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(310).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.

Shear behavior and off-fault damage of saw-cut smooth and tension-induced rough joints in granite

The damage of rock joints or fractures upon shear includes the surface damage occurring at the contact asperities and the damage beneath the shear surface within the host rock.The latter is commonly known as off-fault damage and has been much less investigated than the surface damage.The main contribution of this study is to compare the results of direct shear tests conducted on saw-cut planar joints and tension-induced rough granite joints under normal stresses ranging from 1 MPa to 50 MPa.The shear-induced off-fault damages are quantified and compared with the optical microscope observation.Our results clearly show that the planar joints slip stably under all the normal stresses except under 50 MPa,where some local fractures and regular stick-slip occur towards the end of the test.Both post-peak stress drop and stick-slip occur for all the rough joints.The residual shear strength envelopes for the rough joints and the peak shear strength envelope for the planar joints almost overlap.The root mean square(RMS)of asperity height for the rough joints decreases while it increases for the planar joint after shear,and a larger normal stress usually leads to a more significant decrease or increase in RMS.Besides,the extent of off-fault damage(or damage zone)increases with normal stress for both planar and rough joints,and it is restricted to a very thin layer with limited micro-cracks beneath the planar joint surface.In comparison,the thickness of the damage zone for the rough joints is about an order of magnitude larger than that of the planar joints,and the coalesced micro-cracks are generally inclined to the shear direction with acute angles.The findings obtained in this study contribute to a better understanding on the frictional behavior and damage characteristics of rock joints or fractures with different roughness.

Three‑dimensional numerical simulation of dynamic strength and failure mode of a rock mass with cross joints

To study the dynamic mechanical properties and failure characteristics of intersecting jointed rock masses with different joint distributions under confining pressure,considering the cross angleαand joint persistence ratioη,a numerical model of the biaxial Hopkinson bar test system was established using the finite element method–discrete-element model coupling method.The validity of the model was verified by comparing and analyzing it in conjunction with laboratory test results.Dynamics-static combined impact tests were conducted on specimens under various conditions to investigate the strength characteristics and patterns of crack initiation and expansion.The study revealed the predominant factors influencing intersecting joints with different angles and penetrations under impact loading.The results show that the peak stress of the specimens decreases first and then increases with the increase of the cross angle.Whenα<60°,regardless of the value ofη,the dynamic stress of the specimens is controlled by the main joint.Whenα≥60°,the peak stress borne by the specimens decreases with increasingη.Whenα<60°,the initiation and propagation of cracks in the cross-jointed specimens are mainly controlled by the main joint,and the final failure surface of the specimens is composed of the main joint and wing cracks.Whenα≥60°orη≥0.67,the secondary joint guides the expansion of the wing cracks,and multiple failure surfaces composed of main and secondary joints,wing cracks,and co-planar cracks are formed.Increasing lateral confinement significantly increases the dynamic peak stress able to be borne by the specimens.Under triaxial conditions,the degree of failure of the intersecting jointed specimens is much lower than that under uniaxial and biaxial conditions.

RB-DEM Modeling and Simulation of Non-Persisting Rough Open Joints Based on the IFS-Enhanced Method

When the geological environment of rock masses is disturbed,numerous non-persisting open joints can appear within it.It is crucial to investigate the effect of open joints on the mechanical properties of rock mass.However,it has been challenging to generate realistic open joints in traditional experimental tests and numerical simulations.This paper presents a novel solution to solve the problem.By utilizing the stochastic distribution of joints and an enhanced-fractal interpolation system(IFS)method,rough curves with any orientation can be generated.The Douglas-Peucker algorithm is then applied to simplify these curves by removing unnecessary points while preserving their fundamental shape.Subsequently,open joints are created by connecting points that move to both sides of rough curves based on the aperture distribution.Mesh modeling is performed to construct the final mesh model.Finally,the RB-DEM method is applied to transform the mesh model into a discrete element model containing geometric information about these open joints.Furthermore,this study explores the impacts of rough open joint orientation,aperture,and number on rock fracture mechanics.This method provides a realistic and effective approach for modeling and simulating these non-persisting open joints.

On the calibration of a shear stress criterion for rock joints to represent the full stress-strain profile

Conventional numerical solutions developed to describe the geomechanical behavior of rock interfaces subjected to differential load emphasize peak and residual shear strengths.The detailed analysis of preand post-peak shear stress-displacement behavior is central to various time-dependent and dynamic rock mechanic problems such as rockbursts and structural instabilities in highly stressed conditions.The complete stress-displacement surface(CSDS)model was developed to describe analytically the pre-and post-peak behavior of rock interfaces under differential loads.Original formulations of the CSDS model required extensive curve-fitting iterations which limited its practical applicability and transparent integration into engineering tools.The present work proposes modifications to the CSDS model aimed at developing a comprehensive and modern calibration protocol to describe the complete shear stressdisplacement behavior of rock interfaces under differential loads.The proposed update to the CSDS model incorporates the concept of mobilized shear strength to enhance the post-peak formulations.Barton’s concepts of joint roughness coefficient(JRC)and joint compressive strength(JCS)are incorporated to facilitate empirical estimations for peak shear stress and normal closure relations.Triaxial/uniaxial compression test and direct shear test results are used to validate the updated model and exemplify the proposed calibration method.The results illustrate that the revised model successfully predicts the post-peak and complete axial stressestrain and shear stressedisplacement curves for rock joints.

Effect of cold-working on corrosion induced damage in lug joints

Lug joints are preferred joineries for transferring heavy loads to parent components in aerospace vehicles.They experience corrosion due to environmental conditions,improper surface finishes and rubbing displacement between the pin and lug-hole.This causes damage of different sizes and shapes near the lug-hole.Stiffness degradation due to corrosion-induced damage is modelled as a through-pit at one of the identified critical locations through stress analysis.The effect of this pit on fatigue crack initiation life is estimated.Lug-hole is pre-stressed by cold-working and the benefits of inducing plastic wake on the intended performance of the lug joint during the damages due to corrosion are brought out and compared with non-cold-worked lug-hole.Numerical analysis is performed on this lug joint with pressfit.The results obtained highlight the benefits of cold-working and the methodology can be extended to damage growth and analyse the effect of surface treatments for better structural integrity of components of aerospace vehicles.

Synthesis of organic-inorganic 3D-nanocontainers for smart corrosion protection of friction stir welded AZ31B magnesium alloy-titanium dissimilar joints

The joining of different light metals through friction stir welding(FSW)is gaining interest as a method to decrease weight and improve fuel efficiency.However,to ensure durability,these welded metals may require surface treatments to protect against corrosion or wear.This study presents a novel approach for the simultaneous delivery of two distinct corrosion inhibitors to Ti-Mg dissimilar PEO treated joints on demand.The research focuses on the synthesis,characterization,and application of cerium@polystyrene(Ce@PS)nanocontainers,which are loaded with 8-hydroxyquinoline(8-HQ)to enhance corrosion protection.The synthesis involves several key steps,including the formation of a cerium-based outer layer around polystyrene nanospheres,the selective removal of the polystyrene core to create a porous structure,and the subsequent loading of the 8-HQ inhibitor.Structural and compositional analyses,conducted using scanning transmission electron microscopy(STEM)and energy-dispersive X-ray spectroscopy(EDS),confirmed the successful incorporation of 8-HQ within the nanocontainers.Additionally,Fourier-transform infrared spectroscopy(FTIR)provided detailed information about the chemical composition of the organic materials throughout the synthesis process.Thermal decomposition analysis verified the successful fabrication and stability of the dual-shell nanocontainers.Corrosion tests on Ti-Mg joints treated with plasma electrolytic oxidation(PEO)coatings and loaded nanocontainers demonstrated sig-nificantly improved corrosion resistance compared to untreated joints.This research highlights the potential of dual-shell nanocontainers,containing both organic and inorganic inhibitors,to offer prolonged corrosion protection,particularly against galvanic corrosion in dissimilar joints.The findings suggest that these synthesized nanocontainers hold promise for various industrial applications,particularly in the context of friction stir welded(FSW)Ti-Mg dissimilar joints,providing valuable insights for the development of advanced materials designed to mitigate corrosion.

A comprehensive review of radiation effects on solder alloys and solder joints

In the realm of military and defence applications, exposure to radiation significantly challenges the performance and reliability of solder alloys and joints in electronic systems. This comprehensive review examines radiation-induced effects on solder alloys and solder joints in terms of microstructure and mechanical properties. In this paper, we evaluate the existing literature, including experimental studies and fundamental theory, to provide a comprehensive overview of the behavior of solder materials under radiation. A review of the literature highlights key mechanisms that contribute to radiation-induced changes in the microstructure, such as the formation of intermetallic compounds, grain growth,micro-voids and micro-cracks. Radiation is explored as a factor influencing solder alloy hardness,strength, fatigue and ductility. Moreover, the review addresses the challenges and limitations inherent in studying the effects of radiation on solder materials and offers recommendations for future research. It is crucial to understand radiation-induced effects on solder performance to design robust and radiationresistant electronic systems. A review of radiation effects on solder materials and their applications in electronics serves as a valuable resource for researchers, engineers, and practitioners in that field.

Microstructure,Corrosion and Mechanical Properties of Medium-Thick 6061-T6 Alloy/T2 Pure Cu Dissimilar Joints Produced by Double Side Friction Stir Z Shape Lap-Butt Welding

A novel double side friction stir Z shape lap-butt welding(DS-FSZW)process was proposed to achieve excellent mechanical properties of Al/Cu medium-thick dissimilar joints.The influence of welding parameters on weld microstructure and properties of DS-FSZW joint were systematically investigated.It indicated that defect-free medium-thick Al/Cu DS-FSZW joint could be achieved under an optimal welding parameter.DS-FSZW joint was prone to form void defects in the bottom of the second-pass weld.The recrystallization mechanisms at the top and middle of the weld nugget zone(WNZ)were continuous dynamic recrystallization(CDRX)and geometric dynamic recrystallization(GDRX).While the major recrystallization mechanism at the bottom of the WNZ was GDRX.DS-FSZW joint of the optimal welding condition with 850 r/min-400 mm/min was produced with a continuous thin and crack-free IMCs layer at the Al/Cu interface,and the maximum tensile strength of this joint is 160.57 MPa,which is equivalent to 65.54%of pure Cu base material.Moreover,the corrosion resistance of Al/Cu DS-FSZW joints also achieved its maximum value at the optimal welding parameter of 850 r/min-400 mm/min.It demonstrates that the DS-FSZW process can simultaneously produce medium-thick Al/Cu joints with excellent mechanical performance and corrosion resistance.

A statistical damage-based constitutive model for shearing of rock joints in brittle drop mode

Some rock joints exhibit significant brittleness,characterized by a sharp decrease in shear stress upon reaching the peak strength.However,existing models often fail to accurately represent this behavior and are encumbered by numerous parameters lacking clear mechanical significance.This study presents a new statistical damage constitutive model rooted in both damage mechanics and statistics,containing only three model parameters.The proposed model encompasses all stages of joint shearing,including the compaction stage,linear stage,plastic yielding stage,drop stage,strain softening stage,and residual strength stage.To derive the analytical expression of the constitutive model,three boundary conditions are introduced.Experimental data from both natural and artificial rock joints is utilized to validate the model,resulting in average absolute relative errors ranging from 3%to 8%.Moreover,a comparative analysis with established models illustrates that the proposed model captures stress drop and post-peak strain softening more effectively,with model parameters possessing clearer mechanical interpretations.Furthermore,parameter analysis is conducted to investigate the impacts of model parameters on the curves and unveil the relationship between these parameters and the mechanical properties of rock joints.Importantly,the proposed model is straightforward in form,and all model parameters can be obtained from direct shear tests,thus facilitating the utilization in numerical simulations.

Numerical simulation of formation mechanism of unloading joints in granitic pluton

The Beishan pluton in Gansu of China was selected as the simulated model.The simulation results indicate that the formation of unloading joints in granite is mainly influenced by the unloading rate of confin-ing pressure.Among the rates tested,the slowest unloading rate 0.025 MPa/s is found to be most conducive to the development of unloading joints.Therefore,a slower unloading rate is favourable for the occurrence of unloading joints.A series of simulations with varying initial depths of uplift ranging from 900 m to 200 m were conducted.The results confirm that when the specimen rises to a depth of 550-500 m,the unloading joints begin to form.The uplift from a depth of 700-500 m,with variations in both vertical and lateral un-loading rates,was simulated.The generation of unloading joints exhibits a negative correlation with vertical unloading and no correlation with lateral unloading,indicating that the unloading joints are mainly controlled by the unloading of vertical pressure.Throughout the simulation process,the vertical joints exhibit irregular and unrealistic regularity,suggesting a more complex formation mechanism than that of the unloading joints.

Superconducting joints using reacted multifilament MgB_(2)wires:A technology toward cryogen-free MRI magnets

The development of superconducting joining technology for reacted magnesium diboride(MgB_(2))conductors remains a critical challenge for the advancement of cryogen-free MgB_(2)-based magnets for magnetic resonance imaging(MRI).Herein,the fabrication of superconducting joints using reacted carbon-doped multifilament MgB_(2)wires for MRI magnets is reported.To achieve successful superconducting joints,the powder-in-mold method was employed,which involved tuning the filament protection mechanism,the powder compaction pressure,and the heat treatment condition.The fabricated joints demonstrated clear superconducting-to-normal transitions in self-field,with effective magnetic field screening up to 0.5 T at 20 K.To evaluate the interface between one of the MgB_(2)filaments and the MgB_(2)bulk within the joint,serial sectioning was conducted for the first time in this type of superconducting joint.The serial sectioning revealed space formation at the interface,potentially caused by the volume shrinkage associated with the MgB_(2)formation or the combined effect of the volume shrinkage and the different thermal expansion coefficients of the MgB_(2)bulk,the filament,the mold,and the sealing material.These findings are expected to be pivotal in developing MgB_(2)superconducting joining technology for MRI magnet applications through interface engineering.

Effect of roughness on the shear behavior of rock joints subjected to impact loading

The shear behavior is regarded as the dominant property of rock joints and is dramatically affected by the joint surface roughness.To date,the effect of surface roughness on the shear behavior of rock joints under static or cyclic loading conditions has been extensively studied,but such effect under impact loading conditions keeps unclear.To address this issue,a series of impact shear tests was performed using a novel-designed dynamic experimental system combined with the digital image correlation(DIC)technique.The dynamic shear strength,deformability and failure mode of the jointed specimens with various joint roughness coefficients(JRC)are comprehensively analyzed.Results show that the shear strength and shear displacement characteristics of the rock joint under the impact loading keep consistent with those under static loading conditions.However,the temporal variations of shear stress,slip displacement and normal displacement under the impact loading conditions show obviously different behaviors.An elastic rebound of the slip displacement occurs during the impact shearing and its value increases with increasing joint roughness.Two identifiable stages(i.e.compression and dilation)are observed in the normal displacement curves for the rougher rock joints,whereas the joints with small roughness only manifest normal compression displacement.Besides,as the roughness increases,the maximum compression tends to decrease,while the maximum dilation gradually increases.More-over,the microstructural analysis based on scanning electron microscope(SEM)suggests that the roughness significantly affects the characteristics of the shear fractured zone enclosing the joint surface.

An innovative joint interface design for reducing intermetallic compounds and improving joint strength of thick plate friction stir welded Al/Mg joints

Friction stir welding of dissimilar Al/Mg thick plates still faces severe challenges, such as poor formability, formation of thick intermetallic compounds, and low joint strength. In this work, two joint configurations, namely inclined butt(conventional butt) and serrated interlocking(innovative butt), are proposed for improving weld formation and joint quality. The results show that a continuous and straight intermetallic compound layer appears at the Mg side interface in conventional butt joint, and the maximum average thickness reaches about 60.1 μm.Additionally, the Mg side interface also partially melts, forming a eutectic structure composed of Mg solid solution and Al_(12)Mg_(17) phase.For the innovative butt joint, the Mg side interface presents the curved interlocking feature, and intermetallic compounds can be reduced to less than 10 μm. The joint strength of innovative butt joint is more than three times that of conventional butt joint. This is due to the interlocking effect and thin intermetallic compounds in the innovative joint.

Evaluation of microstructure and mechanical properties of squeeze overcast Al7075-Cu composite joints

Al7075-Cu composite joints were prepared by the squeeze overcast process.The effects of melt temperature,die temperature,and squeeze pressure on hardness and ultimate tensile strength(UTS)of squeeze overcast Al7075-Cu composite joints were studied.The experimental results depict that squeeze pressure is the most significant process parameter affecting the hardness and UTS.The optimal values of UTS(48 MPa)and hardness(76 HRB)are achieved at a melt temperature of 800℃,a die temperature of 250℃,and a squeeze pressure of 90 MPa.Scanning electron microscopy(SEM)shows that fractured surfaces show flatfaced morphology at the optimal experimental condition.Energy-dispersive spectroscopy(EDS)analysis depicts that the atomic weight percentage of Zn decreases with an increase in melt temperature and squeeze pressure.The optimal mechanical properties of the Al7075-Cu overcast joint were achieved at the Al2Cu eutectic phase due to the large number of copper atoms that dispersed into the aluminum melt during the solidification process and the formation of strong intermetallic bonds.Gray relational analysis integrated with the Taguchi method was used to develop an optimal set of control variables for multi-response parametric optimization.Confirmatory tests were performed to validate the effectiveness of the employed technique.The manufacturing of squeeze overcast Al7075-Cu composite joints at optimal process parameters delivers a great indication to acknowledge a new method for foundry practitioners to manufacture materials with superior mechanical properties.

Experimental study on the shear performance of quasi-NPR steel bolted rock joints

Quasi-NPR(negative Poisson’s ratio)steel is a new type of super bolt material with high strength,high ductility,and a micro-negative Poisson’s effect.This material overcomes the contrasting characteristics of the high strength and high ductility of steel and it has significant energy-absorbing characteristics,which is of high value in deep rock and soil support engineering.However,research on the shear resistance of quasi-NPR steel has not been carried out.To study the shear performance of quasi-NPR steel bolted rock joints,indoor shear tests of bolted rock joints under different normal stress conditions were carried out.Q235 steel and#45 steel,two representative ordinary bolt steels,were set up as a control group for comparative tests to compare and analyze the shear strength,deformation and instability mode,shear energy absorption characteristics,and bolting contribution of different types of bolts.The results show that the jointed rock masses without bolt reinforcement undergo brittle failure under shear load,while the bolted jointed rock masses show obvious ductile failure characteristics.The shear deformation ca-pacity of quasi-NPR steel is more than 3.5 times that of Q235 steel and#45 steel.No fracture occurs in the quasi-NPR steel during large shear deformation and it can provide stable shear resistance.However,the other two types of control bolts become fractured under the same conditions.Quasi-NPR steel has significant energy-absorbing characteristics under shear load and has obvious advantages in terms of absorbing the energy released by shear deformation of jointed rock masses as compared with ordinary steel.In particular,the shear force plays a major role in resisting the shear deformation of Q235 steel and#45 steel,therefore,fracture failure occurs under small bolt deformation.However,the axial force of quasi-NPR steel can be fully exerted when resisting joint shear deformation;the steel itself does not break when large shear deformation occurs,and the supporting effect of the jointed rock mass is effectively guaranteed.

DIC Based Strain and Damage Analysis of Large Scale Steel to Composite Adhesive Joints Subjected to Tension and Compression Loading

This paper reports an experimental study of the mechanical response to tensile and compressive force of large scale steel to composite joints adhesively bonded with a thin layer of vinylester resin.In one specimen,the length of the reinforcing fibres in contact with the steel substrate has been reduced by saw cutting at both ends of the joint.This damaged specimen and four intact specimens were subjected to quasi-static tensile testing;six specimens were used for compression testing.The strain distribution at the composite surface and at the steel to hardwood connection of the specimen was monitored by digital image correlation(DIC).DIC allowed identifying the onset of damage in the tensile tested joints near the interface of the composite layer and the steel-hardwood connection.Both tensile and compression tested specimens failed due to significant peel strain concentration at the composite near the connection of steel and hardwood.The average strength of a specimen tested in compression was about 66%higher than the average strength of a specimen tested in tension.The strain concentration zone in the damaged specimen was away from the introduced saw cuts.As a result the damaged and intact tensile specimens showed the same failure strength and stiffness.All specimens failed by adhesive failure between the composite-hardwood interface.

Numerical simulation study on shear resistance of anchorage joints considering tensile-shear fracture criterion of 2G-NPR bolt

2G-NPR bolt (the 2nd generation Negative Poisson’s Ratio bolt) is a new type of bolt with high strength, high toughness and no yield platform. It has signifcant efects on improving the shear strength of jointed rock mass and controlling the stability of surrounding rock. To achieve an accurate simulation of bolted joint shear tests, we have studied a numerical simulation method that takes into account the 2G-NPR bolt's tensile–shear fracture criterion. Firstly, the indoor experimental study on the tensile–shear mechanical properties of 2G-NPR bolt is carried out to explore its mechanical properties under diferent tensile–shear angles, and the fracture criterion of 2G-NPR bolt considering the tensile–shear angle is established. Then, a three-dimensional numerical simulation method considering the tensile–shear mechanical constitutive and fracture criterion of 2G-NPR bolt, the elastoplastic mechanical behavior of surrounding rock and the damage and deterioration of grouting body is proposed. The feasibility and accuracy of the method are verifed by comparing with the indoor shear test results of 2G-NPR bolt anchorage joints. Finally, based on the numerical simulation results, the deformation and stress of the bolt, the distribution of the plastic zone of the rock mass, the stress distribution and the damage of the grouting body are analyzed in detail. The research results can provide a good reference value for the practical engineering application and shear mechanical performance analysis of 2G-NPR bolt.

Shear mechanical properties and energy evolution of rock-like samples containing multiple combinations of non-persistent joints

Discontinuities are often considered as important factors responsible for the instability caused by shear failure in engineering rock mass,and energy-driven instability is the root cause of rock failure.However,few studies focus on the energy evolution during the failure process using a three-dimensional(3D)numerical model.In this study,a series of laboratory direct shear tests on rock-like samples is numer-ically simulated using bonded particle models(BPMs)with multiple combinations of discontinuous in the particle flow code(PFC3D),in which the location and size of the particles conform to the uniform distribution.The effects of joint row number and inclination on the stress-strain characteristics and failure mode of rock were studied from the perspective of microcrack growth and energy evolution.The results showed that,when the number of joint rows Nr>1,the shear failure region does not change with the increase of Nr for the type B(2-columnn multiple-row at center)and the type C(2-column multiple-row at edge)as compared to the type A(1-column multiple-row at center)joint models.Notably,joints significantly increase the post-peak energy dissipation but have little effect on the proportion of energy before the peak.Friction consumes most of the energy while kinetic energy accounts for less than 1%of total energy during the shear process.Peak elastic strain energy follows the variation trend of peak shear displacement.The development and accumulation of microcracks directly affect the energy dissipation,and there is a significant linear relationship between the cumulative number of critical microcracks and the critical dissipated energy at the failure,when the dip direction of joints is opposite to the shear direction,more microcracks will be accumulated at the peak time,resulting in more energy dissipation.The results contribute to deeply understanding the shear failure process of non-persistent jointed mass.

Experimental study on the irreversible displacement evolution and energy dissipation characteristics of disturbance instability of regular joints

To investigate the disturbance-induced shear instability mechanism of structural catastrophe in the deep rock mass,MTS 815 material testing machine was used to carry out quasi-static loading tests and disturbance shear tests on symmetrical regular dentate joints of two materials at three undulation angles under specific initial static stress,disturbance frequency,and peak value.The test results indicate that:(i)the total ultimate instability displacement is only related to the intrinsic properties of the joints but not to the initial static stress and disturbance parameters;(ii)the cumulative irreversible displacement required for the disturbance instability conforms to the logistic inverse function relationship with the number of disturbances,displaying the variation trend of“rapid increase in the front,stable in the middle,and sudden increase in the rear”;(iii)the accumulation of plastic deformation energy is consistent with the evolution law of irreversible displacement of joints and the overall proportion of hysteretic energy is not large;(iv)the dissipated energy required for the instability of each group of joints is basically the same under various disturbance conditions,and this energy is mainly controlled by the initial shear stress and has no connection with the disturbance parameters.The stability of the total disturbance deformation and the disturbance energy law of the joints revealed in the tests provide data support for reasonably determining the disturbance instability criterion of joints.