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.

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.

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.

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.

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.

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.

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.

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.

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.

Progressive Failure Analysis of Composite/Aluminum Riveted Joints Subjected to Pull-Through Loading

Out-of-plane mechanical properties of the riveted joints restrict the performance of the wing box assembly of airplane.It is necessary to investigate the pull-through performance of the composite/metal riveted joints in order to guide the riveting design and ensure the safety of the wing box assembly.The progressive failure mechanism of composite/aluminum riveted joint subjected to pull-through loading was investigated by experiments and finite element method.A progressive damage model based on the Hashin-type criteria and zero-thickness cohesive zone method was developed by VUMAT subroutine,which was validated by both open-hole tensile test and three-point bending test.Predicted load-displacement response,failure modes and damage propagation were analysed and compared with the results of the pull-through tests.There are 4 obvious characteristic stages on the load-displacement curve of the pull-through test and that of the finite element model:first load take-up stage,damage stage,second load take-up stage and failure stage.Relative error of stiffness,first load peak and second load peak between finite element method and experiments were 8.1%,-3.3%and 10.6%,respectively.It was found that the specimen was mainly broken by rivet-penetration fracture and delamination of plies of the composite laminate.And the material within the scope of the rivet head is more dangerous with more serious tensile damages than other regions,especially for 90°plies.This study proposes a numerical method for damage prediction and reveals the progressive failure mechanism of the hybrid material riveted joints subjected to the pull-through loading.

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.

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.

Shear behavior of two-order morphology in rock joints

Two-order morphology of rock joints named as waviness and unevenness can be separated by morphology classification method,which plays a decisive role in the evolution of shear stress during the shear test.The joint morphology is obtained by using 3D printing and 3D laser scanning techniques and the joint model samples in two-order morphology are produced by cement mortar.Then,shear tests are performed under different normal loads.Results shows that the waviness is dominant in the total morphology during the shear test,and the shear contribution of unevenness mainly occurs in the climbing phase of shearing process.Comparing the failure modes of two-order morphology,waviness mainly embodies shear dilation characteristics and unevenness mainly shows shear wear characteristics.Based on this,a quantitative parameter is proposed to represent the ratio of the peak shear strength of the two-order morphology to that of total morphology.The functional relationship between the peak shear strength of total and two-order morphologies is determined,providing a theoretical method for further in-depth study on the shear strength of the interaction with two-order morphology of rock joints.

Shear behaviour of a rock bridge sandwiched between incipient joints under the influence of hydraulic pressures

The rock bridges sandwiched in incipiently jointed rock mass were considered as barriers that block the fluid seepage,and provide certain shear strength reservation.For better revealing the influence of hydraulic pressure on the failure behaviour of rock bridges,direct shear tests were carried out through a newly proposed method on rock samples that contain two parallel incipient joints.By developing the gypsum-silicone pad coupling samples,a conventional triaxial test system was qualified to implement direct shear tests with satisfied sealing capability.The results showed that the rock bridges could be failed through the tensile failure,shear failure and mixed failure mechanism.The hydraulic pressure would facilitate the tensile failure mechanism and induce rougher fracture surfaces;while the normal stress would facilitate the shear failure mechanism and induce less rough fracture.The hydraulic pressure reduced the global shear strength of the rock block through reducing the efficient normal stress applied on the rock bridge area,which was highly dependent on the joint persistence,k.Moreover,because of the iterating occurrence of the hydraulic pressure lag with the fracture propagation,the rock bridge failure stage in the shear stress-shear displacement curves displayed a fluctuation trend.

A method to predict the peak shear strength of rock joints based on machine learning

In geotechnical and tunneling engineering,accurately determining the mechanical properties of jointed rock holds great significance for project safety assessments.Peak shear strength(PSS),being the paramount mechanical property of joints,has been a focal point in the research field.There are limitations in the current peak shear strength(PSS)prediction models for jointed rock:(i)the models do not comprehensively consider various influencing factors,and a PSS prediction model covering seven factors has not been established,including the sampling interval of the joints,the surface roughness of the joints,the normal stress,the basic friction angle,the uniaxial tensile strength,the uniaxial compressive strength,and the joint size for coupled joints;(ii)the datasets used to train the models are relatively limited;and(iii)there is a controversy regarding whether compressive or tensile strength should be used as the strength term among the influencing factors.To overcome these limitations,we developed four machine learning models covering these seven influencing factors,three relying on Support Vector Regression(SVR)with different kernel functions(linear,polynomial,and Radial Basis Function(RBF))and one using deep learning(DL).Based on these seven influencing factors,we compiled a dataset comprising the outcomes of 493 published direct shear tests for the training and validation of these four models.We compared the prediction performance of these four machine learning models with Tang’s and Tatone’s models.The prediction errors of Tang’s and Tatone’s models are 21.8%and 17.7%,respectively,while SVR_linear is at 16.6%,SVR_poly is at 14.0%,and SVR_RBF is at 12.1%.DL outperforms the two existing models with only an 8.5%error.Additionally,we performed shear tests on granite joints to validate the predictive capability of the DL-based model.With the DL approach,the results suggest that uniaxial tensile strength is recommended as the material strength term in the PSS model for more reliable outcomes.

Analytical solution for longitudinal deformation of shield tunnel induced by overcrossing tunnelling considering circumferential joints

This paper presents a new analytical solution for assessing the longitudinal deformation of shield tunnel associated with overcrossing tunnelling in consideration of circumferential joints.A simplified longitudinal beam-spring model(SLBSM)is established to model the longitudinal behaviours of shield tunnel,which can consider the opening and dislocation between segmental rings simultaneously.Then,the existing tunnel is treated as the SLBSM resting on the elastic foundation.The state equations including tunnel displacements and internal forces are constructed to solve the discontinuous deformation of circumferential joint-segmental ring.The feasibility of the proposed solution is verified through three well-documented cases.The predictions from the proposed method are also compared with other analytical methods.It is found that the proposed method can well capture the deformation of tunnel segmental rings and joints,where the rigid displacement mainly occurs in the segmental rings while the rotation and dislocation occur in the circumferential joints.Some dominant parameters are also analysed to explore the effects on existing tunnel deformation,including the rotation stiffness and shearing stiffness of joints,the skew angle and the clearance between new and old tunnels.