Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2401.11951

A Stabilised Semi-Implicit Double-Point Material Point Method for Soil-Water Coupled Problems

Mian Xie·Pedro Navas·Susana Lopez-Querol
View original source ↗Read source document ↗Export metadata ↓

Abstract

A semi-implicit two-phase double-point Material Point Method (MPM) formulation, based on the incremental fractional-step method to model large deformation geotechnical problems has been derived. The semi-implicit formulation has two advantages compared with the explicit approach: the time step is independent of the water phase, and the pore pressure field is more stable. The semi-implicit MPM models based on the incremental fractional-step method available in the literature consist of modelling the soil and water mixture using a single set of material points only, in order to save computational time. In this study, we further derive this formulation with two sets of material points to represent the soil and water phases separately. The stress oscillations that are frequently found in the water and soil phases are stabilised with this approach. A new stabilisation method is developed based on the modified F-bar method. The proposed method is validated with two numerical examples under small and large deformations, respectively. After that, Nor-Sand constitutive soil model is used to simulate landslides. Numerical examples show an excellent performance of the proposed coupled MPM and the stabilisation method. The formulation with two sets of material points yields significantly different but more reliable results in the landslides analysis, compared with the single-point approach. Additionally, this research shows that the additional computational cost caused by the additional water material points is acceptable. Therefore, it is recommended to use two sets of material points for certain large deformation geotechnical problems.

Explore related subjects

math.NAcs.NA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Mian Xie, Pedro Navas, Susana Lopez-Querol. 2025-02-28. A Stabilised Semi-Implicit Double-Point Material Point Method for Soil-Water Coupled Problems. https://doi.org/10.1007/s40571-025-01027-7

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fully spectral scheme for the linear BGK equation on the whole space

In this article, we design a fully spectral method in both space and velocity for a linear inhomogeneous kinetic equation with mass, momentum and energy conservation. We focus on the linear BGK equation with a confinement potential $Φ$, even if the method could be applied to different collision operators. It is based upon the projection on Hermite polynomials in velocity and orthonormal polynomials with respect to the weight $e^{-$Φ$}$ in space. The potential $Φ$ is assumed to be a polynomial. It is, to the author's knowledge, the first scheme which preserves hypocoercive behavior in addition to the conservation laws. These different properties are illustrated numerically on both quadratic and double well potential.

math.NA↗
arXiv2026

Inverse inequalities for kernel-based approximation on bounded domains and Riemannian manifolds

This paper establishes inverse inequalities for kernel-based approximation spaces defined on bounded Lipschitz domains in $\mathbb{R}^d$ and compact Riemannian manifolds. While inverse inequalities are well-studied for polynomial spaces, their extension to kernel-based trial spaces poses significant challenges. For bounded Lipschitz domains, we extend prior Bernstein inequalities, which only apply to a limited range of Sobolev orders, to the full range of lower and upper orders, and derive Nikolskii inequalities that bound $L_\infty$ norms by $L_2$ norms. For compact Riemannian manifolds, we focus on restricted kernels, which are defined as the restriction of positive definite kernels from the ambient Euclidean space to the manifold, and prove their counterparts.

math.NA↗
arXiv2026

Error Estimates for Hyperbolic Scaling Limits of Linear Kinetic Models on Networks

This paper studies linear discrete kinetic models on networks and their asymptotic behavior in the small Knudsen number limit. For coupling conditions at an n-edge junction under a symmetric formulation, we introduce a change of variables that reformulates the system into n independent initial-boundary value problems. The asymptotic expansions are then constructed and rigorously justified by deriving an error estimate based on the energy method.

math.NA↗