岩土材料在非关联流动法则下剪胀角选取探讨

岩土材料属于摩擦型材料,其强度特性时参数指标的选取至关重要。当前对剪胀角存在模糊认识,导致在理论分析和数值模拟分析中常会产生较大误差。在分析传统的滑移线场理论的基础上,采用广义塑性理论,证明了岩土材料在非关联流动法则条件下的剪胀角应取? /2,且此时体变必为0。通过对具有精确理论解的经典Prandtl地基承载力课题的数值模拟分析,分别对关联流动法则、非关联流动法则剪胀角取? /2及非关联流动法则剪胀角取0三种情况下地基的承载力进行了计算。结果表明,上述3种情况下得到的极限荷载的误差为2 %,但滑移线场与理论解有较大差异。其中,在非关联流动法则条件下,采用剪胀角? =? /2所得到的滑移线场与Prandtl理论解一致,而采用? =0所得到的滑移线场与理论解有较大的偏差。这说明目前在非关联流动法则条件下采用? = 0虽然可得到相应的正确的极限荷载,但是相应的滑移线场具有较大的误差,同时也证明了岩土材料在非关联流动法则条件下的剪胀角应该选取? /2,而不是目前通常采用的0。     

Finite deformation analysis of geomaterials

The mathematical structure and numerical analysis of classical small deformation elasto–plasticity is generally well established. However, development of large deformation elastic–plastic numerical formulation for dilatant, pressure sensitive material models is still a research area. In this paper we present development of the finite element formulation and implementation for large deformation, elastic–plastic analysis of geomaterials. Our developments are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A consistent linearization of the right deformation tensor together with the Newton method at the constitutive and global levels leads toward an efficient and robust numerical algorithm. The presented numerical formulation is capable of accurately modelling dilatant, pressure sensitive isotropic and anisotropic geomaterials subjected to large deformations. In particular, the formulation is capable of simulating the behaviour of geomaterials in which eigentriads of stress and strain do not coincide during the loading process. The algorithm is tested in conjunction with the novel hyperelasto–plastic model termed the B material model, which is a single surface (single yield surface, affine single ultimate surface and affine single potential surface) model for dilatant, pressure sensitive, hardening and softening geomaterials. It is specifically developed to model large deformation hyperelasto–plastic problems in geomechanics. We present an application of this formulation to numerical analysis of low confinement tests on cohesionless granular soil specimens recently performed in a SPACEHAB module aboard the Space Shuttle during the STS‐89 mission. We compare numerical modelling with test results and show the significance of added confinement by the thin hyperelastic latex membrane undergoing large stretching. Copyright © 2001 John Wiley & Sons, Ltd.     

Discrete element modelling of fragmentable geomaterials with size dependent strength

This paper presents the application of a discrete element technique to the analysis of the dynamic indentation of either a purely brittle or a brittle viscoplastic geomaterial which can experience fragmentation resulting in fragments with size dependent strength characteristics.     

岩土材料应力路径无关硬化参量的构成方法

在分析砂土试验结果的基础上,揭示了基本硬化内参量（塑性体积应变、塑性剪应变）变化的应力路径相关性,提出了应力路径无关硬化参量的一般表达式。并指出了塑性功硬化参量及其提出的黏土和砂土统一硬化参量均是所提一般表达式框架下的特例。还将该统一硬化参量直接和修正剑桥模型结合,并与试验结果对比,表现出描述剪胀特性的简单性和有效性。     

A four‐node plane parametric element based on quadrilateral area coordinate and its application to coupled solid‐deformation/fluid‐flow simulation for porous geomaterials

A four‐node plane parametric element AQGβ6‐I is constructed on the basis of the quadrilateral area coordinate, the generalized conforming principle and the projection technique with a penalty factor β within an interval of 0–1. When β = 0, the element has excellent bending performance. When β = 1, the element can pass patch test strictly; its performance is as good as many famous elements. When β value is between 0 and 1, such as β = 0.5, the element can arrive at a compromise between (relatively) low sensitivity to mesh distortion and perfect convergence. The work provides an illuminating method to alleviate a difficult problem in finite element modelling using the four‐node quadrilateral element, which can pass the strict patch test, but has poor performance in bending dominated problem; on the contrary, it has excellent performance in bending dominated problem but cannot pass the strong patch test. The AQGβ6‐I with the convergence formulation (β = 1) is then applied to coupled solid‐deformation/fluid‐flow simulation for porous geomaterials. The computational examples are carried out to demonstrate that the AQGβ6‐I (β = 1) element is not only stable, reliable and efficient but also of high accuracy. The present study provides a good applicable element for finite element simulations of solid‐deformation/fluid‐flow for porous geomaterials. Copyright © 2014 John Wiley & Sons, Ltd.     

一种旋转塑性势面模型及非关联塑性流动法则

为了较好地描述软土塑性应变发展规律,提出了一种改进的塑性流动模型。该模型采用了与屈服函数形式相同,但具有一定倾角γ的塑性势函数。土体在变形过程中,塑性流动方向会依赖于塑性势面的旋转而变化,直至达到破坏状态。通过对常规三轴试验结果的分析可以发现:在剪切过程中,塑性势面旋转角的初值γ₀与终值γ_d较为稳定,不受围压变化影响。在此试验观察基础上,引入了归一化的旋转角参数γ’以及描述土体应力状态的参数ξ,在采用蛋形势函数的情况下二者具有良好的分段线性关系。利用该关系,建立了改进的塑性流动法则,只需要2个额外的模型参数。对所提出的塑性流动模型进行了验证,计算结果表明该模型能较好地反映塑性应变的变化趋势。     

A bond failure criterion for DEM simulations of cemented geomaterials considering variable bond thickness

A series of micromechanical tests were conducted to investigate the bond failure criterion of bonded granules considering the effect of bond thickness, with the aim of enhancing the bond contact model used in the distinct element simulations of cemented geomaterials. The granules were idealized in a two‐dimensional context as one pair of aluminum rods bonded by resin epoxy or cement. The mechanical responses of nearly 500 rod pairs were tested under different loading paths to attain the yield loads of bonded granules at variable bond thickness. This study leads to a generic bond failure criterion incorporating the effect of the bond thickness. The results show that the bond compressive resistance largely decreases with increasing bond thickness owing to the presence of the confinement at the bond‐particle interface. The strength envelopes obtained from the combined shear compression tests and combined torsion compression tests have identical functional form, and they decrease in size with increasing bond thickness but remain unchanged in shape. Given the same cementation material, the generic bond strength envelope in a three‐dimensional contact force space under different loading paths remains the same in shape but shrinks with the increase of bond thickness. Copyright © 2014 John Wiley & Sons, Ltd.     

土工极限平衡问题的非线性有限元数值分析

考虑非关联流动法则,采用几类低阶单元对条形基础下地基的极限承载力进行了二维有限元数值分析.计算表明,基于四节点四边形等参单元的有限元分析结果能够较好地吻合Prandtl理论解,且能保证数值计算的稳定性.同时,基于Mohr-Coulomb破坏准则和强度折减方法,对于边坡稳定性进行了有限元计算,建议采用无量纲位移Eδmax/γH2随强度折减系数变化的关系曲线上位移陡然增大时所对应的强度折减系数作为边坡的稳定安全系数,克服了当前强度折减有限元数值计算中关于收敛标准确定的人为不确定性,即使采用四节点四边形单元也能够保证数值解的良好收敛性.     

岩土流动势的存在性及解耦性

基于不可逆热力学岩土损伤理论的流动势理论存在两个基本问题：（1）岩土材料是否存在流动势;（2）流动势可否分解为塑性势和损伤势,即塑性、损伤两种机制可否解耦,给出了流动势存在的充分必要条件并加以严格证明,结合岩土的基本变形性质,证明了岩土不存在流动势。进一步考察流动势的解耦性,给出了流动势的塑性流动与损伤流动可解耦的充分必要条件,并进行了严格论证,结合土体的基本变形性质,证明了岩土塑性流动和损伤流动机制不可解耦,从而也为其他固体材料流动势的存在性和解耦性提供判别依据。     

A non‐coaxial and unbalanced plastic flow rule for geomaterials and its application to the shear band orientation prediction

In this paper, the non‐coaxial relation between the principal plastic strain increments and the principal stresses, which results from the internal friction in geomaterials, is analyzed, and the phenomenon of the unbalanced development of plastic flow in two conjugate directions is discussed. A non‐coaxial, unbalanced plastic flow model for Coulomb frictional materials is developed and used to determine the orientation of shear band in geomaterials. It is shown that the unbalanced index r of plastic flow has important effect on the orientation of the shear band, and the orientation determined by the conventional plastic flow theory is only a special case of the proposed model when r=0. This result soundly explains the reason that the geomaterials with the same internal friction angle and dilatancy angle can have very different shear band orientations. In addition, the difference between the intrinsic and apparent dilatancy angles is analyzed, and it is emphasized that the dilatancy angle commonly used in practice is indeed the apparent dilatancy angle. Copyright © 2010 John Wiley & Sons, Ltd.     

A discrete thermodynamic approach for anisotropic plastic–damage modeling of cohesive‐frictional geomaterials

A discrete plastic–damage model is developed for cohesive‐frictional geomaterials subjected to compression‐dominated stresses. Macroscopic plastic strains of material are physically generated by frictional sliding along weakness planes. The evolution of damage is related to the evolution of weakness planes physically in connection with the propagation of microcracks. A discrete approach is used to account for anisotropic plastic flow and damage evolution, by introducing two stress invariants and one plastic hardening variable for each family of sliding weakness planes. Plastic flow in each family is coupled with damage evolution. The proposed model is applied to typical geomaterials and comparisons between numerical predictions and experimental data are presented. Copyright © 2009 John Wiley & Sons, Ltd.     

Mathematical modelling of groundwater flow at Sellafield, UK

Sellafield in West Cumbria was a potential site for the location of the UK's first underground repository for radioactive, intermediate level waste (ILW). The repository was to lie around 650 m beneath the ground surface within rocks of the Borrowdale volcanic group (BVG), a thick suite of SW dipping, fractured, folded and metamorphosed Ordovician meta-andesites and ignimbrites. These are overlain by an onlapping sequence of Carboniferous and Permo-Triassic sediments. In situ borehole measurements showed that upward trending fluid pressure gradients exist in the area of the potential repository site, and that there are three distinct fluid types in the subsurface; fresh, saline and brine (at depth, to the west of the site). Simulations of fluid flow in the Sellafield region were undertaken with a 2D, steady-state, coupled fluid and heat flow simulation code (OILGEN). In both simplified and geologically complex models, topographically driven flow dominated the regional hydrogeology. Fluids trended persistently upwards through the potential repository site. The dense brine to the west of the site promoted upward deflection of topographically driven groundwaters. The inclusion in hydrogeological models of faults and variably saline sub-surface fluids was essential to the accurate reproduction of regional hydraulic head variations. Sensitivity analyses of geological variables showed that the rate of groundwater flow through the potential repository site was dependent upon the hydraulic conductivity of the BVG, and was unaffected by the hydraulic conductivity of other hydrostratigraphic units. Calibration of the model was achieved by matching simulated subsurface pressures to those measured in situ. Simulations performed with BVG hydraulic conductivity 100 times the base case median value provided the “best-fit” comparison between the calculated equivalent freshwater head and that measured in situ, regardless of the hydraulic conductivity of other hydrostratigraphic units. Transient mass transport simulations utilising the hydraulic conductivities of this “best fit” simulation showed that fluids passing through the potential repository site could reach the surface in 15 000 years. Simple safety case implications drawn from the results of the study showed that the measured BVG hydraulic conductivity must be less than 0.03 m year⁻¹ to be simply declared safe. Recent BVG hydraulic conductivity measurements showed that the maximum BVG hydraulic conductivity is around 1000 times this safety limit.     

Experimental evidence of a unique flow rule of non-cohesive soils under high-cyclic loading

The presented results of cyclic triaxial tests on sand demonstrate that the cumulative effects due to small cycles obey a kind of flow rule. It mainly depends on the average stress ratio about which the cycles are performed. This so-called “cyclic flow rule” is unique and can be well approximated by flow rules for monotonic loading. Amongst others it is shown that the cyclic flow rule is only moderately influenced by the average mean pressure, by the strain loop (span, shape, polarization), the void ratio, the loading frequency, the static preloading and the grain size distribution curve. A slight increase of the compactive portion of the flow rule with increasing residual strain (due to the previous cycles) was observed. These experimental findings prove that the cyclic flow rule is an essential and indispensable concept in explicit (N-type) accumulation models.     

The influence of a non‐associated flow rule on the calculation of the factor of safety of soil slopes

This paper presents a method that incorporates a non‐associated flow rule into the limit analysis to investigate the influence of the dilatancy angle on the factor of safety for the slope stability analysis. The proposed method retain's the advantage of the upper bound method, which is simple and has no stress involvement in the calculation of the energy dissipation and the factor of safety. Copyright © 2001 John Wiley & Sons, Ltd.     

Simulation of cyclic strength degradation of natural clays via bounding surface model with hybrid flow rule

Strength loss of natural clays subjected to seismic loading is a critical factor contributing to earthquake‐induced ground failure and associated hazards. This work proposes a bounding surface constitutive law to simulate cyclic strength degradation of natural clays resulting from the loss of structure and attendant accumulation of excess pore pressures. The proposed model employs an enhanced plastic flow rule that can simulate accurately the development of pore pressure and explicitly incorporates soil structure effects. The validation of the model with reference to the experimental evidence available for 3 structured clays shows that with a single set of parameters the proposed model can reasonably represent the mechanical behavior of natural clays under various loading conditions (1D compression, monotonic shearing in compression and extension, cyclic loading, and postcyclic shearing). Particularly, its satisfactory performance in terms of quantification of cyclic strength degradation encourages the use of the model in simulating boundary value problems related to the stability of geotechnical facilities under earthquakes.     

A Generalized Backward Euler algorithm for the numerical integration of an isotropic hardening elastoplastic model for mechanical and chemical degradation of bonded geomaterials

An extended version of the classical Generalized Backward Euler (GBE) algorithm is proposed for the numerical integration of a three‐invariant isotropic‐hardening elastoplastic model for cemented soils or weak rocks undergoing mechanical and non‐mechanical degradation processes. The restriction to isotropy allows to formulate the return mapping algorithm in the space of principal elastic strains. In this way, an efficient and robust integration scheme is developed which can be applied to relatively complex yield surface and plastic potential functions. Moreover, the proposed algorithm can be linearized in closed form, thus allowing for quadratic convergence in the global Newton iteration. A series of numerical experiments are performed to illustrate the accuracy and convergence properties of the algorithm. Selected results from a finite element analysis of a circular footing on a soft rock layer undergoing chemical weathering are then presented to illustrate the algorithm performance at the boundary value problem level. Copyright © 2002 John Wiley & Sons, Ltd.     

滑坡-碎屑流冲击导引结构的离散元模拟

滑坡碎屑流对拦挡结构的直接冲击常产生较高的峰值冲击力和冲击能量,导致结构发生破坏而失效;而导引结构通过改变碎屑流的运动路径,可减缓其冲击效应,提高结构抗冲击能力。文章运用三维离散元模拟软件,结合室内休止角试验的结果,校准数值模拟参数,以三种不同导引结构(凹型圆弧、直线型、凸型圆弧)为变量进行数值模拟分析。研究结果表明:凹型圆弧结构B1可以有效地将碎屑流颗粒的冲击力进行转化,结构所受的法向力最小,切向力最大,对颗粒的导引作用最大。经过三种不同导引结构后,颗粒与滑槽之间的碰撞和摩擦是导致颗粒动能减小的主要原因;而三种不同导引结构对颗粒动能的耗散效果无显著差异。导引结构的作用对于颗粒堆积体积分布有显著的影响,主要影响区是靠近坡脚处,对导引结构之后的堆积区域的颗粒体积分布影响不显著。通过对冲击效应和堆积特性的研究,得到凹型圆弧结构形式最优,可以为碎屑流的防护工程抗冲击设计提供参考。     

Unified discrete-element approach applying arbitrary undrained loading paths in element testing for granular soils

The discrete element method (DEM) is crucial in investigating and modeling the elementary behavior of granular materials under varying loading conditions, especially those that cannot be adequately investigated via conventional laboratory testing. However, the application of the DEM in simulations that involve complex loading paths under undrained conditions is scarce, primarily owing to the inability to maintain a constant-volume condition. This paper presents a unified discrete element approach that can apply arbitrary loading paths while satisfying the equivalent undrained condition. The proposed method comprises two parts: (1) a novel strategy that determines the virtual pore pressure under complex undrained loading conditions, and (2) an advanced undrained servomechanism that can simultaneously control each stress component independently. Numerical algorithms corresponding to three new undrained loading paths, that is, true triaxial test, rotational shear, and traffic loading path that have never been simulated using DEM are successfully implemented in a unified manner. Macroscale simulation results under these loading paths are qualitatively in good agreement with their experimental counterparts, thereby confirming the practicality and robustness of the proposed approach. Furthermore, in-depth discussions on the DEM results from these three new loading paths are presented from microscopic perspective.     

基于应变响应包络的颗粒材料增量力学行为研究

砂土的力学响应具有显著的增量非线性特征,这与离散颗粒的微观结构,即组构特性密不可分。采用应变响应包络可以较好地获得材料在不同加载方向上的增量力学响应。在物理试验中无法同时获得同一试样在不同加载方向下的宏、微观响应,故采用离散元方法,对具有不同应力历史、不同应力状态和不同级配的试样在Rendulic平面上的增量力学响应进行了系统研究和分析。离散元模拟结果表明,传统的塑性理论不能很好地描述具有复杂应力历史试样的增量力学响应,而基于颗粒间接触法向的组构增量与剪应变之间在多种不同的工况条件下均具有较强的线性相关性。当砂土的相对密实度相同时,该线性系数主要与围压的大小有关,对颗粒级配、应力历史以及应力比的变化均不敏感。由于组构的大小可以较好地量化砂土的内结构各向异性程度,进而表征应力历史的作用。上述模拟结果为在本构建模中引入组构演化机制,综合反映外荷载和内结构各向异性对砂土增量本构关系的影响提供了较好的微观物理依据。     

坡度对碎屑流冲击立式拦挡墙力学特征的影响

由坡度和挡墙倾角的改变造成碎屑流冲击力学模型的改变是目前被忽略的问题。在碎屑流冲击倾式拦挡墙物理试验的基础上,利用离散元数值计算方法研究了坡度对碎屑流冲击立式拦挡墙（墙面与地面的夹角为90°）力学特征的影响,依据死区颗粒堆积特征,流动层颗粒冲击特征以及二者的相互作用特征提出了两种新力学模型：由倾斜冲击挡墙向坡面堆积转变的力学模型和考虑流动层对死区冲切摩擦作用的水平直接冲击力学模型。对不同冲击力学模型进行了验证分析,结果表明：坡度和挡墙倾角改变了死区的堆积特征从而改变了流动层的冲击方向和冲击力大小。当坡度小于40°时,碎屑流流动层首先沿死区上覆面倾斜冲击挡墙,在最大冲击力作用时刻,流动在坡面层状堆积,最大法向冲击合力可按静土压力公式估算。随着坡度的增大,在最大冲击力时刻,流动层颗粒直接冲击挡墙,但由于死区颗粒对流动层颗粒具有摩擦缓冲减速作用,大幅降低了流动层对挡墙的直接冲击力。此时死区对挡墙的作用力主要包括3个部分：流动层沿坡面冲击死区,由死区传递至挡墙的冲击力、流动层对死区的冲切摩擦力以及死区自重的静土压力。死区对挡墙作用力占最大法向冲击合力的比例增大至90%左右。当坡度由40°增大到50°时,在最大法向冲击合力作用时刻,流动层对死区的冲切摩擦力占最大冲击力的比例由15%增大到49%,流动层与死区之间的摩擦系数由滚动摩擦系数转变为静摩擦系数。提出的流动层对死区的冲切摩擦力为碎屑流冲击刚性挡墙力学计算模型提供了新的研究思路。