Stiffness Boundary Conditions Research Articles

Layerwise third-order shear deformation theory with transverse shear stress continuity for piezolaminated plates

Regarding laminated structures, an electromechanically coupled Finite Element (FE) model based on Layerwise Third-Order Shear Deformation (LW-TOSD) theory is proposed for static and dynamic analysis. LW-TOSD ensures the continuity of in-plane displacements and transverse shear stresses. The current LW-TOSD can be applied to arbitrary multi-layer laminated structures with only seven Degrees of Freedom (DOFs) for each element node and eliminates the use of the shear correction factors. Moreover, a shear penalty stiffness matrix is constructed to satisfy artificial constraints to optimize the structural shear strain. A dynamic finite element model is obtained based on LW-TOSD using the Hamilton’s principle. First, the accuracy of the current model is validated by comparing with literature and ABAQUS results. Then, this study carries out numerical investigations of piezolaminated structures for different width-to-thickness ratios, length-to-width ratios, penalty stiffness matrix, boundary conditions, electric fields and dynamics.

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.

Research on the mechanical model of anchorage resistance in deeply filled jointed rock masses

The calculation model of anchorage resistance is the core issue in the study of anchorage theory in jointed rock masses. Due to the complex geological environment of deep rock masses, the anchorage mechanism of soft rock filled in joints is even more complicated and has not yet been clearly defined. Based on the theory of structural mechanics, considering the restraining stress in the plastic extrusion deformation zone of the bolt as a rectangular distribution pattern is more in line with the interaction state between the bolt and the surrounding medium when the rod is at its limit load. Taking into account the influence of the joint filling part, the value of restraining stress is revised to include a formula expression that factors in the strength of the filling material(σcj) and the degree of filling(Δ).Develop a mechanical model of anchorage resistance for filled joint soft rock considering large deformation conditions due to turning angles. Further, conduct shear tests on anchored filled joint rock bodies under various σcj−Δ combination patterns with constant normal stiffness (CNS) boundary conditions to validate and analyze the model. The research results indicate that under the influence of deep rock mass mechanical boundaries, the ratio of the shear deformation section length to the bolt diameter differs from existing research results, with specimens l/D under different σcj−Δ combinations typically ranging between 0.7 and 1.5 times.The displacement of the bolt at turning angle θ increases with the increase of Δ and decreases with the decrease of σcj, where Δ is the main factor affecting the degree of tensile-bending deformation of the bolt. As Δ increases, the calculated contribution rates of bolt shear resistance under three different σcj conditions increase from 9.8% to 34.8%, 40.3%, and 39.4%, respectively. This indicates that an increase in Δ can reduce the increment of normal stress, further decrease the overall stress and compressive deformation zone’s normal constraint stress in the rock mass, leading to a gradual increase in the degree of tensile-bending deformation of the bolt and an increase in resistance contribution.For the specimens with three different values of σcj, the ratio of shear force to axial force providing resistance on the joint surface decreased from a maximum of 2.83 to 0.72, 1.04, and 2.01, respectively. This indicates that when σcj is relatively large, tensile-bending deformation is more likely to occur, mobilizing the axial force of the bolt to provide the main resistance. Further systematic analysis was conducted on the length of the shear deformation section of the bolt and the distribution characteristics of the anchor resistance under condition β=30°∼90°. The reasonableness of the model was verified through the comparison of model calculation results with experimental data. Finally, a series of recommendations were proposed for preventing failure of the anchored system in filled jointed rock masses in actual engineering projects.

Cyclic failure of interfaces between sand and snakeskin-inspired surfaces

Cyclic loading of deep foundations and soil anchorage elements can lead to failure by accumulation of deformations or loss of strength. Snakeskin-inspired surfaces have been shown to mobilise direction-dependent friction angles and volumetric responses due to their asymmetric profile. This paper presents an investigation on the cyclic interface element behavior of sand-structure interfaces with snakeskin-inspired surfaces with the goal of understanding the potential impact of these surfaces on the cyclic behavior of geotechnical elements. Load- and displacement-controlled cyclic interface shear tests were performed with constant stiffness boundary conditions. Four different snakeskin-inspired surfaces and reference rough and smooth surfaces were tested. The results show that under symmetric shear stress cycles, failure always takes place in the caudal direction (i.e. along the scales) due to the smaller interface friction angles. A shear stress bias can produce a change in the failure direction to the cranial one (i.e. against the scales). An equation is introduced to predict the magnitude of shear stress bias that changes the failure direction. This investigation shows that the snakeskin-inspired surfaces can be used to control the direction of failure of soil-structure interface elements which can help in increasing the cyclic stability and reducing the susceptibility of brittle failure.

Direction-dependent failure envelopes of sand-structure interfaces with snakeskin-inspired surfaces

Snakeskin-inspired surfaces generate direction-dependent interface strengths, with shearing in the cranial direction generating greater strength than in the caudal one. This directionality is enabled by the transfer of load in friction and passive resistances. It is unclear if failure of these interfaces can be captured by models used for purely frictional interfaces. Interface shear tests complemented with Particle Image Velocimetry (PIV) analyses were performed on snakeskin-inspired surfaces with different asperity geometries and on reference rough and smooth surfaces. The results of experiments performed at different initial effective stresses under Constant Normal Stiffness (CNS) boundary conditions show significant dilation-induced increases in effective stress. These increases were greater during cranial than caudal shearing, producing greater cranial strengths. These surfaces yielded non-linear failure envelopes, with greater shear to effective stress ratios at smaller effective stresses, while the rough and smooth surfaces mobilized linear failure envelopes. The PIV analyses indicate that the snakeskin-inspired surfaces induce localized strains in the vicinity of the asperities, leading to wavy failure planes. The average shear strains are correlated with the mobilized shear strengths, with increases in effective stress leading to decreases in both strains and stress ratio.

Experimental and theoretical investigation on vibration of laminated composite conical-cylindrical-combining shells with elastic foundation in hygrothermal environment

The present investigation focuses on the vibration of composite conical-cylindrical-combining shells (CCCCSs) subjected to elastic supports and hygrothermal effects by means of experimental and theoretical investigation. The kinetic energy, potential energy and hygrothermal potential energy are derived via the Donnell shell hypothesis. A set of elastic springs are introduced to the free edges of the CCCCSs aiming to simulate the elastic supports and the interface of the two shell. The dynamic equations of laminated CCCCSs with elastic supports in hygrothermal environment have been obtained in frame of Rayleigh-Ritz method by means of a set of modified orthogonal polynomials as the proper admittance displacement functions. Several experimental and finite element simulation research projects were carried out to validate the effectiveness of the proposed analytical strategy. The unique vibration characteristics of CCCCSs with respect to various temperature, humidity, interfacial bonded stiffness and elastic boundary conditions are thoroughly discussed. The results indicated that the coupling phenomenon performs obviously with the increase of the interface joint stiffness of the structures. Furthermore, the effect of the thermal load on the vibration of CCCCSs become more obviously during some specific temperature range which is determined by the mechanics of the material and manufactured scheme.

A bending-shear-torsion resistant beam foundation model for segmental tunnels in longitudinal direction

Segmental tunnels constructed by Shields / TBMs are easily subjected to uneven longitudinal cross-sectional torsion because of asymmetric external loads or deformations along the tunnel. However, the conventional models for soil-tunnel interaction in the longitudinal direction generally regard the tunnel as a one-dimensional beam on elastic springs, ignoring its cross-sectional torsion. To mitigate this gap, the paper proposed a bending-shear-torsion-resistant beam foundation model to explore the effects of cross-sectional torsion on tunnel performance. Firstly, an analytical solution for the longitudinal bending-shearing-torsion stiffness of a segmental tunnel was derived, then a soil-tunnel interaction model based on torsional Timoshenko beam on Winkler foundation was proposed with three-dimensional soil reactions incorporated. The present model is verified by comparing it with the Finite Element program and other published methods based on two case studies. The new contributions and findings are as follows: (1) The longitudinal torsional stiffness is proposed, and it is found that it is greatly affected by the number of bolts and segment size. (2) The governing differential equations and the closed-form solution for the soil-tunnel interaction model under bending-shear-torsion mode are derived, regarding arbitrary loading and two typical boundary conditions. (3) By considering the sectional torsion and three-dimensional soil reactions, the proposed method is proved to be actually more reasonable than the existing analytical methods. (4) A parametric analysis for the proposed solution was conducted to investigate the influence of key parameters on the torsional performance of segmental tunnels, which revealed the effect of torsional stiffness, soil resistance and elastic boundary conditions. The proposed solution and results could promote tunnel engineers better understand the anti-torque behaviors of segmental tunnels and improve the tunnel design in case of complicated circumstances.

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.

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.

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.

Forward calculation of displacement fields with multilayered unsaturated highway system induced by falling weight deflectometer using dynamic response method

A new dynamic forward model of a multilayered highway structure, which considers the unsaturated characteristics of subgrade soil, is established in this paper to assess the dynamic response induced by the falling weight deflectometer (FWD) load. The Laplace-Hankel transform and dynamic stiffness matrix method are employed to solve the governing equations of the unsaturated soil layer. Combined with the global stiffness matrix and boundary conditions, analytical solutions of the entire system can be derived in the transform domain. A numerical integration method is utilized to perform the Laplace-Hankel inverse transform to obtain time-domain solutions. An analysis of the effects of saturation on the stress, displacement, and pore water pressure is presented. It is revealed that the effect of saturation of unsaturated subgrade soil on vertical stress is negligible, whereas vertical displacement and pore water pressure increase significantly with increasing saturation. Additionally, the vertical displacement response on the pavement surface is sensitive to subgrade deterioration and variations in material properties. Moreover, subgrade deterioration can be reflected in the variation in vertical displacement at approximately 1.2 m from the load center for the studied road structure. The proposed model, which is more realistic and reasonable, can provide a theoretical basis for the back-calculation of the elastic modulus of multilayered highway systems.

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.

Evaluation of unbound/subgrade material rutting and resilient behaviour based on initial density and saturation degree

Unbound pavements with thin surface seals constitute the majority of the lightly and moderately trafficked road networks in Australia. In such pavements, it is considered that seals do not offer much structural support, whereas most of the load coming from the traffic is supported by unbound granular materials and subgrade soil. Hence, accurate estimation of the mechanical properties of such materials is crucial for the satisfactory performance of pavements. In the present study, a constant radial stiffness triaxial (CRST) test was performed on a silty sand, which is typical of the material used in subbase and subgrade layers. The major advantage of the CRST test over the conventional repeated load triaxial test is that the confining pressure is dynamically applied due to a constant radial stiffness boundary condition. It is argued that the CRST test better replicates the stress path typically encountered by geo-materials under the action of traffic loading on pavements. A laboratory investigation was undertaken with different initial dry densities and degree of saturations to develop empirical models of plastic strain (rutting), resilient modulus and Rvalue. Based on the models developed, isograms of these aforesaid parameters are drawn on the compaction plane for the first time and a method is conceptualized for compaction control during field construction providing pathways to performance-based compaction specification.

Influence of surface roughness on shear behaviors of rock joints under constant normal load and stiffness boundary conditions

Influence of surface roughness on shear behaviors of rock joints under constant normal load and stiffness boundary conditions

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.

Out-of-Plane Free Vibration Analysis of Continuous Curved Girders with Combined Linetypes Using Differential Quadrature Element Method

In this study, the out-of-plane free vibration equations of circular curved and clothoid transition curved girders with various boundary conditions were derived. The continuous curved girder with combined linetypes was discretized into separate curved girder elements. Based on the differential quadrature element method (DQEM), the Chebyshev–Gauss–Labatto unequal mesh division was applied to discretize the vibration equations of the continuous curved girder into those of the curved girder elements, along with the boundary conditions, internal geometric compatibility conditions, and force balance conditions. The out-of-plane natural frequency equations were derived considering the boundary conditions by the substitution method. The free vibration was solved for continuous curved girders with combined linetypes of circular and clothoid transition curves. The effectiveness of the DQEM was verified, and the effect of the number of grid points on the accuracy of the solution was evaluated. In addition, the effects of the bending/torsional stiffness ratio, warping coefficient, and boundary conditions on the natural frequencies of continuous curved girders with combined linetypes were investigated. The results showed that the DQEM can be efficiently used to solve the free vibration of multispan continuous curved girders with various linetype combinations. The frequencies of the continuous curved girder with combined linetypes decrease with the weakening of boundary constraints, but increase with increasing warping coefficient and bending/torsional stiffness ratio.

Study on shear behavior and damage constitutive model of tendon-grout interface

Ground anchors are responsible for maintaining the stability and integrity as well as controlling the deformation, displacement, and crack development in the surrounding ground. Tendon-grout (T-G) interface, which is the weak part of anchorage structures, affects the anchorage performance of the ground anchor during load-transfer processes. To investigate the shear mechanical properties of the tendon-grout interface, a series of pull-out tests were conducted on anchorage element under constant radial stiffness boundary conditions. Moreover, the equivalent calculation for the constant radial stiffness boundary condition was analyzed. The mechanical performance of cement grouts cured for different periods was investigated, including the compressive strength and shear strength. Additionally, the failure modes of tendon-grout systems and effects of different tendon quantity, spacing and offset, were assessed. The failure evolution mechanism of the interface during the pull-out process was clarified. In addition, the microscopic structural characteristics of the tendon-grout interface were investigated. Two interfacial shear stress-displacement relationships were developed based on the interface failure modes, i.e., stress attenuation type and ideal elasto-plastic type. According to the test results, the peak strength of the interface increased with the tendon spacing, while the residual strength decreased. The effect of the tendon offset on the shear stiffness and strength of the interface is significant. A damage constitutive model was proposed to model the shear behavior of the tendon-grout interface. The proposed model verified by comparing with the test results and further adopted in pull-out test simulation. The conclusions will provide a better understanding on the shear behaviors of tendon-grout interface, and facilitate the development of a general evaluation method for ground anchor systems.

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.

Large-scale characterisation of cemented rock fill performance for exposure stability analysis

A novel large-scale geomechanical laboratory testing program is developed to provide full characterization of the strength and deformational response of cemented rockfill (CRF) material for use in exposure stability analyses. Uniaxial compressive strength (UCS), direct shear, and three-point bending tensile tests are performed on large-scale samples that require the use of novel processes and laboratory equipment. For the first time, the shear properties of large-scale CRF samples have been investigated using direct shear tests under constant normal stiffness (CNS) boundary conditions. Large-scale three-point bending tests are also conducted to obtain true tensile strengths without having to infer them from UCS test results. For up to 28 days curing time, the effects of particle size distribution and binder quantity are experimentally examined for each compression, tension, and shear failure mode through a study of the full stress–strain response. In order to obtain accurate laboratory results, findings are compared against published large-scale tests from various mine sites. The results show that the large-scale samples completed herein provide a reliable UCS estimate with standard deviations of less than one. It is also found that the direct shear responses are substantially larger for simulated CRF: Sidewall contacts than CRF: CRF contacts, and tensile strength responses are higher than previously estimated at 10% of the UCS strength. The effect of particle size distribution on the geomechanical response of the CRF material is highlighted through the large-scale sample testing. The findings of this research study provide increased technical understanding for the development of CRF structures in underground mines that are cost-effective, safe, and durable. Additionally, this research study establishes a practical testing methodology that overcomes the challenges that occur in collecting quantitative geomechanical data from large-scale CRF samples for design purposes.

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.