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.

Data-driven estimation of joint roughness coefficient

Joint roughness is one of the most important issues in the hydromechanical behavior of rock mass.Therefore,the joint roughness coefficient(JRC)estimation is of paramount importance in geomechanics engineering applications.Studies show that the application of statistical parameters alone may not produce a sufficiently reliable estimation of the JRC values.Therefore,alternative data-driven methods are proposed to assess the JRC values.In this study,Gaussian process(GP),K-star,random forest(RF),and extreme gradient boosting(XGBoost)models are employed,and their performance and accuracy are compared with those of benchmark regression formula(i.e.Z2,Rp,and SDi)for the JRC estimation.To analyze the models’performance,112 rock joint profile datasets having eight common statistical parameters(R_(ave),R_(max),SD_(h),iave,SD_(i),Z_(2),R_(p),and SF)and one output variable(JRC)are utilized,of which 89 and 23 datasets are used for training and validation of models,respectively.The interpretability of the developed XGBoost model is presented in terms of feature importance ranking,partial dependence plots(PDPs),feature interaction,and local interpretable model-agnostic explanations(LIME)techniques.Analyses of results show that machine learning models demonstrate higher accuracy and precision for estimating JRC values compared with the benchmark empirical equations,indicating the generalization ability of the data-driven models in better estimation accuracy.

Shear mechanical properties and fracturing responses of layered rough jointed rock-like materials

This study aims to investigate mechanical properties and failure mechanisms of layered rock with rough joint surfaces under direct shear loading.Cubic layered samples with dimensions of 100 mm×100 mm×100 mm were casted using rock-like materials,with anisotropic angle(α)and joint roughness coefficient(JRC)ranging from 15°to 75°and 2-20,respectively.The direct shear tests were conducted under the application of initial normal stress(σ_(n)) ranging from 1-4 MPa.The test results indicate significant differences in mechanical properties,acoustic emission(AE)responses,maximum principal strain fields,and ultimate failure modes of layered samples under different test conditions.The peak stress increases with the increasingαand achieves a maximum value atα=60°or 75°.As σ_(n) increases,the peak stress shows an increasing trend,with correlation coefficients R² ranging from 0.918 to 0.995 for the linear least squares fitting.As JRC increases from 2-4 to 18-20,the cohesion increases by 86.32%whenα=15°,while the cohesion decreases by 27.93%whenα=75°.The differences in roughness characteristics of shear failure surface induced byαresult in anisotropic post-peak AE responses,which is characterized by active AE signals whenαis small and quiet AE signals for a largeα.For a given JRC=6-8 andσ_(n)=1 MPa,asαincreases,the accumulative AE counts increase by 224.31%(αincreased from 15°to 60°),and then decrease by 14.68%(αincreased from 60°to 75°).The shear failure surface is formed along the weak interlayer whenα=15°and penetrates the layered matrix whenα=60°.Whenα=15°,as σ_(n) increases,the adjacent weak interlayer induces a change in the direction of tensile cracks propagation,resulting in a stepped pattern of cracks distribution.The increase in JRC intensifies roughness characteristics of shear failure surface for a smallα,however,it is not pronounced for a largeα.The findings will contribute to a better understanding of the mechanical responses and failure mechanisms of the layered rocks subjected to shear loads.

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.

Measurement of Joint Roughness Coefficient by Using Profilograph and Roughness Ruler

Joint roughness coefficient（JRC） is the key parameter for the empirical estimation of joint shear strength by using the JRC-JCS（joint wall compressive strength） model.Because JRC has such characteristics as nonuniformity,anisotropy,and unhomogeneity,directional statistical measurement of JRC is the precondition for ensuring the reliability of the empirical estimation method.However,the directional statistical measurement of JRC is time-consuming.In order to present an ideal measurement method of JRC,new profilographs and roughness rulers were developed according to the properties of rock joint undulating shape based on the review of measurement methods of JRC.Operation methods of the profilographs and roughness rulers were also introduced.A case study shows that the instruments and operation methods produce an effective means for the statistical measurement of JRC.

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。

JRC修正直边法的数学表达

ＪＲＣ是反映爬坡角力学效应的岩体结构面表面形态等效描述指标。本文在爬坡角力学效应机理研究基础上，阐述了ＪＲＣ直边法的物理意义；通过岩体结构面表面起伏幅度与金属表面粗糙度幅度对比分析，肯定了直边法的合理性；考虑ＪＲＣ的尺寸效应，推导ＪＲＣ修正直边法的数学表达式，编译计算机常用程序。最后，实例检验了ＪＲＣ修正直边法数学表达式的合理性和可用性。

JRC快速测量技术

在回顾粗糙度测量方法的基础上 ,从岩石节理的具体特点出发 ,研制了轮廓曲线仪和粗糙度尺 ,为节理粗糙度系数的统计测量提拱了一种快速测量手段。

JRC-JCS模型与直剪试验对比研究

结构面抗剪强度是影响工程岩体稳定的重要因素,它决定工程岩体破坏的可能性。基于结构面粗糙度系数定向统计测量技术的JRC-JCS模型可以考虑地质和环境因素的影响,具有费用低、速度快、简便易行等特点,是获取工程岩体无填充或少填充硬岩结构面抗剪强度参数的实用方法,已为50多个岩体工程提供了结构面抗剪强度参数。为分析JRC-JCS模型评价结构面抗剪强度参数的可靠性,选取天然岩石结构面试样,进行干燥状态和饱和状态结构面抗剪强度直剪试验和JRC-JCS模型评价的对比研究。结果表明,在结构面粗糙度系数的定向统计测量、尺寸效应分析,以及剪切过程衰减折减的基础上,运用结构面粗糙度系数定向统计测量技术的JRC-JCS模型评价的结构面抗剪强度参数与直剪试验结果具有较好的一致性,JRC-JCS模型对结构面峰值摩擦角有较好的预测能力。

岩体结构面粗糙度系数JRC的研究现状

岩体结构面粗糙度系数JRC是描述岩体结构面粗糙起伏状态的力学参数,对于无填充或少填充的硬性结构面而言是关键性指标。本文介绍了岩体结构面粗糙度系数JRC估算方法的理论及应用研究现状,并探讨了JRC研究中存在的几个问题。

智能JRC测量仪的研制

研制了一种智能 JRC 测量仪,该仪器可直接测量岩体结构面的粗糙度系数 JRC 值,适用于野外任意产状的岩体结构面,可以沿任意方向测量岩体结构面粗糙度系数,具有重量轻、体积小、携带方便、操作简单、测量速度快等特点。

JRC分形估测方法的实用性

基于分形几何的码尺法分维数与岩石节理粗糙度系数的物理意义剖析，认为Ｄ－ＪＲＣ之间不存在必然的相关性．分析标准轮廓曲线的分维数，发现其分维数差级微小，难以实行粗糙度系数分级．根据实测资料阐述了岩石节理表面轮廓曲线的“自相似”是统计意义而不是绝对的，它要求ＪＲＣ分形估测应统计求取，而过繁的分维数测量步骤削弱了ＪＲＣ的分形统计估测的可行性．建立在实测资料统计分析基础上的ＪＲＣ尺寸效应分形模型ＪＲＣｎ＝ＪＲＣ０（Ｌｎ／Ｌ０）－Ｄ客观而真实地刻画了粗糙度系数随取样长度增大而降低的规律，其中，ＪＲＣ尺寸效应分维数（Ｄ）具明确的物理意义，它描述了ＪＲＣ随结构面规模增大而降低的衰减速率．最后，运用ＪＲＣ尺寸效应分维数（Ｄ）探讨了岩石节理粗糙度系数尺寸效应的各向异性规律．

岩体结构面粗糙度系数JRC的定向统计研究

本文回顾了岩体结构面粗糙度系数ＪＲＣ的研究成果，分析了各种ＪＲＣ研究方法的应用范围。在野外实际结构面形态的详细调查和深入研究的基础上，发展了Ｂａｒｔｏｎ直边法，并提出按岩性定向统计研究结构面粗糙度系数ＪＲＣ的科学思想。

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.

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.

甘肃北山花岗岩岩体结构面粗糙度系数(JRC)研究

岩体结构面表面形态研究对岩石工程结构体强度及变形特征研究评价具有重要的指导意义。文章评述了现有岩体结构面粗糙度系数(JRC)的各种测定方法及存在的问题,分析了在高放废物处置库预选场址甘肃北山花岗岩地区,用"简易纵剖面仪"进行地表岩体及钻孔岩心裂隙结构面JRC的测量结果。

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.

基于多元拟合方程的结构面粗糙度系数JRC估算

本文以BARTON的标准粗糙度剖面为研究对象,假定剪切方向为从左向右,量取剖面曲线长L以及"爬坡"时的倾角i_i和与倾角相对应高差h_i、面积S,把不同的因素组合在一起,用MATLAB对测得的数据进行拟合,得到用来估算结构面粗糙度系数且不依赖于结构面长度的解析方程。结果表明:剖面长度比和面积比组合得到的拟合方程较差,剖面长度比、面积比和爬坡高组合得到的方程较好;剖面长度比、倾角i_i和高差h_i三个指标的组合拟合方程最好,可很好地反映结构面粗糙度,拟合优度达97. 1%。

Morphology characteristics of joint surface in rock mass

In order to quantify the characteristics of the surface of jointed rock mass,new equipment,the three-dimensional laser surface topography instrument,was used to accurately measure surface morphology of joints.Scan pictures and parameters were obtained to describe the rock joint surface characteristics,for example,the height frequency of surface,and mean square roughness.Using the method of fractal dimension,the values of joint roughness coefficient(JRC) were calculated based on the above parameters.It could access to the joint surface rock sample morphology of the main parameters of characteristic.The maximum peak height is 2.692 mm in the test joint plane.The maximum profile height is 4.408 mm.JRC value is 6.38 by fractal dimension computing.It belongs to the smooth joint surface.The results show that it is a kind of the effective method to quantitatively evaluate the surface topography by the three-dimensional laser surface topography instrument and the fractal dimension method.According to the results,during the process of underground large-scale mining,safe measures to prevent slip failure of the joint plane by controlling surface tension and shear mechanical response were proposed.