Finite element analysis of bearing capacities in geomechanics considering dilatant and contractant constitutive laws

This paper focuses on the determination of limit-load states and corresponding bearing capacities in geomechanics, In contrast to classical approximative procedures which are mostly based on an a priori assumption of the failure mechanisms, the finite element method provides a more general approach. Very often localization phenomena are encountered which require advanced solution methods for a reliable description as explained in Cramer, Findeiss, Steinl & Wunderlich (1998) and de Borst (1991). In this presentation emphasis is given to the definition of an appropriate material model for dry and saturated soils. The basic requirement for frictional and cohesive geomaterials is the realistic modelling of the volume change characteristics. While dilatant behaviour may be defined by a cone-shaped yield function and a non-associated flow rule the definition of contractant behaviour includes a cap in the region of hydrostatic pressure, additionally. To achieve optimal stability properties for the numerical determination of stresses the formulation proposed in this paper is based on a single surface yield function where the second derivatives with respect to the stress tensor is sufficiently smooth. This is an important fact when consistent tangent operators are employed. The formulation is based on a hyperbolic approximation to the Drucker-Prager cone using five parameters for the shape in the hydrostatic plane and one parameter for the deviatoric plane. An extension to the Cosserat theory is presented as well. Applying the concept of rate-independent plasticity the numerical example of a strip footing on half space is discussed in detail. A comparison with classical solution techniques shows that realistic limit-loads may be computed. Additionally, the influence of other plasticity parameters as for example the dilatation angle or the ratio between the extension and compression radius is demonstrated.