Analytical calculation models versus Finite Element Method FEM

3 Analytical calculation models versus Finite Element Method (FEM) 

In the following paragraphs, several analytical calculation methods will be discussed for the verification of the failure mode and the Ultimate Limit State. 

These analytical methods have proven to give reliable results for the limit states discussed. The factors of safety normally adopted in the analytical analyses cover, to some extent, also the uncertainty with respect to the theoretical calculation model used. 

Another technique used for such calculations is based on the Finite Element Method (FEM). In this calculation method the soil is subdivided into small elements and each element gets a soil model attributed which expresses the stress-strain behaviour of the soil. In fact, the FEM is primarily a method to calculate deformations (Serviceability Limit State) but it is also frequently used to verify the Ultimate Limit State. 

Checking for the ULS in a deformation-related model is normally performed by reducing the shear strength in small iterative steps until large deformations occur in the model. This may, however, lead to numerical problems with the FEM and requires numerical manipulation to allow for such calculations. 

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