Formulation and Application of a Quasi-Static Material Point Method Lars Beuth
Beuth, L. (2012). Formulation and application of a quasi-static material point method.
This work is concerned with the analysis of quasi-static large deformation problems such as the jacking of piles where inertia and damping effects can be neglected, as opposed to dynamic problems such as pile driving. To this end, a novel type of Material Point Method (MPM) that is specifically adapted to the analysis of quasi-static large deformation problems is developed. The quasi-static MPM can be considered as an extension of the classical Updated Lagrangian
Finite Element Method (UL-FEM). As with the UL-FEM, a solid body is discretised by finite elements, but in addition, the solid body is discretised by a cloud of material points which moves through the mesh in the course of a computation. The movement of material points represents the arbitrary large deformations of the solid body. The FE grid is used as with the UL-FEM to compute incremental displacements strain increments at the locations of material points. In contrast to the UL-FEM, the can be reset into its original state or changed arbitrarily if accumulated distortions of the FE grid cause numerical inaccuracies. Material and state parameters of the solid body as well as applied loads are stored in material points. In contrast to most existing implementations of the MPM, the developed quasi-static variant makes use of implicit rather than explicit time integration, which allows for a considerable reduction of the computation time in case of quasi-static problems. The development of the quasi-static MPM and its validation for simple benchmark problems is the first aim of this study. This includes the modelling of soil-structure interaction within the developed method, a feature that is essential to many geotechnical analyses. Here, the novel approach of extending interface elements commonly used in small-strain Finite Element analyses for use with the Material Point Method has been taken.
The application of the quasi-static MPM to the simulation of cone penetration testing (CPT) forms the second aim. This widely-used in-situ test consists of pushing a steel rod with a measuring device attached to its tip into the ground with constant velocity. Numerical studies of cone penetration testing improve the understanding of involved mechanical processes and allow to refine existing or establish new correlations between CPT measurements and soil properties. In the frame of this study, cone penetration testing in undrained soft clay is considered with the aim of investigating the relation between the tip resistance and the undrained shear strength of clay. Both, the loadtype dependency of the shear strength of undrained clay as well as the influence of the anisotropic fabric of natural clay on the undrained shear strength are taken into account through a new material model, the Anisotropic Undrained Clay model. Results indicate that the deformation mechanism relevant for cone penetration in undrained normallyconsolidated clay differs significantly from predictions based on the Tresca model which is often used for such numerical studies, but resulting cone factors appear to be useful.