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.

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.

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 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.

基于物质点和深度积分耦合模型的滑坡数值分析

深度积分算法可将滑坡沿地表滑动的三维模型化简为二维模型进行求解,通过减少控制方程未知量的个数以提升求解效率。物质点法(material point method,MPM)具有无网格法和有网格法的双重优势,模拟滑坡大变形问题时可避免网格畸变现象。采用深度积分耦合物质点法建立滑坡数值模型,给出算法实现具体流程,基于影响域改进的物质点法(influence domain material point method,IDMPM),针对两个典型无倾角底面光滑和有倾角底面不光滑滑坡算例进行基准测试。在计算精度方面,深度积分耦合物质点法模型能较好地预测远端距离、流速、深度等滑移特征参数;在计算效率方面,与常规物质点法求解格式相比,深度积分耦合物质点法模型可大幅度提高运行效率。该研究成果可为滑坡地质灾害破坏范围的分析预测、危害评估、应急抢险提供有效理论依据和时间保障。

一种基于物质点法的熔冰仿真方法

为了解决拉格朗日法模拟熔冰时产生的穿模现象,提出一种基于物质点法的熔冰仿真方法。首先,将欧拉空间中的每个拉格朗日粒子视为固-液双相耦合的集合体,实现固相到液相的平稳过渡;其次,在物质点法背景网格上计算热能,采用预处理共轭梯度法求解相变过程的温度线性系统;最后,对潜热现象进行处理,引入虚拟水模型,通过限制虚拟水的移动来实现对冰块外部水流现象的仿真。实验结果表明,该方法不仅能够利用物质点法处理自碰撞的优势解决穿模现象,而且能模拟出真实的潜热过程的水流现象。

基于物质点法的深部煤层水射流破岩成孔机制和影响因素

我国深部煤层气资源丰富,但深部煤层渗透率极低,高应力−压力环境下深部煤层气解吸困难,导致产量低下。水平井水射流冲孔造穴是一种大范围卸压增透煤层的新技术,但在深部赋存环境下其破岩成孔机制还有待研究。由于深部煤层赋存于高地应力、高应力差的地质环境,室内物理模拟实验难以开展。因此,首先基于黏弹塑性理论和物质点法建立了水射流冲孔破岩数值模型,该模型集成拉格朗日和欧拉算法的优势,能有效模拟射流破岩过程中的动量交换、煤岩大变形、破岩、流体剥蚀携岩反排等全过程。然后,通过该数值模型开展了深部煤层水射流破岩成孔机制和影响因素研究,得到结论如下:①深部煤层以高地应力荷载作用造成的剪切破坏为破岩的主导机制,射流主要起到冲蚀和携岩反排的作用,而无应力荷载时以水射流碰撞煤岩产生的应力波造成张拉破坏为破岩的主导机制,由于煤岩塑性较强,水楔效应不明显。②深部煤层高地应力荷载作用加速了破岩过程,冲出煤量比无应力荷载时高,同时应力荷载促使煤体向开孔方向移动,造成空腔体积减小,但塑性损伤区较无应力荷载时明显增大。③冲出煤量、塑性损伤区面积都随射流时间增加而增加,但增幅逐渐变缓。冲出煤量、塑性损伤区面积随入射角度的增加整体呈下降趋势,射流角度越小,水射流冲孔破岩效果越好,射流垂直入射并不是破岩的最佳方式。④冲出煤量、塑性损伤区面积随应力差、煤岩开孔宽度的增加而增加,但应力差的增加对深部煤层射流破岩的促进作用不大。煤层开孔宽度不宜过高,适当增加开孔宽度可以提高射流破岩效率。

基于MATLAB矢量化物质点法的车身防撞梁碰撞分析

基于MATLAB矢量化的物质点法(material point method,MPM)框架,分析车身前防撞梁的碰撞冲击问题。MPM在每一迭代步将物理参数在物质点和背景网格间相互映射,使用MATLAB矢量化框架可以使用户在快速入门的同时保证求解效率,其应力更新采用车身结构材料的弹塑性本构模型。前防撞梁碰撞冲击数值算例结果表明,MPM可以保证求解精度,同时矢量化技术可以大幅提高求解效率。

基于物质点法的白格滑坡堰塞坝形成过程数值模拟

为准确模拟堰塞坝的形成过程,在物质点方法中引入了滑动速度依赖型的摩擦系数模型,实现了滑面接触算法的求解,并与试验结果对比验证方法的可靠性。在此基础上,反演了白格滑坡堰塞坝的形成过程,探讨了滑床底摩擦对堰塞坝成坝模式的影响规律。研究结果表明:白格滑坡堰塞坝形成过程可分为滑坡体加速运动、河谷制动和堆积成坝三阶段。白格滑坡速度最大达到45 m/s且最大速度位于滑坡体后缘,而滑坡体前缘受到河床底部摩擦影响,速度不稳定,变化幅度大且比滑坡体后缘早20 s制动。不同滑面接触模式决定了滑坡最终堆积成坝的状态:若采用滑动速度依赖型的摩擦系数模型模拟,则能够真实反映白格滑坡堰塞坝堆积状态;采用滑面的峰值摩擦系数计算,则导致计算的白格滑坡运动距离减小了32%,不能形成完全堵塞金沙江的堰塞坝;而采用残余摩擦系数计算,则导致计算的白格滑坡运动距离增大了12%。研究成果对加深堰塞坝成坝模式的认识具有意义,对于滑坡堰塞坝链生灾害预测及防灾减灾应急抢险处置具有一定的参考价值。

物质点法流固交互表面细节优化算法

为了增强现有物质点法流固交互中表面细节,同时改进大量固体粒子对其表面重建没有贡献的问题,提出一种高效的流固交互自适应物质点法.首先使用一种接触面离散积分点方法解决物质点法中出现的数值黏性伪影问题,实现流固移动接触面上粒子的自由滑动;然后引入自适应广义插值方法,在流体和固体的不同区域自适应地调整网格分辨率,增强表面细节;最后采用窄带仿射粒子网格方法,通过粒子重采样减少固体内部粒子数量,从而在节省内存空间的同时减少计算量.利用斯坦福开源模型进行多组消融实验,结果表明,与均匀背景网格物质点法相比,所提方法流固交互表面细节更丰富,消融实验场景下整体粒子数减少80%,平均模拟效率提高50%.

底隙对装药发射安全性影响机理的数值模拟研究

为研究底隙对装药发射安全性的影响机理,基于物质点法建立了冲击载荷下受底隙影响的热-力-固耦合装药燃烧模型。该模型模拟的PBX装药底部温度与实验结果基本一致,验证了模型的正确性。采用该模型模拟了不同底隙厚度时Composition B(COM B)装药的炮弹发射过程,分析了装药温度变化规律。结果表明:发射过程中,COM B装药温度从底部到顶部逐步降低,装药底部最可能出现点火反应;装药底部温度随着底隙厚度的增加而升高。弹底载荷峰值为324.7 MPa时,COM B装药处于安全状态的底隙厚度不超过0.062 cm。底隙中的空气在发射过程中被压缩,其温度极速升高,导致相邻的装药底部易出现点火反应。

基于物质点-特征有限元耦合方法的向后侵蚀管涌模拟

向后侵蚀管涌是汛期堤坝中一种常见的渗透破坏形式,多发生在下游存在无保护出水口的二元结构堤基中。由于土体渗流在出水口处存在较高的水力梯度,使得固、液界面附近的土体极易被侵蚀带走,一旦侵蚀土体的上层存在不透水的黏土层时,便会形成不断向上游迎水侧发展的管涌通道,最终导致堤坝出现失稳破坏。基于向后侵蚀管涌的发展过程,采用局部水力梯度作为管涌发展的判别准则,结合饱和孔隙介质的耦合物质点-特征有限元法,发展了一个能够模拟向后侵蚀管涌的新方法。新方法将求解域内的物质点分为3种粒子类型,对满足管涌触发条件的粒子进行删除,以此表示被侵蚀带走的土颗粒。由于算法中的流体部分采用了广义的Navier-Stokes方程进行描述,因此新方法能够同时计算孔隙水渗流和管道流体的自由流动。通过对小尺度模型试验的计算,验证了新方法在向后侵蚀管涌问题中的适用性。