Review of a new shear-strength criterion for rock joints

Barton, N., 1973. Review of a new shear-strength criterion for rock joints. Eng. Geol., 7: 287–332.

The surface roughness of rock joints depends on their mode of origin, and on the mineralogy of the rock. Amongst the roughest joints will be those that formed in intrusive rocks in a tensile brittle manner, and amongst the smoothest the planar cleavage surface in slates. The range of friction angles exhibited by this spectrum will vary from about 75° or 80° down to 20° or 25°, the maximum values being very dependent on the normal stress, due to the strongly curved nature of the peak strength envelopes for rough unfilled joints.

Direct shear tests performed on model tension fractures have provided a very realistic picture of the behaviour of unfilled joints at the roughest end of the joint spectrum. The peak shear strength of rough—undulating joints such as tension surfaces can now be predicted with acceptable accuracy from a knowledge of only one parameter, namely the effective joint wall compressive strength or JCS value. For an unweathered joint this will be simply the unconfined compression strength of the unweathered rock. However in most cases joint walls will be weathered to some degree. Methods of estimating the strength of the weathered rock are discussed. The predicted values of shear strength compare favourably with experimental results reported in the literature, both for weathered and unweathered rough joints.

The shear strength of unfilled joints of intermediate roughness presents a problem since at present there is insufficient detailed reporting of test results. In an effort to remedy this situation, a simple roughness classification method has been devised which has a sliding scale of roughness. The curvature of the proposed strength envelopes reduces as the roughness coefficient reduces, and also varies with the strength of the weathered joint wall or unweathered rock, whichever is relevant. Values of the Coulomb parameters c and Φ fitted to the curves between the commonly used normal stress range of 5–20 kg/cm² appear to agree quite closely with experimental results.

The presence of water is found in practice to reduce the shear strength of rough unfilled joints but hardly to affect the strength of planar surfaces. This surprising experimental result is also predicted by the proposed criterion for peak strength. The shear strength depends on the compressive strength which is itself reduced by the presence of water. The sliding scale of roughness incorporates a reduced contribution from the compressive strength as the joint roughness reduces. Based on the same model, it is possible to draw an interesting analogy between the effects of weathering, saturation, time to failure, and scale, on the shear strength of non-planar joints. Increasing these parameters causes a reduction in the compressive strength of the rock, and hence a reduction in the peak shear strength. Rough—undulating joints are most affected and smooth—nearly planar joints least of all.     

A Constitutive Model for Shear Behavior of Rock Joints Based on Three-Dimensional Quantification of Joint Roughness

A new constitutive model to describe the shear behavior of rock joints under constant normal stiffness (CNS) and constant normal load (CNL) conditions is proposed. The model was developed using an empirical approach based on the results of a total of 362 direct shear tests on tensile fractured rock joints and replicas of tensile joints and on a new quantitative roughness parameter. This parameter, the active roughness coefficient C _r, is derived from the features of the effective roughness mobilized at the contact areas during shearing. The model involves a shear strength criterion and the relations between stresses and displacements in the normal and shear directions, where the effects of the boundary conditions and joint properties are considered by the shape indices C _d and C _f. The model can be used to predict the shear behavior under CNS as well as CNL conditions. The shear behavior obtained from the experimental results is generally in good agreement with that estimated by the proposed model, and the effects of joint roughness, initial normal stress, and normal stiffness are reasonably reflected in the model.     

New Peak Shear Strength Criterion of Rock Joints Based on Quantified Surface Description

The prime objective of this work is to improve our understanding of the shear behavior of rock joints. Attempts are made to relate the peak shear strength of rock joints with its three-dimensional surface morphology parameters. Three groups of tensile joint replicas with different surface morphology are tested with direct shear tests under constant normal load (CNL) conditions. Firstly, the three-dimensional surface characterization of these joints is evaluated by an improved roughness parameter before being tested. Then, a new empirical criterion is proposed for these joints expressed by three-dimensional quantified surface roughness parameters without any averaging variables in such a way that a rational dilatancy angle function is used instead of ${\text{JRC}} \cdot \log_{10} \left( {{{\text{JCS}} \mathord{\left/ {\vphantom {{\text{JCS}} {\sigma_{\text{n}} }}} \right. \kern-0em} {\sigma_{\text{n}} }}} \right)$ by satisfying the new peak dilatancy angle boundary conditions under zero and critical-state normal stress (not physical infinite normal stress). The proposed criterion has the capability of estimating the peak shear strength at the laboratory scale and the required roughness parameters can be easily measured. Finally, a comparison among the proposed criterion, Grasselli’s criterion, and Barton’s criterion are made from the perspective of both the rationality of the formula and the prediction accuracy for the three groups of joints. The limitations of Grasselli’s criterion are analyzed in detail. Another 37 experimental data points of fresh rock joints by Grasselli are used to further verify the proposed criterion. Although both the proposed criterion and Grasselli’s criterion have almost equal accuracy of predicting the peak shear strength of rock joints, the proposed criterion is easier and more intuitive from an engineering point of view because of its Mohr–Coulomb type of formulation.     

一种新的岩石节理面三维粗糙度分形描述方法

研究并提出一种新的岩石节理面三维粗糙度分形描述方法。首先,基于激光扫描数据将节理表面离散成三角网,并建立与剪切方向相关的三维均方根抵抗角的计算方法。其次,运用分形数学理论,提出一种新的基于三维均方根抵抗角的节理面粗糙度分形描述方法。最后,采用新方法对天然玄武岩节理和花岗岩张拉型节理的粗糙特性进行分析。研究结果表明,提出的新方法能够较全面地反映节理面的三维几何形貌信息,并能描述节理粗糙度的各向异性特性。研究成果为进一步建立岩石节理面的三维剪切强度公式和剪切本构理论奠定了基础。     

一种新型粗糙节理面随机强度模型及其应用

天然岩体在长期地质作用下会生成各种节理裂隙等不连续面,而地下工程结构的稳定性一般取决于这些不连续面的强度。在众多因素中,表面形态对岩石节理面剪切强度具有决定性影响。为了系统研究岩石节理面剪切强度的确定方法,把岩石节理面概化为一系列高度不同的微长方体凸起组成的粗糙表面结构,且微长方体凸起有剪胀破坏和非剪胀破坏两种模式。综合微长方体凸起破坏规律,应用概率密度函数描述节理面表面起伏分布的影响,建立了粗糙节理面随机强度模型,推导了节理面剪切强度理论公式,提出了节理面强度的随机评价方法。基于随机强度模型和评价方法编制Matlab计算程序计算自然粗糙节理面的剪切强度,并将计算结果与试验结果进行比较分析。研究表明:粗糙节理面随机强度模型综合了粗糙节理面表面形态和法向应力对节理剪切强度的影响机制,理论计算值与试验数据吻合良好,可以较好的评价粗糙节理的峰值剪切强度和残余剪切强度。该随机模型可作为进一步深入研究的重要基础,分析结构面的连续剪切过程,建立更完善的节理面强度模型。     

Underestimation of roughness in rough rock joints

Numerous studies have been made to improve Barton's shear strength model for the quantification of rock joints. However, in these previous studies, the roughness and shear strength of the rock joint have been underestimated especially for relatively high undulated profiles (joint roughness coefficient (JRC) >14). The main factors of roughness underestimation in rough rock joints are investigated for the proper quantification of rock joint roughness. The aliasing effect and the roughness characteristics are analyzed by using artificial joint profiles and natural rock joint profiles. A 3D camera scanner is adopted to verify the main source of underestimation when using conventional measurement methods. Shear strength tests are carried out by using two types of shear apparatus to study the roughness mobilization characteristics, which may also affect the roughness underestimation. The results of joint roughness assessment, such as aliasing and undulation of waviness, show that the roughness can be underestimated in relatively rough joint profiles (JRC>14). At least two components of roughness parameters are needed to properly represent the joint roughness, for example, the amplitude and the inclination angle of joint asperity. Roughness mobilization is affected by both the normal stress and the asperity scale. Copyright © 2008 John Wiley & Sons, Ltd.     

基于方向性粗糙度参数的节理峰值抗剪强度理论模型

节理裂隙控制着岩石工程的剪切滑移稳定性。现有的节理峰值抗剪强度模型多为经验模型,且较少考虑粗糙节理峰值抗剪强度的采样点距效应及各向异性。采用3D打印技术制备了5组吻合的粗糙光敏树脂节理模具,利用水泥砂浆复制了25组相同壁面强度的人工粗糙节理,开展了5种法向应力水平下节理直剪试验。基于改进的接触面积比-视倾角门槛值关系,建立了仅含一个方向性粗糙度参数的三维粗糙节理峰值抗剪强度理论模型。该理论模型除粗糙度参数外无需拟合其他参数。对比分析发现,新模型比文献中的经验模型预测精度更高。新模型预测效果受采样点距影响较小,且能有效地反映节理峰值抗剪强度的各向异性。     

A direction-dependent shear strength criterion for rock joints with two new roughness parameters

The surface morphology of a rock joint is closely related to its mechanical properties. To reasonably characterize a rock surface, two new roughness parameters were proposed in this paper. One is related to the average slope angle of asperities that contribute to the shear strength, and the other reflects the frictional behavior of asperities that is defined as the maximum possible contact area in the shear direction. Taking the standard joint roughness coefficient profiles as example, these two roughness parameters can be applied to describe the directional characteristics of shear strength. Based on their relationships with initial dilation angles, the proposed roughness parameters were incorporated into a peak shear strength criterion. It is shown that the predicted peak shear strength is consistent with experimental data, and there is a power–law relationship. The application range of new roughness parameters was determined, which may facilitate a measurement process.     

含坡度均方根的节理峰值剪切强度经验公式

节理的剪切强度涉及到岩体工程的安全。通过CSS–342岩体剪切试验机对3组具有不同形貌特征的节理进行直剪试验,研究形貌对剪切强度的影响。试验结果表明：峰值剪切强度随法向应力和粗糙程度的增加而增加;但就相同的形貌而言,剪切应力与法向应力的比值减小,即由形貌产生的剪胀角随法向应力的增加而减小。通过分析剪胀角存在的边界条件,提出双曲线形式的剪胀角演化模型,并采用抗拉强度体现岩石的性质对节理剪切强度的影响。采用坡度均方根表征节理的三维形貌特征并提出相应的峰值剪切强度公式,与经典的Barton公式进行了比较,总体上新公式的计算值更为接近试验值。     

改进的Maksimovic峰值剪切强度准则的试验验证

Maksimovic峰值剪切强度准则形式简洁,参数的物理含义明确,但由于反映节理粗糙程度的特征量“粗糙度角 ”须由试验值确定,因此不可用于估算岩石节理的峰值剪切强度。改进的Maksimovic峰值剪切强度准则在继承原准则优点的基础上,采用定量化的三维形貌参数表示节理的“粗糙度角 ”。采用岩石节理的直剪切试验数据对改进的Maksimovic峰值剪切强度准则进行了试验验证,计算值与试验值具有很好的相关性,表明可以采用该准则估算岩石节理的峰值剪切强度。     

Effect of different wall roughness on the frictional behavior of rock joints

Rock discontinuities play a crucial and critical role on the deformational and failure behavior of the rock mass. In most investigations, both the surfaces of the rock joints are considered to have same roughness. But, in nature, the walls of a fresh joint is only expected to be complimentary and to have same roughness. Weathered and water percolating rock joint is most likely to develop different surface roughness on the two opposite walls. So, the shear strength and frictional response behavior derived from the single joint roughness coefficient (JRC) assumption cannot be used in such a condition. To address this shortcoming, we have prepared sandstone blocks with different surface roughness and conducted experiments in a tribometer. The static friction, shear stiffness and coefficient-of-friction of the joint surfaces were calculated and their changes with increasing normal load were noted. One of the major findings of this paper is that, shear strength of the joints may not have a direct correlation with the increasing JRC value of the individual joint walls. Hence, some of the joint walls having higher cumulative JRCs were found to show lower shear strength than those with lowers roughness. This is because, the opposing walls of such joints are not anymore complementary and the frictional resistance is completely controlled by the height and contact area of the asperites.     

基于多重分形特征的岩体结构面剪切强度研究

Barton剪切强度模型是目前工程实践中普遍采用的强度公式,而实践应用时,该模型中结构面粗糙性系数（JRC）的评估存在主观性和片面性的缺点。鉴于此,应用多重分形理论,提出了采用多重分形参数准确量化JRC的方法。首先应用数字图像处理技术获取了结构面三维形貌数据信息;然后采用投影覆盖法进行了结构面的分形维数计算,重点对结构面的多重分形特征进行了分析,通过对比分析了构造的15个结构面的多重分形特征值。结果表明：结构面越粗糙,多重分形特征参数 和 值越大, 或 能够很好地描述结构面的形貌特征。最后对9组石膏试件进行了剪切试验,通过不同正应力下对应的剪应力数据分析,结合结构面形貌多重分形参数 或 ,以Barton剪切强度公式为基础,应用最小二乘法原理,给出了JRC与 及JRC与 关系。这样在工程实际中,可以用参数 或 对JRC进行估算,克服了JRC人为估值主观性及采用二维标准轮廓线评估片面性的缺点,为准确评估结构面粗糙度提供了一条新的途径。在此基础上,应用Barton模型可准确估算岩体结构面的剪切强度。     

岩体结构面抗剪强度综合评价

结构面抗剪强度参数是工程岩体稳定性分析和加固治理方案设计的重要指标。本文系统总结了岩体结构面粗糙度系数的各质异性、各向异性、非均一性和尺寸效应特征,回顾了结构面粗糙度系数测量仪器研制过程和结构面粗糙度系数测量技术发展历程,介绍了岩体结构面抗剪强度综合评价的具体步骤,并通过试验对比分析了岩体结构面抗剪强度综合评价方法的可靠性。     

A simple failure criterion for rough joints and compound shear surfaces

The subject under investigation is the strength of a single shear plane which exhibits a regular, asymmetric roughness pattern. In the shear direction the asperities are so steeply inclined that the joint becomes mechanically non-effective with the result that the asperities are sheared off. Against the shear direction the asperities are only gently inclined. It is shown that this particular roughness pattern is of some general importance in geomechanics (examples: unconfined compression test; shear plane with secondary fractures).

Simple analytical considerations allow the formulation of a shear criterion, which is dependent on friction angle ø_m and cohesionc_m of the intact rock and on the inclination γ of the gently inclined parts of the asperities which are dipping against the shear direction. In the Mohr-diagram the criterion results in envelopes which converge at high normal stresses against the envelope of intact rock. Furthermore, the criterion expresses that both the slope of the envelopes and the dilation angle continuously decrease with increasing normal stress. Therefore the criterion adequately describes features which are regarded as most important when shearing rough joints or compound shear surfaces.     

Importance of Tensile Strength on the Shear Behavior of Discontinuities

In this study, the shear behavior of discontinuities possessing two different rock wall types with distinct separate compressive strengths was investigated. The designed profiles consisted of regular artificial joints molded by five types of plaster mortars, each representing a distinct uniaxial compressive strength. The compressive strengths of plaster specimens ranged from 5.9 to 19.5 MPa. These specimens were molded considering a regular triangular asperity profile and were designed so as to achieve joint walls with different strength material combinations. The results showed that the shear behavior of discontinuities possessing different joint wall compressive strengths (DDJCS) tested under constant normal load (CNL) conditions is the same as those possessing identical joint wall strengths, but the shear strength of DDJCS is governed by minor joint wall compressive strength. In addition, it was measured that the predicted values obtained by Barton’s empirical criterion are greater than the experimental results. The finding indicates that there is a correlation between the joint roughness coefficient (JRC), normal stress, and mechanical strength. It was observed that the mode of failure of asperities is either pure tensile, pure shear, or a combination of both. Therefore, Barton’s strength criterion, which considers the compressive strength of joint walls, was modified by substituting the compressive strength with the tensile strength. The validity of the modified criterion was examined by the comparison of the predicted shear values with the laboratory shear test results reported by Grasselli (Ph.D. thesis n.2404, Civil Engineering Department, EPFL, Lausanne, Switzerland, 2001). These comparisons infer that the modified criterion can predict the shear strength of joints more precisely.     

砂土充填大理岩节理的剪切强度经验公式

为研究砂土充填对节理抗剪强度的影响,利用GCTS（RDS?200型）岩石剪切测试系统对4种不同摩擦系数砂土充填的粉晶大理岩节理进行了直剪试验。结果表明：相同法向应力下,未充填节理的峰值剪切应力大于充填节理的峰值剪切应力,说明砂土的存在降低了节理的剪切强度;由节理面三维形貌参数最大谷深 表征节理面粗糙程度,得到了未充填节理的峰值剪切强度公式,公式预测值与试验值基本吻合;得到了用充填砂土摩擦系数表达的充填节理峰值剪切强度公式,公式预测值与试验值较为吻合。研究结论对充填节理岩体稳定性评价具有一定指导意义。     

基于Plesha本构的岩石节理多层结构模型研究

在Dong等工作的基础上[1],研究了基于Plesha本构的岩石节理多层结构模型。模型将节理面分解为不同层次细观结构面,每层结构面代表一级粗糙度,力学响应发生在最底层（基本面）,上层结构面受力性状由其下层结构面平均化得到,依次进行得到节理宏观力学性状。节理破坏由下而上分层次进行,基本面破坏后,其上层结构面转化为基本面,基本面采用Plesha节理模型。模型能模拟弹性变形、滑动变形、磨损、剪断、压碎、分离等作用机理。定义的接触因子与绕流因子能考虑节理接触面积及粗糙度变化对渗流的影响。通过将粗糙度定义为等效起伏角,可以模拟节理循环剪切性状。采用ABAQUS的用户子程序UEL进行了模型验证与参数分析。     

Some recent advances in the modelling of soft rock joints in direct shear

This paper presents a review of recent developments made by the authors into the modelling of rock joints in direct shear. Careful observation of laboratory direct shear testing on concrete/rock joints containing two-dimensional roughness has allowed theoretical models of behaviour to be developed. The processes modelled include asperity sliding, asperity shearing, post-peak behaviour, asperity deformation and distribution of stresses on the joint interface. Model predictions compare extremely well with laboratory test results. These models were then applied to direct shear tests on rock/rock joints, and although behaviour in general was well predicted, the strength of rock/rock joints was over-predicted. Direct shear tests have also been carried out on samples containing both two- and three-dimensional roughness to test the accuracy of the two-dimensional approximation to roughness adopted in the theoretical models.     

甘肃北山地质处置库围岩节理抗剪强度经验估算

节理抗剪强度参数是地质处置库预选地段工程地质对比和围岩稳定性分析的重要指标。本文在旧井地段英云闪长岩节理分组的基础上,运用定向统计测量方法估测节理粗糙度系数,通过评价节理粗糙度系数的尺寸效应,确定节理抗剪强度经验估算有效长度,由JRC-JCS模型求得各组节理4个方向的抗剪强度参数,并评价了地质处置库围岩节理抗剪强度的各向异性特征。     

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。