A Laboratory Shear Cell Used for Simulation of Shear Strength and Asperity Degradation of Rough Rock Fractures

Different failure modes during fracture shearing have been introduced including dilation, sliding, asperity cut-off and degradation. Several laboratory studies have reported the complexity of these failure modes during shear tests performed under either constant normal load (CNL) or constant normal stiffness (CNS) conditions. This paper is concerned with the mechanical behaviour of synthetic fractures during direct shear tests using a modified shear cell and related numerical simulation studies. The modifications made to an existing true triaxial stress cell (TTSC) in order to use it for performing shear tests under CNL conditions are presented. The large loading capacity and the use of accurate hydraulic pumps capable of applying a constant shear velocity are the main elements of this cell. Synthetic mortar specimens with different fracture surface geometries are tested to study the failure modes, including fracture sliding, asperity degradation, and to understand failure during shearing. A bonded particle model of the direct shear test with the PFC2D particle flow code is used to mimic the tests performed. The results of a number of tests are presented and compared with PFC2D simulations. The satisfactory results obtained both qualitatively and quantitatively are discussed.     

A constitutive model for a laboratory rock joint with multi-scale asperity degradation

This paper presents a joint constitutive model that considers separately the mechanical contribution of waviness and unevenness of a joint to shear behaviour. The critical asperities for waviness and unevenness are determined from geometric properties in a lab-scale joint. The wear process is employed to model the degradation in dilation and strength during shear. From dimensional analysis, asperity degradation constants are developed using geometric parameters including asperity angle, wavelength, and amplitude as well as rock strength and stress. The applicability of the proposed model was assessed by performing direct shear tests on three joint roughness coefficient (JRC) profiles and providing its correlation with experimental results. Additionally, experimental data taken from literature were used to validate the model’s performance.     

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.     

Damage characterization during laboratory strength testing: A 3D-finite-discrete element approach

A combined finite-discrete element approach is used to simulate the complete 3D fracture process during conventional laboratory testing, including Brazilian indirect tension and uniaxial and biaxial compression. A typical granite rock type (based on the Lac du Bonnet granite) was simulated to investigate the fracture pattern and mechanical strength of brittle rock in the laboratory. Damage intensity parameters (D₂₁ and D₃₂) are introduced and utilized to characterize the induced damage in the models. These parameters provide an improved representation of the cumulative associated damage and facilitate a quantitative characterization of crack intensity during testing. The numerical simulations included both 3D and 2D models, and show that there is a good agreement between the strength response derived from simulations both in 3D and 2D and the considered rock material. A good correlation also exists between the fracture pattern in 3D and the equivalent 2D models. The influence of confinement on the biaxial strength and the associated damage in compression is investigated. While axial splitting is the dominant failure mode at low confinement, finite-discrete element simulations show that a shear failure mode tends to dominate as the confinement increases. The dependency of dilation upon the confining pressure is also demonstrated, the dilation angle decreasing with increased confinement.     

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     

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     

岩石拉伸剪切破裂试验研究

岩石拉伸剪切破裂是一类特殊应力状态条件下的破裂形式,属于同时受垂直于破裂面的法向拉应力和平行于破裂面的剪应力作用的复合破裂模式。在研制的DSC-800电液伺服测控岩石拉伸剪切试验仪的基础上,进行了大量花岗闪长岩和砂岩的拉伸剪切试验,开展了配套的破裂断口三维激光扫描、扫描电子显微镜（SEM）、岩石物理力学性质试验、颗粒流离散元（PFC）数值模拟等相关试验,利用分形理论研究了岩石拉剪破裂面特征,研究了岩石拉剪-压剪全区破裂准则、剪切速率对岩石拉剪破裂强度的影响,采用颗粒流离散元研究了岩石拉剪破裂过程。研究结论如下:（1）岩石拉剪破裂面的宏观与微观分形维数即粗糙度随着拉应力的增加而增大;（2）岩石的微观断裂形式是拉伸破坏和剪切破坏的结合。当拉应力较小时,岩石的微观断裂形式主要表现为剪切破坏,并且随着拉应力的增加,岩石的拉伸破坏形式表现得更加明显;（3）岩石在拉伸剪切区的破裂拉应力与剪应力成线性负相关关系,在拉伸剪切应力区的岩石破裂线斜率比压缩剪切区大,岩石在拉伸剪切应力条件下比压缩剪切应力条件下容易破裂;（4）在岩石拉伸剪切条件下,剪切速率与剪切强度成非线性反相关关系,随着剪切速率的增加,岩石拉剪破裂面粗糙度增加;（5）建立了岩石拉伸剪切PFC数值试验模型,模拟了岩石拉伸剪切破裂过程中的力链演化以及剪切速率对拉剪破裂面粗糙度的影响,获得了与实验室试验一致的结果。     

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.     

An Elasto-Plastic Constitutive Model for Rock Joints Under Cyclic Loading and Constant Normal Stiffness Conditions

An elasto-plastic constitutive model is introduced for rock joints under cyclic loading, considering the additional shear resistance generated by the asperity damage in the first forward shear cycle and sliding mechanism for further shearing. A series of cyclic loading direct shear tests was conducted on artificial joints with triangular asperities and replicas of a real rock asperity surface under constant normal stiffness (CNS) conditions. The model was calibrated and then validated using selected data sets from the experimental results. Model simulations were found to be in good agreement with the rock joints behaviour under cyclic loading and CNS conditions both in stress prediction and dilation behaviour. In addition, dynamic stability analysis of an underground structure was carried out, using Universal Distinct Element Code and the proposed constitutive model.     

Physical explanation for the displacement-length relationship of faults using a post-yield fracture mechanics model

A plane strain model for a fault is presented that takes into account the inelastic deformation involved in fault growth. The model requires that the stresses at the tip of the fault never exceed the shear strength of the surrounding rock. This is achieved by taking into account a zone, around the perimeter of the fault surface, where the fault is not well developed, and in which sliding involves frictional work in excess of that required for sliding on the fully developed fault. The displacement profiles predicted by the fault model taper out gradually towards the tip of the fault and compare well with observed displacement profiles on faults. Using this model it is found that both (1) the shape of the displacement profile, and (2) the ratio of maximum displacement to fault length are a function of the shear strength of the rock in which the fault forms. For the case of a fault loaded by a constant remote stress, the displacement is linearly related to the length of the fault and the constant of proportionality depends on the shear strength of the surrounding rock normalized by its shear modulus. Using data from faults in different tectonic regions and rock types, the in situ strength of intact rock surrounding a fault is calculated to be on the order of 100 MPa (or a few kilobars). These estimates exceed, by perhaps a factor of 10, the strength of a well developed fault and thus provide an upper bound for the shear strength of the crust. It is also shown that the work required to propagate a fault scales with fault length. This result can explain the observation that the fracture energy calculated for earthquake ruptures and natural faults are several orders of magnitude greater than that for fractures in laboratory experiments.     

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.     

Correlations Developed for Estimation of Hydraulic Parameters of Rough Fractures Through the Simulation of JRC Flow Channels

The hydro-mechanical response of fractured rock masses is complex, due partly to the presence of fractures at different scales. Surface morphology has a significant influence on fluid flow behaviour of a fracture. Different empirical correlations and statistical models have been proposed to estimate the equivalent hydraulic aperture and determine the pressure drop along a fracture. However, the existing models suffer from not being adequately generalised to be applicable to a wide range of real fracture surfaces. To incorporate the effect of profile roughness in the hydro-mechanical behaviour of fractured rock masses, the joint roughness coefficient (JRC) is the most widely used empirical approach. However, the average JRC of two fracture walls in fluid flow analysis, as is a common practice, appears to be inappropriate. It will be shown how different combinations of pairs of JRCs could lead to a similar JRC value. Also, changing the position of the top and bottom walls of a fracture can significantly change the hydraulic response of the fracture while the average JRC is identical in both cases. In this paper, correlations are developed which are based on the simulation of JRCs using estimated fluid flow parameters of 2D fractures can be estimated. In order to widen the application range of the correlations, JRC flow channels were generated: these are 2D channels with their top and bottom walls being made from two of the JRC profiles. To estimate the JRC of linear profiles, a correlation developed between JRC and a newly developed Riemannian roughness parameter, D _R1, is proposed. Considering ten JRC profiles, a total of 100 JRC flow channels were generated. In order to only investigate the effect of surface roughness on fluid flow, the minimum closure between the top and bottom walls of JRC flow channels were considered to be constant. Three cases with minimum closures of 0.01, 0.05 and 0.10 cm were considered in this study. All JRC flow channels were subjected to fluid analysis using FLUENT software. Based on these results, correlations were developed between the geometrical and hydraulic properties of flow channels. Analysis of several real fractures demonstrated the applicability of these correlations.     

3D stability analysis of gravity dams on sloped rock foundations using the limit equilibrium method

A convenient approach to performing stability analysis of concrete gravity dams is the so-called two-dimensional “gravity method.” However, concrete gravity dams located in valleys with sloped rock foundation abutments behave as three-dimensional (3D) structures and are often able to share compressive and shear loads between adjacent monoliths, especially when shear keys are present. A general 3D limit equilibrium method was developed in this study to compute global sliding safety factors (SSF_g) by considering sequential load redistribution among adjacent monoliths when individual monoliths have mobilized their sliding strength. Two validation examples of the sliding safety assessment of existing dams are presented to illustrate the accuracy and efficiency of the proposed approach compared to that of the full 3D numerical analyses conducted using the distinct element method. It is shown that gravity dams may be formed by individual monoliths on sloped rock foundations that will slide if considered as isolated structures but will constitute a stable assembly when the load-sharing capabilities of monoliths are recognized in the analysis.     

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.     

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.     

Influence of Structural Non-Stationarity of Surface Roughness on Morphological Characterization and Mechanical Deformation of Rock Joints

Summary Structural non-stationarity of surface roughness affects accurate morphological characterization as well as mechanical behaviour of rock joints at the laboratory scale using samples with a size below the stationarity threshold. In this paper, the effect of structural non-stationarity of surface roughness is investigated by studying the scale dependence of surface roughness and mechanical behaviour of rock joints. The results show that the structural non-stationarity mainly affects the accurate characterization of the surface roughness of the fracture samples. It also controls the amount and location of the contact areas during shear tests, which in turn affects the mechanical properties and asperity degradation of the samples. It is concluded that for accurate determination of the morphological and mechanical properties of rock joints at laboratory and field scales, samples with size equal to or larger than the stationarity threshold are required. Author’s address: Nader Fardin, Rock Mechanics Group, Department of Mining Engineering, Faculty of Engineering, University of Tehran, P.O. Box: 11365/4563, Tehran, Iran     

DEM Simulation of Direct Shear: 2. Grain Boundary and Mineral Grain Strength Component Influence on Shear Rupture

The influence of mineral grain and grain boundary strength is investigated using a calibrated intact (non-jointed) brittle rock specimen subjected to direct shear with a particle-based distinct element method and its embedded grain-based method. The adopted numerical approach allows one to independently control the grain boundary and mineral grain strength. The investigation reveals that, in direct shear, the normal stress (σ _n) applied to a rock specimen relative to its uniaxial compressive strength (UCS) determines the resulting rupture mechanism, the ultimate rupture zone geometry, and thus its shear stress versus horizontal displacement response. This allows one to develop a rupture matrix based on this controlling parameter (i.e., σ _n/UCS). Mineral grain strength reductions result in the lowering of the apparent cohesion intercept of the peak linear Coulomb strength envelope, while grain boundary strength reductions change the peak linear Coulomb strength envelope to a bi-linear or curved shape. The impact of grain boundary strength is only relevant at σ _n/UCS ratios <0.17 where tensile and dilatant rupture mechanisms dominate. Once shear rupture begins to be the dominant rupture mechanism in a brittle rock (i.e., at σ _n/UCS ratios >0.17), the influence of weakened grain boundaries is minimized and strength is controlled by that of the mineral grains.     

锚固的贯通节理岩体剪切破坏特性分析

为了研究节理对锚固岩体力学特征和失稳损伤演化的影响,采用对锚固贯通节理岩体进行室内剪切试验和PFC2D数值模拟的方法,研究不同节理倾角下锚固贯通节理岩体剪切性能的作用机制和破坏模式,研究结果表明:（1）随着节理倾角变化,贯通节理岩体呈现出不同的破坏形式,锚固贯通节理岩体的抗剪强度与剪切位移曲线并不是呈线性增长,而是呈"双驼峰"趋势。（2）锚固体系在剪切试验的过程中,节理面颗粒的接触方位角会发生一定程度的改变,主要集中在锚杆和节理倾角附近。（3）锚固体系在剪切试验的过程中,会因为颗粒间黏结键的断裂生成裂纹,裂纹数生成的越少,其抗剪强度越高,裂纹分为张拉裂纹和剪切裂纹,并且张拉裂纹的数量要远远大于剪切裂纹的数量。研究结论可用于实际工程破坏模式的预测和岩体工程稳定性评价。     

类节理岩石直剪试验力学特性的数值模拟研究

节理岩体的剪切特性是主导岩体工程稳定性的关键因素。基于PFC2D离散元颗粒流程序,结合室内试验结果对比分析,选取合理的细观参数进行数值模拟,分别从细观角度研究了节理岩石的裂纹发展、能量转化及声发射现象等特性,从宏观角度研究了节理岩石的强度模型和破坏形态。结果表明：节理岩体主要呈现磨损和剪断两种破坏形态,不同的破坏形态对应不同的强度模型;随着剪切变形增加,岩体沿节理面发生破坏,弹性阶段以法向裂纹为主,而塑性阶段切向裂纹起主导作用,滑移区R、P裂纹贯通形成破碎带,节理面产生较大滑移;在应力达到峰值强度前,边界能主要转化为应变能,法向裂纹生成较多;越过峰值强度后,摩擦能快速增长,并伴随大量切向裂纹产生。与室内试验结果相比,PFC2D较好地模拟了节理岩体剪切力学特性,弥补了室内试验中无法进行细观特性研究的缺陷,对于节理岩体后期研究提供了一些参考。