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DR. SPANG

CIVIL ENGINEERING AND GEOTECHNICAL CONSULTANTS LTD.

Company: Register of Companies No. HRB 971, District Court Witten, VAT-IdNo. DE126873490, President Dr. Raymund M. SpangMain Office Witten: Westfalenstrae 5 - 9, D-58455 Witten, Tel. (23 02) 9 14 02 0, Fax (23 02) 9 14 02 20, [email protected],

http://www.dr-spang.de

Branch Offices: D-09596 Freiberg/Sachsen, Halsbrcker Str. 34, Tel. + Fax (37 31) 36 55 31, [email protected] Esslingen/Neckar, Bahnhofstr. 23, Tel. (7 11) 9 31 91 88, Fax (7 11) 9 31 59 93, [email protected]

Bank Accounts: Stadtsparkasse Witten, Code 452 500 35 - Acc. No. 4911 - Deutsche Bank 24, Witten, Code 430 700 24 - Acc. No. 8139511

ROCKFALL 6.1

Rockfall Simulation Program

Manual

November 2001

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Simulationsoftware ROCKFALL 6.1 1

Manual (release: 27.11.2001)

Contents Page

1. INTRODUCTION 2

2. INSTALLATION 3

3. THEORY AND GENERAL OUTLINE OF ROCKFALL SIMULATION 4

4. INPUT DATA 64.1 Slope geometry 64.2 Slope surface qualities 64.3 Qualities of rockfall 74.4 Rockfall barriers 84.5 Sampling cross sections 84.6 Parameter variation 84.7 Start parameters 84.8 Steering parameters 9

5. OUTPUT 95.1 Single rock 95.2 More than one rock 11

6. HANDLING AND USER INTERFACE 13

6.1 Files 146.2 Input and Editing 156.3 View 18

6.3.1 Run 186.3.2 Screen 226.3.3 Print 24

6.4 Options 277. LITERATURE 30

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1. INTRODUCTION

ROCKFALL is a computer program for the simulation of rockfall. It was developed by Dr. rer.

nat. R.M. Spang, Dr.-Ing. L. Weber, Dipl. Geol. N. Graf and Dr.-Ing. B. Romunde. The program

is based on the laws of motion and the collision theory. The path of a single rock block or of up

to 10.000 blocks, can be calculated and interpreted by the same run. At each point within a

profile (especially at the positions of planned interception structures or rockfall barriers) the

kinetic energies and bounce heights can be calculated. The input data are varied by a random

number generator within user defined boundaries. The results are presented in class and

summation histogram.

ROCKFALL can be used for the following applications:

Evaluation of the rockfall risk for slopes.

Examination of existing rockfall barriers.

Positioning of new rockfall protection structures.

Optimization of the position and dimension of protection structures as for height and

energy.

The software can be used with every commercially available computer working under W INDOWS

NT or WINDOWS 95, or 98. There are no requirements for any additional hardware. Any

computer showing sufficient performance under the mentioned operating systems, is suitable.

Installation needs approximately 7 MB free disc space for the exe file, the auxiliary files and

some DLL libraries. As the required disc space for project data and calculation results strongly

depend on your individual project geometry and boundary conditions no general specifications

can be given. At least 5 MB of free space should be available. Some menu images in this

manual may show Version 6.0, but the menus are the same as in the actual version.

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2. INSTALLATION

Within this chapter the installation procedure is described. To install the program execute the

following steps:

Insert the ROCKFALL program CD. If possible close all running applications. Start

SETUP/SYSTEM/SOFTWARE/INSTALLATION.

Choose setup.exe from your CD drive and start the installation procedure.

Indicate drive and directory for program installation. Default path for the program

installation is: C:\PROGRAMS\ROCKFALL61. The installation procedure copies RF6B.EXE,

some auxiliary files and six examples for input data files into the mentioned directory and

establishes an entry in the W INDOWSstart menu.

If ROCKFALL is the first software coded in V ISUAL BASIC6.0, you are going to install at

your computer, WINDOWSneeds a reboot of the system to actualise system files. After

booting your system, simply repeat the installation procedure.

If the following message appears:

File xy.DLL is older than the file to be copied

you should select KEEP EXISTING FILE

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3. THEORY AND GENERAL OUTLINE OF ROCKFALL SIMULATION

For the purpose of rockfall simulation a twodimensional slope profile is established and divided

into slices with vertical boundaries. The width of slices depends on the curvature of the slope

surface and can vary from slice to slice. Each slice can have its own surface properties.

The calculation is based on the laws of motion and considers the change in angular momentum

during collision. The algorithm follows an iterative scheme governed by a variable time interval.

A general flow chart of the algorithm is shown in figure 3.1. Sliding, rolling, toppling or free fall

are possible as initial movement. All possible types of subsequent movements, such as rolling,

sliding, collision and inclined throw are considered. On the occasion of every collision with the

slope surface and every transition from one slice to the next, the actual rock movement is

evaluated as a base for the decision on the type of the subsequent movement.

The calculation is carried out until a collision with a protection structure occurres or the rock

stops. It stops by itself if it has lost its momentum in an area of decreasing slope gradient or by

bouncing backwards after a surface collision. If none of these incidents happens, the

calculation is carried on until the rock leaves the profile or is stopped by a protection structure.

Whether a rock stops or the subsequent movement is rolling or inclined throw depends on the

velocity dropping below certain limit velocities tangential and normal to the slope surface. They

have to be defined by the user. The movement stops, if the velocities of the rock are smaller

than the tangential and normal limit. If the velocity after an impact is smaller than the normal

limit velocity, the subsequent movement is rolling.

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Figure 3.1:General flow diagram for the simulation of movement with the program ROCKFALL

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4. INPUT DATA

Within this chapter the input data of the program are described. They can be divided into the

following groups:

Slope geometry, i.e. geometry of slices.

Slope surface qualities, i.e. dynamic friction, static friction, normal and tangential

damping, rolling resistance and surface roughness.

Qualities of rockfall, i.e. radius, shape, density.

Rockfall barriers, i.e. x-abscissa of the base point, height and inclination.

Start parameters, i.e. position, type of initial movement and number of rocks to be rolled

in one run.

Steering parameters, i.e. time step and limit velocities.

4.1 Slope geometry

The slope surface is idealised by a polygon. The polygon points represent the limits of the

slices, the profile is divided into. The slices are defined by the cartesian coordinates of their

edges. The slope surface between the edges is assumed to be linear. Frequently the

coordinates are already stored on disc from surveying. Therefore the software includes an

import feature for co-ordinates from ASCII files.

4.2 Slope surface qualities

To calculate the interaction between the boulder and the slope surface the following slope

surface qualities have to be defined for each slice:

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Dynamic friction angle, Rgin degrees; governs the friction between boulder and surface

in case of sliding; range of accepted input values: 0 to 89.

Static friction angle,Rh in degrees. governs the friction between boulder and surface in

case of a static contact; range of accepted input values: 0 to 89.The static friction angle

has to be greater than or at least equal to the dynamic friction angle

Normal damping Dn governs the damping of the velocity component normal to the

slope surface during collosion; range of accepted input values: 0 (fully plastic impact) to 1

(fully elastic impact).

TangentialdampingDt governs thedampingof the velocity component parallel to the

slope surface during collosion; range of accepted input values: 0 (fully plastic impact) to 1

(fully elastic impact).

Rolling resistanceRw governs the energy loss of the rollling boulder slope surface;

range of accepted input values: 0 (no rolling resistance) to 0.35 (extreme rolling

resistance).

Amplitude of surface roughness Oa in meters; defines the vertical distance of thepeaks of asperities below and above the connecting line of the edges (see figure 3.1.2-1);

range of accepted input values 0 5 m. With a value of zero for the amplitude, the

calculation will consider no roughness.

Frequency of surface roughness Of in meters; defines the horizontal distance

between the peaks of asperities; range of accepted input values 0 20 m.

4.3 Qualities of rockfall

Shape; sphereor cylindercan be chosen.

Radius, in meter.

Length of cylinderin meter.

Densityin t/m.

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4.4 Rockfall barriers

x -abscissa of the base point in meters,

h -height in meters,

Incli -inclination, in degrees

4.5 Sampling cross sections

x -abscissa in meters, denoting cross sections at which the data of all passing rocks is

sampled for later statistical analysis.

4.6 Parameter variation

Parameter variationV- in %. This percentage defines the limits the given mean value of

the corresponding parameter is varied within.

4.7 Start parameters

Type of initial movement, i.e. free fall, sliding, rolling.

X-Coordiante in meter; abscissa of the rocks centre at the beginning of the movement.

Y-Coordiante in meter; ordinate of the rocks centre at the beginning of the movement

(in case of free fall only).

numberof rocks to be rolled in one run.

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4.8 Steering parameters

Delta T - time step in seconds; a user defined time interval which determines the

accuracy of the path calculation. The value for the time interval can not exceed 0.05

secconds.

Limit Vn, - normal minimum velocity in m/s.

Limit Vt - tangential minimum velocity in m/s; the rock is stopped if it undergoes the

minimum velocities.

Interval of envelope curve in meter; the distribution of the kinetic energy and the bounce

height along the profile is represented by envelope curves. For the generation of these

curves the profile is divided into small sections, which widths is defined by the above

mentioned interval of envelope curve. For each interval the maximum occurring value of

energy or bounce height is stored. Finally these values are used to construct and plot the

envelope curve.

5. OUTPUT

Within this chapter the possibilities for the presentation of the results are described.

5.1 Single rock

Listing of rockfall path data, i.e. time dependent coordinates, kind of movement.

Graphical presentation of slope geometry and rockfall trajectory.

Distribution of energy and bounce height along the slope profile.

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In case of impact on a rockfall barrier:

Required Height in meter; required rockfall barrier height. The rockfall barrier height is

defined as the distance parallel to the structure axis. The algorithm detects an impact on

a barrier if the rockfall trajectory of the centre of mass of a rock intersects the axis of the

barrier below its top. The minimum required barrier height is calculated by adding the

radius of the rock to the height of the intersection between the above given rockfall

trajectory and the barrier axis.

Massof rock in kg.

v, in m/s; translational velocity of the rock at the moment of impact.

v(n), v(t)in m/s; tangential and normal translational velocities with respect to the barrier

axis.

E transin kNm; translational kinetic energy.

Momentumin t m/s; momentum of the rock at the moment of impact.

M(n), M(t)in t m/s; tangential and normal momentum with respect to the barrier axis.

Omegain 1/sec; angular velocity (2/T) (+) clockwise (-) counter clockwise.

Mang. in tm/s; angular momentum at the moment of impact.

Erotin kNm; rotational kinetic energy at the moment of impact.

Etotin kNm; total kinetic energy at the moment of impact.

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5.2 More than one rock

(at least one parameter varied)

Envelope curve along the rockfall trajectories:

total (translational and rotational) kinetic energy,

bounce height.

Statistical distribution at the barrier(s):

total impact energy,

bounce height,

translational kinetic energy and rotational kinetic energy,

translational velocity and angular velocity,

momentum and angular momentum,

angle between trajectory and axis of the barrier.

Statistics only consider rocks hitting the barrier, rocks failing the barrier are neglected. Height

means the distance between the intersection of the trajectory and the barrier axis, measured

along the barrier axis. In case of the envelope curves the bounce height is defined as the

vertical distance between the rocks mass centre and the slope surface. Only in case of a

vertical barrier both quantities are identical.

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Statistical distribution at sampling cross section(s):

total impact energy,

bounce height,

translational kinetic energy and rotational kinetic energy,

translational velocity and angular velocity,

momentum and angular momentum,

Statistics consider all rocks passing the section. Bounce height is considered vertical and thus

directly comparable to bounce height as defined for envelope curves.

Number of passing rocks:

Diagram showing the number of rocks passing a specific point of the profile of slope. This

visualisation implicitly indicates the endpoints of the paths of stopping rocks.

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6. HANDLING AND USER INTERFACE

The following illustration shows the main menu of ROCKFALL. From here each function of the

program is accessible by navigating through the pull down menus.

File serves for opening new and existing files, for saving and import data etc. and the

administration of all general project data.

Editleads to the input and manipulation of data (slope surface geometry, surface qualities and

barriers).

Viewdraws the profile on the screen and opens a submenu. This submenue allows for entering

the remaining input data, starting of the calculation, presentation of results and adjustments of

graphical presentations.

Run requires the input of the qualities of rockfall, the steering parameters and the start

parameters. At the end of this submenue the simulation can be started.

Resultsstands for the visualisation and analysis of results on screen.

Printallows for the output by printer or plotter and data export.

Optionsoffers different features for changing and manipulation of the general settings of the

output. Furthermore the language can be chosen

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6.1 Files

New: is used to initiate a new ROCKFALL file. First the file name has to be selected. The file

name has to follow WINDOWS conventions. Dont give an extension; it will be automatically

added (*.PRF for slope geometry, slice and barrier data). Afterwards there is a possibility to

insert project specific details as project No., date, name of project engineer, etc. For the input

of slope geometry, slope surface qualities and barrier geometry proceed to Edit.

Open: starts an existing ROCKFALL file.

Save: Saves all data including calculation results of the profile under its current file name.

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Save as .......: Saves all data including calculation results of the profile under a new file name.

The rules for file name and project specific data are the same as described in New.

Open surface types: Opens a table containing a set of typical surface qualities for different

surface types, for example hard rock surfaces, meadows, debris slopes etc. This table is

assigned to the current profile. It will be opened automatically, whenever this ROCKFALL file is

opened again.

Save surface types as : Saves the data of the actual table of surface types under a new file

name. This is to create a file for storing specific surface qualities for the current profile or a

group of profiles and projects. This table will be opened automatically, whenever the project file

is opened again.

Import profile coordinates (X/Y) : feature for reading coordinates fromASCII files. The file

needs the extension ".TXT" and must consist of two columns: 1. column x-coordinates, 2.

column y-coordinates. To separate the columns blanks or tabstops are allowed. Commas are

not allowed. Decimal points have to be according to the country settings of W INDOWS. Data can

be saved as described in Save as ........

Quit: Terminates ROCKFALL.

6.2 Input and Editing

Activate the EDIT menu to handle profile geometry, slope surface qualities and barrier data.

Slope geometry has to be fed in first.

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Slope geometry Program function for editing the coordinates of the slices of a profile. Thecoordinates are given by x/y-values in metres, as shown by the example below. The general dip

direction of the slope and thus the general direction of movement has to be from left to right.Overhanging slope sections are possible too. The input sequence has to follow the polygoncontinuously.

Slice (single): Program function for editing slice parameters. Each data line corresponds to a

single slice. For each slice, the full set of parameters as mentioned in chapter 4.2 and 4.5 have

to be fed in.

Slice (acc. table): Enter slice parameters by selecting the number of a surface type, whosevalues will be picked from the surface type table (see below).

Table of surface types: Creates a table of surface types with specific surface qualities. The

parameters are the same as in Slices (single), with the additional entry of a name or a short

explanation of the surface type. The values can be applied for a single slice or a range of slices

(menu Slice (acc. table) see above).

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If editing a parameter, which is already assigned to one or several slices, the value will not be

considered for the calculation unless the menu entry Slice (acc. table) isactivated (at least

open and close it).

Beginning a new project, which has no surface typetable yet, the still empty table can be filled

in. Before leaving the program or opening an other project this input can be saved with Save

parameter table as .Alternatively an existing surface type table can be used(menuOpen

surface type table).

Rockfall barriers: Program function for handling of rockfall barriers. The x - coordinates of the

base and the height of the structures have to be given in metres. ROCKFALL determines the y

- coordinate of the base on the slope surface. In addition the inclination of the barrier has to be

given by the angle between vertical and the axis of the structure. ( Incli= 0 means a vertical

structure, Incli= 5 means a inclination of five degrees downhill). Negative degrees are not

accepted, which would mean a barrier inclined uphill. Up to 10 barriers can be installed per

profile.

Sampling cross sections:The x - coordinates of the sampling cross sections can be given inmetres. Up to 20 sections can be defined per profile.

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6.3 View

Viewdraws the profile onto the screen and opens a submenu. This entry is activated only when

a profile with at least one slice is given. It allows for entering the remaining input data, starting

of the calculation, presentation of results and adjustments of graphical presentations.

6.3.1 Run

Opens an input form for starting parameters, rockfall qualities and steering parameters. Finally

it starts rockfall simulation. This menu entry is activated only with a complete set of surface

qualities for each slice.

Rocks: Describesall qualities related to the rockfall element (boulder) including the number of

rocks to be calculated with a single run. The following parameters have to be defined:

Numberof rocks: Each run can be carried out with a single rock or up to 10000 rocks.

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Sphere / Cylinder: The simulation can be conducted alternatively with a sphere or a

cylinder.

Radius: A sphere is defined by its radius in meter.

Radius variation: If more than one rock is chosen, a variation in percent of the radius

can be given.

Length: A cylinder is defined by its radius and length, both in meter.

Length variation: If more than one rock is chosen, a variation in percent of the cylinder

length can be given.

Density is given in t/m (equivalent to g/cm)

Options: This feature allows for recalculation of surface roughness and interruption of the

calculation after each rock.

Recalculation of Roughness: Usually the random representation of slope roughness iscalculated, if a profile on the screen is activated by View. Recalculation of roughness

creates a new random representation before starting a simulation run.

Run without stop: Normally the rockfall paths for the given number of rocks are

calculated without any stop. Choosing a run with stop means, that the calculation is

interrupted after each rock, which offers the possibility to get a closer look on the results

(path data) before continuing he simulation for the next rock.

Limits: Determines the steering parameters for the calculation.

Delta T: The calculation is executed in time steps. The duration of this time step is

defined by Delta T in seconds. After each time step ROCKFALL checks if the actual

position is physically possible (for example the position is not below the ground surface).

Otherwise the correct position and the corresponding time interval is calculated. The

value determines the accuracy of the path calculation. To avoid improper results it can not

exceed 0.05.

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LimitVNand limitVT: determine the lowest allowed velocities, normal and tangential to

the slope surface. Should the normal and tangential velocity of the actual rock fall below

these limits, the calculation is terminated (compare chapter 3).

Interval of envelope curve in meter; the distribution of the kinetic energy and the bounce

height along the profile is represented by envelope curves. For the generation of these curves

the profile is divided into small sections, which widths is defined by the above mentioned

interval of envelope curve. For each interval the maximum occurring value of energy or bounce

height is stored. Finally these values are used to construct and plot the envelope curve.

The default value of the interval is 0.2 m. For profiles exceeding a length of 600 m the default

value is profile length divided by 3000. Usually there is no need to change this parameter. In

some cases a greater value offers a possibility to smooth the envelope curve a little.

Start position: Determines the location from where the rocks start. The location is given by its

x-coordinate in meter. For runs with more than one rock, the start position will be varied by

random within the given variation. The start position including the variation must lay within the

profile. If start positions lay outside the profile limits, ROCKFALL will place the rock at the

beginning or the end of the profile.

If the profile contains an overhanging section and the start position

lays within the overhanging rock, the start position is not clearly

defined. The rock could start for example either above the

overhanging section (1), from the slope below the overhanging

section (2) or in free fall from the lower rim of the overhanging

section (3) (compare figure).

If the start position is not clearly defined, a message box alerts the

user. Then the location of the starting point has to be specified by

indicating a y-coordinate from the list, which will show up below the

input frame forstart positions.

Title of run: This Input box can be used to specify the actual run.

This specification will appear within all prints.

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OK button: Starts the calculation. In case of any violation of the allowed input ranges or

incomplete input data a message will show up. ROCKFALL requires either to go back to the

input and correct the data or cancel the input procedure.

After starting the calculation, the rockfall paths are drawn on the screen, additionally a window

is opened on the right side showing the corresponding data as described in chapter 5.2.

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6.3.2 Screen

The following functions are only active, if a calculation has been carried out.

Listing of path data: Opens a window showing the path data of a selected rock. Choose the

rock from the presented list. The listing gives generally within a pre selected distance the actual

time dependent coordinates and kind of movement. The pre selected distance is only valid if no

impact occurs and the kind of movement doesnt change, otherwise the distance is selected by

ROCKFALL thus that all relevant points are shown. This feature is only active for calculations

with up to 10 rocks, in order to avoid excessive volume of data stored on disc.

Energy and bounce height distribution: Shows the energy distribution and bounce height

distribution along the slope profile. If more than one rock is initiated envelope curves are

shown.

Statistics barriers: Shows the statistical distributions of the following calculation results at the

selected barrier:

total impact energy

bounce height,

translational kinetic energy

rotational kinetic energy,

translational velocity

angular velocity,

momentum

angular momentum, angle between path axis of the barrier.

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Each combination of this results can be selected for statistical evaluation and output on screen.

The presentation can either be in the form of a class or a summation histogram. This function is

only reasonable if a parameter variation has been carried out. First select the rockfall barrier, in

case there are more than one. In addition the class range or the number of classes can be

adjusted. The default values are approximately 1/20 of the difference between minimum and

maximum value. Simply press okto keep the default values. For less than 5 hits at the selected

barrier no statistics are available.

Statistics cross sections: Shows the statistical distributions of the following calculation results

at the selected cross sections:

total energy

bounce height,

translational kinetic energy

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rotational kinetic energy,

translational velocity

angular velocity,

momentum

angular momentum,

The handling of the selection process, class- or summation histogram, sampling section,

adjustment of class-number and -range goes according to statistics of barriers as described

above.

Passing rocks: Shows the diagram along the slope profile of the number of passing rocks

6.3.3 Print

Print allows for the output by printer or plotter and data export. To print data or diagrams,

choose under Printone of the following output options:

Table of Surface types: prints the actual table of surface

Input Data: Prints a list of the slope surface qualities as fed in

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Profile: Plots the profile as shown on the screen. If a calculation was carried out, the plot

includes the rockfall paths

Listing ofPath data : Prints the path data of a selected rock

Profile, energy and bounce heights :

Profile, energy:

Profile, bounce heights :

Energy and bounce heights :

For different combinations for plots of the slope profile together with the rockfall paths and

envelope curves of energy and bounce height.

Profile; Statistics Barriers:

Statistics Barriers: Plots the statistical distributions at the selected barrier. Either with or

without the profile.

Profile; Statistics cross section:

Statistics cross section: Plots the statistical distributions at the selected sampling cross

section. Either with or without the profile.

For the selection of the barrier and class range etc. please compare the comments to menu

entry Screen/Statistics

Profile; passing rocks: Plots the number of passing rocks

Printer & Plotter:This menu appears automatically before printing or plotting operations start.

It allows for the following selections.

WINDOWSprinter. The format of the WINDOWSprinter is set under Printer Setup, which

leads to the WINDOWSstandard dialog for printer settings.

Format of files for storage, for presentation the program supports: HPGL, POSTSCRIPTand

AUTOCAD-DXF output formats. For HPGL, POSTSCRIPT and AUTOCAD-DXF output

diagrams can be in vertical (Portrait) or in horizontal format (Landscape) up to the size

DIN A2.

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Modify project specifications as project No., date, name of project engineer, etc.

The scale of the profile can be adjusted by the user. The scale for envelope curves and

histograms is determined by ROCKFALL, according to the space left within the output

frame.

OKbutton to start printing.

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6.4 Options

Options offers different features for manipulation of the general settings of the output.

Furthermore the language can be chosen

Boundary values for data output: Function for setting the extent of path data. By

standard each calculated value will be stored on disc and if required printed as listing.

This may lead to extensive amounts of output data. To reduce the volume of output dataa filter can be set limiting the output data to a certain distance of x-coordinates in metres.

This distance is only valid if no impact occurs and the kind of movement doesnt change,

otherwise the distance is selected by ROCKFALL so that all relevant points are listed.

Size of end point: If a rock stopsbecause of the slope geometry and not because an

impact on a barrier its last position is indicated by an asterisk. The size of this asterisk in

millimetre is set by this function.

Plot of slice boundaries: If this function is active, the slice boundaries are drawn in the

profile for screen and printer output.

Zoom: The scale of the profile on screen can be modified. The zoom factor is in percent

of the actual graphics.

New profile coordinates: By this function the output of the profile can be limited to a

certain section. Enter the coordinates of the desired edges, BOTTOM, LEFT (X min/Y

min) and TOP, RIGHT (X max/Y max).

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System language: This function allows for the selection of the system language.

Graphical output: Opens the program function for setting the graphical layout (printing).

Pens: This feature allows for selection of colours and width of pens

Palette.: select thecolour of the corresponding pen from the palette which pops up

after clicking at the corresponding button .

Width:width of the corresponding pen in millimetres.

DXF Colour:choose one of the basic DXF colours for the output of AUTOCAD-DXF

files.

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Size of Output :this feature determines the size of the outer frame of the printer output

Left:left margin in mm; distance from the paper edge to the output frame.

Right:right margin in mm; distance from the paper edge to the output frame.

Bottom:lower margin in mm; distance from the paper edge to the output frame.

Top:upper margin in mm; distance from the paper edge to the output frame.

Layout: this feature allows for the selection of the distance between the slope surface

and the rockfall path and the presentation of the slope profile.

Path lift:the amount of raising the rockfall path from the slope profile in millimeters

for screen and plotter output. This is for better recognition of the rockfall paths in

case of rolling or sliding, when the path and the slope surface lines normally would

collide. Usually the amount should correspond to the selected width of these pens.

Hatching : density in millimetre of the hatching below the slope surface line forpresentation of profiles.

Header: three lines to enter the name of your company etc. These lines will appear in all printer

outputs in the upper left corner.

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7. LITERATURE

JOHN, K. W. & SPANG, R. M. (1979):

Steinschlag - Ursachen, Mechanismen und Sicherungen.

UIC - Tagung Schutz der Verkehrsanlagen gegen Steinschlag,

Kandersteg (Schweiz).

SPANG, R. M. (1987):

Protection against rockfall - stepchild in the design of rock slopes.

Proc. 6th Int. Congr. Rock Mech., Montreal, I, 551-557.

SPANG, R. M. (1988):

Empirical and mathematical approaches to rockfall protection and their

practical applications.

Proc. 5th Int. Symp. Landslides, Lausanne, II, 1237-1243.

SPANG, R. M., KURZ, G. & HALLER, B. (1993):

Rechnergesttzte Planung von Steinschlagschutzbauwerken an der

Geislinger Steige.Geotechnik, Sonderheft 1993, 87-90.

SPANG, R. M. (1994):

Geologisch-Geotechnische Grundlagen des Steinschlagschutzes.

Vortr. 11. Bodensee-Tag. Ing.-geol. Naturgefahren,

Risikoanalysen, Schutzkonzepte, 21.10.1994.

SPANG, R. M. & SNSER, TH. (1995):Optimized Rockfall Protection by "ROCKFALL".

Proc. 8th Int. Congr. Rock Mech., Tokyo.

SPANG, R. M.(1997)

Geologisch-geotechnische Grundlagen des Steinschlagschutzes

Bndnerwald 4/97

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ANGERER, H., SNSER,.TH. & SPANG, R. M. (1998)

Steinschlagrisiko und Investitionsentscheidung Gibt es eine rationale Basis?

Felsbau 16 Nr. 3

SPANG, R. M.( 1998)

Rockfall Barriers Design and Practice in Europe

Seminar on Planning, Design and Implementation of Debris Flow and Rockfall Hazards

Migation Measures, Hong Kong

SPANG, R. M.( 1999)

Dimensioning anchors for rockfall fences

Fatzer AG Sem. Rockfall Tests and Standardization, Davos 25.-26. Jan. Romanshorn

SPANG, R. M.( 2000)

Standardisierung von Prfverfahren fr Steinschlagschutzbarrieren

Ziele und aktueller Stand

2. Kolloquium Bauen in Boden und Fels, Technische Akademie Esslingen

SPANG, R. M. & KRAUTER, E. (2001)Rockfall simulation a state of the art tool for risk assessment and dimensioning of rockfall

barriers.

United Engineering Foundation, Conference on Landslides, Davos, June 2001, in print.

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