cad for high embankments-iit

7/27/2019 CAD for High Embankments-IIT

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COMPUTED AIDED DESIGN SYSTEMFOR

HIGH EMBANKMENT PROBLEMS

Revised Version(Including Users Manual for the Software HED Ver 1 .0)

Sponsoredby

Ministry of Surface Transport

(Roads Wing)

Government of India[Research Scheme : R-65J

Prof. A. VaradarajanProf. K.G. Sharma

DEPARTMENT OF CIVIL ENGINEERING

INDIAN INSTITUTE OF TECHNOLOGY, DELHIHAUZ KHAS, NEW~ELHI- 110016

MARCH, 1998


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ACKNOWLEDGEMENT

We express our thanks to Ministry ofSurface Transport for referring the problem

to us In particular, we are thank f l u to M r. Indu Prakash, Chief Engineer, who provided

uselbi comments in the development ofthe program. Mr. AK. Sharma and M r. AK.

Saxena, Superintending Engineers, extended cooperation for the successful completion of

the project.

Mr A . Ravi Kumar, Project Scientist oflIT Delhi incorporated various features

including graphics with Visual Basic,

We are grateful to ill [)elhi for providing various facilities required for the work.


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Scope

Method ofAnalysis

Soil Parameters 3

Pore Pressure Ratio 4

Reinlbrcement Force 4

Seismic Coefficient 4

Terms used in the Program 5

Program Description 6

installation ofthe Program 7

Data an d Input 8

input data file 8

Il 1 .1 Executing the Program with data in an input file 1 2

Input through User Interactive Windows 1 6

2 1

24

CONTENTS

. 4 i A , zou /ttigcflhi/ul

I U Intiodrictitni

Page No.

TO

o

. 4 0

S 0

~) 0

7 0

S U

)Q

1 0 0

1 1 1 )

III

112

LXampIe.s


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SLOPE STABILITY ANALYSIS

1 .0 INTRODUCTION

Laying of roads for highways often involve cutting a n d filling of earth and

construction of culverts, bridges and flyovers. Construction of embankments is an

important aspect ofhighways be it in filling or for approach for bridges. Embankments

ma~have varying heights and may be constructed on soft ground. They may serve as

water retaining structures besides being a highway and may be located in earthquake

prone regions.

Design ofan embankment essentially requires evaluation ofits stability against

failure Slip circle method based on limit equilibrium is the common method adopted for

conducting stability analysis ofembankments. Due to its improved accuracy simplified

Bishops method is increasingly adopted for the analysis. A computer program has

already been developed earlier using Bishops method, In the present project, the

computer program has been improved to include additional features.

2.() SCOPE

The scope ofthe project is to include (i) earthquake force (ii) pore water pressure

4L~~oln~rinedfrom pore presstiie ratio. r 1 , or flow/water table and (iii) reinforcement force

at the embankment-foundation interface in the existing program. Additional feature is to

incorporate graphics in the program for presentation ofthe results. Procedure to evaluate

material parameters is to be discussed.

3M METHOD OF ANALYSIS

In this method, overall stability ofthe sliding mass on an assumed circular surface

is evaluated using limiting equilibrium method. Factor ofsafety with respect to incipientfailure on the rupture/failure surface is determine~using moment equilibrium conditions.

Method ofslices is adopted and interslice forces are considered.


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I:actc~irof safety F is defined as

Available shear strength ofsoil

Required shear strength to maintain equilibrium

Fhe mohilised shear strength, s is defined as

%:: I[c+(a~ - ii) tan # 1 1

tchere c effective cohesion intercept

4 ) = effective angle ofshearing resistance

= total normal stress

u pore pressure

(onsidering the equilibrium ofpotential sliding mass ofunit thickness bound by a

circular arc ofradius R with centre 0. Fig-l(a), factor ofsafety by simplified Bishops

method (1955) is derived with the following notations

F~,j: ; = The horizontal forces on the sections n and n+l

N,, N1, = The total vertical shear forces

= The total weight ofthe slice ofsoil

1 = The total normal force acting on its base

I i = The height ofthe slice

h = The breadth ofthe element

The length B C

a = T he angle between BC and the horizontal

total normal stress a,, = P/I

F= -~~-- L[lc?h + tan~(W hu)+ (X - X )))]~Wsrna tanYsina

cosa+I .

~~ithearthquake forces in the vertical and horizontal forces ct~Wand a,W and

reinforcement force 1 located as shown in Fig-l(b).

~ tan~lH(I + a~) z e b +(X~- 1 /)~1ni 1 ?

I .-.- I

I tJ(l 4 a,)sina +Wa

2


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Fig.1 (a) Forces in the slices ( Bishop).

(b) Earthquake and reinforcement forces.

nR

V

(0)

P

1~lV

0~hW.

(b)


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where,

tan #sinain = cosa 4-

~1

I,,

In simplified Bishops method, E(x~x~) = 0, then

Ic b tan ~ W~I 4- a ) -- 4 I

F .. ~

1 + a,.)Sifl a + WahR

I)etining pore pressure ratio, !~ Ti,

IchtanW(?+a~)-r~}~?1~a R

EtW(l+a~.)sina+Wah~]

uhie term F occurs on both sides ofthe equation and its value is obtained by trial and errora tier a number ofiterations

4.0 SOIL I~ARAMETERS

The stability analysis of highway enibankments is conducted using Simplified

Rishops method. In the analysis effective stresses are used. The material parameters

that are used are cohesion intercept c and angle of shearing resistance ~ in addition to

total unit weight ofsoil, Yi

The embankment and foundation material may consist ofcoarse grained soil such

as sand and silty sand or fine grained soil such as clay and silty clay.

In the case ofcoarse grained soil, direct shear test or consolidated drained test or

consolidated drained triaxial test may be condUcted. For fine grained soils either

consolidated undrained triaxial test with pore water pressure measurement or

consolidated drained triaxial test with volume change measurement may be performed.

1


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.,

8C

6c~

40

o.

I-

ff1___ __

~~rtsA~(p.s~

Z(.)

C

s..- -

2

~1t,~

Fig.2. Diagramatic variation o~pore pressure parameter ~with principal stress ratio and major principal stress

tRishop & Margenstern ~960J

ko. ~

AO~:k~AtT,(F:1.S)

&3~kf.AOj~

(F: to)


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,

l~hcsamples may he prepared to a density that i s anticipated in the field. The normal

stress for direct shear test and the confining pressure for triaxial tests to be used may be

in the average range ofstress in the embankment foundation system. The details ofthe

tests are found in various books and codes (for example Bishop and Henkel, 1962,

Lambe,1951, IS code IS:272OPart 12(1981)).

The unit weight ofthe soil may be determined using standard procedure outlined

in various 1 3S Codes

~.() PORE PRESSURE RATIO, r~,The procedure for evaluation ofr~1is presented in detail by Bishop and

Morgenstern (1 9(tYt. 1or earth till placed dry ofoptimum, the value ofr,2 is taken as zero

lii he case ot earth lilt placed wet ol opt imu in, the value ofr~is assumed to be equal to

the pore pressure parameter B which is equal to ~ The value of B is essentially a

nction ofstress ratio as shown in Fig. 2. The relationship shown in Fig. 2 is obtained

I~vcnnducting a consolidated undrained triaxial test with pore pressure measurement,

b.0 REINFORCEMENT FORCE

Reinforcement is used at the interface between embankment and foundation to

steepen the slope for the given height ofembankment or to increase the height of

embankment for the given slope. Reinforcement in the form ofgeosynthetic materials is

otten used when the embankment is constructed on soft foundation. The embankment in

~,uchcases is designed taking into consideration various modes offailure viz, sliding

: failure, squeezing failure, bearing capacity failure and rotational failure. Thecinl~rcementforce is determined for reinforcement stiffness with an allowable axial

strain The details on these are found in various books such as Soil Reinforcement with

(~ctextilesby Jewell (1996)

7.0 SEISMIC COEFFICIENT

Based on occurrence ofearthqdake, ?ndia has been-divided into five zones as per

the 13 5 code on criteria for Earthquake Resistant Design ofStructures. The horizontal

earthquake coefficients to he used for various zones are as follows:

4


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___ ______

Zone I - 0.01

Zone 1 1 - 0.02

Zone Ill - 0.04

Zone IV - 0.05

Zone V - 0.08Depending on the location ofthe embankment, suitable earthquake coefficient as

above may he chosen for the analysis

LI) TERMS USED IN THE PROGRAM

I1TLE : Title ofthe problem

NINT : No. of top external soil lines defining the outer

embankment geometry

NLINE : No. of total lines (including external and internal soil

lines)

NSLI No. ofSlices

NRT Indicator for Reinforcement (ONo, PYes)

NPROB : Indicator for pore water pressure (lUsing r ~ 1 , 2Using

Watertable line)

NMAT : No. ofmaterials in the problem

SLUR : Surcharge over the embankment in mass/area2 (assumed

within XTOP & XTOPI)

flOP X- Coordinate for the highest point towards left edge of

the embankment

XiOPl : X-Coordinate for the heighest point towards right edge of

the embankment

N It,!) Starting XCoordinate for the ith line

~ 1(1) Starting Y-Coordinate for the ith line

X2( I) Ending XCoordinate for the ith line

v 2(l) Ending XCoordinate tor.(he ith line

WF( I) l)ensity ofthe soil below the ith line

( IIS~1) C ohcssio n


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*

~

S

~

3

1)

.4

I,

.4

.4

I

FRC(1) :

UPP(l) : r,, for the soil below the ith line ifNPROB

7w for the soil below the ith line ifNPROB = 2

El : X coordinate for starting centre ofcircle

C : Y coordinate for starting centre ofcircle

ItS : incremental shift for X coordinate ofcentre ofcircle

RIIS : Incremental shift for Y coordinate ofcentre ofcircle

AEPHAN : Horizontal seismic coefficient

ALPHAV : Vertical seismic coefficient

I FR : Reinforcenient forceV coordinate ofreinforcement level

(T(Hl Y coordinate for the starting elevation to which all circles are

tangent

DCTCH : Incremental shift for CTCH for finding absolute minimum factor

ofsafety

9.0 PROGRAM DESCRIPTION

The program is written in Visual Basic and compiled using Visual Basic 5.0

Enterprise Edition. It can run on any IBM compatible computer using Micro Soft -

Windows 95 as Operating System.

Program execution starts with the input and output file name query. ifthe input is

saved in a file, give the file name, otherwise give the input through user interactive forms.

After all the input data is read, searched for least factor ofsafety for each value ofCTCH

begins. Initial value ofFactor ofsafety is assumed asone (1.0) and RHS is calculated

an d compared with LHS. Newton Raphson method is followed to achieve an early

convergence. This procedure starts for the centre ofcircle as specified in the input file.

This centre is shifted in both the directions by incremental distances specified (first in X

and then in the Y direction) and the calculation stops if the tendency ofan increase in

factor ofsafety is observed all around a ~oint1~andthis point corresponds to the centre for

the critical circle. I

6


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the above procedure for finding critical circle for a given CTCH (the level to

which all circles are tangent) is repeated changing the values ofCTCH. The least factor

o f safety i s thus located, and the corresponding circle offailure is identified.

While using the program, a consistent system ofunits is to be followed, i.e. all the

input values should have the same unit for Mass, Length and Time.

I t has been noticed that sometimes while executing the programme, the computer

hangs up. To avoid this, rerun the program with changed values ofHS, RHS and CTCHI.

Program can include surcharge ofthe embankment and negative values ofX and

V coordinates can also be specified.

Approaches to bridges are often subjected to high flood level. Due to this, the soil

iii the embankment may be saturated The pore water pressure so generated can be

calculated as u y~.h, where I i is the average depth ofthe slice base from the HFL. Pore

water pressures SO calculated can be reduced to a single value ofr~by averaging out over

the whole area ofthe embankment cross section. The pore water pressures above the

IIFL being generated due to capillary action (predominant in fine grained soils only) can

be ignored as these are negative pore water pressures adding to the stability ofthe slope.After the execution ofthe program the output can be seen in the graphics form. If

the results are not satisfactory, modif~the input data and re execute the program. The

output file consists ofall the input data for verification and safety factor tables for each

value ofCTCH with minimum factor of safety written below it Safety factor table

consists ofcentre ofcircle coordinates, radius ofcircle, intersection points with the outer

soil lines t,XC I and X(.2) and the corresponding safety factor. The output file can be

edited ifrequired before taking the printout.

10.0 INSTALLATION OF THE PROGRAM

- lnsertthe DISKI In drive A(orB) ofyour computer

U - Click the mouse on Start

- Click the mouse on Run

- A window entitled Run will appear

- Type a\setup (or b:\sctup) in the O~ientext box

- (lick the mouse on OK

7


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- Windows will start Copying Installation tiles

- Follow the Instructions displayed on the screen

- Insert I)ISK2 and press OK

- Now a window tiled SSA S e t u p will appear

- Click the mouse on OK bLitton

- A directory c:\program fiIes\SSA\in which SSA setup is installing the software

will be seen

- lithe default directory shown by SSA setup is OK, click the mouse on the

command button with computer icon

- Ifthe software is to be installed in a directory other than the default, click the

mouse on the command button Change Directory

- When a window titled Change Directory is seen, enterthe directory in which the

software is to he installed and click the mouse on OK

a .. Click the mouse on the command button with computer icon

- SSA Setup will start copying the files

- Insert DISK3 and click the mouse on OK

a - After a few seconds a message SSA Setup was completed successfully will

appear

- Click the mouse on OK

11.0 DATA & INPUT

The input data for this program can be given in two ways(1) Input through a input data file

(2) User interactive forms

1 1 . 1 Input data file:

Data Ibr a sample problem (fig ) is also given in the following for each input data set

(AS(lI form only Use MSDOS Editor(Edit.com) to generate the file)

Input Format for data file is as follows:I Title of the problem

T11LF Title ofthe problem (Maximum of80 Characters)

SAMPLE PROBLEM (Sample Data)

8


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N() ~ [:

y,~fir the ith line ifNPROB~~2

2. Control Data -

NINT : No. of top external soil lines defining the outer

embankment geometry

NLINE : No, of total lines (including external and internal soil

lines)(maximum 50 lines)

NSL.~I : No. ofslices (Maximum 200)

NRT Indicator for reinforcement (ONo, lYes)

NPROB Indicator for pore water pressure (lUsing r~. 2Using

water table line)

NMAT : No. ofmaterials in the problem

5 7 100 1 2 3

3. Control Data - 1 1

SUR Surcharge over the embankment in mass/area2 (to be within XTOP

& XTOPI)

XTOP : X- Coordinate for the highest point towards left edge of

the embankment

XTOPI : X-Coordinate for the heighest point towards right edge of

the embankment

0 100.0 108.0

4. Line and soil data

Xt(1)

Yl(I)

X2(I)

Y2(l)

(HS(l)

FRC(l)

IJPP( I)

Starting X-Coordinate for the ith line

Starting V-Coordinate for the ith line

Ending X-Coordinate for the ith line

Ending X-Coordinate for the ith line

Density ofthe soil below the ith line

Cohession

Angle ofinternal friction (4 )

i, for the soil below the ith line ifNPROB r~z

The above line and soil data has to be repeated NLINE (Total n o. of lines) times


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l

,

~

,

,

0~

04

4

,

S

II

2. Lw NPROR 2 some of the lines will represent water line. For these lines an d lines

hclow tJPP( 1) y~is given an d lbr the rest of the lines UPP(l) = 0

O 200 86.5 200 1 5 17 0 9.81

86.5 200 1 0 0 206 20 0 32 0

100 206 108 206 20 0 32 0

lOS 206 121.5 200 20 0 32 0

121.5 200 164 200 15 17 0 9.81

86,5 200 121.5 200 15 17 0 9.8!

0 196 164 196 15 10000 45 0

5. Coordinate Data -

11

(i

[Is,

KIlN

t\[.,Pl IA.NA 1,.. PItA V

X coordinate for starting centre ofcircle

y coordinate for starting centre ofcircle

Incremental shift ofX coordinate ofcentre of circle

Incremental shift ofV coordinate ofcentre ofcircle

Horizontal seismic coefficient (4 away from embankment)Vertical seismic coefficient (+ in the direction ofgravity)

(Fig. 1(b))

092 208 0.5 0.5 0

Reinforcement data (ifNR T > 0 )

TFR Reinfircement force

VT, V

coordinate ofreinfbrcemeni

level263.7 200

7 l)ata tbr tangency

C l(IIi

point and minimum factor ofsafety

\ coordinate for the starting elevation to which all circles are

tangent

Incremental shill fbr CTCI I for finding absolute minimum factor

of safbty

[98 0.5

Xl. X22

c--.cTcHi)

C,:(v2-cTcHI)xts.clcHl

FiG,),It)


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8 Dal a for Label I ing (Used to write the labels in graphics)

Name ofthe material Name of the material to be written in graphics

1)ensit, Cohesion, Angle ofInternal Friction and r 1 1 : Properties ofthe above

material

Label X coordinate X coordinate ofthe label (name ofthe material)

Label V coordinate Y coordinate ofthe label

Note ihe above labels data has to be repeated NMAT times

Soil I

15 1 7 0 9.81 L05 199

Soil 2

20 0 32 0 105 204

Soil 3

1 5 1000 45 0 lOS 195

1 i~ L ti)l ~1t~l)Cl~It~111I C ) 0 : ! ,

lit) 08 01 8 6 5

~ 200 100

101 1 , 08(08 ~0( 1 2 1 c

I 1 5 200 I o4805 200 121.5

(1 19 6 164~2 208 0,52o1 7 2 0 00)8 0.5

Soil IS I

7 0 081 05 199Sod 210 0 .C 0 105 204Soil

S lOiHO 45 0 lO S 195

9,81

0

00

9 8 19.81

0

>,oies

lhc ~t,uideiinest~rfinding F ! & (1 are as shown in fig. 3

. 2Recommended value [Orthe incremental shill is 0 2m

1 1 he in put data file will he

200 1 5 1 7 0

206 20 0 12

206 20 0 32200 20 0 32

200 15 1 7 0200 1 5 1 7 0196 IS 10000 45

0 . 5 0 0

11


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I. I, F~eciitingthe I1t~4)~E~1fl1with data in an input lilt

S hck the mouse on Start

S From the Programs options select SSA ((lick the mouse on NSA)

S A window titled SLOPE SFAI3IJ1ITV ANAIXSIS will appear asking you Is Input

Saved in a file ?

S Pull down I he combo box

S click the mouse on \es

5 1 1 iiter i he Inpul file Name wilt appear

I \pe N a inpie Problem in the I ct box

Slope StabilityAnalysis

Is rnput Saved in a File ? I Yss

Enter the Input File Name JSa.,k Probism

(lick the mouse on the command button Execute

After executing program, a window titled Sample Problem

(lick the mouse on the menu Options

S (lick the mouse on GraI

S 1 1w graphical representation ofthe problem with the slip circle will be seen

12


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;..f~fl,i fn~~~2o,~t.

ti K

i4 ii V ,Mnterj~~Unit W t C P h pSoiti 15 j~

So) 2 20 0 32Soil 4 15 10000 45

Soil I

Soil 3

105 115 1 2 5

PR i .NT I NG

(lick the mouse on Options

(lick the mouse on Print

S Print window will appear10 Enter the number ofcopies required and click the mouse on 01~I

1 ?


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* (lick the mouse on Next >>

N Now anot h t, r window titled Slope Stahily Analysis Lineand Soil Data will

ipptar

N in this window the text box Test 1 D filled with the Test Id given in the previous loriii

will appear

N l nter the da t a for line I an d click the mouse on Update

N ( lick the mouse on Add and enter the. data for line 2

N (lick the mouse on Update

N Repeat the above procedure till the data for all the lines are entered

lestld Sample Problem

ne No,

Starting

Starting V C.nord

F rid ny 8 Coord

lading V

hensityof Soit

Cohesion of Soil

Angle of mt Friction

it for So i t

i i ,

joe-~.

i~

~i ~T[~uo

1 ~PT-

(o.

J9.81 ~P!.: 1

- aJ_~~jbdatj ~U~wd 1 ~ffi:N ~ i~, nIt! in the d~uafk w il l the lines. Click the mnuse on Next >>

N s ~. ~~nd~~ titled Slope Stability Analysis . I ,ahels with the Test Id as given in

F r for in Slope Siahilit Analysis Control Data w ill appear

N ItL data in IH ~. 6 run) is nthtnl% tis~d to displa~on the graphical represt_ntation ofthe

bleniN I ~ the n twe t~ the nat i I id its n~1I;cinttwlu ~ the label is ii. b

1 di~platt.~l)an d

Ii P~N~and click tIic mouse or1 I pdate

I X


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Density

C o hesi on

lest Id:

Name of the Materiot

Sample Problem

Fit

Label X Coord [102

Label V Coord

frF~

[1~..An g of mt Friction

ru * 1 1

S...1~LJ_~e. ,Qpdetc j ____ P_I \ i l i l rnle~ins~all the materials click the mouse on Execute

\ftet ext utii i~tprogran a W I i rdow titled Sa nip Ic Problem will appear

(lick the mouse on the menu Options

N t lick the mouse on Craf

N N ti\V the tu aplut. al r rpresentatiofl of the problem with the slip circle will appear

Peinf Force 263 7 Material Unit Wt. C P h iEQEQ

in.Xdn.inYdn,

:0:0

SoilSoilSoil

1

2

3

152015

17010000

03245

24 U

235

230

225

220

215

210

205

200

Factor of Safety: 177Radius 1250Centre 9300. 2t0,50

Water Table

Soil 1

Soil 3

65 75 85 9 5 1 0 5 115 1 2 5

Samplc Prohkm

19


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PRINTING

N Click the mouse on Options

N Click the mouse on Print

N Now the Print window will appear

N Enter the number ofcopies required and click the mouse on OK

OUTPUT

N Click the mouse on Options

: N Click the mouse on OutputN Now the output file (The file is saved in the directory, where the software is installed

with extension out) will be seen

lidit the output file as per your requirements and from the File menu print the file

4 N Click the mouse on File menu

N Click the mouse on Exit, to exit from the output file

N From the Options menu, Click th e mouse on Exit to exit from the program

4

4

20


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Sample Problem 2 ( Without Reinforcement)79 1001 3

I S 11)11112

2.00 20.00 0 .02.00 20.00 0.0

(it) 1 )0 142 00

8500 14200

~2 50 45 00I 1 0 (~150 00II 2 1 1 ) 150.00

110 50 145.001240014200

)2 50 14500

8800 142.00

4 IS 4.5 0 2

88.00 142.00 2.3092,50 145.00 2.20

100 00 150.00 2.0011200 150.00 2.00119.50 145.00 2.00124.00 142.00 2 20130.00 142.00 2.30

119.50 145,002.20

124.00 4200 2.3002 0 0

0 500.50

0 50

2 002.00

2.002 00

32.00 0.032.00 0.0

32.00 0.0

20.00 0.0

20.00 0.0

20.00 0.0

20.00 0.0

410 c

Soil I2. 2 200 105 140

Soil 2

: 2 20 0 105 144

Soil . 1

U C 0 lOS 148

Pcinf Force 0~ LQ.inXdn. :0

EQ inYdn. :0

180

17 5

1/0

14h~

Material Unit W t, C P h i ruSoilI 2 ,3 2 200Soil 2 2.2 2 20 0Soil3 2 0 ,5 320

Factorof Safety: 1.57Radius: 15.90Centre : 89.20 . 157,90

..... .. . , .. ~... ..65 75 85 9!$~ 1 0 5 11 5

Siunpk P n i t i l e i n 2

t25 1

2 1


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tO) (01 l42 (1(188 00 142 (0)

SI uS ii))(It) 150 101

IY))I0

:1 ~t) 1 )S Ut)

It) ti:IS (Ut

I i:

1 4 S IC

~1

I .1 1 )

22 :n () l0~144

20 S 420 105 14$

Peirif In, e 0EQ nXdn :01EC.~ in V O n : 0

142.00 2 30 2 00 20.00 0 0145.00 2.20 2,00 20.00 0.0

15000 200 050 3200150,002.00 050 32.00

145.00 2 00 1)50 32 00142 00 2 20 2,00 20,00142.00 2 30 200 20.00145.00 2 20 2 00 20 00

142.00 2.30 2.00 20 00

0.0

0.00.0

0.00.0

0 0

0 0

Factor of Sofety:1.39Radius: 14.50Centre: 89.40 156,50

Soinple P i obleili I (With Earthquake force)

7 ~ 10013

[01) 112

8 8 0092 5010000

I 17 . 00

11950

124.01)

1)000

119 50

I 24 00

02 0.1 0

Material Unit Wt C Ph i ruSoil 1 2.3 2 20 05~112 2 .2 2 200Soil3 2 0.5 320

It

IL.

75 65

Sampk Problem 3

F

95 105 115 125

22


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Sample Problem 4310200220 9 15 11.614

(1 0 0. 19.64 1000. 45 0.00 915 6.10 1964 ~1.3l 32. 0.0

n 1 11.614 6.10 1964 431 32 0.0

(I 11.614 0. 19.64 1000 45. 00

2 59 0 566 1 9 64 4.31 32 9 $

2.~)

Ills

12SI)

:1 .18)

4 15 1 )

0 566 2.853 0 890 1 9 64 43! 32 9 8

) 1 890 3 480 1 .538 1964 4 3! 32 9.8

1538 4450 2.185 19.64 4 3! 32 9.8

2185 7527 .1480 l96~4 4.31 32 98

1480 11.614 4775 19.64 4.31 32 9.84~ 0 1 5 0.2 0.2 0. 0.

11 0

U oil I[L) 64 100004500.0-5-0.5

Soil 2

96443132.00.062

Pecnf Force : 0 Material Unit W t. C P h iLQ in X dn, : 0 Soil 1 19.64 1000 45

1 EQ inYdn :0 Soil 2 19.64 4.31 32

Factorof Safety: 1 .2 4Radius: 1 0 .7 8centre : 0.69 1 0 .7 5

Wnler Table

Soil 1

20 -15 -10 - b 0 5 10Sample P r o b l e m 4

2 3


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RFFFRFNCES

Bisho, A.W, (1995), The use ot~hcSlip Circle in the Stability Analysis ofEaflh Slopes,(coiechniq~e~Vol.~ P P 7-17.

Bishop and Henkel, (1962), Measurement of Soil P r o p e f l i e s in the Triaxial T~st~

Edward Arnold Ltd., London, Second Edition.

Bishop, A.W. and Morgenstern, NP. (1960), Stability Coefficients of Earth Slopes,

Geotechni,~ue3,,Vol.10, pp. 129-150,

iS 2720 Part 1 2 (1981), Shear Strength Parameters ofSoil from Consolidated Undrained

Test with Measurement ofPorewater Pressure.

Jewell, RA, (1996), $oil Reinforcement with Geotextiles. CIRIA, 6 Stores Gate,

Westniinister, London SWIP 3AU.

Lambe, TW. (1961), Soil Te~ti~gfor~Engineers.~johnWiley & Sons, New York.

cad for high embankments-iit

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