rock topple user manual 081127
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25/11/2008 4:49 PM
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
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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.
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