1 Slope Stability Failure Planes or Slip Surfaces Text section 14.9 and only

2 Slope Stability In general you have: Driving Force – Weight of Slope Resisting Force – Strength of soil along slip surface Buttress at toe W c

3 Slope Stability In slope stability analysis we determine the Factor of Safety as a ratio of resisting forces to driving forces F s = Resisting / Driving Theoretically, any slope with a Factor of Safety less than one will fail and any slope with a factor of safety greater than one will not. Design focuses on the soil parameters and geometry that will provide the maximum factor of safety. Sometimes, the analysis of an existing slope will be what is called a parametric study – that is establishing a factor of safety and performing an analysis that back calculates the strength parameters. The engineer will then determine his/her confidence level as to whether or not the soil has that strength through experience, lab, and/or field data.

4 Slope Stability Example of Circular Slip Surface (from geoslope software) Circular slip surfaces often used in analysis as the most likely approximated shape of the failure surface

5 Slope Stability Non circular slip surfaces can also be analyzed

6 Slope Stability In the previous slides, notice the slopes divided into slices Common methods break the slope up into slices for analysis α LnLn TnTn PnPn T n+1 P n+1 WnWn N TrTr Assume Side forces cancel out Do They? Now: W n sin α (driving) N= W n cos α T r = shear face = c’ + F ’ tan φ’ (resisting) W n sinα W n cos α α

7 Slope Stability Performing this analysis on each slice and then summing the components from each slice F s = Σ (c L + W cos α tan φ) / Σ (W sin α )

8 Slope Stability This analysis is very conducive to a tabular solution WedgecφαLWW sin αc LW cos α tanφ8 + 9 F s = Σ (10) / Σ (7)

9 Slope Stability - Example Each box is 5’ x 5’ * = 120 pcf c = 300 psf φ = 32 o

10 Slope Stability - Example First, Find the areas for each “slice” A1 A2 A3 A4

11 Slope Stability WedgecφαLWW sin αc LW cos α tanφ F s = Σ (10) / Σ (7)