Abstract
This paper presents a single-point Material Point Method (MPM) for large deformation problems in two-phase porous media such as soils. Many MPM formulations are known to produce numerical oscillations and inaccuracies in the simulated results, largely due to numerical integration and stress recovery performed at non-ideal locations, cell crossing errors, and mass moving from one background grid cell to another. The same drawbacks lead to even worse consequences in the presence of an interstitial fluid phase, especially when undrained/incompressible conditions are approached. In this study, an explicit stabilised MPM, based on the Generalised Interpolation Material Point (GIMP) method with Selective Reduced Integration (SRI), is proposed to mitigate typical numerical oscillations in (nearly) incompressible coupled problems. It includes two additional features to improve stress and pore pressure recovery, namely (i) patch recovery of pore pressure increments based on a Moving Least Squares Approximation, and (ii) two-phase extension of the Composite Material Point Method for effective stress recovery. The combination of components leads to a new method named GC-SRI-patch. After a detailed description of the approach, its effectiveness is verified through analysing various consolidation problems, with emphasis on the representation of pore pressures in time and space.
Highlights
Large deformation problems in two-phase porous media are of great importance in geo-engineering, for instance in the analysis of landslides or foundation installation processes
This paper presents a single-point Material Point Method (MPM) for large deformation problems in two-phase porous media such as soils
It includes two additional features to improve stress and pore pressure recovery, namely (i) patch recovery of pore pressure increments based on a Moving Least Squares Approximation, and (ii) two-phase extension of the Composite Material Point Method for effective stress recovery
Summary
Large deformation problems in two-phase porous media are of great importance in geo-engineering, for instance in the analysis of landslides or foundation installation processes. As reduced integration is exclusively performed to evaluate pore pressure varia tions, computed results appear not to suffer from spurious hourglass modes (Chen et al, 2018) This approach can be readily implemented into existing explicit MPM codes and is further pursued in the present study. When MPs cross grid cell edges, it can cause a sudden change in pore pressure at the MPs, and, as a conse quence, spurious variations of nodal internal forces and stress oscilla tions, especially when a coarse background mesh is adopted In this respect, some authors tested reduced integration in the Generalised Interpolation Material Point (GIMP) method (Bardenhagen and Kober, 2004), as a way to alleviate the stress oscillations related to cell-crossing (Abe et al, 2014).
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