Stabilised Material Point Method for Fluid-Saturated Geomaterials

Large deformations in fluid-saturated geomaterials are central to numerous geotechnical applications, such as landslides and dam failures, pile installations, and underground excavations. An in-depth understanding of the soil's hydromechanical behaviour during large-deformation processes is essential for quantitative predictions about such geotechnical problems, which justifies the considerable importance that detailed numerical simulations have been acquiring in this context. However, such simulations are inevitably associated with significant conceptual and computational complexity, due to the simultaneous presence of possibly very large soil deformations along with dynamic effects. Under such conditions, the most common Lagrangian version of the Finite Element Method (FEM) is known to suffer from the mesh distortion that is induced by large deformations, which has a detrimental impact on the accuracy and stability of the corresponding numerical results. The recently developed Material Point Method (MPM) offers a viable solution to the problem by combining the advantages of both Lagrangian and Eulerian methods, and has therefore received increasing attention within the numerical modelling community.

In this thesis, the MPM has been adopted and further developed for the simulation of dynamic large-deformation problems in fluid-saturated porous materials, with emphasis on the stabilisation of the pore pressure field in the presence of low-order interpolation functions. Particular attention has been placed on developing and verifying the proposed stabilised MPM. As a starting point, an explicit version of the proposed coupled MPM, based on the Generalised Interpolation Material Point (GIMP) method, is implemented. Several numerical challenges, such as (i) the implementation of a single-point two-field dynamic formulation, and (ii) the mitigation of pore pressure oscillations, are tackled and discussed in detail. The resulting explicit GC-SRI-patch method includes the use of: (i) selective reduced integration (SRI) for pore pressure evaluation at the central Gauss points of individual background cells; (ii) patch recovery based on a Moving Least Squares Approximation (MLSA) for mapping pore pressure increments from central GPs to Material Point (MPs); (iii) the Composite Material Point Method (MPM) for enhancing the recovery of effective stresses. The analysis of various poroelastic dynamic consolidation problems over a wide range of loading/drainage conditions demonstrates the effectiveness of the explicit GC-SRI-patch method.

Due to the adoption of explicit time integration, the abovementioned (explicit) GC-SRI-patch method, similar to most coupled MPM formulations from the literature, is only conditionally stable, which imposes extreme limitations on the selection of the time step size. As a consequence, the need for stable time integration restricts the applicability of explicit coupled MPM modelling to problems of considerable size and/or duration. A fully implicit stabilised GIMP using a single-point three-field (u-p-U form) formulation is thus proposed, with pore pressure instabilities being remedied through the same MLSA-based patch recovery. Relevant aspects regarding the numerical implementation of the implicit GIMP-patch method are discussed in detail. This novel method is shown to produce accurate, stable, and oscillation-free results for coupled problems associated with different inertial and deformation regimes, and is generally more efficient than the explicit GC-SRI-patch method owing to the use of larger time steps.

Following the development of the implicit GIMP-patch method in a poroelastic framework, its extension to elastoplastic large-deformation problems is introduced. In particular, in order to analyse coupled large-deformation problems in (nearly) incompressible elastoplastic geomaterials, an anti-locking B-bar algorithm is implemented. The effectiveness of the implicit B-bar GIMP-patch method in mitigating the detrimental effects of volumetric locking is highlighted through several practical examples, including (i) a strip footing undergoing both small and large settlements on an incompressible soil, (ii) the failure of an earthen slope, and (iii) the bearing capacity of a strip footing near the crest of a slope. The proposed method is proven to be a suitable tool for simulating the large-deformation failure mechanisms in realistic fluid-saturated geotechnical problems and the quantification of the unstable soil mass during the corresponding failure processes.

In summary, the work presented in this thesis is believed to make significant progress on the applicability of stabilised MPM for large-deformation problems in fluid-saturated geomaterials. The presented new developments will support more efficient and accurate assessment of geohazards and soil-structure interaction in geotechnical engineering practice.