An anisotropic strength criterion for jointed rock masses and its application in wellbore stability analyses

In this paper, an anisotropic strength criterion is established for jointed rock masses. An orientation distribution function (ODF) of joint connectivity, is introduced to characterize the anisotropic strength of jointed rock masses related to directional distributed joint sets. Coulomb failure condition is formulated for each plane of jointed rock masses by joint connectivity, where the friction coefficient and cohesion of the jointed rock mass are related to those of the intact rock and joint and become orientation dependent. When approximating joint connectivity by its second‐order fabric tensor, an anisotropic strength criterion is derived through an approximate analytical solution to the critical plane problem. To demonstrate the effects of joint distribution on the anisotropic strength of jointed rock masses, the failure envelopes are worked out for different relative orientations of material anisotropy and principal stress axes. The anisotropic strength criterion is also applied to wellbore stability analyses. It is shown that a borehole drilled in the direction of the maximum principal in situ stress is not always the safest due to the anisotropic strength of the jointed rock mass. Copyright © 2007 John Wiley & Sons, Ltd.     

Anisotropic Deformation of a Circular Tunnel Excavated in a Rock Mass Containing Sets of Ubiquitous Joints: Theory Analysis and Numerical Modeling

Determining anisotropic deformation surrounding underground excavations for tunnels is an intuitional task that involves many difficulties due to the inherent anisotropies in the strength and deformability of natural rocks. This study investigates joint-induced anisotropic deformation surrounding a tunnel via a numerical simulation that accounts for the mechanical behavior of intact rock, the orientations of joint sets, and the mechanical behavior of joint planes; this numerical simulation can model the complete stress–strain relationship with anisotropic rock mass characteristics. Simulation results demonstrate that the well-known excavation-induced stress variation–decrease in the radial component and increase in the tangential component–decrease shear strength and increase shear stress for the joint plane tangential to the tunnel wall, resulting in joint sliding failure and considerable shear deformation. This joint sliding failure and significant shear deformation account for the joint-induced anisotropic deformation surrounding a tunnel. When a rock mass has two joint sets with unfavorable joint orientations, the area with joint sliding failure can deteriorate mutually, resulting in large anisotropic deformation. Additionally, for a rock mass containing three joint sets with well-distributed orientations, joint sliding in various joint sets and associated stress variations can counter balance each other, resulting in less anisotropic deformation than those of rock masses containing one or two joint sets.     

单轴压缩荷载下非贯通闭合节理岩体损伤本构模型

目前损伤力学已被认为是研究节理岩体力学行为的有效工具,但是在目前的节理岩体损伤变量定义中大多仅考虑节理几何特征而未考虑节理内摩擦角等力学参数,这显然不能很好地反映节理岩体的力学特征。为此,拟推导出一个能够综合考虑节理几何及力学参数的损伤变量（张量）,并由此建立单轴压缩荷载下岩体损伤本构模型。首先,基于断裂力学的由于单个节理存在引起的附加应变能增量与损伤力学的损伤应变能释放量相关联的观点,推导出了含非贯通节理岩体的损伤变量计算公式;其次,根据断裂力学理论对单轴压缩荷载下的单个节理尖端应力强度因子计算方法进行了研究,得出了应力强度因子K_Ⅰ、K_Ⅱ的计算公式;同时考虑多节理间的相互作用给出了单组单排及多排非贯通节理应力强度因子计算公式。最后,利用该模型对含单条非贯通节理的岩体在单轴压缩荷载作用下的峰值强度及损伤变量进行了分析计算。结果表明,当节理倾角小于其内摩擦角时,岩体强度与完整岩石相同,岩体损伤为零,而后随着节理倾角增加,岩体强度、损伤随节理倾角的变化分别呈开口向上及向下的抛物线,当节理倾角约为60°时,岩体损伤最大,强度最低。随着节理长度增加,岩体损伤增加,而随着节理内摩擦角的增加,岩体损伤则减小。      

Parametric study of the smooth‐joint contact model on the mechanical behavior of jointed rock

The smooth‐joint contact model based on distinct element method has been widely used to represent discontinuity in the simulation of fractured rock mass, but there is rare efficient guidance for the selection of proper parameters of smooth‐joint contact model, which is the basement for using this model properly. In this paper, the effect of smooth joint parameters on the macroscopic properties and failure mechanism of jointed rock under triaxial compression test is investigated. The numerical results reveal that the friction coefficient of smooth joint plays a dominant role in controlling mechanical behaviors. The stiffness of smooth joint has a relative small influence on the mechanical behaviors. Poisson ratio decreases with the reduction of normal stiffness but increases with the reduction of shear stiffness. The reduction of smooth joint strength, which is determined by normal strength, cohesion, and friction angle of smooth joint, contributes to the breakage of bonded smooth joint and ultimately decreases the strength of the specimen. We proposed a detailed calibration process for smooth‐joint contact model according to the relationship between smooth‐joint parameters and mechanical properties. By following this process, the numerical results are validated against corresponding experimental results and good agreement between them can be found in stress‐strain curves and failure modes of different joint orientations. Further analyses from the microperspective are performed by looking at transmission of contact force, the nature and distribution of microcracks, and the particle displacement to show the failure process and failure modes.     

节理岩体超声测试及单轴压缩试验研究

为了获取节理岩体各向异性力学特性和声波传播规律的相互关系,通过制作圆柱形单一预制贯通节理试件,开展了7种不同倾角节理试件的超声波波速测试和单轴压缩试验。试验结果表明：（1）节理试件波速测试值离散性较大,但总体服从正态分布,波速平均值介于石膏试件和完整试件之间,波速随节理倾角增大呈线性递减;（2）不同倾角的节理面对节理试件力学特性的影响很大,在应力-应变关系、变形特征、强度特征和破坏模式上均表现出显著的各向异性特征;（3）节理试件的力学性质和超声波传播特性变化规律区别很大,采用超声波波速确定节理试件的力学参数会存在很大误差。     

On the role of joint roughness on the micromechanics of rock fracturing process: a numerical study

The deformation process and failure mechanism of rock mass with increased joint roughness subjected to unconfined compression are investigated in this study using discrete element method. A numerical model is developed using soft-bonded particle and validated to realistically replicate the mechanical response of the rock mass. The micro-parameters of the rock material are first determined, and the effects of the joint roughness on the macromechanical response and fracture growth mechanism are then investigated. Analyses are also performed to examine the tensile and shear crack distributions, acoustic emission (AE) characteristics, coordination number, and crack anisotropy to advance the current understanding of the role of joint roughness on the mechanical behavior and deformability of rock mass. The results show that strength and deformability of the jointed rocks are highly dependent on the joint orientation and roughness. Joint roughness is found to restrain the propagation and coalescence of microcracks and AE events from the interlocking of asperities. In addition, the spatial distribution of the contact forces allows for better understanding of the effect of joint inclination angle on the response of the investigated rock samples.

     

Strength and Deformational Behaviour of a Jointed Rock Mass

Summary An assessment of the strength and deformational response of jointed rock masses is an essential requirement in the site selection, design and successful execution of Civil and Mining Engineering projects. A quick estimate of these properties for preliminary evaluation of alternate sites, will reduce considerable expenditures for field tests. An attempt has been made in the present study to develop a link between strength and deformability of jointed block masses with the properties of intact specimens, obtained from simple laboratory tests, taking into account the influence of the properties of the joints. Extensive experimentation has been carried out on large specimens of jointed block masses under uniaxial compression. The model material represents a low strength rock. Various joint configurations were introduced to achieve the most common modes of failure occurring in nature. A coefficient called Joint Factor has been used to account for the weakness brought into the intact rock by jointing. Methods of computing the Joint Factor for various modes of failure of a jointed mass in an unconfined state have been established. The effect of Joint Factor on strength and tangent modulus of the mass has been studied and the values have been correlated with those of intact rock. Guidelines for assessing probable modes of failure of a jointed mass will enable one to estimate the relevant strength and tangent modulus of the mass.     

三维梁-颗粒模型在岩石材料破坏模拟中的应用

用三维梁-颗粒模型BPM3D(beam-particlemodelinthreedimensions)对岩石类非均质脆性材料的力学性质和破坏过程进行了数值模拟。梁-颗粒模型是在离散单元法基础上,结合有限单元法中的网格模型提出的用于模拟岩石类材料损伤破坏过程的数值模型。在模型中,材料在细观层次上被离散为颗粒单元集合体,相邻颗粒单元由有限单元法中的弹脆性梁单元联结。梁单元的力学性质均按韦伯(Weibull)分布随机赋值,以模拟岩石类材料力学参数的空间变异性。材料内部裂纹通过断开梁单元来模拟。通过自动生成的非均质材料模型对岩石类材料的破坏机理进行研究。岩石类非均质脆性材料在单轴压缩状态下破坏过程细观数值模拟结果显示,岩石材料宏观破坏是由于其内部细观裂纹产生、扩展、贯通的结果。通过数值模拟结果之间的对比分析,揭示出岩石试样宏观破坏模式随细观层次上韦伯分布参数的变化而不同。与实际矿柱破坏形态的对比分析表明了模型的适用性。根据数值模拟结果对岩石类非均质材料的破坏机理进行了探讨。     

基于颗粒离散元模型的不同加载速率下花岗岩数值试验研究

不同加载速率条件下岩石的力学特性,对于其动载下破裂内在机制的研究具有积极的意义。基于颗粒流理论,通过黏结颗粒模型（bonded particle model,简称BPM）虚拟实现不同加载速率0.001～0.500 m/s下花岗岩单轴压缩和巴西劈裂试验,定量分析加载速率对应力-应变、破裂形态、应变能率及声发射的影响。结果表明：单轴抗压强度和抗拉强度及其对应峰值应变随加载速率增加而非线性增长;单轴压缩作用下,随加载速率增加,试样由单一斜截面破坏向多斜截面破坏转变,且主控裂隙带宽度急剧增大,由裂纹数量及水平向高应变率区域变化规律可明显看出,试样破坏程度随着加载速率增加而逐渐加剧;巴西劈裂作用下试样从一条主控裂隙向多条主控裂隙转变,且裂纹向圆盘试样两侧边缘部分延伸,破坏程度加剧;单轴压缩和巴西劈裂作用下,声发射事件及应变能率均随加载速率增加而呈现出非线性增长趋势。     

单一预制节理试件各向异性力学特性试验研究

节理岩体具有特殊的不连续结构,从而展现出复杂的各向异性力学特性。为了掌握这一复杂力学特性,从理论上分析了单一节理面的力学效应,并通过常规三轴压缩试验研究了单一预制贯通节理试件的各向异性力学特性。结果表明,节理试件的力学特性分为受节理面控制和岩块控制;与完整试件相比,节理试件的力学参数均有不同程度降低,其中弹性模量、抗压强度、黏聚力随节理倾角呈U型分布,最小值均出现在60°倾角节理试件,而内摩擦角与节理倾角呈线性增大关系;随着围压等级升高,不同倾角节理试件弹性模量和抗压强度的最大值与最小值的比值降低,力学性能差异减小。     

预制节理岩体试件强度及破坏模式的试验研究

采用相似材料模型试验对不同节理倾角、节理贯通度、节理组数、载荷应变率、试件长径比、节理充填物厚度及类型等7种工况下的预制节理岩体在单轴压缩下的峰值强度及破坏模式进行了研究。结果表明：节理岩体的破坏模式及峰值强度与节理构造形态密切相关。贯通节理岩体将产生沿节理面的剪切破坏或穿切节理面破坏,且与第1种破坏模式对应的岩体峰值强度更低。非贯通节理岩体的强度介于完整岩体和贯通节理岩体之间。随着平行节理组数的增加,岩体峰值强度逐渐下降。随着载荷应变率的增加,岩体峰值强度逐渐增大,相应地试件的破坏模式也变得更加复杂。试件长径比基本没有改变其破坏模式,完整试件仍主要是以张拉破坏为主,而节理试件仍以剪切破坏为主。随着长径比增加,试件峰值强度逐渐增大。随着节理充填物厚度增加,试件峰值强度降低。不同节理填充物对试件峰值强度也有一定影响。     

多尺度节理岩体力学特性的颗粒流分析

以白云鄂博露天铁矿东矿岩质高边坡为工程背景,结合现场地质调查、室内岩石和节理力学试验等数据,采用等效岩体技术,构建能充分反映节理分布特征的实验室、现场原位试验和工程尺度等多尺度等效岩体模型。通过对各类等效岩体模型进行单轴压缩试验,研究岩体单轴抗压强度、弹性模量等力学特性的尺寸效应和各向异性。研究表明：节理的存在使岩体表现出尺寸效应和各向异性,且随着尺寸的增大,这种特性基本呈逐渐减弱的趋势;研究区域岩体的表征单元体积、单轴抗压强度和弹性模量分别为20 m×10 m×10 m、1.46 MPa和3.91 GPa;岩体单轴抗压强度、弹性模量与轴向尺寸的关系,近似符合渐进式指数函数关系,且该函数能直观地给出工程尺度岩体的力学特性。     

Slope failure analysis considering anisotropic characteristics of foliated rock masses

Weak planes affect the strength and deformational behaviors of rock slopes, and the anisotropic characteristics of rock mass should be considered in slope stability analysis. Effects of joint plane orientations on failure mechanism and strength response of inherently anisotropic rock samples were firstly investigated. The specimens with various orientations of joints were evaluated under uniaxial compression, Brazilian tensile, and direct shear tests. By treating the foliated rock as transversely isotropic materials, the relevant elastic constants and strength parameters were obtained from experimental results. The slope damage zone was then investigated using Comsol Multiphysics code based on Hoffman criterion. It is indicated that the failure mechanism and strength response depend highly on the inclination of specimens with respect to the loading direction. For disks with the same inclination angle, the value of tensile strength has an increasing trend with the total fracture length. Numerical results show that partial slope mass failed in single slope and no large-scale landslide occurred. The failure pattern in numerical results agrees well with the field observations. The cooperation between the experimental results and the numerical results allows an in-depth analysis of the experimental results and thus better understanding the dominant effect of joints on the deformation and failure of rock mass.     

Damage Constitutive and Failure Prediction of Artificial Single-Joint Sandstone Based on Acoustic Emission

The effect law of deformation and failure of a jointed rock mass is essential for underground engineering safety and stability evaluation. In order to study the evolution mechanism and precursory characteristics of instability and failure of jointed rock masses, uniaxial compression and acoustic emission (AE) tests are conducted on sandstones with different joint dip angles. To simulate the mechanical behavior of the rock, a jointed rock mass damage constitutive model with AE characteristic parameters is created based on damage mechanics theory and taking into account the effect of rock mass structure and load coupling. To quantify the mechanism of rock instability, a cusp catastrophe model with AE characteristic parameters is created based on catastrophe theory. The results indicate that when the joint dip angle increases from 0° to 90°, the failure mechanism of sandstone shifts from tensile to shear, with 45° being the critical failure mode. Sandstone's compressive strength reduces initially and subsequently increases, resulting in a U-shaped distribution. The developed damage constitutive model's theoretical curve closely matches the test curve, indicating that the model can reasonably describe the damage evolution of sandstone. The cusp catastrophe model has a high forecast accuracy, and when combined with the damage constitutive model, the prediction accuracy can be increased further. The research results can provide theoretical guidance for the safety and stability evaluation of underground engineering.

     

含结构面岩体试样单轴强度与变形特征

结构面是岩体区别于岩石材料的一大特征,其产状、迹长、密度等参数对岩体的力学性质有着重要影响。本文利用FLAC3D对含结构面岩体试样的单轴压缩特性进行了较为系统的数值模拟研究。文中建立了含不同组贯通性结构面的岩体试样模型和含不同倾角及迹长的非贯通结构面岩体试样模型,对每个试样进行单轴压缩试验的数值模拟,结构体和结构面均采用Mohr-Coulomb剪切和拉伸破坏准则。模拟中用编制的伺服控制程序通过调节加载速度,控制试样内最大不平衡力,研究含结构面试样单轴压缩情况下的变形、强度及破坏方式等特征。模拟结果显示,含1-3组贯通性结构面试样呈现各向异性特征,而含4组贯通性结构面试件呈现各向同性特征。随着贯通性结构面数量的增多,同尺寸试件的变形强度参数劣化。含单组非贯通性结构面试件,其单轴压缩模拟试验的应力-应变曲线峰值后出现应力降。基于Mohr-Coulomb抗剪强度准则和损伤理论所得的解析解与数值模拟结果所得的非贯通性结构面试件的单轴压缩强度不符,说明用抗剪强度准则与损伤理论刻画非贯通结构面试样的强度并不合理。随着非贯通性结构面贯通率的增大,试件的变形、强度参数劣化。含单组结构面试件的破坏方式可分为结构面控制破坏,结构面部分控制破坏和结构面不控制破坏3种类型,而随着结构面组数的增多,结构面控制试样破坏的概率增加。     

基于RJM断续节理岩体强度与破坏特征的数值模拟研究

裂隙结构的存在对于工程岩体的强度和稳定性具有重要影响,岩石宏观裂隙的产生源自于微破裂的积累。针对岩体裂隙的粗糙特性,通过Matlab建立考虑粗糙度的节理模型（Roughness Joint Model）,采用简化的正弦曲线来表示粗糙节理,并将其导入到颗粒流试验模型中进行单轴压缩试验。对比完整岩体、直线型裂隙岩体、RJM岩体三者破坏的应力-应变曲线,改变裂隙倾角（与水平方向夹角）α,岩桥倾角β,裂隙密度γ,建立不同裂隙分布的断续节理岩体数值试样,开展一系列数值模拟试验。研究结果发现:（1）裂隙的存在明显降低了岩体的抗压强度,RJM模型峰值强度和峰值应变均高于直线型裂隙岩体;（2）岩体抗压强度总体上随裂隙倾角增大而增加,随裂隙密度增加而减小,但随岩桥倾角的改变呈非线性变化,岩桥倾角45°时峰值强度最低,峰值应变最小;（3）裂隙分布会影响岩体的破裂模式,微裂隙的扩展反映了岩体力学性质的各向异性;（4）不同倾角下增加裂隙密度,岩体强度下降程度不同,倾角75°时密度对强度影响最小,30°和60°时影响最大。     

缓倾斜层状岩体单轴压缩力学行为的颗粒流数值模拟

针对不同层理面强度的缓倾斜层状岩体在单轴压缩试验中产生不同破坏形式的问题,以室内原岩单轴压缩试验结果为依据,采用颗粒流程序建立了缓倾斜层状岩体单轴压缩数值模型,研究了不同层理面强度条件下的缓倾斜层状岩体强度及破坏形式变化特征,并分析了不同工况时缓倾斜层状岩体微裂纹发育及演化规律和细观颗粒的位移演化规律,研究表明:当层理面强度远小于层理面间完整岩体强度时,层理面在一定程度上降低了层状岩体的整体强度,宏观破断面为沿层理面和贯穿层理面的折线型破断面;当层理面强度与层理面间完整岩体强度相近时,宏观破断面主要为光滑单斜面;当层理面强度远大于层理面间完整岩体强度时,层状岩体的强度由层理面间完整岩体的强度决定,宏观破断面主要为X型共轭破坏面。     

Microplane damage model for jointed rock masses

The paper presents a new microplane constitutive model for the inelastic behavior of jointed rock masses that takes into account the mechanical behavior and geometric characteristics of cracks and joints. The basic idea is that the microplane modeling of rock masses under general triaxial loading, including compression, requires the isotropic rock matrix and the joints to be considered as two distinct phases coupled in parallel. A joint continuity factor is defined as a microplane damage variable to represent the stress‐carrying area fraction of the joint phase. Based on the assumption of parallel coupling between the rock joint and the rock matrix, the overall mechanical behavior of the rock is characterized by microplane constitutive laws for the rock matrix and for the rock joints, along with an evolution law for the microplane joint continuity factor. The inelastic response of the rock matrix and the rock joints is controlled on the microplane level by the stress–strain boundaries. Based on the arguments enunciated in developing the new microplane model M7 for concrete, the previously used volumetric–deviatoric splits of the elastic strains and of the tensile boundary are avoided. The boundaries are tensile normal, compressive normal, and shear. The numerical simulations demonstrate satisfactory fits of published triaxial test data on sandstone and on jointed plaster mortar, including quintessential features such as the strain softening and dilatancy under low confining pressure, as well as the brittle–ductile transition under higher confining pressure, and the decrease of jointed rock strength and Young's modulus with an increasing dip angle of the joint. Copyright © 2014 John Wiley & Sons, Ltd.     

节理岩体圆形隧道滑动区的研究

对于连续介质问题,可以利用Mohr-Coulomb准则很好地解决圆形隧道滑动区问题.但是对于节理岩体问题要复杂得多.由于节理岩体具有复杂的力学特性,因此节理岩体圆形隧道滑动区的确定问题一直都没有很好地解决.节理岩体的力学特性可以很好地用考虑了中间主应力影响的非线性统一强度准则来表达.根据非线性统一强度准则确定了即时摩擦角,进而获得了节理岩体圆形隧道滑动区和支护应力的封闭形式的理论解,并给出了算例.     

单轴压缩条件下岩溶化裂隙岩体损伤破坏特征研究

岩溶化裂隙岩体是普遍发育于自然界中具有初始损伤的岩体。为了研究岩溶化裂隙岩体损伤破坏特征,本文以贵州某地赋存的溶蚀岩体为研究对象,运用损伤力学理论构建岩溶化裂隙岩体在单轴压缩条件下的损伤演化模型,并建立岩溶化裂隙岩体损伤演化方程。采用颗粒流数值软件进行单轴压缩数值试验,进一步研究岩溶化裂隙岩体试件在单轴压缩条件下的损伤演化特征,分析岩溶化裂隙岩体的微观损伤特征。结果表明:岩溶化裂隙岩体的初始损伤主要包括溶蚀损伤和裂隙损伤。岩溶化裂隙岩体的初始损伤随着溶蚀率的增加而增加,最终增加速率趋于平缓;岩溶化裂隙岩体的损伤演化曲线均呈“S”型变化,先缓慢增加,再迅速增加,最后缓慢增加至损伤值1;岩溶化裂隙岩体存在异构特征,导致破坏裂隙起源于具有初始损伤的溶蚀孔洞和裂隙处,随后裂隙经历萌发、扩张和剪切作用、数量和长度增加以及裂隙贯通4个阶段后发生宏观破坏。