Numerical simulation of penetration in sand

This thesis presents a method to simulate penetration of a probe, penetrometer or pile in sand. This is one of the most challenging problems in geomechanics, involving three sources of nonlinearity: material nonlinearity because of the complex constitutive response of sand, geometric nonlinearity caused by extreme deformation of soil during penetration, and contact nonlinearity along the interface between the probe and the sand. The present research focuses on how to address these nonlinearities in theoretical simulations. To describe the complex stress-strain relationship of sand, a sophisticated bounding surface model for sand with consideration of fabric and its evolution during loading was developed. In bounding surface models, hardening often relies on the distance from the current stress state to the bounding surface in stress space. This thesis proposes a rigorous method to determine distances to an arbitrary surface in stress space. It starts by examining operations on stress variables defined in the π plane. Algorithms for determination of an image point on a surface are then presented as a function of the location of the current stress state with respect to the surface. For points within the surface, the bisection method is used; otherwise, the secant method is used. Implementation of the proposed algorithm locates the image point on a surface in stress space with accuracy and rigor, providing an accurate measure of the distance to the surface that can be used in hardening or flow rules. The bounding surface plasticity model is based on critical-state soil mechanics. The bounding surface controls sand stiffness through a relationship that depends on the distance from the current state to the bounding surface. Dilatancy, the plastic volume change caused by plastic shear deformation, is captured through a newly introduced phase transformation line. The fabric is quantified based on the distribution of contact normals between particles; it affects the location of the phase transformation line (thus, the dilatancy). The fabric evolves in such a way as to align it with the direction of loading. Simulation results using the model are in excellent agreement with wide-ranging test data for Toyoura sand. Subsequently, algorithms are proposed to simulate penetration in sand using the material point method (MPM). Background grids are structured but not uniform, with hanging nodes used to improve numerical efficiency. Moving and compressible background grids are used to handle velocity boundary conditions. To deal with contact between a penetrometer and sand, multi-body MPM techniques are implemented. Sand is modeled using the advanced bounding surface model; the interface between sand and steel is modeled using Coulomb\u27s friction law modified based on the bounding surface model. The MPM method is validated through simulation of calibration chamber cone penetration tests