Behaviour Of Rock Joints Research Articles

Determination of Joint Surface Roughness Based on 3D Statistical Morphology Characteristic

Roughness significantly affects the shear behavior of rock joints, which are widely encountered in geotechnical engineering. Since the existing calculation methods on the joint roughness coefficient (JRC) fail to obtain a sufficiently accurate value of JRC, a new determination method was proposed in this study, where the 3D laser scanning technique and self‐compiled Python code, as well as the statistical parameter methods, were applied. Then, the shear strength of jointed rock was evaluated via Barton′s model, and therefore, a comprehensive comparison between the calculating results and experimental results was executed. Ultimately, the influencing factors of roughness profile extraction on the accuracy of JRC value, such as the measuring point interval, profile number, and measuring direction, were investigated. The results show that (1) equipped with the 3D laser scanning technique, the roughness profiles can be accurately extracted via the self‐compiled Python code, (2) an excellent consistency of shear strength could be observed between the calculating value and experimental results, verifying the validity and accuracy of the proposed method, and (3) a smaller measuring point interval can produce a more accurate digital profile and more accurate JRC value. To a certain extent, the more the sample numbers of profiles, the smaller the value of JRC.

Experimental study on shear-seepage behaviour of rock joints under constant normal stiffness

Experimental study on shear-seepage behaviour of rock joints under constant normal stiffness

Modeling shear behavior of rock joints: A focus on interaction of influencing parameters

One of the principal issues in the design of surface and underground structures on/in rock is the shear behavior of rock discontinuities that irreparable damages are caused when neglecting it. Several parameters are involved in the shear behavior of rock discontinuities which can interact with each other. The purpose of this study is to model the shear behavior of rock joints with regard to the individual impact of the influencing parameters and their interaction. To do so, a number of direct shear tests was performed where the values of independent parameters including the compressive strength (σc), normal stress (σn), modulus of elasticity (E), joint roughness coefficient (JRC) and basic friction angle (ϕb) were varied. Then, the response surface methodology (RSM) was used to incorporate the individual influence and interaction of the parameters into constitutive relationships for the peak shear strength, peak shear displacement, and dilation angle. For the shear strength, the most significant interaction was found to be between E and ϕb, for the peak shear displacement between JRC and E, and for the dilation angle between σc and E. The results show that the proposed model performs better in estimating the shear behavior characteristics than the model obtained from the nonlinear regression and the Barton-Bandis model. Therefore, the application of RSM is a winning approach for modeling the rock shear behavior which is capable of modeling the most complex interactions and provides a reliable performance.

Shear Strength of Rock Joints and Its Estimation

This study examined the shear behavior of rock joints and proposed an analytical model for estimating the shear strength at rock joints. Numerous experimental tests indicated that the shear behavior at rock joint depends on many factors including the distribution of initial joint asperity, asperity angle and strength, applied normal stress, and progressive degradation of asperity. Nevertheless, most pre-existing strength models do not consider these features on shearing at rock joints enough. In this study an improved shear strength model, which can consider the complex joint shearing features observed from many experimental tests, was developed and proposed. The improved model considers the joint features more reliably and overcomes the limitations of the pre-existing strength models. The proposed model was compared with some experimental test results along with some pre-existing strength models. The comparison clearly indicated that the improved model can estimate the shear strength at rock joints more reliably than the pre-existing models. From the study results it is expected that a better estimate of joint shear strength could be obtained in the future for various rock, joint, stress, and shearing conditions.

Analytical Modeling of the Shear Behavior of Rock Joints with Two-Order Asperity Dilation and Degradation

Abstract Stability evaluation of rock structures requires a reliable model to assess the shear behavior of rock joints. This study reports an analytical model to predict the complete shear process ...

Experimental Study of Shear Behavior of Rock Joints under Two Types of Boundary Conditions: Constant Normal Load and Constant Normal Stiffness

Shear destruction of rock mass along weakened planes is one of the main reasons of the failure of career boards, underground workings and rock slopes. The paper deals with laboratory testing of rock joints under direct shear loading. Special test and measurement complex was created to study deformation and strength characteristics of rock joints. Test specimens were made from single slab of sandstone of homogeneous structure. Shear tests have been conducted under constant normal load (CNL) and constant normal stiffness (CNS) boundary conditions at three values of normal compressive stress: 0.5 MPa, 1.2 MPa and 1.8 MPa. The analysis of test results allowed to reveal patterns of changes of deformation-strength properties of rock joints depending on the level of normal load, boundary conditions and roughness values. The ultimate shear stress is always higher under CNS boundary condition than CNL for the same values of normal compressive stress. Shear stress practically retains constant value after reaching the ultimate stress under CNL boundary conditions and it decreases under CNS conditions. The values of ultimate shear stresses, shear modulus and the length of linear section on “shear stress–shear displacement” curve increases with increasing surface roughness at the equal levels of normal compressive stress.

Effect of contact surface area on frictional behaviour of dry and saturated rock joints

Frictional behaviour of joints/faults is of great importance in many geo-engineering applications across different scales. It is known that the joint surface roughness is one of the critical parameters controlling the frictional behaviour of rock joints. While nominal normal and shear stresses acting across the joint asperities are calculated based on overall shearing area, the actual normal and shear stresses can be much greater due to smaller actual contact area. The actual contact area on the other hand is known to be related to the joint surface roughness. In order to investigate the effect of contact area on the shear behaviour of rock joints, an extensive set of direct shear experiments at different normal stresses on dry and saturated shale, limestone and sandstone tensile joints were undertaken. To compare the frictional properties of natural and artificial samples, synthetic samples were also fabricated, and their frictional properties were evaluated. Results of this study revealed that the predominant parameter controlling the frictional strength is the actual contact area. While the common models in predicting the shear strength of rock joints were unable to fit the experimental data based on nominal contact area, the results based on actual contact area fit the measured values accurately. In addition, it was observed that when the actual contact area is considered, Mohr-Coulomb criterion is sufficient to fit the experimental data irrespective of the rock type, joint surface roughness or whether dry or saturated. This highlights that the Mohr-Coulomb criterion can appropriately predict the frictional strength if the actual contact area can be estimated. More importantly, the results showed that the surface roughness cannot dictate the shear behaviour of rock joints without considering the actual contact area.

Effect of bolt inclination angle on shear behavior of bolted joints under CNL and CNS conditions

Rock bolts are widely used in rock engineering projects to improve the shear capacity of the jointed rock mass. The bolt inclination angle with respect to the shear plane has a remarkable influence on the bolting performance. In this study, a new artificial molding method based on 3D scanning and printing technology was first proposed to prepare bolted joints with an inclined bolt. Then, the effects of the bolt inclination angle and boundary conditions on the shear behavior and failure characteristic of bolted joints were addressed by conducting direct shear tests under both CNL and CNS conditions. Results indicated that rock bolt could significantly improve the shear behavior of rock joints, especially in the post-yield deformation region. With the increase of bolt inclination angle, both the maximum shear stress and the maximum friction coefficient increased first and then decreased, while the maximum normal displacement decreased monotonously. Compared with CNL conditions, the maximum shear stress was larger, whereas the maximum normal displacement and friction coefficient were smaller under the CNS conditions. Furthermore, more asperity damage was observed under the CNS conditions due to the increased normal stress on the shear plane.

An excess stress model for capturing rate-dependent compressive behavior of rock joint and its validation and applications

The deformational and mechanical behavior of rock masses is determined by discontinuities at different scales, e.g., rock joints. The discontinuous rock masses are often subjected to dynamic loads, e.g. blasts and earthquakes. Therefore, understanding dynamic response of rock joints is crucial. However, the dynamic compressive characteristics of rock joints have not been well understood yet. In this study, an excess stress model, employing the mechanical conceptual models based on the Hooke, the modified Saint Venant and the Newton elements, was developed. It is capable of capturing the nonlinear compressive processes of joints at different loading rates. This new model was validated by the comparison between model predictions and laboratory measurements obtained at loading rates ranging from approximately 200 GPa/s to 600 GPa/s. It was found that certain of rate-dependent compressive characteristics of rough joints can be successfully quantified with the proposed joint model. Compressive strength can be approximately predicted on the assumption that the peak-stress displacement is independent of the loading rate. Both the peak-stress secant stiffness and tangent stiffness predicted by the new joint model increase linearly with the loading rate. The wave energy dissipation at joints calculated by the proposed model decreases with increasing loading rate. Based on this model, the underlying mechanisms responsible for loading rate effects were related to the rate-dependency of crack propagation. Two hypotheses have been proposed: 1)the amount of cracking decreases with the increase of loading rate before the peak stress, causing ‘apparent’ hardening effects; 2) crack propagation velocity is relatively steady under static/quasi-static conditions, but becomes increasingly unstable when the loading rate is higher than the critical transition value. The present findings potentially provide a mechanically sound frame for the rate-dependent characteristics of joints, and have important implications for explicating the rate-dependent phenomena of fracturing, such as crack branching and fracture smoothening.

Investigation of the Mechanical Behavior of 3D Printed Polyamide-12 Joints for Reduced Scale Models of Rock Mass

This study presents the experimental results of the mechanical characterization of artificial rock joints constructed by 3D-printing (3DP). The mechanical behavior of rock masses is controlled by the presence of joints. Understanding the mechanical behavior of rock joints is essential to predict their influence on a rock mass. The application of innovative 3DP technology in rock mechanics to model artificial rock-like joints allows strict control of joint geometry (orientation, roughness, number of rock bridges, etc.), and thus of its mechanical behavior. The 3DP technology used in this work is selective laser sintering, and the material is Polyamide 12. Geometric characterization shows that this technology gives high dimensional precision for details smaller than 0.4 mm. More than 30 discontinuous samples were printed to investigate the global mechanical properties of a joint relative to its geometric features including Young’s Modulus (E), shear stiffness (ks), cohesion (cj), friction angle (φj) and dilation (i). The results show that the number of rock bridges (Nrb) and the roughness significantly influence the mechanical properties. A failure criterion that considers these parameters is proposed. These 3D-printed joints can be used in physical modeling of rock mass to understand the influence of the fractures on its stability by applying scaling laws. The application of scale factors to the experimental results shows the possibility of representing actual rocks with artificial 3DP joints.

The shear stiffness criterion for rock joints considering rock wear behaviour

Rock is a material that is affected by wear, and the curvature of the asperities on a rock joint surface increases with the degree of wear after shearing. Based on the Greenwood and Williamson (GW) model, a new model considering the change of asperity curvature is proposed to explain the wear behaviour of rock joints. First, the shear stiffness formula for a joint surface is derived when the asperity curvature is constant, which shows that the shear stiffness increases with increase of asperity curvature. According to the Mohr–Coulomb criterion, the yield position of a single asperity under normal force and tangential friction force is discussed. Then, the critical normal force for a single asperity at a specific friction coefficient is obtained, which shows that the normal force corresponds to the curvature radius of the asperity. A rough surface model with multi-level curvature radius is proposed. With increase of normal force, the higher-order asperities gradually fail and the curvature radius become larger. A specific pressure value excites a specific radius of curvature, and the larger the pressure, the larger the radius of curvature. The relation between the normal force and the curvature radius is proposed and a shear stiffness formula considering the change of curvature radius of the asperity is derived. The proposed model is verified on the basis of the published experimental results. The calculation results of the proposed model can reflect the test results well: for a given joint surface, with increase in normal force the joint surface gradually becomes smooth; for different joint surfaces, with increase in roughness, the joint surface is more easily smoothed.

Discussion of “Numerical Simulation of the Shear Behavior of Rock Joints Filled with Unsaturated Soil” by Libin Gong, Jan Nemcik, and Ting Ren

Discussion of “Numerical Simulation of the Shear Behavior of Rock Joints Filled with Unsaturated Soil” by Libin Gong, Jan Nemcik, and Ting Ren

Discussion of “Numerical Simulation of the Shear Behavior of Rock Joints Filled with Unsaturated Soil” by Libin Gong, Jan Nemcik, and Ting Ren

Discussion of “Numerical Simulation of the Shear Behavior of Rock Joints Filled with Unsaturated Soil” by Libin Gong, Jan Nemcik, and Ting Ren

Closure to “Numerical Simulation of the Shear Behavior of Rock Joints Filled with Unsaturated Soil” by Libin Gong, Jan Nemcik, and Ting Ren

Closure to “Numerical Simulation of the Shear Behavior of Rock Joints Filled with Unsaturated Soil” by Libin Gong, Jan Nemcik, and Ting Ren

A numerical study to investigate the influence of surface roughness and boundary condition on the shear behaviour of rock joints

The shear behaviours of rock joints with and without rock bolt support are numerically studied using the discrete element code PFC2D. A cohesive contact model was employed to reproduce the damage response of the synthetic intact rock (i.e. asperity degradation). We used the smooth-joint model to simulate the micro-scale roughness of the joint surface. We calibrated and validated the proposed numerical framework against the experimental results. A series of numerical constant normal stiffness (CNS) direct shear tests were conducted on idealised and natural rock joints to investigate the influence of the boundary condition on the shear behaviour of rock joints. In particular, the importance of CNS condition, surface roughness, asperity angle, and the initial normal stress were studied. Additionally, the shear and damage mechanism of bolted rock joints under constant normal load (CNL) and CNS condition was numerically investigated. The results presented show that the shear resistance of the joint increases under both CNL and CNS conditions, but at a high degree of roughness, no significant enhancement was observed on the value of peak shear stress.

Numerical Shear Tests on the Scale Effect of Rock Joints under CNL and CND Conditions

The scale effect of rock joint shear behavior is an important subject in the field of rock mechanics. There is yet a lack of consensus regarding whether the shear strength of rock joints increases, decreases, or remains unchanged as the joint size increases. To explore this issue, a series of repeated and enlarged numerical joint models were established in this study using the particle flow code (PFC2D). The microparameters were calibrated by uniaxial compression tests and shear tests on the concrete material under the constant normal loading (CNL) condition. Three different normal stresses were adopted in numerical shear tests with joint specimen lengths ranging from 100 mm to 800 mm. In addition to the commonly used CNL, the constant normal displacement (CND) condition was established for the purposes of this study; the CND can be considered an extreme case of the constant normal stiffness (CNS) condition. The shear stress‐shear displacement curves changed from brittle failure to ductile failure alongside a gradual decrease in peak shear strength as joint length increased. That is, an overall negative scale effect was observed. Positive scale effect or no scale effect is also possible within a limited joint length range. A positive correlation was also observed between the peak shear displacement and joint length, and a negative correlation between shear stiffness and joint length. These above statements are applicable to both repeated and enlarged joints under either CNL or CND conditions. When the normal stress is sufficiently high and shear dilatancy displacement is very small, the shear behavior of rock joints under CNL and CND conditions seems to be consistent. However, for shear tests under low initial normal stress, the peak shear strength achieved under the CND condition is much higher than that under the CNL condition, as the normal stresses of enlarged joints increase to greater extent than the repeated ones during shearing.

Stability analysis of cut slopes using empirical, kinematical, numerical and limit equilibrium methods: case of old Jeddah–Mecca road (Saudi Arabia)

The stability of natural and man-made rock slopes has always been of great concern for engineering geology studies. To ensure a safe and functional design of excavated slopes, the first and most crucial step is to use reliable input parameters while searching for possible failure modes at the preliminary design stage. It is highly important for practicing engineers to determine the best material property for a chosen failure criterion. This study aims to analyze the stability condition of a case road cut from different aspects. For this purpose, two well-known failure criteria proposed for rock masses and rock joints were applied in the study depending on the scale of the problem in the slope face. The Hoek–Brown failure criterion was used to obtain input data required for modeling intact rock and rock mass behavior, and the Barton-Bandis shear strength criterion to determine the input data necessary for the modeling of rock joint behavior. SMRTool and Dips 7.0 programs were utilized to analyze the structurally controlled instabilities due to discontinuities in the cut slope. Slide 2018 and RS2 9.0 programs were executed to examine the stability condition of cut slope subjected to circular and non-circular failures, respectively. According to the results of numerical and limit equilibrium methods, no stability problem occurred in the case of slope due to non-sliding circular or non-circular slip failures. However, according to the results of empirical and kinematical analyses, some structurally controlled sliding failure modes of planar, wedge, and toppling were expected on the slope face. The result of this study clearly shows that to reach a final decision, different analysis methods should be used to evaluate the stability of cut slopes by considering various conditions of jointed rock masses.

Determination of Joint Roughness Coefficient of 2D Rock Joint Profile Based on Fractal Dimension by Using of the Gene Expression Programming

Rock joint roughness influence the shear behavior of rock joints, which have been extensively studied in last a few decades. Various parameters were recommended to quantify the joint roughness, in these parameters, the joint roughness coefficients (JRC value) were widely applied to depict the joint roughness quantitatively by many researchers. Through analysis the references, it is found that the empirical formula of the JRC value based on fractal dimension were commonly adopted, however, the empirical formulas were determined frequently by a limited number of data point, meanwhile, the type of empirical formula were chosen based on the researchers’ subjectively. For obtaining a suitable and objective empirical formula of JRC values based on fractal dimension, a large number of experimental data were collected from the references, by using the gene expression programming method, an empirical formula was determined objectively. The obtained formula can reflect the relationship between the JRC values and fractal dimension extensively, the empirical formula is \( JRC = 21.0810 - \frac{0.0656}{(\sqrt D - 0.9969)D} \).

Multi-spring Edge-to-Edge Contact Model for Discontinuous Deformation Analysis and Its Application to the Tensile Failure Behavior of Rock Joints

Edge-to-edge is the most common form of contact in a two-dimensional joint block system. Discontinuous deformation analysis (DDA) is a powerful tool for handling block systems and treats an edge-to-edge contact as two vertex-to-edge contacts with a couple of normal and shear springs at the extremes of the contact segment. However, this method is unsuitable for evaluating the tensile failure of a joint under asymmetrical tension conditions, even though it can simplify the contact type and increase computational efficiency. This is mainly because the distributed forces at an edge-to-edge contact are simplified as two couples of concentrated forces. To solve this problem, this paper proposes incorporating a multi-spring edge-to-edge contact model with DDA. In the model, several contact pairs with normal and shear springs on an edge-to-edge contact are set to simulate the distributed forces. Several benchmark tests were performed to demonstrate the discrepancy between the original and improved DDAs. The results revealed that the latter more accurately models the stress distribution across the edge-to-edge contact, providing a more reasonable acceleration required to topple a series of blocks resting on an inclined stepped base.

A cohesive grain based model to simulate shear behaviour of rock joints with asperity damage in polycrystalline rock

A cohesive grain based model is proposed to simulate the fracture behaviour of polycrystalline rocks. The model was employed to characterize the cracking response of both inter- and intra-grain contacts in the grain based model (GBM). The model was implemented in distinct element codes and its ability to mimic the mechanical and failure behaviour of polycrystalline rocks was demonstrated through calibration of several granitic rocks including Adelaide black granite, Eibenstock II granite, and Aue granite. The calibrated model of Aue granite was used to assess the effect of joint roughness coefficient (JRC) on asperity damage and shear mechanism of rock joints (i.e. grain crushing) under constant normal load (CNL) and constant normal stiffness (CNS) conditions. The bond-break in intra-grain contacts contributed to asperity damage in form of grain crushing. The numerical observations showed that under CNS condition asperity damage increased with increasing initial normal stress and JRC, and rough rock joints exhibited more dilative response.