Slope Stability

Question 1

Assumptions for Limit equilibrium methods

Answer 1

i) any failure mechanism can be assumed;
ii) a failure criterion for the soil along the failure lines is also assumed;
iii) depending on the method, the distribution of interslice force magnitude or inclination or point of application are assumed.

To find the factor of safety, the equations of static equilibrium are imposed for each slice. In 2D, for each slice, three equations of equilibrium are imposed (2 equations for translational equilibrium and 1 equation for moment equilibrium).

Main limitations: the failure mechanism is imposed, strong assumptions on the interslice forces.

Question 2

Assumptions for Finite element method with strength reduction

Answer 2

i) a constitutive law for the material is assumed, e.g. elastic-perfectly plastic behaviour;
ii) a failure criterion is assumed (e.g. Mohr Coulomb)

To find the factor of safety, the equations ruling the geotechnical problem (e.g. static equilibrium, kinematic compatibility, constitutive laws) at the level of an infinitesimal element of soil are imposed for various values of the soil strength until the value of soil strength corresponding to failure of the slope is found.

Main limitations: problems of numerical convergence to a solution especially in case of complex failure mechanisms emerging from the analysis (e.g. extensive zones with shear bands).
The main advantage over other methods is the fact that the failure surface is found as a result of the analysis rather than being assumed.