On the role of pre-existing discontinuities on the micromechanical behavior of confined rock samples: a numerical study

The deformation process and failure mechanism of rock mass with increased density of initial joints subjected to confined stress state are investigated in this study using discrete element method (DEM). A numerical model of standard size granite samples is developed and validated using experimental data for both intact and jointed rocks. The micro-parameters of the rock material are first determined, and the effects of the rock discontinuity on strength, deformability, stress–strain relationship, and failure modes are then investigated at the macro-scale level. Analyses are also performed to examine the tensile and shear crack distributions, fragmentation characteristics, particle kinematics, and energy dissipation to advance the current understanding of the deformation processes and failure mechanisms of jointed rock masses. The microscopic evolutions in the fabric and force anisotropy during loading and distributions of contact forces provide insights into the influence of increasing initial jointing on the macroscopic deformational behavior of the rock. The results show how the deceleration in the growth of fabric and contact force anisotropies develops and confirms that the increase in initial jointing and the associated changes in microstructure can restrain the development of anisotropy, thereby reducing significantly the strength of the rock samples.

     

基于Cosserat连续体的颗粒破碎影响研究

颗粒破碎对颗粒材料宏观力学行为有重要影响。 结合Hardin的破碎经验公式,将表征破碎程度的破碎参量与Cosserat连续体的内部长度参数相关联,形成一个基于Cosserat连续体且能考虑颗粒破碎的弹塑性模型。数值算例主要考察了颗粒破碎对颗粒材料承载能力、塑性应变及局部化行为的影响,数值结果表明,颗粒破碎主要发生在剪切带内,颗粒破碎使得剪切带明显变窄且剪切带内外等效塑性应变梯度明显增大。     

抗转动对颗粒材料组构特性的影响研究

颗粒材料大多由不规则形状的颗粒组成,如砂土、谷物等,抵抗转动是不规则形状颗粒的固有特性。已有研究表明,颗粒抗转动特性对其宏观力学特性有显著影响。因此,在颗粒材料的细观数值模拟中或采用非圆颗粒,或在圆颗粒离散元模拟中采用考虑抗转动的接触模型。采用有限元-离散元耦合方法（FDEM）和离散元方法（DEM）分别对椭球形状颗粒和具有抗转动能力的圆球颗粒进行三轴剪切数值模拟,指出了采用抗转动接触模型考虑颗粒形状影响的局限性,并基于颗粒的局部排布结构揭示了形状影响的细观来源。峰值内摩擦角和剪胀均随着转动摩擦系数和形状偏离圆球程度而单调增加,但颗粒形状对它们的影响呈现出明显的收敛趋势。细观组构分析也表明,虽然颗粒形状和转动摩擦都能显著增强组构各向异性,但是组构各向异性的演化模式有明显的区别。造成以上结果的差异在于其抵抗转动的影响机制不同。转动摩擦是通过限制颗粒转动,增强了颗粒间的稳定承载能力,而非圆颗粒是通过咬合作用形成稳定的局部排列结构。由于椭球颗粒腹部比端部能够传递更大的接触力,颗粒受剪切后发生转动,颗粒长轴倾向于正交大主应力方向,呈现交错排列,颗粒间相互锁定。     

Bounding surface plasticity model for stress-strain and grain-crushing behaviors of rockfill materials

Crushing of grains can greatly influence the strength,dilatancy,and stress-strain relationship of rockfill materials.The critical state line(CSL)in the void ratio versus mean effective stress plane was extended to the breakage critical state plane(BCSP).A state void-ratio-pressure index that incorporated the effect of grain crushing was proposed according to the BCSP.Rowe’s stress-dilatancy equation was modified by adding the breakage voidratio-pressure index,which was also incorporated into the formulations of the bounding stress ratio and plastic modulus.A BCSP-based bounding surface plasticity model was proposed to describe the state-dependent stressstrain behaviors and the evolution of grain crushing during shearing process of rockfill materials,and was shown to sufficiently capture the breakage phenomenon.     

Quantification of particle crushing in consideration of grading evolution of granular soils in biaxial shearing: A probability‐based model

A probability‐based model is presented to estimate particle crushing and the associated grading evolution in granular soils during isotropic compression and prepeak shearing in biaxial tests. The model is based on probability density functions of interparticle and intraparticle stress (ie, particle normalized maximum shear stress and particle average maximum shear stress) derived from discrete element method simulations of biaxial tests. We find that the probability density functions of normalized maximum shear stress are dependent on the current sample grading, implying coupling effects between particle crushing and sample grading such that the particle crushing is affected by the current sample grading, and the grading change is also dependent on the current particle crushing extent. To incorporate these coupling effects into the model, particle crushing and grading change are calculated for each load increment, in which the crushing probability of a particle during any loading increment is denoted as the corresponding increment of probability of the internal maximum shear stress exceeding its maximum shear strength. The model shows qualitative agreement with published experimental data. The effects of the model parameters, including initial porosity, particle strength, initial grading, and crushing mode, on the calculated results are discussed and compared with previous studies. Finally, the strengths and limitations of the model are discussed.     

基于离散元法的砂土破碎演化规律研究

颗粒破碎是影响砂土宏-微观力学性质的重要因素。采用改进型的可破碎颗粒生成方法,通过设置不同强度的平行黏结键模拟不同强度的可破碎颗粒,并借用基于离散元方法（DEM）的双轴压缩试验详细研究了可破碎性土在剪切过程中颗粒破碎率/平均破碎程度、微观尺度上的能量耗散分配机制、剪切破碎带形成以及断裂键各向异性的演化过程。结果表明,颗粒破碎强烈地影响砂土在宏观尺度上的力学响应、颗粒尺度上的能量分配机制以及剪切过程中的颗粒的组织结构演化。颗粒破碎主要影响小应变阶段各能量耗散元的分配机制,而在临界状态下剪切带内的颗粒摩擦以及破碎耗能是消耗外界功的主要因素。数值结果亦表明,颗粒的破碎伴随着整个剪切过程,但破碎率的增长速度却随着剪切应变的发展逐渐降低。另外,在剪切过程中,对于低破碎性土,在临界状态下剪切破碎带基本形成,带内的原有组织结构被打乱,断裂键的各向异性也随之弱化。     

Modelling size effect on rock aggregates strength using a DEM bonded-cell model

Empirical evidence has shown that particle breakage affects the mechanical behaviour of granular materials. The source of this mechanism takes place at the particle scale, and the main consequence on the macromechanical behaviour is increasing compressibility. Due to the inverse correlation between particle size and particle crushing strength, coarse rockfill materials are particularly vulnerable to mechanical degradation due to particle breakage. However, such coarse materials do not fit in standard laboratory devices, and the alternative of large sample testing is usually unavailable or too expensive. Alternatively, recent works have proposed multi-scale approaches using the discrete element method (DEM) to carry out numerical testing of coarse crushable materials, although few studies have focused on size effects. This article presents the application of a DEM bonded-cell model to study particle size-strength correlation on angular rock aggregates. Each particle is modelled by a cluster of perfectly rigid polyhedral cells with Mohr–Coulomb contact law. Constant cell density within particles implies that the presence of potential fragmentation planes increases with size. Therefore, particle strength decreases with size. A comprehensive sensitivity analysis was carried out through 1477 particle crushing simulations in a given particle size. Based on published experimental data on calcareous rock aggregates, part of the simulations were used for calibration, and 97 additional simulations of a coarser size fraction were performed for validation. The results show a good agreement with the empirical data in terms of size effect and data scatter through Weibull statistics.

     

颗粒破碎对钙质砂的应力-应变及强度影响研究

压力作用下颗粒发生破碎是引起砂土力学特性变化的重要因素之一, 对于钙质砂这种易破碎的材料更是如此。为进一步弄清颗粒破碎对钙质砂的应力-应变强度影响, 本文对钙质砂进行三轴固结排水剪切试验得到应力-应变曲线, 并筛分得到三轴试验前后钙质砂颗分曲线。通过引入Hardin定义的颗粒相对破碎率Br, 分析了相对密度、围压与颗粒破碎的关系及颗粒破碎对钙质砂应力-应变和抗剪强度的影响。结果表明:随围压的增大颗粒破碎增量逐渐减小, 直到破碎达到一个上限值, 此时围压和相对密度对颗粒破碎影响很小; 颗粒间的滑动标志着应力达到极限状态, 而颗粒破碎会阻碍应力达到极限状态, 在本实验中, 低围压时颗粒破碎少, 颗粒相对运动形式为滑移, 使应力-应变曲线为软化型, 高围压下颗粒破碎严重, 颗粒破碎在剪切过程中始终发生, 使应力-应变曲线呈应变硬化型; 颗粒破碎使体变从剪胀逐渐发展到剪缩, 且破碎越严重剪缩越严重; 在低围压下钙质砂强度主要由剪胀和咬合提供, 高围压下颗粒破碎严重, 剪胀消失, 咬合减小, 使峰值摩擦角减小, 抗剪强度降低。     

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。     

土的基本力学特性及其弹塑性描述

Cam-clay模型是在等向加载试验基础上建立起来的且能够描述正常固结土在常规三轴试验条件下应力-应变关系的最简单弹塑性模型,是建立各种土的弹塑性本构模型的基础。文中分别按加载方式的不同和土组构的不同,对描述与应力状态、应力历史、应力路径、持荷时间等因素有关的加载方式下土应力应变特性的弹塑性本构模型进行了归纳。对反映不同组构所形成的结构性、各向异性和颗粒破碎等特性的弹塑性本构模型进行了综述,并着重介绍了描述应力状态的三维化方法、反映应力历史影响的超固结土模型和模拟渐近状态路径的渐近状态模型等典型研究成果。     

Elastic shear stiffness anisotropy and fabric anisotropy of natural clays

Natural clays usually show anisotropic stiffness due to their deposition process and anisotropic in situ stress state. The stiffness anisotropy depends on both of the stress anisotropy and fabric anisotropy, while the latter can be quantified by the stiffness anisotropy at isotropic stress states. This paper measures the K₀ value (i.e., stress anisotropy) and elastic shear stiffness anisotropy of natural Shanghai clay in a triaxial apparatus with horizontal and vertical bender elements. The results show that the K₀ value of Shanghai clay lies in the range of 0.40–0.66, and an empirical equation is proposed to estimate the K₀ value based on the plasticity index and initial void ratio. The fabric anisotropy of natural Shanghai clay lies in the range of 1.2–1.4 with a stronger fabric in the horizontal plane. Moreover, the experimental data of the stiffness anisotropy and fabric anisotropy of different clays in the literature are reviewed and analyzed. It reveals that the stiffness anisotropy generally increases, while the fabric anisotropy remains nearly the same during K₀ consolidation. For normally consolidated clay, the fabric anisotropy generally lies in the range of 1.1–1.7. For overconsolidated clays, the fabric anisotropy generally increases as the overconsolidation ratio increases. Empirical equations are proposed to approximately estimate the fabric anisotropy of clays based on its stress normalized elastic shear stiffness.

     

Strength anisotropy of granular material consisting of perfectly round particles

The strength anisotropy of granular materials deposited under gravity has mostly been attributed to elongated particles' tendency to align long axes along the bedding plane direction. However, recent experiments on near‐spherical glass beads, for which preferred particle alignment is inapplicable, have exhibited surprisingly strong strength anisotropy. This study tests the hypothesis that certain amount of fabric anisotropy caused by the anisotropic stress during deposition under gravity can be locked in a circular‐particle deposit. Such locked‐in fabric anisotropy can withstand isotropic consolidation and leads to significant strength anisotropy. 2D discrete element method simulations of direct shear tests on circular‐particle deposits are conducted in this study, allowing for the monitoring of both stress and fabric. Simulations on both monodispersed and polydispersed circular‐particle samples generated under downward gravitational acceleration exhibit clear anisotropy in shear strength, thereby proving the hypothesis. When using contact normal‐based and void‐based fabric tensors to quantify fabric anisotropy in the material, we find that the intensity of anisotropy is discernible but low prior to shearing and is dependent on the consolidation process and the dispersity of the sample. The fact that samples with very low anisotropy intensity measurements still exhibit fairly strong strength anisotropy suggests that current typical contact normal‐based and void‐based second‐order fabric tensor formulations may not be very effective in reflecting the anisotropic peak shear strength of granular materials. Copyright © 2017 John Wiley & Sons, Ltd.     

Single-particle crushing strength under different relative humidity conditions

This paper presents a fundamental study on the effect of the relative humidity on the rockfill crushing strength. This aspect plays an important role in the mechanical behaviour of rockfill, and it is known that certain characteristics of the granular materials, such as compressibility and shear strength, depend on the confining stress, which is a function of the particles crushing. An increased interest has been observed regarding the effect of the relative humidity in the mechanical behaviour of rockfill. Unfortunately, limited research has been conducted until now regarding the study of individual particle crushing. Therefore, this paper thoroughly investigated particle crushing, by performing single-particle crushing tests on rockfill particles divided into four size ranges, under different relative humidity conditions. The experimental results reveal a considerable influence of the relative humidity in the studied rockfill particles, whose strength of the particles with the greatest dimensions in saturated conditions was reduced by half. Consistent macro-mechanical evidence demonstrates that particle’s size and relative humidity conditions depict the most important factors that influence particle crushing strength.

     

Evolution of induced fabric in a strain space multiple mechanism model for granular materials

The strain space multiple mechanism model idealizes the behavior of granular materials based on a multitude of virtual simple shear mechanisms oriented in arbitrary directions. Within this modeling framework, the virtual simple shear stress is defined as a quantity that depends on the contact distribution function as well as the normal and tangential components of inter‐particle contact forces, which evolve independently during the loading process. In other terms, the virtual simple shear stress is an intermediate quantity in the upscaling process from the microscopic level (characterized by the contact distribution and inter‐particle contact forces). The stress space fabric (i.e. the orientation distribution of the virtual simple shear stress) produces macroscopic stress through the tensorial average. Thus, the stress space fabric characterizes the fundamental and higher modes of anisotropy induced in granular materials. Comparing an induced fabric associated with the biaxial shear of plane granular assemblies obtained via a simulation using Discrete Element Method to the strain space multiple mechanism model suggests that the strain space multiple mechanism model has the capability to capture the essential features in the evolution of an induced fabric in granular materials. Copyright © 2012 John Wiley & Sons, Ltd.     

炭质页岩的颗粒破碎及其路用性能试验研究

为综合评估炭质页岩的路用性能,充分认识炭质页岩的颗粒破碎行为,测试了炭质页岩块在循环压实过程中各粒组含量的演化规律,结合室内击实试验阐述了颗粒破碎对炭质页岩击实性能的影响,确定了最佳填筑级配,并依据最佳级配进行三轴湿化变形试验,从颗粒破碎角度分析了炭质页岩填料湿化变形的变化规律,最后对炭质页岩现场填筑效果进行了验证。结果表明：炭质页岩压实过程经历结构调整、颗粒破碎、压缩变形3个阶段,形成的相对稳定级配结构为其用作路堤填料提供了基础;填料最大干密度形成机制受颗粒破碎过程中粒径为20～40 mm与粒径小于2 mm颗粒含量变化的影响较大,随粗料含量增加,试样相对破碎率线性增大,最大干密度呈先增大后减小变化,最优粗料含量约为70%;湿化变形是混合料颗粒破碎的外在表现,浸水湿化后混合料强度降低约40%,可采用相对破碎率 B_r 预估混合料遇水产生的湿化变形量,并建立了相对破碎率与围压、应力水平间的数学关系式;现场填筑过程中路堤压实度检测与沉降观测表明,炭质页岩路堤的最佳铺松厚度约为40 cm。     

A hypoplastic model for granular soils incorporating anisotropic critical state theory

It is well known that soil is inherently anisotropic and its mechanical behavior is significantly influenced by its fabric anisotropy. Hypoplasticity is increasingly being accepted in the constitutive modeling for soils, in which many salient features, such as nonlinear stress-strain relations, dilatancy, and critical state failure, can be described by a single tensorial equation. However, within the framework of hypoplasticity, modeling fabric anisotropy remains challenging, as the fabric and its evolution are often vaguely assumed without a sound basis. This paper presents a hypoplastic constitutive model for granular soils based on the newly developed anisotropic critical state theory, in which the conditions of fabric anisotropy are concurrently satisfied along with the traditional conditions at the critical state. A deviatoric fabric tensor is introduced into the Gudehus-Bauer hypoplastic model, and a scalar-valued anisotropic state variable signifying the interplay between the fabric and the stress state is used to characterize its impact on the dilatancy and strength of the soils. In addition, fabric evolution during shearing can explicitly be addressed. Modifications have also been undertaken to improve the performance of the undrained response of the model. The anisotropic hypoplastic model can simulate experimental tests for sand under various combinations of principle stress direction, intermediate principal stress (or mode of shearing), soil densities, and confining pressures, and the associated drastic effect of different principal stress orientations in reference to the material axes of anisotropy can be well captured.     

控制应力路径散体材料真三轴试验强度特征的离散元模拟与细观机制分析

通过一系列真三轴离散元数值试验,模拟了不同应力路径下的等b试验中散体材料的强度特征。根据模拟结果详细地分析了三维应力条件下中主应力和应力路径对散体材料峰值强度的影响,研究了峰值摩擦角、峰值应力比的变化规律,并根据真应力的概念和组构张量的演化结果分析了散体材料的强度成因。研究表明,在不同类型的数值试验中峰值偏应力随b参数的变化规律不同,但采用初始围压归一化后的应力-应变曲线规律一致。峰值强度线的斜率只与b值有关而与应力路径无关,且随着b值的增加,峰值应力比qf /pf逐渐减小,数值模拟结果与室内试验结果吻合较好;随着应变的发展,数值试样的组构也随之发生变化,产生了明显的应力诱发各向异性;散体的强度为颗粒摩擦及材料各向异性共同作用的结果;理论上,组构比-应力比坐标系中破坏点位置仅取决于颗粒摩擦角 ,而数值模拟结果与理论值的差异源于颗粒间咬合和滚动摩擦的影响,其影响与颗粒表面摩擦系数有关,也受空间应力状态的影响。     

考虑颗粒破碎影响的粗粒土本构关系

粗粒土在较大的应力条件下容易产生颗粒破碎现象,而现有的大多数模型都没有考虑剪切过程中的颗粒破碎。模型将塑性功引入土体受力变形过程的能量方程中,推导得到土体流动法则。采用直线型屈服轨迹和非相关联流动法则,利用不排水应力路径计算得到硬化函数,建立了一个考虑颗粒破碎的粗粒土本构模型。对比分析表明：该模型对粗粒土在各种围压下的应力-应变和体应变计算结果与试验曲线吻合较好。     

堆石料单粒强度尺寸效应的颗粒流模拟方法研究

围绕堆石料单粒强度尺寸效应的颗粒流模拟方法展开研究。首先,基于FISH二次开发建立了堆石料的随机不规则单粒模型,充分考虑堆石料的形状特征和破碎现象;然后,建立了堆石料单粒强度尺寸效应的等效模拟方法,以单粒强度随其粒径的变化规律为基础,推导了堆石料模型中细观黏结强度与堆石料等效粒径的负指数经验公式;其次,基于建立的数值模型对堆石料的室内单粒压缩试验进行仿真模拟,验证数值模型的正确性和合理性,并对较大粒径堆石料的单粒强度进行模拟预测,突出数值试验的优势;最后,基于建立的数值模型对相同粒径不同形状特征堆石料的单粒强度分布特征进行模拟研究。研究结果表明：（1）堆石料内部缺陷含量和尺寸随粒径增加对其单粒强度所产生的尺寸效应,可通过堆石料模型中细观强度参数随粒径折减进行等效模拟;（2）形状特征对堆石料的破裂机制具有重要影响,方形颗粒为压剪破裂,单粒强度较高,而随机不规则颗粒和圆形颗粒为拉剪或劈裂,单粒强度相对较低;（3）拉剪或劈裂条件下,堆石料形状越不规则,其单粒强度的离散程度越高,反之则离散程度越低。相关研究成果可为进一步研究荷载作用下堆石体内各粒径段堆石料的破碎量奠定基础,从而更加真实地反映堆石体的级配演化规律。     

DEM modeling of aging or creep in sand based on the effects of microfracturing of asperities and evolution of microstructural anisotropy during triaxial creep

Aging- or creep-related phenomena in sand have been widely studied, and the discrete element method (DEM) has been frequently used to model the associated soil behavior and then to explore the associated underlying mechanisms. However, several difficulties involved in modeling still remain unsolved. To resolve these difficulties, a new approach based on the effect of the microfracturing of asperities is proposed in this study for the DEM modeling of the sand aging or creep process through several aging cycles of associated reduction in the mobilized friction resistance at particle contacts and subsequent particle rearrangement to reach a new equilibrium state. This approach can be easily incorporated into different contact models and DEM simulations of the loading, unloading, and/or reloading processes, in either drained or undrained conditions, before and/or after aging. This new approach is proven effective because the DEM simulations incorporated with this new approach can satisfactorily reproduce the experimental observations in the triaxial creep process, drained and undrained recompression after aging, and 1D secondary compression and rebound. The simulation results also indicate that, based on the stress–force–fabric relationship, the contribution from the contact normal anisotropy to the deviatoric stress q gradually increases, whereas the contribution from the tangential force anisotropy becomes less during triaxial creep under a constant q. Moreover, the contacts between particles are gradually away from the state where the frictional resistance is fully mobilized, and then become more stable. During the subsequent triaxial recompression after creep, the aged samples exhibit enhanced soil stiffness, which is also found to be associated with the evolution of the invariants of the anisotropy tensors. It is worthwhile noting that the aging or creep effects on the microstructural changes, e.g., the invariants of the anisotropy tensors, can be gradually erased upon further recompression. This explains why the stress–strain responses of the aged samples during recompression gradually rejoin the original stress–strain response obtained from the sample without being subjected to aging or creep.