Analytical modelling of the shear behaviour of rock joints with progressive degradation of two-order roughness

We present an analytical model for the shear behaviour of rock joints with progressive degradation of two-order asperities including waviness and unevenness. Critical waviness and critical unevenness are used to respectively represent the mechanical involvements of waviness and unevenness during shear. The degradation process of two-order asperities are predicted by considering the stepwise relationship among dilation angle, sheared and unsheared asperity areas, and plastic tangential work. The dilation angle of each asperity decreases as plastic tangential work accumulates. The progressive degradation transiting from critical unevenness to critical waviness is realised through examining the dilation angle and the unsheared area of critical unevenness. The model's predictions are compared with the experimental data from direct shear tests on both regular- and irregular-shaped joints. Good agreement between analytical and experimental curves demonstrate the credence of the proposed model. Therefore, the model, after implemented in finite and discrete element codes, is practicable for the stability assessment of rock-engineering structures.     

Observation of the Degradation Characteristics and Scale of Unevenness on Three-dimensional Artificial Rock Joint Surfaces Subjected to Shear

The present study explores the degradation characteristics and scale of unevenness (small-scale roughness) on sheared rock joint surfaces at a low-stress regime. While the degradation characteristics of unevenness and the normal stress are mutually interrelated, an understanding of the degradation patterns of the three-dimensional roughness of rock joints is one of the important components needed to identify asperity failure characteristics and to quantify the role of damaged unevenness in establishing a shear strength model. A series of direct shear tests was performed on three-dimensional artificial rock joint surfaces at different normal stress levels. After shearing, the spatial distributions and statistical parameters of degraded roughness were analysed for the different normal stress levels. The length and area of the degraded zones showed bell-shaped distributions in a logarithmic scale, and the dominant scale (or the most frequently occurring scale) of the damaged asperities (i.e., unevenness) ranged from approximately, 0.5 to 5.0 mm in length and 0.1–10 mm² in area. This scale of the damaged unevenness was consistent regardless of the level of normal stress. It was also found that the relative area of damaged unevenness on a given joint area, and thus the contribution of the mechanical asperity failure component to shear strength increased as normal stress increased.     

基于小波分析的岩石节理剪切特性研究

岩体工程中,节理面的轮廓特征是决定节理岩体剪切特性的重要因素,既往研究发现节理的表面轮廓可分解为一阶大起伏和二阶小凸起,且两者在剪切特性中发挥不同的作用。为了定量分析两阶表面特征对节理剪切强度的影响,本文通过小波分析法分解节理表面,并利用二维颗粒流数值模拟结合直剪试验验证,研究了具有不同起伏角(4°、8°、12°、16°、20°)波形节理面的细观破坏模式以及波面参数对剪切特性的影响规律。结果表明,波长对剪切强度影响较小,而起伏角是决定节理剪切强度的关键因素,随着起伏角增大剪切强度和摩擦角线性增大; 直剪切过程中裂纹数量随法向应力的增大而增加,以拉伸裂纹为主; 一阶大起伏与二阶小凸起的波形起伏角和摩擦角正相关。以上研究成果为预测节理岩体强度提供了理论支撑,对保障边坡、隧道等岩体工程的安全稳定性具有参考价值。     

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.     

循环剪切荷载作用下含二阶起伏体模拟岩石节理力学特性研究

利用人工材料浇注含二阶起伏体的模拟岩石节理试样,进行常法向荷载循环剪切试验,研究节理剪切力学特性在循环剪切过程中的劣化规律。试验结果表明：二阶起伏体对节理循环剪切力学特性有重要影响,剪切强度、剪切刚度、剪胀角随剪切循环次数增大而衰减,衰减趋势随着二阶起伏度的增大而加快;法向应力、二阶起伏度较大时,二阶起伏体对剪切力学特性的影响主要体现在第1轮剪切循环中,在随后的剪切循环中影响不明显;法向应力、二阶起伏度较小时,二阶起伏体的影响在前几轮循环剪切过程中均有较清晰的体现。基于Hertz接触力学理论,提出了节理面微凸体球面接触细观模型,揭示了节理循环剪切宏观试验现象的力学机制     

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。     

A Bonded Particle Model Simulation of Shear Strength and Asperity Degradation for Rough Rock Fractures

Different failure modes during fracture shearing have been introduced including normal dilation or sliding, asperity cut-off and degradation. Attempts have been made to study these mechanisms using analytical, experimental and numerical methods. However, the majority of the existing models simplify the problem, which leads to unrealistic results. With this in mind, the aim of this paper is to simulate the mechanical behaviour of synthetic and rock fracture profiles during direct shear tests by using the two-dimensional particle flow computer code PFC2D. Correlations between the simulated peak shear strength and the fracture roughness parameter D _R1 recently proposed by Rasouli and Harrison (2010) are developed. Shear test simulations are carried out with PFC2D and the effects of the geometrical features as well as the model micro-properties on the fracture shear behaviour are studied. The shear strength and asperity degradation processes of synthetic profiles including triangular, sinusoidal and randomly generated profiles are analysed. Different failure modes including asperity sliding, cut-off, and asperity degradation are explicitly observed and compared with the available models. The D _R1 parameter is applied to the analysis of synthetic and rock fracture profiles. Accordingly, correlations are developed between D _R1 and the peak shear strength obtained from simulations and by using analytical solutions. The results are shown to be in good agreement with the basic understanding of rock fracture shear behaviour and asperity contact degradation.     

循环剪切荷载作用下岩石节理变形特性试验研究

以水泥砂浆为相似材料,制备3种岩壁强度、5种起伏角度的锯齿型节理试样;利用试验设备,进行了在4种法向应力下的循环剪切试验。根据试验结果,结合循环剪切试验特点,定义剪胀角来表征节理循环剪切的法向变形特性,以及剪切刚度来表征节理循环剪切的切向变形特性。基于不同起伏角、不同强度等级和不同法向应力下的节理试样循环剪切试验结果,分析了循环剪切过程中剪胀角和剪切刚度的变化规律;并利用不同条件下的试验结果,对比分析初始起伏角度、法向应力、岩壁强度对节理循环剪切变形特性的影响规律。研究发现：剪胀角、剪切刚度均随着剪切循环次数的增加而呈现先快、后慢的降低趋势,并且中低起伏角度节理的剪胀角、剪切刚度的降低趋势随着初始起伏角度、法向应力的增加而加快,随着岩壁强度增加而变慢,高起伏角度节理的剪胀角、剪切刚度的降低趋势基本保持不变。     

Effects of Cyclic Loading on the Shear Behaviour of Infilled Rock Joints Under Constant Normal Stiffness Conditions

The variation of the shear strength of infilled rock joints under cyclic loading and constant normal stiffness conditions is studied. To simulate the joints, triangular asperities inclined at angles of 9.5° and 18.5° to the shear movement were cast using high-strength gypsum plaster and infilled with clayey sand. These joints were sheared cyclically under constant normal stiffness conditions. It was found that, for a particular normal stiffness, the shear strength is a function of the initial normal stress, initial asperity angle, joint surface friction angle, infill thickness, infill friction angle, loading direction and number of loading cycles. Based on the experimental results, a mathematical model is proposed to evaluate the shear strength of infilled rock joints in cyclic loading conditions. The proposed model takes into consideration different initial asperity angles, initial normal stresses and ratios of infill thickness to asperity height.     

Numerical Investigations of the Dynamic Shear Behavior of Rough Rock Joints

The dynamic shear behavior of rock joints is significant to both rock engineering and earthquake dynamics. With the discrete element method (DEM), the dynamic direct-shear tests on the rough rock joints with 3D (sinusoidal or random) surface morphologies are simulated and discussed. Evolution of the friction coefficient with the slip displacement shows that the 3D DEM joint model can accurately reproduce the initial strengthening, slip-weakening, and steady-sliding responses of real rock joints. Energy analyses show that the strengthening and weakening behavior of the rock joint are mainly attributed to the rapid accumulation and release of the elastic energy in the joint. Then, effects of the surface roughness and the normal stress on the friction coefficient and the micro shear deformation mechanisms, mainly volume change and asperity damage, of the rock joint are investigated. The results show that the peak friction coefficient increases logarithmically with the increasing surface roughness, but decreases exponentially with the increasing normal stress. In addition, the rougher rock joint exhibits both higher joint dilation and asperity degradation. However, high normal stress constrains the joint dilation, but promotes the degree of asperity degradation significantly. Lastly, the effects of the 3D surface morphology on the shear behavior of the rock joint are investigated with a directional roughness parameter. It is observed that the anisotropy of the surface roughness consequently results in the variation of the peak friction coefficient of the joint corresponding to different shearing directions as well as the micro shear deformation mechanisms, e.g., the extent of joint dilation.     

Laboratory modelling of shear behaviour of soft joints under constant normal stiffness conditions

Shear behaviour of regular sawtooth rock joints produced from casting plaster are investigated under constant normal stiffness (CNS) conditions. Test results obtained in this investigation are also compared with the constant normal load (CNL) tests. It is observed that the peak shear stress obtained under CNL conditions always underestimates the peak shear stress corresponding to the CNS condition. Plots of shear stress against normal stress show that a nonlinear (curved) strength envelope is acceptable for soft rock joints subjected to a CNS condition, in comparison with the linear or bilinear envelopes often proposed for a CNL condition. Models proposed by Patton (1966) and Barton (1973) have also been considered for the predictions of peak shear stress of soft joints under CNS conditions. Although Patton's model is appropriate for low asperity angles, it overestimates the shear strength in the low to medium normal stress range at higher asperity angles. In contrast, while Barton's model is realistic for the CNL condition, it seems to be inappropriate for modelling the shear behaviour of soft joints under CNS conditions. The effect of infill material on the shear behaviour of the model joints is also investigated, and it is found that a small thickness of bentonite infill reduces the peak stress significantly. The peak shear stress almost approached that of the shear strength of infill when the infill thickness to asperity height ratio (t/a) reached 1.40. This paper also introduces an original, empirical shear strength envelope to account for the change in normal stress and surface degradation during CNS shearing. © Rapid Science Ltd. 1998     

Critical review on shear strength models for soil-infilled joints

An infilled rock joint is likely to be the weakest plane in a rock mass. The presence of infill material within the joint significantly reduces the friction of the discontinuity boundaries (i.e. rock to rock contact of the joint walls). The thicker the infill, the smaller the shear strength of the rock joint. Once the infill reaches a critical thickness, the infill material governs the overall shear strength, and the joint walls (rock) play no significant role. Several models have been proposed to predict the peak shear strength of soil-infilled joints under both constant normal load (CNL) and constant normal stiffness (CNS) boundary conditions, taking into account the ratio of infill thickness (t) to the height of the joint wall asperity (a). CNS models provide a more realistic picture of the soil-infilled joint behaviour in the field. This paper presents a critical review on the existing mathematical models for predicting the shear strength of soil-infilled rock joint and verifies the normalised peak shear stress model with further laboratory investigations carried out on idealised saw-tooth rock joints at the University of Wollongong. Based on the prediction of the experimental data, the normalised peak shear stress model is slightly modified by the authors. A simplified approach for using this model in practice is presented and a new expression for prediction of dilatation at peak shear stress is suggested.     

Friction and degradation of rock joint surfaces under shear loads

The morpho‐mechanical behaviour of one artificial granite joint with hammered surfaces, one artificial regularly undulated joint and one natural schist joint was studied. The hammered granite joints underwent 5 cycles of direct shear under 3 normal stress levels ranging between 0.3 and 4 MPa. The regularly undulated joint underwent 10 cycles of shear under 6 normal stress levels ranging between 0.5 and 5 MPa and the natural schist replicas underwent a monotonics shear under 5 normal stress levels ranging between 0.4 and 2.4 MPa. These direct shear tests were performed using a new computer‐controlled 3D‐shear apparatus. To characterize the morphology evolution of the sheared joints, a laser sensor profilometer was used to perform surface data measurements prior to and after each shear test. Based on a new characterization of joint surface roughness viewed as a combination of primary and secondary roughness and termed by the joint surface roughness, SR_s, one parameter termed ‘joint surface degradation’, D_w, has been defined to quantify the degradation of the sheared joints. Examinations of SR_s and D_w prior to and after shearing indicate that the hammered surfaces are more damaged than the two other surfaces. The peak strength of hammered joint with zero‐dilatancy, therefore, significantly differs from the classical formulation of dilatant joint strength. An attempt has been made to model the peak strength of hammered joint surfaces and dilatant joints with regard to their surface degradation in the course of shearing and two peak strength criteria are proposed. Input parameters are initial morphology and initial surface roughness. For the hammered surfaces, the degradation mechanism is dominant over the phenomenon of dilatancy, whereas for a dilatant joint both mechanisms are present. A comparison between the proposed models and the experimental results indicates a relatively good agreement. In particular, compared to the well‐known shear strength criteria of Ladanyi and Archambault or Saeb, these classical criteria significantly underestimate and overestimate the observed peak strength, respectively, under low and high normal stress levels. In addition and based on our experimental investigations, we put forward a model to predict the evolution of joint morphology and the degree of degradation during the course of shearing. Degradations of the artificial undulated joint and the natural schist joint enable us to verify the proposed model with a relatively good agreement. Finally, the model of Ladanyi and Archambault dealing with the proportion of total joint area sheared through asperities, a_s, once again, tends to underestimate the observed degradation. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

The application of energy principles to the determination of the sliding resistance of rock joints

Summary Energy principles have previously been applied to the analysis of rock joints in order to determine the shear strength of dilatant joints (Ladanyi and Archambault, 1970). This work was based on the analysis of regular triangular asperities and assumed that the asperities were rigid. In recognition of the difficulty of measuring a representative asperity angle in natural, complex rock joints, Ladanyi and Archambault extended their results to natural joints by assuming the equality of joint dilation rate and the effective joint asperity angle. It is shown that the assumption of this equality is not universally valid, and that it may lead to an underestimation of joint shear strength. Further, the effective friction angle for joints in an elastic rock mass, for joints comprising asperities of varying inclination, for post-peak shear displacements and for joints in degradable rock are all analysed using extensions of Ladanyi and Archambault's approach.     

A model for coupled mechanical and hydraulic behaviour of a rock joint

Constitutive laws for rock joints should be able to reproduce the fundamental mechanical behaviour of real joints, such as dilation under shear and strain softening due to surface asperity degradation. In this work, we extend the model of Plesha to include hydraulic behaviour. During shearing, the joint can experience dilation, leading to an initial increase in its permeability. Experiments have shown that the rate of increase of the permeability slows down as shearing proceeds, and, at later stages, the permeability could decrease again. The above behaviour is attributed to gouge production. The stress–strain relationship of the joint is formulated by appeal to classical theories of interface plasticity. It is shown that the parameters of the model can be estimated from the Barton–Bandis empirical coefficients; the Joint Roughness Coefficient (JRC) and the Joint Compresive strength (JSC). We further assume that gouge production is also related to the plastic work of the shear stresses, which enables the derivation of a relationship between the permeability of the joint and its mechanical aperture. The model is implemented in a finite element code (FRACON) developed by the authors for the simulation of the coupled thermal–hydraulic–mechanical behaviour of jointed rock masses. Typical laboratory experiments are simulated with the FRACON code in order to illustrate the trends predicted in the proposed model. © 1998 by John Wiley & Sons. Ltd.     

Study of rock joints under cyclic loading conditions

Summary A conceptual model for the behaviour of rock joints during cyclic shear and under constant normal stresses was proposed according to results from shear tests with 50 concrete replicas of rock joints. The shear strength and deformability of joint samples were found to be both anisotropic and stress dependent. Based on these experimental results, a two-dimensional constitutive model was developed for rock joints undergoing monotonic or cyclic loading sequences. The joint model was formulated in the framework of non-associated plasticity, coupled with empirical relations representing the surface roughness degradation, appearance of peak and residual shear stresses, different rates of dilatancy and contraction, variable normal stiffness with normal deformation, and dependence of shear strength and deformability on the normal stress. The second law of thermodynamics was represented by an inequality and used to restrict the values of some of the material parameters in the joint model. The new joint model was implemented into a two-dimensional Distinct Element Method Code, UDEC, and its predictions agreed well with some well-known test results.     

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.     

Prediction of Unconfined Compressive Strength for Jointed Rocks Using Point Load Index Based on Joint Asperity Angle

This research paper is aimed to briefly highlight the correlation between unconfined compressive strength and point load index for jointed rocks based on joint asperity & orientation. In this observe, specimens were tested to obtain their unconfined compression strength and point load index for a different joint condition. The different joint conditions considered for this study were clean joint and joint filled condition. For both clean joint and joint filled specimens were prepared by various asperity angles of 30°, 45°, 60° and 90° with different orientation angles such as 0°, 30°, 45°, 60°, 90°. Plaster of Paris was used as model material to simulate weak rock mass in the field. By testing intact model specimens for unconfined compressive strength leads to revealing of optimum moisture content for further testing. The curing period for the model specimens is 3 days at room temperature. To simulate jointed rocks, various moulds of different orientation of joint with respect to major principal stress are prepared separately. The inner diameter of the mould is 50 mm and height is 100 mm. After casting, a rough joint was created by cutting the prepared sample using the cutter. The specimens are tested for both clean joint and joint filled condition to determine the favorable joint orientation and asperity angle. After curing, the specimens are tested for unconfined compressive strength and Point load index. The new multi-linear correlation for determining unconfined compressive strength with the help of point load index is developed and cross checked with equations formed for actual rock. On comparing both results it is found that the new equation can suitable for assessing the unconfined compressive strength of limestone and serpentinite rocks through point load index value.     

Hydraulic Characteristics of Rough Fractures in Linear Flow under Normal and Shear Load

Summary A hydro-mechanical testing system, which is capable of measuring both the flow rates and the normal and shear displacement of a rock fracture, was built to investigate the hydraulic behaviour of rough tension fractures. Laboratory hydraulic tests in linear flow were conducted on rough rock fractures, artificially created using a splitter under various normal and shear loading. Prior to the tests, aperture distributions were determined by measuring the topography of upper and lower fracture surfaces using a laser profilometer. Experimental variograms of the initial aperture distributions were classified into four groups of geostatistical model, though the overall experimental variograms could be well fitted to the exponential model. The permeability of the rough rock fractures decayed exponentially with respect to the normal stress increase up to 5 MPa. Hydraulic behaviours during monotonic shear loading were significantly affected by the dilation occurring until the shear stress reached the peak strength. With the further dilation, the permeability of the rough fracture specimens increased more. However, beyond shear displacement of about 7 to 8 mm, permeability gradually reached a maximum threshold value. The combined effects of both asperity degradation and gouge production, which prohibited the subsequent enlargement of mean fracture aperture, mainly caused this phenomenon. Permeability changes during cyclic shear loading showed somewhat irregular variations, especially after the first shear loading cycle, due to the complex interaction from asperity degradations and production of gouge materials. The relation between hydraulic and mechanical apertures was analyzed to investigate the valid range of mechanical apertures to be applied to the cubic law. Received June 12, 2001; accepted February 26, 2002 Published online September 2, 2002