#STABL for WIndows 3 Manual

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.

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

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.

Table of Contents:

Page

STABL FORWINDOWSINTERFACE 6

ABOUTSTABLFORWINDOWS 7

INSTALATIONINSTRUCTIONS 7

RUNNINGSTABLFORWINDOWS 7

GETTINGUPTOSPEED 7

Starting the Program 7

Minimum Data Set 8

CHOICE OF ANALYTICAL METHOD AND SURFACE GENERATION

MODEL 8

FACTOROFSAFETYHISTOGRAM 9

MAINFEATURESOFTHEPROGRAM 10

Unit System Selection 10

Soil Profile 11 Soil Properties 13 Water Tables 14 Boundary Loads 15 Seismic Loads 16 Tiebacks 17 Geosynthetics 18 Soil Nails 19 Analysis 20

Menu Bar Options 21

GENERAL RECOMMENDATIONSFORUSEOFSTABLFORWINDOWS 25

REFERENCE MANUAL 26 PROBLEM GEOMETRY 27 Profile Boundaries 27 Piezometric Surfaces 31 SOIL PARAMETERS 34 Anisotropic Soil 35 BOUNDARY LOADS 37 SOIL REINFORCEMENT 39 Soil Nailing 39 Geosynthetic Reinforcement 40

TIEBACK LOADS 40 Description of the Tieback Routines 43

TIES Input Restrictions 47

EARTHQUAKE LOADING 47

SEARCHING ROUTINES 48

Circular and Irregular Surfaces 48

Sliding Block Surfaces 53

Surface Generation Boundaries 58

Individual Failure Surface 58

BISHOP SIMPLIFIED METHOD 60

JANBU SIMPLIFIED METHOD 63

SPENCER’S METHOD 65

Description of Spencer’s Method 65

SPENCR Option 68

SPENCR Input Restrictions 69

ASSUMPTIONS 70

DATA PREPARATION 74

Input for Each Command 74

ERROR MESSAGES 85

Command Sequence Errors 86

Free-Form Reader Error Codes 87

PROFIL Error Codes 87

WATER Error Codes 88

SURFAC Error Codes 88

LIMITS Error Codes 89

LOADS Error Codes 90

SOIL Error Codes 90

ANISO Error Codes 91

RANDOM and CIRCLE Error Codes 92

BLOCK Error Codes 93

TIES Error Codes 95

SPENCR Error Code 96

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.

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.

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

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

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/m

. 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/m

), and unit weights in terms of

one thousand Newtons per cubic meter (kN/m

).

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.

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;

(c)

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

(d)

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

(e)

The number identifying the soil immediately under the segment;

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

Button.

You must click OK if you wish these properties to be saved. Be sure to

locate the slope in the first quadrant (see STABL for DOS manual). The toe

of the slope should always be to the left of the crest of the slope.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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 180

(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).

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

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

problem.

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).

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]

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).

Well Beyond Crest

Well Beyond Toe

Deep

(1000,1000)

(1500,1000)

(1900,1200)

(2400,1200)

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

of slope.

Figure 2. Output scaling resulting from correct but inadequate definition of the problem geometry

with respect to the origin of the coordinate system.

(0,500)

(700,500)

(900,600)

(1600,600)

b. Too much room allowed beyond the toe and crest of the slope in

comparison to the slope height and length.

(0,0)

Soil 1 Soil 3 Soil 2 Soil 3

1

2

3

13

4

5

6

7

8

9

10

12

11

14

15

A

B

G

H

I

J

K

L

M

D

C

F

E

Boundary

ABCDEF

Soil Type

3

2

Area

5

GHIJK

1

15

-LM-3

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

pressure based on hydrostatic pressure, i.e., the head is the vertical distance from the base of the slice to the phreatic surface immediately above (Figure 5) (Siegel 1975a , Siegel 1975b, Boutrup 1977).

This is a conservative estimate; the steeper the piezometric surface, the more conservative the results of the old method." The resulting pressure head can be as much as 30% higher than the actual head when the piezometric surface is dipping at 35° (Figure 6).

Surface of Seepage Groundwater Table

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

PCSTABL5M PCSTABL5 ACTUAL

PERPENDICULAR

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

1

2

3

1 - 35

o Dipping Piezometric Surface

2 - 29

o Dipping Piezometric Surface

3 - 17

o Dipping Piezometric Surface

5

-PCSTABL5 Method of Pore Pressure Determination

6

-PCSTABL6 Method of Pore Pressure Determination

P

-Perpendicular Method of Pore Pressure Determination

A

-Actual Pore Pressure

Figure 6. Handplot of flownet and slope.

1 2 3 A A P, A 6 P 6 P 6 5 5 5

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

Anisotropic Soil

Soil types exhibiting anisotropic strength properties are described by assigning Mohr-Coulomb strength parameters to discrete ranges of direction. The strength parameters would vary from one discrete direction range to another.

The orientation of all line segments defining any potential failure surface can be referenced with respect to their inclination entirely within a range of direction between -90° and +90° with respect to the horizontal. Therefore, the selection of discrete ranges of direction is confined to these limits. The entire range of potential orientation must be assigned shear strength values.

Each direction range of an anisotropic soil type is established by specifying the maximum (counterclockwise) inclination ai of the range (Figure 7). The data consist of this inclination limit and the Mohr-Coulomb friction angle and strength intercept for each discrete range. Data for each discrete range must be prepared progressing in counterclockwise order, starting with a first range from -90° to a1 (specifying a1 as counterclockwise direction limit). The process is repeated for each anisotropic soil type.

+90 o 4th _{Direction Range} Soil Parameters (φ₄,c₄) 3rd _{Direction Range} Soil Parameters (φ₃,c₃) 2nd _{Direction Range} Soil Parameters (φ₂,c₂) 1s t _{Direction Range} Soil Parameters (φ₁,c₁) a₄ a₃ a₂ a₁ −90 ο

BOUNDARY LOADS

Uniformly distributed boundary loads applied to the ground surface are specified by defining their extent, intensity, and direction of application (Figure 8). The limit equilibrium model used for analysis treats the boundary loads as strip loads of infinite length. The major axis of each strip load is normal to the two-dimensional X-Y plane within which the geometry of slope stability problems is solved. Therefore, the extent of a boundary load is its width in the two-dimensional plane.

Data for each boundary load consist of the left and right X coordinates which defines the horizontal extent of load application, the intensity of the loading, and its inclination. The intensity specified should be in terms of the load acting on a horizontal projection of the ground surface rather than the true length of the ground surface. Inclination is specified positive counterclockwise from the vertical. The boundaries must be ordered from left to right and are not allowed to overlap.

A boundary load whose intensity varies with position can be approximated by substituting a group of statically equivalent uniformly distributed loads which abut one another. The sum of the widths of the substitute loads should equal the width of the load being approximated. The inclinations should be equivalent, and the intensities of substitute loads should vary, as does the load being approximated.

x

Intensity q

Inclination

δ

=0

Extent

x

x

x

q

+

δ

x

-δ

q

Figure 8. Definition of surcharge boundary loads.

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:

NAIL S

NAIL

D

q

L

T

=

π

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

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

Geosynthetic reinforcement

The reinforcement effect can be modelled as follows:

L

'

tan

E

2

T

∆

′

∑

=

σ

φ

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.

point of application of the tieback load, the Y-coordinate of the point of application of the tieback load, the load per tieback, the horizontal spacing between tiebacks, the inclination of tieback load as measured clockwise from the horizontal plane, and the free length of tieback (Figure 9). For concentrated boundary loads such as strut loads in a braced excavation, which do not extend into the ground like tiebacks, the length of the tieback is zero. An equivalent line load is calculated for each tieback load specified, assuming a uniform distribution of load horizontally between point loads. PCSTABL6 allows for the input of concentrated loads applied to a horizontal ground surface boundary, and also allows concentrated loads to be inclined between 0° and 180° from the horizontal. The input parameters for a tieback load have been changed to include also the input of the X-coordinate of the load applied to the ground surface. Previously, only the Y-coordinate was required. Either the X-Y-coordinate of the point of application of the tieback load can be specified and the Y-coordinate calculated, or the Y-coordinate can be specified and the X-coordinate calculated. If the user desires, both the X- and Y-X-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 coordinate, it will automatically calculate the proper Y-coordinate for the X-Y-coordinate and boundary specified. Likewise, if only the Y-Y-coordinate is specified, a value of zero must be input for the X-coordinate.

When the program finds a zero coordinate, it will automatically calculate the proper X-coordinate for the Y-X-coordinate and boundary specified.

The user may input both the X- and Y-coordinates of the point of application of the tieback load on the ground surface boundary. However, the coordinates specified must be sufficiently accurate so that the program will recognize an intersection of the X- and Y-coordinates specified with the ground surface boundary specified. If the difference between the coordinates specified by the user and the coordinates calculated by the program is greater than 0.001, then an error message will be displayed, and the program execution stopped.

A short description of the tieback routines is presented in the next section to help the User understand the method and assumptions used in STABL for analyzing slopes subjected to concentrated loads.

1 2 3

A

P

A

i

L

Elevation

Crest

H

Toe

Tiebacks

Section A-A

TIEBACK INPUT PARAMETERS:

2

X

Y

P

H

I

L

Description of the Tieback Routines

Unlike other slope stability programs, STABL distributes the force from a concentrated load throughout the soil mass to the whole failure surface and hence to all slices of the sliding mass. Most slope stability programs project a concentrated load straight to the base of a single slice. This distribution of load throughout the soil mass is a unique feature of STABL.

First, an equivalent line load is calculated for a row of tiebacks by dividing the specified tieback load (point load) by the corresponding horizontal spacing between tieback loads. The resulting line load is called TLOAD (Figure 10) and is inclined from the horizontal by an angle i. The radial stress on the midpoint of a slice is calculated using Flamant's Formula (Morlier and Tenier, 1982):

d

)

)cos(T

(T

2

π

σ

₌

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:

α

π

cos

d

(DX)

)

(T

cos

)

2(T

P

=

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 T_θ is large.

FAILURE

SURFACE

DX

i

Τ

i

T

α

α

d

P

P

P

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

P

T

P

=

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:

1 RAD NORM (P )cos P = α (6) 1 RAD TAN

(P

)

sin

P

=

α

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.

CONCENTRATED LOAD

FAILURE SURFACE

LIMIT OF STRESS DISTRIBUTION

DUE TO CONCENTRATED

TIEBACK 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).

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

Counterclockwise

Direction Limit

Horizontal

Clockwise

Direction Limit

1

Line Segment

Initiation

Point

β

-5

45

β

θ

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.

Deflection-Constant for each

Succeeding Line Segment

Projection of Preceding

Line Segment

Successful Generation

Short of Left Termination Limit

Beyond Right Termination Limit

Below Depth Limitation

Limits of Termination

Depth Limit

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

Passive

Wedge

Central Block

Active

Wedge

Strong Material

Strong Material

Weak Layer

Left Coordinate Point

for Box Specification

Right Coordinate Point

for Box Specification

Parallelogram Centerline

Length of

Vertical Sides

Passive

Surface

Horizontal

Passive 45

o

Direction

Range

Base of Central Block

Active Surface

Vertical

Figure 17. Generation of active and passive sliding surface.

Passive 45

o

Direction

Extent of

Search

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

Weak

Layer

b. Search in irregular weak layer.

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.

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.

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: 0 )sin S ) T ( cos ) U N' -T ( ) k -(1 W cos Q cos U +∆ +∆ _v + ∆ _NORM ∆ ∆ − ∆ _TAN +∆ _r = ∆ _β β δ _α α α (8)

in which: ∆N’ and ∆Sr = effective normal force and mobilized resisting shear force, respectively, on the base of each slice; ∆Uαand ∆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:

FS

'

tan

N'

C'

S

=

+

∆

φ

∆

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

h

h

DX

α

β

k

∆W

∆W

k

∆W

∆

T

∆N'

∆U

∆S

∆T

δ

∆

Q

∆U

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

β