A comparative study of error assessment techniques for dynamic contact problems of geomechanics

Numerical analysis of dynamic large deformation problems is one of the most challenging and sophisticated tasks in computational geomechanics. The complexity is mainly due to nonlinear soil behaviour, large deformations accompanied by severe mesh distortion, changing boundary conditions due to contact, and time-dependent behaviour. A typical example of such problems is the dynamic penetration of an object into a layer of soil due to its initial kinetic energy. This paper introduces an h-adaptive finite element method to tackle penetration as well as indentation problems of geomechanics in the presence of inertia forces. The h-adaptive finite element procedure automatically changes and optimises the density of the finite element mesh in a region to obtain a more accurate solution as well as to eliminate or reduce possible mesh distortion. A key component of an h-adaptive strategy is the error assessment technique. Although several methods exist for estimating the error in a finite element domain, the advantages as well as the capability of such methods in many geotechnical problems, particularly those involved with dynamic forces and changing boundary conditions, are not clearly understood. This paper describes a comparative study between three alternative error estimation techniques, including those based on the energy norm, the Green-Lagrange strain, and the plastic dissipation. The specific problems investigated involve the static and dynamic analysis of a strip footing on an undrained layer of soil, as well as the penetration of an object into a layer of sand. For these dynamic contact problems of geomechanics, the numerical results clearly show that the error estimator based on the Green-Lagrange strain outperforms the other two methods.