Multiscale modeling of large deformation in geomechanics

Large deformation soil behavior underpins the operation and performance for a wide range of key geotechnical structures and needs to be properly considered in their modeling, analysis, and design. The material point method (MPM) has gained increasing popularity recently over conventional numerical methods such as finite element method (FEM) in tackling large deformation problems. In this study, we present a novel hierarchical coupling scheme to integrate MPM with discrete element method (DEM) for multiscale modeling of large deformation in geomechanics. The MPM is employed to treat a typical boundary value problem that may experience large deformation, and the DEM is used to derive the nonlinear material response from small strain to finite strain required by MPM for each of its material points. The proposed coupling framework not only inherits the advantages of MPM in tackling large deformation engineering problems over the use of FEM (eg, no need for remeshing to avoid mesh distortion in FEM), but also helps avoid the need for complicated, phenomenological assumptions on constitutive material models for soil exhibiting high nonlinearity at finite strain. The proposed framework lends great convenience for us to relate rich grain-scale information and key micromechanical mechanisms to macroscopic observations of granular soils over all deformation levels, from initial small-strain stage en route to large deformation regime before failure. Several classic geomechanics examples are used to demonstrate the key features the new MPM/DEM framework can offer on large deformation simulations, including biaxial compression test, rigid footing, soil-pipe interaction, and soil column collapse.     

Numerical investigation of pile installation effects in sand using material point method

The installation of displacement piles in sand leads to severe changes in the stress state, density and soil properties around the pile tip and shaft, and therefore has a significant influence on the pile bearing capacity. Most current numerical methods predicting pile capacity do not take installation effects into account, as large deformations can lead to mesh distortion and non-converging solutions. In this study, the material point method (MPM) is applied to simulate the pile installation process and subsequent static pile loading tests. MPM is an extension of the finite element method (FEM), which is capable of modelling large deformations and soil-structure interactions. This study utilizes the moving mesh algorithm where a redefined computational mesh is applied in the convective phase. This allows a fine mesh to be maintained around the pile tip during the installation process and improves the accuracy of the numerical scheme, especially for contact formulation. For the analyses a hypoplastic constitutive model for sand is used, which takes into account density and stress dependent behaviour. The model performs well in situations with significant stress level changes because it accounts for very high stresses at the pile tip. Numerical results agree with centrifuge experiments at a gravitational level of 40 g. This analysis confirms the importance of pile installation effects in numerical simulations, as well as the proposed numerical approach’s ability to simulate installation and static load tests of jacked displacement piles.     

A new contact algorithm in the material point method for geotechnical simulations

Contact between stiff structural elements and soil is encountered in many applications in geotechnical engineering. Modelling of such contact is challenging as it often involves impact that would lead to large deformation and failure of the soil. The Material Point Method (MPM) is a mesh‐free method that has been applied to simulate such phenomena. However, the frictional contact algorithm commonly used in MPM only supports Coulomb friction and cannot model fully or partially rough contact conditions in terms of geotechnical engineering. Moreover, because of very different stiffness of contacting materials, the contact force predicted by the previous frictional contact algorithms usually suffers from severe oscillation when applied in structure–soil interaction. This paper presents a new contact algorithm, termed Geo‐contact, designed for geotechnical engineering. In Geo‐contact, a penalty function is incorporated to reduce the oscillation in contact computation, and a limited shear stress is specified along the contact interface. The proposed Geo‐contact algorithm has been implemented to simulate smooth, partially rough and rough contact in typical large deformation penetration problems. The resistance–displacement curves obtained using the Geo‐contact are compared with analytical solutions of limit analysis and large deformation finite element results to verify the accuracy and robustness of the proposed contact algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

Development of an implicit material point method for geotechnical applications

An implicit material point method (MPM), a variant of the finite element method (FEM), is presented in this paper. The key feature of MPM is that the spatial discretisation uses a set of material points, which are allowed to move freely through the background mesh. All history-dependent variables are tracked on the material points and these material points are used as integration points similar to the Gaussian points. A mapping and re-mapping algorithm is employed, to allow the state variables and other information to be mapped back and forth between the material points and background mesh nodes during an analysis. In contrast to an explicit time integration scheme utilised by most researchers, an implicit time integration scheme has been utilised here. The advantages of such an approach are twofold: firstly, it addresses the limitation of the time step size inherent in explicit integration schemes, thereby potentially saving significant computational costs for certain types of problems; secondly, it enables an improved algorithm accuracy, which is important for some constitutive behaviours, such as elasto-plasticity. The main purpose of this paper is to provide a unified MPM framework, in which both quasi-static and dynamic analyses can be solved, and to demonstrate the model behaviour. The implementation closely follows standard FEM approaches, where possible, to allow easy conversion of other FEM codes. Newton’s method is used to solve the equation of motion for both cases, while the formation of the mass matrix and the required updating of the kinematic variables are unique to the dynamic analysis. Comparisons with an Updated Lagrangian FEM and an explicit MPM code are made with respect to the algorithmic accuracy and time step size in a couple of representative examples, which helps to illustrate the relative performance and advantages of the implicit MPM. A geotechnical application is then considered, illustrating the capabilities of the proposed method when applied in the geotechnical field.     

Multiscale insights into classical geomechanics problems

We pay a revisit to some classical geomechanics problems using a novel computational multiscale modelling approach. The multiscale approach employs a hierarchical coupling of the finite element method (FEM) and the discrete element method. It solves a boundary value problem at the continuum scale by FEM and derives the material point response from the discrete element method simulation attached to each Gauss point of the FEM mesh. The multiscale modelling framework not only helps successfully bypass phenomenological constitutive assumptions as required in conventional modelling approaches but also facilitates effective cross‐scale interpretation and understanding of soil behaviour. We examine the classical retaining wall and footing problems by this method and demonstrate that the simulating results can be well validated and verified by their analytical solutions. Furthermore, the study sheds novel multiscale insights into these classical problems and offers a new tool for geotechnical engineers to design and analyse geotechnical applications based directly upon particle‐level information of soils. Copyright © 2015 John Wiley & Sons, Ltd.     

土质滑坡运动全过程物质点法模拟及其应用

物质点法（MPM）属于一种无网格数值计算方法,它可导入各种土体本构模型,考虑土体流固耦合行为,能够有效模拟土质滑坡大变形及超大变形。本文介绍了物质点法基本原理、控制方程与求解格式;基于5种物质点法的多孔介质表征模型,简要回顾了土质滑坡运动全过程物质点法模拟的最新研究进展。采用单套单相物质点模型,对深圳“12·20”人工堆填土滑坡全过程进行了物质点法模拟,使用了线性加载方式确定初始应力场,并使用了Drucker-Prager屈服准则弹塑性本构模型、GIMP算法与MUSL求解格式。模拟结果表明,该边坡发生失稳后,最大滑距达510m,滑坡范围纵向间距为1050m,最小滑坡角5.95°,均与观测结果相吻合。土体内部等效塑性应变区的演化趋势显示,滑坡机制为渐进式破坏,具体表现为:坡趾土体首先沿基岩界面发生剪切破坏,随后坡顶出现拉张裂隙,坡趾与坡顶塑性区分别沿基岩界面向坡体内部发育,形成贯通滑动面后滑动加速,超大变形出现。物质点法模拟滑坡运动全过程有助于理解滑坡致灾行为,可为滑坡防治提供参考。     

弹塑性土质边坡的ALE方法有限元分析

有限元法被广泛用于解决几何和材料非线性的问题,但标准的有限元方法难以有效解决某些材料的大变形问题和计算中的网格扭曲问题。任意拉格朗日-欧拉法（ALE法）吸取了拉格朗日和欧拉法的优点,并克服了两者的缺点,可用于解决仅用拉格朗日或欧拉有限元法所难以解决的问题。基于ALE有限元方法和弹塑性大变形基本原理,研究了岩土工程中土质边坡在自重作用下的稳定问题;计算结果不仅能直观地显示失稳时的大变形状态,并能确定较符合实际的临界滑移面形状;同时分析了含软弱夹层复杂土质边坡的稳定性。结果表明,ALE方法能有效分析土质边坡的稳定性问题,适用于岩土工程的弹塑性分析。     

基于物质点法的土体流动大变形过程数值模拟

土体滑坡作为一种自然地质灾害,受自然因素和人类活动的影响在我国时有发生,给周围居民的生命和财产安全带来了很大威胁,日益受到人们的广泛关注。滑坡防治也逐渐成为工程研究的热点之一。土体本质上是一种具有复杂组成结构的颗粒材料堆积体,通过对颗粒流动的模拟可以深入理解自然界中的土体流动现象,如滑坡、泥石流等,进而预测灾害破坏范围及改进相应工程防护措施。但由于土体流动是一个涉及大变形及大位移的复杂流动过程,传统的基于网格的有限元法（FEM）由于网格畸变,并不适合这类问题的研究。本文采用物质点法（MPM）模拟土体流动大变形问题。作为一种源于particle-in-cell（PIC）法的无网格法,兼具欧拉法和拉格朗日法的优点,因而,物质点法在处理大变形问题上具有独特的优势。目前,国内外利用物质点法模拟边坡滑动问题已有不少研究,但对相关参数进行敏感性分析的较少。本文基于物质点法模拟了黏性土体及无黏性土体流动大变形问题,并进行了参数敏感性分析,包括土体材料的内摩擦角、黏聚力、高宽比、底面坡度对土体滑动距离的影响规律。本文计算中采用Drucker-Prager（DP）弹塑性本构模型描述土的非线性特性。研究结果表明:（1）基于物质点法得到的土体的流动形态、滑动距离以及自然休止角等数值模拟结果均与文献中的实验结果基本吻合,验证了物质点法模拟土体大变形力学行为的精度及有效性;（2）随着内摩擦角、黏聚力的增大,滑动距离相应减小;（3）坡度对边坡稳定的影响是显著的,随着底面坡度的增大,滑动距离相应增大;（4）当土柱高宽比较小时,与滑动距离呈线性增长关系。其中,内摩擦角和黏聚力反映了土体的抗剪切性能,因此通过工程措施提高土体的抗剪能力可以降低土体滑坡带来的危害。研究结果为探索土体滑动破坏规律,降低滑动破坏范围提供了可靠的参考。     

Application of a Coupled Eulerian–Lagrangian approach on geomechanical problems involving large deformations

Geotechnical boundary value problems involving large deformations are often difficult to solve using the classical finite element method. Large mesh distortions and contact problems can occur due to the large deformations such that a convergent solution cannot be achieved. Since Abaqus, Version 6.8, a new Coupled Eulerian–Lagrangian (CEL) approach has been developed to overcome the difficulties with regard to finite element method and large deformation analyses. This new method is investigated regarding its capabilities. First, a benchmark test, a strip footing problem is investigated and compared to analytical solutions and results of comparable finite element analyses. This benchmark test shows that CEL is well suited to deal with problems which cannot be fully solved using FEM. In further applications the CEL approach is applied to more complex geotechnical boundary value problems. First, the installation of a pile into subsoil is simulated. The pile is jacked into the ground and the results received from these analyses are compared to results of classical finite element simulations. A second case study is the simulation of a ship running aground at an embankment. The results of the CEL simulation are compared to in situ measurement data. Finally, the capabilities of the new CEL approach are evaluated regarding its robustness and efficiency.     

An assessment of the material point method for modelling large scale run-out processes in landslides

This paper demonstrates the predictive capabilities of a numerical model based on continuum mechanics for the simulation of run-out processes during landslides. It assesses a particle-based method that takes advantage of a double Lagrangian-Eulerian discretization and known as the material point method (MPM). Attention is given to the post-failure behaviour and, in particular, to the computation of important quantities such as run-out distance, maximum velocity and energy release. The MPM is a step forward in computational solid mechanics and has the potential to simulate large deformations such as those occurring during landslides. A validation is conducted based on simulations of two case studies of different scales, namely the Tokai-Hokuriku expressway failure in Japan and the Vajont landslide in Italy. The results show a very good agreement with field and other numerical observations.     

A novel computational approach for large deformation and post‐failure analyses of segmental retaining wall systems

Segmental retaining wall (SRW) systems are commonly used in geotechnical practice to stabilize cut and fill slopes. Because of their flexibility, these systems can tolerate minor movements and settlements without incurring damage or crack. Despite these advantages, very few numerical studies of large deformations and post‐failure behavior of SRW systems are found in the current literature. Traditional numerical methods, such as the finite element method, suffer from mesh entanglement, thus are unable to simulate large deformations and flexible behavior of retaining wall blocks in SRW systems. To overcome the above limitations, a novel computational framework based on the smoothed particle hydrodynamics (SPH) method was developed to simulate large deformations and post‐failure behavior of soils and retaining wall blocks in SRW systems. The proposed numerical framework is a hybrid continuum/discontinuum approach that can model soil as an elasto‐plastic material and retaining wall blocks as independent rigid bodies associated with both translational and rotational degrees of freedom. A new contact model is proposed within the SPH framework to simulate the interaction between the soil and the blocks and between the blocks. As an application of the proposed numerical method, a two‐dimensional simulation of an SRW collapse was simulated and compared to experimental results conducted under the same conditions. The results showed that the proposed computational approach provided satisfactory agreement with the experiment. This suggests that the new framework is a promising numerical approach to model SRW systems. Copyright © 2014 John Wiley & Sons, Ltd.     

Simulation-based calibration of geotechnical parameters using parallel hybrid moving boundary particle swarm optimization

Simulation-based optimization methods have been recently proposed for calibrating geotechnical models from laboratory and field tests. In these methods, geotechnical parameters are identified by matching model predictions to experimental data, i.e. by minimizing an objective function that measures the difference between the two. Expensive computational models, such as finite difference or finite element models are often required to simulate laboratory or field geotechnical tests. In such cases, simulation-based optimization might prove demanding since every evaluation of the objective function requires a new model simulation until the optimum set of parameter values is achieved. This paper introduces a novel simulation-based “hybrid moving boundary particle swarm optimization” (hmPSO) algorithm that enables calibration of geotechnical models from laboratory or field data. The hmPSO has proven effective in searching for model parameter values and, unlike other optimization methods, does not require information about the gradient of the objective function. Serial and parallel implementations of hmPSO have been validated in this work against a number of benchmarks, including numerical tests, and a challenging geotechnical problem consisting of the calibration of a water infiltration model for unsaturated soils. The latter application demonstrates the potential of hmPSO for interpreting laboratory and field tests as well as a tool for general back-analysis of geotechnical case studies.     

横向荷载下桩-土相互作用的无网格分析

基于新型的岩土工程数值分析方法--无网格Galerkin法,利用移动最小二乘法所具备的局部化技术,引入不同材料介质之间材料不连续问题的无网格求解方法,对横向荷载作用下桩-土相互作用特性进行了无单元数值模拟分析,并采用MATLAB语言编制出相应的计算程序,由此对不同荷载作用大小、桩周土性质及桩-土刚度比等因素对桩身受力变形特性的影响进行了对比分析,获得了一些定性的结论。工程实例应用结果表明,这一方法在精度和后处理方面比传统的有限元等数值方法更具优势,且计算结果与通用有限元软件ANSYS计算结果吻合良好。     

Data assimilation using the particle filter for identifying the elasto‐plastic material properties of geomaterials

A computational method, incorporating the finite element model (FEM) into data assimilation using the particle filter, is presented for identifying elasto‐plastic material properties based on sequential measurements under the known changing traction boundary conditions to overcome some difficulties in identifying the parameters for elasto‐plastic problems from which the existing inverse analysis strategies have suffered. A soil–water coupled problem, which uses the elasto‐plastic constitutive model, is dealt with as the geotechnical application. Measured data on the settlement and the pore pressure are obtained from a synthetic FEM computation as the forward problem under the known parameters to be identified for both the element tests and the ground behavior during the embankment construction sequence. Parameter identification for elasto‐plastic problems, such as soil behavior, should be made by considering the measurements of deformation and/or pore pressure step by step from the initial stage of construction and throughout the deformation history under the changing traction boundary conditions because of the embankment or the excavation because the ground behavior is highly dependent on the loading history. Thus, it appears that sequential data assimilation techniques, such as the particle filter, are the preferable tools that can provide estimates of the state variables, that is, deformation, pore pressure, and unknown parameters, for the constitutive model in geotechnical practice. The present paper discusses the priority of the particle filter in its application to initial/boundary value problems for elasto‐plastic materials and demonstrates a couple of numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.     

A multiscale work-analysis approach for geotechnical structures

This paper presents a second-order work analysis in application to geotechnical problems by using a novel effective multiscale approach. To abandon complicated equations involved in conventional phenomenological models, this multiscale approach employs a micromechanically-based formulation, in which only four parameters are involved. The multiscale approach makes it possible a coupling of the finite element method (FEM) and the micromechanically-based model. The FEM is used to solve the boundary value problem (BVP) while the micromechanically-based model is utilized at the Gauss point of the FEM. Then, the multiscale approach is used to simulate a three-dimensional triaxial test and a plain-strain footing. On the basis of the simulations, material instabilities are analyzed at both mesoscale and global scale. The second-order work criterion is then used to analyze the numerical results. It opens a road to interpret and understand the micromechanisms hiding behind the occurrence of failure in geotechnical issues.     

A GPU parallel computing strategy for the material point method

The material point method (MPM), which is a combination of the finite element and meshfree methods, suffers from significant computational workload due to the fine mesh that is required in spite of its advantages in simulating large deformations. This paper presents a parallel computing strategy for the MPM on the graphics processing unit (GPU) to boost the method’s computational efficiency. The interaction between a structural element and soil is investigated to validate the applicability of the parallelisation strategy. Two techniques are developed to parallelise the interpolation from soil particles to nodes to avoid a data race; the technique that is based on workload parallelisation across threads over the nodes has a higher computational efficiency. Benchmark problems of surface footing penetration and a submarine landslide are analysed to quantify the speedup of GPU parallel computing over sequential simulations on the central processing unit. The maximum speedup with the GPU used is ∼30 for single-precision calculations and decreases to ∼20 for double-precision calculations.     

An operator‐split ALE model for large deformation analysis of geomaterials

Analysis of large deformation of geomaterials subjected to time‐varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator‐split arbitrary Lagrangian–Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid–fluid coupling and strong material non‐linearity. Each time step of the operator‐split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one‐dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd.     

MT有限元模拟中截断边界的影响

利用有限元方法进行大地电磁正演数值模拟时,由于是在有限网格区域上的数值计算,模拟计算时的网格边界为截断边界,而有限元数值模拟时的大地电磁场边界条件需要在足够远处才能够满足,所以截断边界的存在可能会使大地电磁正演模拟的边界条件无法满足,致使对计算结果和计算精度产生影响。利用有限元二维正演程序,在网格边界处加载一维情况下的大地电磁场,然后固定研究区域的网格剖分,并对一维地电模型和二维地电模型在改变有限元网格边界大小的情况下进行计算。在对一维模型进行模拟计算时,截断边界对边界条件没有影响,边界条件自然满足。而对二维模型进行模拟计算时,截断边界的存在对计算结果有较大影响。利用趋肤深度作为有限元网格边界变化的量度,通过改变网格边界大小,对不同的二维地电模型进行计算比较,总结出适合大地电磁有限元正演模拟的参考网格边界。     

Elastic–plastic analysis of geotechnical problems by mathematical programming

A numerical technique, based on a mathematical programming algorithm, is presented for the solution of geotechnical problems where elastic-plastic material behaviour is considered. The proposed approach can be adopted for geotechnical media characterized by any suitable yield condition, accounting, if necessary, for workhardening behaviour. The loading process is subdivided into a series of steps applied to a finite element mesh with geometry and material properties constant along each step, but with possible changes between subsequent steps. As an application some typical geotechnical problems are analysed by means of the proposed algorithm and a comparison is made between the available in situ measurements and the numerical results.     

边坡变形破坏过程的大变形有限元分析

在用有限元法分析边坡稳定性时,引入计算大变形问题的更新的拉格朗日方法,推导了边坡大变形弹塑性有限元分析的方程式。采用边坡某一幅值的等效塑性剪应变区,从坡脚到坡顶贯通前的折减系数作为边坡安全系数。在此基础上,采用弹塑性大变形有限元分析软件计算了均质土坡不同坡角的安全系数,将其与小变形分析的结果进行了对比分析,结果表明：用弹塑性大变形有限元分析边坡失稳破坏的过程中,既考虑了岩土材料的非线性,又考虑了边坡的几何非线性,使计算结果更趋合理。并结合东深供水改造工程BIII2边坡进行了大变形有限元分析,计算结果与勘查到的实际边坡的滑动面分布位置比较接近。研究表明：该方法尤其适宜于软土类边坡或基坑的稳定性分析。