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.

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.

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.

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。

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.

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。

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.

线-面结合的结构面粗糙系数经验计算方法

岩体结构面的剪切力学特性主要取决于其表面粗糙特征,结构面粗糙系数是表征该粗糙特征的主要方法。目前对结构面粗糙系数的研究局限于单一维度,多角度且定量化计算结构面粗糙系数能避免单一维度分析导致计算精度不准的局限性。采用立方体花岗岩,通过巴西劈裂的方式制备含结构面的试样;利用高精度三维扫描仪对试样结构面进行扫描,得到结构面的点云数据,同时借助逆向软件对点云数据进行三维重构。研究了点云数据Z方向上的分布频率,剖面线剖面比与节理粗糙系数(JRC)值的关系,结构面面积比与JRC均值的关系。研究表明:点云数据Z方向上的分布频率可以作为初步评估结构面粗糙度的手段;剖面线剖面比与JRC数值、结构面面积比与JRC均值有二次函数的关系。通过数值分析建立了结构面JRC均值与剖面比、面积比的二元函数关系,并得到结构面JRC均值的经验计算公式。本次研究为结构面粗糙度提供了一种“点-线-面”逐渐深入的多角度评估思路,得到的经验公式为计算结构面JRC均值提供了一种新的计算方法。

高温作用后砂岩-混凝土黏结界面拉伸力学特性研究

热灾害频发对地下工程的安全性提出了挑战,尤其围岩-衬砌黏结界面作为地应力传递的“纽带”,对支护结构的稳定至关重要。文章对不同界面粗糙度的砂岩-混凝土组合圆盘开展25~800℃高温处理后的劈裂试验,结合单一材料性能、界面黏结机理和组合圆盘的破裂演化过程,分析了粗糙程度、温度效应对界面拉伸强度和劈裂模式的影响。结果表明:组成围岩-衬砌结构的混凝土和砂岩的物理力学性能均随温度的升高出现一定程度的劣化,且前者受热损伤程度远大于后者。高温作用下,热裂隙并不局限于界面过渡区,而是主要汇集在砂岩和混凝土结构内部;同时,组合体的拉伸强度基本介于两种材料强度之间,说明岩-混凝土黏结界面未必是组合结构的薄弱面。存在以JRC=5.86的阈值粗糙度,砂岩-混凝土组合试样的拉伸强度以此为界先降低而后增强,这种强度变化趋势在25~400℃温度范围内相当显著(降幅介于49.11%~59.31%,增幅达56.13%~69.79%),而600℃和800℃加热后强度变化基本趋于平缓(降低24.09%~28.85%,无明显回升)。破裂演化过程表明,随着加热温度的提高,组合试样的劈裂模式由端部压剪破坏向中部拉伸破坏过渡;增大界面粗糙度使得界面从端部单点起裂向多点复合断裂转变。

基于有效受剪面积的节理面吻合度量化方法研究

节理粗糙度系数-节理抗压强度(JRC-JCS)模型为岩体节理面抗剪强度估算提供了很好的思路,但对于吻合度较差的节理岩体,该模型往往过高地估算其抗剪强度。节理粗糙度系数-节理吻合系数(JRC-JMC)模型进一步考虑节理吻合度对抗剪强度的影响,为吻合程度较差的节理面的抗剪强度估算提供了很好的思路,但目前节理吻合度的量化分析还存在困难。在以往研究基础上,采用重复剪切试验的方法制备了不同吻合度的节理岩体试样,综合节理面形貌特征和节理面抗剪性能变化规律分析,提出了节理吻合度的量化计算方法。研究结果表明:(1)在重复剪切作用下,岩体节理面的抗剪强度和节理面形貌参数呈现先陡后缓的降低趋势,节理面上下盘的吻合程度逐渐降低;(2)根据剪切前后节理面形貌特征的对比分析,确定了剪切过程节理面的有效接触区域,提出了节理吻合系数JMC的量化计算方法;(3)对比分析表明,与单独考虑JRC相比,将JRC和JMC综合在一起可以更好地反映节理形貌特征对其剪切性能的影响。相关研究方法和分析结果可为岩体节理面抗剪性能分析提供较好的参考。

不同粗糙度系数结构面分级剪切蠕变特性

掌握结构面剪切蠕变特性的规律是揭示岩体时效变形与破坏的根本途径。通过对Barton标准剖面线第1条和第10条人工水泥砂浆结构面分别开展了恒定法向力条件下的分级剪切蠕变试验,研究了结构面剪切蠕变特性随粗糙度系数(JRC)、法向应力、剪应力的变化规律。同时,采用离散元软件(PFC 2D)对不同粗糙度系数的Barton标准剖面线结构面进行了分级剪切蠕变数值模拟研究。结果表明:在恒定法向力条件下,同一结构面剪切蠕变量、蠕变速率均随剪应力增加而增加;在恒定法向应力及剪应力作用下,剪切蠕变随粗糙度系数增加而减小,结构面剪切蠕变数值模拟结果验证了同样的结论;另外,蠕变变形位移云图结果表明结构面试样沿结构面剪切加载方向,剪切蠕变随距离增加而减小;随着粗糙度系数增加,结构面剪切蠕变破坏模式由滑移摩擦为主逐渐向剪断破坏为主过渡。研究成果可为岩体工程的长期安全稳定性评价提供理论依据。

考虑剪切方向的改进Barton模型

为研究节理在剪切过程中的方向性和剪切强度规律,利用直剪仪对复制岩石节理试样进行了爬坡和顺坡两个方向的直剪试验。试验结果表明:剪切方向对岩石节理的剪切强度有明显影响,沿爬坡方向的剪切强度大于沿顺坡方向,但粗糙度系数(joint roughness coefficient,JRC)的减小和法向应力的增大可在一定程度上削弱剪切方向的影响。节理剪切破坏过程具有显著的阶段性特征,中低法向应力条件下以爬坡滑移为主要机制,而高法向应力下以相互啃食和凸起啃断为主要机制。采用平均有效倾角差指标参数描述剪切强度的各向异性,并在此基础上提出了考虑剪切方向的改进剪切强度模型,更好地预测节理正、反方向的剪切强度。通过百分位数参数建立了三维形貌指标与端部轮廓线二维高差指标的联系,大大简化了节理形貌指标的获取难度。该模型参数较少容易获取,物理意义明确,且把岩石节理剪切强度的各向异性考虑在内,具有广阔的潜在工程应用前景。

Developments and Applications of Neutrosophic Theory in Civil Engineering Fields:A Review

Neutrosophic theory can effectively and reasonably express indeterminate,inconsistent,and incomplete information.Since Smarandache proposed the neutrosophic theory in 1998,neutrosophic theory and related research have been developed and applied to many important fields.Indeterminacy and fuzziness are one of the main research issues in the field of civil engineering.Therefore,the neutrosophic theory is very suitable for modeling and applications of civil engineering fields.This review paper mainly describes the recent developments and applications of neutrosophic theory in four important research areas of civil engineering:the neutrosophic decision-making theory and applied methods,the neutrosophic evaluation methods and applications of slope stability,the neutrosophic expressions and analyses of rock joint roughness coefficient,and the neutrosophic structural optimization methods and applications.In terms of these research achievements in the four areas of civil engineering,the neutrosophic theory demonstrates its advantages in dealing with the indeterminate and inconsistent issues in civil engineering and the effectiveness and practicability of existing applied methods.In the future work,the existing research results will be further improved and extended in civil engineering problems.In addition,the neutrosophic theory will also have better application prospects in other fields of civil engineering.

岩石节理Barton标准剖面线数字化重构改进方法

10条Barton标准岩石节理剖面线是定量计算岩石节理粗糙性系数(JRC)的基础,对其进行数字化重构是关键。针对Barton标准岩石节理剖面线原始电子文档存在断口、噪点等缺陷,提出了一种基于Photoshop和Matlab图像处理的Barton标准岩石节理剖面线数字化重构改进方法。利用该方法对标准剖面线原始图像进行处理,所得重构剖面线能够较好地复刻原始标准岩石节理剖面线的形貌特征,在此基础上根据经验公式计算的标准剖面线JRC值与其直剪试验反算值比较一致。此外,采用改进方法对水泥砂浆人工模拟岩石节理剖面线进行重构,比较其JRC经验公式计算值和直剪试验反算值,发现两者误差仅为7.89%,表明上述重构改进方法对于一般岩石节理剖面线也具有较高的准确性,具有推广应用的潜力。

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。