Undrained soft soil modelling with the Material Point Method

For modelling of large deformation problems the Finite Element Method (FEM)is not suitable due to distortion of elements. The Material Point Method(MPM), adopting principles from computational fluid dynamics, is a relatively new method in geotechnical engineering and is suitable for large deformation analysis. The aim of this thesis is to model large deformations in soft soil under undrained conditions with the modified Cam clay material model and the MPMin back-calculating a cone penetration test (CPT). First the theoretical foundation on elasto-plasticity and the equation framework for the MCC model are presented. Then these constitutive equations are transferred into different numerical integration schemes for use in an FE package such as Plaxis and an MPM kernel. The integration methods here examined are the explicit Dormand-Prince method, which is a method in the Runge-Kuttafamily, and an implicit closest-point projection method. Then the theoretical background on the MPM is presented and the difference with the FEM pointedout. Simple shear test simulations are carried out with different material models, with 2D/3D FEM and 3D MPM kernels. For verification of the MPM’s performance with more complex material models than the Mohr-Coloumb (MC) model, an anisotropic undrained clay (AC) model is used. The 3D FEM and MPM simulations gave approximately the same results as the 2D FEM reference solution. To demonstrate the anisotropic behaviour of this material model, 2DFEM simulations are made with the MCC and the MC models. As expected,the AC and MCC models had equal results for triaxial compression conditions, but for the simple shear, the MCC model showed no weakening in the undrained shear strength, whereas the anisotropic model did. 2D FEM simple shear tests are also run in order to compare the performance of the explicit and implicit MCC routines. Although the respective stress paths differed greatly, with the implicit being close to the reference solution and the explicit being too coarse, both routines arrived at the same failure stress state.The explicit method was faster than the implicit method, with the cost of accuracy. Finally, CPT test simulations are done with the two MCC routines on medium and soft clay. The cone factors are calculated and compared to CPT simulation results with the MC model, empirical cone factors and theoretical solutions. Compared with empirical cone factors, the MCC results are in the middle and lower range and the MC in the upper range.