Numerical algorithms for large deformation analysis in geomechanics
Majid Nazem, Discipline of Civil, Surveying and Environmental Engineering, The University of Newcastle
Large deformation analysis is very important in some problems of geomechanics. Soft clays experience large amounts of settlements under applied loads and consolidation, for which the small deformation assumption does not result in precise solutions. The large deformation considerations are vital for these problems especially in Australia, since there is a large amount of soft soils along the east coast of the continent. Studying the footings behaviour under such circumstances demands for large deformation formulation by which load bearing capacity and settlements can be estimated more precisely and therefore more reliable design methods and techniques will be achieved. Two well-known methods for analysing large-deformation geotechnical problems are studied in this work. These methods include the Updated-Lagrangian (UL) and the Arbitrary-Lagrangian-Eulerian (ALE). The ALE method in this study is based on the operator-split technique during which the analysis is performed in two steps; an UL step followed by an Eulerian step. In the first step, a common UL procedure is undertaken to achieve the equilibrium. In the second step, the distorted mesh is refined and all kinematic and static variables are then transferred from the old mesh to the new mesh. Most ALE algorithms require mesh generation to refine the mesh during Eulerian step. This study introduces a new method for mesh refinement which can be used in general cases regardless of problem dimension and element types. The performance and efficiency of the UL and the ALE methods in solving some interesting problems in geomechanics are compared.
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