludated

- soft to hard consistency

(all 3 attributes must be fullfiled),

filling, made – ground

secondary and tertiary sedimetsrocks class R1, R2

0,1

fine soils class F1-F8, not belonging to coefficient

m = 0,1 nor 0,4 nor 0,6

sands and gravels class S1, S2, G1, G2 under GWTrock class R3, R4

0,2

Sands and gravels class S1, S2, G1, G2

above GWT

sands and gravels with clay, silt or fine soil admixture

soils class S3, S4, S5, G3, G4, G5

rocks class R5, R6

0,3

eluvium of igneous and metanorphic rocks 0,4

Modified compression indexThe analysis employing the Soft soil model builds on the elastic-plastic model developed inthe university in Cambridge. Here, the vertical deformation of soil assumes lineardependence on the logarithmic variation of effective stress in a soil. Application of this modelrequires an introduction of the modified compression index usually obtained from triaxialtests.

If the modified compression index is not available from laboratory measurements, it can beapproximately found from the compression index CC:

where: CC - compression index

e - average void ratio (if this value is not available, it can be approximatelysubstituted by the initial void ratio eo)

Index of secondary compressionThe index of secondary compression is proportional to the logarithm of time and the slope ofprimary consolidation (it is strongly dependent on the final effective stress in soil):

- 440 -


where: C - index of secondary compression

- deformation of a soil layer

t1 - initial time of a period of monitoring (measured from the start ofconsolidation)

t2 - final time of a period of monitoring

Determining the value of index of secondary compression C requires either laboratory (e.g.one-dimensional consolidation in oedometer) or in-situ measurements:

Determination of index of secondary compression C

Ranges of values of index of secondary compression C

sand 0,00003 – 0,00006

silty loess 0,0004

clay 0,01

The ratio between the index of secondary compression Cand the compression index Cc isapproximately constant for most of the normally consolidated clays for loading typical inengineering practice. Its average value is 0,05.

Variation of natural moisture of soil as a function of the index of secondary compression Cderived by Mesri appears in figure:

- 441 -


Variation of natural moisture of soil as a function

of the index of secondary compression C after Mesri

1 Whangamarino clay

2 Mexico City clay

3 Calcareous organic silt

4 Leda clay

5 Norwegian plastic clay

6 Amorphous and fibous peat

7 Canadian muskeg

8 Organic marine deposits

9 Boston blue clay

10 Chicago blue clay

11 Organic silty clay

Overconsolidation index of secondary compressionThe overconsolidation index of secondary compression depends on laboratory measurements(e.g. one-dimensional consolidation) and is proportional to the logarithm of time and slope ofvirgin consolidation line providing the preconsolidation pressure was not exceeded:

- 442 -


where: Cr - overconsolidation index of secondary compression

ε - deformation of a soil layer

t1 - initial time of a period of monitoring (measured from the onset ofconsolidation)

t2 - final time of a period of monitoring

Analyses in program Ground LossAnalyses performed in the program "Ground Loss" can be divided into the following groups:

- analysis of the shape of subsidence trough above excavations- analysis of failure of buildings

The failure analysis of building is based on the shape of subsidence trough.

Analysis of subsidence troughThe analysis of subsidence trough consists of several sequential steps:

- determination of the maximum settlement and dimensions of subsidence trough forindividual excavations- back calculation of the shape and dimensions of subsidence trough providing it is calculatedat a given depth below the terrain surface. - determination of the overall shape of subsidence trough for more excavations- post-processing of other variables (horizontal deformation, slope)

The analysis of maximum settlement and dimensions of subsidence trough can be carried outusing either the theory of volume loss or the classical theories (Peck, Fazekas, Limanov).

Volume lossThe volume loss method is a semi-empirical method based partially on theoretical grounds.The method introduces, although indirectly, the basic parameters of excavation into theanalysis (these include mechanical parameters of a medium, technological effects ofexcavation, excavation lining etc) using 2 comprehensive parameters (coefficient k fordetermination of inflection point and a percentage of volume loss VL). Theseparameters uniquely define the shape of subsidence trough and are determined empiricallyfrom years of experience.

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Settlement expressed in terms volumes

The maximum settlement Smax, and location of inflection point Linf are provided by thefollowing expressions:

where: A - excavation area

Z - depth of center point of excavation

k - coefficient to calculate inflection point (material constant)

VL - percentage of volume loss

The roof deformation ua follows from:

where: r - excavation radius

VL - percentage of volume loss

Recommended values of parameters for volume lossanalysisData needed for the determination of subsidence trough using the volume loss method:

Coefficient to calculate inflection point kSoil or rock k

cohesionless soil 0,3

normaly consolidated clay 0,5

overconsolidated clay 0,6-0,7

clay slate 0,6-0,8

quartzite 0,8-0,9

Percentage of volume loss VLTechnology VL

TBM 0,5-1

Sequential excavation method 0,8-1,5

Several relationships were also derived to determine the value of lost volume VL based onstability ratio N defined by Broms and Bennermarkem:

where: v - overall stress along excavation axis

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t - excavation lining resistance (if lining is installed)

Su - undrained stiffness of clay

For N < 2 the soil/rock in the vicinity of excavation is assumed elastic and stable. For N <2,4 local plastic zones begin to develop in the vicinity of excavation, for N < 4,6 a largeplastic zone develops around excavation and for N = 6 the loss of stability of tunnel faceoccurs. Figure shows the dependence of stability ration and lost volume VL.

Classical theoryConvergence analysis of an excavation and calculation of the maximum settlement in ahomogeneous body are the same for all classical theories. The subsidence trough analysesthen differ depending on the assumed theory (Peck, Fazekas, Limanov).

When calculating settlement the program first determines the radial loading of a circularexcavation as:

where: z - geostatic stress in center of excavation

Kr - coefficient of pressure at rest of cohesive soil

The roof ua and the bottom ub deformations of excavation follow from:

where: Z - depth of center point of excavation

r - excavation radius

E - modulus of elasticity of rock/soil in vicinity of excavation

- Poisson's number of rock/soil in vicinity of excavation

The maximum terrain settlement and the length of subsidence trough are determined as

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follows:



E - modulus of elasticity of rock/soil in vicinity of excavation


When the tunnel roof displacement is prescribed the maximum settlement is provided bythe following expression:



ua - tunnel roof displacement


Analysis for layered subsoilWhen determining a settlement of layered subsoil the program first calculates the settlementat the interface between the first layer above excavation and other layers of overburden Sintand determines the length of subsidence trough along layers interfaces. In this case theapproach complies with the one used for a homogeneous soil.

Next (as shown in Figure) the program determines the length of subsidence trough L at theterrain surface.

Analysis of settlement for layered subsoil

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The next computation differs depending on the selected analysis theory:

Solution after Limanov

Limanov described the horizontal displacement above excavation with the help of lost area F:

where: L - length of subsidence trough

F - volume loss of soil per 1m run determined from:

where: Lint - length of subsidence trough along interfaces above excavation

Sint - settlement of respective interface

Solution after Fazekas Fazekas described the horizontal displacement above excavation using the followingexpression:

where: L - length of subsidence trough

Lint - length of subsidence trough along interfaces above excavation


Solution after Peck

Peck described the horizontal displacement above excavation using the following expression:

where: Lint - length of subsidence trough along interfaces above excavation


Linf - distance of inflection point of subsidence trough from excavation axis atterrain surface

Shape of subsidence troughThe program offers two particular shapes of subsidence troughs – according to Gauss orAversin.

Curve based on Gauss

A number of studies carried out both in the USA and Great Britain proved that the transverseshape of subsidence trough can be well approximated using the Gauss function. Thisassumption then allows us to determine the horizontal displacement at a distance x from thevertical axis of symmetry as:

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where: Si - settlement at point with coordinate xi

Smax - maximum terrain settlement

Linf - distance of inflection point

Curve based on Aversin

Aversin derived, based on visual inspection and measurements of underground structures inRussia, the following expression for the shape of subsidence trough:

kde: Si - settlement at point with coordinate xi

Smax - maximum terrain settlement

L - reach of subsidence trough

Coefficient of calculation of inflection pointWhen the classical methods are used the inputted coefficient kinf allows the determination of

the inflection point location based on Linf=L/kinf. In this case the coefficient kinf represents avery important input parameter strongly influencing the shape and slope of subsidencetrough. Its value depends on the average soil or rock, respectively, in overburden – literatureoffers the values of kinf in the range 2,1 - 4,0.Based on a series of FEM calculations the following values are recommended:

- gravel soil G1-G3 kinf =3,5- sand and gravel soil S1-S5,G4,G5, rocks

R5-R6kinf =3,0

- fine-grained soil F1-F4 kinf =2,5- fine-grained soil F5-F8 kinf =2,1

The coefficient for calculation of inflection point is inputted in the frame "Project".

Subsidence trough with several excavationsThe principal of superposition is used when calculating the settlement caused by structured ormultiple excavations. Based on input parameters the program first determines subsidencetroughs and horizontal displacements for individual excavations. The overall subsidencetrough is determined subsequently.

Other variables, horizontal strain and gradient of subsidence trough, are post-processed fromthe overall subsidence trough.

Analysis of subsidence trough at a depthA linear interpolation between the maximal value of the settlement Smax at a terrain surface

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and the displacement of roof excavation ua is used to calculate the maximum settlement S at

a depth h below the terrain surface in a homogeneous body.

Analysis of subsidence trough at a depth

The width of subsidence trough at an overburden l is provided by:

where: L - length of subsidence trough at terrain surface


Z - depth of center point

z - analysis depth

The values l and S are then used to determine the shape of subsidence trough in overburdenabove an excavation.

Calculation of other variablesA vertical settlement is accompanied by the evolution of horizontal displacements which maycause damage to nearby buildings. The horizontal displacement can be derived from thevertical settlement providing the resulting displacement vectors are directed into the center ofexcavation. In such a case the horizontal displacement of the soil is provided by the followingequation:

where: x - distance of point x from axis of excavation

s(x) - settlement at point x


The horizontal displacements are determined in a differential way along the x axis and in thetransverse direction they can be expressed using the following equation:

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where: x - distance of point x from axis of excavation

s(x) - settlement at point x


Linf - distance of inflection point

Analysis of failure of buildingsThe program first determines the shape and dimensions of subsidence trough and thenperforms analysis of their influence on buildings.

The program offers four types of analysis:

- determination of tensile cracks

- determination of gradient damage

- determination of a relative deflection of buildings (hogging, sagging)

- analysis of the inputted section of a building

Tensile cracksOne of the causes responsible for the damage of buildings is the horizontal tensile strain. Theprogram highlights individual parts of a building with a color pattern that corresponds to agiven class of damage. The maximum value of tensile strain is provided in the text output.

The program offers predefined zones of damage for masonry buildings. These values can bemodified in the frame "Settings". Considerable experience with a number of tunnelsexcavated below build-up areas allowed for elaborating the relationship between the shape ofsubsidence trough and damage of buildings to such precision that based on this it is nowpossible to estimate an extent of compensations for possible damage caused by excavationwith accuracy acceptable for both preparation of contractual documents and for contractorspreparing proposals for excavation of tunnels.

Recommended values for masonry buildings from one to six floors are given in the followingtable.

Horizontal strains (per mille)Proportional h.s. (permille)

Damage Description

0.2 – 0.5 Microcracks Microcracks

0.5 - 0.75 Little damage - superficial Cracks in plaster

0.75 – 1.0 Little damage Small cracks in walls

1.0 – 1.8 Medium damage, functional Cracks in walls, problems withwindows and doors

1.8 - Large damage Wide open cracks in bearingwalls and beams

Gradient damageOne of the causes leading to the damage of buildings is the slope subsidence trough. Theprogram highlights individual parts of a building with a color pattern that corresponds to agiven class of damage. The maximum value of tensile strain is provided in the text output.

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The program offers predefined zones of damage for masonry buildings. These values can bemodified in the frame "Settings". Considerable experience with a number of tunnelsexcavated below build-up areas allowed for elaborating the relationship between the shape ofsubsidence trough and damage of buildings to such precision that based on this it is nowpossible to estimate an extent of compensations for possible damage caused by excavationwith accuracy acceptable for both preparation of contractual documents and for contractorspreparing proposals for excavation of tunnels.

Recommended values for masonry buildings from one to six floors are given in the followingtable.

GradientGradient Damage Description

1:1200 - 800 Microcracks Microcracks

1:800 - 500 Little damage - superficial Cracks in plaster

1:500 - 300 Little damage Small cracks in walls

1:300 - 150 Medium damage, functional Cracks in walls, problemswith windows and doors

1:150 - 0 Large damage Wide open cracks in bearingwalls and beams

Relative deflectionDefinition of the term relative deflection is evident from the figure. The program searchesregions on buildings with the maximum relative deflection both upwards and downwards.Clearly, from the damage of building point of view the most critical is the relative deflectionupwards leading to "tensile opening" of building.

Relative deflection

Verification of the maximum relative deflection is left to the user – the following tables listthe ultimate values recommended by literature.

Type ofstructure

Type ofdamage

Ultimate relative deflection /l

Burland and Wroth Meyerhof Polshin aTokar

ČSN 73 1001

Unreinforcedbearingwalls

Cracks inwalls

For L/H = 1 - 0.0004For L/H = 5 - 0.0008

0,0004 0,0004 0,0015

Cracks inbearingstructures

For L/H = 1 - 0.0002For L/H = 5 - 0.0004

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Failure of a section of building

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In a given section the program determines the following variables:

- maximum tensile strain- maximum gradient- maximum relative deflection- relative gradient between inputted points of a building

Evaluation of the analyzed section is left to the user – the following tables list therecommended ultimate values of relative rotation and deflection.

Type ofstructure

Type ofdamage

Ultimate relative gradient

Skempton Meyerhof Polshin aTokar

Bjerrum ČSN 73 1001

Framestructuresandreinforcedbearingwalls

Structural 1/150 1/250 1/200 1/150

Cracks inwalls

1/300 1/500 1/500 1/500 1/500

Type ofstructure

Type ofdamage

Ultimate relative deflection /l

Burland and Wroth Meyerhof Polshin aTokar

ČSN 73 1001

Unreinforcedbearingwalls

Cracks inwalls

For L/H = 1 - 0.0004For L/H = 5 - 0.0008

0,0004 0,0004 0,0015

Cracks inbearingstructures.

For L/H = 1 - 0.0002For L/H = 5 - 0.0004

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Rock slopeProgram for stability analysis of rock slope treats the following types of failure of rock faces:

- sliding on the plane slip surface

- translation on the polygonal slip surface

- fall of the rock wedge

Failure of a rock face due to sliding on the plane slip surface

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Translation on the polygonal slip surface

Fall of the rock wedge

Plane slip surfaceFailure on the plane slip surface is manifested by a rock block sliding down along this surface.The solution procedure requires determination of the normal force N acting on the slipsurface, the shear force Tact (active) and the resisting shear force Tres (passive).

Forces on the slip surface

The shear strength parameters and the normal force N acting on the slip surface are the main

input data for the determination of the resisting shear forces Tres. Calculation of the active

shear force Tact and the normal force N is further influenced by the weight of block (dependson the geometry and bulk weight of rock), anchorage, surcharge, influence of water andseismic effects. The active force and the normal force are determined as a sum of all forcesentering the analysis.

The program offers several types of plane slip surfaces:

- smooth

- undulating

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- stepped

The slip surface can be specified with a tension crack.

The resulting verification can be carried out either according to the theory of limit states orfactors of safety.

The resulting verification can be carried out according to the theory of limit states or factorsof safety.

Stepped slip surfaceIf the rock body contains a system of parallel discontinuous cracks inclined to the top face ofa rock and the second system is indistinctive, then it is possible to consider a formation of astepped (jagged) slip surface in the rock body. This surface can be introduced into theprogram using the Calla and Nicholas theory, which increases resistance on the slip surfaceby .

where: n - normal stress acting in the direction normal to the slipsurface

- waviness angle

T - effective tensile strength of steps in the intact rock

k - part of the height ht associated with steps in the intact rock(not created by a secondary system of planes)

ht - normal height of stepped wedge resting on an inclined planeof principal system of discontinuity planes

T0 - tensile strength of intact rock

Stepped slip surface

Tensile strength of rock

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Tensile strength Te is 20 to 30 x smaller than the strength of rock in simple compression c.

Strength in simple tension To for selected intact rocks [MPa]

Basalt 3 - 18

Gneiss 7 - 16

Granite 11 - 21

Limestone 3 - 5

Marble 7 - 12

Quarzite 4 - 23

Sandstone 5 - 11

Schist 5 - 12

Slate 2 - 17

Tuff 2 - 4

Undulating slip surfaceIf undulating surface is considered (on scale I to 10 m) – it is possible to account for wavinessby angle :

where: - slip surface gradient

i - gradient of the i-th fault of slip surface

The waviness increases the tensile strength on slip surface by :

where: n - normal stress acting in the direction normal to the slip surface

- waviness angle

Undulating slip surface

Anchorage of rock slopeTwo types of anchors can be defined when running the slope stability analysis on a plane slipsurface:

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ActiveAn active anchor is represented by a pre-stressed anchor, for which the anchor forces areactivated before the sliding of a rock block takes place. The normal force increases the normalstress on a slip surface and as such also the resisting forces; the tangent component of thenormal force is either added to or subtracted from the shear (active) forces.

PassiveA passive anchor is activated by sliding of a rock block (i.e. not pre-stressed anchors). Thenormal force increases the normal stress on a slip surface and as such also the resistingforces; the tangent component of the normal force is added to the resisting forces.

Resolution of anchor force

Surcharge of rock slopeThe surcharge resultant is determined first. The normal component of the resultant forceincreases the normal stress on a slip surface and as such also the resisting forces Tres, the

tangent component is either added to or subtracted from the shear (active) forces Tact.

Resolution of surcharge

Influence of water acting on slip surface

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The following options to account for water effects are available in the program:

Without ground water, water is notconsidered

Hydrostatic pressure, GWT abovetoe of slope

Hydrostatic pressure, GWT ontension crack

Hydrostatic pressure, GWT ontension crack, max

Hydrostatic pressure, water actingon tension crack only

Own water force acting on slipsurface only

Own water force behavior

GWT above toe of slope

Hydrostatic pressure, GWT above toe of slope

The slip surface is either entirely or partially below the ground water table, the maximalwater pressure is at the toe of face.

Hydrostatic pressure on slip surface

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The value of water pressure u at the heel of slope is given by:

where: w - bulk weight of water

ht - height of GWT above toe of slope

The resulting compressive water force acting in the direction normal to the slip surface isgiven by:


ht - height of GWT above toe of slope

- deflection of slip surface from horizontal

GWT on tension crack

GTW on tension crack

The slip surface is entirely below the ground water table; the GWT either intersects thetension crack or is aligned with terrain, the maximal value of uplift pressure is at the toe offace.

Hydrostatic pressure on slip surface and on tension crack, max. value at the toe of slope

The value of uplift pressure u at the intersection of slip surface and tension crack is given by:


ht - height of GWT above the line of intersection of slip surface and tensioncrack

The resulting compressive water force V acting in the direction normal to the tension crack isgiven by:

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- deflection of tension crack from vertical

The value of pressure u1 at the toe of slope is given by:

kde: w - bulk weight of water

Hw - height of GWT above toe of slope

The resulting compressive water force U acting in the direction normal to the tension crack isgiven:

kde: u - water pressure acting on the line of intersection of slip surface andtension crack

u1 - water pressure at toe of slope




GWT on tension crack, max

GWT on tension crack

The slip surface is entirely below the ground water table, the GWT either intersects thetension crack or is aligned with terrain, the maximal value of uplift pressure is at theintersection of tension crack and slip surface.

Hydrostatic pressure on slip surface and on tension crack

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The resulting value of pressure u1 at the toe of slope is equal to zero.

The resulting compressive water force U acting in the direction normal to the tension crack isgiven:

where: u - water pressure acting on the line of intersection of slip surface andtension crack




Water acting on tension crack only


The slip surface is fully dry; the GWT either intersects the tension crack or is aligned withterrain, the maximal value of uplift pressure is at the intersection of slip surface and tensioncrack.

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The value of water pressure acting on slip surface is equal to zero.

Own water force acting on slip surface only

Own water force acting on slip surface only

The program allows for a manual input of the value of water pressure ps in [kPa] acting on aslip surface, providing the pressure distribution is constant.

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Own value of water pressure acting on slip surface



The program allows for a manual input of the value of water pressure pt in [kPa] acting on atension crack, providing the pressure distributions are constant.

Own values of water pressure on slip surface and on tension crack

Polygonal slip surfaceThe program performs stability analysis of rock blocks moving along the polygonal slipsurface. Owing to the complexity of the general solution the program admits the followingassumptions:

motion of rock blocks is only translational blocks translate along the polygonal slip surface formed either by planar planes or

planes with moderate waviness rock blocks are divided by joints with known directions actual deformation of rock mass inside the blocks is negligible failure on the polygonal slip surface and along joints is driven by the

Mohr-coulomb failure criterion the same factor of safety is assumed for all joints and along the entire polygonal

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slip surface all rock blocks are in contact (opening of joints is not allowed) the shear forces on the polygonal slip surface have the same sign

The Mohr-Coulomb shear strength parameters on the slip surface and on joints separatingindividual block are the main input data for the determination of stability of rock blocks. Thesolution is further influenced by the weight of block (depends on the geometry and bulkweight of rock), anchorage, surcharge, influence of water and seismic effects.

The basic theoretical grounds of the solution are described here.

Polygonal slip surface

Geometry of rock blockThe block geometry is determined by the gradient , by the length of a given slip surface andby the gradient of a dividing joint separating the subsequent block as well as by thegradient and the length l of the top face of external surface of a rock slope (natural profile).Lengths of planes can be defined either by the total length or by the lengths of theirhorizontal and vertical projections. It is necessary to ensure the condition that all rock blocksare in contact (the opening between joints is not allowed).

Geometry of the i-th element

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Anchor forces, surchargeIt is possible to introduce anchor forces and surcharges of rock blocks. The resultant of forcesacting on the i-th block in kN/m is then determined. All forces acting on the block excludingthe water pressure on the slip surface and the joints are taken into account.

Surcharge acting on the blockIt is possible to input surface, strip and trapezoidal surcharge of terrain. The program thendetermines their effect on individual rock blocks.

Anchor forces

The applied anchor force is adjusted per 1m run based on the specified horizontal spacing ofanchors.

External forces on the i-th element

Influence of waterThe water pressure along the joints and on the slip surface can be taken into account. It isintroduced as external loading:

Water pressure on joints (water between blocks) FvIt must be introduced into the analysis whenever the presence of water in the joints betweenblocks is expected. It is applied as a resultant force Fv in kN (the pressure acting on theimmerse part of the joint per 1m run is considered).

Water pressure on the external slip surface (uplift pressure) UIt is defined as hydrostatic pressure on each slip surface of the polygon (external slip surface)separately and introduced as an external loading (uplift pressure) U in kN, which can bereduced depending on the slip surface permeability (the pressure acting on the immerse partof the slip surface per 1m run is considered).

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Water forces acting on a rock block

Solution procedureFor each rock block resting on the polygonal slip surface the program applies the basicequation of the stability of rock slope sliding along the plane slip surface as:

where: R - resultant of all active forces

k1 ,k2 - coefficients depending on slope gradient, inclination of anchorforce, angle of internal friction and factor of safety

c - cohesion on slip surface

G - tíha horninového tělesa ohroženého weight of a rock body indanger of sliding

such that the resultant of all active forces is assumed as an unknown interaction force Kibetween rock blocks (see figure). If, apart from interaction force, the i-th rock block is furtherloaded by other external forces, it is possible to write the interaction force of the i-th block inthe form:

where: ci - cohesion on slip surface of i-th block

Gi - weight of i-th rock block

PiG - overall external force acting on i-th block in vertical direction

PiK - overall external force acting on i-th block in the direction ofinteraction force

KiG - magnitude of interaction force on i-th block in vertical direction

KiK - magnitude of interaction force on i-th in the direction of K

k1i - coefficient depending on gradient of slip surface , gradient ofexternal loading i, stability of rock slope and angle of internal

friction i

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k2i - coefficient depending on gradient of slip surface , gradient ofexternal loading i, stability of rock slope and angle of internal

friction i

By combining the above forces it is possible to implicitly express the gradient of interactionforce Ki of the i-th block as:

where: i - gradient of interaction force Ki of i-th block

ci - cohesion on slip surface of i-th block

Ai - slip surface of i-th rock block

Ri - interaction force on i-th block

F - ratio of maximal shear resistance and acting shear force

i - angle of internal friction on slip surface of i-th block

Forces acting on slip surfaces between blocks (internal slip surfaces)

Rock wedgeThe program performs stability analysis of a rock wedge that is wedged in between twosurfaces (planes) and slides in the direction of the line of interaction (tray) of these planes.

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Gradient of this intersection must be considerably larger than the angle of internal frictionalong dividing planes, whereas the falling line of both dividing planes must be directedtowards the line of intersection. It is further assumed that the tray is located in a stable rockbody.

The solution requires determination of the normal force N, the shear force Tact (active)

and the resisting (passive) shear force Tres acting on slip surfaces A1 and A2. The active

force Tact and the normal force N are obtained as a summation all forces entering the analysisafter performing the space resolution of these forces.

The Mohr-Coulomb shear strength parameters and the normal force N acting on the slip

surface are the main input data for the determination of the resisting shear forces Tres.

Calculation of the active shear force Tact and the normal force N is further influenced by theweight of block (depends on the geometry and bulk weight of rock), anchorage, surcharge,influence of water and seismic effects.

The slip surface can be specified with a tension crack. The resulting verification can be carriedout either according to the theory of limit states or factors of safety.

Components acting on a rock wedge

Geometry of rock wedgeEntering geometry of a rock wedge using either gradient or falling line gradient directionrequires definition of space orientation of the rock face, terrain (top face), slip surfaces N1and N2 and/or tension crack, such that:

Gradient (gradient angle) is an inclination angle representing inclination of surfacefrom horizontal (it may receive values from 0° to 90°)

Gradient direction (falling line) is an angle between horizontal projection of the linenormal to the strike direction measured as an azimuth angle (from the north in theclockwise direction) (the falling line corresponds to inclination of the plane), it mayreceive values from 0° to 360°

The program when defining space orientation of planes displays these planes using a stereographic projection.

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Description of orientation of surfaces (vertical cut through a rock mass and plane projection)

Stereographic projectionWhen defining geometry of the wedge and slip surfaces using space projection, the programdisplays individual surfaces with the help of great circles of Lambert's hemisphericalprojection.

Hemispherical projection of the inclined plane

Influence of ground waterBy default the program performs the stability analysis of a rock wedge without consideringground water. If interested on the influence of ground water on a rock wedge it is necessaryto introduce the height of GWT from the line of intersection of slip surfaces and rock face (theGWT takes an arbitrary position over the entire height of a rock wedge). The programassumes that water can flow freely discontinuities located below the GWT (no restrictions,e.g. due to ice blocks, are considered).

The water pressure acts in the direction normal to the slip surfaces against normalcomponents of the passive forces. If the height yw above the point of maximal pressure Pmaxis equal or larger than Z/2 and it is fully contained by the rock wedge, then its value isassumed to be equal to Z/2 (case A). If the height yw above the point of maximal pressure Pmax is less than Z/2 (case B), then its value reduced as:

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where: L* - length of the line of intersection of slip surfaces A1, A2

1 - gradient of rock face

- gradient of the of line of intersection of slip surfaces

The resulting water pressure on slip surfaces 1 and 2 is given by:

where: Z - height of GWT above the line of intersection of slip surfaces and rockface

Pmax - maximal water pressure on the line of intersection of slip surfaces

w - bulk weight of water

A1w - are of the wetted part of the slip surface 1

A2w - area of the wetted part of the slip surface 2

A) B)

Distribution of water pressure on the line of intersection of slip surfaces

If a tension crack is found either entirely or partially below the GWT, then the influence ofwater pressure is reflected both on slip surfaces 1 and 2 through forces P1 and P2 acting on

intersection of these surfaces and on tension crack through force P3 acting in the directionnormal to the tension crack.

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Distribution of water pressure when considering GWT in tension crack

Resolution of acting forcesForces acting on a rock wedge (weight of rock wedge, external loading, anchor force) areresolved into directions normal to planes A1 and A2 (the block is wedged in between thesesurfaces) and into the direction of their intersection. The resolution of forces results into thenormal forces N1, N2 acting on planes A1 and A2, resisting (passive) forces Tres1, Tres2 acting

along planes A1 and A2.

This step further generates the shear (active) force Tact acting in the direction of the line of

intersection of slip surfaces. The resulting shear (active) force Tact is obtained as a sum of

individual shear forces Tact,i.

The resisting (passive) force Tres is found by summing up the components Tres1, Tres2 (e.g.

due to external loading) and friction forces on planes A1 and A2 due to normal forces:

where: c1 - cohesion on slip surface A1

c2 - cohesion on slip surface A2

φ1 - angle of internal friction on slip surface A1

φ2 - angle of internal friction on slip surface A2

Tvzd1 - resisting forces on slip surface A1

Tvzd2 - resisting forces on slip surface A2

Space resolution of self weight of earth wedge W

VerificationVerification can be carried out either according to the theory of limit states or factor ofsafety.

Verification according to the factor of safetyWhen performing verification according to the factor of safety the program directly

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determines the value of the factor of safety FS. Verification condition has the form:

where: Tpos - shear forces along the slip surface

Tvzd - passive forces along the slip surface

Fs - required factor of safety

When analyzing the polygonal slip surface the program directly determines the value of thefactor of safety FS. Verification condition has the form:

where: FS - calculated factor of safety

SB - required factor of safety

Typical values for most cases when studying stability of rock slopes are, e.g. for walls offoundation pits F =1,1 to 1,25, for rock cuts of highways F =1,2 to 1,5, etc.

Verification according to the theory of limit statesWhen performing verification according to the theory of limit states the program reducesmaterial parameters of rocks (angle of internal friction or tangent of the angle of internalfriction, cohesion) using partial coefficients entered in the frame "Settings".

Verification condition has the form:

where: Tpos - shear forces along the slip surface

Tvzd - passive forces along the slip surface

s - coefficient of the overall stability of the structure

When analyzing the polygonal slip surface the program compares the calculated value withthe value corresponding to the fully stressed design (state of equilibrium with zero reserve). Verification condition has the form:

where: FS - factor of safety calculated with the reduced material parameters

s - coefficient of the overall stability of the structure

Recommended partial coefficients according to EC7:

- coefficient of reduction of the angle of internal friction m = 1.25

- coefficient of reduction of the cohesion mc = 1.25

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Rock - shear resistance criteriaThe shear strength is the basic criterion to determine resisting passive forces. The resistingforce is given by the following expression:

where: - shear strength on the slip surface

l - length of the slip surface

The shear strength for the planar slip surface can be written as:

- Mohr - Coulomb

- Hoek - Brown

- Barton - Bandis

Mohr - CoulombThe shear strength according to the Mohr-Coulomb is given by:

where: N - normal force acting on the slip surface

l - length of the slip surface

c - cohesion of soil / rock


Approximate ranges of parameters of the Mohr-Coulomb failure criterion for selected soils aregiven here.

Parameters Mohr – CoulombIf possible the strength parameters should be determined in-situ measurements. The resultsof in-situ and laboratory experiments show that the angle of internal friction is found formajority of discontinuities in the rock mass in the range of 27° to 47°. Approximate values ofthe angle of internal friction and cohesion c for rocks based on the RMR classification arestored in the following table:

Rock class I II III IV V

RMR 100 - 81 80 - 61 60 - 41 40 - 21 < 20

angle of internalfriction

> 45 35 - 45 25 - 45 15 - 25 < 15

cohesion c [kPa] > 400 300 - 400 200 - 300 100 - 200 < 100

Hoek - BrownThe modified Hoek-Brown failure criterion describes the failure of a rock mass (based on theperformed analyses of hundreds of underground structures and rock slopes) as:

where: 1ef - major principal stress during rock failure

ef - minor principal stress during rock failure

- 472 -


c - strength of the intact rock in simple compression

mb,s - nonlinear material constant depending on the rock quality

a - coefficient depending on the rock breaking

Basic parameters of the modified Hoek-Brown model should be determined from in-situ andlaboratory measurements. To become more acquainted with this model, a brief list of rangesof individual parameters is provided.

If rock mass classification using GSI is known then it is possible to let the program todetermine the H-B parameters by itself. For actual analysis the H-B parameters are transformed into the M-C parameters. Thesolution procedure then becomes identical to that of the Mohr-Coulomb criterion.This transformation employs the solution derived by Hoek and Brown in 1990 for known valueof the effective normal stress n, which is typical for the solution of slope stability problem.

where: c - strength of the intact rock in simple compression

m - nonlinear material constant depending on the rock quality

a - coefficient depending on the rock breaking

Parameters Hoek – BrownParameter of rock breaking aParameter a is an exponent receiving values from 0,5 to 0,65 (for the original Hoek-Browncondition it is equal to 0,5) and depends on the degree of rock breaking.

Nonlinear parameters mb = m, s for a = 0,5(index r denotes residual values)

Carbonaterocks withwelldevelopedcleavage –dolomite,limestone,marble

Argillaceousrocks –mudstone,siltstone,shale, slate

Arenaceousrocks –sandstone,quartzite

Fine grainedigneouscrystallinerocks –andesite,dolerite,basalt,rhyolite

Coarsemetamorphicand igneousrocks –gabbro, gneiss,granite

- 473 -


Intact rockmaterialLaboratoryspecimens haveno discontinuitiesRMR=100Q=500

m = 7.00

s = 1.00

mr = 7.00

sr = 1,00

m = 10.00

s = 1.00

mr = 10.00

sr = 1.00

m = 15.00

s = 1.00

mr = 15.00

s = 1.00

m = 17.00

s = 1.00

mr = 17.00

s = 1.00

m = 25.00

s = 1.00

mr = 25.00

s = 1.00Very good qualityrock massRocks withoutisolated blocks,withnon-weathereddiscontinuitiesRMR=85Q=100

m = 2.40

s = 0.082

mr = 4.10

sr = 0.189

m = 3.43

s = 0.082

mr = 5.85

sr = 0.189

m = 5.14

s = 0.082

mr = 8.78

sr = 0.189

m = 5.82

s = 0.082

mr = 9.95

sr = 0.189

m = 8.56

s = 0.082

mr = 14.63

sr = 0.189Good quality rockmassSlightly damagedrocks withnon-weathereddiscontinuitiesspaced from 1 to3 mRMR=65Q=10

m = 0.575

s = 0.00293

mr = 2.006

sr = 0.0205

m = 0.821

s = 0.00293

mr = 2.865

sr = 0.0205

m = 1.231

s = 0.00293

mr = 4.298

sr = 0.0205

m = 1.395

s = 0.00293

mr = 4.871

sr = 0.0205

m = 2.052

s = 0.00293

mr = 7.163

sr = 0.0205

Fair quality rockmassPartiallyweathereddiscontinuitiesspaced from 0,3to 1 mRMR=44Q=1

m = 0.128

s = 0.00009

mr = 0.947

sr = 0.00198

m = 0.183

s = 0.00009

mr = 1.353

sr = 0.00198

m = 0.275

s = 0.00009

mr = 2.030

sr = 0.00198

m = 0.311

s = 0.00009

mr = 2.301

sr = 0.00198

m = 0.458

s = 0.00009

mr = 3.383

sr = 0.00198Poor quality rockmassNumerousweathereddiscontinuitiesspaced from 30 to500 mmRMR=23Q=0,1

m = 0.029

s = 0.000003

mr = 0.447

sr = 0.00019

m = 0.041

s = 0.000003

mr = 0.639

sr = 0.00019

m = 0.061

s = 0.000003

mr = 0.959

sr = 0.00019

m = 0.069

s = 0.000003

mr = 1.087

sr = 0.00019

m = 0.102

s = 0.000003

mr = 1.598

sr = 0.00019

- 474 -


Very poor qualityrock massNumerousextremelyweathereddiscontinuitieswith filling spacedby less than 50mm, fine grainedwaste rockRMR=3Q=0,01

m = 0.007

s =0.0000001

mr = 0.219

sr = 0.00002

m = 0.010

s =0.0000001

mr = 0.313

sr = 0.00002

m = 0.015

s = 0.0000001

mr = 0.469

sr = 0.00002

m = 0.017

s =0.0000001

mr = 0.532

sr = 0.00002

m = 0.025

s = 0.0000001

mr = 0.782

sr = 0.00002

Strength of rocks in simple compression c , Poisson's number and bulk weight of

rock Rockstrength

Types of rock (examples) Strength c[MPa]

Poisson'snumber

Bulk weight ofrock [kN/m3]

Solid rock most hard solid rock, intact,compact and dense quartz rockand basalt, other extraordinaryhard rocks

>150 0,1 28,00 - 30,00

Highlyhard rock

very hard granit rock, quartzporphyry, very hard granite,hard flinty shale, quartzite, veryhard sand rock and very hardcacite

100 - 150 0,15 26,00 - 27,00

Hard rock granite, very hard sandstoneand calcite, quarzite lode, hardconglomerate, very hard ore,hard limestone, marble,dolomite, pyrite

80 - 100 0,20 25,00 - 26,00

Rock sandstone, ore, medium sandyshale, flagstone

50 - 80 0,25 24,00

Mediumrock

hard mudstone, softer sandrock and calcite, chalky clay

20 - 50 0,25 – 0,30 23 - 24,00

Soft rock shale, soft limestone, calk, saltrock, frozen ground, anthracite,marl, remoulded sandstone,soft conglomerate, ground withfels

5 - 20 0,3 – 0,35 22,00 – 26,00

Weak soil compact clay, soil eluvium,black coal

0,5 - 5 0,35 – 0,40 20,00 - 22,0

18,00 - 20,00

Calculation of Hoek-Brown parametersIf rock mass classification using GSI (Geological Structure Index) is known then it is possibleto let the program to determine the H-B parameters as follows:

- 475 -


where: GSI - Geological Structure Index

D - damage coefficient of rock mass

mi - strength material constant of the intact rock for peakconditions

Values of damage coefficient D for rock slope

Description of rock massSuggestedvalue ofcoefficient D

Small scale blasting in engineeringslopes results in modest rock massdamage, particularly if controlledblasting is used. However, stressrelief results in some disturbance.(Good blasting).

0,7

Small scale blasting in engineeringslopes results in modest rock massdamage, particularly if controlledblasting is used. However, stressrelief results in some disturbance.(Poor blasting).

1

Very large open pit mine slopessignificant disturbance due to heavyproduction blasting and due to stressrelief from overburden removal.(Production blasting).

1

In some softer rocks excavation canbe carried out by ripping and dozingand the degree of damage to theslope is less.(Mechanical excavation).

0,7

Approximate vlaues of strength material constant of the intact rock mi (after Hoek)

Type of rock Representative rocks mi [-]

Limestone rocks with welldeveloped crystallinecleavage

Dolomite, calcite, marble

Consolidated clayey rocks Mudstone, siltstone, siltyshale, slate

Sandy rocks with solidcrystals and poorlydeveloped crystallinecleavage

Sandstone, quarzite

Fine grained igneouscrystalline rocks

Andesite, dolerite, diabase,rhyolite

- 476 -


Coarse grained andmetamorphic rocks

Amphibolite, gabbro,gneiss, granite, diorite

Barton - BandisThe Barton-Bandis shear strength failure criterion for the rock mass takes the following form:

where: JRC - joint roughness coefficient

n - normal stress acting on the surface of the rock joint

JCS - joint compressive strength

b - basic angle of internal friction of the slip surface

If possible the shear strength parameters should be determined from in-situ measurements.Approximate ranges of parameters of the Barton-Bandis failure criterion are given here.

Barton – Bandis parametersJoint roughness coefficient JRC

If the value of JRC cannot be determined by direct measurements on the joint surface, it ispossible to obtain this value from the Barton graph (see figure) showing the variation of thecoefficient JRC as a function of length of profile and roughness depth.

- 477 -


Diagram to determine JRC (after Barton)

Rock joint roughness profiles showing the typical range of JRC are plotted next.

- 478 -


Rock joint roughness profiles showing the typical range of JRC (Barton & Chubey 1977)

Compressive strength of discontinuity JCS

Methods allowing us to determine the compressive strength of discontinuity (slip surface) JCSare generally recommended by ISRM. The value of JCS can be obtained from the Deer-Millergraph showing its dependence on the rock strength found from the Schmidt hammermeasurements, see figure below.

- 479 -


Basic angle of internal friction on slip surface bThe basic value of the angle of internal friction on the surface is approximately equal to theresidual value r . Nevertheless, it can be generally measured in laboratories using shearmeasurement devices (typical area of the specimen is 50 x 50 mm). Typical ranges of thebasic angle of internal friction for weathered rock surfaces are 25° to 35°.

Bulk weight of rocksBulk weight or rock Rock strength Rock category (examples) Bulk weight of rock

[kN/m3]Solid rock most hard solid rock, intact, compact and

dense quartz rock and basalt, otherextraordinary hard rocks

28,00 - 30,00

Highly hardrock

very hard granit rock, quartz porphyry, veryhard granite, hard flinty shale, quartzite, veryhard sand rock and very hard cacite

26,00 - 27,00

Hard rock granite, very hard sandstone and calcite,quarzite lode, hard conglomerate, very hardore, hard limestone, marble, dolomite, pyrite

25,00 - 26,00

- 480 -


Rock sandstone, ore, medium sandy shale,flagstone

24,00

Medium rock hard mudstone, softer sand rock and calcite,chalky clay

23 - 24,00

Soft rock shale, soft limestone, calk, salt rock, frozenground, anthracite, marl, remouldedsandstone, soft conglomerate, ground withfels

22,00 – 26,00

Weak soil compact clay, soil eluvium, black coal 20,00 - 22,0

18,00 - 20,00

Influence of seismic effectsThe programs allows for taking into account the earthquake effects using two variables –coefficient of horizontal acceleration Kh and coefficient of vertical acceleration Kv.

The coefficient of acceleration is a dimensionless number, which represents the seismicacceleration as a fraction of the gravity acceleration. Earthquake effects are introducedthrough the seismic force S, which is determined by multiplying the weight of the rocksubjected to earthquake (i.e. rock block) by the coefficient of acceleration. When assuming seismic waves only in the horizontal direction the seismic force is given by:

where: Kh - coefficient of horizontal acceleration

W - weight of the rock body

The seismic force always acts in the center of gravity of the rock body. Usually, only seismiceffects in the horizontal direction are considered. Nevertheless, the program also allows fortreating the vertical direction (with the help of vertical coefficient of acceleration Kv). Effectsin both directions are then combined.

M_C_S grade horizontal acceleration coefficient of horizontalacceleration

(MSK-64) [mm/s2] Kh

1 0,0 - 2,5 0,0 - 0.00025

2 2,5 - 5,0 0,00025 - 0.0005

3 5,0 - 10,0 0,0005 - 0.001

4 10,0 - 25,0 0,001 - 0.0025

5 25,0 - 50,0 0,0025 - 0.005

6 50,0 - 100,0 0,005 - 0.01

7 100,0 - 250,0 0,01 - 0.025

8 250,0 - 500,0 0,025 - 0.05

- 481 -


9 500,0 - 1000,0 0,05 - 0.1

10 1000,0 - 2500,0 0,1 - 0.25

11 2500,0 - 5000,0 0,25 - 0.5

12 > 5000,0 > 0.5

The values of factor Kh correspond to individual degrees of earthquake according to M-C-Sscale

Dimensioning of concrete structuresConcrete structures can by analyze by folowing standards:

CSN 73 1201R

EC2 (EN 1992 1-1)

PN-B-03264

BS 8110

IS 456

ACI 31802

AS 3600-2001

CSN 73 1201 RThis help contains the following computationals methods:

Materials, coefficients, notation

Verification of cross-section made from plain concrete

RC rectangular cross-section under M

RC rectangular cross-section under the bending momentand normal compression force

Verification of spread footing for punching shear

Verification of circular RC cross-section

Materials, coefficients, notationThe following notation for material parameters is used:

Rbd - design strength of concrete in compression

Rbtd - design strength of concrete in tension

u - coefficient of the shape of cross-section

z - lever arm (arm of internal forces)

Coefficient u is given by equation:

- 482 -


The most common notation for geometrical parameters:

b - cross-section width

h - cross-section depth

he - effective depth of cross-section


Verification of cross-sections made from plain concreteThe cross-section is rectangular, loaded by the bending moment M, normal force N (appliedin the cross-section centroid) and by the shear force Q. The cross-section bearing capacitysubjected to bending moment is given by:

The shear strength is provided by:

Strength of concrete cross-section subject to the com bination of bending moment and normalforce is derived from the following expressions depending on the normal force eccentricity e:

for:

The ultimate bearing capacity is checket using the following formula:

RC rectangular cross-section under MThe cross-section is rectangular, reinforced on one side and loaded by the bending moment Md.

The ultimate moment is provided by:

- 483 -


The program further checks whether the location of neutral axis x is less than the limitlocation of neutral axis xlim given by:

The computed degree of reinforcement is checked using the following expressions:

RC rectangular cross-section under the bending momentand normal compression forceThe cross-section is rectangular, unilaterally reinforced and loaded by the bending moment Mand normal compression force. The location of the neutral axis follows from:

where:

For x < xlim permissible normal force is given by:

For x > xlim the corrected location of neutral axis is found from:

where:

Permissible normal force is given by:

- 484 -


Permissible bending moment is provided by:

Compression reinforcement is not taken into account.

Verification of spread footing for punching shearThe program allows for the verification of spread footing for punching shear or for the designof shear reinforcement. The critical section loaded in shear Ucr is distant from the column

edge by one half of the footing thickness. It is loaded by the prescribed moments Mx, My and

by the shear force Qr provided by:

where: A - area of footing

Q - assigned vertical force developed in column

At - hatched area in fig.

Dimensioning of shear reinforcement area At

The program computes the maximal shear force Qdmax developed in the critical section, the

shear force transmitted by concrete with no shear reinforcement Qbu, and the maximal

allowable force Qmax:

where for: is: or else:

For Qdmax < Qbu no shear reinforcement is needed.

- 485 -


For Qdmax > Qbu and Qdmax < Qmax the shear reinforcement must be introduced. The ultimate

shear force is given by:

where: Ucr - critical cross-section span

- is angle of crooks

As - overall area of crooks in footing

For Qdmax > Qmax the shear reinforcement cannot be designed. It is therefore necessary to

increase the cross-section height.

Verification of circular RC cross-sectionThe program verifies a reinforced concrete pile using the method of limit deformation. Themaximum allowable strain of concrete in compression is 0,002 - 0.0035. The degree ofreinforcement is checked using the formula:


As - reinforcement area

EC2 (EN 1992 1-1)This help contains the following computationals methods:


Standard values of coefficiens







fck - charakteristic value of cylindrical strength of concrete in copression

fcd - design strength of concrete in compression

fcm - average value of tensile strength of concrete

fctk0,05 - dolní hodnota charakteristické pevnosti betonu v tahu

- 486 -


fctd - design strength of concrete in tension

fyk - characteristic strength of steel

fyd - design strength of steel in tension

The characteristic compressive strength of concrete is the basic input parameter given by theclass of concrete – it serves to derive the remaining coefficients of reliability.

pro:

pro :

Standard values of coefficients cc,c,ct,s are built in the program – these values can alsobe inputted by the user depending on the selected National supplement.




d - effective depth of cross-section


Standard values of coefficientsThe standard contains a number of coefficients, which can be adjusted in supplements of National standards. The table provides description of individual coefficients, their valuesand corresponding artical of the standard. In some cases the formula contains a variable,which has no symbol in the standard - in such a case the variable in the expression isdenoted by X.

Coefficient Value Annotations Article

c 1,5 2.4.2.4

s 1,15 2.4.2.4

cc 1 3.1.6

ct 1 3.1.6

cc,pl 0,8 12.3.1

- 487 -


ct,pl 0,8 12.3.1

kf 1,1 2.4.2.4

k 1,5 12.6.3

min 0,0013 9.2.1.1

X 0,26 9.2.1.1

max 0,04 9.2.1.1

X 0,18 6.2.2

min - 6.2.2

X 0,5 6.2.2

- 6.2.2

RC rectangular cross-section under MThe cross-section is rectangular, reinforced on one side and loaded by the bending moment Msd. The permissible moment for a given area of reinforcements As reads:


Standard values of coefficients min, max are built in the program – these values can also beinputted by the user depending on the selected National supplement.


- 488 -


where:



where:




Verification of spread footing for punching shearThe critical section loaded in shear u is distant from the column edge by one half of thefooting thickness. It is loaded by the prescribed moments MEx, MEy and by the shear force Veprovided by:


V - assigned vertical force developed in column


- 489 -



The program computes the maximal shear force Ved developed in the critical section, the

shear force transmitted by concrete with no shear reinforcement VRd,c and the maximal

allowable force VRd,max:

Standard values of coefficients CRd,c, min,max are built in the program – these values canalso be inputted by the user depending on the selected National supplement.The subsequent verification then depends on the magnitude of maximal shear force VEd.

For VEd < VRd,c no shear reinforcement is needed.

For VEd > VRd,c and VEd < VRd,max the shear reinforcement must be introduced. The ultimate


where: u - critical cross-section span


Asw - overall area of crooks in footing

For VEd > VRd,max the shear reinforcement cannot be designed. It is therefore necessary to


Verification of cross-sections made from plain concreteThe cross-section is rectangular, loaded by the bending moment Msd, normal force Nsd(applied in the cross-section centroid) and by the shear force Vsd. The shear strength is provided by:

- 490 -


where: Acc - tlačená plocha betonu

Standard value of the coefficient k is built in the program (Art. 12.6.3) – this value can alsobe adjusted in the program based on the selected National supplement.Strength of concrete cross-section subject to the com bination of bending moment and normalforce is derived from the following expressions depending on the normal force eccentricity e:

Standard values of coefficients cc,pl, ct,pl, c are built in the program – these values can alsobe inputted by the user depending on the selected National supplement.

Verification of circular RC cross-sectionThe program verifies a reinforced concrete pile using the method of limit deformation. Themaximum allowable strain of concrete in compression is 0,002 - 0.0035. Cocrete strength fcd is reduced by ten percent due to shape of cross-section (Art. 3.1.7).

The degree of reinforcement is checked using the formula:

- 491 -



As - cross sectional area of reinfocement

Standard values of coefficients min, max are built in the program – these values can also beinputted by the user depending on the selected National supplement.

PN-B-03264This help contains the following computationals methods:



RC rectangular cross-section under the bending moment andnormal compression force





fck - characteristic strength of concrete in compression


fctk - characteristic strength of concrete in tension



fyd - design strength of steel

fctm - design strength of steel in tension

where: cc=1

ct=1

c=1,5 - for steel reinforced concrete structures

c=1,8 - for concrete strustures



- 492 -






The permissible moment for a given area of reinforcements As reads:

The program further checks whether the location of neutral axis x is less than the limitlocation of neutral axis xlim given by:

- for steel class A0

- for steel class AI

- for steel class AII

- for steel class AIII

- for steel class AIIIN


where:


where:

- 493 -




where:




Verification of spread footing for punching shearThe critical section loaded in shear u is distant from the column edge by one half of thefooting thickness. It is loaded by the prescribed moments Mx, My and by the shear force Nsdprovided by:




- 494 -



The program computes the maximal shear force Nsd developed in the critical section, the

shear force transmitted by concrete with no shear reinforcement Nrd1 and the maximal

allowable force Nmax:

For Nsd < Nrd no shear reinforcement is needed.

For Nsd > Nrd and Nsd < Nmax the shear reinforcement must be introduced. The ultimate




Asw - overall area of crooks in footing

For Nsd > Nmax the shear reinforcement cannot be designed. It is therefore necessary to


Verification of cross-sections made from plain concreteThe cross-section is rectangular, loaded by the bending moment Msd, normal force Nsd(applied in the cross-section centroid) and by the shear force Vsd. The cross-section bearing

capacity subjected to bending moment is given by:


where:

- 495 -


Strength of concrete cross-section subject to the com bination of bending moment and normalforce is derived from the following expressions depending on the normal force eccentricity e:

where:

Verification of circular RC cross-sectionProgramThe program verifies a reinforced concrete pile using the method of limitdeformation. The maximum allowable strain of concrete in compression is 0,002 - 0.0035.The degree of reinforcement is checked using the formula:

where:



BS 8110This help contains the following computationals methods:





Verification of cross-sections made from plain concrete

- 496 -




fcu - characteristic cube compressive strength of concrete

fy - characteristic strength of reinforcement


The characteristic compressive strength of concrete is the basic input parameter given by theclass of concrete.The most common notation for geometrical parameters:





All computations are carried out according to the theory of limit states.

RC rectangular cross-section under MThe cross-section is rectangular, reinforced on one side and loaded by the bending momentM.The permissible moment for a given area of reinforcements As reads:

The program further checks whether the location of neutral axis x is less than the limitlocation of neutral axis xmax given by:


where:

- for fy = 460 N/mm2


- 497 -



where:



where:




Verification of spread footing for punching shearThe critical section loaded in shear (Ucr) is distant from the column edge by one half of the

footing thickness. It is loaded by the prescribed moments Mx, My and by the shear force Vrprovided by:

- 498 -






The program computes the maximum shear force V developed in the critical section, theshear force transmitted by concrete with no shear reinforcement Vc, and the maximal

allowable force Vu:

where: c - is design concrete shear stress given by following table:

Effective dept d [mm]

100.As / b.h 150 175 200 225 250 300 400

1,15 0,50 0,48 0,47 0,45 0,44 0,42 0,40

0,25 0,60 0,57 0,55 0,54 0,53 0,50 0,47

0,50 0,75 0,73 0,70 0,68 0,65 0,63 0,59

0,75 0,85 0,83 0,80 0,77 0,76 0,72 0,67

1,00 0,95 0,91 0,88 0,85 0,83 0,80 0,74

1,50 1,08 1,04 1,01 0,97 0,95 0,91 0,84

2,00 1,19 1,15 1,11 1,08 1,04 1,01 0,94

3,00 1,36 1,31 1,27 1,23 1,19 1,15 1,07

The c values are for fcu below 40N/mm2 multiplied by (fcu/40)1/3

or 5 N/mm2

- 499 -


c - is ultimate shear stress

For V<Vc no shear reinforcement is needed.

For V>Vc and Vc<Vu it is necessary to design shear reinforcement. The permissable shear

force is given by:


- angle of crooks

Aus - overall area of crooks in footing

For Vc>Vu the shear reinforcement cannot be designed. It is therefore necessary to increase

the cross-section depth.

Verification of cross-sections made from plain concreteThe cross-section is rectangular, loaded by the bending moment M, normal force N (appliedin the cross-section centroid) and by the shear force V.Strength of concrete cross-section subject to the com bination of bending moment and normalforce with eccentricity e is derived from the following expressions:

where:


where: c - is the design value of shear stress in concrete for degree of longitudinalreinforcement =0 (see :Verification of spread footing for punchingshear).

Verification of circular RC cross-sectionThe program verifies a reinforced concrete pile using the method of limit deformation. Themaximum allowable strain of concrete in compression is 0,002 - 0.0035.


where:

- 500 -






IS 456This help contains the following computationals methods:



RC rectangular cross-section under the bendingmoment and normal compression force





fck - characteristic cube compressive strength of concrete


fctk - characteristic strength of concrete in tension




The characteristic compressive strength of concrete is the basic input parameter given by theclass of concrete – it serves to derive the remaining coefficients of reliability.

- 501 -








RC rectangular cross-section under MThe cross-section is rectangular, reinforced on one side and loaded by the bending momentM.The permissible moment for a given area of reinforcements As reads:

The program further checks whether the location of neutral axis x is less than the limitlocation of neutral axis xmax given by:

- for steel Fe 250

- for steel Fe 400

- for steel Fe 500



- 502 -


where:



where:




Verification of spread footing for punching shearThe critical section loaded in shear Ucr is distant from the column edge by one half of the

footing thickness. It is loaded by the prescribed moments Mx, My and by the shear force Vrprovided by:




- 503 -



The program computes the maximum shear force V developed in the critical section, theshear force transmitted by concrete with no shear reinforcement Vc, and the maximal

allowable force Vmax:

where:

where: cx,cy - are dimensions of footing column

c,max - is the maximum allowable shear stress in concrete listed in table 20of the IS 456 standard

For V<Vc no shear reinforcement is needed.

For V>Vc and Vc<Vmax it is necessary to design shear reinforcement. The permissable shear

force is given by:



Aus - overall area of crooks in footing

For Vc>Vmax the shear reinforcement cannot be designed. It is therefore necessary to

increase the cross-section depth.

Verification of cross-sections made from plain concreteThe cross-section is rectangular, loaded by the bending moment M, normal force N (appliedin the cross-section centroid) and by the shear force V:

- 504 -



where: c - is the design value of stress in concrete obtained from table 19 of theIS456 standard for degree of longitudinal reinforcement =0.

Strength of concrete cross-section subject to the com bination of bending moment and normalforce with eccentricity e is derived from the following expressions:

where:

Verification of circular RC cross-sectionThe program verifies a reinforced concrete pile using the method of limit deformation. Themaximum allowable strain of concrete in compression is 0,002 - 0.0035.


where:



IS Road Bridges

ACI 31802This help contains the following computationals methods:

- 505 -









f´c - design strength of concrete in compression

Ec - modulus of elasticity

The modulus of elasticity is provided by:





Verification of cross-sections made from plain concreteThe cross-section is rectangular, loaded by the bending moment M, normal force N (appliedin the cross-section centroid) and by the shear force Vn.The shear strength is provided by:

Strength of concrete cross-section subject to the com bination of bending moment and normalforce is derived from the following expressions:for compression side:

where:

A1 - loaded area

for tension side:

- 506 -


where:


The ultimate moment is provided by:



- 507 -


where:



where:




Verification of spread footing for punching shearThe program allows for the verification of spread footing for punching shear or for the designof shear reinforcement. The critical section loaded in shear Ucr is distant from the column

edge by one half of the footing thickness. It is loaded by the prescribed moments Mx, My and

by the shear force Vu provided by:


- 508 -





The program computes the maximal shear force Vu developed in the critical section, the shear

force transmitted by concrete with no shear reinforcement Vc, and the maximal allowable

force Vmax:

For Vu < Vc no shear reinforcement is needed.

For Vu > Vc and Vc < Vmax the shear reinforcement must be introduced. The ultimate shear

force is given by:

where: Ucr - critical cross-section span


As - overall area of crooks in footing

For Vc > Vmax the shear reinforcement cannot be designed. It is therefore necessary to



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AS 3600-2001This help contains the following computationals methods:








f'c - characteristic copressive cylinder strength of concrete at 28 days

Ec - mean value of the modulus of elasticity of concrete at 28 days

- density of concrete , in kilograms per cubic metre (kg/m3)

f'cf - characteristic flexural tensile strength of concrete

f'ct - characteristic principal tensile strength of concrete

fsy - yield strength of reinforcing steel

The characteristic compressive strength of concrete is the basic input parameter given by theclass of concrete.The most common notation for geometrical parameters:


D - cross-section depth



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Verification of cross-sections made from plain concreteThe cross-section is rectangular, loaded by the bending moment M, normal force N (appliedin the cross-section centroid) and by the shear force V.The shear strength is provided by:

Strength of concrete cross-section subject to the com bination of bending moment and normalforce is derived from the following expressions:

where:

Ag - loaded area

RC rectangular cross-section under M, VThe cross-section is rectangular, reinforced on one side and loaded by the bending momentM.The permissible moment for a given area of reinforcements As reads:

The program further checks whether the of neutral axis parameter Ku is less than the limit

value:

where:

x - depth of neutral axis

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where:

The program further checks ultimate shear strength:

where:


where:



where:

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where: D - pile diameter


Verification of spread footing for punching shearThe program allows for the verification of spread footing for punching shear. The criticalsection loaded in shear Ucr is distant from the column edge by one half of the footing

thickness. It is loaded by the prescribed moments Mx, My and by the shear force V* providedby:




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The program checks, whether the cross-section bursting strength is sufficient according to therelation:

where:

where: h - the ratio of the longest overall dimension of the effective loaded area, Y, to the overall dimension, X, measured perpendicular to Y

a - the dimension of the critical shear perimeter measured parallel to thedirection of M*v

M*v - the bending moment transferred from the slab to a support in thedirection being considered

The analysis is carried out independently in directions x and y, as the decisive one the lowervalue of Vu is accepted.

Verification according to CSN 73 6206When selecting "CSN 73 6206", frame "Project", the verification analysis of decisive jointsis performed according to the standard CSN 73 6206 "Design of concrete and steel reinforcedconcrete bridge structures", including changes a-10/1989 a Z2/1994. The program allows forverification of cross-sections from plain concrete or single-ended steel reinforced concrete. Allcalculations related to concrete are carried out using the theory of allowable stresses.

The main difference when compared to other standards appears in the dimensioning ofconcrete joints where the earth pressure is computed always without reduction of inputparameters independently of the input in the frame "Settings".

When performing the verification analysis of cross-sections made either from plain or steelreinforced concrete it is possible input the coefficient of allowable stress according to art.

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47 CSN 73 6206 to increase the material allowable stress.

The following joints can be verified by the program:

Abutment stem – foundation, construction joint - the cross-section can be made eitherfrom plain or steel reinforced concrete. The joint is verified for the load due to normal forceand bending moment. The allowable stresses of concrete, steel and concrete in concentricpressure are checked. In case of reinforced concrete the program also checks the degree ofreinforcement, cross-sections from plain concrete are then checked for overturning (h/2e<1,35) and translation (N.f<1,5; friction concrete-concrete is assumed as f=0.5),

Closure wall - bearing block - the cross-section is verified for the load due to normal forceand bending moment. The steel reinforced concrete cross-section is always assumed. Theallowable stresses of concrete and steel and the degree of reinforcement are checked.

Wing wall – abutment – the joint can be made either from concrete or steel reinforcedconcrete. The allowable stresses of concrete, steel and concrete in concentric pressure arechecked. In case of reinforced concrete the program also checks the degree of reinforcement.

Front jump of abutment foundation – the front jump of abutment is verified according toits projection. In case of jump projection v < 0.5 hz (hz is the height of foundation jump) the

program checks the magnitude of stress in principal tension due to forces developed in theabove-foundation joint. The stress is determined as:

where: d - width of above-foundation joint

M,N - moment and normal force in above-foundation joint

In case of jump projection v > 0.5 hz the jump is analyzed as cantilever bended by the

reaction (stress) of foundation soil. The joint can be made either from concrete or steelreinforced concrete. The allowable stresses of concrete, steel and concrete in concentricpressure are checked. In case of reinforced concrete the program also checks the degree ofreinforcement.

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Index

- 1 -1.LS - bearing of a footing 194

- 2 -2.LS - settlement and rotation of a footing 195

- 3 -3D View 264

- A -About company 295Accounting for wall jump 358ACI 31802 504Active dimensions and objects 25Active earth pressure 303, 307, 306, 304, 305, 303, 308Adding and editing section 73Adding interface 35Adding picture 287Adhesion of soil 345Alternate angel of internal friction of soil 319Analyses in program Ground Loss 442Analysis 69, 84, 98, 57, 215, 251Analysis 69, 84, 98, 57, 215, 251Analysis according to EC 7-1 (EN 1997-1:2003) 395Analysis according to NEN (Buismann, Ladd) 420Analysis according to the Janbu theory 422Analysis according to the theory of limit states / factor of safety 385Analysis for coarse-grained soils after Janbu 422Analysis for cohesionless soils after Janbu 422Analysis for cohesive soils after Janbu 424Analysis for layered subsoil 445Analysis for overconsolidated cohesive soils after Janbu 424Analysis for overconsolidated sands and silts after Janbu 423Analysis for sands and silts after Janbu 423Analysis of anchored wall fixed in heel 368Analysis of anchored wall simply supported at heel 369Analysis of bearing capacity of foundation 391Analysis of failure of buildings 449Analysis of internal stability 349Analysis of nails bearing capacity 347Analysis of sheet pile wall 367Analysis of subsidence trough 442Analysis of subsidence trough at a depth 447Analysis of walls 353Analysis using the compression constant 419Analysis using the compression index 419Analysis using the oedometric modulus 418Analysis using the Soft soil model 421Analysis – plane slip surface 262Analysis – polygonal slip surface 263Analysis – rock wedge 268Anchor forces, surcharge 463Anchorage of rock slope 455Anchors 61, 80, 93, 384Anchors – plane and polygonal slip surface 260Anchors – rock wedge 267Arrango theory 340AS 3600-2001 509Assign 60, 75, 146, 173, 92, 200, 106, 134, 185, 272, 161, 53, 120, 223, 212, 237, 249Assign 60, 75, 146, 173, 92, 200, 106, 134, 185, 272, 161, 53, 120, 223, 212, 237, 249Assigning soils 38

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Automatic calculation of height 274

- B -Barton - Bandis 476Barton – Bandis parameters 476Base anchorage 125, 111, 354Basic data 269Bearing capacity 152, 179, 114, 140, 168, 243, 128, 231Bearing capacity of foundation on bedrock 394Bearing capacity of foundation soil 360Bearing capacity on drained subsoil 391Bearing capacity on undrained subsoil 393Blocks 156Bore holes 278Braced sheeting 379BS 8110 495Buildings 246Bulk weight of rocks 479

- C -Calculating abutment forces 366Calculation of Hoek-Brown parameters 474Calculation of other variables 448Changing inclination of dividing planes 388Characteristics of settlement analyses 431Circular slip surface – Petterson, Bishop 389Classical theory 444Coefficient m 439Coefficient of calculation of inflection point 447Coefficient of increase of limit skin friction 406Coefficient of passive earth pressure Kp 312Common input 29Compression constant 434Compression constant 10 435Compression index 431Concentrated surcharge 331, 336Connecting programs 41Constant distribution of modulus of subsoil reaction 413Constrains on the optimization procedure 100Control menu 13Control menu Print and export 291Copy to clipboard 26Corrector of inputted interface 36CSN 73 1201 R 481

- D -Damages 252Dependence of shear on deformation 412Depth of deformation zone 406Design coefficients 39Determination of cross-sectional internal forces 402Determination of the depth of influence zone 429Dialogue windows 24Dimensioning 196, 180, 169, 231, 244, 114, 141, 153, 128Dimensioning of concrete cover 352Dimensioning of concrete structures 481Dimensioning of masonry wall 359Distribution of earth pressures in case of broken terrain 320Distributions of forces acting on pile 412

- E -Earth - pressure wedge 327Earth cut 210, 90Earth grading 279

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Earth pressure 302Earth pressure at rest 316Earth pressure at rest for inclined ground surface at the back of structure 317Earthquake 67, 83, 166, 241, 56, 111, 139, 151, 178, 97, 125, 229, 261Earthquake 67, 83, 166, 241, 56, 111, 139, 151, 178, 97, 125, 229, 261Earthquake effect 384EC2 (EN 1992 1-1) 485Edges 275Editing interface 36Effective area 401Effective/total stress in soil 298Embankment 209, 89Envelopes 88Estimated bond strength 349Excavation 76Export DXF 49External stability 245, 87

- F -Factor of safety 350Failure of a section of building 451Foliation 389Footing 158Force of transmitted by nails 350Forces 67, 80Foundation steps 220Frames 21Front face resistance 164, 109, 137, 149, 176, 123, 227

- G -Generate 281Geo-reinforcements, mesh overhangs 354Geometry 61, 73, 157, 234, 51, 103, 131, 188, 143, 171, 201, 117, 249, 264Geometry 61, 73, 157, 234, 51, 103, 131, 188, 143, 171, 201, 117, 249, 264Geometry 61, 73, 157, 234, 51, 103, 131, 188, 143, 171, 201, 117, 249, 264Geometry cut 217Geometry of nails 235Geometry of rock block 462Geometry of rock wedge 466Geometry plane view 219Georeinforcements 384Geostatic stress, uplift pressure 297Global coordinate system 270Gradient damage 450GWT above toe of slope 456GWT on tension crack 457GWT on tension crack, max 458

- H -Height multiplier 101Hoek - Brown 471Homogenization of layered subsoil 400Horizontal bearing capacity 207, 412Horizontal bearing capacity of foundation 398Horizontal tool bars 14Hydrodynamic pressure 323Hydrostatic pressure, ground water 321, 322

- I -Import - export DXF 46Import of loading 187Import of points 274Incompressible subsoil 211, 409Increment of earth pressure due to surcharge 299

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Increment of earth pressure under footing 300Increments of vertical loading 412Index of secondary compression 440Influence of earthquake 337Influence of foundation depth and incompressible subsoil 417Influence of friction between soil and back of structure 343Influence of ground water 467Influence of loading history 438Influence of sand-gravel cushion 418Influence of seismic effects 480Influence of technology 410Influence of tensile cracks 326, 390Influence of water 321, 341, 382, 463Influence of water 321, 341, 382, 463Influence of water acting on slip surface 456Input regimes and analysis 50Inputted forces 165, 110, 138, 150, 177, 124, 228Inputting and editing soils 30Inputting data using template 47Interface 89, 208Interfaces in 2D environment 34Internal stability 86, 242Internal stability of gabion 362Internal stability of gabion wall – factor of safety 365Internal stability of gabion wall – limit states 364IS 456 500IS Road Bridges 504

- J -Janbu characteristics 437

- L -Launching 285Limit loading curve 405Line constructions 284Line surcharge 332Linear modulus of subsoil reaction 413Load 186, 201Loading - LC 223

- M -Manual classification of soil 33Material 103, 131, 190, 170, 202, 117, 220, 236Materials, coefficients, notation 481, 486, 491, 496, 500, 505, 509, 372Measurement 250Method of restriction of the magnitude of primary stress 430Minimal dimensioning pressure 326Modeling terrain on edges 282Modified compression index 439Modifying template during data input 48Modulus of subsoil reaction 71, 198, 373Modulus of subsoil reaction - Chadeisson 376Modulus of subsoil reaction - CSN 73 1004 414Modulus of subsoil reaction - CUR 166 374Modulus of subsoil reaction - iterations 376Modulus of subsoil reaction - Matlock and Rees 414Modulus of subsoil reaction - Ménard 375Modulus of subsoil reaction - Schmitt 375Modulus of subsoil reaction - Vesic 415Mohr - Coulomb 471Mononobe–Okabe theory 340

- N -Nailed slopes 347

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Negative skin friction 204, 409Nonlinear modulus of subsoil reaction 380

- O -Oedometric modulus 433Optimization of circular slip surface 390Optimization of polygonal slip surface 388Options 26Options - input 29Options – copy to clipboard 27Options – print picture 28Outputs 287Overall settlement and rotation of foundation 417Overconsolidation index of secondary compression 441Own water force acting on slip surface only 460Own water force behavior 461

- P -Page numbering 295Page properties 294Parameters Hoek – Brown 472Parameters Mohr – Coulomb 471Parameters of rocks 346Parameters to compute foundation bearing cap. 396Parameters – polygonal slip surface 258Parameters – rock wedge 266Passive earth pressure 308Passive earth pressure - Absi theory 314Passive earth pressure - Caquot – Kérisel theory 310Passive earth pressure - Coulomb theory 310Passive earth pressure - Müller – Breslau theory 313Passive earth pressure - Rankin and Mazindrani 309Passive earth pressure - Sokolovski theory 314Passive earth pressure – total stress 316Picture list 288Pile analysis 403Plane slip surface 452PN-B-03264 491Point constructions 283Points 272Polygonal slip surface 461Polygonal slip surface - Sarma 386Pressure specification 63Primary settlement 426Print and export document 289Print and export picture 290Profile 159, 51, 59, 71, 104, 132, 183, 144, 172, 198, 118, 221, 236, 247Profile 159, 51, 59, 71, 104, 132, 183, 144, 172, 198, 118, 221, 236, 247Program Abutment 216Program Block Wall 143Program Cantilever Wall 102Program Earth Pressure 50Program Gabion 170Program Gravity Wall 130Program Ground Loss 246Program Masonry wall 116Program Nailed slopes 233Program Pile 197Program RediRock Wall 155Program Rock slope 254Program Settlement 208Program Sheeting Check 70Program Sheeting Design 58Program Slope Stability 88

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Program Spread Footing 182Program Terrain 269Project 88, 50, 58, 143, 170, 197, 102, 130, 182, 155, 70, 116, 208, 216, 233, 246, 254, 269Project 88, 50, 58, 143, 170, 197, 102, 130, 182, 155, 70, 116, 208, 216, 233, 246, 254, 269Project 88, 50, 58, 143, 170, 197, 102, 130, 182, 155, 70, 116, 208, 216, 233, 246, 254, 269Project 88, 50, 58, 143, 170, 197, 102, 130, 182, 155, 70, 116, 208, 216, 233, 246, 254, 269Project - Analyses 182Project – Earth pressures 29Props 62, 81

- R -RC rectangular cross-section - bending moment 483, 487, 492, 497, 501, 506RC rectangular cross-section - bending moment.. 511RC rectangular cross-section under M 482, 487, 492, 496, 501, 506, 510Reading data into template 47Recommended values of parameters for volume loss analysis 443Recompression index 436Reduction coefficient of passive earth pressure 313Reinforcements 94Reinforcements 94Relative deflection 450Resolution of acting forces 469Rigid body 92Rock 256Rock - shear resistance criteria 471Rock slope 451Rock wedge 466Running more analyses / verifications 40

- S -Sand-gravel cushion 189Scale color definition 45Secondary settlement 428Selecting and storing views 42Setbacks 156Setting 166, 57, 68, 84, 112, 139, 193, 151, 178, 98, 205, 126, 229, 215, 241, 262Setting 166, 57, 68, 84, 112, 139, 193, 151, 178, 98, 205, 126, 229, 215, 241, 262Setting color range 44Setting header and footer 293Setting results visualization 43Setting visualization style 19Settings 251Settlement analysis 415Settlement analysis using DMT 425Shape of subsidence trough 446Shear resistance on skin 410Shear strength of skin 406Sheeting check 370Sheeting design 367Sign convention 302Slip surface - polygonal 257Slip surface – plane 256Slip surface – rock wedge 265Slope stability analysis 381Soil and rock labels 33Soil body 381Soil classification 32Soils 160, 248, 52, 59, 72, 105, 133, 184, 145, 173, 91, 199, 119, 222, 212, 237, 271Soils 160, 248, 52, 59, 72, 105, 133, 184, 145, 173, 91, 199, 119, 222, 212, 237, 271Soils 160, 248, 52, 59, 72, 105, 133, 184, 145, 173, 91, 199, 119, 222, 212, 237, 271Solution according to CSN 73 1001 395Solution procedure 464Special distribution of water pressure 324Stability 169, 115, 142, 154, 181, 129, 233

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Standard analysis 392, 394, 395Standard values of coefficients 486Stepped slip surface 453Stereographic projection 467Stiffness of subsoil below the pile heel 411Stress in a soil body 297Stress in the footing bottom 416Strip surcharge 330, 335Style manager 20Subsidence trough with several excavations 447Supports 62, 82Surcharge 163, 329, 55, 66, 79, 108, 136, 191, 148, 175, 95, 122, 226, 213, 240, 383Surcharge in non-homogeneous soil 334Surcharge of rock slope 455Surcharge – plane and polygonal slip surface 260Surcharge – rock wedge 266Surface surcharge 329, 334, 337

- T -Table of recommended values DELTA/FÍ 345Table of ultimate friction factors 344Tables 22Tensile cracks 449Tensile strength of rock 454Terrain 161, 54, 64, 77, 106, 134, 146, 174, 120, 224, 238, 255Terrain 161, 54, 64, 77, 106, 134, 146, 174, 120, 224, 238, 255Theory 297Theory of limit states 351Theory of settlement 425Theory of structural strength 429Tool bar 3D visualization 17Tool bar Files 14Tool bar Plot setting 16Tool bar Print and export 292Tool bar Scale and shift 15Tool bar Selections 18Tool bar Stage of construction 16Trapezoidal surcharge 331, 336Types of nails 234

- U -Undulating slip surface 454Unit metric / imperial 26Uplift pressure in footing bottom 325User catalogue 74User defined environment 12Using function Find 12

- V -Verification 167, 113, 140, 152, 179, 127, 230, 242, 469Verification 167, 113, 140, 152, 179, 127, 230, 242, 469Verification - factor of safety 357Verification according to CSN 73 6206 513Verification according to the factor of safety 470Verification according to the theory of limit states 470Verification of bearing capacity of nails 352Verification of circular RC cross-section 485, 490, 495, 499, 504, 508, 512Verification of cross-sections - plain concrete 482, 489, 494, 499, 503, 505, 510Verification of internal stability of structure 378Verification of spread footing for punching shear 484, 488, 493, 497, 502, 507, 512Verification – limit states 356Vertical bearing capacity 205Vertical bearing capacity - FEM 404Vertical bearing capacity CSN 205

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Vertical bearing capacity FEM 206Vertical bearing capacity – according to CSN 403Vertical tool bars 18Void ratio 436Volume loss 442

- W -Wall dimensioning 361Water 277, 162, 54, 65, 78, 107, 135, 147, 175, 96, 121, 225, 214, 239Water 277, 162, 54, 65, 78, 107, 135, 147, 175, 96, 121, 225, 214, 239Water acting on tension crack only 459Water – plane slip surface 259Water – rock wedge 268Water, incompressible subsoil 192, 203Window for application 12Wings 218Without ground water, water is not considered 321World coordinates 38

ggeo5manual

Documents

tool bar scale

setting visualization

tool bar selections

tool bar files

tool bar plot

setting results visualization

assigning soils

program slope stability