#STABL for WIndows 3 Manual

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 USER’S MANUAL © Geotechnical Software Solutions, LLC

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.

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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 Minimum Data Set

7 8

CHOICE OF ANALYTICAL METHOD AND SURFACE GENERATION MODEL

8

FACTOR OF SAFETY HISTOGRAM

9

MAIN FEATURES OF THE PROGRAM

10

Unit System Selection Soil Profile Soil Properties Water Tables Boundary Loads Seismic Loads Tiebacks Geosynthetics Soil Nails Analysis Menu Bar Options

10 11 13 14 15 16 17 18 19 20 21

GENERAL RECOMMENDATIONS FOR USE OF STABL FOR WINDOWS

25

REFERENCE MANUAL

26

PROBLEM GEOMETRY Profile Boundaries Piezometric Surfaces

27 27 31

SOIL PARAMETERS Anisotropic Soil

34 35

BOUNDARY LOADS SOIL REINFORCEMENT Soil Nailing Geosynthetic Reinforcement

37 39 39 40

3

TIEBACK LOADS Description of the Tieback Routines TIES Input Restrictions

40 43 47

EARTHQUAKE LOADING

47

SEARCHING ROUTINES Circular and Irregular Surfaces Sliding Block Surfaces Surface Generation Boundaries Individual Failure Surface

48 48 53 58 58

BISHOP SIMPLIFIED METHOD JANBU SIMPLIFIED METHOD SPENCER’S METHOD Description of Spencer’s Method SPENCR Option SPENCR Input Restrictions

60 63 65 65 68 69

ASSUMPTIONS

70

DATA PREPARATION Input for Each Command

74 74

ERROR MESSAGES Command Sequence Errors Free-Form Reader Error Codes PROFIL Error Codes WATER Error Codes SURFAC Error Codes LIMITS Error Codes LOADS Error Codes SOIL Error Codes ANISO Error Codes RANDOM and CIRCLE Error Codes BLOCK Error Codes TIES Error Codes SPENCR Error Code

85 86 87 87 88 88 89 90 90 91 92 93 95 96

REFERENCES

97

4

5

STABL for WINDOWS INTERFACE

6

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 Bishop’s Simplified, Janbu’s and Spencer’s 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.

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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 point’s 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 slope’s 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.

Figure 1. Essential Data

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 8

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 9

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.

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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; 11

(c) (d) (e)

The abscissa of the right end-point of the segment; The ordinate of the right end-point of the segment; 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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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7.10. Analysis

Figure 12. Bishop’s 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 Bishop’s Simplified Method, Janbu’s Method, or Spencer’s 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. Janbu’s method can be combined with sliding-block mechanisms, circular or randomly shaped slip surfaces. Bishop’s 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 Bishop’s 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 Bishop’s method selected.

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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. 21

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 problem’s 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 problem’s 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

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

Figure 19. Use of command Mirror to manipulate the coordinates of the original problem. 23

Figure 20. Use of comma nd 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).

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Figure 22. Critical failure surfaces for the sfwe x1.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: [email protected] Bugs: [email protected] 25

REFERENCE MANUAL

26

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 whic h different soil parameters would be defined (Figure 3).

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Figure 1. Extent of potential failure surfaces.

Well Beyond Crest Well Beyond Toe Deep

(1900,1200)

(2400,1200)

(1000,1000) (1500,1000)

(0,0) a. Coordinates are too large in comparison with height and length of slope.

(900,600)

(1600,600)

(0,500) (700,500)

(0,0) b. Too much room allowed beyond the toe and crest of the slope in comparison to the slope height and length.

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

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30 Soil 3

13

2

F

A

Area ABCDEF GHIJK -LM-

Soil 2

3

E

D

Soil Type 2 1 3

Figure 3. Relationships among soil types and boundaries.

1

Boundary 3 5 15

C

B

11

Soil 3

9

4

6

14

K

12

G

L

10

7

J

15

Soil 1

5

8

M

I

H

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

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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).

Groundwater Table

Surface of Seepage

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

PCSTABL5M PCSTABL5 ACTUAL PERPENDICULAR

Slice base

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

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33

P, A

1

PCSTABL5 Method of Pore Pressure Determination PCSTABL6 Method of Pore Pressure Determination Perpendicular Method of Pore Pressure Determination Actual Pore Pressure

P

6 A P 5 6 A

5

Figure 6. Handplot of flownet and slope.

56PA-

1

2

3

5 6

2

3

1 - 35o Dipping Piezometric Surface 2 - 29o Dipping Piezometric Surface 3 - 17o Dipping Piezometric Surface

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', φ') or total stress analysis (c, φ = 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.

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Anisotropic Soil

Soil types exhibiting anisotropic strength properties are described by assigning MohrCoulomb 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.

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+90 o 4th Direction Range Soil Parameters φ(4,c4)

3rd Direction Range Soil Parameters φ(3,c3 )

a3 a4 a2

2nd Direction Range Soil Parameters φ(2 ,c2 )

a1

1s t Direction Range Soil Parameters φ(1 ,c1 )

−90 ο

Figure 7. Strength assignment to four discrete direction ranges.

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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 twodimensional 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.

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38

x1R

x2L

Figure 8. Definition of surcharge boundary loads.

x1L

Extent

Intensity q1 Inclination δ1=0

q2 x2R

+δ2

x3L

-δ3 q3

x3R

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 Ortigão 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:

T NAIL = π D q S L NAIL

(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

39

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: LGEOSYN

TGEOSYN = 2 ∑ σ v′ E f tanφ ' ∆L

(2)

0

where: TGEOSYN = tensile force in each reinforcement layer; LGEOSYN = geosynthetic length in the stable zone; σ’v = vertical effective stress at the reinforcement level; φ’ = soil peak friction angle; ∆L = 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

40

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 Ycoordinate 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 Xcoordinate 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 Ycoordinate 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 Xcoordinate 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 Ycoordinates 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.

41

42

A Elevation

2

i

Figure 9. Tieback input parameters.

1

P

A

L

(X,Y)

3

X Y P H I L

2

Ground surface boundary number where tieback load is applied X-coordinate of point of application (ft or m) Y-coordinate of point of application (ft or m) Magnitude of load per tieback (lb or kN) Horizontal spacing between tiebacks (ft or m) Inclination of tieback load (deg) Free length of tieback (ft or m)

TIEBACK INPUT PARAMETERS:

Section A-A

Toe

Tiebacks

H

Crest

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):

σr =

2(TLOAD )cos(Tθ ) πd

(3)

where: σr = radial stress on the midpoint of a slice; TLOAD = equivalent tieback line load; Tθ = 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:

PRAD =

2(T LOAD ) cos (Tθ ) (DX) π d cos α

(4)

where: α = 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 (Tθ). 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 Tθ is large.

43

44

Figure 10. Transfer of tieback line load to failure surface.

i

TLOAD

d

Τθ

i

PTAN

P RAD

P NORM

DX

α1

α

FAILURE SURFACE

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:

PRAD =

TLOAD PSUM

(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: P NORM = (P RAD ) cos α

1

(6)

PTAN = (PRAD ) sin α 1

(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 slidin g 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.

45

46

LIMIT OF STRESS DISTRIBUTION DUE TO CONCENTRATED TIEBACK LOAD

FAILURE SURFACE

Figure 11. Limit of stress distribution to potential failure due to concentrated tieback load.

CONCENTRATED LOAD

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).

47

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.

48

49

o

45o

β-5

Figure 12. Generation of the first line segment to define a trial failure surface.

Initiation Point θ

β

Clockwise Direction Limit

1st Line Segment

Horizontal

Counterclockwise Direction Limit

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.

50

51

Figure 13. Circular surface generation.

Projection of Preceding Line Segment

Deflection-Constant for each Succeeding Line Segment

52

Figure 14. Trial failure surface acceptance criteria.

Depth Limit

Successful Generation Short of Left Termination Limit Beyond Right Termination Limit Below Depth Limitation

Limits of Termination

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 Rankine’s 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

53

54

Figure 15. Simple sliding block problem.

Passive Wedge

Strong Material

Central Block

Active Wedge

Weak Layer

Strong Material

55 Figure 16. Sliding block box specifications.

Left Coordinate Point for Box Specification

Parallelogram Centerline

Right Coordinate Point for Box Specification

Length of Vertical Sides

56

Horizontal

Vertical

Base of Central Block

Figure 17. Generation of active and passive sliding surface.

Passive Surface

Passive 45o Direction Range

Passive 45 o Direction Range

Active Surface

Extent of Search

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

Weak Layer

b. Search in irregular weak layer.

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

57

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

58

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.

59

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 ∆N’ 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:

∆U β cosβ + ∆Q cosδ + ∆W (1 - k v ) + (∆TNORM - ∆N'-∆Uα )cos α − ( ∆TTAN ) + ∆Sr )sin α = 0

(8)

in which: ∆N’ and ∆Sr = effective normal force and mobilized resisting shear force, respectively, on the base of each slice; ∆Uα and ∆Uβ = water force acting on base and top of the slice; ∆W = weight of the slice soil mass; kv = vertical earthquake coefficient; ∆Q = resultant of uniform surcharge acting on the slice top; ∆TNORM and ∆TTAN = 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; α = inclination of shear surface with respect to the horizontal; β = slope inclination angle; δ = inclination of the uniform surcharge acting on the slice top, measured positive counterclockwise from the vertical. Based on Coulomb’s failure criterion, ∆Sr can be written as:

∆S r =

C' =

C'+∆N' tanφ ' FS

(9)

c' DX cos α

(10)

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

60

∆Q

δ

β ∆Uβ

β

DX

kh ∆W

h

kv ∆W

∆W

h eq ∆TNORM

∆T TAN ∆Sr ∆N'

α ∆U α

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

61

Substituting (9) and (10) into (8), and solving for ∆N’:

∆N' =

∆U β cosβ + ∆Q cosδ + ∆W(1 - k v ) + ( ∆T NORM - ∆U α )cos α - ∆TTAN sin α tanφ ' sin α cosα + FS

C' sin α FS

(11)

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

∑ {{[ ∆W(1 - k ) + ∆U v

i =1

β

cosβ + ∆Q cos δ ] (R sin α )} − [(∆S r + ∆TTAN ) R ]

[

] [

(

− (∆Uβ sinβ + ∆Q sinδ )(R cosα - h ) + ∆W k h R cosα - h e q

)] } = 0

(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

∑ i =1

FS =

n

∑ (A i =1

3

A1 A 1+ 2 FS

(13)

- A4 + A5 - A6 )

in which:

[

A1 = C'+ tan φ' secα ∆W (1 - kv ) + (∆TNORM - ∆Uα ) cosα + ∆Uβ cos β + ∆Q cosδ − ∆TTAN sin α

A2 = tanα tanφ '

]

(14) (15)

62

[

]

A3 = ∆W (1 - kv ) + ∆Uβ cos β + ∆Q cosδ sin α

(

(16)

)

h  A 4 = ∆U β + ∆Q sin δ  cosα −  R 

(17)

h eq    A 5 = ∆W k h  cosα R  

(18)

A 6 = ∆TTAN

(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 ∆N’ 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: n ∑ {∆Sr + ∆TTAN - [(∆Q cos δ + ∆Uα cosβ ) sin α ]- ∆W (1 - k v ) sin α i =1 − ∆W kh cos α + [ ( ∆Q sin δ + ∆U β sin β ) cos α ] } = 0

(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

∑ i =1

FS =

B1 B 1+ 2 FS

(21)

n

∑ B3 i =1

63

in which:

B1 =

[

C' + tan φ' secα ∆W (1- kv ) − ∆TTAN sinα + (∆TNORM - ∆Uα ) cosα + ∆Uβ cos β + ∆Q cos δ

]

cosα

(22)

B2 = tanα tan φ'

(23)

 ∆T  B3 = ∆W (tan α + kh − kv tan α) + ∆Uβ (cos β tan α - sin β ) + ∆Q (cos δ tan α − sin δ ) − TAN cos α  

(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.).

64

SPENCER'S METHOD

Spencer’s Method of slices has been incorporated into STABL to enhance the versatility of the program. Spencer’s 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 Spencer’s Method Spencer’s Method was first developed for circular slip surfaces assuming parallel interslice side forces inclined at a constant angle, θ, 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, θ. 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):

∆N'+ ∆Uα + QF sin (α - θ ) + ∆W[k h sin α - (1 - k v )cos α ]

(25) - ∆U β cos (α − β ) − ∆Q cos (α - δ ) - ∆TNORM = 0

∆ Sr - QF cos (α - θ ) - ∆W[(1 - k v ) sin α − k h cos α ] + ∆ U β sin (α - β ) + ∆ Q sin (α - δ ) + ∆ TTAN = 0

65

(26)

∆Q

δ

β ∆Uβ

β

DX

kh ∆W

kv ∆W

∆W

h eq ∆TNORM

∆T TAN ∆Sr

θ

∆N'

QF

α ∆Uα

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

66

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

∆N' = ∆W[(1 - k v )cos α - kh sin α )] - ∆ U α + ∆U β cos (α − β ) (27)

+ ∆ Qcos(α - δ ) - QF sin( α - θ ) + ∆ TNORM

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

S1 + S2 FS QF =  S  cos(α - θ ) 1 + 3   FS 

(28)

where:

{

}

S1 = C'+tanφ ' ∆W[(1- k v ) cosα − k h sinα ] − ∆Uα + ∆U β cos(α − β) + ∆Q cos(α - δ ) + ∆TNORM)

(29)

S 2 = ∆U β sin (α − β ) − ∆W[(1- k v )sinα + k h cosα ] + ∆Q sin(α - δ ) + ∆TTAN)

(30)

S 3 = tanφ ' tan(α -θ )

(31)

Overall moment and force equilibrium are satisfied by the conditions: n

cos(α − θ )] = 0

∑ QF [ R

i =1

n

∑ QF =

i =1

(32)

0

(33)

Two FS values are obtained when (32) and (33) are solved for each assumed value of θ. The solution is reached by iteration when a unique value of FS, and its corresponding θ, 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).

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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 (F f), the value of the factor of safety with respect to moment equilibrium (Fm), and the angle of the interslice forces θ calculated during iteration, along with the value of FS and θ 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 θ 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.

68

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°.

69

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.

70

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

71

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

72

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.

73

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.

Input for Profile Geometry: LINE

COMMAND

Command line

PROFIL

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code

First data line

Title and description of the problem

Second data line

Integer

Total number of boundaries

Third data line

Integer Real

Number of surface boundaries X-coordinate of left end of boundary

ft or m

Real

Y-coordinate of left end of boundary

ft or m

Real

X-coordinate of right end of boundary

ft or m

Real

Y-coordinate of right end of boundary

ft or m

Integer

Soil type index number for material immediately beneath boundary

NOTE: Repeat proceeding of third data line for each boundary.

Input for Soil Types: LINE

COMMAND

Command line

SOIL

First data line Second data line

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code Integer Real

Number of soil types Moist unit weight

pcf or kN/m3

Real

Saturated unit weight

pcf or kN/m3

Real

Isotropic strength intercept

Real

Isotropic friction angle

Real

Pore pressure parameter

Real

Pore pressure constant (1)

Integer

Piezometric surface number

74

psf or kPa deg psf or kPa

(1) If no piezometric surface is specified, any number excepting zero can be used. NOTE: Repeat proceeding of second data line for each soil type.

Input for Modifying Soil Types (if Specified): LINE

COMMAND

Command line

SOIL

First data line

VARIABLE TYPE

Integer Integer

Second data line

DESCRIPTION

UNITS

Command Code Number zero (0) Number of soil types to be modified

Real

Moist unit weight

pcf or kN/m3

Real

Saturated unit weight

pcf or kN/m3

Real

Isotropic strength intercept

Real

Isotropic friction angle

Real

Pore pressure parameter

Real

Pore pressure constant

Integer(1)

psf or kPa deg psf or kPa

Piezometric surface number

(1) If no piezometric surface is specified, any number excepting zero can be used. NOTE: Repeat proceeding of second data line for each soil type to be modified.

Input for Strength Anisotropy (if Specified): LINE

COMMAND

Command line

ANISO

First data line Second data line

Third data line

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code Integer Integer

Number of anisotropic soil types Soil type index number

Integer

Number of directional strength parameter data sets

Real

Counterclockwise direction limit

Real

Strength intercept

Real

Friction angle

NOTE: Repeat proceeding of third data line for each range of direction.

75

deg psf or kPa deg

NOTE: Repeat proceeding of second and third data lines for each anisotropic soil type.

Input for Suppressing or Reactivating Strength Anisotropy (if Specified): LINE

COMMAND

Command line

ANISO

First data line

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code Integer

Number zero (0)

Input for Water Surface (if Specified): LINE

COMMAND

Command line

WATER

First data line

Second data line Third data line

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code Integer Real

Number of piezometric surfaces defined Unit weight of water (1)

Integer Real Real

Number of points defining the water surface X-coordinate of point on water surface Y-coordinate of point on water surface

pcf or kN/m3 ft or m ft or m

(1) If zero (0) is specified, 62.4 (pcf) or 9.81 (kN/m3 ) is assumed. NOTE: Repeat proceeding of third data line for each point on the water surface. NOTE: Repeat the second and third data lines for each piezometric surface

Input for Suppressing or Reactivating Water Surface (if Specified): LINE

COMMAND

Command line

WATER

First data line

VARIABLE TYPE

DESCRIPTION

Command Code Integer

Number zero (0)

76

UNITS

Input for Boundary Loads (if Specified): LINE

COMMAND

Command line

LOADS

First data line Second data line

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code Integer Real Real Real Real

Number of boundary loads X-coordinate of left end of boundary load X-coordinate of right end of boundary load Intensity of boundary load Angle of inclination of boundary load (positive counterclockwise from vertical)

ft or m ft or m psf or kPa deg

NOTE: Repeat proceeding of second data line for each boundary load.

Input for Suppressing or Reactivating Boundary Loads (if Specified): LINE

COMMAND

Command line

LOADS

First data line

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code Integer

Number zero (0)

Input for Earthquake Load (if Specified): LINE

COMMAND

Command line

EQUAKE

First data line

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code Real

Real Real

Earthquake coefficient for horizontal acceleration (defined positive outwards from face of slope)(1) Earthquake coefficient for vertical acceleration (defined positive upwards)(1) Cavitation pressure

(1) Negative values may be specified.

77

psf or kPa

Input for Specific Failure Surface (if Specified): LINE

COMMAND

Command line

SURFAC

First data line Second data line

VARIABLE TYPE

DESCRIPTION

Command Code (or SURBIS Integer Real Real

(1)

UNITS

)

Number of points defining the failure surface X-coordinate of point on failure surface Y-coordinate of point on failure surface

(1) SURBIS for circular surfaces, Modified Bishop’s Factor of Safety. NOTE: Repeat proceeding of second data line for each point on the failure surface.

Input for Analysis of Specified Trial Surface (if Specified): LINE

COMMAND

Command line

EXECUT

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code

Input for Trial Surface Generation Limits (if Specified): LINE

COMMAND

Command line

LIMITS

First data line

Second data line

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code Integer

Total number of generation boundaries

Integer

Number of generation boundaries that deflect upward X-coordinate of left end of generation boundary Y-coordinate of left end of generation boundary

Real Real Real Real

X-coordinate of right end of generation boundary Y-coordinate of right end of generation boundary

78

ft or m ft or m ft or m ft or m

NOTE: Repeat proceeding of second data line for each generation boundary.

Input for Suppressing or Reactivating Trial Surface Generation Limits (if Specified): LINE

COMMAND

Command line

LIMITS

First data line

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code Integer

Number zero (0)

Input for Circular Surface (if Specified):

THE JANBU SIMPLIFIED METHOD: LINE

COMMAND

Command line

CIRCLE

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code

First data line

Integer

0 = Do not use Janbu’s correction factor; 1, 2, or 3 = Use Janbu’s correction factor (1 if φ = 0; 2 if c > 0 and φ > 0; 3 if c = 0)

Second data line

Integer

Number of initiation points

Integer Real

Number of surfaces to be generated from each initiation point X-coordinate of leftmost initiation point

ft or m

Real

X-coordinate of rightmost initiation point

ft or m

Real

X-coordinate of left termination limit

ft or m

Real

X-coordinate of right termination limit

ft or m

Real

Minimum elevation of surface development

ft or m

Real

Length of segments defining surfaces

ft or m

Real

Counterclockwise direction limit for surface initiation; 0 = no restriction on direction limit Clockwise direction limit for surface initiation; 0 = no restriction on direction limit

Third data line

Fourth data line

Real

79

deg deg

THE BISHOP SIMPLIFIED METHOD: LINE

COMMAND

Command line

CIRCL2

First data line

Second data line

Third data line

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code Integer

Number of initiation points

Integer Real

Number of surfaces to be generated from each initiation point X-coordinate of leftmost initiation point

ft or m

Real

X-coordinate of rightmost initiation point

ft or m

Real

X-coordinate of left termination limit

ft or m

Real

X-coordinate of right termination limit

ft or m

Real

Minimum elevation of surface development

ft or m

Real

Length of segments defining surfaces

ft or m

Real

Counterclockwise direction limit for surface initiation; 0 = no restriction on direction limit Clockwise direction limit for surface initiation; 0 = no restriction on direction limit

Real

deg deg

Input for Irregular Surface Searching (if Specified): LINE

COMMAND

Command line

RANDOM

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code

First data line

Integer

0 = Do not use Janbu’s correction factor; 1, 2, or 3 = Use Janbu’s correction factor (1 if φ = 0; 2 if c > 0 and φ > 0; 3 if c = 0)

Second data line

Integer

Number of initiation points

Integer Real

Number of surfaces to be generated from each initiation point X-coordinate of leftmost initiation point

ft or m

Real

X-coordinate of rightmost init iation point

ft or m

Real

X-coordinate of left termination limit

ft or m

Real

X-coordinate of right termination limit

ft or m

Third data line

80

Input for Irregular Surface Searching (if Specified) (Cont.): LINE

COMMAND

Fourth data line

VARIABLE TYPE

DESCRIPTION

UNITS

Real

Minimum elevation of surface development

ft or m

Real

Length of segments defining surfaces

ft or m

Real

Counterclockwise direction limit for surface initiation; 0 = no restriction on direction limit Clockwise direction limit for surface initiation; 0 = no restriction on direction limit

Real

deg deg

Input for Block Surface Searching (if Specified): LINE

COMMAND

Command line

BLOCK

VARIABLE TYPE

Command Code (or BLOCK2

First data line

Integer

Second data line

Integer Integer Real

Third data line

DESCRIPTION

Real Real Real Real Real

UNITS (1)

)

0 = Do not use Janbu’s correction factor; 1, 2, or 3 = Use Janbu’s correction factor (1 if φ = 0; 2 if c > 0 and φ > 0; 3 if c = 0) Number of surfaces to be generated Number of boxes used to generate base of central block Length of segments defining surfaces X-coordinate of left end of centerline defining the box Y-coordinate of left end of centerline defining the box X-coordinate of right end of centerline defining the box Y-coordinate of right end of centerline defining the box Length of vertical side of the box

ft or m ft or m ft or m ft or m ft or m ft or m

(1) BLOCK2 is a sliding block surface modified from BLOCK, the difference being that BLOCK2 generates active and passive portions of the sliding blocks according to the Rankine theory, where BLOCK generates these more randomly.

81

NOTE: Repeat proceeding of third data line for each box.

Input for TIES: LINE

COMMAND

Command line

TIES

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code

First data line

Integer

Number of tieback loads

Second data line

Integer

Real

Boundary number where tieback load is applied X-coordinate of the point of application of tieback load Y-coordinate of the point of application of tieback load Load per tieback

Real

Horizontal spacing between tiebacks

Real

Inclination of tieback load as measured clockwise from the horizontal plane Free length of tieback (equal to zero if other than a tie back load)

Real Real

Real

ft or m ft or m lb or kN ft or m deg ft or m

NOTE: Repeat preceding of second data line for each tieback load.

Input for Suppressing or Reactivating Tieback Loads (if Specified): LINE

COMMAND

Command line

TIES

First data line

VARIABLE TYPE

DESCRIPTION

Command Code Integer

Number zero (0)

82

UNITS

Input for NAILS: LINE

COMMAND

Command line

NAILS

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code

First data line

Integer

Number of groups of soil reinforcement

Second data line

Integer

Boundary number where reinforcement is applied

Real

Y-coordinate of top nail head of the group

ft or m

Real

ft or m

Real

Y-coordinate of bottom nail head of the group Number of reinforcement levels between the top and the bottom nail of the group Length of the nails in the group

Real

Horizontal spacing between nails

ft or m

Real

Inclination of nails

Real

Diameter of the steel section of nails

Real

Allowable tensile stress of nails

psf or kPa

Real

Unit friction along soil-nail interface

psf or kPa

Real

Diameter of nail borehole

Integer

Integer Real

Nail head condition: 0 = nails are free at the head; 1 = nails are fixed Maximum allowable head load in free nails; 0 = 100% free nails

NOTE: Repeat preceding of second data line for each nail group.

83

ft or m deg ft or m

ft or m

lb or kN

Input for GEOSYN: LINE

COMMAND

Command line

GEOSYN

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code

First data line

Integer

Second data line

Integer Real

Real Integer

Number of groups of geosynthetic reinforcement Boundary number where reinforcement is applied Y-coordinate of the intersection between the top layer of the geosynthetic group and the slope surface Y-coordinate of bottom layer of the geosynthetic group Number of reinforcement levels between the top and the bottom layers of the geosynthetic group

ft or m

ft or m

Real

Length of the geosynthetic in the group

ft or m

Real

Allowable tensile strength of the geosynthetic per unit of slope Friction efficiency of the geosynthetic

lb/ft or kN/m

Real

NOTE: Repeat preceding of second data line for each geosynthetic group.

Input for S PENCR: LINE

COMMAND

Command line

SPENCR

First data line

VARIABLE TYPE

DESCRIPTION

UNITS

Command Code Real

Estimate of approximate slope angle with respect to horizontal

84

deg

ERROR MESSAGES STABL is intended to be error free, assuming that the input data are correctly prepared. To avoid

problems when the data have been incorrectly prepared, STABL checks all data, as they are being read in, for consistency with program requirements. If an inconsistency is found in data submitted, STABL points it out by displaying an error indication. Unless the error is of a nature that demands immediate termination of execution, STABL continues reading data and checking for more errors until a point is reached in execution where termination is required as a consequence of previously determined errors. The errors are coded and referenced to descriptions in the next section. Each input error has a two-digit number prefixed with two letters, associating the error with a particular command or class of errors. The prefixes are listed below.

ERROR

ASSOCIATED COMMAND OR ERROR CLASS

PREFIXES

SQ

Command Sequence errors

FR

Free-form Reader errors

PF WA SF

Errors associated with the command PROFIL Errors associated with the command WATER Errors associated with the command SURFAC

LM

Errors associated with the command LIMITS

LD

Errors associated with the command LOADS

SL AI

Errors associated with the command SOIL Errors associated with the command ANISO

RC BK

Errors associated with the command RANDOM and CIRCLE Errors associated with the command BLOCK

TI

Errors associated with the command TIES

SP

Errors associated with the command SPENCR

85

Command Sequence Errors

SQ01 - A command other than PROFIL has been used as the first command in the execution sequence. The first command must be PROFIL. PROFIL initializes STABL prior to reading all data pertinent to the definition of a problem. All data that would have been read prior to encountering the first use of the command PROFIL would have been nullified and would not have been made available to STABL for the purpose of analyzing the first problem. SQ02 - An attempt to compute the factor of safety of a specified trial failure surface with the command EXECUT has been aborted. The isotropic soil parameters describing the soil types of the current problem do not exist. After each use of the command PROFIL in an execution sequence, the isotropic soil parameters of each soil type must be specified by use of the command SOIL before the command EXECUT may be used. Each time a new problem is introduced in an execution sequence by the command PROFIL, the soil parameters describing soil types of preceding problems are no longer available for use. SQ03 - An attempt to compute the factor of safety of an unspecified trial failure surface with the command EXECUT has been aborted. After each use of the commands PROFIL, CIRCLE, RANDOM or BLOCK, a trial failure surface must be specified with the command SURFAC before the command EXECUT may be used. SQ04 - The command ANISO has been used without the isotropic soil parameters being defined. Anisotropic strength data may not be specified unless the isotropic parameters have been defined by the command SOIL after the last use of the command PROFIL. SQ05 - An attempt to use one of the commands, RANDOM, CIRCLE, or BLOCK has been aborted. The isotropic soil parameters describing the soil types of the current problem do not exist. After each use of the command PROFIL in an execution sequence, the isotropic soil parameters of each soil type must be specified by use of the command SOIL before any of the above mentioned commands may be used. Each time a new problem is introduced in an execution sequence by the command PROFIL, the soil parameters describing soil types of preceding problems are no longer available for use.

86

Free-form Reader Error Code FR01 - Data are insufficient to continue execution. An attempt was made to read beyond the last data item specified. Check for missing data items. Or, within the line of data displayed, a decimal point has been detected for a number read as an integer. An integer is not allowed to contain a decimal point. Check is any number intended to be integer contains a decimal point.

PROFIL Error Codes

PF01 - The number of ground surface boundaries exceeds the total number of profile boundaries. The number of profile boundaries must be less than or equal to the total number of profile boundaries. PF02 - The number of profile boundaries specified may not exceed 100. The problem must be either redefined so fewer profile boundaries are used, or the dimensioning of the program must be increased to accommodate the problem so defined. PF03 - A negative coordinate has been specified for the profile boundary indicated. All problem geometry must be located within the first quadrant. PF04 - The coordinates of the end points of the profile boundary indicated have not been specified in the required order. The coordinates of the left end point must precede those of the right. PF05 - The ground surface boundaries indicated are not properly ordered or are not continuously connected. The ground surface boundaries must be specified from left to right and the ground surface described must be continuous. PF06 - The required subsurface boundary order is unsatisfied for the boundaries indicated. boundaries that overlap horizontally, those above the others must be specified first.

87

Of

WATER Error Codes WA01 - An attempt has been made to suppress or reactivate undefined water surface data. Data must be defined by a prior use of the command WATER before they can be suppressed. Suppressed data cannot be reactivated if the command PROFIL has been used in the execution sequence subsequent to their suppression. The command PROFIL nullifies all data prior to their use whether the data are active or suppressed. WA02 - The number of points specified to define the water surface exceeds 40. The problem must be either redefined so fewer points are used, or the dimensioning of the program must be increased to accommodate the problem as defined. WA03 - Only one point has been specified to define the water surface. A minimum of two points is required. WA04 - A negative coordinate has been specified for the water surface point indicated. All problem geometry must be located within the first quadrant. WA05 - The water surface point indicates that it is not to the right of the points specified prior to it. The points defining the water surface must be specified in left to right order.

SURFAC Error Codes

SF01 - The number of points specified to define a trial failure surface exceeds 500. The problem must be either redefined so fewer points are used, or the dimensioning of the program must be increased to accommodate the problem as defined. SF02 - Only one point has been specified to define the trial failure surface. A minimum of two points is required. SF03 - A negative coordinate has been specified for the trial failure surface point indicated. All problem geometry must be located within the first quadrant.

88

SF04 - The trial failure surface point indicated is not to the right of the points specified prior to fit. The points defining the trial failure surface must be specified in left to right order, and no two points are allowed to define a vertical line. SF05 - The first point specified for the trial failure surface is not within the horizontal extent of the defined ground surface. All points defining a trial failure surface must be within the horizontal extent of the defined ground surface. SF06 - The specified trial failure surface does not entirely exist within defined extent of ground surface. Check that the coordinates of the first and last points of the failure surface exist on a ground surface boundary. Check the number of boundaries specifying the ground surface boundaries in the command PROFILE.

LIMITS Error Codes

LM01 - An attempt has been made to suppress or reactivate undefined surface generation boundary data. Data must be defined by a prior use of the command LIMITS before they can be suppressed. Suppressed data can not be reactivated if the command PROFIL has been used in the execution sequence subsequent to their suppression. The command PROFIL nullifies all data read prior to their use whether the data are active or suppressed. LM02 - The number of surface generation boundaries specified to deflect upwards exceeds the total number of boundaries specified. The number of upward deflecting boundaries must not exceed the total number of boundaries. LM03 - The number of surface generation boundaries specified exceeds 20. The problem must be either redefined so fewer surface generation boundaries are used, or the dimensioning of the program must be increased to accommodate the problem as defined. LM04 - A negative coordinate has been specified for the surface generation boundary indicated. All problem geometry must be located within the first quadrant.

89

LM05 - The coordinates of the end points of the surface generation boundary indicated have not been specified in the required order. The coordinates of the left end point must precede those of the right.

LOADS Error Codes

LD01 - An attempt has been made to suppress or reactivate undefined surcharge boundary loads. Data must be defined by a prior use of the command LOADS before they can be suppressed. Suppressed data can not be reactivated if the command PROFIL has been used in the execution sequence subsequent to their suppression. The command PROFIL nullifies all data read prior to their use, whether the data are active or suppressed. LD02 - The number of surcharge boundary loads specified exceeds 10. The problem must be either redefined so fewer loads are used, or the dimensioning of the program must be increased to accommodate the problem as defined. LD03 - A negative coordinate has been specified for the surcharge boundary load indicated. All problem geometry must be located within the first quadrant. LD04 - The X-coordinates defining the horizontal extend of the surcharge boundary load indicated have not been specified in the required order. The X-coordinate of the left end of the load must precede the X-coordinate of the right end. LD05 - The surcharge boundary load indicated is not to the right of all the loads specified prior to it or overlaps one or more of them. The loads must be specified left to right and are not allowed to overlap.

SOIL Error Codes SL01 - The profile boundary indicated with this error message has an undefined soil type index. The number of soil types specified must be greater than or equal to each soil type index that has been assigned to profile boundaries.

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SL02 - The number of soil types may not exceed 20. The problem must be either redefined so fewer soil types are used, or the dimensioning of the program must be increased to accommodate the problem as defined. SL03 - An attempt has been made to change the parameters of one or more soil types that are undefined. No soil types have been defined since the last use of the command PROFIL. When a new problem is introduced by the command PROFIL, the soil parameters, describing soil types of preceding problems in the execution sequence, are no longer available for use and cannot therefore be changed. SL04 - The number of soil types to be changed is greater than the total number of soil types already defined. This implies changing isotropic soil parameters of soil types that have not been specified and therefore is not permitted. The number of soil types to be changed must be less than or equal to the number of soil types specified by a previous use of the command SOIL. Each soil type must be previously specified, before its parameters may be changed. SL05 - An attempt has been made to change the parameters describing an unspecified soil type. The soil type must be defined before it may be modified. The index of each soil type to be changed must be less than the total number of soil types.

ANISO Error Codes

AI01 - An attempt has been made to suppress or reactivate undefined anisotropic strength data. Data must be defined by a prior use of the command ANISO before they can be suppressed. Suppressed data can not be reactivated if the command PROFIL has been used in the execution sequence subsequent to their suppression. The command PROFIL nullifies all data read prior to their use whether the data are active or suppressed. AI02 - The number of anisotropic soil types specified may not exceed the number of soil types specified by the command SOIL. AI03 - The number of anisotropic soil types specified exceeds 5. The problem must be either redefined so fewer anisotropic soil types are used, or the dimensioning of the program must be increased to accommodate the problem as defined.

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AI04 - The soil type index indicated is greater than the number of soil types specified by the command SOIL. The index of each anisotropic soil type must be less than or equal to the number of soil types specified. AI05 - The number of direction ranges specified for the anisotropic soil type indicated is less than 2 or exceeds 10. No soil type should be defined anisotropic with number of direction ranges less than 2, as this means soil is isotropic. Also no soil type should exceed 10 direction ranges. If this is desired, the dimensions of the program must be increased. AI06 - The counterclockwise limit of each direction range must be specified in counterclockwise order, if the anisotropic strength is to be properly defined for the anisotropic soil type indicated. AI07 - The total direction range for the anisotropic soil type indicated has not been completely defined. The counterclockwise limit of the last direction range specified must be 90°.

RANDOM and CIRCLE Error Codes

RC01 - The first initiation point lies to the left of the defined ground surface. The X-coordinate of the first initiation point must be specified so all trial failure surfaces generated will intersect the defined ground surface when they initiate. RC02 - The first and last initiation points are not correctly specified. They must be specified in left to right order. RC03 - The last initiation point lies to the right of the defined ground surface. The X-coordinate of the last initiation point must be specified so all trial failure surfaces generated will intersect the defined ground surface when they initiate. RC04 - The right termination limit lies to the right of the defined ground surface. The right termination limit must be specified so all trial failure surfaces generated will intersect the defined ground surface when they terminate. RC05 - The left and right termination limits are not correctly specified. They must be specified in leftright order.

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RC06 - The last initiation point lies to the right of the right termination limit. It is impossible to successfully generate any trial failure surfaces, when the initiation point lies to the right termination limit. RC07 - The depth limitation for trial failure surface development is negative. The depth limitation must be set at or above the X-axis so the generated trial failure surfaces will not be allowed to develop below it. RC08 - The length specified for the line segments used to generate trial failure surfaces is less than or equal to zero. The length must be greater than zero. RC09 - An initiation point is below the depth limitation. The depth limitation must be set lower to enable the successful generation of trial failure surfaces from all initiation points. RC10 - The number of points defining a generated trial failure surface exceeds 500. The length specified for the line segments must be increased. RC11 - 200 attempts to generate a single trial failure surface have failed. The search limitations are either too restrictive, or they actually prevent successful generation of a trial failure surface from one to more of the initiation points. Check and revise the search limitations or use an alternative trial surface generator. RC12 - Fewer than 10 trial surfaces have been specified to be generated. A minimum of 10 must be generated. RC13 - The angle specified as clockwise direction limit for surface generation is larger than the angle specified as counterclockwise direction limit. This is not correct. Check to see if angles have been reversed. RC16 - If the Janbu’s empirical coefficient is being used, the soil case was chosen incorrectly, i.e., not equal to one of the following integers: 0, 1, 2, or 3.

BLOCK Error Codes

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BK01 - The number of boxes specified for a sliding block search exceeds 10. The problem must be either redefined so fewer points are used, or the dimensioning of the program must be increased to accommodate the problem as defined. BK02 - The length specified for the line segments used to generate the active and passive portions of the trial failure surfaces is less than or equal to zero. The length must be greater than zero. BK03 - The two coordinate points specified to define the centerline of the box indicated have not been specified correctly. The left point must be specified first. BK04 - The box indicated and the one specified before it are not properly ordered, or they overlap. All boxes must be specified in left to right order and the boxes are not allowed to overlap one another. BK05 - The box indicated is wholly or partially defined outside of the first quadrant. All problem geometry must be located within the first quadrant. BK06 - The box indicated is wholly or partially above the defined ground surface. Each box must be defined totally below the ground surface. BK07 - It is not possible to complete the active portion of the failure surface from part of or all of the last box specified. The last box specified must be entirely to the left of the right end of the defined ground surface. BK08 - It is not possible to complete the passive portion of the failure surface from part of or all of the first box specified. The first box specified must be entirely to the right of a fictitious line extended downward at 45° with the horizontal from the left end of the defined ground surface. BK09 - The number of points defining a generated trial failure surface exceeds 500. The length specified for the line segments of the active and passive portions of the generated trial failure surfaces must be increased. BK10 - 200 attempts to generate a single trial failure surface have failed. The search limitations are either too restrictive or they actually prevent successful generation of a trial failure surface. Check and revise the search limitations or use an alternate trial surface generator.

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BK11 - Fewer than 10 trial failure surfaces have been specified to be generated. A minimum of 10 must be generated. BK12 - The point(s) calculated on active or passive portion of the sliding block is not within the horizontal extent of the defined ground surface. Either the specified boxes should be changed or the geometry of the problem should be extended to include the point(s) in question. BK16 - If the Janbu’s empirical coefficient is being used, the soil case was chosen incorrectly, i.e., not equal to one of the following integers: 0, 1, 2, or 3.

TIES Error Codes

TI01 - An attempt has been made to suppress or reactivate undefined tieback loads. Data must be defined by a prior use of the command TIES before they can be suppressed. Suppressed data can not be reactivated if the command PROFIL has been used in the execution sequence subsequent to their use, whether the data are active or suppressed. TI02 - The number of tieback loads specified exceeds 20. The problem must either be redefined so fewer tieback loads are used, or dimensioning of the program must be increased to accommodate the problem as defined. TI03 - A negative coordinate has been specified for the tieback load indicated or the calculated Ycoordinate of the end of the tieback is negative. All problem geometry must be located within the first quadrant. TI04 - The inclination limits have been exceeded for the tieback load indicated. The inclination of a tieback load must be equal to or greater than 0° and less than 180° as measured clockwise from the horizontal. TI05 - The point of application of the tieback load specified does not lie on the ground surface boundary specified. Check the boundary number specified and the X- and Y-coordinates at the point of application of the tieback load indicated.

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TI06 - The horizontal spacing between tiebacks for the two of tiebacks indicated is incorrect. The horizontal spacing between tiebacks must be greater than or equal to 1 ft (or 1 m is using SI units). TI07 - The length of the tieback indicated is incorrect. The length of a tieback must be greater than or equal to zero (ft or m). Zero is used for loads other than tieback type of loads.

SPENCR Error Code

SP01 - An incorrect value for the approximate slope angle has been specifie d. The slope angle specified must be greater than 0° and less than 90°.

96

REFERENCES

Boutrup, E. (1977) "Computerized Slope Stability Analysis for Indiana Highways." Joint Highway Research Project, JHRP-77-25, JHRP-77-26 (volumes); School of Civil Engineering, Purdue University, West Lafayette, Indiana; 512p. Carpenter, J.R. (1985) "STABL5...The Spencer Method of Slices: Final Report." Joint Highway Research Project, JHRP-85-17; School of Civil Engineering, Purdue University, West Lafayette, Indiana. Carpenter, J.R. (1986) "Slope Stability Analysis Considering Tiebacks and Other Concentrated Loads." Joint Highway Research Project, JHRP-86-21; International Report; School of Civil Engineering, Purdue University, West Lafayette, Indiana. Carter, R.K. (1971) "Computer Oriented Slope Stability Analysis by Method of Slices." MSCE Thesis, Purdue University, West Lafayette, Indiana; 120p. Chen, R.-H. (1981) "Three-Dimensional Slope Stability Analysis." Joint Highway Research Project, JHRP-81-17; School of Civil Engineering, Purdue University, West Lafayette, Indiana; 298p. Kim, J. (1998) “Limit Analysis of Soil Slope Stability Using Finite Elements and Linear Programming.” Ph.D. Thesis, Purdue University. Kim, J. and Salgado, R. (1999) “Limit Analysis of Complex Soil Slopes Subjected to Porewater Pressures.” Geotechnical Engineering Report (1999-1); School of Civil Engineering, Purdue University. Kim, J.; Salgado, R.; and Yu, H.S. (1999) “Limit Analysis of Soil Slopes Subjected to Pore-water Pressures.” Journal of Geotechnical and Geoenvironmental Engineering; ASCE; 125 (1) , 4958. Koerner, R.M. (1994) “Desgining with Geosynthetics.” Third Edition; Prentice Hall, New Jersey. Lovell, C.W. (1982) "Three-Dimensional Slope Stability." Proceedings 13 th Annual Ohio River Valley Soils Seminar, Lexington, Kentucky; 9p. Morlier, P. and Tenier P. (1982) "Influence of Concentrated Loads on Slope Stability." Canadian Geotechnical Journal, 19; 396-400. Ortigão, J.A.R.; Palmeira, E.M.; and Zirlis, A. (1995) "Experience with Soil Nailing in Brazil: 19701994." Proceedings of the Institution of Civil Engineers (Geotechnical Engineering), 113, London; 93-106. Siegel, R.A. (1975a) "Computer Analysis of General Slope Stability Problems." Joint Highway Research Project, JHRP-75-8; School of Civil Engineering, Purdue University, West Lafayette, Indiana, May 1975; 210p. Siegel, R.A. (1975b) "STABL User Manual." Joint Highway Research Project, JHRP-75-9; School of Civil Engineering, Purdue University, West Lafayette, Indiana; 104p (Revised by E. Boutrup, 1978). Yu, H.S.; Salgado, R.; and Sloan, S.W. (1998) “Limit Analysis Versus Limit Equilibrium for Slope Stability.” Journal of Geotechnical and Geoenvironmental Engineering; ASCE; 124 (1), 1-11.

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