Some Notes on STABL for Windows 3.0 New features

The Options/Geometry Plot submenus let the user activate or deactivate the display of the segment numbers and data points that compose the geometry plot. Notice that these options only affect the display in the Geometry tab. This is the plot the user should use to make sure that the data reflects the intended profile. The other tabs where slip surfaces appear never display any segment numbering or data points.

Right clicking the mouse over the plots Right clicking the mouse over a plot will bring up a small menu with options to copy the graphic into the clipboard, insert or delete an annotation, activate the display of soil properties when the user clicks on the graphic and to redraw the image. The Activate Soil Properties Display option, when checked, allows the user to identify what that soil is, see its shear strength properties and the segment number and coordinates that is associated with that soil, just by clicking on it with the mouse. It is mostly intended to help the user find when segments are entered out of order or incorrectly.

As one can see below, there is an obvious error in the geometry as entered. By clicking on the vertical column of soil that seems to be obviously out of place, the user will see that the culprit is segment 27, associated with soil 2. It is incorrectly ordered.

The colors associated with the soils can be changed by the user, and saved, using the menu Options/Soil Colors.

STABL FOR WINDOWS 2.0

MANUAL

GEOTECHNICAL SOFTWARE SOLUTIONS

2001

STABL FOR WINDOWS VERSION 2.0

USERS MANUAL

Geotechnical Software Solutions, LLC

2

Disclaimer:

This program was developed by Geotechnical Software Solutions, LLC. Although this software has been tested considerably to ensure its accuracy, GSS accepts no responsibility for the accuracy of the results obtained from its use. It is the user's responsibility to check and evaluate the validity and applicability of the results.

3

Table of Contents: Page

STABL FOR WINDOWS INTERFACE 6

ABOUT STABL FOR WINDOWS 7

INSTALATION INSTRUCTIONS 7

RUNNING STABL FOR WINDOWS 7

GETTING UP TO SPEED 7 Starting the Program 7 Minimum Data Set 8

CHOICE OF ANALYTICAL METHOD AND SURFACE GENERATION MODEL 8

FACTOR OF SAFETY HISTOGRAM 9

MAIN FEATURES OF THE PROGRAM 10 Unit System Selection 10 Soil Profile 11 Soil Properties 13 Water Tables 14 Boundary Loads 15 Seismic Loads 16 Tiebacks 17 Geosynthetics 18 Soil Nails 19 Analysis 20 Menu Bar Options 21

GENERAL RECOMMENDATIONS FOR USE OF STABL FOR WINDOWS 25 REFERENCE MANUAL 26 PROBLEM GEOMETRY 27 Profile Boundaries 27 Piezometric Surfaces 31 SOIL PARAMETERS 34 Anisotropic Soil 35 BOUNDARY LOADS 37 SOIL REINFORCEMENT 39 Soil Nailing 39 Geosynthetic Reinforcement 40

4

TIEBACK LOADS 40 Description of the Tieback Routines 43 TIES Input Restrictions 47 EARTHQUAKE LOADING 47 SEARCHING ROUTINES 48 Circular and Irregular Surfaces 48 Sliding Block Surfaces 53 Surface Generation Boundaries 58 Individual Failure Surface 58 BISHOP SIMPLIFIED METHOD 60 JANBU SIMPLIFIED METHOD 63 SPENCERS METHOD 65 Description of Spencers Method 65 SPENCR Option 68 SPENCR Input Restrictions 69 ASSUMPTIONS 70 DATA PREPARATION 74 Input for Each Command 74 ERROR MESSAGES 85 Command Sequence Errors 86 Free-Form Reader Error Codes 87 PROFIL Error Codes 87 WATER Error Codes 88 SURFAC Error Codes 88 LIMITS Error Codes 89 LOADS Error Codes 90 SOIL Error Codes 90 ANISO Error Codes 91 RANDOM and CIRCLE Error Codes 92 BLOCK Error Codes 93 TIES Error Codes 95 SPENCR Error Code 96 REFERENCES 97

5

6

STABL for WINDOWS INTERFACE

7

1. About STABL for Windows STABL for Windows (SFW) is a Windows-based program that works under Windows 95/98 or Windows NT; and it will also be available for Windows 2000. It uses as an engine the PCSTABL slope stability analysis program from Purdue University. It allows calculations using Bishops Simplified, Janbus and Spencers methods; and a variety of different slip surfaces. Tiebacks, soil nails, and geosynthetics can also be used. STABL for Windows is currently available in English. Versions in Spanish and Italian will be available in the near future. 2. Installation Instructions Place the CD in the CD drive. Either (a) click on setup within the CD folder or (b) run setup from START, browsing to locate the setup installation file. Follow the instructions from there on. 3. Running STABL for Windows We recommend that you read this manual while running the program with one of the example input files provided. This will help you get acquainted with the program, particularly if you have never used STABL before. We also strongly recommend that you first read the STABL for DOS manual. STABL for Windows is designed for ease of use. We will continue to improve the program with this goal in mind.

4. Getting up to speed 4.1. Starting the Program When you run STABL for Windows, the main screen will display the problem description elements on the left side and a blank graphical frame on the right. Your first step will usually be entering new geometry data or retrieving data previously saved in a file. As soon as geometric data is available, it will be automatically displayed in the graphical frame. Any modifications to the geometric elements will be immediately reflected in the display.

8

The coordinates of a point can be determined either by referring to the coordinate axes or by moving the mouse on top of the graphical frame. When the mouse is placed on the graphic, the points coordinates will be displayed in the small message panel located below the graphical frame. This feature will help you identify where to place other elements, such as loads or soil reinforcements. 4.2. Minimum Data Set There is a minimum amount of data (highlighted in Figure 1) you need to input before you can successfully run a search for the slopes critical slip surface. At a minimum, you must enter data for the following:

1. Soil Profile 2. Soil Properties 3. At least one analytical model for the surface generation

routine The data needed for the Soil Profile and Soil Properties elements are discussed in detail in the original STABL manual, as well as elsewhere in this manual.

At this time, it is important to understand how the selection of the analytical model is made in STABL for Windows.

5. Choice of Analytical Method and Surface Generation Model There are seven combinations of surface generation algorithms and analytical models. The Spencer option must be used along with any of the other six. You can enter data for as many different methods as you wish by marking the respective checkboxes and pressing the Edit button. After entering data for the methods you wish to use, you should choose which one to run. This is done by pressing one of the square buttons on the right of the desired model. Notice that only one model choice at a time will be possible, even when you entered data for more than one model. The only exception is

Figure 1. Essential Data

9

the Spencer option, which will always be chosen along with one of the other methods. When you save the data in a file, all models with active checkmarks will be saved. When you open a previously saved file, the model selected to run is the last model for which data were supplied in the file (which is a text file that the program reads and that you can also view using notepad or other text-viewing program). Looking at Figure 1, the default choice to be run is the Janbu Block, which was read in from the file after the Bishop Circular option. Nevertheless, both options have data and are available for running (you just need to click on the appropriate button). After the search is finished, the graphical display will show all the surfaces generated as a green cloud, as well as the ten most critical ones in black and the most critical surface in red. The factor of safety will also be displayed at the top, appended to the title of the project. You can view only the ten most critical surfaces by clicking on the button 10 Most Critical. At any point the graphical display can be printed to the default printer by using the File > Print Image submenu.

6. Factor of Safety Histogram

Figure 2: On the left, an unsuitable histogram distribution; on the right, a more appropriate distribution, probably indicative of an effective search. A histogram showing the percent distribution of calculated factors of safety for all surfaces generated is automatically generated when a search is completed.This histogram may be useful in determining whether the progressive search refinements are indeed improving the number of surfaces being generated

10

close to the critical region. The user should run successive searches, refining the search boundaries until the histogram displays the largest percentages of surfaces with factors of safety close to the minimum (skewed to the left). This indicates a higher chance that the minimum for the search is indeed the minimum for the slope (Figure 2). Future versions will expand the statistical capabilities of the program.

7. Main Features of the Program 7.1. Unit System Selection You must always select a unit system (S.I. units or English Units) to be used in the analysis (Figure 3). All the numbers entered will be expressed in the selected unit system. S.I.-based units commonly used in slope stability calculations include the meter (m) for length and the Newton (N) for force. It follows that stress is expressed in terms of the Pascal = N/m2. Since Newtons and Pascals are somewhat small units, it is common to express stress in terms of one thousand Pascals (the kilo Pascal kPa = kN/m2), and unit weights in terms of one thousand Newtons per cubic meter (kN/m3). English units are still often used in the United States. The feet (ft) and pound (lb) are used to express length and force. Technically, the force unit is actually pound-force, since pound is the unit of mass, but no such distinction is usually made. Unit weights are expressed in terms of pounds per cubic foot (pcf), and stresses, in terms of pounds per square feet (psf). When you read from one of the example files or a file previously saved, the unit system is automatically selected, based on the file termination (in or si). For example, the file example2.in uses English units while sfwex1.si uses the international unit system.You can open any of the examples used in the STABL for DOS manual or the example referred to in this manual. If you choose to open the file sfwex1.si, for example, all the information provided in the input forms are shown graphically in a window. In this case, as seen in Figure 3, you can observe the geometry of the slope, the soil layers, the water table, and the boundary loads.

11

Figure 3. Main window with file sfwex1.si open. 7.2. Soil Profile This selection allows you to define the soil layers composing the slope as well as the slope geometry. It leads to a window (Figure 4) where you should provide the following information:

(a) The title of your project; (b) The total number of soil boundaries (these include segments on the

ground surface, which are considered soil boundaries); this number will automatically generate the number of rows in a spreadsheet.

(c) The number of soil boundaries that are ground surface segments. The rows in the spreadsheet corresponding to ground surface segments will be identified with the word (Top) in parentheses.

For each soil boundary segment you need to provide:

(a) The abscissa of the left end-point of the segment; (b) The ordinate of the left end-point of the segment;

12

(c) The abscissa of the right end-point of the segment; (d) The ordinate of the right end-point of the segment; (e) The number identifying the soil immediately under the segment;

each soil is named and its properties defined in the Soil Properties Button.

You must click OK if you wish these properties to be saved. Be sure to locate the slope in the first quadrant (see STABL for DOS manual). The toe of the slope should always be to the left of the crest of the slope.

Figure 4. Soil profile window with file sfwex1.si open.

13

7.3. Soil Properties SFW can handle either isotropic or anisotropic soils. The number of soils generates the number of rows in the spreadsheet (Figure 5). Each row, corresponding to one particular soil, requires a wet unit weight, a saturated unit weight, a cohesive intercept, a friction angle, and one of three numbers: the number of the water table to be used to calculate pore pressures within the slope, the pressure head or the pore pressure ratio. We recommend working with water tables, and not with pore pressure ratios, unless there is strong reason to the contrary. Notice that water table numbers should always be greater than 0, even if there is no water in the problem. When there is water present in the problem, the Water Table number entered in the soil properties section will be matched to the water tables defined in the water section of the data.

Figure 5. Soil properties window with the file sfwex1.si open.

14

7.4. Water Tables Use this button to define the groundwater pattern for the slope. The window that opens when you make this selection requires the number of water tables you are defining. Usually, only one water table is defined, but in some special situations, such as when a perched water table is present, more than one water table may be specified. You must also state how many points you will use to define the position of each groundwater table. When you click on Enter after you specify the number of points, a spreadsheet opens on the right-hand side of the window where you can enter the coordinates of each of those points (Figure 6).

Figure 6. Water Tables window with the file sfwex1.si open.

15

7.5. Boundary Loads This button opens a window where you enter one or more boundary loads, if present. In order to locate each load on the slope, you only need to specify the left and right endpoints of the load. You also need to specify the magnitude of the load; if a tangential component is present, an angle of rotation of the load corresponding to the arc-tangent of the ratio of the shear to the normal component of the load must be specified. Figure 7 illustrates the window displayed when the Boundary Loads Button is clicked with the file sfwex1.si open. Notice that the units for the loads must be consistent with the unit system adopted.

Figure 7. Boundary loads window with file sfwex1.si open.

16

7.6. Seismic Loads If subject to an earthquake, the slope is acted upon by inertial forces that are related to the accelerations within the slope. In this window (Figure 8) you enter the horizontal and vertical accelerations and the cavitation pressure. Figure 8 shows the data used in the sfwex1.si example file.

Figure 8. Seismic loads window with the sfwex1.si file open.

17

7.7. Tiebacks For this selection you will provide the number of tiebacks. This creates a spreadsheet where the data for each tieback is needed (Figure 9). You need to state which boundary segment the head of the tieback is in contact with and the ordinate (Y) to define its location. The spacing between tiebacks within a given line of tiebacks, the angle the tieback makes with the horizontal and the free length are still needed to fully define the geometry of the problem.

Figure 9. Tieback window.

18

7.8. Geosynthetics Enter the number of groups of reinforcement that you will be defining. A group is a set of reinforcement layers with the same length and properties. For each group, enter the information discussed next (Figure 10)

(a) Group number: this refers to a group of geosynthetics with the same characteristics. (b) Number of the boundary segment where the geosynthetics intercept the slope surface. (c) The ordinate (Y) of the points where the bottom and top layer of the geosynthetic group intercept the slope surface (d) Number of geosynthetic elements between top and bottom. (e) Length of the geosynthetics in the group. (f)Allowable tensile strength (per unit length of slope) for the geosynthetic layers in the group. (g) Soil-geosynthetic coefficient of interaction.

Figure 10. Geosynthetics window.

19

7.9. Soil Nails You will need to enter the number of nail groups for this selection. A group is a set of soil nails with the same length and same properties. For each group, provide the following information: (a) Group number: this refers to a group of soil nails with the same characteristics. (b) Number of the boundary segment where the nail group intercepts the slope surface. (c) The ordinate (Y) of the bottom and top nail heads (located at the slope surface). (d) Number of layers of nails in the group. (e) Length of the soil nails in the group. (f) Horizontal spacing between adjacent nails. (g) Inclination of nails, measured clockwise from horizontal. (h) Diameter of steel section of nails. (i) Allowable tensile strength of nails. (j) Side resistance along nail-soil interface. (k) Diameter of nail borehole. (l) Nail head condition (this defines the degree of interaction between the nail head and

the slope; a fixed head allows full transfer of loads between the two). (m) For free nail head, specify the percent load transfer between the nail and head and the

slope surface.

Figure 11. Soil nails window.

20

7.10. Analysis

Figure 12. Bishops analysis with search for a critical circular surface with the data introduced for file sfwex1.si. Under the analysis heading, you can specify the type of analysis you wish to perform (the options are Bishops Simplified Method, Janbus Method, or Spencers Method), as well as the type of sliding mechanism to go with the method. The sliding mechanism options are: circular failure surface, sliding blocks, randomly shaped failure surface and user-defined failure surface. Janbus method can be combined with sliding-block mechanisms, circular or randomly shaped slip surfaces. Bishops method can only be used with circular slip surfaces (Figure 12). Both methods can be used with a single user-specified surface, but such a surface should be circular in the case of Bishops method. Once you have selected the method you wish to use in the analysis, click on the button "Edit". Provide the information required in the window that follows. This information is needed for the program to perform such analysis. Figure 12 illustrates for the file sfwex1.si, the form displayed when the "Edit" button is clicked with Bishops method selected.

21

If you select the option "deactivate" in the water tables, load, and stabilization forms that have already been completed, the analysis will be performed disregarding that data.

Having entered all the information required in the Edit forms, you can select one method to run, and the desired analysis for the slope at hand will be performed by clicking the "Run" button. Be sure to save your data before you run the analysis. 7.11. Menu Bar Options The menu bar (Figure 13) offers six options: File, Edit, Results, Transforms, Units, and Random Generation.

Figure 13. Menu Bar of STABL for Windows 2.0. 1) In File, you find the following options: start a new file, open an existing file, close a file, save a file, save a file with a specific name, save an image with a specific name, save a summary file, print an image, and exit (Figure 14).

Figure 14. Option File.

2) You can either copy the plot of the problem you are working on to the clipboard or save it to a file using the option Edit > Image Copy (Figure 15). If you choose to save the image to a file, five formats are available (Figure 16).

Figure 15. Option Edit. Figure 16. File extensions for saving a plot.

22

3) In Results, the option STABL 6 Output can be used to see the results provided by STABL 6 for DOS. 4) The options available in Transforms, Mirror and Translade, can be used to manipulate the coordinates of a particular problem (Figure 17). Figure 17. Option Transforms. For example, input data from a problem whose geometry presents a slope facing East can be used to initially set up the analysis (Figure 18). Then, by using the command Mirror, the problems geometry can be rotated 180o (along an imaginary vertical axis), resulting in a slope facing West (Figure 19). In those cases where the procedure previously mentioned will result in negative values for the x-coordinates (see Figure 19), the command Translade should be used sequentially to make sure all the coordinates lie within the first quadrant (Figure 20). Detailed information on setting up a problems geometry is presented in the STABL for DOS manual. 5) Units: the conversion of units from the English System to the S.I. System, or vice-versa, can be easily performed at any stage by means of the option Convert (Figure 21). 6) Random Generation

23

Figure 18. Geometry of a slope facing East (right side).

Figure 19. Use of command Mirror to manipulate the coordinates of the original

problem.

24

Figure 20. Use of command Translade to manipulate the coordinates of the original

problem.

Figure 21. Option Units

There are four buttons on top of the graphical display that can be selected at any point during the analysis: Geometry, Generated Surfaces, 10 Most Critical and FS Histogram. Geometry is the default graphical display that will appear when you run the program. The second and third options show all the surfaces generated in the analysis (green lines) and the ten most critical failure surfaces (black lines), respectively (Figure 22). The most critical one is shown in red. Finally, there is the FS Histogram button that can be used to display the results of the statistical analysis mentioned previously (item 6).

25

Figure 22. Critical failure surfaces for the sfwex1.si example. 8. General Recommendations for Use of STABL for Windows When you open the STABL 6 output option from the results menu, you are actually opening a file used by STABL for Windows to output the results of a critical surface search being executed. Every time you run a new critical surface search, that file is overwritten. For this reason, before running a new search, make sure that you either close the output file or rename it. Renaming it is probably more advisable, since you will be able to go back and review it later for comparison. In Conclusion: Thank you for your purchase of SFW. Please let us know of your experiences using SFW. Your feedback will allow us to continue to improve the program in order to better serve you. Our contact e-mail addresses are: Sales: sales@winstabl.com Bugs: support@winstabl.com

26

REFERENCE MANUAL

27

PROBLEM GEOMETRY The first step in a slope stability analysis using STABL is to plot the problem geometry to scale on a rectangular coordinate grid. Coordinate axes should be chosen carefully such that the problem is completely defined within the first quadrant. This enables the graphical aspects of the program to function properly. In doing this, potential failure surfaces which may develop beyond the toe or the crest of the slope should be anticipated (Figure 1). Neither deep trial failure surfaces passing below the horizontal axis nor trial failure surfaces extending beyond the defined ground surface in either direction are allowed. If any coordinate point defining the problem geometry is detected by the program to lie outside the first quadrant, an appropriate error code is displayed and execution of STABL is terminated. Graphic output resulting from execution of STABL is scaled to a 5" x 8" plot of the problem geometry. The origin of the coordinate system referencing the problem geometry is retained as the origin of the plot, and the scale is maximized so that the extreme geometry point or points lie just within the boundaries of the 5" x 8" plot. Therefore, it is advantageous to fit the problem geometry to the coordinate axes with this in mind. Situations where the resulting plotted profile would be too small in scale to be useful for interpretation should be avoided (Figure 2). Figure 1 is an excellent example of well chosen coordinates, where there is enough room for possible failure surface development, and the profile geometry is plotted to the largest scale possible within the allowed format. If these requirements are not considered before the input data are prepared, revision of the entire set of data could later become a necessity.

Profile Boundaries

The ground surface and subsurface demarcations between regions of differing soil parameters are approximated by straight-line segments. Any configuration can be portrayed so long as the sloping ground surface faces the vertical axis and does not contain an overhang. Vertical boundaries should be specified slightly inclined to the right for computational reasons (i.e., Xleft = 100.0, Xright = 100.1). Assigned with each surface and subsurface boundary is a soil type which represents a set of soil parameters describing the area projected beneath. Vertical lines, passing through the end points of each boundary, bound the area in lateral extent. The area below a boundary may or may not be bound at its bottom by another boundary beneath which different soil parameters would be defined (Figure 3).

28

We

ll B

eyo

nd

Cre

stW

ell

Be

yon

d T

oe

De

ep

Figu

re 1

. Ext

ent o

f po

tent

ial f

ailu

re s

urfa

ces.

29

(1000,1000)(1500,1000)

(1900,1200) (2400,1200)

a. Coordinates are too large in comparison with height and length of slope.

Figure 2. Output scaling resulting from correct but inadequate definition of the problem geometry with respect to the origin of the coordinate system.

(0,500)(700,500)

(900,600) (1600,600)

b. Too much room allowed beyond the toe and crest of the slope in comparison to the slope height and length.

(0,0)

(0,0)

30

Soi

l 1

Soi

l 3

Soi

l 2

Soi

l 3

12

3

13

4

5

6

78

9

10

12

11

14

15

A

B

GH I

JK

L

M

DC

FE

Bou

ndar

yA

BC

DE

FS

oil T

ype

32

Are

a

5G

HIJ

K1

15

-LM

-3

Figu

re 3

. Rel

atio

nshi

ps a

mon

g so

il ty

pes

and

boun

dari

es.

31

The program requires an order by which boundary data are prepared. The boundaries may be assigned temporary index numbers for ordering by the following procedure. The ground surface boundaries are numbered first, from left to right consecutively, starting with 1. All subsurface boundaries are then numbered in any manner as long as no boundary lies below another having a higher number. That is, at any position which a vertical line might be drawn, the temporary index numbers of all boundaries intersecting that line must increase in numerical order from the ground surface downward. After all the boundaries have been temporarily indexed, the data for each boundary should be prepared in that order. The data set describing a profile boundary line segment consists of X- and Y-coordinates of the left and right end points, and a soil type number indicating the soil type beneath. The end points of each boundary are specified with the left point preceding the right, and with the X-coordinate of each point preceding its Y-coordinate. Piezometric Surfaces If the problem contains one or more piezometric surfaces that would intersect a potential failure surface, they can be approximated by a series of coordinate points connected by straight-line segments. If used, the piezometric surfaces must be defined continuously across the horizontal extent of the region to be investigated for possible failure surfaces. It is wise to extend the piezometric surfaces as far in each lateral direction as the ground surface is defined, to insure meeting this last requirement (Figure 4). Data for the coordinate points must be ordered progressing from left to right. Each point on a piezometric surface is defined by X- and Y-coordinates specified in that order. The connecting line segments defining a piezometric surface may lie above the ground surface and also may lie coincident with the ground surface or any profile boundary. This enables expression of not only the ground water table but also surfaces of seepage and water surfaces of bodies of water such as lakes and streams. The option of defining several piezometric surfaces makes it possible to model conditions of artesian or perched water tables. When the first water surface is above the ground surface, and associated with the ground surface soils, hydrostatic pressures generated by the elevated water surface are assumed to act upon the ground surface. The simulation of artesian conditions is possible by placing the second or higher count water tables above the ground, and not associated with the ground surface soils. In early versions of STABL (up to STABL5) the pore pressure was calculated using a method referred in this manual as the "old method". When a phreatic surface is specified, the "old method" computes pore

32

pressure based on hydrostatic pressure, i.e., the head is the vertical distance from the base of the slice to the phreatic surface immediately above (Figure 5) (Siegel 1975a , Siegel 1975b, Boutrup 1977). This is a conservative estimate; the steeper the piezometric surface, the more conservative the results of the old method." The resulting pressure head can be as much as 30% higher than the actual head when the piezometric surface is dipping at 35 (Figure 6).

Surface of Seepage Groundwater Table

Figure 4. Water surface defined across entire extent of defined problem.

PCSTABL5MPCSTABL5ACTUALPERPENDICULAR

Figure 5. Comparison of methods for calculation of pore pressure distribution.

Slice base

33

1

2

3

1 -

35 o

Dip

pin

g P

iezo

metr

ic S

urf

ace

2 -

29 o

Dip

pin

g P

iezo

metr

ic S

urf

ace

3 -

17 o

Dip

pin

g P

iezo

metr

ic S

urf

ace

5 -

PC

ST

AB

L5

Me

tho

d o

f P

ore

Pre

ssu

re D

ete

rmin

atio

n6

-P

CS

TA

BL

6 M

eth

od

of

Po

re P

ress

ure

De

term

ina

tion

P -

Perp

endic

ula

r M

eth

od o

f Pore

Pre

ssure

Dete

rmin

atio

nA

-A

ctual P

ore

Pre

ssure

Fig

ure

6. H

andp

lot o

f fl

owne

t and

slo

pe.

123

AAP, A

PP 666 5 55

34

To overcome this conservatism a new method was proposed referred as the "perpendicular method". The perpendicular method approximates the equipotential line as a straight line from the base of the slice perpendicular to the line through the piezometric surface bounding the top of that slice (Figure 5). However, this tends to produce unconservative pore pressures; the steeper the piezometric surface, the more unconservative the results. The pressure head can be as much as 10% lower than the actual head when the piezometric surface is dipping at 35 (Figure 6). Since the "old method" produces results that are increasingly conservative while the perpendicular method produces results that are increasingly unconservative as the slope of the piezometric surface increases, if the average value of the two pressure heads is taken the degree of conservatism is limited. Use of the average pressure head still produces a conservative result, for the old method is more conservative than the perpendicular method is unconservative. As illustration, the average pressure head is about 9% higher than the actual head when the piezometric surface is dipping at 35 (Figure 6).

SOIL PARAMETERS Each soil type is described by the following set of isotropic parameters: the moist unit weight, the saturated unit weight, the Mohr-Coulomb strength intercept, the Mohr-Coulomb friction angle, a pore pressure parameter, a pore pressure constant, and an integer representing the number of the piezometric surface that applies to this soil. The moist unit weight and the saturated unit weight are total unit weights, and both are specified to enable STABL to handle zones divided by a water surface. In the case of a soil zone totally above the water surface, the saturated unit weight will not be used; however, some value must be used for input regardless. Any value including zero will do. Similarly for the case where a soil zone is totally submerged, the moist unit weight will not be used. Again, some value must

be used for input. Either an effective stress analysis (c', f ') or total stress analysis (c, f = 0) may be performed by using the appropriate values for the Mohr-Coulomb strength parameters. Porewater pressure can be assumed to be related to the overburden stress by the pore pressure parameter ru. The overburden stress does not include surcharge boundary loads. The pore pressure constant uc of a soil type defines a constant pore pressure for any point within the soil described. Either or both of these two options for specifying pore pressures may be used, in combination with pore pressure related to a specified piezometric surface, to describe the pore pressure regime.

35

Anisotropic Soil Soil types exhibiting anisotropic strength properties are described by assigning Mohr-Coulomb strength parameters to discrete ranges of direction. The strength parameters would vary from one discrete direction range to another. The orientation of all line segments defining any potential failure surface can be referenced with respect to their inclination entirely within a range of direction between -90 and +90 with respect to the horizontal. Therefore, the selection of discrete ranges of direction is confined to these limits. The entire range of potential orientation must be assigned shear strength values. Each direction range of an anisotropic soil type is established by specifying the maximum (counterclockwise) inclination ai of the range (Figure 7). The data consist of this inclination limit and the Mohr-Coulomb friction angle and strength intercept for each discrete range. Data for each discrete range must be prepared progressing in counterclockwise order, starting with a first range from -90 to a1 (specifying a1 as counterclockwise direction limit). The process is repeated for each anisotropic soil type.

36

+90 o

4th Direction RangeSoil Parameters (f4,c4)

3rd Direction RangeSoil Parameters (f3,c3)

2nd Direction RangeSoil Parameters (f2,c2)

1st Direction RangeSoil Parameters (f1,c1)

a4

a3

a2

a1

-90 o

Figure 7. Strength assignment to four discrete direction ranges.

37

BOUNDARY LOADS Uniformly distributed boundary loads applied to the ground surface are specified by defining their extent, intensity, and direction of application (Figure 8). The limit equilibrium model used for analysis treats the boundary loads as strip loads of infinite length. The major axis of each strip load is normal to the two-dimensional X-Y plane within which the geometry of slope stability problems is solved. Therefore, the extent of a boundary load is its width in the two-dimensional plane. Data for each boundary load consist of the left and right X coordinates which defines the horizontal extent of load application, the intensity of the loading, and its inclination. The intensity specified should be in terms of the load acting on a horizontal projection of the ground surface rather than the true length of the ground surface. Inclination is specified positive counterclockwise from the vertical. The boundaries must be ordered from left to right and are not allowed to overlap. A boundary load whose intensity varies with position can be approximated by substituting a group of statically equivalent uniformly distributed loads which abut one another. The sum of the widths of the substitute loads should equal the width of the load being approximated. The inclinations should be equivalent, and the intensities of substitute loads should vary, as does the load being approximated.

38

x 3R

Inte

nsity

q 1

Incl

inat

ion

d 1=0

Ext

ent

x 1L

x 1R

x 2L

q 2

+d2

x 3L-d

3

q 3

Figu

re 8

. Def

initi

on o

f sur

char

ge b

ound

ary

load

s.

x 2R

39

SOIL REINFORCEMENT

PCSTABL6 handles two different types of soil reinforcement: soil nailing and geosynthetic reinforcement. Both nail and geosynthetic reinforcement tension forces acting at the base of each slice are decomposed in normal and tangential forces.

Soil nailing

Soil nailing is a cost-effective technique for slope stabilization and support of excavations. Theoretical background is summarized in Ortigo et al. (1995). Tension in the reinforcement is the major contributor to stability; bending and shear resistances of the nails are minor factors and PCSTABL6 does not take them into account. The soil mass is divided by a slip surface in a stable and a potentially unstable zone. The reinforcement force TNAIL acting in the stable zone is:

NAILSNAIL Lq D T p= (1)

where: TNAIL = tensile force on each nail; qs = unit friction along the soil-nail interface; LNAIL = nail length in the stable zone; D = borehole diameter. PCSTABL6 performs an internal check to ensure that the value of TNAIL is less than the tensile resistance of the nail. For the input data, nails should be divided into groups with the same characteristics (i.e., nails with same length). The soil-nail skin friction value qs may be obtained from pull-out tests before or during construction or estimated by other means. PCSTABL6 requires the user to specify the nail head condition, which can be fixed or free. The fixed condition applies when nails transfer all head loads to the facing. Alternatively, nails are totally free when no load is transferred from the head to the facing. For free nails, there is an additional case when a certain amount of loading, less than the nail capacity, is transferred from the head to the facing. The input data for the command NAILS also includes the inclination and spacing between nails within each group. In addition, the diameter of the nail borehole, the diameter of

40

the steel section, the allowable tensile stress of the nails, and the unit friction along the soil-nail interface should be also specified by the user.

Geosynthetic reinforcement The reinforcement effect can be modelled as follows:

L 'tanE 2T fL

0GEOSYN

GEOSYN

D= fs v (2)

where: TGEOSYN = tensile force in each reinforcement layer; LGEOSYN = geosynthetic length in the stable zone; sv = vertical effective stress at the reinforcement level; f = soil peak friction angle; DL = interval in which LGEOSYN is divided; Ci = coefficient of interaction defined as the relationship between the soil friction angle and the soil-geosynthetic interface. Values of Ci should be determined by appropriate means (see, for example, Koerner 1994).

For the input data, geosynthetic layers should be divided into groups with the same characteristics (i.e., geosynthetic layers with the same length). The reinforcement length should not be extended beyond the problem domain.

TIEBACK LOADS STABL uses tieback load computation routines that use Flamant's Formulas as proposed by Morlier and Tenier (1982). These routines are available for use with the Bishop Simplified Method of analysis for circular failure surfaces, the Janbu Simplified Method of analysis for noncircular failure surfaces, and Spencer's Method of slices for both circular and non-circular failure surfaces. The tieback option may be used with either random or specified failure surface generation methods for irregular, block, or circular failure surfaces. Throughout this section and within PCSTABL6, the word "tieback" is used to mean tieback or other types of concentrated loads applied on the surface of the slope. Tieback (or other types of concentrated loads) are specified in the input file by providing the ground surface boundary number where the load is to be applied, the X-coordinate of the

41

point of application of the tieback load, the Y-coordinate of the point of application of the tieback load, the load per tieback, the horizontal spacing between tiebacks, the inclination of tieback load as measured clockwise from the horizontal plane, and the free length of tieback (Figure 9). For concentrated boundary loads such as strut loads in a braced excavation, which do not extend into the ground like tiebacks, the length of the tieback is zero. An equivalent line load is calculated for each tieback load specified, assuming a uniform distribution of load horizontally between point

loads. PCSTABL6 allows for the input of concentrated loads applied to a horizontal ground surface boundary, and also allows concentrated loads to be inclined between 0 and 180 from the horizontal. The input parameters for a tieback load have been changed to include also the input of the X-coordinate of the load applied to the ground surface. Previously, only the Y-coordinate was required. Either the X-coordinate of the point of application of the tieback load can be specified and the Y-coordinate calculated, or the Y-coordinate can be specified and the X-coordinate calculated. If the user desires, both the X- and Y-coordinates may be input. If only the X-coordinate is specified, a value of zero must be input for the Y-coordinate. When the program encounters a zero Y-coordinate, it will automatically calculate the proper Y-coordinate for the X-coordinate and boundary specified. Likewise, if only the Y-coordinate is specified, a value of zero must be input for the X-coordinate. When the program finds a zero X-coordinate, it will automatically calculate the proper X-coordinate for the Y-coordinate and boundary specified. The user may input both the X- and Y-coordinates of the point of application of the tieback load on the ground surface boundary. However, the coordinates specified must be sufficiently accurate so that the program will recognize an intersection of the X- and Y-coordinates specified with the ground surface boundary specified. If the difference between the coordinates specified by the user and the coordinates calculated by the program is greater than 0.001, then an error message will be displayed, and the program execution stopped. A short description of the tieback routines is presented in the next section to help the User understand the method and assumptions used in STABL for analyzing slopes subjected to concentrated loads.

42

1

2

3

A A

P(X

,Y)

i

L

Ele

vatio

n

Cre

st

Toe

H

Tie

back

s

Sec

tion

A-A

TIE

BA

CK

INP

UT

PA

RA

ME

TE

RS

:

2 X Y P H I L

Gro

und

surf

ace

boun

dary

num

ber

whe

re ti

ebac

k lo

ad is

app

lied

X-c

oord

inat

e of

poi

nt o

f app

licat

ion

(ft o

r m

)Y

-coo

rdin

ate

of p

oint

of a

pplic

atio

n (f

t or

m)

Mag

nitu

de o

f loa

d pe

r tie

back

(lb

or k

N)

Hor

izon

tal s

paci

ng b

etw

een

tieba

cks

(ft o

r m

)In

clin

atio

n of

tieb

ack

load

(deg

)Fr

ee le

ngth

of t

ieba

ck (f

t or

m)

Figu

re 9

. Ti

ebac

k in

put p

aram

eter

s.

43

Description of the Tieback Routines Unlike other slope stability programs, STABL distributes the force from a concentrated load throughout the soil mass to the whole failure surface and hence to all slices of the sliding mass. Most slope stability programs project a concentrated load straight to the base of a single slice. This distribution of load throughout the soil mass is a unique feature of STABL. First, an equivalent line load is calculated for a row of tiebacks by dividing the specified tieback load (point load) by the corresponding horizontal spacing between tieback loads. The resulting line load is called TLOAD (Figure 10) and is inclined from the horizontal by an angle i. The radial stress on the midpoint of a slice is calculated using Flamant's Formula (Morlier and Tenier, 1982):

d ))cos(T(T2 LOAD

ps q=r (3)

where: sr = radial stress on the midpoint of a slice; TLOAD = equivalent tieback line load; Tq = angle between the line of action of the tieback and the line between the point of application of the tieback on the ground surface and the midpoint of the slice base; d = distance between the point of application of the tieback on the ground surface and the midpoint of the slice base.

The radial force, PRAD, at the midpoint of the base of the slice due to the concentrated load is calculated by multiplying the radial stress by the length of the base of the slice:

apq

cos d (DX) )(T cos )2(T

P LOADRAD = (4)

where: a = inclination of slice base; DX = slice width. Note that the radial stress produced on the base of the slice by the concentrated load (Figure 10) is proportional to the load applied (TLOAD) and the width of the slice (DX), inversely proportional to the distance between the point of application of the load and the midpoint of the base of the slice (d), and dependent upon the angle between the line of action of the load and the

line between the point of application of the load and the midpoint of the base of the slice (Tq). Therefore, slices which are in line with the direction of the concentrated load will receive a larger portion of the total load than will slices which are farther away and whose angle Tq is large.

44

FAIL

UR

ES

UR

FAC

E

DX

i T q

iT

LOA

D

a

a 1

d

PN

OR

M

PR

AD

PT

AN

Figu

re 1

0. T

rans

fer o

f tie

back

line

load

to fa

ilure

sur

face

.

45

The radial force PRAD is distributed in the same manner to all the slices of the sliding mass. The radial forces on all the slices are then summed in the direction of the concentrated load, PSUM, and compared with the applied load, TLOAD. Since the sum of radial forces for a failure surface, PSUM, is not always exactly equal to the applied load due to slope geometry and the shape of the failure surface, the radial force applied to the base of each slice is modified as follows:

SUM

LOADRAD P

TP = (5)

The refined radial force for each slice, PRAD, is broken into its components normal and tangential to the base of the slice for calculation of the factor of safety. The normal and tangential components of the force due to the concentrated load are respectively:

1RADNORM cos )(PP a= (6)

1 RADTAN sin )(PP a= (7)

The same process is repeated for all additional rows of tiebacks. The sum of the normal components and the sum of the tangential components due to all rows of tiebacks are then used in the slice equilibrium equations for calculating the factor of safety. There is a special case where the tieback loads will not be distributed to quite all the slices of the sliding mass and is shown in Figure 11. Figure 11 shows the limit of the stress distribution for a benched slope. The force due to the applied load is not distributed to the slices of the far left or the slices of the far right since this would require distrib ution of load through air and not the soil mass.

46

CO

NC

EN

TR

AT

ED

LO

AD

FA

ILU

RE

SU

RF

AC

E

LIM

IT O

F S

TR

ES

S D

IST

RIB

UT

ION

DU

E T

O C

ON

CE

NT

RA

TE

DT

IEB

AC

K L

OA

D

Fig

ure

11. L

imit

of s

tres

s di

stri

butio

n to

pot

entia

l fai

lure

due

to c

once

ntra

ted

tieba

ck lo

ad.

47

TIES Input Restrictions The point of application of a tieback on the ground surface may not be at a ground surface

boundary node. Use a slight offset from the node (i.e., 70.01 instead of 70). No more than 20 tieback loads can be specified; however, they can be in any order. The inclination of a tieback must be equal to or greater than 0 and less than 180 as

measured clockwise from the horizontal. The horizontal spacing between tiebacks must be greater than or equal to 1 ft (or 1 m if using

SI units). The length of a tieback must be equal to or greater than 0. Zero is used for loads other than

tieback loads, such as loads on bracing elements.

EARTHQUAKE LOADING The use of earthquake coefficients allows for a pseudo-static representation of earthquake effects within the limiting equilibrium model. An inertial force acting on the sliding mass is assumed to develop in direct proportion to the weight of the sliding mass. Specified horizontal and vertical coefficients are used to scale the horizontal and vertical components of the earthquake force relative to the weight of the sliding mass. Positive horizontal and vertical earthquake coefficients indicate that the horizontal and vertical components of the earthquake force are directed leftward and upward, respectively. Negative coefficients are allowed. The inertial forces due to the seismic coefficients are at the center of gravity of each slice. These forces do not change the pre-earthquake static pore pressures in the slope. If significant excess pore pressures changes or loss of shear strength is expected, or in the case of a "high risk" slope, a complete dynamic analysis should be performed. Examples of slope stability analysis encountering pseudo-static earthquake loads are described in Section 4.5.4 of Boutrup (1977).

48

SEARCHING ROUTINES

STABL can generate any specified number of trial failure surfaces in random fashion. The only limitation is computation time. Usually 100 surfaces are adequate. Each surface must meet specified requirements. As each acceptable surface is generated, the corresponding factor of safety is calculated. The ten most critical are accumulated and sorted by the values of their factors of safety. After all the specified number of surfaces are successfully generated and analyzed, the ten most critical surfaces are plotted so that the pattern may be studied.

Circular and Irregular Surfaces The searching routines, which generate circular and irregular shaped trial failure surfaces, are basically similar in use and are, therefore, discussed together. Trial failure surfaces are generated from the left to the right. Each surface is composed of a series of straight-line segments of equal length, except for the last segment, which will most likely be shorter. The length used for the line segments is specified by the user and should be sufficiently small for the accuracy desired. Generation of an individual trial failure surface begins at an initiation point on the ground surface. The direction of the first line segment of the trial failure surface is chosen randomly between two direction limits. An angle of 5 less than the inclination of the ground surface to the

right of the initiation point is one limit, while an angle of -45 to the horizontal is another limit (Figure 12). The first line segment can fall anywhere between these two limits, but the random

technique of choosing its position is biased so that it will lie closer to the -45 limit more often than the other. By specifying zero values for both of the direction limits, the direction limits as described above are implicitly selected. However, the counterclockwise and clockwise direction limits may also be specif ied. After a preliminary search for the critical surface, it is usually found that all or most of the ten most critical surfaces have about the same angle of inclination for the initial line segments. By restricting the initial line segment within direction limits having a directional range smaller than that which would be used automatically by PCSTABL6 , and at inclinations which would bracket the initial line segments of surfaces previously determined to be critical, subsequent searches can be conducted more efficiently.

49

Cou

nter

cloc

kwis

eD

irect

ion

Lim

it

Hor

izon

tal

Clo

ckw

ise

Dire

ctio

n Li

mit

1st L

ine

Seg

men

t

Initi

atio

nP

oint

b-5o

45o

b q

Figu

re 1

2. G

ener

atio

n of

the

firs

t lin

e se

gmen

t to

defi

ne a

tria

l fai

lure

sur

face

.

50

After establishment of the first line segment, a circular shaped trial failure surface is generated by changing the direction of each succeeding line segment by some constant angle (Figure 13) until an intersection of the trial failure surface with the ground surface occurs. In effect, the chords of a circle are generated rather than the circle itself. The constant angle of deflection is obtained randomly. An irregular shaped surface is generated somewhat differently after establishment of the first line segment. The direction of each succeeding line segment is chosen randomly within limits determined by the direction of the preceding line segment. Surfaces with reverse curvature are likely, and if a very short length is used for the line segments, a significant amount of kinkiness in the surfaces will be inevitable. Some reverse curvature is desirable but extreme kinkiness is not. To avoid the second case the length of the line segment selected should in general not be shorter than 1/4 to 1/3 the height of the slope. When using either of these generation techniques to search for a critical failure surface, the following scheme is employed. STABL directs computation of a specified number of initiation points along the ground surface. The initiation points are equally spaced horizontally between two specified points, which are the leftmost and rightmost initiation points. Only the X-coordinates of these two points, specified in left-right order, are required. From each initiation point, a specified number of trial failure surfaces are generated. If the left point coincides with the right, a single initiation point results, from which all surfaces are generated. The total number of surfaces generated will equal the product of the number of initiation points and the number of surfaces generated from each. Termination limits are specified to minimize the chance of proceeding with a calculation of the factor of safety for an unlikely failure surface. If a generated trial failure surface terminates at the ground surface short of the left initiation limit (Figure 14), the surface is rejected prior to calculation of a factor of safety and a replacement is generated. If a generating surface goes beyond the right termination limit, it will be rejected requiring a replacement. The termination limits are also specified in left-right order. A depth limitation is imposed by specifying an elevation below which no surface is allowed to extend. This is used, for example, to eliminate calculation of the factor of safety for generated surfaces that would extend into a strong horizontal bedrock layer. When a shallow failure surface is expected, the use of the depth limitation prevents generation and analysis of deep trial failure surfaces. An additional type of search limitation may be imposed to handle situations such as variable elevation of bedrock or delimitating a weak zone and confining the search for a critical surface to that area. This type of limitation will be discussed later.

51

Def

lect

ion-

Con

stan

t for

eac

hS

ucce

edin

g Li

ne S

egm

ent

Pro

ject

ion

of P

rece

ding

Line

Seg

men

t

Figu

re 1

3. C

ircul

ar s

urfa

ce g

ener

atio

n.

52

Suc

cess

ful G

ener

atio

nS

hort

of L

eft T

erm

inat

ion

Lim

itB

eyon

d R

ight

Ter

min

atio

n Li

mit

Bel

ow D

epth

Lim

itatio

n

Lim

its o

f Ter

min

atio

n

Dep

th L

imit

Figu

re 1

4. T

rial f

ailu

re s

urfa

ce a

ccep

tanc

e cr

iteria

.

53

Sliding Block Surfaces A sliding block trial failure surface generator provides a means through which a concentrated search for the critical failure surface may be performed within a well-defined weak zone of a soil profile. In a simple problem involving a sliding block shaped failure face (Figure 15), the following procedure is used. Two boxes are established within the weak layer with the intent that from within each, a point will be chosen randomly. The two points once chosen define a line segment that is then used as the base of the central block of the sliding mass. Any point within each box has equal likelihood of being chosen. Therefore, a random orientation, position and width of the central block is obtained. The boxes are required to be parallelograms with vertical sides. The top and bottom of a box may have any common inclination. Each box is specified by the length of its vertical sides and two coordinate points that define the intersections of its centerline with its vertical sides (Figure 16). After the base of the central block is created, the active and passive portions of the trial failure surface are generated using line segments of equal specified length by techniques similar to those used by the circle and irregular trial failure surface generators. Starting at the left end of the central block base, a line segment of specified length is randomly directed between the limits of 0 and 45 with respect to the horizontal (Figure 17). The

chosen direction is biased towards selection of an angle closer to 45. This process is repeated as necessary until intersection of a line segment with the ground surface occurs, completing the passive portion of the trial surface. For the active portion of the trial failure surface, a similar process is used with the limits for selection of the random direction being 0 and 45 with respect to the vertical (Figure 17). The

chosen direction is biased towards selection of an angle nearer 45. A modified version of the sliding block surface generator, named BLOCK2, generates active and passive portions of the sliding block surface according to the Rankines theory. To avoid the problem of the active or passive wedges terminating out of the defined slope boundaries, sketches should be drawn. STABL allows the use of more than two boxes for the formation of the central block (Figure 18). The search may be limited to an irregularly shaped weak zone in this way. Another

54

Pas

sive

We

dg

e

Cen

tral

Blo

ck

Act

ive

We

dg

e

Str

ong

Mat

eria

l

Str

ong

Mat

eria

l

Wea

k La

yer

Figu

re 1

5. S

impl

e sl

idin

g bl

ock

prob

lem

.

55

Le

ft C

oo

rdin

ate

Po

int

for

Bo

x S

pe

cific

atio

n

Rig

ht

Co

ord

ina

te P

oin

tfo

r B

ox

Sp

eci

fica

tion

Pa

ralle

log

ram

Ce

nte

rlin

e

Le

ng

th o

fV

ert

ica

l Sid

es

Figu

re 1

6. S

lidin

g bl

ock

box

spec

ific

atio

ns.

56

Pas

sive

Sur

face

Hor

izon

talPas

sive

45 o

Dire

ctio

nR

ange

Bas

e of

Cen

tral

Blo

ck

Act

ive

Sur

face

Ver

tical

Figu

re 1

7. G

ener

atio

n of

act

ive

and

pass

ive

slid

ing

surf

ace.

Pas

sive

45

o D

irect

ion

Ran

ge

57

Extent ofSearch

a. Intensive search of critical zone previously defined by CIRCLE or RANDOM.

WeakLayer

b. Search in irregular weak layer.

Figure 18. Sliding block generator using more than two boxes.

58

application might be to conduct a search within a zone previously defined as being critical by use of the analysis command RANDOM.

Degenerate cases of parallelogram boxes are permitted. For example, if both points specified as the intersections of a parallelogram centerline with its vertical sides are identical, and the length of the parallelograms vertical sides is non-zero, then a vertical line segment, in effect, is defined. When a trial failure surface is generated, each point along the vertical line segment's length has an equal likelihood of becoming a point defining the surface. The vertical line segment could further degenerate into a point if a zero value is specified for the length of the parallelogram vertical sides. Then all surfaces generated would pass through the single point. One more case of a degenerate parallelogram is a line segment whose inclination and position is that of the parallelogram's centerline. For this case, the length of the vertical sides is zero but the intersections of the parallelogram centerline with its vertical sides are not identical. Again, any point along the length of the line segment has equal likelihood of becoming a point defining a generated trial failure surface.

Surface Generation Boundaries As an additional criterion for acceptance of generated trial failure surfaces, an ability to establish boundaries through which a surface may NOT pass has been provided. Such boundaries may be used with all surface- generating routines except BLOCK2. Each generation boundary specified is defined by two coordinate points. If a generating surface intersects the line segment defined by the pair of coordinate points, it will either be rejected and a replacement surface will be generated, or the surface will be deflected so that it may be successfully completed. The amount of deflection permitted for a trial failure surface is limited, and when it is insufficient to clear the surface generation boundary intersected, the surface is rejected. When specifying surface generation boundaries the coordinate points of the left end point should precede those of the right end point. For the case of vertical boundaries, the order is not important. Along with the total number of boundaries, the number of vertical boundaries that deflects generating surfaces upward is specified. The data for these boundaries are required to precede the data for boundaries that deflect downward. As mentioned previously, a variable elevation bedrock surface can be bounded so that no generated surfaces will pass through the rock. For this case, all the surface generation boundaries defining the bedrock surface would be specified to deflect intersecting trial failure surfaces upward. Another use might occur after a critical zone has been roughly defined by a searching technique. This zone could be bound so that the subsequent search will be completely confined to it. Surface

59

generation boundaries above the zone would be specified to deflect downward, and those below the zone would be specified to deflect upward. An important consideration that should be given whenever any type of limitation is imposed for conducting a search for a critical surface is how many generating surfaces are likely to be rejected. A rejected surface is lost effort regardless of how efficiently it was generated by

STABL. Perhaps for example, a multiple box search using the command BLOCK would be more efficient than using the command RANDOM with strict limitations.

Individual Failure Surface If the failure of the slope is being studied and the location of the actual failure surface is known, STABL offers the option of specifying the known surface as an individual surface for analysis. Another situation for which this option would be useful is when the geologic pattern and shear strength data indicate one or more well-defined weak paths along which failure would be expected to occur. An individual failure surface is approximated by straight-line segments defined by a series of points. The end points of the specified trial failure surface are checked for proper location within the horizontal extent of the defined ground surface. The Y-coordinates for these two points need not be correctly specified. STABL directs the calculation of the Y-coordinate, for each of these two points, from the intersection of a vertical line defined by the specified X-coordinate and the ground surface. Data for the coordinate points must be ordered from left to right.

60

BISHOP SIMPLIFIED METHOD The Bishop Simplified Method was initially developed for circular failure surfaces, but it can be applied for non-circular slip surfaces by adopting a fictional center of rotation. This method neglects the vertical components of the interslice forces and satisfies moment equilibrium only. Figure 19 shows the forces acting on a slice including tieback and reinforcement loads. The total normal force DN is assumed to act at the center of the base of each slice, and it is determine by imposing equilibrium of vertical forces on each slice (Figure 19), as follows:

0)sinS)T(cos)UN'--T()k-(1W cos Qcos U rTANNORMv =D+D-DDD+D+D+D aadb ab (8)

in which: DN and DSr = effective normal force and mobilized resisting shear force, respectively,

on the base of each slice; DUa and DUb = water force acting on base and top of the slice; DW = weight of the slice soil mass; kv = vertical earthquake coefficient; DQ = resultant of uniform

surcharge acting on the slice top; DTNORM and DTTAN = normal and tangential forces acting on the midpoint of the base of the slice produced by all rows of tiebacks or/and by soil reinforcement, whatever applies; a = inclination of shear surface with respect to the horizontal; b = slope

inclination angle; d = inclination of the uniform surcharge acting on the slice top, measured positive counterclockwise from the vertical. Based on Coulombs failure criterion, DSr can be written as:

FS'tanN'C'

S rfD+

=D (9)

acosDXc'

C' = (10)

in which C = cohesion force at the slice base; FS = factor of safety; c and f = effective soil strength parameters; DX = slice width.

61

h

heq

DX

a

b

kv DW

DW

kh DW

DTNORM

DN'

DUa

DSr

DTTAN

dDQ

DUb

Figure 19. Slice forces considered by in the Bishop and Janbu methods.

b

62

Substituting (9) and (10) into (8), and solving for DN:

FSsin 'tan

cos

FSsin C'

-sin T-cos)U-T()k-W(1cos QcosUN'

TANNORMv

afa

aaadb ab

+

DDD+D+D+D=D (11)

Overall moment equilibrium of forces acting on the sliding circular surface is given by the expression:

( ) ( ) ( )[ ]R TS}sin R ]cos QcosUk-1W{{[ TANrn

1v D+D-D+D+D

=

adbbi

( )( )[ ] ( )[ ] 0} h -cos RkW h-cos Rsin QsinU qe h =D+D+D- aadbb (12) where: R = distance from center of rotation about which moments are summed to the center of each slice; kh = horizontal earthquake coefficient; h = height of the slice at midpoint; heq = vertical distance from point of application of kh to the slice base; n = number of slices. The Bishop Simplified Method assumes that FS is the same for each slice. Substituting (9) and (11) into (12), and solving for FS, it is obtained the expression for FS:

( )

=

=

+

+=

n

1i6543

n

1 2

1

A-AA-A

FSA

1

A

FS

i

(13)

in which:

( ) ( )[ ] sin T cos Q cosU cos U-Tk-1W sec ' tan C'A TAN NORMv1 adbaaf ba D-D+D+DD+D+= (14)

' tan tanA2 fa= (15)

63

( )[ ] adbb sin cos Q cosUk-1W A v3 D+D+D= (16)

( )

-D+D=

Rh

cos sin QUA4 adb (17)

eq

h5 R

h-cos kW A

D= a (18)

TAN6 TA D= (19)

JANBU SIMPLIFIED METHOD The Janbu Simplified Method assumes that the failure occurs by sliding of a block of soil on a non-circular slip surface. Also, in this method the interslice shear forces are assumed to be zero. Thus, the expression for the effective normal force DN on the base of each slice is the same as that obtained for the Bishop Simplified Method (Eq. 11). Overall equilibrium of forces acting parallel to the sliding circular surface (Figure 19) is given by the expression:

[ ]=

DD+DD+Dn

1sin )k-(1W -sin ) cosUcos Q(-TS{ v TANr

iaabd a

0} ] cos )sin Usin Q ( [ cos kW h =D+D+D- abda b (20)

The Janbu Simplified Method assumes that FS is the same for each slice. Substituting (9) into (11), and solving (20) for FS, it is obtained the expression for the factor of safety:

=

= +=

n

13

n

1 2

1

B

FSB

1

B

FS

i

i

(21)

64

in which:

( ) ( )[ ]

cos

cos Q cosU cos U-Tsin Tk-1W sec ' tan C'B

NORMTANv1 a

dbaaaf ba D+D+DD+D-D+= (22)

' tan tanB2 fa= (23)

( ) ( ) ( ) cos

T sin tan cos Qsin - tan cosU tan kktan W B TAN vh3

D--D+D++D= -

adadbabaa b (24)

Since the Bishop Simplified and the Janbu Simplified Methods assume that the factor of safety on each slice is the same, results from (13) and (21) are average FS for all the slices. This assumption implies that each slice must fail simultaneously.

Boutrup (1977) found that STABL with the Janbu Simplified Method may give non conservative and erroneous results for failure surfaces that intersect the top of the slope at steep angles, and where the strength of the soil is defined mainly in terms of strength intercept c'. Since this problem arose mainly for deep circular failure surfaces, it was solved by

including in the STABL program the Bishop Simplified solution, applicable to circular failure surfaces. It is recommended that the Simplified Bishop Method be used for circular failure surfaces in general (use CIRCL2 instead of CIRCLE). Precautions should be taken if a similar situation occurs for irregular shaped failure surfaces. In any case, it is advisable to make a preliminary estimate of the factor of safety by means of simple slope stability charts for homogeneous slopes (averaging soil parameters, etc.).

65

SPENCER'S METHOD Spencers Method of slices has been incorporated into STABL to enhance the versatility of the program. Spencers Method is a limiting equilibrium method which satisfies both force and moment equilibrium of a sliding mass of soil, whereas the Janbu Simplified and the Bishop Simplified Methods satisfy only force or moment equilibrium, respectively.

Description of Spencers Method Spencers Method was first developed for circular slip surfaces assuming parallel interslice side forces inclined at a constant angle, q, on each slice (Figure 20). This method was later extended to general or irregular failure surfaces. The factor of safety, FS, on each slice is assumed to be the same such that all slices of the sliding mass will fail simultaneously. The interslice forces acting at both sides of each slide can be replaced with a single statically equivalent resultant interslice force, QF, acting through the midpoint of the base of the slice and inclined at an angle, q. The method also assumes a constant inclination of the resultant force, QF, throughout the slope. The equilibrium equations for the forces normal and tangent to the base of each slice are (Figure 20), respectively (Carpenter 1985):

0T-)-( cos Q)( cosU-

])cosk-(1-sin W[k)-(sin QFUN'

NORM

vh

=DD--D

D++D+D

daba

aaqa

b

a

(25)

0 T)-(sin Q)-(sin U

]cos ksin )k-W[(1-)-( cos QF-S

TAN

hvr

=D+D+D+

-DD

daba

aaqa

b

(26)

66

heq

DX

a

b

kv DW

DW

kh DW

DN'

DUa

DSr

dDQ

DUb

Figure 20. Slice forces considered by Spencer's method.

b

qQF

DTTAN

DTNORM

67

From (25) the effective normal force DN acting on the base of each slice is found to be equal to:

NORM

hv

T)-sin( QF-)-Qcos(

)(cosUU-)]sin k-)cosk-W[(1 N'

D+D+

-D+DD=D

qada

baaa ba

(27)

Combining (9) and (27) into (26), and solving for QF, it is obtained the following expression:

+

+=

FSS

1)-cos(

SFSS

QF3

21

qa (28)

where:

( )[ ]{ })T)-( cos Q)( cosUUsinkcos k-1W'tanC'S NORM hv1 D+D+-D+D--D+= dabaaaf ba (29)

[ ] )T)-sin( Qcosk)sink-(1W)(sinUS TAN hv 2 D+D++D--D= daaabab (30)

)-tan('tanS3 qaf= (31) Overall moment and force equilibrium are satisfied by the conditions:

0)](cos R [ QFn

1=-

=qa

i (32)

=

=n

10QF

i (33)

Two FS values are obtained when (32) and (33) are solved for each assumed value of q. The solution is reached by iteration when a unique value of FS, and its corresponding q, that satisfies both force and moment equilibrium is found. More detailed information concerning the derivation, and method of solution of Spencer's method of slices implemented in STABL5M, PCSTABL5M, PCSTABL5M2, and PCSTABL6 may be found in Carpenter (1985, 1986).

68

SPENCR Option The Spencer option may be invoked by specifying the command SPENCR. The command SPENCR precedes specification of the surface type and method of solution; i.e., SURFAC, SURBIS, CIRCLE, CIRCL2, RANDOM, BLOCK, or BLOCK2. Since significantly more computation time is required for analysis of potential failure surfaces using Spencer's method of slices than either the Bishop Simplified or the Janbu Simplified Methods, the most efficient use of the PCSTABL6 capabilities will be realized if the user first

investigates a number of potential failure surfaces using one of STABL's random surface generation techniques, which determine the factor of safety using either the Janbu Simplified or the Bishop Simplified Methods of slices. Once critical potential failure surfaces have been identified, they may be analyzed using the SPENCR option in conjunction with either the SURFAC or SURBIS option, to obtain a factor of safety (FS) satisfying both force and moment, i.e., complete equilibrium. The reasonableness of the solution obtained may be evaluated through examination of the line of thrust calculated by the Spencer routines. When a user-input potential failure surface is analyzed, the program outputs the value of the factor of safety with respect to force equilibrium (Ff), the value of the factor of safety with respect to moment equilibrium (Fm), and the angle of the interslice forces q calculated during iteration, along with the value of FS and q satisfying complete equilibrium. When a user-input potential failure surface is analyzed, the coordinates of the line of thrust, the ratio of the height of the line of thrust above the sliding surface to the slice height for each slice, and the values of the interslice forces are all output. The Spencer option may also be used with the STABL options that generate surfaces randomly. However, when the Spencer option is used in conjunction with randomly generated surfaces, only the FS and angle of the interslice forces satisfying complete equilibrium are output for the ten most critical surfaces. Information regarding the line of thrust, interslice forces or values of Ff, Fm and q calculated during iteration is not output for randomly generated surfaces; hence the reasonableness of a solution obtained for a randomly generated surface will not be readily apparent. When the reasonableness of the solution of a randomly generated surface is desired, the surface should be analyzed using the SPENCR option in conjunction with either the SURBIS or SURFAC options.

69

SPENCR Input Restrictions The only input restrictions require that specification of the "SPENCR" option occur prior to specification of the method of surface generation and solution, i.e., SURFAC, CIRCL2, etc., and the slope angle be greater than 0 and less than or equal to 90.

70

ASSUMPTIONS STABL assumes that the instability to be prevented would be two-dimensional. In reality, all sliding failures must be 3-D, with the end/edge resistance furnishing additional safety against instability. For more quantitative information on the comparison of FS3D to FS2D, see Chen (1981) and Lovell (1982). In general, FS3D > FS2D, but the difference may be small, and in certain special cases FS2D > FS3D. Where the stability problem is perceived to be definitely 3-D, the engineer is encouraged to use BLOCK3 or LEMIX codes of Chen (1981). STABL uses Simplified methods of slices for determination of FS. The alternative requires solutions with extensive iteration and the consequent problems of nonconvergence in these iterations. Boutrup (1977) has shown that the Simplified methods after Janbu and Bishop give reasonably precise values of FS. The selection of a center of moments for the slice analysis is an intriguing point. In the simplified approaches, the free body is not iterated into equilibrium, and accordingly , the FS value is peculiar to the center selected. This is true even for the circle, where the circle center is arbitrarily selected in the Bishop Simplified Method. For other shapes, there is usually no "center" to select for moments. After much study of this question (Carter, 1971; Siegel, 1975a; Boutrup, 1977), the circle center is used for CIRCL2, and a very long moment arm is used for BLOCK, BLOCK2, and RANDOM. The latter choice means that these noncircular surfaces are analyzed with the same slice assumptions as the Janbu Simplified Method.

STABL values may be checked for a specific failure surface in several ways. CIRCL2 should yield about the same FS (for the same circle) as any other computerized analysis for circles. To determine that this is indeed the case, the new user of STABL can run CIRCL2 in parallel with his present method. BLOCK or BLOCK2 can be checked approximately (for a specific block) either manually or perhaps by existing charts. RANDOM is amenable to approximate manual checks.

71

COMMENTS ABOUT THE CHOICE OF PARAMETERS FOR

USE IN STABL

The most common problems faced by users take place at the time they define the search parameters. Many times, conflicting combinations of such parameters are a mere result of user attempts to perform in one single step a search that should be broken in several steps. In other words, users often try to create search boundaries so general that the program is faced with inconsistent conditions. Some guidelines on how to avoid inconsistencies are listed in the following paragraphs. 1) When a circular surface searching procedure is specified, most of the problems during runtime are caused by inappropriate combinations of the one or more of the following parameters:

length of segments defining surface clockwise and counterclockwise initiation angle limits

"X" leftmost and rightmost initiation and/or termination points. The following checks should be followed to assure proper parameter selection:

When defining the initiation and termination intervals, do not overlap the rightmost initiation point and the leftmost termination point.

When defining the length of the segments forming the surface, make sure that the

length is such that if the first segment's angle was the counterclockwise angle limit, it would not end above the ground. This can happen when surfaces are being initiated close to the top of a slope.

When defining the initiation angle limits, remember that the counterclockwise angle

should not let the first segment of a surface being generated go above the ground. This means that it should be smaller or equal to the minimum ground slope inside the initiation region.

2) Another problem frequently happens when using the block search option. It occurs when the user places the extreme boxes in positions where active or passive wedges starting from these boxes would fall outside the bounds of the geometry. To avoid this problem the user should estimate the passive and active lines passing through the leftmost point of the initiation

72

region and the rightmost point of the termination region respectively, and make sure that the boxes are inside the zone defined by these two lines. Some users have attempted to perform general sensitivity studies about how the number and size of boxes or the number of surfaces generated affect the search and/or the minimum factor of safety. Unfortunately, there are no such general correlations. Each slope being evaluated has an initially unknown failure surface which has the minimum factor of safety possible. The program evaluates surfaces generated randomly within a user specified region of that slope. The generation of random surfaces can be seen as a Monte Carlo simulation process and the number of generated surfaces necessary to find the minimum factor of safety depends on how close to the originally unknown critical surface the search region was specified. In the same way, the optimum number of boxes is case specific. For instance, if a user tried to find the most critical surface in a homogeneous slope, where the critical surface is close to circular, a large number of boxes would be necessary, since the curvature of the surface would have to be accommodated. On the other hand, in a slope where the failure surface is bound to pass within a very thin and linearly inclined layer, a large number of boxes will bring no consistent improvement to the analyses whatsoever. The influence of the size of the boxes on the number of surfaces necessary to reach the minimum factor of safety is also dependent on how close their positions are with respect to the unknown most critical surface. The larger the boxes, the larger the number of surfaces necessary to cover thoroughly the region defined. Consequently large boxes should be used only when the user is trying to locate the most critical region of the slope. After the region has been located, the size of the boxes should be reduced to concentrate the surfaces being generated in the important zone and avoid waste of computational effort. In other words, small boxes placed far from the actual critical surface would never let the program find the minimum factor of safety, no matter how many trial surfaces were generated. On the other hand, if boxes as small as points where placed by coincidence right on the top of the critical surface, we would have an optimum search (when only one surface would need to be generated), and increasing their sizes would bring no benefit to the search. 3) Another aspect relevant to the analysis is the number of slices used during the factor of safety calculations. Figure A10 displays the typical expected variance of the factor of safety as a function of the used number of slices. These results were obtained as an average from many cases with different slopes and soils. There seemed to be no particular trend that would justify separating the influence for different soil-profile combinations. Consequently, in general, the

73

factor of safety obtained with a smaller number of slices will be more conservative. Since a larger number of slices results in longer calculation times, the user is advised to perform search with a segment length that results in about 15 to 20 slices. This would keep the factors of safety only about 2% conservative and the search would not suffer speed decay. The most critical surface can latter be individually analyzed with a smaller segment length so that the accuracy can be increased.

74

DATA PREPARATION

Input for Each Command The data for each command and their organization are outlined below. A new line of data should be started, wherever a data line or command is encountered.

I