Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic–plastic soil constitutive model

Simulation of large deformation and post‐failure of geomaterial in the framework of smoothed particle hydrodynamics (SPH) are presented in this study. The Drucker–Prager model with associated and non‐associated plastic flow rules is implemented into the SPH code to describe elastic–plastic soil behavior. In contrast to previous work on SPH for solids, where the hydrostatic pressure is often estimated from density by an equation of state, this study proposes to calculate the hydrostatic pressure of soil directly from constitutive models. Results obtained in this paper show that the original SPH method, which has been successfully applied to a vast range of problems, is unable to directly solve elastic–plastic flows of soil because of the so‐called SPH tensile instability. This numerical instability may result in unrealistic fracture and particles clustering in SPH simulation. For non‐cohesive soil, the instability is not serious and can be completely removed by using a tension cracking treatment from soil constitutive model and thereby give realistic soil behavior. However, the serious tensile instability that is found in SPH application for cohesive soil requires a special treatment to overcome this problem. In this paper, an artificial stress method is applied to remove the SPH numerical instability in cohesive soil. A number of numerical tests are carried out to check the capability of SPH in the current application. Numerical results are then compared with experimental and finite element method solutions. The good agreement obtained from these comparisons suggests that SPH can be extended to general geotechnical problems. Copyright © 2008 John Wiley & Sons, Ltd.     

门架式双排抗滑桩的弹塑性模型与计算分析

门架式双排抗滑桩的计算模型大部分将桩排间岩土体视为弹性材料,而岩土体为弹塑性材料,使得抗滑桩内力、位移计算结果与实际情况相差较大。假设桩排间岩土体为弹塑性材料,提出一种弹塑性计算模型,该模型将桩排间岩土体看作线弹性单元和塑性单元的组合,根据结构力学知识、土的本构关系和数值分析方法建立一种计算前后排抗滑桩内力的计算方法。首先,由已知的桩顶位移,并结合结构力学位移法求出桩间土总应力。根据Lade-Duncan模型导出这两个单元的基本参数,然后,结合数值分析方法计算出抗滑桩的内力,最后,结合工程实例,运用ANSYS有限元软件进行计算分析,得出门架式双排抗滑桩的内力图。对比监测数据和弹性模型计算结果表明,弹塑性模型的计算结果比弹性模型更加接近监测值。     

Dynamic torsional response of an end bearing pile in saturated poroelastic medium

A comprehensive analytical solution is developed in this paper to investigate the torsional vibration of an end bearing pile embedded in a homogeneous poroelastic medium and subjected to a time-harmonic torsional loading. The poroelastic medium is modeled using Biot’s two-phased linear theory and the pile using one-dimensional elastic theory. By using the separation of variables technique, the torsional response of the soil layer is solved first. Then based on perfect contact between the pile and soil, the dynamic response of the pile is obtained in a closed form. Numerical results for torsional impedance of the soil layer are presented first to portray the influence of wave modes, slenderness ratio, pile–soil modulus ratio and poroelastic properties. A comparison with the plane strain theory is performed. The selected numerical results are obtained to analyze the influence of the major parameters on the torsional impedance at the level of the pile head. Finally, the dynamic torsional impedance of this study is compared with that for floating pile in elastic soil.     

Dynamic analysis of an axially loaded pile embedded in elastic-poroelasitc layered soil of finite thickness

This paper presents an analytical solution for determining the dynamic characteristics of axially loaded piles embedded in elastic-poroelastic layered soil of finite thickness. The interface between the elastic and poroelastic soil coincides with the groundwater table level, which is explicitly taken into account in the solution. The pile is modelled as elastic one-dimensional rod to account for the effect of its dynamic characteristics on the response of the soil-pile system. The solution is based on Biot's poroelastodynamic theory and the classical elastodynamic theory, which we use to establish the governing equations of the soil and pile. Accordingly, the pile base resistance, shaft reaction, and the complex impedance of soil-pile system are obtained using the method of Hankel integral transformation. Following the validation of the derived solution, we identify the main parameters affecting the vertical dynamic impedance of the pile via a parametric study. The presented method poses as an efficient alternative for quickly estimating the dynamic characteristics of axially loaded piles, without having to resort to complex numerical analyses.     

Finite element analyses of soil plug response

Open-ended pipe piles are often used in offshore foundations. The response of the soil plug inside a pipe pile is poorly understood, and only limited work has been performed to quantify the response under the different loading conditions relevant to offshore platforms. This paper describes numerical analyses that have been carried out in order to assess the end-bearing capacity of the soil plug under loading conditions which range from undrained to fully drained. The soil plug has been modelled as either elastic, elastic–perfectly-plastic or elastoplastic. The soil–pile interface, an important aspect of the problem, has been examined critically. Comparison with experimental data from model test at laboratory scale indicates that the load–deformation behaviour of the soil plug is modelled well using an elastoplastic model for the soil plug, and an elastic–perfectly-plastic joint element to model the soil–pile interface. The finite element analyses show that, under typical loading conditions, adequate end bearing may be mobilized by the soil plug, largely by high effective stresses in the bottom 3–5 diameters of the soil plug.     

Numerical analysis of rafts on visco-elastic media using eigenvector expansions

Problems of a raft on a visco-elastic continuum may be converted to equivalent elastic problems by means of a Laplace transformation. In this paper a numerical solution of the equivalent problem is obtained by finite element or other techniques. This solution is converted into the form of an eigenvector expansion and then transformed into a numerical solution to the original problem by inverting the Laplace transform. This form of solution has the advantage of applying to any visco-elastic model, and of requiring little additional computation as a result of changing the visco-elastic model, the relative raft-soil stiffness or the load pattern. The application of the method is illustrated by results for circular rafts, strip footings of finite length and rectangular rafts, and particular attention is paid to a realistic soil creep function which is asymptotic to a linear function of log time.     

六面体有限覆盖的三维数值流形方法的非线性分析

对三维问题的分析是数值流形方法发展的必然,在数值流形方法覆盖位移函数的基础上构造了一种六面体有限覆盖的三维流形单元,推导了相应的应变矩阵、刚度矩阵及平衡方程等表达式。同时,由于目前数值流形方法的模拟分析主要是采用线弹性模型,而对于非线性模型分析研究很少;根据数值流形方法的特点和岩土体的本构模型,给出了适用于数值流形方法进行非线性分析的算法。该方法利用中点增量法进行求解,以改变 模型和 模型中弹性模量的方式来反映非线性,其实质是用分段线性来取代非线性。通过地基沉降计算算例表明,数值流形方法在三维岩土体中进行非线性分析中是有效的。     

Calculation of vibration transmission over bedrock using a waveguide finite element model

A finite element method is developed for the study of elastic wave propagation in layered ground environments. The formulation is based on a spectral finite‐element approach using a mixture of high‐order element shape functions and wave solutions. The numerical method provides solutions to vibration transmission on and within layered elastic waveguides. Examples of its use include the theoretical analysis of transmission of vibrations in the vicinity of the surface of the ground. The mathematical model is two dimensional, and the interior of the ground is modelled as an elastic layer overlying a rigid foundation. An analysis of the natural modes of free vibration in a single layer and two layers is presented and compared with known results. In addition the forced response of the layers, for which the surface is assumed to be subjected to a harmonic point force load is shown. These results also include an illustration of the attenuation of surface vibration due to ‘wave impedance blocks’ in the ‘near field’ of the source up to a frequency of 200 Hz for two soil types. Copyright © 2007 John Wiley & Sons, Ltd.     

Three‐dimensional finite element analysis of lined tunnels

This paper describes finite element procedures that have been developed to model the ground movements that occur when a shallow tunnel is installed in a clay soil. This study is part of a wider project concerned with the development of new methods to predict the likely extent of damage to surface structures caused by nearby shallow tunnelling. This particular paper, however, is concerned only with the numerical model of tunnel installation. The structural liner is an important component of this tunnel installation model; two different ways of modelling the liner (based on continuum elements and shell elements) are discussed in the paper. A test problem consisting of the installation of a lined tunnel in an elastic continuum is used to investigate the merits of these different approaches. When continuum elements are used to model the liner, the numerical results agree well with an analytical solution to the problem. When shell elements are used to model the liner, however, the results were found to be significantly influenced by the particular formulation adopted for the shell elements. Example analyses, involving incremental tunnel construction in a clay soil where the soil is modelled using a kinematic hardening plasticity model, are described. These analyses confirm that a thin layer of continuum elements may be used, satisfactorily, to model tunnel linings in a soil–structure interaction analysis of this sort. Copyright © 2001 John Wiley & Sons, Ltd.     

Vertical vibration of a rigid strip footing on viscoelastic half-space

This paper presents an analytical method for modeling the dynamic response of a rigid strip footing subjected to vertical-only loads. The footing is assumed to rest on the surface of a viscoelastic half-space; therefore, effects of hysteretic soil damping on the impedance of the foundation and the generated ground vibrations are considered in the solution. To solve the mixed boundary value problem, we use the Fourier transform to cast a pair of dual integral equations providing contact stresses, which are solved by means of Jacobi orthogonal polynomials. The resulting soil and footing displacements and stresses are obtained by means of the Fourier inverse transform. The solution provides more realistic estimates of footing impedance, compared to existing solutions for elastic soil, as well as of the attenuation of ground vibrations with distance of the footing. The latter is important for the estimation of machine vibration effects on nearby structures and installations.     

Analysis of undrained cavity expansion in elasto‐plastic soils with non‐linear elasticity

A large strain analysis of undrained expansion of a spherical/cylindrical cavity in a soil modelled as non‐linear elastic modified Cam clay material is presented. The stress–strain response of the soil is assumed to obey non‐linear elasticity until yielding. A power‐law characteristic or a hyperbolic stress–strain curve is used to describe the gradual reduction of soil stiffness with shear strain. It is assumed that, after yielding, the elasto‐plastic behaviour of the soil can be described by the modified Cam clay model. Based on a closed‐form stress–strain response in undrained condition, a numerical solution is obtained with the aid of simple numerical integration technique. The results show that the stresses and the pore pressure in the soil around an expanded cavity are significantly affected by the non‐linear elasticity, especially if the soil is overconsolidated. The difference between large strain and small strain solutions in the elastic zone is not significant. The stresses and the pore pressure at the cavity wall can be expressed as an approximate closed‐form solution. Copyright © 2001 John Wiley & Sons, Ltd.     

裂缝型HTI介质中的弹性阻抗

在回顾封闭平行硬币状裂缝模型的基础上,将裂缝填充物性质、分布密度与背景介质的横纵波速度比,引入裂缝型水平横向各向同性介质纵波、转换横波弹性阻抗公式,并进行归一化弹性阻抗响应特征模拟。分析表明：裂缝介质弹性阻抗呈现方位各向异性,且随裂缝密度加大而增强;纵波、转换横波弹性阻抗在值域分布规律上具有较大区别;在典型砂岩介质的前提下,弹性阻抗差可以作为裂缝含气、含水指示因子定性地识别裂缝填充物性质。     

Finite-element analysis of time-dependent large-deformation problems

An updated Lagrangian finite-element formulation has been developed for time-dependent problems of soil consolidation involving finite deformations. Large plastic strains as well as rotations occur in such problems and nominal stress measures are introduced in the formulation to redefine stresses. This leads to corrective terms for equilibrium and yield violations in addition to geometric stiffening terms in the governing integral equations. The soil is considered to be either a linear elastic or an elastoplastic, critical-state material. Some simple numerical examples are studied to validate the formulation, followed by a detailed analysis of the problem of penetration of a pile into soil. The results of this problem are viewed with emphasis on the physical interpretation and practical significance.     

非均匀层状介质一维波动方程精确解的有限差分算法

平面波的传播问题通常可以归结为一维波动方程的定解问题。在非均匀介质中,即使简单的一维波动方程也需要借助于数值方法获得近似解。3层5点古典差分格式是计算偏微分方程一种常用算法,作为一种显式迭代格式,需要满足稳定性条件 ,其中 为波速, 为空间采样间隔, 为时间采样间隔。当 时, ,古典差分格式达到临界稳定状态。在这种情况下,平面波在 时间内的传播距离恰好等于空间采样间隔,差分格式真实地反映了平面波的传播原理,因而可以得到一维波动方程的精确解。但是,由于在非均匀介质中存在不连续的波阻抗界面,此方法不适于计算非均匀介质的波场。为了将临界稳定情况下的古典差分格式推广应用至非均匀层状介质,提出了一种能够处理波阻抗界面的有限差分格式,并应用傅里叶分析法得到其稳定性条件。模型算例验证了此算法的正确性。     

Dynamic response of a pile considering the interaction of pile variable cross section with the surrounding layered soil

Assuming that the pile variable cross section interacts with the surrounding soil in the same way as the pile toe does with the bearing stratus, the interaction of pile variable cross section with the surrounding soil is represented by a Voigt model, which consists of a spring and a damper connected in parallel, and the spring constant and damper coefficient are derived. Thus, a more rigid pile–soil interaction model is proposed. The surrounding soil layers are modeled as axisymmetric continuum in which its vertical displacements are taken into account and the pile is assumed to be a Rayleigh–Love rod with material damping. Allowing for soil properties and pile defects, the pile–soil system is divided into several layers. By means of Laplace transform, the governing equations of soil layers are solved in frequency domain, and a new relationship linking the impedance functions at the variable‐section interface between the adjacent pile segments is derived using a Heaviside step function, which is called amended impedance function transfer method. On this basis, the impedance function at pile top is derived by amended impedance function transfer method proposed in this paper. Then, the velocity response at pile top can be obtained by means of inverse Fourier transform and convolution theorem. The effects of pile–soil system parameters are studied, and some conclusions are proposed. Then, an engineering example is given to confirm the rationality of the solution proposed in this paper. Copyright © 2017 John Wiley & Sons, Ltd.     

Analysis of stone-column reinforced foundations

A numerical model is proposed to analyse elastic as well as elastoplastic behaviour of stone-column reinforced foundations. The stone-columns are assumed to be dispersed within the in situ soil and a homogenization technique is invoked to establish equivalent material properties for in situ soil and stone-column composite. The difficulties encountered in carrying out elastoplastic analyses of composite materials are overcome by adopting a separate yield function for each of the constituent materials and a sub-iteration procedure within an implicit backward Euler stress integration scheme. In the proposed procedure, equilibrium as well as kinematic conditions implied in the homogenization procedure are satisfied for both elastic as well as elastoplastic stress states. The proposed model is implemented in an axi-symmetric finite element code and numerical prediction is made for the behaviour of model circular footings resting on stone-column reinforced foundations. This prediction indicates good agreement with experimental observation. Finally, a new scheme in which the length of stone-column is variable is proposed and its behaviour is examined through a numerical example. © 1998 John Wiley & Sons, Ltd.     

A method of time-dependent analysis using elastic solutions for nonlinear materials

The formulation of viscoelastic solutions from elastic equations using the ‘correspondence principle’ and an inverse Laplace transform has been discussed extensively in the literature. Because this method has been developed, many time-dependent solutions can be obtained from closed form elastic solutions and conditions have been delineated in which the ‘quasi-elastic’ approximation of the viscoelastic solution is within acceptable tolerance. This communication shows the feasibility of the application of these methods to formulate approximate nonlinear viscoelastic solutions with nonlinear stress-strain materials, and for want of a specific nonlinear model to demonstrate this, the hyperbolic model was selected. The ‘power law’ is used to model the relaxation modulus of the viscoelastic materials. There are five related development that are discussed here using a simple numerical example to illustrate each of them and they are: (1) a linear elastic solution, (2) a linear viscoelastic solution, (3) a nonlinear elastic solution, (4) a nonlinear viscoelastic solution and finally, (5) a ‘regression’ approximation of the nonlinear viscoelastic solution which is suggested by the series form of the elastic solution. All of these are related to one another and each provides an acceptably accurate solution of the problem it addresses. The latter is of particular practical interest since it can be used to provide answers to problems involving nonlinear viscoelastic materials while requiring only very small calculation times. The problem used as an example is the calculation of the displacement of a circular hole in an infinite plate made of a material with a nonlinear time-dependent stress-strain relationship. The nonlinear elastic form of the solution was developed by matching results from nonlinear finite element analysis.     

Arbitrary Lagrangian Eulerian based finite element analysis of cone penetration in soft clay

This paper presents a numerical model for the analysis of cone penetration in soft clay based on the finite element method. The constitutive behaviour of the soil is modelled by modifying an elastic, perfectly-plastic soil model obeying Von-Mises yield criterion to take into account the strain-softening, rate dependent behaviour of soft clay. Since this is a problem involving large soil deformations, the analysis is carried out using an Arbitrary Lagrangian Eulerian method where the quality of the mesh is preserved during penetration. The variation of cone resistance is examined with various parameters such as rigidity index of the soil, in situ stress anisotropy and roughness at the cone–soil interface, which influence the penetration resistance of the cone. A theoretical correlation has been developed incorporating these parameters and the results have been compared with previous correlations based on the cavity expansion theory, finite element method and strain path method. With the increase in strain-softening, relative brittleness of the soil increases and the penetration resistance is significantly reduced. With the rising strain-rate dependency, penetration resistance increases but this increase is independent of the degree of brittleness of the soil.     

深基坑PCMW工法开挖过程离散元数值模拟分析

深基坑稳定性问题是重要的工程问题,其中,有效支护结构是保证基坑工程顺利实施的基础。本文引入离散元法,提出了基坑及支护结构建模和数值模拟方法。采用紧密堆积离散单元构建模型初始地层,引入了离散单元团簇模型来构建表面较为光滑的管桩。以南京某深基坑工程为例,采用三维离散元模拟软件MatDEM3D构建几何模型,并根据土体的力学性质设定相应单元的力学参数。数值模拟中,通过预平衡操作实现土层的压实,进而模拟了基坑开挖过程中土体和管桩的变形。将数值模拟结果与实测监测数据进行了对比分析,评价了基坑支护结构的有效性。这种基坑离散元数值模拟方法在基坑开挖过程的稳定性预判和支护结构的有效性评价上具有潜在的应用前景。     

Spatial foundation structures over no tension soil

The problem of the stress distribution induced in the soil by a single circular foundation structure is approached in a three‐dimensional analysis. Since the soil is typically made by not‐cohesive materials, its behaviour is modelled by means of the not resisting tension (NRT) hypothesis, thus assuming that its very low resistance to tensile stresses can be completely neglected and that it keeps linearly elastic under pure compression. After developing the problem from a theoretical point of view on the basis of an energetic approach, a numerical application—which is able to reproduce the stress distribution induced by a circular foundation on the soil—is performed. Copyright © 2005 John Wiley & Sons, Ltd.