The shear performance of bolts plays a crucial role in controlling rock mass stability,and the roughness of the joint surface is one of the main factors affecting the mechanical properties of anchored joints.The 2nd g...The shear performance of bolts plays a crucial role in controlling rock mass stability,and the roughness of the joint surface is one of the main factors affecting the mechanical properties of anchored joints.The 2nd generation of negative Poisson ratio(2G-NPR)bolt is a new independently developed material characterized by high strength and toughness.However,the influence of joint surface roughness on its anchorage shear performance remains unexplored.This study involves preparing regular saw-tooth jointed rock masses and conducting laboratory shear comparison tests on unbolted samples,2G-NPR bolts,and Q235 steel anchors.A three-dimensional finite element method,developed by the author,was employed for numerical simulations to analyze the influence of saw-tooth angles on the shear resistance of anchored bolts.The findings show that the anchorage of bolts enhances the shear strength and deformation of saw-tooth rock joints.The 2G-NPR bolts demonstrate superior performance in shear strength and deformation enhancement compared to Q235 steel anchors,including improved toughening and crack-arresting effects.Furthermore,the improvement of the shear strength and displacement of the bolt decreases with the increase of the joint saw-tooth angle.These findings provide a valuable test basis for the engineering application of 2G-NPR bolts in rock mass stabilization.展开更多
The primary objective of this work is to improve our understanding of the mechanical involvements of two-order roughness in shear.First,wavelet analysis is used to separate the waviness(first-order)and unevenness(seco...The primary objective of this work is to improve our understanding of the mechanical involvements of two-order roughness in shear.First,wavelet analysis is used to separate the waviness(first-order)and unevenness(second-order)from four granite joint surfaces,with roughness characterized using Grasselli’s 3D morphology parameters.The results reveal that first-order roughness is more pronounced than second-order roughness,highlighting the dominant role of waviness in joint surface roughness.Additionally,the variation in first-order roughness with strike direction corresponds to the total roughness,while second-order roughness remains largely constant,indicating that roughness anisotropy is primarily driven by waviness.Then,direct shear tests on joint replicas are performed to investigate the contributions of both roughness orders to peak shear strength.The results show that the peak dilation angle is closely related to first-order roughness,while the shear component angle is closely associated with second-order roughness,both exhibiting a linear correlation.Based on these findings,relationships are established between the angles and their respective roughness orders.Finally,a joint shear strength criterion based on two-order roughness is proposed.A comparative analysis of prediction accuracy reveals that the average relative error for the proposed criterion is 13.79%,while the errors for Xia's,Yang's,and Ban's criteria are 15.19%,16.29%,and 13.87%,respectively.It demonstrates the proposed criterion can predict the peak shear strength of rock joints.展开更多
We present a grid-growth method to reconstruct 3D rock joints with arbitrary joint roughness and persistence.In the first step of this workflow,the joint model is divided into uniform grids.Then by adjusting the posit...We present a grid-growth method to reconstruct 3D rock joints with arbitrary joint roughness and persistence.In the first step of this workflow,the joint model is divided into uniform grids.Then by adjusting the positions of the grids,the joint morphology can be modified to construct models with desired joint roughness and persistence.Accordingly,numerous joint models with different joint roughness and persistence were built.The effects of relevant parameters(such as the number,height,slope of asperities,and the number,area of rock bridges)on the joint roughness coefficient(JRC)and joint persistence were investigated.Finally,an artificially split joint was reconstructed using the method,and the method's accuracy was evaluated by comparing the JRC of the models with that of the artificially split joint.The results showed that the proposed method can effectively control the JRC of joint models by adjusting the number,height,and slope of asperities.The method can also modify the joint persistence of joint models by adjusting the number and area of rock bridges.Additionally,the JRC of models obtained by our method agrees with that of the artificially split surface.Overall,the method demonstrated high accuracy for 3D rock joint reconstruction.展开更多
Joint surface roughness is comprised of two components:large-scale(waviness,first-order)and smallscale(unevenness,second-order).To investigate the scale effect of two-order roughness,a surface area method is used to s...Joint surface roughness is comprised of two components:large-scale(waviness,first-order)and smallscale(unevenness,second-order).To investigate the scale effect of two-order roughness,a surface area method is used to separate the waviness and unevenness from the whole joint surface of each size.The results show that as the joint size increases,the first-order roughness exhibits a decrease,whereas the second-order roughness remains constant.This indicates that the roughness scale effect is primarily attributed to the waviness.Then,the influence of two-order roughness on the scale effect of joint shear strength is examined through a series of laboratory tests.The test results reveal a negative scale effect on the peak friction angle,which exhibits a strong correlation with the first-order roughness.The decrease in the peak friction angle with normal stress can be attributed primarily to the degradation of second-order roughness,which shows a negative exponential trend.Finally,an empirical model for estimating the peak friction angle of rock joints at different scales is proposed based on two-order roughness.The prediction accuracy of this model is validated by comparing the existing criteria.展开更多
Experiments on rock joint behaviors have shown that joint surface roughness is mobilized under shearing,inducing dilation and resulting in nonlinear joint shear strength and shear stress vs.shear displacement behavior...Experiments on rock joint behaviors have shown that joint surface roughness is mobilized under shearing,inducing dilation and resulting in nonlinear joint shear strength and shear stress vs.shear displacement behaviors.The Barton-Bandis(B-B) joint model provides the most realistic prediction for the nonlinear shear behavior of rock joints.The B-B model accounts for asperity roughness and strength through the joint roughness coefficient(JRC) and joint wall compressive strength(JCS) parameters.Nevertheless,many computer codes for rock engineering analysis still use the constant shear strength parameters from the linear Mohr-Coulomb(M-C) model,which is only appropriate for smooth and non-dilatant joints.This limitation prevents fractured rock models from capturing the nonlinearity of joint shear behavior.To bridge the B-B and the M C models,this paper aims to provide a linearized implementation of the B-B model using a tangential technique to obtain the equivalent M-C parameters that can satisfy the nonlinear shear behavior of rock joints.These equivalent parameters,namely the equivalent peak cohesion,friction angle,and dilation angle,are then converted into their mobilized forms to account for the mobilization and degradation of JRC under shearing.The conversion is done by expressing JRC in the equivalent peak parameters as functions of joint shear displacement using proposed hyperbolic and logarithmic functions at the pre-and post-peak regions of shear displacement,respectively.Likewise,the pre-and post-peak joint shear stiffnesses are derived so that a complete shear stress-shear displacement relationship can be established.Verifications of the linearized implementation of the B-B model show that the shear stress-shear displacement curves,the dilation behavior,and the shear strength envelopes of rock joints are consistent with available experimental and numerical results.展开更多
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 hi...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.展开更多
This study aims at proposing a reasonable roughness parameter that can reflect the peak shear strength(PSS)of rock joints.Firstly,the contribution of the asperities with different apparent dip angles to shear strength...This study aims at proposing a reasonable roughness parameter that can reflect the peak shear strength(PSS)of rock joints.Firstly,the contribution of the asperities with different apparent dip angles to shear strength is studied.Then the shear strength of the entire joint asperities is derived.The results showed that the PSS of the entire joint asperities is proportional to a key parameter hs,which is related to the geometric character of the joint surface and the joint material properties.The parameter hsis taken as the new roughness parameter,and it is reasonable to associate the PSS with the geometric characteristics of the joint surface.Based on the new roughness parameter and shear test results of 20 sets of joint specimens,a new PSS model for rock joints is proposed.The new model is validated with the artificial joints in this paper and real rock joints in published studies.Results showed that it is suitable for different types of rock joints except for gneiss joints.The new model has the form of the Mohr-Coulomb model,which can directly reflect the relationship between the 3 D roughness parameters and the peak dilation angle.展开更多
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 mo...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.展开更多
Although many intact rock types can be very strong,a critical confining pressure can eventually be reached in triaxial testing,such that the Mohr shear strength envelope becomes horizontal.This critical state has rece...Although many intact rock types can be very strong,a critical confining pressure can eventually be reached in triaxial testing,such that the Mohr shear strength envelope becomes horizontal.This critical state has recently been better defined,and correct curvature or correct deviation from linear Mohr-Coulomb（MC） has finally been found.Standard shear testing procedures for rock joints,using multiple testing of the same sample,in case of insufficient samples,can be shown to exaggerate apparent cohesion.Even rough joints do not have any cohesion,but instead have very high friction angles at low stress,due to strong dilation.Rock masses,implying problems of large-scale interaction with engineering structures,may have both cohesive and frictional strength components.However,it is not correct to add these,following linear M-C or nonlinear Hoek-Brown（H-B） standard routines.Cohesion is broken at small strain,while friction is mobilized at larger strain and remains to the end of the shear deformation.The criterion ＇c then σn tan φ＇ should replace ＇c plus σn tan φ＇ for improved fit to reality.Transformation of principal stresses to a shear plane seems to ignore mobilized dilation,and caused great experimental difficulties until understood.There seems to be plenty of room for continued research,so that errors of judgement of the last 50 years can be corrected.展开更多
The storage of hydrogen gas in lined rock caverns(LRCs)may enable the implementation of the firstlarge-scale fossil-free steelmaking process in Sweden,but filling such storage causes joints in the rockmass to open,con...The storage of hydrogen gas in lined rock caverns(LRCs)may enable the implementation of the firstlarge-scale fossil-free steelmaking process in Sweden,but filling such storage causes joints in the rockmass to open,concentrating strains in the lining.The structural interaction between the LRC componentsmust be able to reduce the strain concentration in the sealing steel lining;however,this interaction iscomplex and difficult to predict with analytical methods.In this paper,the strain concentration in LRCsfrom the opening of rock joints is studied using finite element(FE)analyses,where the large-and small-scale deformation behaviors of the LRC are coupled.The model also includes concrete crack initiation anddevelopment with increasing gas pressure and rock joint width.The interaction between the jointed rockmass and the reinforced concrete,the sliding layer,and the steel lining is demonstrated.The results showthat the rock mass quality and the spacing of the rock joints have the greatest influence on the straindistributions in the steel lining.The largest effect of rock joints on the maximum strains in the steellining was observed for geological conditions of“good”quality rock masses.展开更多
Rock joints infilled with sediments can strongly influence the strength of rock mass. As infilled joints often exist under unsaturated condition, this study investigated the influence of matric suction of infill on th...Rock joints infilled with sediments can strongly influence the strength of rock mass. As infilled joints often exist under unsaturated condition, this study investigated the influence of matric suction of infill on the overall joint shear strength. A novel technique that allows direct measurement of matric suction of infill using high capacity tensiometers(HCTs) during direct shear of infilled joints under constant normal stiffness(CNS) is described. The CNS apparatus was modified to accommodate the HCT and the procedure is explained in detail. Joint specimens were simulated by gypsum plaster using threedimensional(3D) printed surface moulds, and filled with kaolin and sand mixture prepared at different water contents. Shear behaviours of both planar infilled joints and rough joints having joint roughness coefficients(JRCs) of 8-10 and 18-20 with the ratios of infill thickness to asperity height(t/a)equal to 0.5 were investigated. Matric suction shows predominantly unimodal behaviour during shearing of both planar and rough joints, which is closely associated with the variation of unloading rate and volumetric changes of the infill material. As expected, two-peak behaviour was observed for the rough joints and both peaks increased with the increase of infill matric suction. The results suggest that the contribution of matric suction of infill on the joint peak normalised shear stress is relatively independent of the joint roughness.展开更多
Rock bolts have been widely used in slopes as a reinforcement measure.Modelling the shear mechanical behaviours of bolted rock joints is very complicated due to the complex factors that affect the axial force and shea...Rock bolts have been widely used in slopes as a reinforcement measure.Modelling the shear mechanical behaviours of bolted rock joints is very complicated due to the complex factors that affect the axial force and shear force on the bolts.Rock bolts under shear action exhibit the guide rail effect;that is,the rock mass slides along the rock bolt as if the rock bolt is a rail.The normal stress can inhibit the guide rail effect and reduce the axial force on bolts.However,this factor is not considered by the existing analysis models.Shear tests of bolted joints under different normal stresses were carried out in the laboratory.During the test,the axial force on each point monitored on the bolt was recorded by a strain gauge,and the attenuation trend of the strain was studied.An analytical model that considers the inhibition of the bolt rail effect due to an increase in the normal stress was proposed to predict the shear mechanical behaviour of rock bolted joints.The new model accommodates the bolt shear behaviours in the elastic stage and plastic stage,and the estimated values agree well with the results of the direct shear tests in the laboratory.The validation shows that the proposed model can effectively describe the deformation characteristics of the bolts in the shear tests.展开更多
A recently developed computerized method for assessing the rock joint coefficients is discussed. The performances of formerly introduced relative similarity indicators, along with the correlation coefficient, are subj...A recently developed computerized method for assessing the rock joint coefficients is discussed. The performances of formerly introduced relative similarity indicators, along with the correlation coefficient, are subjected to critical analysis. These relative numerical indicators are replaced by two absolute indicators whose properties better describe surface textures of rock joints. The first absolute indicator results from the Fourier Matrix and evaluates wavy shapes of surfaces. The second absolute indicator quantifies the heights of surface reliefs, and is defined as the root mean square height of the surface outline. The behavior of the newly introduced numerical indicators are investigated by means of the deterministic periodic surface reliefs. The practical application of the new indicators is presented and the convenient performances of both the indicators are documented.展开更多
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 encum...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.展开更多
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 mechanica...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.展开更多
A hybrid finite-discrete element method was implemented to study the fracture process of rough rock joints under direct shearing. The hybrid method reproduced the joint shear resistance evolution process from asperity...A hybrid finite-discrete element method was implemented to study the fracture process of rough rock joints under direct shearing. The hybrid method reproduced the joint shear resistance evolution process from asperity sliding to degradation and from gouge formation to grinding. It is found that, in the direct shear test of rough rock joints under constant normal displacement loading conditions, higher shearing rate promotes the asperity degradation but constraints the volume dilation, which then results in higher peak shear resistance, more gouge formation and grinding, and smoother new joint surfaces. Moreover, it is found that the joint roughness affects the joint shear resistance evolution through influencing the joint fracture micro mechanism. The asperity degradation and gouge grinding are the main failure micro-mechanism in shearing rougher rock joints with deeper asperities while the asperity sliding is the main failure micro-mechanism in shearing smoother rock joints with shallower asperities. It is concluded that the hybrid finite-discrete element method is a valuable numerical tool better than traditional finite element method and discrete element method for modelling the joint sliding, asperity degradation, gouge formation, and gouge grinding occurred in the direct shear tests of rough rock joints.展开更多
Structural defects such as joints or faults are inherent to almost any rock mass.In many situations those defects have a major impact on slope stability as they can control the possible failure mechanisms.Having a goo...Structural defects such as joints or faults are inherent to almost any rock mass.In many situations those defects have a major impact on slope stability as they can control the possible failure mechanisms.Having a good estimate of their strength then becomes crucial.The roughness of a structure is a major contributor to its strength through two different aspects,i.e.the morphology of the surface(or the shape)and the strength of the asperities(related to the strength of the rock).In the current state of practice,roughness is assessed through idealized descriptions(Patton strength criterion)or through empirical parameters(Barton JRC).In both cases,the multi-dimensionality of the roughness is ignored.In this study,we propose to take advantage of the latest developments in numerical techniques.With3D photogrammetry and/or laser mapping,practitioners have access to the real morphology of an exposed structure.The derived triangulated surface was introduced into the DEM(discrete element method)code PFC3D to create a synthetic rock joint.The interaction between particles on either side of the discontinuity was described by a smooth-joint model(SJM),hence suppressing the artificial roughness introduced by the particle discretization.Shear tests were then performed on the synthetic rock joint.A good correspondence between strengths predicted by the model and strengths derived from well-established techniques was obtained for thefirst time.Amongst the benefits of the methodology is the possibility offered by the model to be used in a quantitative way for shear strength estimates,to reproduce the progressive degradation of the asperities upon shearing and to analyze structures of different scales without introducing any empirical relation.展开更多
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 sta...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.展开更多
In underground rock engineering,water-bearing faults may be subjected to dynamic loading,resulting in the coupling of hydraulic and dynamic hazards.Understanding the interaction mechanism between the stress waves indu...In underground rock engineering,water-bearing faults may be subjected to dynamic loading,resulting in the coupling of hydraulic and dynamic hazards.Understanding the interaction mechanism between the stress waves induced by dynamic loadings and liquid-filled rock joints is therefore crucial.In this study,an auxiliary device for simulating the liquid-filled layer was developed to analyze the dynamic response characteristics of liquid-filled rock joints in laboratory.Granite and polymethyl methacrylate(PMMA)specimens were chosen for testing,and high-amplitude shock waves induced by a split Hopkinson pressure bar(SHPB)were used to produce dynamic loadings.Impact loading tests were conducted on liquid-filled rock joints with different joint inclinations.The energy propagation coefficient and peak liquid pressure were proposed to investigate the energy propagation and attenuation of waves propagating across the joints,as well as the dynamic response characteristics of the liquid in the liquid-filled rock joints.For the inclination angle range considered herein,the experimental results showed that the energy propagation coefficient gently diminished with increasing joint inclination,and smaller coefficient values were obtained for granite specimens compared with PMMA specimens.The peak liquid pressure exhibited a gradually decreasing trend with increasing joint inclination,and the peak pressure for granite specimens was slightly higher than that for PMMA specimens.Overall,this paper may provide a considerably better method for studying liquid-filled rock joints at the laboratory scale,and serves as a guide for interpreting the underlying mechanisms for interactions between stress waves and liquid-filled rock joints.展开更多
Rock joints exhibit hysteresis shearing behavior and produce energy dissipation under shear cyclic loads,which however cannot be accurately depicted by existing constitutive models.This paper establishes a constitutiv...Rock joints exhibit hysteresis shearing behavior and produce energy dissipation under shear cyclic loads,which however cannot be accurately depicted by existing constitutive models.This paper establishes a constitutive model for hysteresis shearing and associated energy dissipation of rock joints.Analytical expressions of the model during cyclic shearing processes are derived.Derivation of the model indicates no energy dissipation in the elastic stage.When the shear load exceeds elastic boundary,nonlinear energy dissipation takes place.Validations with experiments show that the proposed model provides good conformities with direct shear curves and hysteresis loops,and can predict the energy dissipation characteristics of rock joints under different working conditions.Compared to the constitutive models using Weibull's distribution,the proposed one is smooth at the elastic boundary and can accurately capture the maximum shear stress.Unlike the existing incremental-type models,the proposed one provides clear and direct analytical expressions for both shear stress and energy dissipation during the whole displacement domain,which is more convenient in application.展开更多
基金Project(GZB202405561)supported by the Postdoctoral Fellowship Program of China Postdoctoral Science FoundationProject(42377154)supported by the National Natural Science Foundation of China。
文摘The shear performance of bolts plays a crucial role in controlling rock mass stability,and the roughness of the joint surface is one of the main factors affecting the mechanical properties of anchored joints.The 2nd generation of negative Poisson ratio(2G-NPR)bolt is a new independently developed material characterized by high strength and toughness.However,the influence of joint surface roughness on its anchorage shear performance remains unexplored.This study involves preparing regular saw-tooth jointed rock masses and conducting laboratory shear comparison tests on unbolted samples,2G-NPR bolts,and Q235 steel anchors.A three-dimensional finite element method,developed by the author,was employed for numerical simulations to analyze the influence of saw-tooth angles on the shear resistance of anchored bolts.The findings show that the anchorage of bolts enhances the shear strength and deformation of saw-tooth rock joints.The 2G-NPR bolts demonstrate superior performance in shear strength and deformation enhancement compared to Q235 steel anchors,including improved toughening and crack-arresting effects.Furthermore,the improvement of the shear strength and displacement of the bolt decreases with the increase of the joint saw-tooth angle.These findings provide a valuable test basis for the engineering application of 2G-NPR bolts in rock mass stabilization.
基金funded by the National Natural Science Foundation of China (Grant nos. 42272333 and 42377154)the China Association for Science and Technology Youth Talent Support Program for PhD Students.
文摘The primary objective of this work is to improve our understanding of the mechanical involvements of two-order roughness in shear.First,wavelet analysis is used to separate the waviness(first-order)and unevenness(second-order)from four granite joint surfaces,with roughness characterized using Grasselli’s 3D morphology parameters.The results reveal that first-order roughness is more pronounced than second-order roughness,highlighting the dominant role of waviness in joint surface roughness.Additionally,the variation in first-order roughness with strike direction corresponds to the total roughness,while second-order roughness remains largely constant,indicating that roughness anisotropy is primarily driven by waviness.Then,direct shear tests on joint replicas are performed to investigate the contributions of both roughness orders to peak shear strength.The results show that the peak dilation angle is closely related to first-order roughness,while the shear component angle is closely associated with second-order roughness,both exhibiting a linear correlation.Based on these findings,relationships are established between the angles and their respective roughness orders.Finally,a joint shear strength criterion based on two-order roughness is proposed.A comparative analysis of prediction accuracy reveals that the average relative error for the proposed criterion is 13.79%,while the errors for Xia's,Yang's,and Ban's criteria are 15.19%,16.29%,and 13.87%,respectively.It demonstrates the proposed criterion can predict the peak shear strength of rock joints.
基金supported by the National Natural Science Foundation of China(Nos.12172019 and 42477210).
文摘We present a grid-growth method to reconstruct 3D rock joints with arbitrary joint roughness and persistence.In the first step of this workflow,the joint model is divided into uniform grids.Then by adjusting the positions of the grids,the joint morphology can be modified to construct models with desired joint roughness and persistence.Accordingly,numerous joint models with different joint roughness and persistence were built.The effects of relevant parameters(such as the number,height,slope of asperities,and the number,area of rock bridges)on the joint roughness coefficient(JRC)and joint persistence were investigated.Finally,an artificially split joint was reconstructed using the method,and the method's accuracy was evaluated by comparing the JRC of the models with that of the artificially split joint.The results showed that the proposed method can effectively control the JRC of joint models by adjusting the number,height,and slope of asperities.The method can also modify the joint persistence of joint models by adjusting the number and area of rock bridges.Additionally,the JRC of models obtained by our method agrees with that of the artificially split surface.Overall,the method demonstrated high accuracy for 3D rock joint reconstruction.
基金supported by the National Natural Science Foundation of China(Grant Nos.42272333 and 42377154)the Ningbo Natural Science Foundation(Grant No.2023J085).
文摘Joint surface roughness is comprised of two components:large-scale(waviness,first-order)and smallscale(unevenness,second-order).To investigate the scale effect of two-order roughness,a surface area method is used to separate the waviness and unevenness from the whole joint surface of each size.The results show that as the joint size increases,the first-order roughness exhibits a decrease,whereas the second-order roughness remains constant.This indicates that the roughness scale effect is primarily attributed to the waviness.Then,the influence of two-order roughness on the scale effect of joint shear strength is examined through a series of laboratory tests.The test results reveal a negative scale effect on the peak friction angle,which exhibits a strong correlation with the first-order roughness.The decrease in the peak friction angle with normal stress can be attributed primarily to the degradation of second-order roughness,which shows a negative exponential trend.Finally,an empirical model for estimating the peak friction angle of rock joints at different scales is proposed based on two-order roughness.The prediction accuracy of this model is validated by comparing the existing criteria.
基金support from the University Transportation Center for Underground Transportation Infrastructure at the Colorado School of Mines for partially funding this research under Grant No.69A3551747118 of the Fixing America's Surface Transportation Act(FAST Act) of U.S.DoT FY2016
文摘Experiments on rock joint behaviors have shown that joint surface roughness is mobilized under shearing,inducing dilation and resulting in nonlinear joint shear strength and shear stress vs.shear displacement behaviors.The Barton-Bandis(B-B) joint model provides the most realistic prediction for the nonlinear shear behavior of rock joints.The B-B model accounts for asperity roughness and strength through the joint roughness coefficient(JRC) and joint wall compressive strength(JCS) parameters.Nevertheless,many computer codes for rock engineering analysis still use the constant shear strength parameters from the linear Mohr-Coulomb(M-C) model,which is only appropriate for smooth and non-dilatant joints.This limitation prevents fractured rock models from capturing the nonlinearity of joint shear behavior.To bridge the B-B and the M C models,this paper aims to provide a linearized implementation of the B-B model using a tangential technique to obtain the equivalent M-C parameters that can satisfy the nonlinear shear behavior of rock joints.These equivalent parameters,namely the equivalent peak cohesion,friction angle,and dilation angle,are then converted into their mobilized forms to account for the mobilization and degradation of JRC under shearing.The conversion is done by expressing JRC in the equivalent peak parameters as functions of joint shear displacement using proposed hyperbolic and logarithmic functions at the pre-and post-peak regions of shear displacement,respectively.Likewise,the pre-and post-peak joint shear stiffnesses are derived so that a complete shear stress-shear displacement relationship can be established.Verifications of the linearized implementation of the B-B model show that the shear stress-shear displacement curves,the dilation behavior,and the shear strength envelopes of rock joints are consistent with available experimental and numerical results.
基金This study has been funded by the National Natural Science Foundation of China(Grant No.41941018)and the Second Tibetan Plateau Scientific Expedition and Research Grant(Grant No.2019QZKK0708).
文摘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.
基金supported by China Postdoctoral Science Foundation(No.2020M680007)Beijing Postdoctoral Research Foundation(No.2020-zz-087)+1 种基金National Natural Science Foundation of China(Nos.51478027 and 51174012)Fundamental Research Funds for Beijing Civil Engineering and Architecture(No.X20031)。
文摘This study aims at proposing a reasonable roughness parameter that can reflect the peak shear strength(PSS)of rock joints.Firstly,the contribution of the asperities with different apparent dip angles to shear strength is studied.Then the shear strength of the entire joint asperities is derived.The results showed that the PSS of the entire joint asperities is proportional to a key parameter hs,which is related to the geometric character of the joint surface and the joint material properties.The parameter hsis taken as the new roughness parameter,and it is reasonable to associate the PSS with the geometric characteristics of the joint surface.Based on the new roughness parameter and shear test results of 20 sets of joint specimens,a new PSS model for rock joints is proposed.The new model is validated with the artificial joints in this paper and real rock joints in published studies.Results showed that it is suitable for different types of rock joints except for gneiss joints.The new model has the form of the Mohr-Coulomb model,which can directly reflect the relationship between the 3 D roughness parameters and the peak dilation angle.
基金funded by National Natural Science Foundation of China(Grant Nos.42272333 and 42277147)。
文摘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.
文摘Although many intact rock types can be very strong,a critical confining pressure can eventually be reached in triaxial testing,such that the Mohr shear strength envelope becomes horizontal.This critical state has recently been better defined,and correct curvature or correct deviation from linear Mohr-Coulomb（MC） has finally been found.Standard shear testing procedures for rock joints,using multiple testing of the same sample,in case of insufficient samples,can be shown to exaggerate apparent cohesion.Even rough joints do not have any cohesion,but instead have very high friction angles at low stress,due to strong dilation.Rock masses,implying problems of large-scale interaction with engineering structures,may have both cohesive and frictional strength components.However,it is not correct to add these,following linear M-C or nonlinear Hoek-Brown（H-B） standard routines.Cohesion is broken at small strain,while friction is mobilized at larger strain and remains to the end of the shear deformation.The criterion ＇c then σn tan φ＇ should replace ＇c plus σn tan φ＇ for improved fit to reality.Transformation of principal stresses to a shear plane seems to ignore mobilized dilation,and caused great experimental difficulties until understood.There seems to be plenty of room for continued research,so that errors of judgement of the last 50 years can be corrected.
基金supported by the Swedish Energy Agency(Grant Nos.42684-2,P2022-00209).
文摘The storage of hydrogen gas in lined rock caverns(LRCs)may enable the implementation of the firstlarge-scale fossil-free steelmaking process in Sweden,but filling such storage causes joints in the rockmass to open,concentrating strains in the lining.The structural interaction between the LRC componentsmust be able to reduce the strain concentration in the sealing steel lining;however,this interaction iscomplex and difficult to predict with analytical methods.In this paper,the strain concentration in LRCsfrom the opening of rock joints is studied using finite element(FE)analyses,where the large-and small-scale deformation behaviors of the LRC are coupled.The model also includes concrete crack initiation anddevelopment with increasing gas pressure and rock joint width.The interaction between the jointed rockmass and the reinforced concrete,the sliding layer,and the steel lining is demonstrated.The results showthat the rock mass quality and the spacing of the rock joints have the greatest influence on the straindistributions in the steel lining.The largest effect of rock joints on the maximum strains in the steellining was observed for geological conditions of“good”quality rock masses.
基金The financial support provided by the China Scholarship Council (Grant No. 201406420027)
文摘Rock joints infilled with sediments can strongly influence the strength of rock mass. As infilled joints often exist under unsaturated condition, this study investigated the influence of matric suction of infill on the overall joint shear strength. A novel technique that allows direct measurement of matric suction of infill using high capacity tensiometers(HCTs) during direct shear of infilled joints under constant normal stiffness(CNS) is described. The CNS apparatus was modified to accommodate the HCT and the procedure is explained in detail. Joint specimens were simulated by gypsum plaster using threedimensional(3D) printed surface moulds, and filled with kaolin and sand mixture prepared at different water contents. Shear behaviours of both planar infilled joints and rough joints having joint roughness coefficients(JRCs) of 8-10 and 18-20 with the ratios of infill thickness to asperity height(t/a)equal to 0.5 were investigated. Matric suction shows predominantly unimodal behaviour during shearing of both planar and rough joints, which is closely associated with the variation of unloading rate and volumetric changes of the infill material. As expected, two-peak behaviour was observed for the rough joints and both peaks increased with the increase of infill matric suction. The results suggest that the contribution of matric suction of infill on the joint peak normalised shear stress is relatively independent of the joint roughness.
基金Projects(41931295,41877258)supported by the National Natural Science Foundation of ChinaProject(2017YFC1501305)supported by the National Key Research and Development Program of China。
文摘Rock bolts have been widely used in slopes as a reinforcement measure.Modelling the shear mechanical behaviours of bolted rock joints is very complicated due to the complex factors that affect the axial force and shear force on the bolts.Rock bolts under shear action exhibit the guide rail effect;that is,the rock mass slides along the rock bolt as if the rock bolt is a rail.The normal stress can inhibit the guide rail effect and reduce the axial force on bolts.However,this factor is not considered by the existing analysis models.Shear tests of bolted joints under different normal stresses were carried out in the laboratory.During the test,the axial force on each point monitored on the bolt was recorded by a strain gauge,and the attenuation trend of the strain was studied.An analytical model that considers the inhibition of the bolt rail effect due to an increase in the normal stress was proposed to predict the shear mechanical behaviour of rock bolted joints.The new model accommodates the bolt shear behaviours in the elastic stage and plastic stage,and the estimated values agree well with the results of the direct shear tests in the laboratory.The validation shows that the proposed model can effectively describe the deformation characteristics of the bolts in the shear tests.
基金supported by the Grant Agency of the Czech Republic (No. 13-03403S)
文摘A recently developed computerized method for assessing the rock joint coefficients is discussed. The performances of formerly introduced relative similarity indicators, along with the correlation coefficient, are subjected to critical analysis. These relative numerical indicators are replaced by two absolute indicators whose properties better describe surface textures of rock joints. The first absolute indicator results from the Fourier Matrix and evaluates wavy shapes of surfaces. The second absolute indicator quantifies the heights of surface reliefs, and is defined as the root mean square height of the surface outline. The behavior of the newly introduced numerical indicators are investigated by means of the deterministic periodic surface reliefs. The practical application of the new indicators is presented and the convenient performances of both the indicators are documented.
基金funded by the National Natural Science Foundation of China(No.41972266)Chongqing Natural Science Foundation(No.CSTB2024NSCQ-MSX0006).
文摘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.
基金supported by the National Key Research and Development Program of China(2022YFC3080100)the National Natural Science Foundation of China(Nos.52104090,52208328 and 12272353)+1 种基金the Open Fund of Anhui Province Key Laboratory of Building Structure and Underground Engineering,Anhui Jianzhu University(No.KLBSUE-2022-06)the Open Research Fund of Key Laboratory of Construction and Safety of Water Engineering of the Ministry of Water Resources,China Institute of Water Resources and Hydropower Research(Grant No.IWHR-ENGI-202302)。
文摘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.
基金The first author would like to thank the supports of the NARGS, IRGS and AAS grants of Australia, and the National Science Foundation grants （No. 51574060 and No. 51079017） of China, in which the first author is the intemational collaborator. The academic visits of the third and fourth authors to the University of Tasmania are partly supported by a PhD visiting scholarship and an academic visiting scholarship, respectively, provided by the China Scholarship Council, which are greatly appreciated.
文摘A hybrid finite-discrete element method was implemented to study the fracture process of rough rock joints under direct shearing. The hybrid method reproduced the joint shear resistance evolution process from asperity sliding to degradation and from gouge formation to grinding. It is found that, in the direct shear test of rough rock joints under constant normal displacement loading conditions, higher shearing rate promotes the asperity degradation but constraints the volume dilation, which then results in higher peak shear resistance, more gouge formation and grinding, and smoother new joint surfaces. Moreover, it is found that the joint roughness affects the joint shear resistance evolution through influencing the joint fracture micro mechanism. The asperity degradation and gouge grinding are the main failure micro-mechanism in shearing rougher rock joints with deeper asperities while the asperity sliding is the main failure micro-mechanism in shearing smoother rock joints with shallower asperities. It is concluded that the hybrid finite-discrete element method is a valuable numerical tool better than traditional finite element method and discrete element method for modelling the joint sliding, asperity degradation, gouge formation, and gouge grinding occurred in the direct shear tests of rough rock joints.
基金funding provided by the Swiss Federal Office for Water and Geology
文摘Structural defects such as joints or faults are inherent to almost any rock mass.In many situations those defects have a major impact on slope stability as they can control the possible failure mechanisms.Having a good estimate of their strength then becomes crucial.The roughness of a structure is a major contributor to its strength through two different aspects,i.e.the morphology of the surface(or the shape)and the strength of the asperities(related to the strength of the rock).In the current state of practice,roughness is assessed through idealized descriptions(Patton strength criterion)or through empirical parameters(Barton JRC).In both cases,the multi-dimensionality of the roughness is ignored.In this study,we propose to take advantage of the latest developments in numerical techniques.With3D photogrammetry and/or laser mapping,practitioners have access to the real morphology of an exposed structure.The derived triangulated surface was introduced into the DEM(discrete element method)code PFC3D to create a synthetic rock joint.The interaction between particles on either side of the discontinuity was described by a smooth-joint model(SJM),hence suppressing the artificial roughness introduced by the particle discretization.Shear tests were then performed on the synthetic rock joint.A good correspondence between strengths predicted by the model and strengths derived from well-established techniques was obtained for thefirst time.Amongst the benefits of the methodology is the possibility offered by the model to be used in a quantitative way for shear strength estimates,to reproduce the progressive degradation of the asperities upon shearing and to analyze structures of different scales without introducing any empirical relation.
基金We acknowledge the funding support from the National Natural Science Foundation of China(Grant Nos.51879135 and 51879184)the Natural Sciences and Engineering Research Council of Canada(NSERC)through the Discovery Grant No.72031326.
文摘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.
基金financially supported by the National Key Research and Development Plan of China(Grant No.2018YFC1504902)the National Natural Science Foundation of China(Grant No.52079068)the State Key Laboratory of Hydroscience and Engineering,China(Grant No.2021-KY-04)。
文摘In underground rock engineering,water-bearing faults may be subjected to dynamic loading,resulting in the coupling of hydraulic and dynamic hazards.Understanding the interaction mechanism between the stress waves induced by dynamic loadings and liquid-filled rock joints is therefore crucial.In this study,an auxiliary device for simulating the liquid-filled layer was developed to analyze the dynamic response characteristics of liquid-filled rock joints in laboratory.Granite and polymethyl methacrylate(PMMA)specimens were chosen for testing,and high-amplitude shock waves induced by a split Hopkinson pressure bar(SHPB)were used to produce dynamic loadings.Impact loading tests were conducted on liquid-filled rock joints with different joint inclinations.The energy propagation coefficient and peak liquid pressure were proposed to investigate the energy propagation and attenuation of waves propagating across the joints,as well as the dynamic response characteristics of the liquid in the liquid-filled rock joints.For the inclination angle range considered herein,the experimental results showed that the energy propagation coefficient gently diminished with increasing joint inclination,and smaller coefficient values were obtained for granite specimens compared with PMMA specimens.The peak liquid pressure exhibited a gradually decreasing trend with increasing joint inclination,and the peak pressure for granite specimens was slightly higher than that for PMMA specimens.Overall,this paper may provide a considerably better method for studying liquid-filled rock joints at the laboratory scale,and serves as a guide for interpreting the underlying mechanisms for interactions between stress waves and liquid-filled rock joints.
基金supported by the National Natural Science Foundation of China(No.51974171)the Major Program of Shandong Provincial Natural Science Foundation(No.ZR2019ZD13)the Major Scientific and Technological Innovation Project of Shandong Provincial Key Research Development Program(No.2019SDZY02)。
文摘Rock joints exhibit hysteresis shearing behavior and produce energy dissipation under shear cyclic loads,which however cannot be accurately depicted by existing constitutive models.This paper establishes a constitutive model for hysteresis shearing and associated energy dissipation of rock joints.Analytical expressions of the model during cyclic shearing processes are derived.Derivation of the model indicates no energy dissipation in the elastic stage.When the shear load exceeds elastic boundary,nonlinear energy dissipation takes place.Validations with experiments show that the proposed model provides good conformities with direct shear curves and hysteresis loops,and can predict the energy dissipation characteristics of rock joints under different working conditions.Compared to the constitutive models using Weibull's distribution,the proposed one is smooth at the elastic boundary and can accurately capture the maximum shear stress.Unlike the existing incremental-type models,the proposed one provides clear and direct analytical expressions for both shear stress and energy dissipation during the whole displacement domain,which is more convenient in application.
