Slope Stability Info Sheet

Prior to the construction of slope, it is important to ensure the soil mass can support itself.

Failure modes of slope include rotational slip, translational slip and compound slip. Among these failures, rotational slip is deemed the most important type.

When analysing slope stability against rotational slip, we often assume the failure surface is a circular arc with center O and radius r. Method of slices is deployed to determine the factor of safety, FOS for slope to resist against the failure.

When using this method, soil mass above failure surface is divided into slices with constant width b. The base of each slice is assumed straight, and FOS is considered the same for all slices.

There are two solutions available for method of slices, namely Fellenius solution and Bishop routine solution. Fellenius solution assumes the resultant inter-slice forces is zero, while Bishop routine solution considers only neglect the shear force at the sides of slices. As a result, Bishop routine solution is statically indeterminate and successive approximation is required to reach convergence for FOS.

To analyse a slope properly, a number of failure surfaces needs to be established. Only then, we will be able to determine the critical failure surface with the lowest FOS.

We can also determine the slope stability against translational slip in terms of FOS. Prior to the analysis, several assumptions need to be made. First, the failure surface, water table and direction of seepage is assumed parallel to the slope surface. Moreover, the depth of failure surface is small compared to the length of slope.

We are now tasked to determine the factor of safety, FOS for a 5m height slope to resist against rotational slip.

The rise to run ratio for the slope is 1:2. Meanwhile, the analysis requires us to calculate its FOS against only one trial failure surface. The center of the trial failure surface is (20,15), while the radius of that surface is 12m.

The slope geometry needs to be drawn to scale to ease the measurement process. Then, we need to cut the soil mass above failure surface into slices of uniform width. When producing the slices, we need to make sure all of them will be either triangular or quadrilateral in shape.

Next, we need to measure the slice area. In this worked example, we utilize AutoCAD to reduce our workload. Once we obtain the area of all slices, we can then calculate the weight of slices.

We will then implement both Fellenius and Bishop routine solution. Both solutions require post-processing of data, while the Bishop routine solution alone needs iterative calculation to achieve convergence for FOS.

At the end of example, we found the FOS for this slope is 2.441 using Fellenius solution, and 2.705 using Bishop routine solution. This result has been validated using Slope/W. By using more slices, Slope/W found that the FOS for the slope would be 2.430 and 2.695 using ordinary (Fellenius) solution and Bishop solution respectively.