The method of slice is the standard method used in most commercial software for slope stability analysis. Stepwise, the method begins by dividing the slope into slices with equal widths. Variants of this method exist, but they differ by the level of simplification and the number of equilibrium equations used in their derivation.

In this blog, we consider the simplest variant of the method of slice, the ordinary method of slice. In the end, we will compare the hand calculation results with Bishop's method obtained by GEO5 software.

In the ordinary method of slice, vertical equilibrium is used to determine N. Factor safety can be computed by taking moment about the center point of rotation O, i.e.,

Simply for circular slip surfaces,

FS = Total Shear Resistance / Total Tangential force

__Example__

Consider a cohesionless soil slope (c = 0) with unit weight = 20 kN/m3 and friction angle = 30 deg. There is no groundwater above the slip surface.

The slope is divided into six slices; the following table shows the sheet to find tangential and shear resistance along the slip surface and then the Factor of Safety against slope failure (for assumed slip circle).

Similar results are obtained from GEO5 using the Bishop method.

Typically, the program will search for the location of the slip circle that gives the minimum FS value. The optimization solver is also available in most commercial software like GEO5. In this example, the ordinary method of slice gives the too-safe value of FS. However, most practices use the Bishop method (Das, 2002).

Ref.

BM Das, Principles of Geotechnical Engineering, 5th edition, Brooks/Cole, 2002