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.

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.

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.

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.

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.

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

Simulation of Dynamic 3D Crack Propagation within the Material Point Method

This paper presents the principles and algorithms for simulation of dynamic crack propagation in elastic bodies by the material point method(MPM),from relatively simple two-dimensional cases to full three-dimensional,mixed-mode crack propagation.The paper is intended to give a summary of the latest achievements on simulation of three-dimensional dynamic crack propagation,which is essentially an unexplored area.Application of the methodology presented in this paper to several dynamic crack propagation problems has shown that the MPM is a reliable and powerful approach for simulating three-dimensional,mixed-mode crack propagation.

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.

Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials

In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip.In addition,the effects of the electrical conductivity of the foundation are taken into account.This model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric potential.The existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point argument.Then,a finite element approximation of the problem is presented.Under some regularity conditions,an optimal order error estimate of the approximate solution is derived.Finally,a successive iteration technique is used to solve the problem numerically and a convergence result is established.

Impact dynamics of granular flow on rigid barriers:insights from numerical investigation using material point method

In order to advance the understanding of the impact dynamics of granular flow in complex geological settings,this paper studied the impact dynamics of granular flow on rigid barriers with a number of Material Point Method(MPM)numerical tests.The impact behavior of granular flow on a rigid barrier was characterized by the initial dynamic impact stage,dynamic surge impact stage,compression impact stage and static stage of granular flow,where the impact force of granular flow was comprised of the dynamic and static forces of granular flow.The impact behavior of granular flow on a rigid barrier was characterized by the states of the fast or slow impact behavior of granular flow.The angle of slope and aspect ratio of granular soil greatly affected the impact behavior of granular flow on a column rigid barrier,where a power model was proposed to quantify the residual(Fnr)-over-maximum(Fnmax)normal impact force ratio of granular flow Fnr⁄Fnmax incorporating the effects of the angle of slope and aspect ratio of granular soil.With the increase of the column rigid barrier up to the semi-infinite column rigid barrier,the impact dynamics of granular flow gradually increased up to a maximum by progressively transforming the overflow into the dynamic surge impact of the incoming flow on the rigid barrier to capture more granular soil of granular flow against the rigid barrier.Presence of water in granular flow,i.e.,a mixture of solid and liquid in granular flow,yielded a dynamic coupling contribution of the solid and liquid,being accompanied by the whole dynamic process of granular flow,on the impact behavior of granular flow on a rigid barrier,where the liquid-phase material of granular flow,i.e.,the water,was predominant to contribute on the normal impact force of granular flow in comparison with the solid-phase material of granular flow.In addition,other factors,e.g.,the shape of rigid barrier(i.e.,the column barrier,arch barrier and circle barrier),and the gravity(i.e.,in the gravitational environment of the Moon,Earth and Mars),greatly affected the impact behavior of granular flow on a rigid barrier as well.

基于t-SNE-AMARS-MPM的空间变异性边坡可靠度分析及大变形破坏模式研究

在考虑参数空间变异性对大变形边坡可靠度评估的影响,特别是在小失效概率的情况下,传统分析方法常因耗时冗长或难以评估大变形失稳破坏而受限.针对这一问题,提出一种结合t分布-随机邻近嵌入、主动学习多元自适应回归样条法和物质点法的新方法,并深入探讨了t分布-随机邻近嵌入对代理模型的优化作用.首先,利用Cholesky分解法离散边坡参数随机场,并通过确定性分析获取训练样本.随后,采用主动学习函数优化代理模型,高效求解边坡安全系数并按升序排列.最后,使用物质点法依次模拟并获取失效样本.以一个两层不排水土坡为例,验证了该方法的有效性.结果表明,所提方法相较于传统随机物质点法,计算量仅为其1.64%,显著提高了计算效率.同时,通过对失效样本的深入剖析,识别出边坡失稳具有4种不同的破坏模式,这些破坏模式的演化过程与土体参数的空间分布紧密相关.尤为值得注意的是,多层渐进破坏模式作为其中破坏过程最为复杂的类型,其对周边环境的威胁尤为显著,需要重点防范.这为边坡工程的风险评估和加固提供了重要依据.

Dynamic collapse characteristics of the tunnel face induced by the shutdown of earth pressure balance shields(EPB):A 3D material point method study

The collapse of the tunnel face is a prevalent geological disaster in tunnelling.This study employs a three-dimensional(3D)material point method(MPM)to simulate the dynamic collapse process and post-failure mechanisms of the tunnel face.The specific focus is on the scenario where the auxiliary air pressure balanced shield with a partially filled chamber is shut down.To assess the suitability of the 3D MPM,numerical solutions are compared with the results from small-scale experimental tests.Subsequently,a series of large-scale numerical simulations is conducted to explore the dynamic collapse characteristics of the tunnel face induced by the shutdown of the EPB shield under various support air pressures and cutter head conditions.The temporal evolution of the accumulated soil masses in the soil chamber and ground responses under different support air pressures,cutter head types and opening ratios are discussed.In particular,the associated surface subsidence due to the tunnel face collapse is determined and compared with empirical solutions.Numerical results confirm the applicability of the 3D MPM for simulating the large-scale tunnel face collapse scenarios,spanning from small to large deformation analysis.

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.

MPM2019 2^(nd) International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction

Objectives We are delighted to invite you to join us at the second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction organised by the Anura3D MPM Research Community （www.Anura3D.com） in January 2019 in Cambridge （MPM2019）. This is the second international conference organised by the Community, following a series of workshops and symposia, sponsored by the FP7 Marie-Curie project MPM-DREDGE, and the success of MPM2017 held in Delft in January 2017.

MPM2019 2^(nd) International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction

Objectives We are delighted to invite you to join us at the second Intemational Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction organised by the Anura3D MPM Research Community （www.Anura3D.com） in January 2019 in Cambridge （MPM2019）. This is the second interna- tional conference organised by the Community, following a series of workshops and symposia, sponsored by the FP7 Marie-Curie project MPM-DREDGE, and the success of MPM2017 held in Delft in January 2017.

MPM 2019 2^(nd) International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction

8-11 January 2019,Cambridge,UK Objectives We are delighted to invite you to join us at the second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction organised by the Anura3D MPM Research Community（www.Anura3D.com）in January 2019 in Cambridge（MPM2019）.

爆轰波碰撞聚能无网格MPM法数值模拟

爆轰聚能经常被应用于工程爆破切割,为了探索新的聚能爆破形式,本文应用无网格MPM法对圆柱筒装药和导爆索多点起爆形式的爆轰波碰撞聚能问题进行三维数值模拟,采用显式积分算法完成爆轰波形成和汇聚过程以及爆轰压力场分布的数值计算,并将数值模拟结果与实验结果做了对比分析。由此验证了无网格MPM法的准确性,也为炸药聚能爆破提供了新的思路和高效的操作方法。