A generic approach to modelling flexible confined boundary conditions in SPH and its application

In this paper, a new approach to applying confining stress to flexible boundaries in the smoothed particle hydrodynamics (SPH) method is developed to facilitate its applications in geomechanics. Unlike the conventional SPH methods that impose confining boundary conditions by creating extra boundary particles, the proposed approach makes use of kernel truncation properties of SPH approximations that occur naturally at free-surface boundaries. Therefore, it does not require extra boundary particles and, as a consequence, can be utilised to apply confining stresses onto any boundary with arbitrary geometry without the need for tracking the curvature change during the computation. This enables more complicated problems that involve moving confining boundaries, such as confining triaxial tests, to be simulated in SPH without difficulties. To further enhance SPH applications in elasto-plastic computations of geomaterials, a robust numerical procedure to implement Mohr-Coulomb plasticity model in SPH is presented for the first time to avoid difficulties associated with corner singularities in Mohr-Coulomb model. The proposed approach was first validated against two-dimensional finite element (FE) solutions for confining biaxial compression tests to demonstrate its predictive capability at small deformation range when FE solutions are still valid. It is then further extended to three-dimensional conditions and utilised to simulate triaxial compression experiments. Simulation results predicted by SPH show good agreement with experiments, FE solutions, and other numerical results available in the literature. This suggests that the proposed approach of imposing confining stress boundaries is promising and can handle complex problems that involve moving confining boundary conditions.     

考虑物理性质参数变化的膨润土缓冲材料水-热耦合SPH数值解

为了研究热源温度和外界水压对缓冲层中水-热迁移规律的影响,以GMZ膨润土为例,从基于势能的非饱和土的水-热迁移控制方程出发,考虑了蒸发效应的影响,得到了水-热耦合的方程组,采用改进的光滑粒子流体动力学(SPH)算法,能够对每一处土体根据不同时刻的不同状态实时更新计算参数,得到参数变化的水-热耦合解。计算结果表明：土的物理性质参数与土体的温度和饱和度密切相关,是否考虑这些参数的变化会对计算结果产生较大影响;核废料释放的热量能够在较短的时间内扩散到外边界,水分迁移的速度则相对慢很多;缓冲层温度的升高会加快水分的迁移速度,外界水压对温度的分布则影响较小。     

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.     

土-结构-流体动力相互作用的实时耦联动力试验

针对振动台试验中无限地基难以模拟和数值分析中流-固耦合作用难以计算两个难题,将最近发展的实时耦联动力试验方法引入土-结构-流体动力相互作用问题的研究。以一个渡槽结构为例,其中渡槽-水体作为物理子结构,采用振动台进行物理试验,而无限地基作为数值子结构,采用集总参数模型进行数值模拟。两个子结构之间实时交换数据,联合评估整个耦合体系的动力响应。试验结果和有限元数值模拟结果吻合良好,表明该试验方法具有较高精度。对不同特性地基土进行的试验对比分析结果表明：对于软土地基,考虑土-结构相互作用(SSI)的结构反应幅值明显减小,周期延长;随着地基土变硬,SSI效应逐渐变弱,结构反应最终收敛至刚性地基解。     

Frictional contact algorithms in SPH for the simulation of soil–structure interaction

Simulation of frictional contact between soils and rigid or deformable structure in the framework of smoothed particle hydrodynamics (SPH) is presented in this study. Two algorithms are implemented into the SPH code to describe contact behavior, where the contact forces are calculated using the law of conservation of momentum based on ideal plastic collision or using the criteria of partial penetrating. In both algorithms, the problem of boundary deficiency inherited from SPH is properly handled so that the particles located at contact boundary can have precise acceleration, which is critical for contact detection. And the movement and rotation of the rigid structure are taken into account so that it is easy to simulate the process of pile driving or movement of a retaining wall in geotechnical engineering analysis. Furthermore, the capability of modeling deformability of a structure during frictional contact simulations broadens the fields of SPH application. In contrast to previous work dealing with contact in SPH, which usually use particle‐to‐particle contact or ignoring sliding between particles and solid structure, the method proposed here is more efficient and accurate, and it is suitable to simulate interaction between soft materials and rigid or deformable structures, which are very common in geotechnical engineering. A number of numerical tests are carried out to verify the accuracy and stability of the proposed algorithms, and their results are compared with analytical solutions or results from finite element method analysis. Good agreement obtained from these comparisons suggests that the proposed algorithms are robust and can be applied to extend the capability of SPH in solving geotechnical problems. Copyright © 2013 John Wiley & Sons, Ltd.     

刚性基础-桩-土非线性共同作用的近似分析方法

提出了一种刚性基础-桩-土共同作用非线性分析更为简便的近似方法。刚性基础基底单元（桩或土单元）本身受力变形的非线性关系采用静载试验得到的Q-s曲线,这种单元自身非线性及单元之间线弹性共同作用,可同时用迭代法计算。算例表明,这种方法方便、实用,能较好地反映桩、土非线性特性对基础受力变形的影响。     

A generalized rigid particle contact model for fracture analysis

Rigid particle models taking directly into consideration the physical mechanisms and the influence of the material meso‐structure have recently been developed for fracture studies of quasi‐brittle material such as concrete. The formulation of a generalized contact model for rigid particle simulations is presented in which the contact discretization is a model parameter. The contact model performance for different discretizations is evaluated for uniaxial tensile tests, for uniaxial compression tests and for a notched beam in mode I. Copyright © 2005 John Wiley & Sons, Ltd.     

土-结构动力相互作用体系阻尼及地震反应分析

通过全面考虑土-结构动力相互作用体系中上部结构阻尼、地基土黏滞材料阻尼以及地基基础平动与转动时的辐射阻尼,推导了土-结构相互作用体系的耦合阻尼比公式。结合国内外关于阻尼调整系数的研究成果,提出了基于加速度反应谱的阻尼影响因子概念,建立阻尼影响因子 与《规范》中地震影响系数 的关系式。通过耦合阻尼比公式以及提出的 与 的关系式,对土-结构相互作用体系地震作用加以研究。结果表明考虑土与上部结构的相互作用后能够增大体系的阻尼性能,并大大降低上部结构的地震作用,提高体系的整体抗震性能。其成果为未来抗震防灾研究与工程的抗震设计提供了理论依据。     

An improved SPH method for saturated soils and its application to investigate the mechanisms of embankment failure: Case of hydrostatic pore‐water pressure

The method of smoothed particle hydrodynamics (SPH) has recently been applied to computational geomechanics and has been shown to be a powerful alternative to the standard numerical method, that is, the finite element method, for handling large deformation and post‐failure of geomaterials. However, very few studies apply the SPH method to model saturated or submerged soil problems. Our recent studies of this matter revealed that significant errors may be made if the gradient of the pore‐water pressure is handled using the standard SPH formulation. To overcome this problem and to enhance the SPH applications to computational geomechanics, this article proposes a general SPH formulation, which can be applied straightforwardly to dry and saturated soils. For simplicity, the current work assumes hydrostatic pore‐water pressure. It is shown that the proposed formulation can remove the numerical error mentioned earlier. Moreover, this formulation automatically satisfies the dynamic boundary conditions at a submerged ground surface, thereby saving computational cost. Discussions on the applications of the standard and new SPH formulations are also given through some numerical tests. Furthermore, techniques to obtain the correct SPH solution are also proposed and discussed throughout. As an application of the proposed method, the effect of the dilatancy angle on the failure mechanism of a two‐sided embankment subjected to a high groundwater table is presented and compared with that of other solutions. Finally, the proposed formulation can be considered a basic formulation for further developments of SPH for saturated soils. Copyright © 2011 John Wiley & Sons, Ltd.     

山区公路拓宽路基与衡重式挡土墙动态相互作用的数值模拟

针对山区公路路基拓宽改建的特殊性,运用非线性有限元法,开展衡重式挡土墙修建、新路基逐层分步填筑的动态施工力学行为数值模拟。针对新路基是否加筋、加筋层位以及衡重台上下方新路基填土压实状况的差异性,对新旧路基稳定安全性、滑动面形态、沉降、挡土墙变位等力学响应的影响开展参数敏感性分析。结合室内模拟墙体不同主动位移模式下拓宽路基土工离心模型试验成果,考察新旧路基顶面沉降与挡土墙变位的动态耦合关系。在山区公路路基拓宽改建动态施工中,挡土墙的变位和新旧路基顶面沉降、差异沉降相互耦合,呈正相关关系。衡重台下方新路基填土压实不足会导致新旧路基顶面差异沉降增大。挡土墙主动外倾诱发新旧路基顶面产生较大附加（差异）沉降,宜对新路基自重压密作用造成的差异沉降予以适当修正放大后进行上承路面结构设计。     

A coupling method for soil structure interaction problems

This paper describes a soil‐structure coupling method to simulate blast loading in soil and structure response. For the last decade, simulation of soil behavior under blast loading and its interaction with semi buried structure in soil becomes the focus of computational engineering in civil and mechanical engineering communities. In current design practice, soil‐structure interaction analysis often assumes linear elastic properties of the soil and uses small displacement theory. However, there are numerous problems, which require a more advanced approach that account for soil‐structure interaction and appropriate constitutive models for soil. In simplified approaches, the effect of soil on structure is considered using spring‐dashpot‐mass system, and the blast loading is modeled using linearly decaying pressure–time history based on equivalent trinitrotoluene and standoff distance, using ConWep, a computer program based on semi‐empirical equations. This strategy is very efficient from a CPU time computing point of view but may not provide accurate results for the dynamic response of the structure, because of its significant limitations, mainly when soil behavior is strongly nonlinear and when the buried charge is close to the structure. In this paper, both soil and explosive are modeled using solid elements with a constitutive material law for soil, and a Jones–Wilkins–Lee equation of state for explosive. One of the problems we have encountered when solving fluid structure interaction problems is the high mesh distortion at the contact interface because of high fluid nodal displacements and velocities. Similar problems have been encountered in soil structure interaction problems. To prevent high mesh distortion for soil, a new coupling algorithm is performed at the soil structure interface for structure loading. The coupling method is commonly used for fluid structure interaction problems in automotive and aerospace industry for fuel sloshing tank, and bird impact problems, but rarely used for soil structure interaction problems, where Lagrangian contact type algorithms are still dominant. Copyright © 2012 John Wiley & Sons, Ltd.     

地震分析中人工边界处理与地震动输入方法研究

基于柱面波波动方程,推导建立了适用于土-结构地震动力相互作用分析的地震动输入和人工边界的处理方法.其中,地震动的输入是通过在人工边界上施加等效节点力来实现的,等效节点力的大小与入射地震波波速成正比;而人工边界的处理方法使得人工边界条件不仅在时间上是局部的,而且在空间上也是局部的.这种处理方法简单、有效,物理意义清晰,且很容易在有限元法中实现,结合Newmark时间积分是无条件稳定的.为了验证方法的有效性和精度,给出了两个算例,分别用于检验人工边界条件的性能以及地震动输入方法的正确性.算例分析结果表明,所提出的方法是十分有效的.     

Beam–solid contact formulation for finite element analysis of pile–soil interaction with arbitrary discretization

This paper presents an embedded beam formulation for discretization independent finite element (FE) analyses of interactions between pile foundations or rock anchors and the surrounding soil in geotechnical and tunneling engineering. Piles are represented by means of finite beam elements embedded within FEs for the soil represented by 3D solid elements. The proposed formulation allows consideration of piles and pile groups with arbitrary orientation independently from the FE discretization of the surrounding soil. The interface behavior between piles and the surrounding soil is represented numerically by means of a contact formulation considering skin friction as well as pile tip resistance. The pile–soil interaction along the pile skin is considered by means of a 3D frictional point‐to‐point contact formulation using the integration points of the beam elements and reference points arbitrarily located within the solid elements as control points. The ability of the proposed embedded pile model to represent groups of piles objected to combined axial and shear loading and their interactions with the surrounding soil is demonstrated by selected benchmark examples. The pile model is applied to the numerical simulation of shield driven tunnel construction in the vicinity of an existing building resting upon pile foundation to demonstrate the performance of the proposed model in complex simulation environments. Copyright © 2014 John Wiley & Sons, Ltd.     

Study of the interaction between dry granular flows and rigid barriers with an SPH model

This study uses an incompressible smoothed‐particle hydrodynamics model to investigate the interaction between dry granular material flows and rigid barriers. The primary aim is to summarise some practical guidelines for the design of debris‐resisting barriers. The granular materials are modelled as a rigid‐perfectly plastic material where the plastic flow corresponds to the critical state. The coupled continuity equation and momentum equation are solved by a semi‐implicit algorithm. Compared with flows in controlled flume experiments, the model adequately reproduces both the kinetic of the flows and the impact force under various conditions. Then the numerical simulations are used to study the detailed interaction process. It is illustrated quantitatively that the interaction force consists of two parts, ie, the earth pressure force caused by the weight of the soil and a dynamic force caused by the internal deformation (flowing mass on top of a dead zone). For the estimation of impact load, this study suggests that an increased earth pressure coefficient depending on the Froude number should be incorporated into the hydrostatic model.     

土体冻胀与地基梁相互作用的叠加法研究

根据随机介质的思想,土体冻胀引起的地表隆起近似为正态分布。以上海体育场穿越工程为研究背景,由叠加法基本原理,得出多管冻结冻胀叠加法表达式。将非均布的冻胀荷载简化成多段均布荷载,编制matlab程序求解冻土地基上的弹性地基梁方程,得到冻胀与地基梁（结构）相互作用的位移及接触压力,并用实测数据进行了验证。最后对冻胀与基础梁相互作用的影响因素进行计算分析,得出相互作用的冻胀量随地基梁刚度与外荷载增加而减小、随地基弹性接触系数与自由冻胀量增加而增加。     

模拟摩擦接触问题的新型无网格数值方法

针对摩擦接触问题,给出一种新型的无网格数值方法。该方法基于单位分解思想,在标准无网格Galerkin法的位移模式中嵌入不连续函数和裂尖奇异函数,分别反映接触面的不连续性和接触面端点的奇异性;结合接触摩擦定律,继而构造出求解摩擦接触问题的无网格线性互补模型。在该方法中,接触面方程使用接触点对离散,全局离散系统方程则转化为标准的线性互补问题,可以很方便地使用Lemke算法求解。算例分析证明,本文方法的正确性和有效性。     

Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method

A finite element algorithm for frictionless contact problems in a two‐phase saturated porous medium, considering finite deformation and inertia effects, has been formulated and implemented in a finite element programme. The mechanical behaviour of the saturated porous medium is predicted using mixture theory, which models the dynamic advection of fluids through a fully saturated porous solid matrix. The resulting mixed formulation predicts all field variables including the solid displacement, pore fluid pressure and Darcy velocity of the pore fluid. The contact constraints arising from the requirement for continuity of the contact traction, as well as the fluid flow across the contact interface, are enforced using a penalty approach that is regularised with an augmented Lagrangian method. The contact formulation is based on a mortar segment‐to‐segment scheme that allows the interpolation functions of the contact elements to be of order N. The main thrust of this paper is therefore how to deal with contact interfaces in problems that involve both dynamics and consolidation and possibly large deformations of porous media. The numerical algorithm is first verified using several illustrative examples. This algorithm is then employed to solve a pipe‐seabed interaction problem, involving large deformations and dynamic effects, and the results of the analysis are also compared with those obtained using a node‐to‐segment contact algorithm. The results of this study indicate that the proposed method is able to solve the highly nonlinear problem of dynamic soil–structure interaction when coupled with pore water pressures and Darcy velocity. Copyright © 2015 John Wiley & Sons, Ltd.     

A hybrid calibration approach to Hertz-type contact parameters for discrete element models

This study aims at providing a hybrid calibration framework to estimate Hertz-type contact parameters (particle-scale shear modulus and Poisson ratio) for both two-dimensional and three-dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle-scale Hertz-type contact parameters for granular systems are derived under small-strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle-level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro-micro relationship in Hertz-based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. The proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.     

模型试验的分离相似设计方法——以锚索格构加固边坡模型试验为例

提出了模型试验的分离相似设计方法,以锚索、格构梁加固边坡振动台试验为例进行介绍。将传统量纲分析法中描述振动台试验各个相关参数之间关系的函数关系式定义为1级特征方程。根据边坡、锚索、格构和地震波特性的不同,将1级特征方程进行分离处理,得到分别用于边坡、锚索、格构和地震波相似设计的2级特征方程。根据每个2级特征方程中参数的重要程度不同,将关键设计参数从2级特征方程中分离出来,组成3级特征方程。根据3级、2级和1级特征方程可以分别推导得到针对边坡、锚索、格构梁和地震波各自的关键参数、相关参数和无关参数相似比,选择关键参数相似比作为模型设计的主要依据,并对试验模型进行了相似设计。解决了按照传统量纲分析法要求,模型试验无法同时满足所有参数相似比要求的问题。