ABSTRACT
In diverse applications including pile driving, excavations, foundations, prediction of land-slides and slope failure, large deformation and material movement is observed in the soil medium. In order to simulate these processes, pure Lagrangian based numerical methods, popularly known as the Finite Element Method pose certain challenges. This can be overcome by coupling the Lagrangian method with the Eulerian approach. Material Point Method (MPM) is one such implementation capable of simulating large deformations in soil. Certain numerical difficulties in MPM such as grid-crossing error, incapability for extension etc., are alleviated in the Convected Particle Domain Interpolation (CPDI) approach, an improvement bought about to MPM.
CPDI is further extended to a two-phase model for simulating saturated soil. Soil and water phases are represented by a single particle, based on their respective porosities. The third phase—air/void is neglected in the present work. A multi-velocity formulation, i.e. solid-water velocity formulation (v-w formulation) is adopted to precisely capture the saturated soil behavior. This includes a full set of equation for soil and water; which can capture both stress and pressure waves. Effective stress concept is followed by accounting pore pressure effects in the deformation of soil. A few examples are presented to validate the two-phase CPDI implementation. The method is then evaluated by means of a dynamic application, a pile installation simulation in saturated sand. A 2D axisymmetric model is considered together, with a penalty contact method for evaluating the interaction between soil and pile. The pile is hammered into the sand by means of pulse loading applied on head of the pile. A Hypoplastic constitutive model is chosen for the sand which allows the study of soil parameters such as stress, void ratio, friction angle, pore pressure etc., during the installation process. The effect of saturated soil on pile installation is studied and compared with the results from the installation in dry soil.
