Constant Normal Stiffness Boundary Conditions Research Articles

Investigation on the cyclic shear properties of steel-crushed red mudstone particles interface

The cyclic shear characteristics between the structure and soil are critical to the bearing capacity of an infrastructure. In this study, the cyclic shear behavior of the interface between rough steel and crushed red mudstone particles under constant normal load (CNL) and constant normal stiffness (CNS) boundary conditions are investigated using an improved large-scale cyclic shear apparatus. Under the two normal boundary conditions, the variation rule of the interface shear stress with shear displacement is similar, and the interface generally exhibits softening behavior during cyclic shear. Nevertheless, the interface shear strength and deformation values are not equal for the two boundary conditions, i.e., under the CNL boundary condition, higher interface shear strengths are usually obtained, and more significant normal densification behavior is exhibited compared to the CNS boundary condition. The peak shear strength of the interface has a linear relationship with the normal stress, which conforms to the Mohr-Coulomb failure criterion. Additionally, the influence of water content on the interface deformation and cyclic shear strength under the above boundary conditions are explored. The water content does not change the interface volumetric response pattern but is reflected in the magnitude. Regarding interface shear strength, the interface softening phenomenon is more significant with increased water content. The interface shear strength of the initial and residual states is analyzed, while the relationship between the interface shear strength parameters and water content is established.

Experimental study of the direct shear characteristics of cement grout under constant normal loading and stiffness boundary conditions

Grouting cable is one of the most critical technologies in mine support. However, there are few studies on the effect of post-peak residual strength of cement grout under direct shear testing, which is of great significance for evaluating the bearing capacity of grouting cables in the whole life cycle. Hence, in this study, we carried out a systematic direct shear test to reveal the shear characteristics of cement grout under both constant normal loading (CNL) and constant normal stiffness (CNS) boundary conditions. The test results show that, under the same initial normal stress, the peak shear strength of the cement grout obtained under the CNS boundary conditions is greater than that under the CNL boundary conditions. The high initial normal force reduces the effect of boundary conditions on the post-peak mechanical shear properties of the cement specimens. Moreover, under CNS boundary conditions, the acoustic emission activity of the sample has an obvious signal before the peak shear strength, accompanied by multiple large ringing counts, indicating that the internal damage of the cement grout starts before the peak intensity. This work enhances the understanding of cement grouting fracture characteristics in mining support engineering.

Shear Behavior and Asperity Damage of 3D Rough Joints under CNS Boundary Conditions Based on CZM Simulation

Although boundary conditions can significantly impact the shear behaviors and asperity damage evolution of jointed rocks, numerical studies on the damage of 3D rough rock joints under the constant normal stiffness (CNS) boundary condition have rarely been reported. In this work, the three-dimensional model of the irregular joint surface is established by using point cloud reconstruction technology. Based on the cohesive zone model (CZM), we simulate the shear behavior of three-dimensional rough rock joints under the CNS boundary condition, which is realized by using embedded spring elements implemented with a Python subroutine. We conducted laboratory direct shear tests under CNS boundary conditions. The agreement with the laboratory experimental results verifies the fidelity of the numerical method. Our results show that boundary conditions can significantly affect the shear behavior of rock joints, especially in the post-peak stage. Under the same initial normal stress, the peak shear stress and the number of microcracks in the asperities increase significantly with the increase of normal stiffness. The proportion of shear cracks positively correlates with the normal stiffness, indicating that the normal stiffness affects the joint failure mode. The damaged area and the volume of asperities increase with the increase of normal stiffness. Moreover, the distribution of shear-induced asperity loss becomes more nonuniform, and the loss of joint roughness increases rapidly and nonlinearly.

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.

Enhancement of constant normal stiffness direct shear testing protocols for determining geomechanical properties of fractures

Discontinuity behaviour can have a large impact on geotechnical engineering design; therefore, it is essential to determine their geomechanical properties to predict rockmass behaviour and mitigate any potential failure that may affect personnel safety or damage property. Geotechnical numerical software programmes that discretely simulate discontinuities rely on direct shear laboratory tests to provide the properties needed as inputs to these tools. This study presents valuable direct shear laboratory test results for the mechanical properties and behaviours of fresh, unweathered, rough fractures in the Pointe du Bois granite. The testing programme considers three separate boundary conditions: constant normal stress (CNL*) and two variations of constant normal stiffness (CNS). A new machine stiffness model is proposed to estimate the machine stiffness for tunnelling applications. Measurements of shear strength and a proposed secant dilation angle are assessed and critically evaluated. It is found in this study that there is no significant difference between shear strength parameters determined from direct shear data from CNL* and CNS boundary conditions when comparing maximum strength and residual strength. In addition, it is found that the proposed secant dilation angle, critical shear displacement, and total dilation potential all have a negative relationship with increasing normal stress.

Numerical Simulation on Shear Behavior of Double Rough Parallel Joints Under Constant Normal Stiffness Boundary Condition

The shear characteristics of rock joints under constant normal stiffness (CNS) boundary condition are critical to the stability of underground engineering rock mass. Five different rock joint profiles with random morphology were constructed using the independent segmentation method of the Hurst exponent. Based on the continuously yielding joint model, the discrete element calculation models of double rough parallel joints with different joint surface roughness and spacing of joints under CNS boundary condition were established using UDEC software to investigate the shear effect of joints under CNS boundary condition. The results show that under CNS boundary condition, the shear stress, normal displacement, normal stress, and surface resistance index (SRI) all increase with the increase of joint surface roughness coefficient (JRC) for both single- and double-joint specimens, and these of the single-joint are greater than these of the double-joint. With the increase of the joint spacing d, the peak shear stress τy, and the peak surface resistance index (SRIp) show a gradually increasing trend, and the influence of d on τy and SRIp is greater with the increase of JRC, and both τy and SRIp show a linear increasing trend with the increase of JRC. With the increase of d for the same JRC, both normal displacement and normal stress show a gradually increasing trend, and also, the increased amplitudes gradually increase; with the increase of JRC for the same d, the two parameters also show an increasing trend.

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.

Impact of shear displacement on advective transport in a laboratory-scale fracture

The impact of shear displacement under different mechanical boundary conditions on fluid flow and advective transport in a single fracture at the laboratory scale is demonstrated in the present study. The shear-induced changes of fracture aperture structures are determined by using the measured normal displacements and digitalized fracture surfaces from laboratory shear tests. Five shear tests on concrete replicas of the same fracture under different mechanical boundary conditions, including constant normal loading (CNL) and constant normal stiffness (CNS), are conducted to analyse the influence of mechanical boundary conditions on the shear-flow-transport processes. Fluid flow in the fracture with different shear displacements are simulated by solving the Reynolds equation. The Lagrangian particle tracking method is applied to model the advective transport in the fracture after shearing. The results generally show that the shear displacements and the normal loading conditions can significantly affect flow patterns and advective travel time distributions in the fracture. For mated fractures, the flow and transport will be enhanced by the increasing shear displacement because of shear dilation. For cases with the same shear displacement, the median advective travel time increases with the increasing boundary normal stiffness. The median advective travel time under the CNS boundary condition is generally longer than that under the CNL boundary condition. The results from this study can help to improve our understanding of stress-dependent solute transport processes in natural rock fractures.

Research Progress on Shear Characteristics of Rock Joints under Constant Normal Stiffness Boundary Conditions

The constant normal stiffness (CNS) boundary condition is more representative for the underground engineering, in which the shear-induced dilation is restricted by surrounding rocks, resulting in an increase in the normal stress. Therefore, the use of CNS boundary conditions in the research of shear-slip failure of underground rock engineering is more in line with the actual situation. Taking the instability and failure of surrounding rock in underground engineering as the background, the present study introduces the engineering background of CNS boundary conditions and the research progress on shear characteristics of rock joints under CNS boundary conditions. Three key directions for future research are proposed based on the latest research results of shear characteristics of rock joint under CNS boundary conditions: ① developing a rock joint shear test system that can realize the function of “CNS boundary conditions + shear-seepage test + visualization”; ② carrying out the shear tests of real rock joints under CNS boundary conditions based on 3D scanning and 3D carving technology; and ③ carrying out the shear tests of rock joint network under CNS boundary conditions.

Shear mechanical responses of sandstone exposed to high temperature under constant normal stiffness boundary conditions

Shear mechanical responses of sandstone exposed to high temperature under constant normal stiffness boundary conditions

Numerical Research of Fluid Flow and Solute Transport in Rough Fractures under Different Normal Stress

The effects of roughness and normal stress on hydraulic properties of fractures are significant during the coupled shear flow test. Knowing the laws of fluid flow and solute transport in fractures is essential to ensure the nature and safety of geological projects. Although many experiments and numerical simulations of coupled shear flow test have been conducted, there is still a lack of research on using the full Navier-Stokes (N-S) equation to solve the real flow characteristics of fluid in three-dimensional rough fractures. The main purpose of this paper is to study the influence of roughness and normal stress on the fluid flow and solute transport through fractures under the constant normal stiffness boundary condition. Based on the corrected successive random addition (SRA) algorithm, fracture surfaces with different roughness expressed by the Hurst coefficient ( H ) were generated. By applying a shear displacement of 5 mm, the sheared fracture models with normal stresses of 1 MPa, 3 MPa, and 5 MPa were obtained, respectively. The hydraulic characteristics of three-dimensional fractures were analyzed by solving the full N-S equation. The particle tracking method was employed to obtain the breakthrough curves based on the calculated flow field. The numerical method was verified with experimental results. It has been found that, for the same normal stress, the smaller the fracture H value is (i.e., more tough the fracture is), the larger the mechanical aperture is. The ratio of hydraulic aperture to mechanical aperture ( e h / e m ) decreases with the increasing of normal stress. The smaller the H value, the effect of the normal stress on the ratio e h / e m is more significant. The variation of transmissivity of fractures with the flow rate exhibits similar manner with that of e h / e m . With the normal stress and H value increasing, the mean velocity of particles becomes higher and more particles move to the outlet boundary. The dispersive transport behavior becomes obvious when normal stress is larger.

Permeability Evolution of Two-Dimensional Fracture Networks During Shear Under Constant Normal Stiffness Boundary Conditions

The permeability evolution of fractal-based two-dimensional discrete fracture networks (DFNs) during shearing under constant normal stiffness (CNS) boundary conditions is numerically modeled and analyzed based on a fully coupled hydromechanical (HM) model. The effects of fractal dimension, boundary normal stiffness and hydraulic pressure on the evolutions of mechanical behaviors, aperture distributions and permeability are quantitatively investigated. The results show that with increasing confining pressure from 0 to 30 MPa, the permeability decreases from the magnitude of 10−13 m2 to 10−16 m2, which is generally consistent with previous models reported in the literature. With the increment of shear displacement from 0 to 500 mm, the variations in shear stress, normal stress and normal displacement exhibit the same patterns with the conceptual model. As shear advances, the permeability evolution exhibits a three-stage behavior. In the first stage, the permeability decreases due to the compaction of fractures induced by the increasing shear stress from 0 to the peak value. In the second stage, the permeability holds almost constant values under constant normal load (CNL) boundary conditions, whereas that under CNS boundary conditions decreases by approximately one order of magnitude. Under CNS boundary conditions, although the aperture of shearing fracture increases enhancing its own permeability, the apertures of surrounding fractures are compacted due to the simultaneous increases in the normal and shear stresses, which result in the decrease in the total permeability of DFNs. When the fractal dimension increases from 1.4 to 1.5, the permeability increases following exponential functions in the early stage of shear, which fail to characterize the permeability in the residual stage due to the complex flow path distributions. At the start of shear, the ratio of permeability perpendicular to the shear direction to that parallel to shear decreases approximately from 1.0 to 0.5 and then gradually decreases from 0.5 to 0.3 in the residual stage. The hydraulic pressure tends to open up the fractures and enhances the permeability. The magnitude in permeability enhancement is of approximately the same order with the increase in the hydraulic pressure.

Shear behaviour of multi-joint specimens: role of surface roughness and spacing of joints

Although many previous studies have investigated the shear behaviour of single rock joints, few of them have focused on the shear behaviour of multi-joint rock specimens under constant normal stiffness boundary conditions. This study describes the manufacture of a series of rock specimens containing multiple parallel rough joints and estimates the role of surface roughness and spacing of joints during shearing. The results show that the upper joint is crushed while the lower joint is scratched after shearing for a two-joint specimen. The middle joint is more significantly damaged/scratched than the upper and lower joints after shearing for a three-joint specimen. The joint surface roughness plays a clearer role on the variations in shear stress, normal displacement and normal stress for a three-joint specimen than that for a two-joint specimen. With the increment of shear displacement, the surface resistance index (SRI) defined as the ratio of shear stress to normal stress exhibits peak values and residual values. As the spacing of joints increases, the peak SRI generally increases at a rate in the range of 0·15–0·22/cm, except for one specimen containing three joints with a relatively rough surface.

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.

Effects of mica content on rock foliation strength

Foliation is a planar geological structure characterized by the alignment of minerals, including mica grains. Foliated metamorphic rocks exhibit anisotropic mechanical behaviors, wherein the weakest properties are usually oriented parallel to the foliation planes. Rock mechanics research on this subject has been focused on characterizing the full anisotropic behaviors of rocks with stresses applied parallel, oblique and perpendicular to the anisotropy direction (foliation planes). However, less effort has been given to characterizing the mechanical behaviors of isolated foliation planes and describing the influences of mineralogical properties on the weaknesses associated with such geological structures. This paper presents a laboratory testing program, including direct shear tests and pull-off tests, to characterize the influences of mica content on the shear and tensile strengths of foliation planes of the biotite gneiss (which is basically composed of biotite, quartz and feldspar). Direct shear tests were performed under constant normal load and constant normal stiffness boundary conditions, wherein the foliation planes were isolated in 1 cm-thick shear zones. The mica content was estimated by a practical digital image analysis approach that was capable of quantifying the percentage of biotite area on the foliation surfaces that failed in shear and tension. The results showed that the mica (e.g., biotite) content had substantial effects on the mechanical behaviors of isolated foliation planes, especially on the peak shear and tensile strengths. A practical 3D strength envelope was proposed that included the mica content as an independent variable, which can be quantified from foliation surfaces on rock blocks and outcrops. The results provided new insights into the influences of mica-rich foliation planes on the mechanical behaviors of metamorphic rocks, which is directly applicable to rock engineering problems.

A mechanical-hydraulic-solute transport model for rough-walled rock fractures subjected to shear under constant normal stiffness conditions

The present study developed a two dimensional mechanical-hydraulic-solute transport model for rough-walled rock fractures under constant normal stiffness boundary conditions. First, the mechanical responses of a fracture during shear including the shear stress, the normal stress, the dilation and the sheared-off area of asperities at each shear step were calculated in a mechanical module. The surface roughness was characterized by two-order asperities, i.e., waviness and unevenness, and the degradation of asperities was estimated based on the principle of wear. The mechanical module was validated by comparison with laboratory experiments. The surface geometry and the dilation behavior were subsequently incorporated into a hydraulic module to estimate the hydraulic aperture and flow rate based on the cubic law. Finally, these data were input into a solute transport module to investigate the influences of the mechanical boundary conditions on the solute transport in the fracture and the matrix at different shear displacements and time. The model linked the complex mechanisms involved in the mechanical, hydraulic and solute transport processes for fractures subjected to shear, and revealed a controlling effect of normal stiffness on the transport behavior. The results show that the normal displacement, normal stress, cumulative sheared-off area and porosity of matrix change quickly in the initial stage of shear, and gradually reach some constant values when the fracture surface is sufficiently smoothed in the residual stage. In the entire shear process, the major asperities are substantially damaged, producing abundant gouge particles that contribute to the retardation of solute transport. The shear-induced dilation and the retardation induced by gouge particles from damaged asperities played competitive roles in solute transport that resulted in the nonlinear variations in the coefficient of retardation. The model established a solid platform for estimating the mechanical-hydraulic-solute transport processes in fractures subjected to shear, upon which more sophisticated modules such as pressure solution and clogging by particles may be developed to improve the understanding on the outstanding issues involved in the coupled processes.

Experimental Study on the Shear-Flow Coupled Behavior of Tension Fractures Under Constant Normal Stiffness Boundary Conditions

This study experimentally investigated the effects of fracture surface roughness, normal stiffness, and initial normal stress on the shear-flow behavior of rough-walled rock fractures. A series of shear-flow tests were performed on two rough fractures, under various constant normal stiffness (CNS) boundary conditions. The results showed that the CNS boundary conditions have a significant influence on the mechanical and hydraulic behaviors of fractures, during shearing. The peak shear stress shows an increasing trend with the increases in the initial normal stress and fracture roughness. The residual shear stress increases with increasing the surface roughness, normal stiffness, and initial normal stress. The dilation of fracture is restrained more significantly under high normal stiffness and initial normal stress conditions. The hydraulic tests show that the evolutions of transmissivity and hydraulic aperture exhibit a three-stage behavior, during the shear process—a slight decrease stage due to the shear contraction, a fast growth stage due to shear dilation, and a slow growth stage due to the reduction rate of the mechanical aperture increment. The transmissivity and hydraulic aperture decreased, gradually, as the normal stiffness and initial normal stress increase.

Distinct element method simulations of rock-concrete interfaces under different boundary conditions

The shear behaviour of concrete-rock interfaces has been the aim of extensive research in geotechnical engineering applications such as rock socketed piles, rock bolts and concrete dam arch bridge foundations. Several experimental studies through direct shear tests have been conducted to evaluate the shear behaviour of rock-concrete interfaces under CNL (Constant Normal Load) and CNS (Constant Normal Stiffness) conditions. In this paper, PFC2D numerical simulations of unbonded rock-concrete planar and saw-tooth triangular joints under CNL and CNS boundary conditions are conducted using the Shear Box Genesis (SBG) approach proposed by Bahaaddini et al. (2013b). The numerical simulation results are compared with experimental data published by Gutiérrez (2013) and Gu et al. (2003). Results indicate that the SBG approach reproduces suitably the shear behaviour, failure mode and asperity damage of unbonded (planar and triangular) rock-concrete interfaces, specially under CNL conditions.

Automatic Static and Cyclic Shear Testing Machine under Constant Normal Stiffness Boundary Conditions

Abstract Dynamic loads, including earthquake, blasting, and vibration loads, induce cyclic shear loads along the joints in rock masses; hence, the risk of failure increases on the joints due to changing shear resistance. On the other hand, joints are under different boundary conditions: constant normal load (CNL) and constant normal stiffness (CNS). Normal stiffness increases on the joints with increasing depth, and it can affect shear resistance. For an accurate assessment of joint shear resistance under varying normal stiffness and number of cycles, advanced laboratory shear apparatus is essential for the shear test. Conventional direct shear apparatuses have limitations such as boundary conditions, working under monotonic (static) shear loads only, or cyclic shear loads with no change of frequency and amplitude of shear loads. Therefore, a new large-scale servo-controlled direct shear testing machine was developed to conduct cyclic shear test (as well as monotonic shear test) under CNL and CNS boundary conditions with varying normal stiffness at different frequencies and amplitudes of shear loads. In the present study, the cyclic shear tests were conducted on nonplanar joints under varying normal stiffness. Moreover, the effects of different frequencies and amplitudes of shear loads were investigated. The test results indicate that peak shear stress increases with increasing normal stiffness at the first cycle, but the influence of normal stiffness decreases with an increase in the number of shear cycles. The frequency of shear load influences peak shear stress, i.e., peak shear stress increases with increasing frequency. The number of cycles does not affect peak shear stress on the joints at low shear amplitude, but peak shear stress decreases with higher amplitude.