Abstract

This paper investigates the possibility of using the material point method (MPM) to solve small strains quasi-static problems and dynamic problems related to large distortions. Traditional methods such as the finite element method (FEM) face difficulties when large strains are involved. Therefore, tools such as the MPM have become more important in recent years. As a new tool, the MPM needs to prove its functionality for geotechnical engineering problems. In first place the MPM mathematical formulation is shortly described. Next, numerical simulations of a shallow foundation, an unconfined compression test and a slope problem are performed in an open source MPM code. The results are compared with FEM simulations, analytical solutions and real laboratory tests. The study shows qualitative and quantitative agreement when compared; a better performance of MPM for solving stresses better than strains is detected. The set of simulations validates the MPM to solve geotechnical engineering problems when dealing with small and large strains. However, the traditional FEM showed a better performance for quasi-static cases.

Abstract

The main objective of this work lies in the development of a variational implicit Material Point Method (MPM), implemented in the open source Kratos Multiphysics framework. The ability of the MPM technique to solve large displacement and large deformation problems is widely recognised and its use ranges over many problems in industrial and civil engineering. In the current work the continuum based implicit MPM is applied to engineering applications, where granular material flow is involved.

For the resolution of the length and time scale of these particular problems, both continuum and discrete models are typically used. Even if discrete techniques predict more feasible results, nowadays, their use is limited to the investigation of element tests of particles, or to the simulation of reduced systems, not allowing to make important decisions in the analysis and design of granular processes. Some advantages of MPM over discrete methods are tested, such as, the ability to simulate granular flow at the large scale with acceptable computational cost and the capability to get information of stress and strain state in a more straightforward way.

The focus of this paper is a comparative study between an irreducible and a mixed formulation, both implemented in the MPM code, to assess the improvement in accuracy and reliability of the numerical results when the latter formulation is adopted.

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Landslides triggered by earthquakes are one of the major seismic hazards and can cause large damages and fatalities. The material point method (MPM) has become a popular technique to model such large mass movements. A limitation of existing MPM implementations is the lack of appropriate boundary conditions to perform seismic response analysis of slopes. To bridge this gap, an extension to the basic MPM framework is presented for simulating the seismic triggering and subsequent collapse of slopes within a single analysis step. The concepts of a compliant base boundary and free-field columns are applied within the MPM framework enabling the direct application of input ground motions and accounting for the absorption of outgoing waves.

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