Advances in joint roughness coefficient (JRC) and its engineering applications

The joint roughness coefficient (JRC), introduced in Barton (1973) represented a new method in rock mechanics and rock engineering to deal with problems related to joint roughness and shear strength estimation. It has the advantages of its simple form, easy estimation, and explicit consideration of scale effects, which make it the most widely accepted parameter for roughness quantification since it was proposed. As a result, JRC has attracted the attention of many scholars who have developed JRC-related methods in many areas, such as geological engineering, multidisciplinary geosciences, mining mineral processing, civil engineering, environmental engineering, and water resources. Because of such a developing trend, an overview of JRC is presented here to provide a clear perspective on the concepts, methods, applications, and trends related to its extensions. This review mainly introduces the origin and connotation of JRC, JRC-related roughness measurement, JRC estimation methods, JRC-based roughness characteristics investigation, JRC-based rock joint property description, JRC's influence on rock mass properties, and JRC-based rock engineering applications. Moreover, the representativeness of the joint samples and the determination of the sampling interval for rock joint roughness measurements are discussed. In the future, the existing JRC-related methods will likely be further improved and extended in rock engineering.

On the calibration of a shear stress criterion for rock joints to represent the full stress-strain profile

Conventional numerical solutions developed to describe the geomechanical behavior of rock interfaces subjected to differential load emphasize peak and residual shear strengths.The detailed analysis of preand post-peak shear stress-displacement behavior is central to various time-dependent and dynamic rock mechanic problems such as rockbursts and structural instabilities in highly stressed conditions.The complete stress-displacement surface(CSDS)model was developed to describe analytically the pre-and post-peak behavior of rock interfaces under differential loads.Original formulations of the CSDS model required extensive curve-fitting iterations which limited its practical applicability and transparent integration into engineering tools.The present work proposes modifications to the CSDS model aimed at developing a comprehensive and modern calibration protocol to describe the complete shear stressdisplacement behavior of rock interfaces under differential loads.The proposed update to the CSDS model incorporates the concept of mobilized shear strength to enhance the post-peak formulations.Barton’s concepts of joint roughness coefficient(JRC)and joint compressive strength(JCS)are incorporated to facilitate empirical estimations for peak shear stress and normal closure relations.Triaxial/uniaxial compression test and direct shear test results are used to validate the updated model and exemplify the proposed calibration method.The results illustrate that the revised model successfully predicts the post-peak and complete axial stressestrain and shear stressedisplacement curves for rock joints.

Investigation on the Indeterminate Information of Rock Joint Roughness through a Neutrosophic Number Approach

To better estimate the rock joint shear strength,accurately determining the rock joint roughness coefficient(JRC)is the first step faced by researchers and engineers.However,there are incomplete,imprecise,and indeterminate problems during the process of calculating the JRC.This paper proposed to investigate the indeterminate information of rock joint roughness through a neutrosophic number approach and,based on this information,reported a method to capture the incomplete,uncertain,and imprecise information of the JRC in uncertain environments.The uncertainties in the JRC determination were investigated by the regression correlations based on commonly used statistical parameters,which demonstrated the drawbacks of traditional JRC regression correlations in handling the indeterminate information of the JRC.Moreover,the commonly used statistical parameters cannot reflect the roughness contribution differences of the asperities with various scales,which induces additional indeterminate information.A method based on the neutrosophic number(NN)and spectral analysis was proposed to capture the indeterminate information of the JRC.The proposed method was then applied to determine the JRC values for sandstone joint samples collected from a rock landslide.The comparison between the JRC results obtained by the proposed method and experimental results validated the effectiveness of the NN.Additionally,comparisons made between the spectral analysis and common statistical parameters based on the NN also demonstrated the advantage of spectral analysis.Thus,the NN and spectral analysis combined can effectively handle the indeterminate information in the rock joint roughness.

Macro and meso characteristics evolution on shear behavior of rock joints

Direct shear tests were conducted on the rock joints under constant normal load(CNL), while the acoustic emission(AE) signals generated during shear tests were monitored with PAC Micro-II system. Before and after shearing, the surfaces of rock joints were measured by the Talysurf CLI 2000. By correlating the AE events with the shear stress-shear displacement curve, one can observe four periods of the whole course of shearing of rock joints. By the contrast of AE location and actual damage zone, it is elucidated that the AE event is related to the morphology of the joint. With the increase of shearing times, the shear behavior of rock joints gradually presents from the response of brittle behavior to that of ductile behavior. By combining the results of topography measurement, four morphological parameters of joint surface, S p(the maximum height of joint surface), N(number of islands), A(projection area) and V(volume of joint) were introduced, which decrease with shearing. Both the joint roughness coefficient(JRC) and joint matching coefficient(JMC) drop with shearing, and the shear strength of rock joints can be predicted by the JRC-JMC model. It establishes the relationship between micro-topography and macroscopic strength, which have the same change rule with shearing.

Probabilistic prediction on three-dimensional roughness of discontinuity based on two-dimensional traces under rock tunnel excavation based on Bayesian theory

Three-dimensional(3D)roughness of discontinuity affects the quality of the rock mass,but 3D roughness is hard to be measured due to that the discontinuity is invisible in the engineering.Two-dimensional(2D)roughness can be calculated from the visible traces,but it is difficult to obtain enough quantity of the traces to directly derive 3D roughness during the tunnel excavation.In this study,a new method using Bayesian theory is proposed to derive 3D roughness from the low quantity of 2D roughness samples.For more accurately calculating 3D roughness,a new regression formula of 2D roughness is established firstly based on wavelet analysis.The new JRC3D prediction model based on Bayesian theory is then developed,and Markov chain Monte Carlo(MCMC)sampling is adopted to process JRC3D prediction model.The discontinuity sample collected from the literature is used to verify the proposed method.Twenty groups with the sampling size of 2,3,4,and 5 of each group are randomly sampled from JRC2D values of 170 profiles of the discontinuity,respectively.The research results indicate that 100%,90%,85%,and 60%predicting JRC3D of the sample groups corresponding to the sampling size of 5,4,3,and 2 fall into the tolerance interval[JRC_(true)–1,JRC_(true)+1].It is validated that the sampling size of 5 is enough for predicting JRC3D.The sensitivities of sampling results are then analyzed on the influencing factors,which are the correlation function,the prior distribution,and the prior information.The discontinuity across the excavation face at ZK78+67.5 of Daxiagu tunnel is taken as the tunnel engineering application,and the results further verify that the predicting JRC3D with the sampling size of 5 is generally in good agreement with JRC3D true values.

Development of an improved three-dimensional rough discrete fracture network model:Method and application

Structure plane is one of the important factors affecting the stability and failure mode of rock mass engineering.Rock mass structure characterization is the basic work of rock mechanics research and the important content of numerical simulation.A new 3-dimensional rough discrete fracture network(RDFN3D)model and its modeling method based on the Weierstrass-Mandelbrot(W-M)function were presented in this paper.The RDFN3D model,which improves and unifies the modelling methods for the complex structural planes,has been realized.The influence of fractal dimension,amplitude,and surface precision on the modeling parameters of RDFN3D was discussed.The reasonable W-M parameters suitable for the roughness coefficient of JRC were proposed,and the relationship between the mathematical model and the joint characterization was established.The RDFN3D together with the smooth 3-dimensional discrete fracture network(DFN3D)models were successfully exported to the drawing exchange format,which will provide a wide application in numerous numerical simulation codes including both the continuous and discontinuous methods.The numerical models were discussed using the COMSOL Multiphysics code and the 3-dimensional particle flow code,respectively.The reliability of the RDFN3D model was preliminarily discussed and analyzed.The roughness and spatial connectivity of the fracture networks have a dominant effect on the fluid flow patterns.The research results can provide a new geological model and analysis model for numerical simulation and engineering analysis of jointed rock mass.

基于Weierstrass-Mandelbrot函数的岩体裂隙映射重构

重构岩体裂隙对精准构建裂隙岩体模型以及准确获取其力学性质具有重要意义。鉴于此,为使重构裂隙与天然状态相吻合,提出了D-n_(max)阈值公式,修正了用于岩体裂隙模拟的Weierstrass-Mandelbrot(W-M)函数。通过二值化灰度图像对Barton10条剖面线进行数字化,经试错法及综合分析法,以等差方式确定10个粗糙度水平的Hurst值。通过对10条剖面线进行傅里叶变换得到了幅值特征新参数Spp,结合起伏角标准差σ_i线性构建新裂隙粗糙度系数(joint roughness coefficient,简称JRC)计算公式。采用二分法获得目标JRC值对应W-M函数的最佳尺度常数G值,建立了JRC与W-M函数的映射关系。W-M函数考虑了随机项,实现了重构裂隙的差异化。对重构裂隙进行粗糙度定量化研究和室内试验,验证了新参数Spp、新JRC计算公式及映射关系的有效性。所作研究为拓展岩体裂隙获取方法提供了新的思路,为裂隙岩体力学性质研究奠定了基础。

岩体结构面粗糙度系数确定方法研究现状

岩体结构面粗糙度系数(Joint Roughness Coefficient,JRC)是影响结构面抗剪强度的重要参数,而抗剪强度是影响岩体稳定性的重要因素,因此对结构面粗糙度系数的研究具有十分重要的意义.在过去50年里,研究人员提出了各种方法来量化结构面粗糙度,但到目前为止研究提出的所有粗糙度参数中,结构面粗糙度系数仍然是实践中使用最广泛的参数.JRC具有形式简单、易于估计和明确考虑尺寸效应的优点,使其成为自提出以来应用最广泛的结构面粗糙度量化参数.因此,JRC引起了许多学者的关注,并在众多领域开发了定量表征JRC的相关方法.鉴于这种发展趋势,针对结构面粗糙度系数的确定方法进行了概述,并主要介绍了岩体结构面表面形态获取方法,粗糙度定量化表征参数的本质特性及适用性,以及对岩体结构面尺寸效应及各向异性的描述.此外,还讨论了采样间距和结构面趋势向对JRC的影响,以及现有JRC相关方法可能会在岩石工程中得到进一步改进和扩展的趋势.

岩体结构面三维粗糙度系数表征新方法

岩体结构面粗糙度系数JRC影响着岩体的变形、破坏以及渗流特性,其数据采集与评价取值问题一直是岩石力学领域的热点和难点。目前研究方法多集中于二维,无法体现JRC的三维特性;即使现有的三维评价方法,也多数仅从几何数据单方面入手,没有考虑JRC的各向异性。鉴于此,提出基于光亮面积百分比BAP的岩体结构面三维粗糙度系数表征新方法。首先,运用三维激光扫描技术,建立岩体结构面三维数字模型;其次,通过模拟虚拟光源,在岩体结构面表面产生光亮与阴影,并生成图片;然后,基于图像分割技术,设置灰度阈值,提取大于灰度阈值的光亮部分面积,并计算岩体结构面的光亮面积百分比;最后,结合R.Tse和D.M.Cruden提出的JRC计算公式,考虑剪切或渗流方向,得出岩体结构面三维粗糙度系数估算公式。以鱼简河水库工程为例,实验结果表明:(1)在光源照射角度相等的情况下,光亮面积百分比与岩体结构面三维粗糙度系数成正比关系。(2)通过对比分析,光源照射角度过大(70°～85°)或过小(5°～35°)时,易产生误差,入射角介于35°～70°范围内时为最佳入射角。(3)基于该工程数据推导出JRC3D与BAP之间的估算公式。通过验证,试样Y10,Y11,Y12根据R.Tse和D.M.Cruden公式所得到的JRC3D分别为16.47,16.81,16.69,根据新估算公式计算的JRC3D分别为17.20,17.40,17.17,具有较好的一致性。

考虑应力历史的岩石单裂隙渗流特性试验研究

通过开展单裂隙花岗岩不同围压加、卸载和不同水力梯度作用下的渗透试验,研究应力历史对裂隙渗透性能演化的影响。试验结果表明:在围压加载过程中,渗流流量与渗透压差大致呈线性关系;在渗透压差相同的条件下,围压越小,流量越大,随着围压上升,裂隙渗流流量持续减小,但随着围压的进一步增大,流量的减小有减缓的趋势。在围压相同以及渗透压差相同的条件下,单裂隙花岗岩在卸载条件下的渗流特性与加载条件下相比,其渗流流量明显降低,且卸载过程中渗流流量与渗透压差开始偏离线性关系。从试验前、后裂隙面粗糙度系数值的对比可以看出,由于法向应力挤压以及渗流流体的冲蚀作用,试验后裂隙面粗糙度系数明显降低。卸载的过程中,裂隙渗透性能的恢复具有明显的滞后效应,表明在法向应力和流体冲蚀的共同作用下,裂隙产生了不可恢复的非弹性变形。

不同节理粗糙度系数单裂隙渗流特性试验研究

实际岩石裂隙的裂隙面具有不同的粗糙度,难以满足立方定律的使用条件。根据N.Barton和V.Choubey(1977年)提出的10条节理粗糙度(JRC)标准剖面轮廓曲线,本试验运用数控电火花线切割技术,加工出具有不同节理粗糙度系数(JRC=0～20)的10个钢模板,制作出10个包含不同JRC值单裂隙的圆柱形水泥试样(直径φ50mm,高度100mm),采用RCCP联测系统测试不同JRC值单裂隙在不同应力水平下的渗透性。试验结果表明:(1)在低应力水平下,JRC值对单裂隙的渗流特性有较大影响;随应力水平的增大,JRC值对单裂隙渗流特性的影响迅速减小;(2)不同JRC值单裂隙的渗透率与有效应力之间的关系可用负指数函数描述,并表现出明显的非线性特征,低有效应力阶段试样渗透率随有效应力的变化速度大于中高有效应力阶段的变化速度。

考虑曲折效应的粗糙节理渗流计算新公式研究

粗糙节理的隙宽分布不均匀是引起节理渗流出现曲折现象的主要原因。针对节理试件B01和B02,在获得节理的三维表面形貌并计算节理的三维空腔组合形貌后,分别进行室内渗流试验和Reynolds方程下的节理渗流数值模拟,得到节理中的曲折流径分布,在此基础上根据节理三维空腔组合形貌定义定量描述节理渗流曲折效应的平均曲折因子。在考虑节理表面粗糙性的立方定理修正经验公式的基础上,采用分析岩石渗透系数的等效沟槽模型对粗糙节理的渗流进行分析,推导得到考虑曲折效应的节理渗流计算公式,并根据节理试件B01的数值计算结果确定渗流计算公式中的待定常数。然后采用节理试件B02的数值计算结果对渗流计算公式的准确性进行验证,计算结果表明考虑节理渗流曲折效应的渗流计算公式可以较好地反映节理中的渗流情况。在此基础上,将根据本文渗流计算公式得到的节理试件渗流结果与渗流试验实测值及速宝玉经验公式计算结果进行比较,结果表明:考虑曲折效应的节理渗流计算公式渗流结果与实测值一致,而速宝玉经验公式过高地估计了节理的渗流量,进一步验证了节理渗流计算公式的准确性。

岩石结构面粗糙度系数尺寸效应的推拉试验研究

粗糙度系数是结构面抗剪强度的主要影响因素,然而由于结构面表面形态的复杂性,粗糙度系数尺寸效应研究并未获得较大进展。总结了结构面粗糙度系数的3种获取手段:标准剖面对比法、理论公式法、试验反分析法。在此基础上分析了3种方法在研究粗糙度系数尺寸效应方面存在的问题和困难。为了研究结构面粗糙度系数与试样尺寸的相关度,对中砂、硅粉、水泥、非引气型萘系减水剂等原材料的配比进行了研究,获得了与天然钙质板岩物理力学特性相类似的岩石模型材料,然后采用研发的结构面制作模具及其制备工艺制作了8组共176对具有不同尺寸和表面起伏粗糙程度的结构面,并利用改进的高精度岩石结构面推拉仪对结构面粗糙度系数进行了推拉试验研究和数据统计分析,结果表明:模型结构面粗糙度系数的统计均值随试样尺寸的增加而降低,但特定结构面粗糙度系数的尺寸效应规律需要根据结构面的具体表面形貌进行测试;Barton理论公式计算的结构面粗糙度系数尺寸效应变化规律与推拉试验测试规律总体上一致,但试验值与理论值有差异,且结构面试样尺寸越小,二者的差异就越大;具有特定表面形貌的模型结构面粗糙度系数也有差异,工程大尺寸岩体结构面粗糙度系数需要根据表面形貌和分布特征进行综合判定。

节理抗剪强度综合评价的试验研究

选取不同吻合度自然节理试样,进行干燥状态和饱和状态的JRC-JCS模型和JRC-JMS模型试验研究。结果表明,在节理粗糙度系数的定向统计测量和尺寸效应分析,以及剪切过程衰减折减的基础上,运用JRC-JCS模型综合评价节理抗剪强度可靠性较好,考虑吻合度系数的JRC-JMC模型比JRC-JCS模型具更好的预测能力。

深部花岗岩中天然开启节理剪切性能试验研究

针对取自中国高放废物地质处置首选预选区深部花岗岩中的天然开启节理,基于室内试验对其剪切性能进行了测试分析。首先开展了垂直于节理面的压应力循环加卸载测试,之后在不同压应力条件下开展了天然节理直剪试验。同时,借助三维激光扫描技术获得了剪切面精确面积,并实现了节理面粗糙度评价。测试结果表明:在对应的深部地应力条件下,天然开启节理处于压密状态,且压应力幅值的变化不会使得开启节理产生不可恢复的变形;同一条节理在室内试验尺度上的剪切性能具有一致性,不同深度处节理的剪切性能也具有相似性;节理粗糙系数(JRC)与剪切强度参数之间未发现明显的相关关系。上述研究结论以及获得的Mohr-Coulomb强度参数可以为后续现场试验和数值分析提供初步依据。

重复剪切作用下节理强度和形貌特征劣化规律

为了分析重复剪切作用下节理面剪切力学特性及微观形貌特征劣化规律,制备了单节理砂岩试样,考虑4种法向应力分别进行了6次重复剪切试验。研究结果发现:(1)在重复剪切作用下,节理面剪应力–剪切变形曲线变化特征明显,经过2~3次剪切,不再出现明显峰值,剪切硬化现象明显,残余抗剪强度逐渐趋于稳定;(2)随着重复剪切次数增加,节理面的抗剪强度劣化趋势明显,呈先陡后缓的劣化趋势,前2次剪切的劣化幅度占总劣化值的65%以上,而且法向应力越大,抗剪强度劣化幅度和劣化速度越大;(3)在重复剪切作用下,节理面上相互咬合的微凸起和凹陷部分发生切齿、磨损和填充,节理面的凹凸起伏程度逐渐减小,使得其形貌特征参数及粗糙度系数逐渐降低,进而导致其剪切力学特性逐渐劣化;(4)建立了重复剪切作用下节理面粗糙度系数劣化方程,结合N.Barton提出的结构面抗剪强度经验公式,建立了考虑重复剪切作用的节理面抗剪强度计算公式,结果表明计算值与试验值吻合的较好。

岩体节理粗糙度系数与统计参数的相关关系研究

测定节理粗糙度系数JRC的方法均基于10条标准剖面,其人为误差大,且未考虑采用不同取样长度离散节理剖面对各统计参数与JRC的影响。为避免对10条标准剖面JRC的测量误差,考虑JRC的取值范围及离散节理剖面时不同取样长度的影响,从数值模拟粗糙节理的角度出发,采用截断正态分布随机抽样得出节理凸起高度,由每段的凸起高度及取样长度形成凸起表面,叠加生成具有一定迹长的粗糙节理,根据Barton直边法测量其JRC,计算相应的统计参数,研究不同取样长度下各统计参数与JRC的回归关系。研究结果表明:JRC与均方根RMS和中线均值CLA呈线性关系,JRC与均方值MSV,均方根一阶导数Z2,粗糙剖面系数Rp和结构函数SF之间呈抛物线关系,且相关系数均较高;取样长度对统计参数、JRC及其回归关系式有较大影响,在数值模拟粗糙节理时应使取样长度与岩体粒径相近。由于MSV,RMS和CLA只能反映节理起伏高度的均值状况,不能反映各凸起高度所占权重对JRC的影响,因此,建议采用Z2,SF对JRC进行估算。

考虑接触面积影响的粗糙节理渗流分析

节理中接触面积的存在使得渗流曲折效应更加明显,将对渗流产生显著影响。为了研究节理接触面积对节理渗流的影响,建立节理渗流概念模型,推导得到了节理渗流的接触面积影响系数;然后在节理渗流计算公式中引入该影响系数,得到了考虑接触面积影响的渗流计算公式。同时,由于接触面积的存在使得渗流曲折因子的计算更为复杂,在获得节理隙宽分布的基础上提出了计算节理渗流曲折因子的五点比较法。然后以人工大理岩节理试件为研究对象,在获得其三维表面形貌的基础上,一方面对其进行不同接触状态下5级法向应力作用下的渗流试验;另一方面,在根据节理试件的三维表面形貌数据计算节理的渗流平均曲折因子和接触面积比的基础上,分别采用考虑接触面积影响的渗流计算公式和Zimmerman计算公式对节理试件在不同法向应力作用下的渗流体积流量进行计算,并将计算结果与实测值进行比较。结果表明:考虑接触面积影响的渗流计算公式计算结果与实测值吻合较好,从而验证了考虑接触面积影响的渗流计算公式的正确性,而Zimmerman计算公式高估了节理的渗流流量。

基于离散傅立叶变换的岩石节理形貌分析与随机重构

为了进一步开展节理面细观形貌特征对其宏观剪切特性影响的数值模拟研究,提出既可以定量地对实地采集节理试样的形貌特征进行正向分析,又能够根据预定的形貌特征范围随机地进行节理试样逆向重构的傅里叶形貌分析法。分别采用传统粗糙度分析法与傅里叶分析法对50 224个实测的节理样本进行形貌分析,得到傅里叶参数计算的经验公式;确定采用离散傅立叶变换法进行不同粗糙度节理试样逆向重构时的傅里叶参数取值范围;研究成果能为快速随机重构符合一定粗糙度特性的节理轮廓,建立一个完全数字化的虚拟试验系统提供重要基础。

岩体裂隙粗糙度表征及其对裂隙渗流特性的影响

岩体裂隙粗糙程度对裂隙渗流特性的影响显著。利用三维光学扫描系统获取岩体裂隙面点云数据,结合SURFER和GEOMAGIC STUDIO等软件计算裂隙面节理粗糙度系数JRC和表面粗糙比率Rs,建立JRC与Rs的定量关系,开展应力、渗流和化学耦合作用下石灰岩裂隙渗流试验,研究JRC和Rs对粗糙裂隙渗流特性的影响。结果表明:JRC与Rs呈对数函数关系,其平方根R2为0.9128,该表征公式与裂隙渗流试验结果最大相对误差MRE、平均绝对误差MAE和均方根误差RMSE分别为6.93%、0.34和0.27。JRC与渗流量、稳定期渗透率分别呈二次函数和对数函数关系,Rs和各参数的拟合关系与JRC相同。JRC值越大,渗流量和渗透率越小,且三场耦合作用下裂隙面JRC和Rs值均有所增大。该表征方法可用于岩体裂隙面粗糙度估算,由裂隙面JRC值可预测该裂隙渗流量和稳定时刻渗透率。