Computational analysis of dry soil containing stiff objects

Chiang Shih, Purdue University

Abstract

The objective of this research is to formulate a general finite element algorithm to treat a mixture of deformable and rigid solids subjected to large geometrical changes. This algorithm provides a solution for the study of soil and rock media containing very stiff objects, a common geotechnical problem. For deformable solids, each element is associated with a local coordinate system that rotates and translates with the element but does not deform. For each time increment, the local coordinate system has a new orientation and the element geometry also has a new shape. The corresponding strain-displacement and nodal force-stress relationships are defined in the updated local coordinates and are based on the updated geometrical shape. Hence, the rigid body motion and the deformation displacement are decomposed. If the time or load increment is small, the deformation increment may be small. Small strain theory and linear stress-strain relationships can thus be applied by using the updated geometry as the convected material reference frame. The nonlinearities associated with the large geometrical change are incorporated in the analysis through the continuous updating of the material geometry. The deformable material behavior assumes a linearly elastic-hardening plastic model. Newton's law of motion governs nodal displacements of deformable solids, whereas momentum equations are assumed for the motions of rigid solids. Displacement and force compatibilities are enforced at the interfaces. This leads to an explicit finite element analysis which involves only vector assemblages and vector storage if element masses are lumped at the nodes. The formulation is extended to include a fragmentation algorithm to handle tension crack or opening within solid media. A contact algorithm is adopted to handle the interactions between free surface boundaries. Two patch tests are performed to study the fragmentation and contact algorithms. Numerical verifications are presented for the soil response during excavation and under footing, the failure of an earth retaining wall, and a centrifugal test of the uplift of a buried strip anchor in dry sand.

Degree

Ph.D.

Advisors

Ting, Purdue University.

Subject Area

Civil engineering

COinS