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Slope Stability Calculator - HELP (Draft)

(last updated 11 Dec 2014)

Contents:

Introduction

This calculator determines the factor of safety for a soil slope. It uses the Bishop Modified and/or Ordinary Method of Slices for a 2-dimensional setting. It is a slightly modified JavaScript clone of the slope stability software STABR Ver. 2.84 (MS-DOS).

The calculator searches the circular slip surface for which the factor of safety is minimal. Then, it calculates for this slip circle the corresponding critical seismic coefficient for which the factor of safety is 1.

Slope failure schematic

The properties of the slope are defined in the Input Data table.

The Result field shows the calculation results.
The contents of the Result field can be highlighted and copied for further use.

See special instructions for offline use of this calculator.

For background information, see also Properties of Tailings Dams and Safety of Tailings Dams.

 
Factor of Safety

The Factor of Safety is defined as the ratio of the available shear strength of the soil to that required to keep the slope stable. It is common practice to use the following empirical guidelines for slope stability assessments:

Factor of SafetyGuidelines for limit equilibrium of a slope

< 1.0

Unsafe

1.0 - 1.25

Questionable safety

1.25 - 1.4

 Satisfactory for routine cuts and fills,
Questionable for dams, or where failure would be catastrophic

> 1.4

Satisfactory for dams

 

The Units can be selected for the whole calculator as Imperial or Metric. This selection must be made before any other entry, since it resets the complete calculator.

ImperialMetric
Lengthft.feetmmeters
Line Loadlbs/ft.pounds per footkN/mkilo Newton per meter
Pressure, Cohesionp.s.f.pounds per square footkPakilo Pascal
Unit Weightp.c.f.pounds per cubic footkN/m3kilo Newton per cubic meter
Unit Weight of Water62.4 p.c.f.9.81 kN/m3
(all pounds are pounds force)

1 ft. = 0.3048 m1 m = 3.281 ft.
1 lb = 4.448 N1 kN = 224.8 lb
1 lb/ft. = 14.59 N/m1 kN/m = 68.52 lb/ft.
1 p.s.f. = 47.88 Pa1 kPa = 20.89 p.s.f.
1 p.c.f. = 157.1 N/m31 kN/m3 = 6.366 p.c.f.
(all pounds are pounds force)
See also Unit Converter.

 

Input Data

Some Sample Data Sets can be selected from a pick list. These sets include the three examples supplied with STABR, and several tailings dams of various heights and slopes.
The "Crescent Junction, UT" sample data sets are the original sets used for the proposed alternate disposal site for the Atlas Moab tailings, as given in: Attachment 1 of Remedial Action Plan, Moab Uranium Mill Tailings Remedial Action Project - Disposal Cell Design and Engineering Specifications - June 2006, Calculation MOA-02-05-2006-03-17-00 Through End (ADAMS Accession No. ML061700032 ). The layers for these data sets are defined as follows:
  1. Radon Barrier
  2. Tailings
  3. Clean-Fill Dike
  4. Alluvial/Eolian Soil
  5. Weathered Mancos Shale
  6. Competent Mancos Shale

For the entry of user defined problems, it is highly recommended to draw the problem to scale on gridded paper first. The ground surface should extend beyond any slip surface at each end of the slope.
Once the input data has been entered, the Draw Input button draws a schematic of the situation, including geometry data, pore pressure lines and slip circle tangents (only with HTML 5-capable browsers).

Note: Y-coordinate values increase downward!

Slope failure schematic with input conventions

 

Geometry

Sections [ft.] · [m]
X-coordinates (in increasing order) of the vertical soil sections
If not all of the sections are required, leave excess trailing sections empty.

Boundary n [ft.] · [m]
Y-coordinates of the boundaries between different horizontal soil layers, for each vertical section. Boundary 1 describes the exposed surface of the slope.
If not all of the boundaries are required, leave excess trailing boundaries empty.

W in Crack [ft.] · [m]
Y-coordinates of depth of water in tension cracks for each vertical section.

T. Cracks [ft.] · [m]
Y-coordinates of depth of tension cracks for each vertical section.

 

Pore Pressure Data (optional)

Enter either Pore Pressure and Coordinates, or Ru Factor
Pore Pressure [p.s.f.] · [kPa]
Pore-water pressure (in increasing order), for each of the Equi-Pressure Lines.
If only one line is entered (with Pore Pressure = 0), then this is used as the phreatic surface.
If not all of the available lines are required, leave trailing fields open.

Coordinates of Equi-Pressure Lines [ft.] · [m]
Y-coordinates of lines of equal pore pressure in the soil, for each vertical section.

Phreatic Surface in Upstream Tailings Dams

kL = permeability at the edge of the ponded water at the slimes zone
k0 = permeability at the spigot point (dam crest)
kF = permeability of foundation
kh / kv = anisotropy ratio (horizontal vs. vertical)

Ru Factor (unitless)
Average pore pressure ratio. This factor allows for an alternate pore pressure specification in terms of a fraction of the pressure caused from the overlying soil column.
Caution: If this value is entered, any above defined pore-water pressure data is disregarded.

 

Soil Properties

Layer Properties

The soil properties are specified for the soil layers as defined by the above boundaries. Layer No.1 is the top layer and is situated between Boundary 1 and Boundary 2; layer No.2 is situated between Boundary 2 and Boundary 3, and so forth.
Cohesion [p.s.f.] · [kPa]
Soil cohesion, for each soil layer
Leave field open (or enter negative number), if a cohesion profile is to be used instead (see below).
Enter 0 for tailings layers.

Friction Angle [°]
for each soil layer
Enter 0 for water layers

Density [p.c.f.] · [kN/m3]
unit weight of the soil, for each soil layer
For layers of water, enter the exact value of 62.4 p.c.f., or 9.81 kN/m3, respectively.

 

Cohesion Profile

The cohesion profile is only used for those soil layers, for which the Cohesion field in the Soil Properties table is left open (or contains a negative number). The cohesion profile is defined independently of the soil layer boundaries.
Elevation [ft] · [m]
Y-coordinates (in increasing order) for which a soil cohesion vs. depth is to be specified
If not all of the available elevations are required, leave trailing fields open.

Cohesion [p.s.f.] · [kPa]
soil cohesion for each depth defined

 

Slip Circle

Slip Circles are specified by their center and by points or lines their circumference has to pass.

Centers

Enter either Specified Centers, or Search Start Center and Final Search Grid.
Specified Centers [ft.] · [m]
X- and Y-coordinates of centers of slip circles to be used.
If not all of the available centers are required, leave trailing fields open.
Caution: If this parameter is entered, any Search Start Center or Grid specifications are disregarded.

Search Start Center [ft.] · [m]
X- and Y-coordinates of the center of the first slip circle to be analyzed

Final Search Grid [ft.] · [m]
finest grid width to be used for the centers of the slip circles to be analyzed

Circumference

Enter either Tangent Depths or Toe Point.
Tangent Depths [ft.] · [m]
Y-coordinates of the horizontal tangents which the slip circles to be analyzed must touch.
If not all of the available tangents are required, leave trailing fields open.

Toe Point [ft.] · [m]
X- and Y-coordinates of the toe point of the slope which the slip circles have to pass.
Caution: If this parameter is entered, any defined tangent coordinates are disregarded.

 

General

Method
Select Bishop Modified or Ordinary Method of Slices

Seismic Coefficient (unitless)
multiplier on the weight of the potential sliding mass; also fraction of peak horizontal ground acceleration vs. gravity
If no value is entered, 0 is assumed.

Peak acceleration vs. magnitude and distance for earthquakes in the Western United States

Seismic Option
...

 

Calculation Details

The two Limit Equilibrium Methods implemented in this calculator differ in regard of how they deal with interslice forces: Other, more sophisticated methods, such as Spencer, Morgenstern-Price etc., also consider interslice shear forces, however, the factors of safety obtained often do not differ very much.
For details on the Limit Equilibrium Methods, see, for example, the Theoretical Background chapter in the TSLOPE Software documentation by TAGAsoft, or the Help File distributed with the free Slope/W Student Edition by Geo-Slope International Ltd.

...

 

Bibliography

PROGRAM STABR VERSION 2.84 (MS-DOS)

PROGRAM FOR SLOPE STABILITY ANALYSIS BY THE BISHOPS MODIFIED METHOD,
WRITTEN BY GUY LEFEBVRE, JANUARY 1971
MODIFIED BY S. CHIRAPUNTU, FEB. 1973, APR. 1974
MODIFIED BY J. TAYLOR, MARCH 1981
CONVERSION TO MS-DOS IS CODED BY KAI WONG ON FEBRUARY 1984.

 

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