High-Performance, High-Order Implicit Material Point Method for Progressive Levee Failure Simulations

In the past 15 years, the material point method (MPM) has been extensively used and developed to simulate large deformation problems in geomechanics, particularly landslides and other types of mass movements. The original formulation of the MPM, which assumes explicit dynamic time integration, often suffers from accuracy issues and numerical oscillation associated with its spatial and temporal discretization. On top of that, for fully undrained, i.e., incompressible, fluid-like flow slide problems, the numerical results obtained degrade significantly due to incompressibility-induced volumetric locking. At the same time, the incompressibility constraint also influences the allowable time step size for the explicit scheme, particularly since the numerical stability is strongly governed by the Courant–Friedrichs–Lewy condition. In the current work, a fully implicit MPM is implemented by incorporating the $\overline{\mathrm{B}}$ method to combat the volumetric locking issues. Higher-order basis functions are utilized to further improve the accuracy to alleviate errors associated with cell-crossing and numerical fracture. In the current work, the quadratic B-spline and the local maximum entropy basis functions are employed. Furthermore, to reduce the computational step associated with the rather expensive implicit time integration scheme and the higher-order basis function, a hybrid shared-distributed memory parallelization scheme is proposed by employing open-source domain decomposition and parallel linear solver software. The effectiveness and improvement of the proposed framework are qualitatively shown through simulations of progressive undrained failure of a 2D levee under gravitational loading.