Numerical study on finite element implementation of hypoplastic models

A comprehensive numerical study on finite element implementation of hypoplastic models is presented. Two crucial aspects, local integration of the constitutive equations (the local problem) and forming tangent operators for Newton–Raphson iteration (the global problem), are investigated. For solving the local problem, different integration algorithms, including explicit and implicit methods, are examined using tri-axial compression tests and incremental stress response envelopes, as well as typical boundary value problems. For solving global problems, three different ways of generating the tangent operator are compared. The numerical evidences indicate that, in terms of accuracy, efficiency and robustness, explicit methods with substepping and error control are the best choices for constitutive integration of hypoplastic models while the so-called continuum tangent operators have certain advantages over two other types of numerically-generated consistent tangent operators.     

An approach to calculating large strain accumulation for discrete element simulations of granular media

For research on granular materials, establishing a method to calculate continuum strain from particle displacements is necessary for understanding the material behaviour at macro-level and developing continuum constitutive models. Existing methods are generally based on constructing a mesh or background grid to calculate strain from particle motions. These methods offer rigorous ways to measure strain for granular materials; however, they suffer from several problems such as mesh distortion and lacking grid-to-particle strain mapping procedure, which hinders their capability of calculating strain accumulation during large deformation processes of granular media. To address this issue, this study proposes a new strain calculation method for discrete element simulations of granular materials. This method describes a particle assembly as an equivalent continuum system of material points, each of which corresponds to a particle centre and represents a continuous region with its initial volume/area presumably equal to the volume/area of Voronoi cells generated in accordance with the particle assembly configuration. Smooth Particle Hydrodynamics (SPH) interpolation functions are then employed to calculate strain for these material points. This SPH-based method does not require any mesh or background grid for computation, leading to advantages in calculating strain accumulation under large deformation. Simulations of granular materials in both uniform and heterogeneous gradations were carried out, and strain results obtained by the proposed method indicate good agreements with analytical and numerical solutions. This demonstrates its potential for strain calculations in discrete element simulations of granular materials involving large deformations and/or large displacements.     

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.     

Numerical studies of anchored sheet pile wall behavior constructed in cut and fill conditions

The construction of sheet pile walls may involve either excavation of soils in front or backfilling of soils behind the wall. These construction procedures generate different loading conditions in the soil and therefore different wall behavior should also be expected. The conventional methods, which are based on limit equilibrium approach, commonly used in the design of anchored sheet pile walls do not consider the method of construction. However, continuum mechanics numerical methods, such as finite element method, make it possible to incorporate the construction method during the analyses and design of sheet pile walls. The effect of wall construction type for varying soil conditions and wall heights were investigated using finite element modeling and analysis. The influence of construction method on soil behavior, wall deformations, wall bending moments, and anchor forces were investigated. The study results indicate that walls constructed by backfill method yield significantly higher bending moments and wall deformations. This paper presents the results of the numerical parametric study performed and comparative analyses of the anchored sheet pile walls constructed by different construction methods.     

Two‐dimensional finite element analysis of gravitational and lateral‐driven deformation in sedimentary basins

The paper deals with the modeling of some aspects, such as the formulation of constitutive equations for sediment material or finite element approach for basin analysis, related to mechanical compaction in sedimentary basins. In addition to compaction due to gravity forces and pore‐pressure dissipation, particular emphasis is given to the study of deformation induced by tectonic sequences. The numerical model relies upon the implementation of a comprehensive constitutive model for the sediment material formulated within the framework of finite poroplasticity. The theoretical model accounts for both hydromechanical and elasticity–plasticity coupling due to the effects of irreversible large strains. From the numerical viewpoint, a finite element procedure specifically devised for dealing with sedimentary basins as open systems allows to simulate within a two‐dimensional setting the process of sediment accretion or erosion. Several basin simulations are presented. The main objective is to analyze the behavior of a sedimentary basin during the different phases of its life cycle: accretion phase, pore‐pressure dissipation phase and compressive/extensional tectonic motions. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive integration of constitutive rate equations

In finite element calculations the constitutive model plays a key role. The evaluation of the stress response of the constitutive relation for a given strain increment, which is a time integration in the case of models of the rate type, is a typical sub task in such calculations. Adaptive behaviour of the time integration is essential to assure numerical stability and to control the accuracy of the solution. An adaptive second order semi-implicit method is developed in this paper. Its numerical behaviour is compared with an adaptive second order explicit scheme. The two proposed methods control the local error and guarantee numerical stability of the time integration. We include several numerical geotechnical element tests using hypoplasticity with intergranular strain. The element tests simulate the behaviour of a finite element method based on the displacement formulation.     

海冰动力学数值方法研究进展

在海冰动力学数值模拟和预测研究中,人们将海冰视为连续介质分别建立了欧拉坐标下的有限差分（FD）方法、拉格朗日坐标下的光滑质点流体动力学（SPH）方法、欧拉和拉格朗日坐标相结合的质点网格法（PIC）,近年来又发展了基于非连续介质的颗粒流（GF）方法。对以上几种海冰动力学数值方法的特点和适用性进行了讨论,结果表明：FD、PIC和SPH方法可适用于中长期海冰动力学数值模拟,但SPH方法的计算效率需进一步提高;GF方法在不同尺度下的海冰动力学数值模拟中的计算精度均有很强的适用性,但目前较适用于小尺度下海冰动力学基本特性的数值试验研究,计算时效还不能满足实际海冰数值模拟和预测的要求。为进一步提高海冰动力学模拟的精度和适用性,在不同时空尺度下分别发展与其相适应的数值方法是必要的。     

A new approach for calculating strain for particulate media

Discrete element modelling is a viable alternative to conventional continuum‐based analysis for analysing problems involving localized deformations of particulate media. However, to aid in the interpretation of the results, it is useful to express the results of discrete element analyses in terms of the continuum parameters of stress and strain. A number of homogenization methods have been proposed to calculate strain in discrete systems; however, two significant limitations of these methods remain. First, none of these methods incorporate particle rotation effects satisfactorily, although significant particle rotation occurs in shear bands in both physical tests and numerical simulations of granular materials. Additionally, observations of the particle displacement fields in shear bands in granular materials indicate that the displacements within the localizations are erratic. Consequently, existing linear, local interpolation approaches produce substantial variations in the strain values calculated in adjacent elements in the region of localization, hindering clear visualization of the strain localization as it evolves. A new method of domain discretization for calculating strain is proposed. This method is capable of capturing particle rotation and employs a non‐local meshfree interpolation procedure capable of smoothing the erratic displacements in strain localizations, which better defines their evolution. The proposed method is validated for problems involving both two and three dimensions. A number of methods are compared with the proposed method and pertinent insights are made. Copyright © 2003 John Wiley & Sons, Ltd.     

Limit state analysis of earthen slopes using dual continuum/FEM approaches

A framework alternative to that of classical slope stability analysis is developed, wherein the soil mass is treated as a continuum and in-situ soil stresses and strengths are computed accurately using inelastic finite element methods with general constitutive models. Within this framework, two alternative methods of stability analysis are presented. In the first, the strength characteristics of the soil mass are held constant, and the gravitational loading on the slope system is increased until failure is initiated by well-defined mechanisms. In the second approach, the gravity loading on the slope system is held constant, while the strength parameters of the soil mass are gradually decreased until well-defined failure mechanisms develop. Details on applying both of the proposed methods, and comparisons of their characteristics on a number of solved example problems are presented. Copyright © 1999 John Wiley & Sons, Ltd.     

Finite element simulation of the thermoviscoplastic behaviour of bituminous concrete

The general framework of the paper deals with the finite element modelling of thermomechanical problems involving viscous materials. The study focuses on the statement of constitutive equations describing the thermoviscoplastic behaviour of bituminous concrete, as well as on their implementation in a finite element program. After stating the general equations of the space- and time-continuous problem and the constitutive relations governing the viscoplastic component of the bituminous concrete behaviour, we deal with their integration over finite time steps, considering two different schemes. Eventually, two sets of numerical results are presented. The first one, an homogeneous triaxial test, is used to compare those schemes, whereas the second one consists of numerical simulations of real-size experiments performed on a road structure subjected to thermal and mechanical loadings. By comparing the numerical results with experimental ones, it allows us to test the finite element code on a more complex and realistic problem. Copyright © 1999 John Wiley & Sons Ltd.     

Assessment of strut forces for braced excavation in clays from numerical analysis and field measurements

One important consideration in the design of a braced excavation system is to ensure that the structural bracing system is designed both safely and economically. The forces acting on the struts are often determined using empirical methods such as the Apparent Pressure Diagram (APD) method developed by Peck (1969). Most of these empirical methods that were developed from either numerical analysis or field studies have been for excavations with flexible wall types such as sheetpile walls. There have been only limited studies on the excavation performance for stiffer wall systems such as diaphragm walls and bored piles. In this paper, both 2D and 3D finite element analyses were carried out to study the forces acting on the struts for braced excavations in clays, with focus on the performance for the stiffer wall systems. Subsequently, based on this numerical study as well as field measurements from a number of reported case histories, empirical charts have been proposed for determining strut loads for excavations in stiff wall systems.     

Modeling 3-D desiccation soil crack networks using a mesh fragmentation technique

The problem of desiccation cracks in soils has received increasing attention in the last few years, in both experimental investigations and modeling. Experimental research has been mainly focused on the behavior of slurries subjected to drying in plates of different shapes, sizes and thickness. The main objectives of these studies were to learn about the process of crack formation under controlled environmental conditions, and also to understand better the impact of different factors (e.g. soil type, boundary conditions, soil thickness) on the morphology of the crack network. As for the numerical modeling, different approaches have been proposed to describe the behavior of drying cracks in soils. One aspect that it is still difficult to simulate properly is the 3-D crack pattern typically observed in desiccated soils. In this work we present a numerical technique to model the behavior of drying soils. The proposed approach inserts high aspect ratio elements in-between standard elements of a finite element mesh. This mesh fragmentation technique can be easily adapted to standard finite element programs. We used this technique to analyze multiple case studies related to soil desiccation cracks developed under laboratory and field conditions. We focused our attention in some key factors that control the 3-D morphology of the drying cracks network in soils. We show that the proposed technique is able to simulate very satisfactorily the main patterns typically observed in cracked soils.     

软岩巷道围岩流变大变形有限元计算方法

本文针对软岩工程中围岩流变大变形问题，以有限变形力学理论为依据，采用更新拖带坐标法编制非线性大变形有限元计算程序，对软岩巷道流变大变形问题进行了数值模拟计算。在计算中，选用了适合描述软岩流变大变形的物性方程，并考虑了锚杆和拱两种支护方式。结合表明，本文采用的理论和计算方法合理，计算程序具有精度高、收敛速度快等优点，展示了良好的应用前景。     

基于离散裂隙网络模型的核素粒子迁移数值模拟研究

高放废物地质处置过程中涉及的核素在围岩裂隙地下水中的迁移问题已引起广泛关注,数值模拟是研究核素粒子运移的重要方法。目前裂隙介质中渗流模型主要是等效连续介质模型、双重介质模型和离散裂隙网络模型。对于岩体尺度裂隙地下水的流动,离散裂隙网络模型能充分表现裂隙介质的各向异性、不连续性等特征。因此,针对裂隙介质准确概化及核素迁移模拟等难点,文章结合Monte Carlo随机生成裂隙方法、裂隙渗流有限元算法和高放射性核素衰变方程等方法,依据花岗岩深钻孔裂隙统计数据,采用离散裂隙网络模型对内蒙古阿拉善高放废物地质处置预选区展开了核素粒子迁移数值模拟研究,并讨论了实例预测分析结果。结果显示:针对设定的地质模型,核素粒子从中心运移到边界的迁移路径长度平均为1293.35 m,粒子运移到边界耗费的时间平均为1.70E+11 d。     

Analysis of strength and moduli of jointed rocks

This paper deals with two aspects of jointed rock mass behavior, first the finite element modeling of a jointed rock mass as an equivalent continuum, second the comparison of empirical strength criteria of a jointed rock mass. In finite element modeling the jointed rock properties are represented by a set of empirical relationships, which express the properties of the jointed medium as a function of joint factor and the properties of the intact rock. These relationships have been derived from a large set of experimental data of tangent elastic modulus. It is concluded that equivalent continuum analysis gives the best results for both single and multiple jointed rock. The reliability of the analysis depends on the estimation of joint factor, which is a function of the joint orientation, joint frequency and joint strength.Empirical strength criteria for jointed rocks, namely Hoek and Brown, Yudhbir et al., Ramamurthy and Arora, Mohr–Coulomb have been incorporated in a nonlinear finite element analysis of jointed rock using the equivalent continuum approach, to determine the failure stress. The major principal stress at failure, obtained using Ramamurthy's criteria, compares very well with experimental results.     

一种有限元转化为颗粒离散元的方法及其应用研究

为了充分发挥有限元与颗粒离散元各自的优势,提出了一种由有限元转化为颗粒流的方法。数值模型首先用较粗的有限元网格进行离散,并在单元上引入连续介质本构模型。力学计算开始后,实时跟踪各单元的应力状态。一旦某单元的应力满足Mohr-Coulomb准则或最大拉应力准则,删除该单元,同时创建具有一定数目、随机分布且微嵌入的颗粒簇。其后,该单元所在区域的非连续变形及失稳断裂由颗粒簇演化获得。各颗粒的质量、材料参数、速度、位移、接触力等信息根据插值从有限元单元中继承。为了实现有限元与颗粒流接触面的耦合计算,引入了点-棱（二维）及点-面（三维）接触模型,通过法向及切向弹簧实现接触力的计算。颗粒球与有限元板的碰撞分析、单轴压缩、岩石切割等案例展示了上述方法的精确性及合理性。     

XFEM,strong discontinuities and second-order work in shear band modeling of saturated porous media

We investigate shear band initiation and propagation in fully saturated porous media by means of a combination of strong discontinuities (discontinuities in the displacement field) and XFEM. As a constitutive behavior of the solid phase, a Drucker–Prager model is used within a framework of non-associated plasticity to account for dilation of the sample. Strong discontinuities circumvent the difficulties which appear when trying to model shear band formation in the context of classical nonlinear continuum mechanics and when trying to resolve them with classical numerical methods like the finite element method. XFEM, on the other hand, is well suited to deal with problems where a discontinuity propagates, without the need of remeshing. The numerical results are confirmed by the application of Hill’s second-order work criterion which allows to evaluate the material point instability not only locally but also for the whole domain.     

高边坡岩体渐进性破坏粘弹塑性有限元数值模拟

根据边坡实际地质模型 ,基于弹塑性与粘弹 -粘塑性理论的本构方程 ,通过有限元模拟分析 ,定量地揭示和模拟再现了高边坡岩体破裂、变形、破坏及失稳前后锁固段岩体渐进性破坏的机制和过程 ,探讨了高压水流作用下滑坡启程剧动的破坏机理。     

A constitutive and numerical model for mechanical compaction in sedimentary basins

The aim of the paper is to provide new elements concerning the constitutive behavior of sedimentary rocks and the numerical aspects for basin simulators. A comprehensive model for mechanical compaction of sedimentary basins is developed within finite poroplasticity setting. Particular concern is paid to the effects of large porosity changes on the poromechanical properties of the sediment material. A simplified micromechanics-based approach is used to account for the stiffness increase and hardening induced by large plastic strains.A key challenge for numerical assessment of sedimentary basin evolution is to integrate multiple coupled processes in the context of open material systems. To this end, a numerical approach inspired from the ‘deactivation/reactivation’ method used for the simulation of excavation process and lining placement in tunnel engineering, has been developed. Periods of sediments accretion are simulated by progressive activation of the gravity forces within a fictitious closed system. Fundamental components of the constitutive model developed before (hydromechanical coupling, dependence of poroelastic properties on large plasticity, impact of irreversible porosity changes on the hardening rule, evolution of permeability with porosity) are included into our finite element code.Illustrative examples of basin simulation are performed in the one-dimensional case. Various aspects of the constitutive model are investigated. Their influence on the corresponding basin response is analyzed in terms of compaction law, porosity and fluid pressure profiles.     

The mechanics of intersecting echelon veins and pressure solution seams in limestone

Many studies that describe the formation of echelon vein arrays relate the causative stresses implicitly to the deformation, reliant on simple shear kinematics, such that the vein-to-array angle and the array width are the primary physical quantities. In contrast, we identify twelve physical quantities to describe echelon veins in two dimensions, including coeval, vein-intersecting, pressure solution seams. A finite element method is used to reproduce vein shapes in linear elastic and elastic-perfectly plastic model limestone. Model vein geometries are designed using values within the range of geometries measured from echelon veins at Raplee Anticline and Comb Monocline, Utah.Four physical quantities are significant for describing echelon vein shapes: vein spacing, vein-array angle, limestone elastic stiffness, and closing of orthogonal pressure solution seams. Pressure solution seam closing influences the mechanical interaction between adjacent veins, and for a range of conditions, causes a nearly linear vein opening distribution (triangular shapes) and encourages straight vein propagation, both of which approximate field measurements. Model results show that small spacing of veins with seams and large vein-array angles promote straight vein traces in limestone with stiffness typical of laboratory measurements, given the physical geologic conditions inferred from the burial history of the limestone strata.