Material point method simulation of hydro-mechanical behaviour in twophase porous geomaterials: A state-of-the-art review

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.

Mobility and dynamic erosion process of granular flow:insights from numerical investigation using material point method

In order to understand the dynamics of granular flow on an erodible base soil,in this paper,a series of material point method-based granular column collapse tests were conducted to investigate numerically the mobility and dynamic erosion process of granular flow subjected to the complex settings,i.e.,the aspect ratio,granular mass,friction and dilatancy resistance,gravity and presence of water.A set of power scaling laws were proposed to describe the final deposit characteristics of granular flow by the relations of the normalized run-out distance and the normalized final height of granular flow against the aspect ratio,being greatly affected by the complex geological settings,e.g.,granular mass,the friction and dilatancy resistance of granular soil,and presence of water in granular flow.An index of the coefficient of friction of granular soil was defined as a ratio of the target coefficient of friction over the initial coefficient of friction to quantify the scaling extent of friction change(i.e.,friction strengthening or weakening).There is a characteristic aspect ratio of granular column corresponding to the maximum mobility of granular flow with the minimum index of the apparent coefficient of friction.The index of the repose coefficient of friction of granular flow decreased gradually with the increase in aspect ratio because higher potential energy of granular column at a larger aspect ratio causes a larger kinetic energy of granular soil to weaken the friction of granular soil as a kind of velocity-related friction weakening.An increase in granular mass reduces gradually the indexes of the apparent and repose coefficients of friction of granular soil to enhance the mobility of granular flow.The mobility of granular flow increases gradually with the decrease in friction angle or increase in dilatancy angle of granular soil.However,the increase of gravity accelerates granular flow but showing the same final deposit profile without any dependence on gravity.The mobility of granular flow increases gradually by lowering the indexes of the apparent and repose coefficients of friction of granular flow while changing the surroundings,in turn,the dry soil,submerged soil and saturated soil,implying a gradually increased excessive mobility of granular flow with the friction weakening of granular soil.Presence of water in granular flow may be a potential catalyzer to yield a long run-out granular flow,as revealed in comparison of water-absent and water-present granular flows.In addition,the dynamic erosion and entrainment of based soil induced by granular flow subjected to the complex geological settings,i.e.,the aspect ratio,granular mass,gravity,friction and dilatancy resistance,and presence of water,were comprehensively investigated as well.

A hybrid contact approach for modeling soil-structure interaction using the material point method

The grid-based multi-velocity field technique has become increasingly popular for simulating the Material Point Method(MPM)in contact problems.However,this traditional technique has some shortcomings,such as(1)early contact and contact penetration can occur when the contact conditions are unsuitable,and(2)the method is not available for contact problems involving rigid-nonrigid materials,which can cause numerical instability.This study presents a new hybrid contact approach for the MPM to address these limitations to simulate the soil and structure interactions.The approach combines the advantages of point-point and point-segment contacts to implement contact detection,satisfying the impenetrability condition and smoothing the corner contact problem.The proposed approach is first validated through a disk test on an inclined slope.Then,several typical cases,such as granular collapse,bearing capacity,and deformation of a flexible retaining wall,are simulated to demonstrate the robustness of the proposed approach compared with FEM or analytical solutions.Finally,the proposed method is used to simulate the impact of sand flow on a deformable structure.The results show that the proposed contact approach can well describe the phenomenon of soil-structure interaction problems.

Modeling footing resting on anisotropic sand using material point method

Sand typically exhibits anisotropic internal structure which may significantly influence its mechanical behavior. The material point method (MPM) can eliminate mesh distortion and thus is suitable for investigating geotechnical problems with large deformation. In this study, an advanced anisotropic critical state theory (ACST)-based soil model is implemented in MPM to study the response of strip footing resting on anisotropic sand. The capability of the model is verified by simulating several element tests and strip footing tests with different soil densities and fabric bedding plane orientations. For the footing problem with a vertical load, as the fabric bedding plane orientation increases, the bearing capacity decreases and its corresponding settlement increases. The failure pattern becomes asymmetrical when the bedding plane orientation or the loading direction is inclined. A comparison between the simulation results predicted by the anisotropic and isotropic models is made, which demonstrates that neglecting the fabric anisotropy may lead to the overestimation of the bearing capacity.

Modeling pipe-soil interaction under vertical downward relative offset using B-spline material point method

To analyze the pipeline response under permanent ground deformation,the evolution of resistance acting on the pipe during the vertical downward offset is an essential ingredient.However,the efficient simulation of pipe penetration into soil is challenging for the conventional finite element(FE)method due to the large deformation of the surrounding soils.In this study,the B-spline material point method(MPM)is employed to investigate the pipe-soil interaction during the downward movement of rigid pipes buried in medium and dense sand.To describe the density-and stress-dependent behaviors of sand,the J2-deformation type model with state-dependent dilatancy is adopted.The effectiveness of the model is demonstrated by element tests and biaxial compression tests.Afterwards,the pipe penetration process is simulated,and the numerical outcomes are compared with the physical model tests.The effects of pipe size and burial depth are investigated with an emphasis on the mobilization of the soil resistance and the failure mechanisms.The simulation results indicate that the bearing capacity formulas given in the guidelines can provide essentially reasonable estimates for the ultimate force acting on buried pipes,and the recommended value of yield displacement may be underestimated to a certain extent.

Coseismic site response and slope instability using periodic boundary conditions in the material point method

This paper proposed the explicit generalized-a time scheme and periodic boundary conditions in the material point method(MPM)for the simulation of coseismic site response.The proposed boundary condition uses an intuitive particle-relocation algorithm ensuring material points always remain within the computational mesh.The explicit generalized-a time scheme was implemented in MPM to enable the damping of spurious high frequency oscillations.Firstly,the MPM was verified against finite element method(FEM).Secondly,ability of the MPM in capturing the analytical transfer function was investigated.Thirdly,a symmetric embankment was adopted to investigate the effects of ground motion arias intensity(I_(a)),geometry dimensions,and constitutive models.The results show that the larger the model size,the higher the crest runout and settlement for the same ground motion.When using a Mohr-Coulomb model,the crest runout increases with increasing I_(a).However,if the strain-softening law is activated,the results are less influenced by the ground motion.Finally,the MPM results were compared with the Newmark sliding block solution.The simplified analysis herein highlights the capabilities of MPM to capture the full deformation process for earthquake engineering applications,the importance of geometry characterization,and the selection of appropriate constitutive models when simulating coseismic site response and subsequent large deformations.

Coupled GIMP and CPDI material point method in modelling blast-induced three-dimensional rock fracture

Three-dimensional rock fracture induced by blasting is a highly complex problem and has received considerable attention in geotechnical engineering.The material point method is firstly applied to treat this challenging task.Some inherent weaknesses can be overcome by coupling the generalized interpolation material point(GIMP)and the convected particle domain interpolation technique(CPDI).For the media in the borehole,unchanged GIMP-type particles are used to guarantee a homogenous blast pressure.CPDITetrahedron type particles are employed to avoid the fake numerical fracture near the borehole for the rock material.A blasting experiment using three-dimensional single-borehole rock was simulated to examine the applicability of the coupled model under realistic loading and boundary conditions.A good agreement was achieved between the simulation and experimental results.Moreover,the mechanism of three-dimensional rock fracture was analyzed.It was concluded that rock particle size and material parameters play an important role in rock damage.The reflected tensile waves cause severe damage in the lower part of the model.Rayleigh waves occur on the top face of the rock model to induce a hoop failure band.

A Flux Based Approximation to Simulate Coupled Hydromechanical Problems for Mines with Heterogeneous Rock Types Using the Material Point Method

Advances in numerical simulation techniques play an important role in helpingmining engineers understand those parts of the rock mass that cannot be readily observed.The Material Point Method(MPM)is an example of such a tool that is gaining popularity for studying geotechnical problems.In recent years,the original formulation of MPM has been extended to not only account for simulating the mechanical behaviour of rock under different loading conditions,but also to describe the coupled interaction of pore water and solid phases in materials.These methods assume that the permeability of mediums is homogeneous,and we show that these MPM techniques fail to accurately capture the correct behaviour of the fluid phase if the permeability of the material is heterogeneous.In this work,we propose a novel implementation of the coupled MPM to address this problem.We employ an approach commonly used in coupled Finite Volume Methods,known as the Two Point Flux Approximation(TPFA).Our new method is benchmarked against two well-known analytical expressions(a one-dimensional geostatic consolidation and the so-called Mandel-Cryer effect).Its performance is compared to existing coupled MPM approaches for homogeneous materials.In order to gauge the possible effectiveness of our technique in the field,we apply ourmethod to a case study relating to a mine known to experience severe problems with pore water.

A multiscale material point method for impact simulation

To better simulate multi-phase interactions involving failure evolution, the material point method （MPM） has evolved for almost twenty years. Recently, a particle-based multiscale simulation procedure is being developed, within the framework of the MPM, to describe the detonation process of energetic nano-composites from molecular to continuum level so that a multiscale equation of state could be formulated. In this letter, a multiscale MPM is proposed via both hierarchical and concurrent schemes to simulate the impact response between two microrods with different nanostructures. Preliminary results are presented to illustrate that a transition region is not required between different spatial scales with the proposed approach.

Coupling between finite element method and material point method for problems with extreme deformation

As a Lagrangian meshless method, the material point method （MPM） is suitable for dynamic problems with extreme deformation, but its efficiency and accuracy are not as good as that of the finite element method （FEM） for small deformation problems. Therefore, an algorithm for the coupling of FEM and MPM is proposed to take advantages of both methods. Furthermore, a conversion scheme of elements to particles is developed. Hence, the material domain is firstly discretized by finite elements, and then the distorted elements are automatically converted into MPM particles to avoid element entanglement. The interaction between finite elements and MPM particles is implemented based on the background grid in MPM framework. Numerical results are in good agreement with that of both FEM and MPM

Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method

This paper presents a quasi-static implicit generalized interpolation material point method(i GIMP)with B-bar approach for large deformation geotechnical problems.The i GIMP algorithm is an extension of the implicit material point method(iMPM).The global stiffness matrix is formed explicitly and the Newton-Raphson iterative method is used to solve the equilibrium equations.Where possible,the implementation procedure closely follows standard finite element method(FEM)approaches to allow easy conversion of other FEM codes.The generalized interpolation function is assigned to eliminate the inherent cell crossing noise within conventional MPM.For the first time,the B-bar approach is used to overcome volumetric locking in standard GIMP method for near-incompressible non-linear geomechanics.The proposed i GIMP was tested and compared with i MPM and analytical solutions via a 1 D column compression problem.Results highlighted the superiority of the i GIMP approach in reducing stress oscillations,thereby improving computational accuracy.Then,elasto-plastic slope stabilities and rigid footing problems were considered,further illustrating the ability of the proposed method to overcome volumetric locking due to incompressibility.Results showed that the proposed i GIMP with B-bar approach can be used to simulate geotechnical problems with large deformations.

Large deformation analysis of slope failure using material point method with cross-correlated random fields

Large deformation analysis of slope failure is important for hazard and risk assessment of infrastructure.Recent studies have revealed that spatial variability of soil properties can significantly affect the probability of slope failure.However,due to limitations of traditional numerical tools,the influence of spatial variability of soil properties on the post-failure behavior of slopes has not been fully understood.Therefore,in this study,we aimed to investigate the effects of the cross-correlation between cohesion and the friction angle on the probability of slope failure and post-failure behavior(e.g.run-out distance,influence distance,and influence zone)using a random material point method(RMPM).The study showed that mesh size,strength reduction shape factor parameter,and residual strength all play critical roles in the calculated post-failure behavior of a slope.Based on stochastic Monte Carlo simulation,the effects of cross-correlation between cohesion and the friction angle on the probability of slope failure,and its run-out distance,influence distance,influence zone,and sliding volume were studied.The study also showed that material point method(MPM)has great advantages compared with the finite element method(FEM)in handling large deformations.

Runout of submarine landslide simulated with material point method

Most of the present knowledge on submarine landslides relies upon back-analysis of post-failure deposits identified using geophysical techniques.In this paper,the runout of slides on rigid bases is explored using the material point method（MPM）with focus on the geotechnical aspects of the morphologies.In MPM,the sliding material and bases are discretised into a number of Lagrangian particles,and a background Eulerian mesh is employed to update the state of the particles.The morphologies of the slide can be reproduced by tracking the Lagrangian particles in the dynamic processes.A real case history of a submarine slide is back-analyzed with the MPM and also a depth-averaged method.Runout of the slides from steep slopes to moderate bases are reproduced.Then different combinations of soil and basal parameters are assumed to trigger runout mechanisms of elongation,block sliding and spreading.The runout distances predicted by the MPM match well with those from large deformation finite element analysis for the elongation and block sliding patterns.Horst and grabens are shaped in a spreading pattern.However,the current MPM simulations for materials with high sensitivities are relatively mesh sensitive.

Implementation of absorbing boundary conditions in dynamic simulation of the material point method

Outgoing waves arising from high-velocity impacts between soil and structure can be reflected by the conventional truncated boundaries.Absorbing boundary conditions(ABCs),to attenuate the energy of the outward waves,are necessary to ensure the proper representation of the kinematic field and the accurate quantification of impact forces.In this paper,damping layer and dashpot ABCs are implemented in the material point method(MPM)with slight adjustments.Benchmark scenarios of different dynamic problems are modelled with the ABCs configured.Feasibility of the ABCs is assessed through the velocity fluctuations at specific observation points and the impact force fluctuations on the structures.The impact forces predicted by the MPM with ABCs are verified by comparison with those estimated using a computational fluid dynamics approach.

Comparative study of material point method and upper bound limit analysis in slope stability analysis

The upper bound limit analysis(UBLA)is one of the key research directions in geotechnical engineering and is widely used in engineering practice.UBLA assumes that the slip surface with the minimum factor of safety(FSmin)is the critical slip surface,and then applies it to slope stability analysis.However,the hypothesis of UBLA has not been systematically verified,which may be due to the fact that the traditional numerical method is difficult to simulate the large deformation.In this study,in order to systematically verify the assumption of UBLA,material point method(MPM),which is suitable to simulate the large deformation of continuous media,is used to simulate the whole process of the slope failure,including the large-scale transportation and deposition of soil mass after slope failure.And a series of comparative studies are conducted on the stability of cohesive slopes using UBLA and MPM.The proposed study indicated that the slope angle,internal friction angle and cohesion have a remarkable effect on the slip surface of the cohesive slope.Also,for stable slopes,the calculation results of the two are relatively close.However,for unstable slopes,the slider volume determined by the UBLA is much smaller than the slider volume determined by the MPM.In other words,for unstable slopes,the critical slip surface of UBLA is very different from the slip surface when the slope failure occurs,and when the UBLA is applied to the stability analysis of unstable slope,it will lead to extremely unfavorable results.

Validation of material point method for soil fluidisation analysis

The main aim of this paper is to describe and analyse the modelling of vertical column tests that undergo fluidisation by the application of a hydraulic gradient.A recent advancement of the material point method（MPM）,allows studying both stationary and non-stationary fluid flow while interacting with the solid phase.The fluidisation initiation and post-fluidisation processes of the soil will be investigated with an advanced MPM formulation（Double Point）in which the behavior of the solid and the liquid phase is evaluated separately,assigning to each of them a set of material points（MPs）.The result of these simulations are compared to analytic solutions and measurements from laboratory experiments.This work is used as a benchmark test for the MPM double point formulation in the Anura3D software and to verify the feasibility of the software for possible future engineering applications.

Modelling large deformation and soil–water–structure interaction with material point method:Briefing on MPM2017 conference

The 1st International Conference on the Material Point Method for ＂Modelling Large Deformation and Soil–Water–Structure Interaction＂（MPM2017）was held in Delft,The Netherlands on 10-13 January 2017.This is the first conference organised by the Anura3D MPM Research Community,following a series of international workshops and symposia previously held in The Netherlands,UK,Spain and Italy,as part of the European Commission FP7 Marie-Curie project MPM-DREDGE.We are delighted to present seven contributions in this Special Column of the Journal of Hydrodynamics,and take this opportunity to announce that the 2nd conference,MPM2019,will be held in Cambridge,UK in January 2019.

A Hybrid Fluid-Solid Interaction Scheme Combining the Multi-Component Diffuse Interface Method and the Material Point Method

We propose a hybrid scheme combing the diffuse interface method and the material point method to simulate the complex interactions between the multiphase compressible flow and elastoplastic solid.The multiphase flow is modelled by the multi-component model and solved using a generalized Godunov method in the Eulerian grids,while the elastoplastic solid is solved by the classical material point method in a combination of Lagrangian particles and Eulerian background grids.In order to facilitate the simulation of fluid-solid interactions,the solid variables are further interpolated to the cell center and coexist with the fluid in the same cell.An instantaneous relaxation procedure of velocity and pressure is adopted to simulate the momentum and energy transfers between various materials,and to keep the system within a tightly coupled interaction.Several numerical examples,including shock tube problem,gasbubble problem,air blast,underwater explosion and high speed impact applications are presented to validate the numerical scheme.

An Efficient Particle Subdomain Quadrature Scheme for the Material Point Method

The material point method(MPM)has been proved to be an effective numerical method for large deformation problems.However,the MPM suffers from the cell crossing error as that the material particles are used to represent the deformed material and to perform the particle quadrature.In this paper,an efficient subdomain quadrature material point method(sqMPM)is proposed to eliminate the cell crossing error efficiently.The particle domain is approximated to be the line segment,rectangle,and cuboid for the one-,two-,and three-dimensional problems,respectively,which are divided into several different subdomains based on the topological relationship between the particle domain and background grid.A single Gauss quadrature point is placed at the center of each subdomain and used for the information mapping.The material quantities of each Gauss quadrature point are determined by the corresponding material particle and the subdomain volume without the cumbersome reconstruction algorithm.Numerical examples for one-,two-,and three-dimensional large deformation problems demonstrate the effectiveness and highly enhanced convergence and efficiency of the proposed sqMPM.

Coupled Shell-Material Point Method for Bird Strike Simulation

In a bird strike, the bird undergoes large deformation like flows; while most part of the structure is in small deformation, the region near the impact point may experience large deformations, even fail. This paper develops a coupled shell-material point method （CSMPM） for bird strike simulation, in which the bird is modeled by the material point method （MPM） and the aircraft structure is modeled by the Belytschko-Lin-Tsay shell element. The interaction between the bird and the structure is handled by a particle-to-surface contact algorithm. The distorted and failed shell elements will be eroded if a certain criterion is reached. The proposed CSMPM takes full advantages of both the finite element method and the MPM for bird strike simulation and is validated by several numerical examples.