CIRCLE POL YGONAL BEZIER COMPOSITE FIXED PLANE COMPOSITE FIXED PLANE c'
optional
NENVE
optional
NENVE
BGSLOPE
6.16
BGSLOPE
6.16
PC
for
Stability
Slope
by
Dr
Milan
Maksimoviæ
by
Dr
Milan
Maksimoviæ
2006
Fs=1.415 f(x) 1.0 Fs=1.417 f(x) 1.0 Fs=1.422 f(x) 1.0B G S L O P E 6.16
(ver. 2006)
SLOPE STABILITY SOFTWARE FOR PERSONAL COMPUTERS
By Milan Maksimović ABSTRACT
The package for IBM-PC and compatibles performs 2D limit equilibrium analyses, of non-homogeneous sections of soil and rock slopes with arbitrary distribution of pore water pressures, external loading and inertia forces due to earthquake acceleration in any direction, by the methods of slices, considering arbitrary and circular slip surfaces.
The shearing strength can be defined with the standard linear Coulomb or the nonlinear failure envelope in terms of effective stresses. The undrained shear strength can vary linearly with depth in each material zone.
Circular slip surfaces are analyzed by the extended Bishop's method. An automatic search option, using the method of the steepest descent, can be selected for determination of the critical slip circle as well as the option using the grid of centers with the range of passing points which may automatically define more than 3000 slip circles in the single run.
Arbitrary slip surfaces are analyzed by the General method that satisfies all equilibrium conditions. Five arbitrary shape types of slip surfaces can be generated as polygonal, circular, composite, fixed plane shape and Bezier curves. The fully interactive and fast search procedure for the critical slip surface of the arbitrary shape is used. The back analyses of the failed slopes and landslides can be performed in a single run.
Programs are menu driven; variety of branching in the data preparation stage and computation can be carried out in an interactive work, including graphic presentation of cross sections, slip surfaces, line of thrust, etc., on monitor and hard copy graphic. Program exports HP-GL (.plt) files for graphic presentation. Running of the programs is made as simple as possible without any need for the programming knowledge. User, the geotechnical engineer, can see what he/she is doing, in each step of the analysis using all the user-friendly features of the package.
The geometry of the cross section can be described with up to 100 lines, up to 25 material zones, up to 10 surcharge loads and up to 20 line loads in any direction. Arbitrary slip surfaces can be defined with up to 100 points, either automatically generated (Bezier or composite slip surfaces), or entered explicitly (polygonal slip surface). The number of slices is initially specified by a user up to 100, (default is 40), though the software can handle up to 150 automatically generated slices.
BGSLOPE 6.16
SLOPE STABILITY SOFTWARE FOR PERSONAL COMPUTERS
LIST OF CONTENTS
Page
1. INTRODUCTION 1
2. GETTING STARTED 3
3. GENERAL FEATURES OF THE PACKAGE 9
4. SOIL and ROCK STRENGTH and THE FACTOR OF SAFETY 12
5. METHODS OF THE ANALYSIS 22
5.1 PROGRAM BE.EXE 23
5.2 PROGRAM GE.EXE 29
6. PREPARATION OF INPUT DATA 32
6.1 MAIN DATA 33
7. USING BE.EXE 46
7.1 RESULTS FROM BE.EXE 67
8. USING GE.EXE 71
8.1 RESULTS FROM GE.EXE 91
9. MORE ON MENU OPTIONS - CHANGES 96
10. EXAMPLES OF STABILITY COMPUTATIONS 104
11. PROGRAM BGP.EXE 129
11.1 MENU 129
11.2 NOTES ON GRAPHIC POST-PROCESSING 134
11.3 EXAMPLES 134
Addendum No. 1 HANDLING TENSION CRACK 149
REFERENCES 152 INDEX 155
BGSLOPE 6.16
SLOPE STABILITY SOFTWARE FOR PERSONAL COMPUTERS 1. INTRODUCTION
BGSLOPE is a software package written for PC and compatibles for the general solution of slope stability problems by a two-dimensional limiting equilibrium methods. The programs were originally developed for the DOS operating system, although accessible from the WINDOWS environment. Programs can handle arbitrary non-homogeneous cross sections, external loading including seismic accelerations and the nonlinear failure envelope, in addition to the conventional Coulomb failure law for soils, rock mass and rock discontinuities. The application is rather wide and covers the problems of stability of embankments, cuts, landslides, earth dams, mine-tailings dams, soil and rock slopes in open pit mining, deep excavations, retaining structures and bearing capacity problems in non-homogeneous and/or inclined soil.
The development of this package started in l968 for main frame computers and that phase of application and the development has practically ended in 1979. The early version of the package for PC (Ver. 1.0) is briefly described by author (Maksimović, 1988). Software was continuously upgraded, and the present version BGSLOPE 6.16 is the results of development completed in year 2006, after 37 years of the development and application in hundreds of different projects worldwide. Some improvements were suggested by users and other envisaged and introduced by writer during intensive use in many projects.
The software package BGSLOPE 6.16 consists of the setup program, three main
programs and five supporting files:
(0) BGSETUP.EXE Setup program performs initialization of five supporting files and sets parameters for your hardware configuration. You can start any of the main programs from here after saving configuration. You will not need this program again unless you change your hardware configuration, if at all.
Main programs are:
(1) BE.EXE (Bishop Extended method), uses CIRCULAR slip surfaces and handles the grid or automatic search option, or interactive search for finding the critical slip circle. (2) GE.EXE (GEneral method) is used for the analysis of ARBITRARY slip surfaces which
can be generated as POLYGONAL, BEZIER CURVES, FIXED PLANE, COMPOSITE, and CIRCULAR, using the method developed by author,
(3) BGP.EXE exports HP-GL files for graphic presentation of results by other programs which can handle *.plt files and produce graphs using printer for presentation of results obtained by programs (1) and (2). It can produce text files with final results transferred or saved by BE.EXE and GE.EXE.
In this text two programs (1) BE.EXE and (2) GE.EXE, which actually perform computations, are called stability programs.
You can shift from one to another main program transferring main data without exiting to DOS or WINDOWS as shown in Fig. 1.1, which indicates the possible shifting from one program to another. That means that the whole package works as a single larger program. Running of the package can be started from any of the four programs i.e. BGSETUP.EXE, BE.EXE, GE.EXE or BGP.EXE. In most practical cases in the routine analyses you will usually start from BE.EXE or GE.EXE.
Fig. 1.1 Switches and flow of data and results
An optional software package NENVE may be included. This package handles results of soil shear strength tests (direct shear or triaxial). It is used for derivation of parameters of the nonlinear failure envelope of hyperbolic type proposed by writer (Maksimović, 1988, 1996-a,b). Appropriate curve fitting techniques are programmed and graphic presentation of results is included. Besides, the optional NENVE package contains a database of collected results published in international literature and options to convert some other forms of the nonlinear failure envelopes like Hoek-Brown, Barton, and power type strength envelopes. Processing of data is interactive and enhanced to a level of final presentation of graphs on the screen and hard copy can be obtained using HP-GL graphic format. Some examples of the nonlinear failure envelopes are presented in Section 4 of this Manual.
Note:
In this manual it is not possible to give examples for all the imaginable combinations that might occur in the practical application. Intelligent user will note, after certain short practice, that the use of these programs is rather simple and that programs work efficiently if the physical and the soil mechanics aspects of the problem are properly defined. This manual is not a textbook. In the case of difficulty, user is advised to examine given examples in more detail, and/or to consult some references on the subject.
2. GETTING STARTED
You can install the BGSLOPE package on either a hard disk or floppy-disk system. The graphic card VGA is required in order to use graphics. Working from hard disk is highly recommended. Create a new directory (say BGSLOPE) on your hard disk and copy all the files from directory BGSLOPE in this directory on the hard disk. Initially, BGSLOPE is configured by assuming that you have an IBM-VGA color card and the appropriate color monitor. Only if these assumptions are not valid for your system configuration, you should run BGSETUP which will display the following menu:
1 GRAPHIC MODE - CURRENT is VGA-COLOR (640x480) 30 ROWS
2 ORIGIN ( X0 = 320 Y0= 240 )
3 HEADINGS ARE 1: (Left blank in this Manual) 2: Manual-examples
3: (Left blank in this Manual) Cap. start is 4: Fig.
4 VIEW-CHECK IF GRAPHIC MODE IS ADEQUATE 5 SAVE CONFIGURATION
6 R U N BE.EXE... (Bishop method) 7 R U N GE.EXE... (General method) 8 R U N BGP.EXE... (*.PLT & Printing ) 9 Q U I T
CHOICE ?
1 GRAPHIC MODE.... The graphic mode, best available for your system and the software package, (640 x 480 pixels) will be selected automatically. The package is delivered with the blue background color. You can select some other background color (black, green, cyan, red, magenta or brown) from the sub-menu offered after you have initiated your graphic mode.
2 ORIGIN... Initially, the origin for the graphic presentation of cross sections and slip surfaces is placed automatically in the central point of the screen, as shown in Fig. 2.1 and the scale is taken as 10 (pixels horizontal size per meter). The initial position of the origin can be easily changed by using this ORIGIN option. Note that the origin of the screen is in the top left corner of the visible area of the screen. The sub-menu offers the following choices:
SELECT THE POSITION OF ORIGIN
1 CENTER – DEFAULT (See Fig.2.1, p.5)
2 DOWN – CENTER (See Fig.2.2, p.5)
3 DOWN – LEFT (See Fig.2.3, p.6)
4 MID-HEIGHT – LEFT (See Fig.2.4, p.6)
5 OTHER CHOICE ?
The conventional position of the origin using option 3 (DOWN - LEFT) is shown in Fig. 2.3. You may select any OTHER position of the origin, but the position of the origin must remain within the visible area of the screen. Program will check your entry for the new ORIGIN and will force its position within the permissible area if necessary. During the initial stage of the application of the package you may accept the default position, because the position of the origin as well as the scale can be easily changed later in any of the other main programs to suit the need in any particular circumstances using MOVE/ ZOOM ... option available in all three programs.
3 HEADINGS... Option permits the entry of three headings which will appear in the top right corner of the graph produced by the program BGP.EXE and the beginning of the figure caption (Cap. start) as the fourth. In this Manual, the first heading is left empty, the second is Manual-examples, the third is empty, and the Caption start is Fig.. For the beginning you may wish to leave all headings as they are, or enter empty strings, or enter your personal name, etc.
If you press 3 and <Enter>, the following sub-menu will appear: HEADINGS ARE 1: (Left blank, could be yours or company name)
2: Manual-examples(should be replaced or left blank)
3: (Left blank in this Manual) Cap. start is 4: Fig.
OK (Y/N) ?
If you enter Y or y or just press <Enter>, that would mean YES, it is OK, confirming that you wish that these four labels on your drawings produced by BGP.EXE.
If you enter N or n, that would mean NO, it is NOT OK for these four labels and the possibility to change any of these, one by one, is offered in this form:
CHANGE No. (1/ 2/ 3/ 4) : ?
Press the number of the heading which you wish to enter or change and <Enter>, type the corresponding new heading and <Enter>. Again you will have on the screen:
OK (Y/N) ?
The new loop starts until you make all the changes which you wish answering to respond to
OK (Y/N) ? with Y or y.
At any rate, these 4 headings can be also entered or changed in program BGP.EXE, (Section 11) in some later stage during the use of the program for solving particular tasks.
Fig. 2.1 The default position of origin
Fig. 2.3 Down - left position of the origin
4 VIEW-CHECK... Performs a simple check of graphics. The screen should show a graph similar to one of those shown in Fig. 2.1, to Fig. 2.4. The geometry of simple embankment should be shown with multiple colored lines if you are using color monitor. If OK, the system of coordinate axes should appear on the screen and the local screen coordinates will be shown in the top left as values X0 and Y0. Entered headings previously described in 3. (if any) will appear in the top right corner of the screen and Cap. start will be shown in the bottom left.
5 SAVE... Save your configuration. This procedure will generate five supporting files with the names INI.* with different extensions, as follows:
INI.BG, INI.BGP, INI.PLT, INI.SS and INI.TXT
If you had run BGSETUP from your floppy, you can copy all INI.* files in the newly opened directory of your hard disk, or floppies. You will probably not need to run BGSETUP again on your system,
6. RUN BE.EXE... Starts the program based on Bishop Extended method using last options previously saved in INI.* files and the INITIAL MENU (BE) of BE.EXE is offered for further action. It is unlikely that you will use this option frequently, as you will usually start running the stability programs directly from WINDOWS (or rarely from DOS). 7. RUN GE.EXE... Starts the program based on General Extended method using last options
previously saved in INI.* files and the INITIAL MENU (GE) of GE.EXE is offered for further work. It is unlikely that you will use this option frequently, as you will usually start running the stability programs directly from WINDOWS (or rarely from DOS). 8. RUN BGP.EXE… Starts the program BGP.EXE which handles results (printing and
graphics) from both stability programs using last options previously saved in INI.* files. It is unlikely that you will use this option very often, as you will usually start running this program directly from WINDOWS (or rarely from DOS).
9. QUIT - exit to DOS or WINDOWS
You must place the whole BGSLOPE package in one directory. Be sure that you have the appropriate five supporting INI.* files in the same directory or in the same floppy.
EXAMPLES of MAIN input DATA used in this Manual and enclosed with the software, are stored in 8 files as follows:
1. EX-1.BG Simple slope, Linear envelope
2. EX-2.BG Simple slope, Nonlinear envelope
3. EX-3A.BG Simple slope, Tension crack empty
4. EX-3B.BG Simple slope, Tension crack + water
5. EX-4A.BG Riverside, Linear envelopes
6. EX-4B.BG Riverside, Nonlinear envelopes
7. CULIIN.BG SOFT CLAY, Cu increases with depth.
8. PRANDTL.BG Bearing capacity to be used only with PRANDTL.SS
MAIN DATA from #1 to #7 can be used by both stability programs (BE.EXE and
GE.EXE), while the data set #8 is for GE.EXE only in conjunction with the slip surface
of the same name (#6 below).
EXAMPLES of ARBITRARY SLIP SURFACES handled with GE.EXE used in this Manual and enclosed with the software, are:
1. P-1.SS Polygonal
2. Z-1.SS Bezier type
3. F-1.SS Fixed plane type
4. M-1.SS coMposite type
5. C-1.SS Circular
6. PRANDTL.SS Polygonal to be used only with PRANDTL.BG SLIP SURFACES from #1 to #5 can be used with MAIN DATA #1 to #6.
Novice user is encouraged to run some of the examples given here in order to initialize some familiarity with the software, even before further reading the Manual in detail.
Author hopes that the user will not need to look at the Manual frequently. The effort is made to provide immediate user friendly interface on the screen.
3. GENERAL FEATURES OF THE PACKAGE
Running of the programs is made as simple as possible. You can concentrate on the geotechnical aspects of the problem, without any need for the use of the programming knowledge. You will be able to see what are you doing in each step of the analysis. All programs are menu driven. Menus are displayed in a logical sequence and the optimum selection of options is offered in each stage of the analysis.
Stability programs (BE.EXE and GE.EXE) offer basically three main menus,
namely: INITIAL..., WORKING... and CHANGES.... Flow between menus in stability programs is shown in Fig. 3.1. The INITIAL MENUs are described in Section 5, the WORKING MENU options for the program BE.EXE are shown in Section 7, for the program GE.EXE in Section 8, and MENU CHANGES in Section 9. Each menu contains several options as well as branching to other submenus and to other two programs. Most of the menu options are self-explanatory.
Fig. 3.1 Flow between menus of stability programs and the possibility to switch to BGP which handles export of HP-GL - .plt files
Choices offered in both stability programs can be briefly summarized as follows:
-INITIAL MENU permits entering the data via keyboard or loading from the saved file, display the cross-section and slip surface(s) on the screen, initiation of the computation, saving input data and exiting from the program. VIEW GRAPH from this menu displays the geometry of the cross section and slip surfaces before computation. VIEW GRAPH will show SOIL LIMITS in different colors for different materials. Handy to check if material zoning is adequately described. ZOOM/ MOVE... option permits you to change the scale of the graph and to change the location of the origin of the coordinate axes.
-WORKING MENU controls the branching after the initial computation stage has been completed. One of the important options here is INTERACTIVE SEARCH for Fs,min. which is placed in an interactive window (Fig. 7.8 to Fig. 7.14, p. 53-57, and
Fig. 8.14 to Fig. 8.17, p. 85-88. You can perform search for the critical slip surface by varying the parameters of the failure line and see the result immediately. Besides, you can try, for example, to select the new initial circle for the automatic search in BE.EXE or check the solution for some different choice of the f(x) function in GE.EXE. VIEW GRAPH option from this menu displays the results of computation, showing, for example, grid of centers with the critical slip circle, (first example shown in Fig. 7.7, p.51, or the path of the finite difference cross with smallest safety factor in program BE.EXE, as shown in the first example of this kind in Fig. 7.2, p. 47. The graph in GE.EXE will show the result, the cross section with the slip surface analyzed and line of thrust of interslice forces for used f(x), as shown in Fig. 8.8 to Fig. 8.13, p.79-82, and Fig. 10.23 to Fig. 10.33, p.120-125. SAVE .BGP FILE (*.PLT & Printing) is used to save file for further processing, like exporting graphic HP-GL files (written in Hewlett-Packard Graphic Language) and text files for printing, which is handled by the program BGP.EXE. Direct transfer of data and results to BGP.EXE is also possible using SWITCH… option via temporary file which is transparent to all programs and named TEMP.BGT. From this menu you can SWITCH and transfer MAIN DATA as well as some slip surfaces to any of the other two programs (see Fig.1.1, p. 2).
-CHANGES is the menu that permits data editing or variation of parameters. It is rather handy in data input stage as well. If you enter some wrong input, you do not have to restart the typing procedure from the beginning, but just continue as nothing wrong is done, and after completing the entering, call this menu and correct typing error(s) and check the effects on the graphic display before initiating the computation. ZOOM/ MOVE option permits you to change the scale of the graph and to change the origin of the coordinate axes in order to adjust the graph according to changes performed. SHIFTING THE CROSS SECTION shifts the section with respect to the system of axes; combined with options ZOOM and/or MOVE provides the full control of the screen graphics during the work, or at some stage when the output of the screen graph to the file or to the printer via .PLT file is asked for. VIEW GRAPH will show SOIL LIMITS in different colors for different materials. Handy to check if material zoning is adequately described after you had made some changes. Options offered by this menu are described in more detail in Section 9.
Note that all the changes on the input data are performed in the computer memory only and changes are not made permanent until you explicitly save the file on your hard disk or diskette.
Menu functions in BGP.EXE, all placed in a single menu and shown in Section 11, can be summarized as follows:
It reads files with results produced by stability programs and handles printing output of results. It can export HP-GL files which can be used for producing graphics on printer or processed with other programs which can handle HP-GL graphic format. This program has all the graphic control features as in both stability programs described previously.
GENERAL NOTES:
SAVING and LOADING files. Whenever you choose any of these options, files with relevant extensions residing in a directory will be shown.
When typing the file name of up to 8 characters for SAVING or EXPORT, never type
extension, as it will be automatically added to the entered file name.
Files for LOADING are easily selected using arrow keys and typing of the file name for loading is completely avoided.
Five file types are defined by extensions as follows:
*.BG file with main input data which describe the geometry of the cross-section, soil parameters and loading. It can be formed, saved or loaded by the both stability programs, BE.EXE and GE.EXE.
*.SS file with slip surface of arbitrary shape. It can be generated, saved and loaded by GE.EXE only, though the file describing circular slip surface can be formed from BE.EXE. Once defined, the slip surface can be saved from BGP.EXE as well. *.BGP file with input data and results of computation can be formed by any of the two
stability programs. Such a file can be loaded by BGP.EXE program for final presentation of results. It is also convenient to store some intermediate results in this form and use them for further analyses as all the MAIN DATA and RESULTS can be transferred to stability programs for further processing.
*.PLT is a HP-GL file formed and saved by BGP.EXE which is used for graphical presentation of results on plotters or printers with commercially available programs which handle HP-GL (.PLT) graphic format.
*.TXT text file which contains saved printable input data with results of computation. The number of data files with the same extension i.e. *.BG, *.SS, *.BGP , *.TXT and *.PLT) is limited to 80 in the directory. You will be warned if this limit is approached and advised to move some files to other directory or delete files which are not needed.
In order to avoid the possible problem which may arise during or after extensive analyses, it is advisable to save (or move) some files occasionally to some other directory if their number approaches close to 80 (say 70-75).
This limitation of 80 files might be more critical for *.BGP files. Pay attention in advance.
4. SOIL or ROCK STRENGTH AND THE FACTOR OF SAFETY
Methods for the computation of the index of relative stability called the factor of safety are oriented toward the calculation of the value:
m f s
F
τ
τ
=
( 1 ) whereτf is the actual available shearing strength of the soil
τm is the average shear stress on the hypothetical failure surface
mobilized to maintain the body of soil in equilibrium.
The value of Fs is the chief unknown in a limit equilibrium analysis. The shear
strength of soil or the rock τf is traditionally described as the Coulomb's linear relationship
between the effective normal stress on the failure plane. Linear parameters are cohesion
′
c and the angle of the shearing resistance φ′, parameters being constant and independent
of the stress level, or:
φ σ
τf =c′+ ′n tan ′ ( 2 )
Total stress analysis for saturated clays may be performed by using the values for cu ,
(which can vary linearly with the depth), and φu =0 for the Mohr-Coulomb strength
parameters.
Straight line is considered as an approximation, which is conventionally used for all types of soil. The linear Coulomb failure envelope could be considered, more or less, only as the reasonable approximation for loose sands and normally consolidated clays.
Fig. 4.1 Real failure envelope with c’=0 and the linear approximation
Most soil types and rocks exhibit curved failure envelopes (Fig. 4.1). The cohesion term in noncemented soils is the consequence of the extrapolation of the line to the zero stress level. The angle of the shearing resistance decreases with the increase of normal effective stress level. Early work on this topic is reported by Maksimović (1978), who presented several forms of nonlinear failure envelopes. Charles (1982), Charles & Soares (1984) and
Costa Filho & Thomaz (1984) used power type expression, which has significant limitation due to the fact that it is valid in a limited stress range and parameters depend on units. The power type failure envelope does not have an asymptote and has vertical tangent in the origin, if cohesion is zero, and parameters have no physical meaning.
New expression, (Maksimović 1988, 1989-a,b,c, 1992, 1993, 1995, 1996-a,b), very suitable for description of the nonlinear failure envelope in terms of effective stresses for most soil and rock types, describes the secant angle of the shearing resistance as the function of the normal effective stress on the plane of failure in the form:
N n B p σ φ φ φ ′ + ′ ∆ + ′ = ′ 1 ( 3 )
and the soil or the rock shearing strength becomes:
′ + ′ ∆ + ′ ′ + ′ = N n B n f p c / 1 tan σ φ φ σ τ ( 4 ) where
c′ is cohesion, (c > 0′ for cemented soils and rock only and c′=0 for most soils and
rock discontinuities)
φ′B is the basic angle of friction, (usually equal to the friction angle at constant volume).
φ∆ ′ is the maximum angle difference, (contribution of dilatancy and/or particle
reorientation)
N
p is the mean angle stress, the value of the normal effective stress for which the secant
angle of the shearing resistance equals to the mean value between the initial value
φ
φ′ +B ∆ ′ and basic
φ
′B i.e., for the stress level at which φ′=φ′B+∆φ′/2.(Itbasically reflects the deformability of the material).
The geometrical description of these parameters and functions of the hyperbolic failure criterion is shown in Fig. 4.2.
The envelope in Fig. 4.2-a has a tangent in the origin inclined at angle φ′0 which is
the sum of the basic angle φ′B and the maximum angle difference φ∆ ′.
In a semi-logarithmic plot (Fig. 4.2-c) the point M corresponding to pN is a point of
central symmetry, while φ′0 and φ′B are the left and the right asymptotes.
Both expressions, (3) and (4), are dimensionally consistent. Values of the angles can
be taken in degrees or radians and the description of the normal effective stress σ′ must be in
the same units as the median angle pressure pN.
The optional software package NENVE can be used to convert the variety of the proposed nonlinear failure envelopes for soils, rock mass and rock discontinuities to the more general but simple nonlinear failure envelope of the hyperbolic type briefly described here.
Fig. 4.2 Parameters of the non-linear failure envelope
The hyperbolic expression described here reduces to the conventional Coulomb straight-line envelope for three combinations of parameters, i.e.
when ∆φ′=0 then φ′=φ′B or
when pN=0 then φ′=φ′B and
when pN=∞ then φ′=φ′B+∆φ′.
In this sense the conventional Coulomb linear failure envelope is simply just one special case of the described nonlinear failure envelope for geotechnical materials. The first case listed above is also handy in practical application of this software.
This nonlinear failure law applies to the peak shearing strength of coarse-grained materials (rockfill, gravel and sand), dense fine-grained soils (clays) and for the residual shearing strength of clays and clay minerals, rock discontinuity and rock mass, or almost to all types of soils and rocks with better accuracy then the conventional linear failure law. The dimensionally consistent expression is valid from the zero stress level to practical infinity. Some examples are shown here, and for more, user may consult papers listed in literature or examine examples shown here.
For the first example, (Maksimović, 1989), which is shown in Fig. 4.3, and Fig. 4.4, parameters in eq. (2) are derived by considering the relationship between the angle of the shearing resistance and the normal stress based on data for the compacted London clay (Atkinson & Farrar, 1985). In the conventional range of testing stresses (150-300 kPa) the failure envelope can be described by a linear relationship defined by the angle of the shearing resistance (Fig. 4.4-a). However, in the low stress range (5-25 kPa) the envelope is curved and can be described by a power type expression, as shown in the enlarged detail in Fig. 4.3.
Fig. 4.3 Detail of the envelope from Fig. 4.4-a in the low stress range
Four points for mentioned values of normal stresses are selected for the derivation of the proposed parameters as shown in Fig. 4.4. It can be seen (Fig. 4.4-a) that in the stress range from 100 kPa to 400 kPa the failure envelope is very close to the straight line, but at the lower stresses, (Fig. 4.3) the linear extrapolation towards the zero normal stress gives the cohesion value and the unsafe, higher values of the shearing strength. Plots shown in Fig. 4.4-b and Fig. 4.4-c indicate that the description of the shearing strength from com4.4-bined linear and the power type expressions can be substituted by a single expression of the proposed hyperbolic type with rather high accuracy. The implication of the NON-LINEARITY of the failure envelope for compacted clays is discussed by Charles (1982), Charles & Soares (1984), Day & Axten (1989), Day (1994,1996), Day & Maksimović (1994) and others.
The angle of the residual shearing resistance very often depends on the magnitude of normal stress acting on the failure plane, as shown by Skempton & Petley (1967), Bishop (1971), Lupini, Skinner & Vaughan (1981), Chandler (1984), Skempton (1985), Lambe (1985), Maksimović (1989, 1995), Stark & Eid (1994) and others. The curvature of the envelope of the residual shearing strength can be attributed to the different degree of orientation of platy particles with increasing parallelism to the failure plane as the normal stress on the failure plane increases.
The residual failure envelope can be described using the expression of the same type, and adding the subscript r to parameters to designate that it describes the shearing strength after large shearing displacements.
An example based on data reported by Stark & Eid (1994) and discussed by Maksimović (1995) is shown in Fig. 4.5. The curvature of the envelope does not seem very significant in the graph of the envelope, but the variation of the angle, in a relative sense is very pronounced. The shape of the actual envelope shown in Fig. 4.5-a is not very clear unless it is shown as the variation of the angle of the shearing resistance with stress level in linear (Fig. 4.5-b) and in semi-logarithmic plot (Fig. 4.5-c). It can be seen that the curve fits the data with remarkable accuracy.
The NON-LINEARITY of the coarse grained material like sand, gravel and rockfill is the consequence of the variable dilatancy that decreases with the rise of the normal stress level and grain crushing. The peak shearing strength envelopes of coarse-grained materials used for construction of large dams are shown in Fig. 4.6 and Fig. 4.7. Strength-density relationship for sands in terms of parameters of the nonlinear failure envelope is described by Maksimović (1993), as an alternative to the logarithmic description described by Bolton (1986).
Fig. 4.7 Crushed basalt rockfill, Dmax = 76.2 mm, Cu=11.6.
It is worth noting that the same form of the failure law applies to rock discontinuities and to jointed rock mass.
Fig. 4.8 Failure envelope of the rock discontinuity
The most popular failure criterion for rock discontinuities of the logarithmic type proposed by Barton and Choubey (1977) can be easily converted to the failure criterion of the proposed hyperbolic type (Maksimović, 1996) without using the software simply by taking
the basic angle unchanged, taking pN=JCS/10 and ∆φ=2 JRC. The results of the direct shear
test on sandstone discontinuity are evaluated. Six data points based on results reported by Barla, Forlati and Zaninetti (1985) are used and a very good approximation obtained, as shown in Fig. 4.8. This failure envelope in terms of Barton and Choubey parameters for the shear strength along the rock discontinuity would correspond to JRC=28.82/2=14.41 and JCS=10 x 2277 kPa =22.77 MPa.
The nonlinear failure criterion of the power type for the jointed rock mass by Hoek & Bray (1981) as well as recent version Hoek (1995) can be also converted to the hyperbolic
form of equation 3 using “NENVE” package. The main principle for the conversion of Hoek
(1995) strength envelope for the rock mass into the envelope of the hyperbolic type, is to compute c’ as the shearing strength for the zero value of the normal and select three non-zero normal stresses to compute unknown parameters. In this way it is achieved that the hyperbolic failure envelope and the Hoek (1995) envelope have 4 identical points: at zero normal stress, this is the cohesion term, and at three different non-zero normal stresses. The difference between the two envelopes (Hoek 1995 and hyperbolic) is negligible for all practical purposes within the stress range considered. The maximum difference in terms of the angle of shear resistance for the normal stresses between points used for conversion is of the order of (+/-) 0.1-0.2 degrees only. An example of such conversion is shown in Fig. 4.9. It can be seen that the approximation within rather wide stress range is very good and in this case, the non-zero cohesion term is included in the equation 4.
The main advantage of this approach is that the Hoek (1995) failure criterion, which is
essentially defined in terms of principal stresses σ1 and σ3, is expressed in terms of shear
strength
τ
f and the normal effective stress on the failure planeσ
n.
The non-linearity of thefailure envelope is maintained.
Fig. 4.9 Failure envelope of the rock mass - conversion of Hoek 1995 criterion.
Slope stability software package described in this manual can handle both the conventional linear Coulomb's failure law, (eq. 2, Fig. 4.1), as well as the described nonlinear failure envelope of hyperbolic type, (eq. 4) shown in Fig. 4.2 through Fig. 4.9 as a very versatile one.
The nonlinear envelope and its variations, as well as the methods of derivation of the parameters from tests or conversion from a number of other proposed forms of the nonlinear failure envelope are described in more detail separately. The optional package "NENVE" is used for derivation of parameters from the shearing test data and presentation of the failure envelopes on suitable plots. Package contains a database with a number of results of test and derived parameters for various geotechnical materials. All data on the shape of the curved failure envelopes indicate that the curvature of the failure envelope is most pronounced in the lower stress range. In general, the significance of the stress level can be expressed in terms of the Stress Level Ratio (SLR) for the curvature of the failure envelope (Maksimović 1996) using the described parameters.
Any failure envelope of the proposed type can be separated approximately into two or three segments, in terms of SLR (Stress Level Ratio), as defined and shown in Fig.4.10. High curvature is in the stress range SLR<1/2 though the significant transitional curvature is evident for the stress interval SLR<2 approximately. For SLR>2 to any higher value of the normal stress level ratio, the failure envelope can be assumed as a straight line (Coulomb line) for the practical application without significant error, though the parameters of the line will depend on the stress interval considered.
Fig. 4.10. Variability of the curvature of the failure envelope. The failure envelope is practically straight line only for SLR>2.
5. METHODS OF THE ANALYSES
Of the limiting equilibrium models available, those which divide the mass above the assumed shear surface into slices, are most ideally suited to being programmed to solve general slope stability problems. It is widely accepted that methods, which satisfy all equilibrium conditions, give essentially the same results.
Bishop (1955) simplified method, limited to circular shear surfaces, gives virtually the same results as methods that satisfy complete equilibrium.
The Morgenstern and Price (1965) method for the slip surfaces of arbitrary shape requires numerical integration over each slice, which is a lengthy procedure.
The General method developed by writer (Maksimović 1970, 1979, 1988, see also Bromhead 1986) can be considered as an equivalent to the Morgenstern & Price method, but significantly simpler. For the discussion on different methods you may consult Bromhead (1986, 1992, 1999) and/or Fredlund (1984).
This software package is based on the following two methods: 1. Bishop's method, for circular slip surfaces, and
2. General method developed by writer, for slip surfaces of arbitrary shape.
Arbitrary slip surfaces can be generated as polygonal, Bezier curves, fixed plane,
composite and circular arcs as shown in Fig. 5.7, page 30.
As mentioned earlier, the methods implemented in this software package are extended to handle external loading, earthquake accelerations and the nonlinear strength envelope.
Due to the nature of the methods, all computations for the safety factor are iterative. In the Bishop Method there are two nested iterative loops and in the General method, three.
Tolerances adopted for the convergence are very small. All the computations are carried out in a DOUBLE PRECISION mode, involving sign and 15 digits.
5.1 Program BE.EXE
Large number of circular slip surfaces are usually treated by the application of the Bishop (1955) Extended method, which is extended here by the introduction of the nonlinear failure envelope and modified to include external line loads, distributed (surcharge) loads and inertia forces due to earthquake loading in any direction.
At the very beginning of the run, only options 1, 3, 5, 10, 11 and 12 are offered, though the complete set of options on the screen in the INITIAL MENU are as follows:
CHOICE I N I T I A L M E N U ( BE ) 1 ENTER MAIN DATA (kbd)
2 ENTER SLIP-CIRCLES 3 LOAD MAIN DATA
4 PRINT MAIN DATA (Screen) 5 VIEW GRAPH
6 ZOOM/ MOVE/ AXES/ MIRROR 7 SAVE MAIN DATA
8 PRINTING OPTION IS: (Blank) 9 C O M P U T E !
10 W O R K I N G M E N U. . . 11 C H A N G E S. . .
12 Q U I T CHOICE No.?
1 ENTER MAIN DATA (kbd) is an option described in detail in Section 6.
2 ENTER SLIP-CIRCLES initiates the computation aiming for the critical slip-circle. The
practical problem is to find the minimum of the function FS=FS(x,y,R) with three
variables, i.e., two center coordinates of the circle and the radius. The time for execution of the search for the minimum of the function of three variables (3D search) will be of the order of a seconds. The computation is for an order of magnitude shorter and significantly safer, if the problem is, at least initially, reduced to the search for the
minimum of the function FS(x,y,R) of two variables only (2D search), where "r" is a
parameter treated in each search as the constant selected by the user. Two options are made available initially in this menu. First, shown in Fig. 5.1-a, is that each family of slip circles has one common PASSING POINT (an exit point P in the zone of the toe, for example). The second option is that the family of slip-circles is tangential to certain horizontal plane defined with elevation YP, as shown in Fig. 5.1-b, which in some cases could be the lower boundary of some weak zone or only a trial level not related to any particular feature of the cross section under consideration. However, 3D search can be performed either in an interactive way dealing with only successive slip-circles at the time, or by massive computation with up to 3025 clip circles in a single run starting from WORKING MENU. For details see Section 7.
(a) ( b)
Fig. 5.1 The single passing point and the single passing horizontal tangent (point P).
For the search of the critical slip-circle four options are built in the program:
i Automatic search (steepest descent) ii Grid of centers
iii Local grid
iv Interactive search
The routine for the Automatic search (i) is based on the method of steepest descent. This method is very valuable during the practical work, though the Grid option (ii) is common in most computer programs of this kind. These two options can be initiated from the INITIAL MENU. Options (iii) and (iv) can be initiated from WORKING MENU (BE).
Fig. 5.2 Path of steepest descent Fig. 5.3 Spider - 5 trial centers
i. Automatic search (steepest descent). To reach the solution it is necessary to start from
some reasonable and arbitrary center T (Fig. 5.2) and arrive to the center C, which is such that
FS(x,y,R)=FS,min. The paths from point T to C will follow the trajectory of steepest gradient
forming "the finite difference cross," which is in the program referred to as SPIDER, as shown in Fig. 5.3, is defined with the central point T, as point number 1, placed initially by the user. Factors of safety for five trial slip-circle centers, and the direction of steepest descent are automatically computed. By using Taylor's expansion to the polynomial of second degree, estimated length and the direction of the step is calculated, central point of the finite difference cross moved to the new point and the procedure automatically repeated until the calculated step becomes some small tolerable value. In the program this tolerance is taken as 0.2 of the opening "a" of the grid, (SPIDER'S LEG), as at the stationary point first partial derivatives vanish.
Fig. 5.4 An example of the Automatic search option
Practical experience show that the value of "a", can be taken as about 1/10 to 1/20 of the slope height. Then the error in the location of the critical circle center becomes not more than 1-2% of the slope height, being within the zone surrounded by the smallest circle with the center in the central point 1 (Fig. 5.3) of the “spider”. To avoid excessive long jumps from one position of the point 1 to the next trial location, it is limited in the program to the length
of the diagonal or R = 2a 2, as indicated with a large dotted circle shown in Fig. 5.3, p.24.
An example of this option is outlined in Fig. 5.4 showing the initial center, path, and the critical circle. The number of steps is limited to 30 and in usual circumstances the minimum will be reached for the fixed tangential level or one common point for all slip circles. In the case that the initially assumed center is far away from the critical one, or if step "spiders leg" is too short, after making 30 steps and the criterion for the minimum Fs has not been reached after 30 steps, you are going to get suggestion on the screen. Usual restriction on the practical significance of the automatic search is the consequence of continuity and unimodality of the
function FS(x,y,R). It might have more than one minimum, and the procedure will reveal the
minimum along the path of the steepest descent from the chosen starting point T. To check if some another minimum exists, you can try another starting point, (Fig. 7.1 to Fig. 7.4, p.47-48), or use the GRID OF CENTERS, (Fig. 5.5 and Fig. 7.5 to Fig. 7.7, p.50-51).
ii. Grid of centers. The Grid option, shown in Fig. 5.5, as an alternative to Automatic search
from the first option in MAIN MENU, offers a possibility to generate the grid containing up to 150 centers. It is convenient to use this option in any stage of computation, usually to prove previously estimated critical circle based on Automatic search and show that in rather wide area of possible centers the estimated critical is the only one, or to indicate if some other local minimum might be considered.
Fig. 5.5 Grid option. Application of Local grid of smaller size could be next.
iii. Local grid. The LOCAL GRID option (No. 5, pages 57-58) in the WORKING MENU,
is used after some computation is performed and some smallest safety factor found for a particular circle or set of circles and the particular passing point. This option, when chosen, will automatically generate the quadrilateral grid of the prescribed SIZE with the last critical center placed in the center of the local grid, as shown in Fig. 5.6. You can chose variable size and shape of the local grid in order to find the accurate position of the critical circle. The LOCAL GRID density is fixed to 11, meaning that 11 x 11 =121 centers will be generated within the given size of the local grid (see Fig. 5.6, Fig. 7.15 through Fig. 7.22). Besides, you can select up to 25 passing points within the prescribed range of positions for the same grid and generate 3025 slip circles for a 3 D search in a single run. The LOCAL GRID proportions (H/S), pages 57-58, can be altered in menu CHANGES (option 11, page 65) and than tilted left or right, as explained in Section 7, page 57.
iv. Interactive search option (No. 2, p. 53-57) INTERACTIVE SEARCH for Fs,min., in
the WORKING MENU (see Section 7) deals with a single slip circle in such a manner that the changes of the value of Fs due to changes of the coordinates of the circle center and/or the passing point P (see Fig. 5.1) performed by using only arrow and +/- keys, can be followed in an interactive window (Fig. 7.8 to Fig. 7.14, p.54-57).
Fig. 5.6 Local grid placed after Automatic search.
A set of up to 25 tangents or passing points can be prescribed in a single run.
Options (iii) and (iv) are not offered in the INITIAL MENU shown in page 23, but they are offered in the WORKING MENU which will be described later in Section 7. Some other possibilities are also described in WORKING MENU (BE).
In some cases, particularly when the size of the spiders leg “a” is small, the function
FS(x,y,R) might be rather irregular in the vicinity of local minimum, and the procedure might
fail to converge to the minimum, oscillating in the vicinity of that point. In such a case you might find the use of the LOCAL GRID option rather helpful.
This LOCAL GRID option with a large number of slip-circles might be used after Automatic search or the Grid had been executed, to investigate the area in the zone of the slip-circle with the smallest factor of safety obtained in the previous computation. The size of the grid and the spacing of passing points can be arbitrary small making the accuracy of the critical center coordinates very high with high density of slip-circles. Examples of the LOCAL GRID are shown in Fig. 5.6, Fig. 7.16 through Fig. 7.22, Fig. 10.12 and Fig.10.13.
The combined procedures of Automatic search, the predefined, usually larger Grid and the LOCAL GRID option as well as the INTERACTIVE SEARCH for Fs,min., when
used sensibly, will provide the satisfactory answer for a critical slip circle and the smallest FS
to an engineer with reasonable geotechnical training and experience. For more on the slip-circle analyses see Section 7.
Other options from the MAIN MENU (BE) shown in page 23 are rather self-explanatory, and will be described here for completeness.
3 LOAD MAIN DATA When this item is selected, a list is obtained with all the available *.BG files in the directory. Move the highlighted bar to the name of the file you wish to load and press the <Enter> key. The screen shall display the cross section of the slope.
4 PRINT MAIN DATA (Screen) or (File) Input data will be printed depending on the active option 8 PRINTING OPTION. In the case that the active option is Blank, main data will be printed on the screen.
5 VIEW GRAPH Self-explanatory. Graph on the screen will show the definitions of slip surfaces and the cross section, before computation. The soil limit lines will be shown in different colors; one color for one material. Useful for rough checking whether the zoning of the cross section is properly described.
6 ZOOM/ MOVE/ AXES/ MIRROR Option is explained in Section 6, page 38.
7 SAVE MAIN DATA When this item is selected, a list is obtained with all the existing *.BG files in the directory. Type the name of the data file you wish to save and press the <Enter> key. Do not type extension. If you enter the name of the already existing data file, it will be overwritten by the new one. Pay attention, there is no warning message. 8 PRINTING OPTION IS: (Blank) or (Screen) or (File) permits you to control printing of
input data and results of computation. PRINTING OPTION might be:
(Blank) is default option meaning that the whole process of computation will not be shown on the screen when COMPUTE ! option is chosen. It will affect printing of the results of computation only. The message COMPUTING...PLEASE WAIT... appears and only the final result, (Fs) will be shown on the screen without details, and THAT WILL SIGNIFICANTLY SHORTEN THE TIME OF EXECUTION.
(Screen) means that main data or intermediate phases of computation, when requested by this option from the menu, will be displayed on the screen.
(File) option implies that, input data and results will be saved in the *.TXT file and later if needed, sent to the printer or simply examined on the screen. Note that this option, even if selected, will be deactivated during computation.
9 C O M P U T E ! Initiates computation for the defined slip circles. When computation for this set is finished, the graph showing results will appear, and the further control of the program is transferred to WORKING MENU (BE) shown in page 52.
10 W O R K I N G M E N U. . .Shows and offers WORKING MENU (BE)… 11 C H A N G E S. . . Shows and offers menu CHANGES (BE), page 65.
12 Q U I T You will be asked to confirm that you are quitting the program. Be sure that you have saved the files before you quit the program.
5.2 Program GE.EXE
General slip surfaces, including the circular ones, are analyzed by the method that satisfies all equilibrium conditions. For more details and the critical review, you may consult Bromhead (1986, 1992, 1999) and Maksimovic (1979, 1988). The method is analogous to the Morgenstern and Price (1965) method as it uses the distribution function of inclinations of interslice forces f(x), though computationally simpler.
At the beginning, the screen shows the following INITIAL MENU: CHOICE I N I T I A L M E N U ( GE )
1 ENTER MAIN DATA (kbd) 2 ENTER SLIP-SURFACE (kbd) 3 LOAD MAIN DATA
4 LOAD SLIP-SURFACE 5 PRINT MAIN DATA (Screen) 6 PRINT SLIP-SURFACE (Screen) 7 VIEW GRAPH
8 ZOOM/ MOVE/ AXES/ MIRROR 9 C O M P U T E !
10 PRINTING OPTION IS: (Blank) 11 SAVE MAIN DATA
12 SAVE SLIP-SURFACE 13 W O R K I N G M E N U. . . 14 C H A N G E S. . .
15 Q U I T CHOICE No.?
1 ENTER MAIN DATA (kbd) is an option described in detail in Section 6, page 33.
2 ENTER SLIP-SURFACE initiates the definition of the slip surface. The description of the slip surface of arbitrary shape can be entered in five different ways. The Arbitrary slip surfaces shown in Fig. 5.7 can be described as:
Polygonal slip surface defined by point coordinates,
Bezier curves generated by control points linked to Bezier polygon,
Fixed plane type defines the fixed central plane and polygonal shapes on sides
Composite defined by a circular arc and an intersecting fixed straight line,
Circular shape which is treated as any arbitrary slip surface.
You may decide which one to use in a process of the continuous application, depending on circumstances in each particular problem. For details see Section 8, page 71.
Fig. 5.7 Five shapes of slip surfaces handled by GE.EXE
To simplify the definition of the function f(x) with minimum number of parameters, six types are envisaged, and presented later in more detail, (see Fig 8.6 and pages 77-78). The final result, the factor of safety, is rather insensitive to the choice of f(x), if the solution is physically admissible. Examples of the application of different f(x) are shown in sequence of figures from Fig. 8.8 to Fig. 8.15 and from Fig. 10.18 to Fig. 10.28 and in some other figures in Section 10.
This program GE.EXE can be also used for computation of the critical horizontal
acceleration that gives FS=1.0 for a given slip surface. Rigid body displacements due to the
square acceleration pulse with a value larger than critical can be easily calculated in addition to the conventional pseudo-static seismic analysis (option 7 in pages 83-84).
For more on the analyses using arbitrary slip surfaces see Section 8 and Section 10. 3 LOAD MAIN DATA When this item is selected, a list is obtained with all the available
*.BG files in the directory. Using arrow keys, move the highlighted bar to the name of the file you wish to load and press the <Enter> key. The screen should display the cross section.
4 LOAD SLIP SURFACE When this item is selected, a list is obtained with all the available *.SS files in the directory. Using arrow keys, move the highlighted bar to the name of the file you wish to load and press the <Enter> key. The screen should display the cross section of the slope including the slip surface.
5 PRINT MAIN DATA (Screen) or (File) Input data will be either shown on the screen or saved in the *.TXT file depending on the active option 10 PRINTING OPTION. In the case that the active option is Blank, main data will be shown on the screen.
6 PRINT SLIP SURFACE (Screen) or (File) Data describing the slip surface will be either shown on the screen or saved in the .TXT file, depending on the active option 10 PRINTING OPTION. In the case that the active option is Blank, slip surface data will be shown on the screen just Screen option was active.
7 VIEW GRAPH Self-explanatory. Graph will show the definition of the slip surface and the cross section, before computation. The soil limit lines will be shown in different colors; one color for one material beneath the line. Useful for rough checking whether the zoning of the cross section is properly described.
8 ZOOM/ MOVE/ AXES/ MIRROR Option is explained in Section 6, page 38.
9 C O M P U T E ! Initiates computation for the defined slip surface. When computation for the slip surface is finished, the graph showing results will appear, and the further control of the program is transferred to WORKING MENU (GE), page 83.
10 PRINTING OPTION IS: (Blank) or (Screen) or (File) permits you to control printing of input data and results of computation. Initially, as the program is started, this PRINTING OPTION might be:
(Blank) meaning that the whole process of computation will not be shown on the screen when COMPUTE ! option is chosen. If used, option will skip printing details of the results of iterative computation. Only the final result, (Fs) will be shown on the graphic screen without details.
(Screen) means that main data or intermediate phases of computation, when requested from the menu, will be displayed on the screen.
(File) option implies that, input data and/or results will be saved in the .txt file which can be later sent to the printer or examined. This option, is automatically made inactive during iterative computation in order not to produce huge redundant files. 11 SAVE MAIN DATA When this item is selected, a list is obtained with all the existing
*.BG files in the directory. Type the name of the data file you wish to save and press the <Enter> key. Do not type extension. If you enter the name of the already existing data file, it will be overwritten by the new one. Pay attention, there is no warning.
12 SAVE SLIP-SURFACE When this item is selected, a list is obtained with all the existing *.SS files in the directory. Type the name of the slip surface file you wish to save and press the <Enter> key. Do not type extension. If you enter the name of the already existing data file, it will be overwritten by the new one. Pay attention, there is no warning message.
13 W O R K I N G M E N U. . . Shows and offers WORKING MENU (GE)…(see p. 83) 14 C H A N G E S. . . Shows and offers menu CHANGES (GE)…(see p.90)
6. PREPARATION OF INPUT DATA
Input data for both stability programs consist of the two separate sets as follows.
1. MAIN DATA must be given first for definition of the geometry of the cross section,
distribution of materials, material properties, pore water pressures, external loading, seismic coefficients, etc.
This set of data is identical for both stability programs, BE.EXE and GE.EXE.
MAIN DATA can be saved or read from files by both stability programs, regardless of the program used for entering and saving of the data. File name extension is .BG
Preparation of this set of input data is described in the next Section 6.1.
2. SLIP-SURFACE(s) is the second set and it depends on the program used (BE.EXE or
GE.EXE).
Slip surfaces of circular shape for BE.EXE (Bishop Extended method) are described in Section 7.
Slip surfaces for GE.EXE (General Method) of arbitrary or circular shape are described in Section 8.
The slip circle analysis by the Bishop Extended method and BE.EXE is usually done first. After completion of the slip circle analysis by BE.EXE, you can read the same main data file by GE.EXE and check some non-circular slip surfaces, or compare the results computed by the extended Bishop's method with the result obtained by the General Method, which satisfies all equilibrium conditions, using SWITCH to… option.
6.1 MAIN DATA
Trial slip-surfaces may be used for either the right or left face of the slope. No restrictions are placed on the direction in which the slope faces. See Addendum 1, page 149. Positive direction of "x" is horizontal with coordinates increasing to the right hand side. The positive direction of "y" is upward.
The cross-section to be analysed is drawn in a convenient scale, basically as shown in Fig. 6.1 (simple slope, p.39), Fig.6.2 (slope with vertical crack, p.39) and Fig. 6.3 (moderate size problem, p.41).
It is recommended to use A-3 size millimeter paper or similar to draw moderate size and/or complex sections, and to follow the principles shown in Fig. 6.2. Draw your x & y axes. Writer's preference is to place "x" in such way that all or most points have positive values of "y" and that major part of the cross section is on the (+)ve side of "x" for the right face slope.
Smallest example for preparation of input data is given in Fig. 6.1, p.39 and Fig. 6.2, p.39. A moderate sized example for preparation of input data is given in Fig. 6.3, p.41. Boundaries of the cross section, limits of soil zones and piezometric lines are approximated by a straight line segments.
* End points of line segments are numbered from 1 to "N",
* Zone boundary lines and piezometric lines are numbered from 1 to "L", and
* Soil zones are numbered from 1 to "M". If the shear strength of some material zone(s) has to be described with the nonlinear failure envelope, these material zones must be either numbered first, or all materials should be defined as they had the nonlinear failure envelope. Linear envelope can be described with nonlinear
parameters by taking ∆φ=0 and with an nonzero value for parameter pN
The sequence of numbering of points and lines in the section is arbitrary.
Vertical lines are not needed for computational description of the cross section. If vertical line is prescribed, with the material definition in the range from 0 to the number of defined materials “M”, stability programs will warn you that this is not permitted. If, in spite of that, you start computation without making corrections, an error will be reported. However, if you want to have some vertical lines or any line of arbitrary orientation on your graph, you can prescribe to a line the material number outside the predefined range (0 to M). The negative material numbers are appropriate for such a purpose as they will show as discontinuous lines on the graphs on the screen and on HPGL plots, but will be ignored in computations. Such lines are called dummy lines.
ALL VALUES ENTERED IN THE PROGRAM MUST BE IN "SI" UNITS, in kN, m, (kilo-Newton, meter).
The unit weight of water is fixed value in the stability programs γw= 9,807 kN/m3.
MAIN DATA are entered after the first option is chosen in the INITIAL MENU of each stability program. The entering is performed in a "question and answer bases", or simply by following the screen instructions.
(i)
TITLE : is an alpha-numeric label giving the name of the problem. title. The suggested length of the title is not more than 40 characters, preferably less, if you wish to have a neat appearance on the screen. If you just press <Enter> without any title, the title will be automatically entered as "Untitled".
(ii)
COMNT : is the additional alpha-numeric comment to the problem with the suggested length as in (i). Make your comment as brief as possible. If you just press <Enter> without any comment, this label will remain empty.
(iii)
NUMBER OF POINTS (max.100) for the definition of the geometry of the cross section (N). Entering 0 (zero) or pressing only <Enter> will return you to the INITIAL MENU. This comes handy if you initiated the procedure by not wishing to do so.
(iv)
NUMBER OF LINES (max.100) which describe the boundaries of the cross section, internal zoning and piezometric lines (L). Entering 0 (zero) or pressing only <Enter> will return you to the INITIAL MENU.
(v)
NUMBER of MATERIALS (max.30) with different properties in the cross section, (M). Entering 0 (zero) or pressing only <Enter> will return you to the INITIAL MENU.
(vi)
NUMBER OF MATERIALS WITH NONLINEAR ENVELOPES is the number of zones for which the soil shearing strength is to be described in the proposed unconventional manner (MN). Note that MN<=M. Advanced users would take MN=M, see (x) and (xi).
(vii)
TAILWATER LEVEL (YW) defines the "y" value of the free water surface (Fig. 6.3). In the case that such a level does not exist, some negative value, ("y" is positive upward) beyond the soil zone in consideration, should be given (Fig. 6.1 and Fig. 6.2). This level, if defined within the visible area of the screen, will be marked with a blue triangle on the extreme left or right side of the screen or graph. Soil zones beneath this level
should be defined with the submerged unit weight ′γ in soil data set (x).
Note: Each time after entering (vii) or (viii) or (ix) or (x) and (xi) the following question will appear:
CONFIRM (Y/N) ?.
Pressing "Y" or "y" or only <Enter> would mean that you are satisfied with previous entries and you want to proceed with entering the next set of data. If you answer "N" or "n", meaning that you are not satisfied with previous entries (you made some errors), the program will automatically offer you an opportunity to make corrections.
When you correct this group of data the program will offer you to continue entering the next group of data.
(viii)
COORDINATES x,y. Program asks the sequential entering of pairs of coordinates, separated by ",", starting from Point No. 1 and ending with Point No. N
(ix)
SOIL LIMITS AND PIEZ. LINES Program asks the sequential entering of definition of lines, described by the sequential number of end points T1,T2, and the material number MT beneath the line (T1,T2,MT). The strata beneath the lowest soil limit lines are assumed to extend down indefinitely. If the material number MT is entered as 0 (zero), then it describes a piezometric line. Note that only one piezometric line can be given for any vertical section, but several can be simulated using the option described in (x).
Vertical lines with 0≤ MT ≤ M are not allowed. If you really need a vertical line which separates soil zones, like for example in the description of the vertical tension crack, line 1-5 in Fig. 6.2, prescribe very small difference in x coordinates, say 0.001 to 0.01 meters.
Sequence of entering lines is arbitrary.
Note that the piezometric line will appear in blue color. Central point of each piezometric line segment will be marked with a small blue triangle.
If the material number (MT) beneath the line is either negative or larger then the number of materials M defined in (v), it will be the dummy line. Such a line will appear in the graphical displays, though discontinuous line on the screen and in the plotted graph, but it will be ignored in computations. Only a dummy line can be defined as a true vertical line.
(x)
SOIL PARAMETERS (Gamma, C, PhiB, PP) define unit weight γ , cohesion c′, or c , u
the angle of the shearing resistance φ′ or φ′B or φu (in degrees), and the Pore Pressure
indicator PP, respectively.
All soil unit weights for zones beneath the horizontal line corresponding to the tailwater
level YW must be entered as submerged γ′=γsat -γw.
Strength parameters can be either in terms of total or effective stresses.
In the case that the shearing strength of material is to be described with nonlinear failure
envelope, the parameter "PhiB" is the "basic angle of friction", (φ′B) and the additional
PARAMETERS FOR NONLINEAR ENVELOPES (pNand ∆ ′φ ) will be entered
with the next group of data (xi). Note that materials with nonlinear failure envelopes should be numbered first, or if sequence of is mixed, all materials should be treated as nonlinear.
In the case that φu=0, the value of c corresponds to y = 0, what permits the u
description of the undrained strength linearly varying with depth, see PP option 3), in the next page.
The Pore Pressure indicator PP can be used in three ways:
1). PP>=0 Pore water pressure in the base of the slice will be computed by taking that
u
r = PP (pore pressure ratio), and the value of the pore water pressure will be
computed from u = r xW / bu where W is the weight and b is width of the slice.
2). PP<0 Pore pressure is computed from piezometric line. Program calculates the height of the piezometric line above the base of the slice, or above the tail water level (whichever is smaller), multiplies it by the unit weight of water and by the
absolute value of PP. In such a way, variable piezometric head in a single
