The Application Of The Material Point Method In Geotechnical Engineering Problems

Large deformation problems in geotechnical engineering always lead to catastrophic damages. Gravity-driven flows such as landslides, debris flows and collapse of the foundation pit or the subway; seepage failures in man-made structures such as levees and embankments; and liquefaction of loose saturated granular soils have been extensively studied by researchers. Both physical and numerical simulations are very important to understand the mechanics and to predict failures of these problems. Experimental investigations on these types of large scale problems are very difficult to perform and require large quantity of resources. In the past few years, numerical simulation was developed rapidly in this field. However, the dynamics of these problems during the failure_are less explored due to the limitations of the numerical methods.The Material Point Method (MPM) is a novel numerical method that combines the best aspects of Lagrangian and Eulerian techniques. In this paper, MPM is used to do some numerical simulation analysis of large deformation problems in geotechnical engineering. This article consists of three main parts as bellows.Firstly, the research background and its geotechnical engineering significance are introduced, and the existing theoretical models and numerical methods in the field of large deformation in geotechnical engineering are reviewed. Several typical meshfree methods are surveyed briefly, but the development and application of the material point method is discussed in detail. MPM is compared with the traditional finite element method and other meshfree methods, the advantages and disadvantages of MPM are summarized subsequently. Finally, the major contents of the dissertation are outlined.Secondly, the traditional single-phase material point method is introduced in detail, the discrete formula and the numerical algorithm of the MPM are provided explicitly, the initial conditions and the boundary conditions are discussed, several kinds of commonly used soil models are established for geotechnical engineering problems. Based on the mixture theory form governing equations of saturated porous media, a two-phase coupling MPM is developed. Two sets of material points are invoked to represent the deformation of solid skeleton and the pore fluid flow, and the numerical algorithm is provided particularly. Bandara’s MPM numerical program has been modified and supplemented to model large deformation problems in geotechnical engineering.Thirdly, MPM is used for simulating the classic problems such as the collapse of granule columns and the process of slope instability, compared with experimental results or other numerical simulation results, the simulation results verify the accuracy and availability of the MPM theory and the numerical procedure, showing its unique advantages in the simulation of large deformation problems. As for a Ningbo cyclone well hole problem, MPM is used to simulate the whole process of the soil outside flowing into the well.The theoretical analysis and simulation results show that MPM can preferably simulate the dynamic failure process of geotechnical engineering problems and has a great potential in development and application prospect.