
Higher order hydromechnical MPM to simulate runout in brittle soils
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The simulation of large deformations plays an important role in predicting landslide runout. The Material Point Method (MPM) is a prominent tool in geotechnical engineering that has garnered attention due to its hybrid nature involving particles moving in a background grid. However, the stability and convergence of the MPM are still under research. Particularly, two errors are hindering the application of the MPM with advanced constitutive models for soils, namely cell-crossing error and volumetric locking error. Cell-crossing error is brought about by the commonly adopted lower-order interpolation functions, which have discontinuities in their derivatives. It induces a ringing error in the stress and a base drift in the displacement. It is known to often result in unstable MPM simulation of runouts. This is one of the most challenging errors to tackle in MPM, and it has not been explored within the context of multiphase landslide simulations in geotechnical engineering. Volumetric error is a pathological error in MPM that exists in dynamic multiphase formulations, resulting in ‘checkerboarded’ stress patterns. Volumetric locking particularly manifests when simulating undrained and elasto-plastic materials. This hinders multiphase formulations from capturing the complete consolidation process in soils. This research aims to put these MPM errors in a pragmatic context. First, a higher-order B-spline framework is used with a 2-phase 1-point formulation and F ̅ smoothing. Second, large strain linear-elastic oedometer simulations are used to verify the framework against the analytical solution. Third, the Selborne large scale slope failure experiment is presented and used for validation to compare the framework deployed at different orders (linear to quartic). A strain-softening Mohr-Coulomb constitutive model is used. The dynamic behaviour is analyzed in the context of acceleration, velocity, displacement, pore pressure, and effective stress paths, at different locations within the slope. The insights are crucial in establishing how cell-crossing numerical error and volumetric locking manifest in real-scale problems. We also highlight the crucial need for a higher order framework in dynamic geotechnical applications using MPM.