Formulation of a Dynamic Material Point Method (MPM) for Geomechanical Problems
Kafaji, I. K. A. (2013). Formulation of a dynamic material point method (MPM) for geomechanical problems.
In geomechanics one often encounters large deformations, soil-structure interaction and dynamical problems, e.g., in pile driving and installation of anchors. Moreover, geomechanical phenomena that include excessive movement of soil masses like landslides can pose a danger to human life and property. The numerical simulation of the physics is challenging, particularly if a saturated soil is subjected to dynamic loading, leading to propagation of different waves in the soil.
Because of the reliance of Lagrangian finite element methods (FEM) on a mesh, they are not well suited for the treatment of extremely large deformations of solids. The need for overcoming this limitation urged researchers throughout the last decades to devote considerable effort to the development of more advanced computational techniques. Such techniques include the combination of Lagrangian and Eulerian finite element methods, meshless methods and mesh-based particle methods.
The intent of this thesis is to further develop and extend the material point method (MPM), which is a mesh-based particle method, for use in geomechanics. MPM can be conceived as an extension of FEM, in which soil and structural bodies are represented by Lagrangian particles that move through an Eulerian fixed mesh. The physical properties of the continuum reside with particles throughout the computations (deformations), whereas the Eulerian mesh and its Gauss points carry no permanent information. Hence, MPM combines the best aspects of both Lagrangian and Eulerian formulations and avoids as much as possible the shortcomings of them.
Three novel MPM development are described in this thesis. In the analysis of geomechanical problems that involve dynamics, absorbing boundaries are introduced to prevent the reflection ofwaves at the selected boundary of the domain. The well-known viscous boundaries, which will continuously creep under load, are modified to viscoelastic boundaries by introducing Kelvin-Voigt elements to limit such non-physical displacements.
The novel extension of MPM to model the behavior of saturated soils under dynamic loading is formulated. Enhancement of volumetric strains is adopted to mitigate the spurious pressure oscillations which plague low-order finite element implementations. The algorithm is applied to predict the generation and dissipation of pore pressures in a sea dike under heavy dynamic loading by wave attack.
Numerical simulation of pile driving is investigated. Results of shallow and deep penetration are presented. Due to the complex behavior of sand in pile driving, a highly non-linear advanced hypoplastic model is to be used for sand. Explicit Euler forward scheme with sub-stepping technique is used in the integration of this model.
MPM is applied to analyze different geomechanical problems, including the collapse of a tunnel face, the instability of a slope and the deep installation of a dynamic anchor. The dynamic MPM can be applied to quasi-static problems. To this end, a local damping procedure for single and two-phase materials is discussed, being applied to reach fast convergence to quasi-static equilibrium. Such convergence is detected by two proposed criteria on force and energy. Mass scaling is presented as a procedure that allows the use of large time step size for problems, in which inertia effect can be disregarded.