考虑微凸体变形相互作用的节理闭合变形模型

法向应力作用下节理的闭合变形是工程实践中常见但又未被很好解决的节理力学性质之一。依据弹性接触理论,提出考虑微凸体变形相互作用影响的闭合变形理论模型,该相互作用由一个均布荷载体现。模型采用不同接触下节理的组合形貌参数,适用于含起伏度分量的节理的闭合变形问题。较之于不考虑微凸体变形相互作用影响的Xia模型,新模型的计算值更为接近试验值。     

考虑基体变形的节理闭合变形理论模型

节理的表面形貌对其法向闭合变形有重要影响,对给定的节理而言,接触状态也是影响闭合变形的重要因素,不同接触状态得出的闭合变形曲线差异较大。基于Hertz理论的Greenwood模型不能考虑接触状态对闭合变形的影响,Brown模型引入不同接触状态节理的组合形貌拓展了Greenwood模型。对单个微凸体的弹性分析表明:Greenwood模型与Brown模型均没有考虑基体变形的影响,基于统计理论将考虑基体变形的单微凸体变形模型应用于整个粗糙节理表面得到一个新的节理闭合模型。最后,采用该模型分析处于不同接触状态的节理闭合变形数据并与Brown模型的计算结果进行比较,验证该模型的合理性。     

UDEC中Saeb-Amadei节理本构模型的二次开发

控制岩体水力学特性的节理在常法向应力边界条件和常法向刚度边界条件2种情况下的力学变形行为不同。由于Saeb-Amadei节理模型考虑了节理法向变形对节理剪切变形及剪胀的影响及节理吻合度对结果的影响,且适用于常法向应力边界与常法向刚度边界。引入Saeb-Amadei节理模型以研究裂隙岩体水力耦合特性。结合UDEC中的User-defined joint constitutive models接口,采用C++语言,编写Saeb-Amadei节理模型的数值嵌入程序Userjsa,进行单裂隙岩体的数值直剪和数值单轴压缩试验,对比计算结果与解析结果表明,计算结果与解析结果有很好的一致性,验证了数值嵌入程序Userjsa的正确性,为裂隙岩体水力耦合计算提供基础。     

法向循环加卸载条件下节理力学特征研究

将节理法向循环加卸载试验所得的法向应力–闭合量曲线分别采用半对数、双曲线本构方程进行拟合,得到2种类型节理法向刚度表达式,并将其引入持续屈服节理模型中,同时编写节理法向循环加卸载程序,首次实现节理非线性本构循环加卸载数值模拟分析。研究结果表明:建立的节理法向非线性本构循环加卸载数值试验方法行之有效;由双曲线方程得到的节理法向刚度值较由半对数方程得到的法向刚度值略有不同,但2种方法得到的节理法向应力–闭合量曲线数值模拟结果均与室内试验十分接近,均可有效表征节理法向循环加卸载力学特征。研究成果可为后续节理岩体动力学性质研究,边坡动力响应分析以及边坡稳定性、安全性评价等奠定基础。     

考虑实际接触三维粗糙度退化的软岩节理剪胀规律预测模型

为预测岩石节理的剪胀变形行为,分析了恒法向荷载作用下实际接触微凸体三维粗糙度在剪切过程中的退化规律,提出了一个适用于软岩节理的剪胀曲线预测模型。在剪切荷载作用下节理法向位移的变化是节理在三角形微凸体侧面爬坡上升行为与爬越一些微凸体顶点后闭合行为的叠加,爬坡行为与闭合行为引起的位移都正比于节理最大可能剪胀角。最大可能剪胀角退化的实质是实际接触节理微凸体平均等效倾角的退化。通过分析初始剪切与残余应力阶段的节理形貌特征,提出了计算初始最大可能剪胀角与残余应力阶段剪胀角的模型。基于软岩节理不发生突然脆性破坏的假设,进一步通过研究剪切过程中节理微凸体退化规律,量化了最大可能剪胀角的变化规律。定量了节理爬坡行为、闭合行为与最大可能剪胀角之间的关系,进而提出了节理剪胀规律预测模型,通过试验验证了模型的有效性。模型可较准确预测软岩节理的剪胀规律,并可合理描述节理初始阶段剪切压密行为。     

基于岩桥力学性质弱化机制的非贯通节理岩体直剪试验研究

 基于岩桥力学性质弱化机制,采用带伺服系统的直剪试验仪进行试验,在5级法向应力下,对3种含齿形节理的非贯通节理岩体进行直剪试验,研究非贯通节理岩体的强度特性和变形特性。在较低的法向应力下,含起伏角较低齿形节理面的非贯通节理岩体出现破坏模式I(张拉破坏模式)。在较高的法向应力下,含起伏角较高齿形节理面的非贯通节理岩体可能出现破坏模式II(先张拉后剪切破坏模式)。相同齿形节理面形貌的非贯通节理岩体,随着法向应力增大,峰值切向位移增大,抗剪强度增大。在相同的法向应力下,随着齿形节理面起伏角增大,非贯通节理岩体的峰值切向位移减小,抗剪强度增大。非贯通节理岩体黏聚力按Jennings方法计算值大于按试验拟合值;节理面较粗糙非贯通节理岩体内摩擦角按Jennings方法计算值大于按试验拟合值。     

弹性纵波在具有非线性法向变形本构关系的节理处的传播特征

对正向入射弹性纵波穿越岩石节理的过程及特性进行理论研究，所研究的岩石节理具有非线性法向变形本构关系。在没有剪切波的情况下，探讨节理的非线性法向变形行为对弹性纵波传播的影响。传统的有关应力波在节理处传播的线性位移不连续理论模型。发展为非线性模型-双曲模型（BB模型），依据此模型，获得了节理透射和反射系数的数值解。该数值解用来进行一系列的参数研究，包括节理初始刚度，节理闭合量相对于最大允许闭合量的比率以及入射波的振幅和频率对节理透射系数的影响等参数研究。也对线性和非线性位移不连续理论模型作了比较。结果表明，线性模型得到的透射和反射系数解是非线性解的一种特例，即当入射波的振幅很弱以至于在波传播中产生的最大节理闭合量相对于最大允许闭合量足够小的条件下，非线性与线性解等同，此外，还发现当波在节理处传播时，节理的非线性变形行为会引起一种高谐波现象。     

岩体节理法向变形的数学模型分析

法向变形是岩体节理的重要特征之一。在分析了岩体节理法向变形的对数模型、双曲线模型的基础上,提出了一种幂函数模型。用幂函数模型描述的回归曲线以及根据试验参数得到模拟曲线与试验值比较误差均较小。最后,对模型中参数的影响因素进行了分析。     

多组贯穿节理岩体正交各向异性变形参数研究

目前对于节理岩体各向异性变形参数的解析方法研究不多。假设岩块为各向同性线弹性体,结构面的应力与位移之间满足线性刚度关系,建立多组贯穿节理岩体的正交各向异性变形参数计算模型,相关计算公式简单实用。进一步的研究结果表明：对于贯穿节理岩体,其体积变形具有正交各向异性变形特性,而剪切变形并不具有明显的正交各向异性。最后通过3DEC数值验证与辅助研究,相关数值成果与理论计算相差较小,说明该理论模型对于岩体各向异性变形与稳定性评价有一定的参考价值。     

改进的岩石节理弹性非线性法向变形本构模型研究

回顾了已有的几类岩石节理法向变形本构模型,指出以往模型在中应力水平条件下模拟结果与试验结果发生偏离的现象。针对这一问题,引入"半值节理最大闭合量应力"σ1/2概念,着重论述了传统的BB模型与经典指数模型本身所固有的数学缺陷。随后,以Malama和Kulatilake(2003)提出的统一指数模型为例,进一步阐明模型改进的必要性,同时分析了该模型因采用对σn/σ1/2项添加幂函数n的修正方式而丢失节理法向初始刚度Kni的物理意义这一不足之处。基于上述研究,根据前人试验数据分析建立单调加载条件下岩石节理法向应力–位移关系曲线的控制微分方程,定义拟节理最大允许闭合量Dmax=ξdmax的概念,提出一种新的三参数本构模型--改进的岩石节理弹性非线性法向变形本构关系,并在数学上严格证明了BB模型与经典指数模型是新模型的两个特例。新模型克服了前述模型数学上的缺陷,弥补了以往模型模拟结果与试验结果发生偏离的不足,且没有因新参数ξ的添加丢失Kni的物理意义。最后采用新模型对他人试验结果进行预测,建议了修正参数ξ的确定方法。模型预测结果与试验结果吻合良好,进而验证了本文模型的可行性。     

Influence of asperity degradation on the mechanical behavior of rough rock joints under cyclic shear loading

A cyclic shear testing system was established to investigate the mechanical behavior of rough rock joints under cyclic loading conditions. Laboratory cyclic shear tests were conducted for two joint types of Hwangdeung granite and Yeosan marble: saw-cut and split tensile joints. Prior to test, the roughness of each specimen was characterized by measuring the surface topography using a laser profilometer. Several important aspects of cyclic joint behavior, such as high peak shear strength and non-linear dilation in the first loading cycle, different frictional resistance for the reversed shear loading direction, and anisotropic shear behavior and its dependence on the normal stress level were identified from the cyclic shear test results. These features and their variations in the subsequent loading cycles are mainly due to the effect of second order asperities and strength of rock material. It was also observed from experimental results that degradation of asperities under cyclic shear loading also followed the exponential degradation laws for asperity angle and the mechanism for asperity degradation would be different depending upon the shearing direction and the type of asperities. Based on the experimental results an elasto-plastic constitutive model, which can consider the degradation of second order asperities, was proposed. Numerical simulations for the monotonic and cyclic shear loading indicated agreement with the laboratory test results.     

The implications of joint deformation in analyzing the properties and behavior of fractured rock masses, underground excavations, and faults

For a given stress state, joint deformation depends on the joint’s geometry, including surface roughness, spatial geometry of the contact area, and large-scale topographical features such as dips. Under normal stress, contacting asperities compress, and the half spaces bounding the joint are deformed. A very significant consequence of half-space deformation is that it allows mechanical interaction among all contact points between the joint surfaces. As a result, the contact area’s overall spatial geometry plays an important role in determining the distribution of stress across joint surfaces and the change in geometry of the void space between surfaces that occurs with changes in stress. Mechanical interaction among contact points is important in determining normal joint stiffness: two joints with the same total contact area can have substantially different stiffnesses depending on the spatial geometry of their contact areas. Modeling results indicate that joints with small contact areas uniformly distributed across the surfaces can be nearly as stiff as a perfectly mated interface. These results have significant implications for almost any endeavor in fractured rock, including designing underground excavations, predicting the hydraulic response of a rock mass to changes in stress, understanding the deformation and failure of joints under shear stress, and analyzing the stability of faults. In underground excavations, for example, deformation of the roof and floor means that the load acting on any supporting pillar and the distribution of stress throughout the pillar depend on: the pillar’s size and shape; the size, shape, and proximity of neighboring pillars; and the spatial geometry of the pillar array. Purely elastic deformation can lead to either catastrophic or progressive failure. Similarly, to accurately predict fluid flow through jointed rock, changes in void space geometry that result from changes in stress must be considered; these changes in geometry are not predicted by methods that assume that aperture changes uniformly across the joint. For joints and faults, the nonuniform distribution of normal and shear stresses resulting from surface roughness and mechanical interaction between contact points suggests a progressive form of shear failure. Failure is initiated at points of low normal stress and propagates as stress from failed asperities is redistributed to neighboring asperities. Consistent with observations on many faults, modeling and analytical results predict that earthquakes on a fault would be clustered in time and space because of mechanical interaction between persistent asperities.     

Quantifying topography and closure deformation of rock joints

This paper presents a study for quantifying both the joint topography characteristics and the load–closure deformation of a rock joint under normal compressive loading condition. The study covers (1) laboratory measurements of rock joint surface profiles using a profilometer designed and fabricated by the research team, (2) development of a mathematical method to identify the waviness and unevenness components in joint surface profiles and the associated composite topography, (3) development of a general load–closure deformation model by using both the waviness and unevenness components in the composite topography, (4) unconfined compressive testing of rock samples with joints for the experimental load–closure deformation of joints and, (5) verification of the general load–closure deformation model by the experimental load–closure deformation results. The study leads to the following four findings: (a) the mathematical method can be used to identify the waviness and unevenness components for joint surface profiles and its composite topography. The height characteristic parameters of the complete surface topography of a joint are mainly determined by the waviness component. The texture characteristic parameters of the complete surface topography of a joint are mainly determined by the unevenness component, (b) joints can be classified into the three contact state cases using the waviness and unevenness components for both the joint surface profiles and the associated composite topography. The load–closure deformation behavior of a joint is determined by the waviness and unevenness components of the composite topography for a specific contact state, (c) the general load–closure deformation model developed in this paper is applicable to the three contact state cases. The general load–closure deformation model uses the composite topography of a joint and can take into account the effects of the contact states, the initial aperture and the waviness and unevenness components; (d) parametric studies and verifications with the uniaxial compression test results show that the general load–closure deformation model gives reasonable estimations of the load–closure deformation behavior of rock joint under compressive loading and can be reduced to those given by other researchers in the relevant literature.     

考虑多尺度结构的贯通节理岩体损伤摩擦耦合模型

基于贯通节理岩体结构的多尺度特征,采用两步均匀化方法,给出了节理岩体在复杂荷载作用下的自由焓表达式,建立了节理岩体损伤摩擦耦合本构模型。模型可同时考虑岩块损伤扩展、微裂纹滑移剪胀、法向刚度恢复,节理面多阶凸起体滑移磨损、剪胀演化以及节理与岩块相互作用等特征,较好地反映岩体内部微裂纹、节理等不同尺度微结构变化对其力学特性的影响。采用Lac du Bonnet花岗岩三轴压缩试验、花岗岩节理剪切试验以及不同节理倾角与不同围压下Martinsburg板岩三轴压缩强度试验等成果对模型进行了验证,模型预测值与实测值相当吻合,论证了模型的准确性。     

不同频率载荷作用下的岩石节理本构模型

用Instron1342材料试验机对表面含二、三、四锯齿状人工节理试样进行4种不同频率载荷下的动态压缩试验。通过对试验结果的分析,获得加载频率和表面形态对节理闭合变形性质的影响规律。通过5种常用函数方程对节理动态压缩试验数据的拟合,发现用幂函数模型来描述人工节理动态压缩闭合变形性质较好。根据试验数据,得出模型参数与载荷频率之间的关系,从而建立考虑率效应的节理本构模型,并进行试验验证。     

A constitutive model for the deformation of a rock mass containing sets of ubiquitous joints

As part of the rock mass, the discontinuities inherently affect the strength and the deformational behavior of rock mass. Existing models can either handle the pre- or post-peak deformation of intact rock or joints alone; however, a model which can determine the failure mode and simulate the complete pre- and post-deformation of rock mass with multi-sets of joints is not yet available. This study focusses on rock mass with multi-sets of ubiquitous joints and establishes a mathematic model and an associated numerical implementation accounting for the anisotropy in strength and deformation induced by the existence of joints. Accordingly, an approach incorporating the existing models or methods to enable simulation of the complete deformation of rock mass is proposed. In addition to the pre- and post-peak deformation characteristics for intact rock, the pre-peak deformation of joint, such as the closure, shear and dilatancy effect as well as its post-peak deformation, such as the reduction on roughness, have also been taken into account. A series of comparisons validates that the proposed model is capable of presenting the joint-induced anisotropy in strength and deformation of rock mass, determining the possible failure modes and reasonably simulating the complete stress–strain relationship as well.     

剪切过程中岩石节理粗糙度分形演化及力学特征

在系统测量和试验的基础上，研究了剪切过程中岩石节理粗糙面的分形特征和岩石节理的力学行为，阐述了岩石节理面分形维数Ｄ和截距Ａ与岩石节理在载荷作用下法向、切向变形以及抗剪强度之间的关系，得出岩石节理在剪切过程中由于表面损伤而引起的表面分维Ｄ和截距Ａ的演化规律。研究表明：分维Ｄ和截距Ａ是描述节理面粗糙性的两个重要的参数。前者反映节理粗糙面的不规则程度，后者则与节理面粗糙体（ａｓｐｅｒｉｔｉｅｓ）的坡度密切相关。仅依据分形维数Ｄ不足以确定岩石节理的粗糙性与岩石节理力学行为之间的关系。在许多情况下，岩石节理的力学性质对截距Ａ的依赖程度大于对分维Ｄ的依赖程度     

剪胀和破坏耦合的节理岩体本构模型的研究

 摘要：根据节理岩体切向加载作用下的变形机制,把微凸体在磨损破坏过程中引起的剪胀软化现象和伴随的强化现象分开考虑,提出一种新的本构模型。试验结果表明,在法向和切向载荷共同作用下,由于微凸体的爬坡和啃断作用,节理岩体均会发生一定程度的剪胀和磨损,累积到一定程度就产生软化现象,在此引入一个初始剪应力概念体现上述特征。另一方面,由于破碎颗粒的碾压和迁移作用,使得抗剪力学行为由微凸体粗糙度控制逐渐转变为由结构面上形成的紧密夹层的力学行为所控制,抗剪强度提高,在此通过弹塑性随动强化模型来体现这一变形行为。当随动强化模型与初始剪应力相结合时,即为节理岩体切向加载作用下的剪应力–切向位移本构关系。通过对各种已有试验曲线的对比分析,验证该模型的正确性。     

Instantaneous stress release in fault surface asperities during mining-induced fault-slip

Fault-slip taking place in underground mines occasionally causes severe damage to mine openings as a result of strong ground motion induced by seismic waves arising from fault-slip.It is indicated from previous studies that intense seismic waves could be generated with the shock unloading of fault surface asperities during fault-slip.This study investigates the shock unloading with numerical simulation.A three-dimensional(3D) numerical model with idealized asperities is constructed with the help of discrete element code 3DEC.The idealization is conducted to particularly focus on simulating the shock unloading that previous numerical models,which replicate asperity degradation and crack development during the shear behavior of a joint surface in previous studies,fail to capture and simulate.With the numerical model,static and dynamic analyses are carried out to simulate unloading of asperities in the course of fault-slip.The results obtained from the dynamic analysis show that gradual stress release takes place around the center of the asperity tip at a rate of 45 MPa/ms for the base case,while an instantaneous stress release greater than 80 MPa occurs near the periphery of the asperity tip when the contact between the upper and lower asperities is lost.The instantaneous stress release becomes more intense in the vicinity of the asperity tip,causing tensile stress more than 20 MPa.It is deduced that the tensile stress could further increase if the numerical model is discretized more densely and analysis is carried out under stress conditions at a great depth.A model parametric study shows that in-situ stress state has a significant influence on the magnitude of the generated tensile stress.The results imply that the rapid stress release generating extremely high tensile stress on the asperity tip can cause intense seismic waves when it occurs at a great depth.