STABILITY OF SLOPES WITH SIMPLE GEOMETRY
Let us reconsider the stability of a slope using a TSA, as expressed by Equation . We can rewrite
where No is called stability number and depends mainly on the geometry of the slope. Taylor (1948) used Equation to prepare a chart to determine the stability of slopes in a homogeneous deposit of soil underlain by a much stiffer soil or rock. He assumed no tension crack, failure occurring by rotation, no surcharge or external loading, and no open water outside the slope. The procedure to use Taylor’s chart to determine the safe slope in a homogeneous deposit of soil using a TSA, with reference to Figure , is as follows:
1. Calculatewhere Do is the depth from the toe to the top of the stiff layer and Ho is the height of the slope.
3. Read the value of as at the intersection of nd and No.
If you wish to check the factor of safety of an existing slope or a desired slope, the procedure is as follows:
Values for m and n for the Bishop–Morgenstern method
Bishop and Morgenstern (1960) prepared a number of charts for homogeneous soil slopes with simple geometry using Bishop’s simplifi ed method. Equation was written as
where m and n are stability coeffi cients (Figure that depend on the friction angle and the geometry of the slope.
The procedure to use the Bishop–Morgenstern method is as follows:
1. Assume a circular slip surface.
2. Draw the phreatic surface
4. With f' = f'cs and the assumed slope angle, determine the values of m and n from Figure
5. Calculate FS using Equation