Rock Topple User Manual 081127

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Geomechanics Research Group, Lassonde Institute, Department of Civil Engineering,

University of Toronto

USER MANUAL FOR ROCKTOPPLE: A SPREADSHEET-BASED PROGRAM FOR PROBABILISTIC BLOCK TOPPLING ANALYSIS

Prepared by:

Bryan Tatone

Rev 1.0

Fall 2008

Rock Topple User Manual of 11

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TABLE OF CONTENTS TABLE OF CONTENTS ....................................................................................................................... 2 LIST OF FIGURES .............................................................................................................................. 2 1. PROGRAM SUMMARY ............................................................................................................... 3 2. OPENING PROGRAM ................................................................................................................. 3 3. INPUTS ..................................................................................................................................... 3

3.1. “Analysis Input” Sheet .................................................................................................... 3 3.1. “Add Support” Sheet ....................................................................................................... 7

4. RUNNING ANALYSIS ................................................................................................................ 7 5. OUTPUTS ................................................................................................................................ 10

5.1. “Results” Sheet ............................................................................................................. 10 5.2. Analysis Details ............................................................................................................ 10

6. REFERENCES .......................................................................................................................... 11

List of Figures Figure 3.1 – Input interface for Rock Topple program ................................................................... 4 Figure 3.2 – Idealized geometry of rock slope subject to toppling (after Scavia et al., 1990). ...... 5 Figure 3.3 – Predefined drop-down list of available probability distributions ............................... 5 Figure 3.4 – Pre-defined drop down menu for the number of Monte Carlo trials .......................... 6 Figure 3.5 – Example of data input message .................................................................................. 6 Figure 3.6 – Example of invalid input alert .................................................................................... 6 Figure 3.7 – Rock support interface for Rock Topple program ...................................................... 7 Figure 4.1 – User-prompt upon initiation of analysis procedure .................................................... 8 Figure 4.2 – (a) and (b) examples of error messages displayed following initiation of the analysis

procedure; (c) message indicating the analysis has been halted. ........................................... 8 Figure 4.3 – (a) Preview Geometry message box; (b) Perform Analysis message box; (c)

progress bar showing percent completion............................................................................... 9 Figure 4.4 – Message box indicating the model run is complete.................................................... 9 Figure 5.1 – Example of results generated by the Rock Topple program .................................... 10


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1. PROGRAM SUMMARY 'Purpose: This program computes the probability of slope failure for rock slopes subject to the

block toppling mode of failure. The analysis considers both kinematic and kinetic stability

conditions.

'

'Methodology: The adopted analysis procedure is based on the limit equilibrium approach

proposed by Goodman and Bray (1976). However, it has been modified to allow probabilistic

analysis via a Monte Carlo simulation.

'

'Program Input: Geometric and shear strength parameters of the rock slope defined by the user

as either fixed values or probability distributions.

'

Program Output: Average (mean and median) factor of safety and probability of kinematic and

kinetic block toppling slope failure.

2. OPENING PROGRAM

ROCKTOPPLE is a spreadsheet-based program created using Microsoft Excel™ using Visual

Basic for Applications (VBA). To use the program Microsoft Excel must be installed on your

computer and Macros enabled. To open the program file ROCKTOPPLE v.1.0.xls, first save the

file to the host computer and then double click on the file.

3. INPUTS

3.1. “Analysis Input” Sheet

Figure 3.1 illustrates the “Analysis Input” spreadsheet of the ROCKTOPPLE program. The cells

shaded in green represent input parameters that must be defined by the user (see Figure 3.2 for

definition of geometric parameters). The input parameters are divided into several categories

including: overall slope geometry, discontinuity orientations, rock mass properties, and external


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loads. The user must specify the mean value (first column), the appropriate statistical distribution

(second column) and corresponding standard deviation (third column) for each input parameter.

The desired type of probability distribution must be selected from a predefined drop-down list

(Figure 3.3). The following distribution types are supported for the rock mass and external

loading parameters: Fixed value, Normal, Lognormal, and Exponential. The discontinuity

orientations, however, are assumed to be defined by Fisher distributions which require the user

to enter the mean dip/dip direction of the discontinuity sets along with the appropriate Fisher

constant, K. If desired, the discontinuity orientations can also be considered as fixed values by

entering a Fisher K value of 0.

* Although the Fisher distribution is 3D and the limit equilibrium analysis is 2D. The 3D

joint orientations are only used to perform kinematic analysis. Given that the sample

discontinuity orientations make block toppling kinematically feasible, appropriate

approximations of the 2D joint orientations are used to perform the limit equilibrium

calculations.

Figure 3.1 – Input interface for Rock Topple program


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Sa

Joint set B

Joint set ASb

H

Stepped failure surface

ψs

ψts

ψb

ψaψs : slope angle

ψts : top angle

ψb : dip of set B

Sb : spacing of set B

ψa : dip of set A

Sa : spacing of set A

Figure 3.2 – Idealized geometry of rock slope subject to toppling (after Scavia et al., 1990).

Figure 3.3 – Predefined drop-down list of available probability distributions

Below the main input parameters there are two check boxes that allow specified support

measures to be applied to the slope model (see Section 3.1). Below the check boxes, the number

of Monte Carlo trials is specified from a predefined drop-down list (Figure 3.4) To help ensure

that valid input parameters are entered by the user, a combination of Excel’s data validation tools

and VBA code are employed. To help the user enter proper input parameters, message boxes

describing the requirements for each parameter are displayed as each input cell is selected

(Figure 3.5). If an invalid value is entered by the user, an alert appears and the analysis cannot

proceed until a suitable value is entered (Figure 3.6).


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*Although an effort has been made to check the validity of all user-defined input

parameters before the analysis proceeds, there may be some combinations of slope

geometry, joint orientations, and joint spacing that cause abnormal termination of the

analysis. An example of this includes the case where the specified top angle is steep while

the spacing and dip angle of “set A” are very small. In this case, the stepped failure plane

will not reach the top of the slope for a very long horizontal distance. Thus, the program

may appear to “freeze” as it attempts to preview the mean slope geometry.

Figure 3.4 – Pre-defined drop down menu for the number of Monte Carlo trials

Figure 3.5 – Example of data input message

Figure 3.6 – Example of invalid input alert


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3.1. “Add Support” Sheet

Figure 3.7 illustrates the “Add Support” spreadsheet. In this sheet, the user can specify two

different types of support which include bolting the toe block or bolting the toppling blocks

together. The user must enter the magnitude and orientation of the support applied to the toe

block and/or the effective width of the toppling blocks. The optimum orientation, iopt, of the

support to prevent sliding of the toe block is calculated using the mean values of the base plane

friction angle (φa) and dip (ψa) according to the following equation (Wyllie and Mah, 2004):

aaopti ψφ −= (1)while, the optimum orientation of the support to prevent toppling failure is simply -ψa (Goodman

and Bray, 1976). Both support methods can be easily applied or removed from the slope using

the check boxes located on the input spreadsheet, as previously shown (Figure 3.1 & Figure 3.4).

Figure 3.7 – Rock support interface for Rock Topple program

4. RUNNING ANALYSIS

The “Validate Data and Run Monte Carlo Simulation” button on the “Analysis Input” sheet

initiates the analysis is procedure. Upon pressing the button, the user is first alerted that all

previous output will be deleted (Figure 4.1). If the user chooses to continue, the input data are

further checked for validity. If there is a problem with any of the inputs, the user is alerted and


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the analysis is halted (e.g. Figure 4.2). However, if all inputs are valid, the user is asked whether

they want to preview the mean slope geometry (Figure 4.3a). Selecting “yes” generates a slope

preview on the right side of “Analysis Input” sheet (as previously shown in Figure 3.1); if “No”

is selected, the preview is not generated. Subsequently, the user is asked if they want to perform

the Monte Carlo simulation (Figure 4.3b). “Yes” commences the simulation, while “no” stops

the analysis and returns the user to the “Analysis Input” sheet. When the Monte Carlo simulation

is initiated, the percent completion is displayed via a progress bar (Figure 4.3c). The progress bar

also contains a cancel button to safely terminate the analysis early. Once the analysis is

completed, a message box (Figure 4.4) alerts the user and the results of the analysis are then

displayed (See Section 5.1).

Figure 4.1 – User-prompt upon initiation of analysis procedure

(a)

(b) (c)

Figure 4.2 – (a) and (b) examples of error messages displayed following initiation of the analysis procedure; (c) message indicating the analysis has been halted.


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(a)

(b)

(c)

Figure 4.3 – (a) Preview Geometry message box; (b) Perform Analysis message box; (c) progress bar showing percent completion.

Figure 4.4 – Message box indicating the model run is complete


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5. OUTPUTS

5.1. “Results” Sheet

Figure 5.1 illustrates the “Results” spreadsheet of ROCKTOPPLE. The “Results” sheet provides

a detailed summary of the kinematic and kinetic probabilities of failure, the average factor of

safety, a histogram of the factors of safety, and a summary of the applied rock support.

Figure 5.1 – Example of results generated by the Rock Topple program

5.2. Analysis Details

In addition to the Results sheet, the Rock Topple program generates three sheets containing

details of the analysis. The sheet titled “Analysis Details 1” contains the coordinates defining the

mean slope geometry and the coordinates defining the water table.


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The sheet titled “Analysis Details 2” contains the factors of safety for the toe block calculated for

each Monte Carlo trial. In addition to the factor of safety, the sheet includes the resisting and

driving forces and the resisting and driving moments acting on the toe block during each trial.

The sheet titled “Analysis Details 3” provides a complete summary of the first kinematically

feasible Monte Carlo Trial including: the randomly sampled input parameters, the coordinates of

each toppling block, the magnitude and position of the forces acting on each block, and the

stability (stable, toppling, or sliding) of each block comprising the slope.

6. REFERENCES Goodman, R. E., & Bray, J. W. (1976). Toppling of rock slopes; rock engineering for foundations and

slopes; proceedings of a specialty conference, vol. 2. Rock Engineering for Foundations and Slopes, Boulder, Colorado, United States.

Scavia, C., Barla, G., Bernaudo, V., 1990. Probabilistic stability analysis of block toppling failure in rock slopes. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 27 (6), 465-478.

Wyllie, D. C., Mah, C. W., & Hoek, E. (2004). Rock slope engineering: Civil and mining (4th ed.). London ; New York: Spon Press.

Rock Topple User Manual 081127

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