This paper presents a stability study on the collapse mechanisms of a plane-strain tunnel face in c-ϕ soils using the upper bound finite element method with rigid translatory moving elements (UBFELA-RTME) and nonlinear programming technique. Practical considerations are given to the unlined length influence behind the tunnel face. An advanced mesh adaptive updating strategy is adopted, aiming to improve the computational efficiency, the accuracy of upper-bound solutions, as well as the produced collapse mechanisms. The unlined length influence on the face stability and collapse mechanism of the tunnel face are determined with various combinations of tunnel depth ratios, soil friction angles, and dilatancy angles. Using the UBFELA-RTME with the Davis's approach and a mesh adapting strategy, the non-associated plasticity flow rule can be well approximated. The developed technique was validated against different numerical methods, and it is concluded that the tunnel face stability can be improved by increasing soil friction and dilatancy angles, and yet weakens as the unlined length increases where a mesh-liked collapse zone gradually appears on the tunnel vault top. It gradually evolves to a global collapse failure till the ground surface. The findings contribute to a better understanding of the ground surface failure under the unlined support length influence in tunnel construction.@en

The material point method (MPM) has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformation. In this paper, we survey the current state-of-the-art in the MPM simulation of hydro-mechanical behaviour in two-phase porous geomaterials. The review covers the recent advances and developments in the MPM and their extensions to capture the coupled hydro-mechanical problems involving large deformations. The focus of this review is aiming at providing a clear picture of what has or has not been developed or implemented for simulating two-phase coupled large deformation problems, which will provide some direct reference for both practitioners and researchers.@en

The Material Point Method (MPM) has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformations. This study extends the implicit GIMP-patch method for coupled poroelastic problems recently proposed by Zheng et al. (2021b) to tackle large-deformation problems in (nearly) isochoric elastoplastic geomaterials, particularly by remedying the numerical inaccuracies caused by volumetric locking, such as spurious stress oscillations and an excessively stiff overall response of the system at hand. To overcome these difficulties in two-phase coupled analyses, the B¯ approach of Hughes (1980) is incorporated into an existing version of the implicit GIMP-patch method. Details regarding the formulation and implementation of the proposed method are provided, while several benchmark problems are numerically analysed to evaluate its performance in the presence of elastoplastic behaviour. Particular emphasis is placed on (i) mitigating effective stress oscillations and (ii) solving several two-phase, coupled, large deformation geotechnical problems. The numerical results confirm the suitability of the implicit B¯ GIMP-patch method for the solution of geotechnical problems spanning weak to strong hydro-mechanical coupling and small to large deformations.@en

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.@en

This study presents the formulation and implementation of a fully implicit stabilised Material Point Method (MPM) for dynamic problems in two-phase porous media. In particular, the proposed method is built on a three-field formulation of the governing conservation laws, which uses solid displacement, pore pressure and fluid displacement as primary variables (u–p–U formulation). Stress oscillations associated with grid-crossing and pore pressure instabilities near the undrained/incompressible limit are mitigated by implementing enhanced shape functions according to the Generalised Interpolation Material Point (GIMP) method, as well as a patch recovery of pore pressures – from background nodes to material points – based on the same Moving Least Square Approximation (MLSA) approach investigated by Zheng et al. [1]. The accuracy and computational convenience of the proposed method are discussed with reference to several poroelastic verification examples, spanning different regimes of material deformation (small versus large) and dynamic motion (slow versus fast). The computational performance of the proposed method in combination with the PARDISO solver for the discrete linear system is also compared to explicit MPM modelling [1] in terms of accuracy, convergence rate, and computation time.@en

Water spewing and muck plugging often occur during earth pressure balance (EPB) shield machines tunnelling in water-rich sandy strata, even though the conventional foam has been employed to condition sandy soils. In this study, a novel thickened foaming agent suitable for EPB shield tunnelling in water-rich sandy strata is developed. In contrast to conventional foam-conditioned sands, the thickened foam-conditioned sand has a low permeability due to the consistent filling of soil pores with the thickened foam, and the initial permeability coefficient decreases by approximately two orders of magnitude. It also exhibits a suitable workability, which is attributed to the enhanced capability of the thickened foam to condition sandy soils. In addition, the effect of concentration on the stability of the foam is explained by the Gibbs-Marangoni effect, and conditioning mechanisms for the thickened foam on sands are discussed from the evolution of foam bubbles.@en

Stress oscillations in the material point method (MPM) are one of the major reasons unrealistic results are obtained. In this paper an investigation of the stress oscillations occurring when using one- and two-phase approaches is performed. Specifically, an axisymmetric benchmark and a two-dimensional plane strain problem are used to demonstrate and investigate the oscillations. Furthermore, a partially reduced integration combined with the GIMP technique (GIMP-R) is implemented to reduce large oscillations. @en

A hybrid material point/finite volume method for the numerical simulation of shallow water waves caused by large dynamic deformations in the bathymetry is presented. The proposed model consists of coupling the nonlinear shallow water equations for the water flow and a dynamic elastoplastic system for the seabed deformation. As a constitutive law, we consider a linear elastic-non-associative plastic model with the Drucker-Prager yield criterion allowing for large deformations under undrained cases. The transfer conditions between these models are achieved by using forces sampled from the hydraulic pressure and the friction terms along the interface between the seabed soil and shallow water. A detailed description regarding the coupled algorithm for the hybrid material point/finite volume method is presented. Several numerical examples are investigated to demonstrate the performance of the finite volume method for simulations of shallow water flow and the material point method for capturing the large deformation process of the solid phase. We also present numerical simulations of an undrained clay column collapse that induced shallow water waves and a dam-break problem to demonstrate the excellent performance of the proposed hybrid material point/finite volume method.@en

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.@en

The material point method (MPM) shows promise for the simulation of large deformations in history-dependent materials such as soils. However, in general, it suffers from oscillations and inaccuracies due to its use of numerical integration and stress recovery at non-ideal locations. The development of a hydro-mechanical model, which does not suffer from oscillations is presented, including a number of benchmarks which prove its accuracy, robustness and numerical convergence. In this study, particular attention has been paid to the formulation of two-phase coupled material point method and the mitigation of volumetric locking caused numerical instability when using low-order finite elements for (nearly) incompressible problems. The numerical results show that the generalized interpolation material point (GIMP) method with selective reduced integration (SRI), patch recovery and composite material point method (CMPM) (named as GC-SRI-patch) is able to capture key processes such as pore pressure build-up and consolidation.@en

Because of the extreme terrain limitations and heavy traffic in congested urban areas, the supporting structures for deep excavations often undergo an asymmetric loading condition at two sides. This article reports the results of an investigation based on detailed numerical modeling of the supporting scheme and mechanical performance of a deep excavation of a metro station having different elevations at two sides. The two proposed types of design schemes for support and excavation were discussed and analyzed to evaluate the suitability of using regular or irregular supporting structures. The mechanical performance of the adopted supporting scheme was then evaluated using three-dimensional numerical analysis and verified via field observations. The results show that the irregular supporting structure functions satisfactorily when subjected to asymmetric loading, and it can also realize semicovered excavation in narrow and congested downtown areas to effectively solve the problem of traffic. The solution presented in this study can provide valuable references for the design of urban deep excavations with an asymmetric side elevation.@en

The stability and collapse mechanism of tunnel faces are simplified conservatively to two-dimensional plane strain models along the longitudinal middle line of tunnel. Using the upper bound finite element method with rigid translatory moving element (UBFEM-RTME), a series of stability factors Ncr and collapse mechanisms displayed with active discontinuities are deduced. The influences of dimensionless buried depth ratio H/D, internal friction angle φ and dilatancy angle ψ on the variations of Ncr and mesh-like collapse mechanisms that are identical to the form of slip lines are discussed. A fitting formula of Ncr for the influence factors H/D and φ is deduced, and the effects of numbers and locations of active discontinuities are also investigated. This study illustrates that the UBFEM-RTME with combination of mesh adaptive updating strategies and reasonable and sufficient mesh density can improve the accuracy of the obtained Ncr values and the refinement of mesh-like collapse mechanism. The results reveal the main characteristics of the ultimate collapse mechanisms of tunnel faces, and they can provide theoretical supports for the stability evaluations of tunnel faces and pre-reinforcement scheme of soil strata.@en

The stability and collapse mechanism of tunnel faces are simplified conservatively to two-dimensional plane strain models along the longitudinal middle line of tunnel. Using the upper bound finite element method with rigid translatory moving element (UBFEM-RTME), a series of stability factors Ncr and collapse mechanisms displayed with active discontinuities are deduced. The influences of dimensionless buried depth ratio H/D, internal friction angle φ and dilatancy angle ψ on the variations of Ncr and mesh-like collapse mechanisms that are identical to the form of slip lines are discussed. A fitting formula of Ncr for the influence factors H/D and φ is deduced, and the effects of numbers and locations of active discontinuities are also investigated. This study illustrates that the UBFEM-RTME with combination of mesh adaptive updating strategies and reasonable and sufficient mesh density can improve the accuracy of the obtained Ncr values and the refinement of mesh-like collapse mechanism. The results reveal the main characteristics of the ultimate collapse mechanisms of tunnel faces, and they can provide theoretical supports for the stability evaluations of tunnel faces and pre-reinforcement scheme of soil strata.@en