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.     

基于二阶锥规划有限元增量加载法的条形浅基础极限承载力分析

地基极限承载力分析是土力学研究中的一个经典课题。基于Hellinger-Reissner混合变分原理和有限元方法,将岩土体弹塑性问题构造成基于有限元框架的二阶锥规划（second-order cone programming,SOCP）问题,进而提出一种基于二阶锥规划理论的增量有限元法,即FEM-SOCP法。将岩土体弹塑性问题构造成二阶锥规划的数学优化问题,可以避免采用传统弹塑性计算中复杂的应力点积分等算法和屈服面棱角的平滑处理。此外,对于二阶锥规划问题,可以采用具有原始?对偶内点求解法的标准数学规划求解器MOSEK进行求解。将增量加载FEM-SOCP法应用于经典的基底粗糙的条形浅基础地基极限承载力分析中,分别考虑了关联和非关联塑性条件下的Mohr-Coulomb屈服准则。数值结果表明：所提出的增量加载FEM-SOCP法获得的地基承载力系数及地基承载力与传统FEM计算结果基本一致,而与常规有限元计算结果相比,基于增量加载的FEM-SOCP法所获得的屈服区更加平滑。     

A practical co-simulation approach for multiscale analysis of geotechnical systems

The particulate nature of granular soils can be accurately simulated at a microscale level. However, due to the huge spatial extent of geotechnical systems, a model fully constructed at such a scale is almost impossible with current computing technologies. Hence, continuum-based approaches are considered as the practical scale for modeling the majority of problems. Combining both scales enables benefiting from the advantages of both techniques while trying to overcome their drawbacks. Although a significant number of publications have addressed coupling both scales, only a few provide information regarding implementing the proposed procedures. In this study, an efficient co-simulation framework for conducting multiscale analysis is introduced. The framework is based on integrating existing continuum and micromechanical modeling software packages and therefore benefitting from already existing codes. A computational simulation of a rigid pile in contact with granular soil demonstrating the capabilities of such technique is presented. The near-field zone surrounding the pile is modeled using DEM whereas FEM is utilized to model far-field zones that are not affected by the presence of the pile. Results of conducted simulations resemble those obtained from experimental results. The proposed approach appears to be a very effective and promising tool to model boundary value problems of geotechnical systems.     

强度折减有限元法中锚杆计算模型研究

针对目前岩土工程中锚杆数值模型存在的局限性,受商用软件中锚杆强度模型的启发而提出了一种适用于强度折减有限元法的锚杆强度模型,并建议了考虑锚杆强度折减的强度折减方法,研制了相应程序。该模型应用于岩坡锚固计算,计算结果说明了模型的有效性;应用于土质边坡稳定性评估计算,结果表明模型方便可行。     

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 modelling of seismic slope failure using MPM

The Finite Element Method (FEM) is widely used in the simulation of geotechnical applications. Owing to the limitations of FEM to model problems involving large deformations, many efforts have been made to develop methods free of mesh entanglement. One of these methods is the Material Point Method (MPM) which models the material as Lagrangian particles capable of moving through a background computational mesh in Eulerian manner. Although MPM represents the continuum by material points, solution is performed on the computational mesh. Thus, imposing boundary conditions is not aligned with the material representation. In this paper, a non-zero kinematic condition is introduced where an additional set of particles is incorporated to track the moving boundary. This approach is then applied to simulate the seismic motion resulting in failure of slopes. To validate this simulation procedure, two geotechnical applications are modelled using MPM. The first is to reproduce a shaking table experiment where the results of another numerical method are available. After validating the present numerical scheme for relatively large deformation problem, it is applied to simulate progression of a large-scale landslide during the Chi-Chi earthquake of Taiwan in which excessive material deformation and transportation is taking place.     

基于饱和渗透系数空间变异结构的斜坡渗流及失稳特征

以往研究一般采用单随机变量方法（SRV）或基于水平或垂直方向波动范围生成的空间变异随机场来模拟岩土参数的空间变异性,对具有倾斜定向特征的空间变异随机场未有涉及.基于条件模拟相关理论和非侵入式随机有限元的理论框架,提出了利用序贯高斯模拟方法进行斜坡参数条件随机场模拟并运用有限元方法进行斜坡渗流和稳定性分析的方法.针对理想边坡,对各向同性和几何各向异性的共7种空间变异结构的饱和渗透系数（K_s）各进行了200次条件随机场模拟,基于条件随机场模拟结果进行了有限元渗流和稳定性计算,对每种空间变异结构多次计算结果进行了统计分析.结果表明:本文所提出的方法不仅再现了研究区域参数的空间二阶统计特性,通过设定变异函数参数进行不同空间变异类型、变异程度、变异定向性的随机场模拟,同时利用现场观测数据对随机场模拟结果进行条件限制,从而提高了随机场的赋值精度;K_s的空间变异结构对孔隙水压力的分布规律、地下水位线变化范围、稳定性系数和最危险滑动面分布特征均有一定程度的影响.本研究为库岸斜坡稳定性评价提供方法支撑.      

桩基水平位移的有限元模拟

有限元数值计算方法在岩土工程中已有较多的应用,但在水平受荷桩分析计算中的应用尚不普遍。有关水平受荷桩土体系水平承载力及变形的数值模拟方法少有文献报道。采用有限元数值模拟方法来研究水平受荷桩土体系的水平位移。首先简要分析了水平受荷桩的主要计算方法及原理。然后,基于ABAQUS软件建立了桩土系统二维及三维的有限单元模型,分别通过按现行规范推荐的m法和按Poulos的弹性理论法计算的两个算例,将数值计算方法与解析方法进行了对比计算分析。有限元数值计算结果与解析解基本吻合,说明了所采用有限元数值模拟方法的可靠性及有效性。     

自然单元法在岩土工程中应用两例

自然单元法(NEM)是较近出现的一种无网格方法,其形函数兼有无网格的特点和传统有限元的优点,是一种理想的适合岩土工程问题计算的新型数值方法。介绍了自然单元法的基本原理和特性,并讨论了其在岩土工程中的具体应用。将Goodman单元引入自然单元法以实现对不连续面的模拟,研究表明,在NEM中加入节理单元的总体原则和具体的实施细节与FEM中完全相同;而在一般的无网格方法中,则稍微复杂一点。为了实现对岩土工程中常见的无限域或半无限域问题的模拟,引入了无界单元;由于自然单元法的特性,自然单元法和无界元可实现无缝“耦合”。具体的数值算例验证了上述思路。     

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.     

Three‐dimensional simulations of tensile cracks in geomaterials by coupling meshless and finite element method

Failure in geotechnical engineering is often related to tension‐induced cracking in geomaterials. In this paper, a coupled meshless method and FEM is developed to analyze the problem of three‐dimensional cracking. The radial point interpolation method (RPIM) is used to model cracks in the smeared crack framework with an isotropic damage model. The identification of the meshless region is based on the stress state computed by FEM, and the adaptive coupling of RPIM and FEM is achieved by a direct algorithm. Mesh‐bias dependency, which poses difficulties in FEM‐based cracking simulations, is circumvented by a crack tracking algorithm. The performance of our scheme is demonstrated by two numerical examples, that is, the four‐point bending test on concrete beam and the surface cracks caused by tunnel excavation. Copyright © 2014 John Wiley & Sons, Ltd.     

基于PSO-MLSSVR的土体参数反演方法在深基坑工程中的应用

为了确保基坑工程安全,常常会采用数值模拟的方法预测支护结构的位移,其中岩土体力学参数的选取对于结果的影响最大.本文使用了一种粒子群(PSO)算法结合多输出最小二乘支持向量回归机(MLSSVR)的基坑土体参数位移反分析法,以深圳某深基坑的支护桩顶水平位移监测数据为依据,基于正交设计生成具有代表性的土体参数组合,通过有限元...     

Efficient conditional modeling for geotechnical uncertainty evaluation

A first‐order Taylor series method including direct derivative coding (DDC) is presented as a computationally efficient method for producing the probability distribution associated with calculated geotechnical performance. The probability distribution is employed in reliability analyses to calculate the probability of failure, valuable information that is not typically associated with deterministic analyses. The probability distribution also is used to identify important input parameters and to direct sampling efforts. Another approach to generate the probability distribution is the Monte Carlo (MC) method, however, Taylor series results generally are calculated in less time than the MC approach. One key to the implementation of the Taylor series approach is efficient approximation of the sensitivities required by the Taylor series calculation. DDC provides the technique to produce an efficient Taylor series algorithm. Directly coding the sensitivity analysis into the engineering model is accomplished by automatic and hand programming of derivatives. ADIFOR 2.0 was employed to automatically add derivatives to an existing engineering analysis model. For this paper a meshing program and 3D FEM for soil deformation is used to demonstrate the DDC approach. Although DDC requires a large up‐front programming effort, it is not site or data specific. Therefore, once the derivative programming has been performed, the numerical model can be applied to a wide variety of problems without additional user intervention. Copyright © 2001 John Wiley & Sons, Ltd.     

多尺度有限单元法求解非均质多孔介质中的三维地下水流问题

应用多尺度有限单元法模拟非均质多孔介质中的三维地下水流问题。与传统有限单元法相比，多尺度有限单元法的基函数具有能反映单元内参数变化的优点，所以这种方法能在大尺度上抓住解的小尺度特征获得较精确的解。在介绍多尺度有限单元法求解非均质多孔介质中三维地下水流问题的基本原理之后，对参数水平方向渐变垂直方向突变的非均质多孔介质中的三维地下水流和Borden实验场的三维地下水流分别用多尺度有限单元法和传统等参有限单元法进行了计算，结果表明在模拟高度非均质多孔介质中的三维地下水流问题时，多尺度有限单元法比传统有限单元法有效，既节省计算量又有较高的精度；在模拟非均质性弱的多孔介质中的三维地下水流问题时，多尺度有限单元法虽然也能在大尺度上获得较为精确的解，但效果不明显。     

Probabilistic stability analyses of slopes using the ANN-based response surface

Slope stability analysis is a geotechnical engineering problem characterized by many sources of uncertainty. Some of these sources are connected to the uncertainties of soil properties involved in the analysis. In this paper, a numerical procedure for integrating a commercial finite difference method into a probabilistic analysis of slope stability is presented. Given that the limit state function cannot be expressed in an explicit form, an artificial neural network (ANN)-based response surface is adopted to approximate the limit state function, thereby reducing the number of stability analysis calculations. A trained ANN model is used to calculate the probability of failure through the first- and second-order reliability methods and a Monte Carlo simulation technique. Probabilistic stability assessments for a hypothetical two-layer slope as well as for the Cannon Dam in Missouri, USA are performed to verify the application potential of the proposed method.     

对岩土工程有限元强度折减法的几点思考

有限元强度折减法是岩土工程极限分析有限元法中研究和应用较多的一种。近年来获得了快速发展,且成果丰硕,初步显示出在岩土工程中的可行性、优越性和实用性。在充分肯定其优势及特点的同时,从安全系数定义、摩尔-库仑准则的应用条件、计算参数选取等方面,探讨了有限元强度折减法的若干问题。认为应注意该方法的使用条件和计算参数选取;研究以变形控制设计为主的岩土结构安全系数及稳定性,与传统极限平衡方法结合互补,研发多种方法和用途的专业计算软件是较好的发展方向。     

Integration of Information Technology into Geotechnical Engineering Practice: Concept and Development

Information Technology (IT) has been extensively used to predict, visualize, and analyze physical parameters in order to expedite routine geotechnical design procedures. This paper presents an example of the combined technique of IT and numerical analysis for routine geotechnical design projects. The proposed approach involves the development of ANN(s) using a calibrated finite element model(s) for use as a prediction tool and implementation of the developed ANN(s) into a GIS platform for visualization and analysis of spatial distribution of predicted results. A novel feature of the proposed approach is an ability to expedite a routine geotechnical design process that otherwise requires significant time and effort in performing numerical analyses for different design scenarios. A knowledge-based underground excavation design system that utilizes artificial neural networks (ANNs) as prediction tools is also introduced. Practical implications of the use of IT in geotechnical design are discussed in great detail.     

Slope stabilization in difficult conditions: the case study of a debris slide in NW Italian Alps

A case study of a debris slide (estimated volume of about 35,000 m³) is described in this paper. This slide occurred in April 2009 in the North Western Italian Alps (Aosta valley) and damaged the SR25 road along the Valgrisenche valley. Ground investigations started with severe safety and logistic issues being posed. Given the need to open as soon as possible the road, the design of the landslide stabilization works was carried out using a “design as you go” approach. The stabilization measures were conceived to be flexible in order to allow for changes and integration during construction, in line with the progressive refinement of the geological–geotechnical slope model being developed. Back analysis by means of the limit equilibrium method (LEM) and the finite element method (FEM) was used. Groundwater level rise following heavy rainfall and spring snow melting was found to be the main cause of the debris slide. The stabilization works were designed by using both the LEM and FEM methods. The stability conditions of the engineered slope were assessed based on the available performance monitoring data.     

Application of the dynamic bounds method in the safety assessment of flood defences,a case study: 17th Street flood wall,New Orleans

In this paper we provide a computational framework for evaluation of reliability and safety assessment of infrastructures. It is based on the combined application of the dynamic bounds (DB) method and a probabilistic finite element model (FEM). The DB improves the computational efficiency of the FEM when calculating time-dependent failure analyses of coastal and offshore structures, and can speed up the simulation process by several orders of magnitude.

Our approach is demonstrated here for an example problem, and shown to be the most efficient method in applications with a limited number of influential variables, which is true for geotechnical and coastal flood defence systems. It is applied to the 17th Street flood wall, a failing component of the flood defence system in New Orleans during Hurricane Katrina. The variation in soil parameters is a critical input in the reliability estimation of this structure, and the calculated probability of failure depends on these assumed values.     

General coupling extended multiscale FEM for elasto‐plastic consolidation analysis of heterogeneous saturated porous media

This paper presents a general coupling extended multiscale FEM (GCEMs) for solving the coupling problem of elasto‐plastic consolidation of heterogeneous saturated porous media. In the GCEMs, the numerical multiscale base functions for the solid skeleton and fluid phase of the coupling system are all constructed on the basis of the equivalent stiffness matrix of the unit cell, which not only contain the interaction between the solid and fluid phases but also consider the time effect. Furthermore, in order to improve the computational accuracy for two‐dimensional problems, a multi‐node coarse element strategy for the GCEMs is proposed, and a two‐scale iteration algorithm for the elasto‐plastic consolidation analysis is developed. Some one‐dimensional and two‐dimensional homogeneous and heterogeneous numerical examples are carried out to validate the proposed method through the comparison with the coupling multiscale FEM and standard FEM. Numerical results show that the newly developed GCEMs can almost preserve the same convergent property as the standard FEM and also possesses the advantages of high computational efficiency. In addition, the GCEMs can be easily applied to other coupling multifield and multiphase transient problems. Copyright © 2014 John Wiley & Sons, Ltd.