Excercise - Swedish Method of Slices

The Swedish method of slices is a method used to calculate the factor of safety of a slope under undrained (\(\phi=0\)) conditions. The method is based on the assumption that the slope can be divided into a number of slices. Consider a slope with a failure surface as shown below:

We can analyze each slice as follows:

The weight of the slice (\(W\)) can be calculated by summing the height of each material in the slice multiplied by the width of the slice and the unit weight of the material (\(\gamma_i h_i \Delta x\)). The length along the slice can be computed as \(\Delta l = \Delta x / cos \alpha\). The overall factor of safety for the slope is then calculated as:

\(F = \dfrac{\sum{c\Delta l}}{\sum{W sin\alpha}}\)

where:

\(c\) = the undrained cohesion of the soil
\(\Delta l\) = the length of the slice along the failure surface
\(W\) = the weight of the slice
\(\alpha\) = the angle of the failure surface with the horizontal

Use the following spreadsheet to calculate the factor of safety for the slope. The slice widths (\(\Delta x\)), heights (\(h_i\)), slope angles (\(\alpha\)), unit weights (\(\gamma\)), and cohesions (\(c\)) are given in the spreadsheet. Fill in the remaining values and calculate the factor of safety.

Excel starter file: swedish.xlsx

Excel solution file: swedish_KEY.xlsx