The Material Point Method (MPM) has become a powerful numerical framework for simulating large-deformation solid dynamics, particularly in geohazard problems such as landslides, debris flows, soil liquefaction, and seepage-induced failures. By combining Lagrangian material points with an Eulerian background grid, MPM avoids the severe mesh distortion that often limits conventional finite element methods. However, challenges remain, including numerical instability, incompressibility, boundary-condition enforcement, and the cost of large-scale simulations.

This study focuses on recent developments of enhanced B-spline-based MPM formulations for accurate and robust geohazard simulations. A key feature is the use of extended B-spline basis functions, which provide smooth interpolation while alleviating the small-mass issue causing ill-conditioning in implicit MPM formulations. Building upon this framework, an implicit dynamic MPM employing the generalized-α time integration scheme is introduced. Unlike conventional approaches requiring mass lumping or acceleration smoothing, the method selectively damps high-frequency responses while preserving second-order accuracy. This enables stable and accurate simulations of geohazard processes. In addition, mixed displacement–pressure formulations are incorporated for compressible and nearly incompressible geomaterials.

To address coupled soil–water interaction problems, a hybrid MPM–FEM framework based on Biot’s mixture theory is further developed. In this approach, the soil skeleton is discretized by MPM and pore fluids by Eulerian finite elements. Furthermore, a multi-patch B-spline discretization is introduced to overcome the trade-off between smooth interpolation and accurate boundary-condition enforcement. The proposed framework enables reliable simulations of localized hydraulic phenomena, including seepage, soil heaving, and piping around geotechnical structures frequently associated with flood- and rainfall-induced disasters.
For real-scale geohazard applications, efficient high-performance computing is also essential. A unified implementation supporting MPI, OpenMP, and GPU acceleration has therefore been developed, enabling large-scale three-dimensional simulations on heterogeneous supercomputing architectures and providing a foundation for realistic hazard assessment.

Finally, the lecture highlights recent developments in contact modeling for geohazard applications. Reliable prediction of contact forces is crucial for understanding interactions between moving soil masses as well as impacts of landslides and debris flows on infrastructure. A new contact algorithm has been developed within the MPM framework to accurately capture such interactions under large deformations while preserving computational efficiency. The proposed formulation improves the representation of soil–soil and soil–structure contacts and enhances the predictive capability of MPM for hazard assessment and mitigation design.

These developments demonstrate that enhanced B-spline-based MPM provides a unified framework combining accuracy, stability, and scalability for next-generation geohazard simulations and resilient infrastructure systems.

Material point method,B-splines,Geohazard,High-Performance Computing,contact stress