3 PRINT RESULTS … with the appropriate 4 PRINTING OPTION … should be used if you wish to see results in detail on the screen or save results to the .TXT file. Note that in this repeated printing, after completion of the computation, the iteration cycles will not be shown.
4 PRINTING OPTION IS: … This option in routine computation should be kept Blank while computing in this menu for reasons explained earlier, page 31, unless you wish to use the previous option 3.
5 COEFF. OF SEISMICITY kx, ky can be altered. The convention on the sign of acceleration described in MAIN DATA preparation applies here. As new kx and ky are entered, computation starts automatically. Note that ky=0 (the vertical acceleration) is the usual entry. Only values Fs =1.0 and Fs>1 have physical meaning.
6 f(x) SHAPE No. … can be altered. Some examples are shown in Section 10.
7 EQUIVALENT BLOCK & kc When chosen, the program will map all acting loads and resultant stresses on the slip surface into the system of resultant forces acting on an equivalent block on an inclined plane, give the equivalent inclination, show the average normal and shear stresses on the slip surface and give the initial estimate of the critical acceleration for which the safety factor might become equal to one. After that the following will appear on the screen:
Type KC or DIS or press ENTER to continue ?
KC if called repeatedly a few times in sequence, will compute the critical acceleration to desired number of significant digits or to obtain Fs=1.0000. The main purpose of this option is to provide data for an estimate of the rigid body displacements due to earthquake acceleration for which the safety factor is less than one by using the Newmark's (1965) principle.
DIS in the same sub-menu will ask for the acting acceleration and the duration of the rectangular pulse T/2. The application of this option will give the magnitude of the components of the rigid body displacements.
Note that the EQUIVALENT BLOCK option can be used to compute the point which repre-sents the average normal and shear stresses on the slip surface. This point can be used for evaluation of the resistance envelope proposed by Casagrande and advocated by Janbu (1977).
8 ZOOM/ MOVE . . . option is basically described previously in Section 6, page 38.
9 INTERACTIVE SEARCH for Fs,min. This is one of the most important options in this program. It offers a possibility to vary the shape of the previously defined slip surface and immediately see the results. The interactive search is performed in an “interactive window” in which the definition of the change will depend on the TYPE OF THE SLIP SURFACE, though the basic principle is always the same. The windows for these changes are shown in the following pages. Previous result is shown in bottom right corner, second row from the bottom line as Old safety factor. Select and press the control point number which you wish to move. The selected control point number and the circle representing the point will become of red color and point is ready for moving using arrow ← ↑ → ↓ keys or +/- signs. After performing a change you can Compute!
by pressing either the letter C or number 9. After the Compute option is executed, in the bottom right corner the result of computation as New factor of safety appears indicating the type of the change in FS. which can be either No change, (white color), or Increase (red color) or Decrease (green color). Green color encourages you to move the point (or to change the variable) in same direction until you get Increase in red in order to obtain minimum. It works like the traffic signal. The minimum is obtained when moving of any point in any direction indicates red color meaning that any change in slip surfaces causes the safety factor to increase for the current value of the Step. Step for the movement of a control point can be changed pressing S (S for Step) and entering the new desired value. The default Step value is 1.0 meter, but it is
usually reduced to some smaller value at the final stages of iteration for the critical slip surface. From the practical experience, the Step should be reduced to 1/5 to 1/10 of the previous value for the next set of the interactive iterations. The interactive iterative procedure is based on the concept that you keep changing one variable while the safety factor is decreasing, and to skip to the other variable until the Fs is further decreasing.
When all the variables (points which define the slip surface) arrive to such a position that any change causes the Increase of New Fs, the Step is reduced, and the procedure repeated. The minimum is obtained when moving of any point in any direction indicates red color meaning that any change in slip surfaces causes the safety factor to Increase. You can iterate to any desired accuracy or until all 5 visible significant digits stop decreasing and the only changes you can see is the change of the color in front of the New computed Fs. Press SPACE (bar) TO EXIT, and that will automatically compute again and automatically call option 2 VIEW GRAPH with the result, just as shown in Fig.8.9 to Fig.8.13, p. 80-82.
Polygonal slip surface can be changed by selecting the number of point for which the coordinates will be changed, as shown in Fig. 8.14. Coordinates of the point which define the polygon are changed using arrow keys ← ↑ → ↓ .
Fig. 8.14. Interactive window for the Polygonal slip surface
Bezier line can be easily varied by moving the control points of the Bezier polygon. The interactive window for these changes is shown in Fig. 8.15. Select and press the control point number which you wish to move. The selected control point number and the circle representing the point will become of red color and point is ready for moving using arrow ← ↑ → ↓ keys. After performing a change, simply by moving the selected point in a trial direction, you should Compute! by pressing either the letter C or number 9.
Decrease in green color encourages you to move the point in the same direction until you get Increase in red and than you move point back in order to obtain minimum.
Pressing N you can change the number of points which approximate the Bezier curve.
The default value for the number of poiNts N is 40, and the max. is 100, both values sufficiently large for a rather smooth and continuous appearance of the Bezier curve.
Fig. 8.15. Interactive window for the Bezier type slip surface
The application of the Bezier curve for the description of the arbitrary slip surface with an interactive search for the critical slip surface and Fs,min. is probably, the unique and the most versatile feature of this software package. It is the author’s experience from many practical jobs that it almost always gives the slip surface with the safety factor smaller than the factor of safety of the critical surface of circular shape. In this manual an example is shown where the Bezier slip surface gives the smallest Fs, in comparison with all other shapes (circle, polygon and composite).
Fixed plane polygonal slip surface, see Fig. 8.16, can be varied using any of four arrow keys
← ↑ → ↓ for all points (1, 2, 5 and 6 in the example) except for two points which define the fixed plane. Point which define the fixed plane (points 3 & 4 in the example shown here) are moved along the defined plane using only ← → (horizontal) arrows, though the fixed plane can be inclined. The program shall not respond to ↑ ↓ (vertical) arrows when points which define the fixed plane are active.
The amount of change of the coordinate is defined with Step which you can make active by pressing the letter S or s. After performing a change, simply by moving the selected point(s) in a trial direction, you should Compute! by pressing either the letter C or number 9. Observe the lower right corner. Decrease in green color encourages you to move the point in the same direction until you get Increase in red and than you move point back in order to obtain minimum.
Results of the Interactive search are shown Fig. 10.29 and Fig. 10.30, page 123.
Fig. 8.16 Interactive window for the Fixed plane type slip surface
Composite slip surface can be varied by either changing the circle center coordinates using arrow keys ← ↑ → ↓ or changing the radius of the circular arcs using + or – keys which will MOVE PPT (meaning move the Passing PoinT), or both as shown in Fig.
8.17. By changing the number of points, pressing N previously, a set of polygonal slip surfaces can be generated and varied. The default value for the number of points is 50, and the max. is 100, both values sufficiently large for a rather smooth and continuous appearance of circular arc segments.
Fig. 8.17 Interactive window for the coMposite type slip surface
Circular slip surface can be altered, and the initial slip circle for the interactive search will be the one from the previous run. The search is performed in an identical interactive window like the one used in BE.EXE, described and shown in Section 7, and shown from Fig.7.8 to Fig. 7.14, pages 53 to 57.
10 SWITCH to BE…(Bishop Method) will save MAIN DATA to a temporary file (TEMP.BG), start running BE.EXE which reads this temporary file. MAIN DATA are transferred and any slip surface of general shape is lost unless it is a CIRCLE for which the safety factor will be automatically computed using Bishop Extended method.
11 C H A N G E S . . .Brings menu CHANGES (GE) (see next page)
12 SAVE .BGP FILE ( HP-GL & Printing )... is offered in WORKING MENU of both stability programs. This option is used to save file with MAIN DATA and results for later use by a program BGP.EXE for graphic presentation and/or printing. You have to give the name of the file only, and the extension will be automatically set to .BGP.
13 SWITCH to BGP ... ( HP-GL & Printing ) Alternatively to the previous option 12, you may select the option which will start running BGP.EXE and transfer MAIN DATA and results of computation for graphic presentation and/or printing. Note that in this case the file with results (TEMP.BGT) will be temporary only. You may save this file from BGP.EXE. You can return from BGP.EXE back to GE.EXE with results of computation and continue the analyses after, for example, saving (export) graphics in HP-GL format.
14 TOLERANCES: Default or Small. Works as a toggle. This option permits you to chose between two levels of the numerical tolerances, which differ for two orders of magnitude for forces and moments and one order of magnitude for normal stresses. The alternative tolerances are for the unbalanced horizontal force ∆En acting on the right hand side end of the sliding body i.e. or on the last slice, unbalanced moment for the last slice ∆Mn and stresses at the base of each slice ∆σi:
The tolerance for ∆En(kN/m1) ∆Mn (kNm/m1) ∆σi(%)
Default 0.000100 0.00100 0.10
Small 0.000001 0.00001 0.01
For slopes of the height in the conventional range from, say, 5 m to 150 m, the option Default is suggested. For very small slopes or stability problems involving only a few meters of the size of the sliding body, the option Small might be required, though this tolerance is preferred in general.
In the unlikely case that you encounter the instability in convergence in the iterative computation and/or during INTERACTIVE SEARCH for Fs,min, try to change (switch) the current tolerance.
IN THE CASE THAT THE TOLERANCES ARE NOT MET AFTER 2000 ITERATIONS, DO NOT PANIC, SEE HINTS IN THE BOTTOM OF PAGE 92.
15 Q U I T You will be asked to confirm that you are leaving the program GE.EXE.
Menu C H A N G E S (GE) contains 10 options (1 to 10) for MAIN DATA editing which are the same for both stability programs and described in more detail in Section 9, page 96. Other options in GE.EXE can be described as follows:
11 S-S:
Some other options are also given with identical purpose but have different number, in BE.EXE, and a few only are different to match the requirements of the particular method of the analysis, i.e.:
11 S-S: is the TITLE FOR SLIP SURFACE. It can be altered if you wish to do so for some book keeping purposes.
12 f(x) SHAPE No.__ can be changed here in CHANGES (GE) and in WORKING MENU (GE). In the former case, immediately as the new function shape is entered, computation does not restart automatically. If you wish to compute, you should use option 18.
13 ZOOM/ MOVE/ AXES/ MIRROR ( X0=__ Y0= __ ) option is described in Section 6, page 38 and Section 9, pages 101-102.
14 SHIFT SECTION and/or CHANGE SCALE RMX=__ (same as option 13 in BE.EXE) can be used to relocate the geometry of the cross section by shifting it for some increment in x and y directions with dx and dy values with respect to the origin. See Section 9, page 101-103, Fig. 9.4, Fig. 9.5, Fig. 9.6 and Fig.9.7.
15 VIEW GRAPH in both stability programs (BE & GE) will show the cross section with lines in different colors. Namely, each line describing the upper boundary of the same material zone will be of the same color. It is used to check if material zoning is described properly.
16, 17 & 18 are self-explanatory.
8.1 RESULTS FROM GE.EXE
Details of results of computation for each slip-surface are shown in three tables. First two tables describe the values of computed constants and parameters for each slice, and the third table shows results obtained by iterative solution of the system of nonlinear equations. A sample output for the case shown in Fig. 10.25, p.121 and Fig. 11.11, p.143, is shown in pages 93 to 95 with the explanations for heading as follows:
Heading of the first table: DATA 1 (See page 93) I Slice number (starting from 1)
Heading of the second table: DATA 2 (See page 94) I Slice number (starting from 1)
RHor Horizontal component due to pore pressure, horizontal inertia force due to earthquake and external loading
RVert Vertical component due to the weight of the slice, pore pressure, vertical component if inertia force due to earthquake and external loading
RM Moment with respect to the center point at the base of the slice due to known forces
Phi The angle of the shearing resistance at the base of the slice c The cohesion value at the base of the slice
f(x) The value of f(x) in the interslice section.
Note that in the printouts there is the difference between the Slice Number I in DATA 1 and DATA 2 which start from 1, and the Interslice section number in DATA 3, which starts from 0 (zero) at the left end of the slip surface. In DATA 3, I has dual meaning; for XML, R, E and tanBeta I represents the interslice section number, and for Sig and Tau, I represents the slice number.
Results listed above are mainly used for checking the input data. It is recommended not to use F (File) option while COMPUTING with GE.EXE. Program prevents the possibility to form a .TXT file with all intermediate results of iterative computation because the amount of printout, showing all the iterations, would be huge.
If you wish to produce the hard copy of all results, it is much more efficient to use the option from the WORKING MENU: 3 PRINT RESULTS (Screen) or (File) after the computation run under Blank printer option. As an alternative you might save results as .BGP file and perform printing to a text file (.TXT) of the same results from BGP.EXE.
RESULTS OF INTERMEDIATE ITERATIVE COMPUTATION can be traced during computation as they are printed in an outline form only and contain the following:
FS Current value of the factor of safety, which satisfies the condition that interslice forces at both ends of the sliding body are equal to practical zero.
A Current value of the unknown A
ENL The unbalanced horizontal force at the end of the sliding body, rather small value, as it is printed after the convergence to the tolerable value is reached.
DM The unbalanced moment for the last slice. The solution is reached after this value is smaller than the prescribed tolerance. This value monotonously decreases in the iteration process after the second iteration on moments.
ITFS Iteration number in the internal iteration cycle with fixed value of A.
These intermediate results of computation can be seen on the screen if PRINTING OPTION IS: (Screen) or (File). You will be able to control scrolling during iteration (as the File option will be automatically reverted to Screen during iterations) . It is rather unlikely that you will feel the need to see this iteration process unless you encounter some iteration problems. Results of intermediate iteration cannot be saved as the .TXT file.
MAIN UNKNOWNS Fs and A are printed as result of computation after all the tolerance criteria are satisfied. (See page 95)
Heading of the last, the third table: RESULTS OF COMPUTATION I Interslice section number (starting from 0)
XML x of the interslice section
R Position of the horizontal component of the interslice force defined as the vertical distance from the slip surface in the same section
E Horizontal component of the interslice force
T Vertical (shearing) component of the interslice force (frequently used symbol X) tanBeta tan of the inclination of the interslice force or simply T/E = A f(x) = tanBeta.
Sig Effective normal stress on the base of the slice I Tau Shear stress on the base of the slice I
These tables with described results appear on the screen during computation if the current PRINTING OPTION is (Screen) or (File). If the option is (Blank), these results can be recovered by using the option from the WORKING MENU: 3 PRINT RESULTS (Screen) or (File). Printed output in the next pages corresponds to the case shown in Fig.
10.25, p.121 and Fig. 11.11, p.143.
Failure of convergence. Program stops computation sending the appropriate message if tolerances are not satisfied after 2000 iterations. Six suggestions on the screen what to try if that happens are: Swap TOLERANCES, Try some other f(x), Change the NUMBER OF SLICES, Change the number of poiNts (if Bezier or coMposite slip surface), Use miRror and then CHOOSE COMPUTE, CHECK YOUR DATA for errors or physical admissibility and PAUSE AND THINK if nothing of the above helps. If any of these suggestions do not help, the main reason is most frequently the physical inadmissibility of the defined problem with your (wrong) input data.
Bezier 5 4b
RESULTS OF COMPUTATION: Fs= 1.4101 A= 0.2984