Constant Normal Stiffness Conditions Research Articles

Experiment study on shear behavior and properties of granite fractures under real-time high-temperature conditions

Direct shear tests were conducted on granite fractures with similar joint roughness coefficients under real-time high temperatures (up to 400 °C) and constant normal stiffness conditions. In this study, the shearing process was monitored via acoustic emission, and fracture surface morphology was measured with three-dimensional laser scanning. With increasing temperature, peak and residual shear strengths, peak friction coefficient, and maximum normal dilation became higher. In contrast, peak normal displacement and peak shear displacement decreased. The apparent cohesion and internal friction angle exhibited opposite trends as temperature increased, primarily due to competition between thermal hardening and thermal cracking. The elastic strain energy of stick-slip events increased with temperature. From 100 °C to 400 °C, the degradation of fracture roughness and the volume of sheared-off asperities grew. Real-time temperature influences shear properties and is mainly attributed to physical and geometrical changes. Acoustic emission parameters, including count, energy, and hit, show segmented variation during fracture shearing. Based on parameter analyses of the average frequency and rise angle values, during the shearing process, the proportion of shear cracks at each stage varied with temperature. Shear failure was the predominant failure mode. Results from this study provide insight into the shear behavior of granite fractures under real-time high temperatures.

Cyclic shear behavior of en-echelon joints under constant normal stiffness conditions

To reveal the mechanism of shear failure of en-echelon joints under cyclic loading, such as during earthquakes, we conducted a series of cyclic shear tests of en-echelon joints under constant normal stiffness (CNS) conditions. We analyzed the evolution of shear stress, normal stress, stress path, dilatancy characteristics, and friction coefficient and revealed the failure mechanisms of en-echelon joints at different angles. The results show that the cyclic shear behavior of the en-echelon joints is closely related to the joint angle, with the shear strength at a positive angle exceeding that at a negative angle during shear cycles. As the number of cycles increases, the shear strength decreases rapidly, and the difference between the varying angles gradually decreases. Dilation occurs in the early shear cycles (1 and 2), while contraction is the main feature in later cycles (3−10). The friction coefficient decreases with the number of cycles and exhibits a more significant sensitivity to joint angles than shear cycles. The joint angle determines the asperities on the rupture surfaces and the block size, and thus determines the subsequent shear failure mode (block crushing and asperity degradation). At positive angles, block size is more greater and asperities on the rupture surface are smaller than at nonpositive angles. Therefore, the cyclic shear behavior is controlled by block crushing at positive angles and asperity degradation at negative angles.

A multifunctional shear apparatus for rocks subjected to true triaxial stress and high temperature in real-time

Deep engineering disasters, such as rockbursts and collapses, are more related to the shear slip of rock joints. A novel multifunctional device was developed to study the shear failure mechanism in rocks. Using this device, the complete shear–deformation process and long-term shear creep tests could be performed on rocks under constant normal stiffness (CNS) or constant normal loading (CNL) conditions in real-time at high temperature and true-triaxial stress. During the research and development process, five key technologies were successfully broken through: (1) the ability to perform true-triaxial compression–shear loading tests on rock samples with high stiffness; (2) a shear box with ultra-low friction throughout the entire stress space of the rock sample during loading; (3) a control system capable of maintaining high stress for a long time and responding rapidly to the brittle fracture of a rock sample as well; (4) a refined ability to measure the volumetric deformation of rock samples subjected to true triaxial shearing; and (5) a heating system capable of maintaining uniform heating of the rock sample over a long time. By developing these technologies, loading under high true triaxial stress conditions was realized. The apparatus has a maximum normal stiffness of 1000 GPa/m and a maximum operating temperature of 300 °C. The differences in the surface temperature of the sample are constant to within ±5 °C. Five types of true triaxial shear tests were conducted on homogeneous sandstone to verify that the apparatus has good performance and reliability. The results show that temperature, lateral stress, normal stress and time influence the shear deformation, failure mode and strength of the sandstone. The novel apparatus can be reliably used to conduct true-triaxial shear tests on rocks subjected to high temperatures and stress.

Unified Modeling of Interface between Structured Clay or Crushable Sand and Structure

The purpose of this paper is to develop a unified elastoplastic model for describing both monotonic and cyclic behaviors of natural structured clay–structure and crushable sand–structure interfaces based on the bounding surface plasticity and the critical state concept with three features: (1) a more general yield surface with two shape parameters is adopted to improve the prediction of the shear yield and the critical state of the soil–structure interface, (2) the degradation of bounding surface size and the adhesive normal stress is introduced into the model to consider the shear strength reduction of natural structured clay–structure interface, and (3) the grain breakage effect on the behavior of crushable sand–structure interface is considered by incorporating the location of the critical-state line with the broadening of grain-size distribution induced by grain breakage. Then, explicit simulation schemes with substepping and error control are established for simulating interface shear tests under constant volume, constant normal load, and constant normal stiffness conditions. Finally, comparisons between experimental and numerical results indicate that the unified soil–structure interface model is able to not only predict the state-dependent monotonic stress–strain behavior of structured clay–structure or crushable sand–structure interfaces, but also reproduce the cyclic accumulative contraction and stabilization, as well as the stress degradation observed in both structured clay–structure and crushable sand–structure interfaces.

Towards boundary conditions in concrete-rock joint shearing with STAs profile by PFC2D

Boundary conditions significantly affect the shear behavior of concrete-rock joints. Most of the joint models have been developed for the constant normal load (CNL) conditions but cannot be directly extended to the more general constant normal stiffness (CNS) conditions, as a ‘normal stiffness (K)’ serves as a spring in such a condition to constantly adjust the normal confinements in terms of the dilation. In this study, the authors attempted to set up numerical modeling of concrete-rock joint shearing by layered over-compaction method based on PFC2D. An obvious extension is that explicit spring-based kinetic equations were employed to govern the travel of the upper shear chamber, by which the system can be dynamically balanced at each timestep to permit CNS conditions. Also, an alternative joint profile consisting of multiple similar triangular asperities (STAs) was defined in the presented modeling, taking account of both varied asperity heights and sizes. The comparisons with laboratory observations, recently published by the authors, demonstrated that the model makes reasonable predictions of shear behavior, especially well capturing the essential mechanisms of STAs profile, including dilation, shearing, and local lift-off. Compared with CNL conditions, the CNS conditions can better mobilize the peak shear strength, maximum normal stress, micro-cracks, and force chain. Results indicate that an adequate choice of CNL or CNS conditions is of significance to evaluate the side resistance, loading capacity, or engineering stability in geotechnical engineering practices.

Shear behaviour of anchored jointed rock mass under different engineering conditions considering damage and joint surface morphology

According to different geological conditions and engineering disturbance, three dimensional numerical models of anchored jointed rock mass with two kinds of boundary conditions of constant normal load (CNL) and constant normal stiffness (CNS) were constructed considering the ductility damage of rockbolt, the stiffness degradation of grouting layer and the joint surface roughness. The effects of anchorage angle, joint surface morphology, and boundary conditions on the shear performance of anchorage system were analyzed, and the failure characteristics under different working conditions were revealed. Finally, the analytical solution of shear strength of anchored system was established. Results show that the larger the anchorage angle is, the more serious the necking phenomenon of rockbolt will be. The damage degree of the bonding layer and the horizontal displacement of the bedding rock mass decrease with the increase of the joint surface roughness. The CNL condition is to instantaneously apply high normal stress, and the CNS condition is to gradually form a high normal stress environment through the superposition of increment on the basis of the initial value, which can resist greater transverse load. This is equivalent to enhancing the ductility of the rockbolt. The shear strength of the system increases with the increase of normal stress and normal stiffness. Ignoring the normal stiffness will underestimate the shear strength.

Sliding modes of fault activation under constant normal stiffness conditions

Fault activation has been the focus of research community for years. However, the studies of fault activation remain immature, such as the fault activation mode and its major factors under constant normal stiffness (CNS) conditions associated with large thickness of fault surrounding rock mass. In this study, the rock friction experiments were conducted to understand the fault activation modes under the CNS conditions. Two major parameters, i.e. the initial normal stress and loading rate, were considered and calibrated in the tests. To reveal the response mechanism of fault activation, the local strains near the fault plane were recorded, and the macroscopic stresses and displacements were analyzed. The testing results show that the effect of displacement-controlled loading rate is more pronounced under the CNS conditions than that under constant normal load (CNL) conditions. Both the normal and shear stresses drop suddenly when the stick-slip occurs. The decrease and increase of the normal stress are synchronous with the shear stress in the regular stick-slip scenario, but mismatch with the shear stress during the chaotic stick-slip process. The results are helpful for understanding the fault sliding mode and the prediction and prevention of fault slip.

Numerical study on the shear behavior of concrete-rock joints with similar triangular asperities

The shear behavior of concrete-rock joints with similar triangular asperities (STAs) was investigated by numerical direct shear tests under constant normal stiffness (CNS) conditions based on particle flow code (PFC), and numerical models were validated by laboratory observations recently published by the authors. The failure patterns and shear load transfer of asperities on the joints were revealed in terms of shear micro-cracks and shear force chains on the micro-scale. For comparison, joints with conventional profile, regular triangular asperities (RTAs), were also examined. The comparisons showed that a prominent ductile behavior at post-peak most likely occurred for the STAs profile owing to asynchronous asperity failure rather than brittle shear caused by a synchronous failure of the RTAs profile. Results also indicated that there would exist a critical inclination to limit the further mobilization of joint dilation and it may be useful to guide the preliminary design of the rock-socketed pile foundation.

Modeling of granular soil-structure interface under monotonic and cyclic loading with the nonlinear approach

A constitutive model that can accurately predict the behavior of the soil-structure interface is beneficial to the analysis and design for foundation engineering performance. This paper develops a new model with the nonlinear approach for simulating the monotonic and cyclic behaviors of the granular soil-structure interface. Based on the hyperbolic function, the concept of normalized shear displacement is proposed, and the basic model for the effects of the normal stress, the nonlinear shear modulus, and the friction angle on shear strength during shearing is deduced. On this basis, the Pyke criterion is modified to describe the cyclic loading responses. The relation between the friction angle and the state parameter of the interface in different interface states is established under the framework of critical state soil mechanics (CSSM) theory to further reflect the interface behaviors corresponding to the changes of void. Taking the phase transformation state as a reference state of volume increment, the incremental equation of stress-dilatancy induced by shearing is developed. In addition, the basic model is extended to be able to describe the interface mechanical behaviors under constant normal load (CNL), constant stiffness (CNS), and constant volume (CV) conditions by considering the characteristics of three typical stress loading paths. Only 10 calibrated parameters are required to reproduce the complex properties in the monotonic and cyclic behaviors. The predictive performance of the proposed interface model is examined by the previous experimental results.

Numerical simulations on shear behaviour of rock joint network under constant normal stiffness conditions.

In this study, the numerical direct shear tests were conducted to investigate the shear mechanical properties of joint networks under constant normal stiffness (CNS) boundary conditions. The influence of random joint number on shear stress (τ), dilation (normal displacement, δv) and normal stress (σn) of rock mass were studied quantitatively with fixed main slip surface. At the same time, the internal stress evolution process and failure process were analyzed. The results reveal that the number of random joints (γ) has little effect on the shear and normal stresses. The normal displacement of the sample generally decreases as the number of random joints increases. In addition, the normal displacement of the specimen is absorbed by the random joints when the number of random joints in the specimen increases to a certain level: when γ is greater than 6 and the shear displacement (μ) reaching 10 mm, the specimen exhibits shear contraction. Therefore, the internal random joints mainly control the failure mode and dilatancy performance of the specimen, while the main joint of the rock controls the shear stress of the specimen.

A three-dimensional (3D) analytical solution for the ultimate side shear resistance of rock-socketed shafts

This paper presents a new analytical solution to the ultimate side shear resistance τsf of rock socketed shafts with consideration of three-dimensional (3D) strength and shaft sidewall roughness. Specifically, the shaft sidewall profile is simplified as triangular asperities and micro-mechanical analysis is performed on the shear behavior of one representative asperity. A 3D version of the Hoek-Brown (HB) criterion for rock mass and the equilibrium equations in a cylindrical coordinate system are first utilized to derive the governing equations. Then the governing equations are solved by using the method of characteristics. Finally, the τsf is obtained by considering the constant normal stiffness condition and the relative displacement of the rock mass due to sliding along the shaft-rock mass interface. Twenty-four (24) model and field test shafts with measured τsf are collected for analysis to verify the proposed solution. The results indicate that the predicted τsf values are in good agreement with the measured τsf values. Extensive parametric studies are also conducted to investigate the effects of rock mass properties, shaft dimensions, and sidewall roughness parameters on the ultimate side shear resistance factor αf (the ratio of τsf to the unconfined compressive strength of intact rock σc) of rock socketed shafts. The results indicate that the αf increases with rock constant mi, geological strength index (GSI) and asperity half chord length λ, but decreases with shaft diameter B, σc and disturbance D. Furthermore, the αf first increases and then decreases with the asperity inclination angle δ, resulting in an optimum asperity inclination angle δOp. Therefore, it is important to reduce the disturbance of rock mass from construction and select a proper asperity inclination angle when designing a rock socketed shaft.

A micromechanics-based model for concrete-rock interface with similar triangular asperities

Direct shear tests on samples containing similar triangular asperities have been carried out under constant normal stiffness (CNS) conditions, and observations demonstrated that there exists local lift-off of shallower asperities across the interface, resulting in a redistribution of local stresses and further impacting the global shear behavior . This study further modifies the existing theoretical model based on multiple-asperity configurations, previously presented by the authors. The proposed method relates the normal and shear stresses on the individual asperity to interface strength and corresponding displacement in terms of the asperity inclination and contact areas. The emphasis is on quantifying the number of shallower asperities that would be lifted off when the closely contacted asperities are dislocated by an amount of interface dilation. In addition to the mechanism of local lift-off itself, the resultant redistribution of global shear stress on remaining asperities can be also taken into account. The proposed model is verified by predicting experimental observations published elsewhere, and the comparison appears to be satisfactory.

Experimental Study on the Influence of Hydromechanical Boundary Conditions on Shear-Flow Coupling Characteristics of Granite Joints

The instability of jointed rock mass is usually the shear process of the rock mass along discontinuities under the influence of groundwater flow. By conducting laboratory tests and numerical experiments on the shear-flow coupling of rock joints under constant normal stiffness (CNS) and constant normal stress (CNL) boundary conditions, the influence of normal boundary conditions and seepage pressure on the shear mechanical and flow characteristics of joints were investigated. The test results were as follows: The joint shear stiffness, peak, and residual shear strength under the CNS boundary condition were predominantly larger than those under the CNL boundary condition. Overall, these parameters were positively correlated with the initial normal stress σ n 0 . When σ n 0 > 2 MPa, the postpeak shear stress of the CNS boundary condition showed a sharp decrease, whereas that of the CNL boundary condition changed from a slowly decreasing type ( σ n 0 = 4 MPa, 6 MPa) to a sharply decreasing type at σ n 0 = 8 MPa. The peak dilation rate under the CNS boundary condition at all levels of normal stress was lower than that of CNL, and the strain softening in postpeak of the latter was more remarkable. In the process of joint shear, the hydraulic aperture displayed a four-stage variation law of “steady-sudden increase-slow increase-basically stable.” Moreover, the hydraulic aperture under the CNS boundary condition was always lower than that under the CNL boundary condition. The seepage pressure increased from 0.5 MPa to 1.5 MPa, and the average hydraulic aperture in the stable stage under normal stress at all levels increased from 0.146 mm to 0.187 mm. In addition, the average peak shear stress and average shear stiffness decreased by 0.9 MPa and 0.83 GPa/m, respectively. We also established a numerical model of a real rough three-dimensional joint, compiled a calculation program for the shear-flow process of a joint under CNS boundary conditions, and visualized the flow channel inside the joint. The seepage flow bypassed the area where the joints contacted each other, forming obvious flow channels. The flow rate increased at the intersection of the flow channels.

Shear behaviour of infilled rock joints under different boundary conditions

The use of commercial software for the analysis and design of rock slopes, underground structures, mining projects, foundations of infrastructure projects, piles and so on is becoming more commonplace. However, such software sometimes has limitations and cannot be used directly for determining the strength and deformation behaviour of rock joints when they are subjected to external loads due to construction. Correct predictions of the strength and deformation behaviour of rock joints are important for safe, economical and sustainable design. The strength and deformation behaviour of unfilled and infilled rock joints were numerically studied using the commercial software Universal Distinct Element Code (Udec) under different boundary conditions (constant normal stiffness (CNS) and constant normal load (CNL)). The numerical results were compared with experimental results of physical model tests. The strength predicted by the numerical model was in close agreement with the experimental results at low initial normal stress and for CNL boundary conditions, as asperity degradation during the shearing process was almost same throughout the test. However, the numerical model did not correctly predict the shear strength of rock joints under CNS boundary conditions and at high normal stress under both CNL and CNS conditions because Udec does not consider the effect of asperity degradation during shearing. The Udec code was thus modified for applicability under both CNL and CNS boundary conditions and at high initial normal stress at CNL boundary conditions. Comparison of the predicted and experimental results indicated most predictions to lie in the 95% confidence band.

Effect of particle breakage on the behavior of soil-structure interface under constant normal stiffness condition with DEM

Previous studies show that extensive particle breakage occurs at the soil-structure interface, which may influence the shear strength, but a corresponding comprehensive micro-mechanical analysis, particularly with constant normal stiffness (CNS), is missing. In this study, a series of interface shear tests under CNSs are simulated with the discrete element method (DEM) to understand the role of particle breakage at the interface. Through a rigorous calibration process, the interface model in DEM is first validated with identifying micro-mechanical parameters. Then, by modifying the reference tensile strength of particles, the effect of particle breakage on the behavior of soil-structure interface is quantitatively investigated. All results demonstrate that, particle breakage decreases the dilation, normal stress, shear stress, and shear zone thickness in the interface shear test; particle breakage decreases the peak friction angle while increases the residual friction angle at the interface; and particle breakage decreases soil anisotropy at the interface. In addition, the degree of particle breakage is increased by normal stiffness. The findings of this study may provide deeper insights on the role of particle breakage at the interface with CNS and allow engineers to have a better estimation of the interface strength.

Anchorage effect of bolt on en-echelon fractures: A comparison between energy-absorbing bolt and conventional rigid bolt

Widespread en-echelon fractures may induce some disasters such as landslides of rock slopes and destabilization of underground excavations. Bolt support has been widely used in various rock engineerings for many years, but the bolting behavior of en-echelon fractures has rarely been studied. In this study, the anchorage effect of conventional rigid bolt and energy-absorbing bolt was investigated by direct shear tests under constant normal stiffness conditions. The bolting performance of the two bolts was quantitatively evaluated based on shear strength and dilation indices. The test results show that the anchorage effect of bolt is closely related to the bolt material and fracture angle. This is essentially determined by the deformation mechanism of bolt in different shear failure structures. A bolt deformation factor was proposed to predict the breakage displacement of bolt at different fracture angles and a bolt contribution index was defined to comprehensively evaluate the bolting performance.

Micro-mechanical analysis of soil–structure interface behavior under constant normal stiffness condition with DEM

Micro-mechanical analysis of soil–structure interface behavior under constant normal stiffness condition with DEM

Linear and nonlinear fluid flow responses of connected fractures subject to shearing under constant normal load and constant normal stiffness boundary conditions

Linear and nonlinear fluid flow behaviors of connected fractures during shearing under constant normal load and constant normal stiffness boundary conditions are numerically characterized solving the Navier-Stokes equations. The model consists of three fractures having an identical length of 200 mm and a width of 100 mm, among which the bridge fracture is sheared. Both smooth and rough-walled fracture surfaces are generated to investigate the effect of surface roughness on flow streamline distributions and the ratio of flow rate to hydraulic gradient. The results show that the permeability monotonically increases during shearing under constant normal load conditions, due to the shear-induced dilation of fractures. Under constant normal stiffness conditions, the permeability either increases or decreases during shearing, controlled by the competing role played by the shearing fracture and nearby fractures. As shear advances, the shearing fracture dilates and increases the permeability, whereas the surrounding fractures are compressed that decrease the permeability. The flow rate of rough-walled models is overestimated by approximately 45 ∼ 80% comparing to the smooth parallel plate model. For smooth models, the critical hydraulic gradient dramatically decreases with increasing the shear strain from 0.015 to 0.025 and then slightly fluctuates with the increment of shear strain from 0.025 to 0.05. The critical hydraulic gradient monotonically decreases during the shearing process for rough-walled models. The range of critical hydraulic gradient is between 0.001 and 0.02.

Experimental program on mechanical properties of large rock fractures

Predictions of fracture displacements are required to support the safety assessments of a deep geological repository for nuclear spent fuel. Laboratory and in-situ experiments are used to estimate these properties. Despite significant contributions in the last decades, there is a knowledge gap in terms of the impact of high normal stresses on the mechanical properties of large-scale fractures under Constant Normal Stiffness (CNS) boundary conditions. Within the framework of the POST project, a cooperative effort was made by SKB (Sweden), NWMO (Canada), and Posiva from Finland (in phase 1) to study these questions. In the second phase of the POST project, a first of a kind direct shear testing machine was manufactured and calibrated that can accommodate samples up to 400 × 600 mm under normal stresses up to 10 MPa, for both CNS and Constant Normal Load (CNL) conditions, with the ability to shear the sample up to 50 mm. Several best practice procedures were developed for fracture characterization pre-, syn-, and post-shear test which utilize high resolution optical scanning, contact pressure measurements, Digital Image Correlation (DIC) measurements, and acoustic emission measurements during the shear test. Natural and tensile-induced fractures of a granitic rock as well as replicas of the hard rock fractures, at three different fracture sizes of 35×60 mm, 70×100 mm, and 300×500 mm, are now being tested. It is hoped that this program will provide a set of high-quality data which will help reduce the knowledge gap in the understanding of fracture behavior.

Laboratory modeling of deformation of specimens with discontinuity under direct shear in constant normal stiffness conditions

This study presents tests of specimens with discontinuity made of artificial geomaterial (concrete-sand mixture) having triangular profile of surface roughness under shear loading with the boundary “constant normal stiffness” condition, with three values of normal compressive load: 0.5, 0.9 and 1.2 MPa. The patterns of deformation were determined at each stage of loading diagrams: linear, nonlinear, peak load and residual strength. The empirical dependences of the ultimate shear stress on normal stress were constructed for different values of roughness.