Program Features:
Stability Analysis of Slopes using Monte-Carlo Technique (SAS-MCT4.0)
is a computer software programmed in Microsoft® Visual Basic 6.0 capable of analyzing stability of man-made or natural slopes under static and earthquake loading. The most critical slip surface and its corresponding safety factor are evaluated using Monte-Carlo technique and methods of slices. The main frame of the program is shown in Fig. (4.1). The program aims at solving the following problems in slope stability analysis:
1- Two-dimensional analysis of any slope stability configuration assuming circular slip surface, and using either one of the following methods- as specified by the user:
a- Ordinary method, b- Bishop’s method, c- Janbu’s method,
d- Spencer’s method, and
e- Morgenstern-Price method (GLE).
The program aims at evaluating the global minimum safety factor using Monte Carlo technique. In this respect, the program supports a user friendly interface wizard for file preparation in which the geometry of slopes, layers, and the properties of materials are encoded. The program also shows the critical surface searching routine graphically, and locates the most critical slip surface. See Fig. (4.2).
2- The program can be used to search for the critical circular slip surface as in point (10 above, but based on maximum probability of failure. First-order second-moment approximation is used to estimate the probability of failure (pf). This option is valid for ordinary method. See Fig. (4.3).
3- Two-dimensional analysis of slope stability assuming irregular slip surface using one of the following methods;
a- Janbu’s method,
b- Spencer’s method, and
c- Morgenstern-Price method (GLE).
In this respect, the program searches for the most critical slip surface by representing every trial surface by 4,5,6, …. to 12 vertices trying to simulate the shape of the real slip surface. The most critical slip surface corresponding to these vertices will also be shown graphically. See Fig. (4.4).
4- The program also calculates the safety factor for a specified circular and non-circular slip surfaces.
5- Seismic slope stability analysis using the Pseudo-static method. The program computes the reduction in the safety factor due to a specified acceleration input- expressed in percent of ground acceleration (g).
6- Three-dimensional slope stability analysis using one of the extensions of Bishop’s or Janbu’s two-dimensional methods. The most critical slip surface will also be shown in three-dimensional view.
7- SAS-MCT program user may perform Reliability Analysis. In this part, the program generates a large number of different expected soil parameters assuming either normal or log-normal distribution and calculates the safety factor for each random set. These trails are used to construct the distribution of the safety factor and the corresponding reliability index (β) and the probability of failure Pf.
8- Stability analysis can be conducted using either total or effective parameters.
Fig. 4.1 Main Frame of SAS-MCT Program.
Generation of N Different Values of Soil Properties c, φ, and γ to estimate the Uncertainty in the calculated Safety Factor.
Circular Non-Circular
Start
Prepare Input File
Specified Slip Surface Search for Min. Factor of Safety
Circular Non-Circular
Input Xc,Yc,R Input Vertices See Figure(4.2 and 4.4) See Figure (4.3)
Ordinary Bishop Janbu Spencer Morg-Price
Calculate Factor of Safety
No
Yes
Input Seismic Coefficient
Prepare Output File
No
Yes
Generate New C,Phi,Gama Prepare Normal Probability
Paper
Tables End Graphs Reliability?
Seismic?
Search for Max. Probability of Failure
Fig. 4.2 Search for Critical Circular Slip Surface Based on Min. Safety Factor.
Yes Yes
Yes
Yes
Loop Until Tolerable Difference between the Values of Safety Factor in the Iterative Procedure.
SW=Search Width. Prepare Output File
Tables End Graphs Start
Search for Critical Slip Surface Based on Min. Safety Factor
Ordinary Bishop Janbu Spencer Morg-Price
Generates the First Slip Surface, Points A, B
Calculate the Safety Factor for this Slip Surface, Fmin = F1
Random Walking Random Jumping & Walking Random Jumping Move Point A Calculate the Safety Factor F F>Fmin. Decrease Width of the Search SW>dmin Move Point B Generate a New Slip Surface i = i + 1 i>2000 Calculate the Safety Factor Fi Fi>Fmin Jumping or Jumping & Walking F=Fmin Increase Search Width Fmin.=Fi Random Jumping Only Random Jumping and Walking
Fig. 4.3 Search for Critical Circular Slip Surface Based on Max. Probability of Failure. Yes Yes Yes Yes
Loop Until Tolerable Difference between the Values of Safety Factor in the Iterative Procedure.
SW=Search Width. Prepare Output File
Tables End Graphs Start
Search for Critical Circular Slip Surface Based on Max. Probability of Failure
Generates the First Slip Surface, Points A, B
Calculate the Probability of Failure for this Slip Surface, PfMax. = Pf1
Random Walking Random Jumping & Walking Random Jumping Move Point A Calculate the Safety Factor F Pf>Max Decrease Width of the Search SW>dmin Move Point B Generate a New Slip Surface i = i + 1 i>2000 Calculate the Prob. of Failure Pf<Max Jumping or Jumping & Walking PfMax=Pf Increase Search Width PfMax=Pf Random Jumping Only Random Jumping and Walking Ordinary Method (Only)
Note: The Probability of Failure are Calculated Based on First Order Approximation.
Fig. 4.4 Search for Critical General Slip Surface.
Start with New Segment
Yes
Yes
Yes Yes
Prepare Output File
Tables End Graphs Start
Search for Critical General Slip Surface
Generate the First Slip Surface with Four Vertices n=4
Calculate the Safety Factor for this Slip Surface, Fmin=F1
F>Fmin
Janbu Spencer Morg-Price
i = 1
Rotate Segment i
Calculate the Safety Factor, F
Decrease the Angle of Rotation
D.R>drmin
Increase the Number of Vertices i = i + 1 nVertices>12 F=Fmin Increase the Angle of Rotation nSegment>n-1 D.R = Degree of Rotation. drMin. = Min. Degree of Rotation. n = Number of Vertices. i = Number of Segments.
Program Description and Organization:
The program is composed of different classes and modules written in Microsoft® Visual Basic 6.0. The following are the main subroutines and functions that are used in the program:
1- Subroutine ORDINARY is used to determine the factor of safety by Ordinary method, i.e., Fellenius method of slices.
2- Subroutine BISHOP is used to determine the factor of safety by simplified Bishop’s method of slices.
3- Subroutine JANBU is used to determine the factor of safety using Janbu’s simplified method of stability analysis.
4- Subroutine SPENCER is used to determine the safety factor via Spencer’s method of stability analysis.
5- Subroutine MORG is used to determine the factor of safety using Morganstern-Price method of stability analysis.
6- Subroutine 3DBISH is used to determine the three-dimensional safety factor for the most critical slip surface observed in two-dimensional analysis using the extension of Bishop’s two-dimensional analysis.
7- Subroutine 3DJANBU is used to determine the three-dimensional safety factor for the most critical slip surface observed in two-dimensional analysis using the extension of Janbu’s two-dimensional analysis.
8- Subroutine JANNON is used to calculate the safety factor for non-circular slip surface using Janbu’s simplified method of stability.
9- Subroutine SPENNON is used to calculate the safety factor for non- circular slip surface using Spencer’s simplified method of stability for non- circular slip surface.
10- Subroutine DEVIDER is used to increase the number of vertices of the critical slip surface by putting a new one in the center of the largest distance between two adjacent vertices. The subroutine checks that the new vertex satisfies the boundary condition.
11- Function RAN1 is used to generate random numbers extracted from a uniformly distributed population in the range [0,1].
12- Function FO is used to calculate the correction factor of Janbu’s simplified method. This function depends on the relative depth of the landslide in relation to its length and on the nature of the soil properties.
13- Subroutine NORMAL is used to generate (n) random sets of the parameters (c, φ, and γ) and to calculate the safety factor for every set of values, where n varies from 50 to 1000.
14- Subroutine AREANOR is used to calculate the standard normal variate (gasdev) for the (n) cumulative probabilities generated by Subroutine
NORMAL.
15- Subroutine ZNOR numerically integrates the standard normal distribution equation using Least Square method.
16- Subroutine PAPER is used to construct the normal probability paper.
17- Subroutine GAWS is used to fit the data in the normal probability paper.