Aiming at solving the challenges of insufficient data samples and low detection efficiency in tunnel lining crack detection methods based on deep learning,a novel detection approach for tunnel lining crack was propose...Aiming at solving the challenges of insufficient data samples and low detection efficiency in tunnel lining crack detection methods based on deep learning,a novel detection approach for tunnel lining crack was proposed,which is based on pruned You Look Only Once v4(YOLOv4)and Wasserstein Generative Adversarial Network enhanced by Residual Block and Efficient Channel Attention Module(WGAN-RE).In this study,a data augmentation method named WGAN-RE was proposed,which can achieve the automatic generation of crack images to enrich data set.Furthermore,YOLOv4 was selected as the basic model for training,and a pruning algo-rithm was introduced to lighten the model size,thereby effectively improving the detection speed.Average Precision(AP),F1 Score(F1),model size,and Frames Per Second(FPS)were selected as evaluation indexes of the model performance.Results indicate that the storage space of the pruned YOLOv4 model is only 49.16 MB,which is 80%compressed compared with the model before pruning.In addition,the FPS of the model reaches 40.58f/s,which provides a basis for the real-time detection of tunnel lining cracks.Findings also demon-strate that the F1 score and AP of the pruned YOLOv4 are only 0.77%and 0.50%lower than that before pruning,respectively.Besides,the pruned YOLOv4 is superior in both model accuracy and efficiency compared with YOLOv3,SSD,and Faster RCNN,which indi-cated that the pruned YOLOv4 model can realize the accurate,fast and intelligent detection of tunnel lining cracks in practical tunnel engineering.展开更多
The numerical simulation results utilizing the Peridynamics(PD)method reveal that the initial crack and crack propagation of the tunnel concrete lining structure agree with the experimental data compared to the Japane...The numerical simulation results utilizing the Peridynamics(PD)method reveal that the initial crack and crack propagation of the tunnel concrete lining structure agree with the experimental data compared to the Japanese prototype lining test.The load structure model takes into account the cracking process and distribution of the lining segment under the influence of local bias pressure and lining thickness.In addition,the influence of preset cracks and lining section formon the crack propagation of the concrete lining model is studied.This study evaluates the stability and sustainability of tunnel structure by the Peridynamics method,which provides a reference for the analysis of the causes of lining cracks,and also lays a foundation for the prevention,reinforcement and repair of tunnel lining cracks.展开更多
High-speed railway tunnels in various countries have continuously reported accidents of vault falling concrete blocks.Once the concrete block falling occurs,serious consequences follow,and traffic safety may be endang...High-speed railway tunnels in various countries have continuously reported accidents of vault falling concrete blocks.Once the concrete block falling occurs,serious consequences follow,and traffic safety may be endangered.The aerodynamic shockwave evolves from the initial compression wave may be an important inducement causing the tunnel lining cracks to grow and form falling concrete blocks.A joint calculation framework is established based on ANSYS Fluent,ABAQUS,and FRANC3D for calculating the crack tip field under the aerodynamic shockwave.The intensification effect of aerodynamic shockwaves in the crack is revealed,and the evolution characteristics of the crack tip field and the influence factors of stress intensity factor(SIF)are analyzed.Results show that(1)the aerodynamic shockwave intensifies after entering the crack,resulting in more significant pressure in the crack than the input pressure.The maximum pressure of the inclined and longitudinal cracks is higher than the corresponding values of the circumferential crack,respectively.(2)The maximum SIF of the circumferential,inclined,and longitudinal crack appears at 0.5,0.68,and 0.78 times the crack front length.The maximum SIF of the circumferential crack is higher than that of the inclined and longitudinal crack.The possibility of crack growth of the circumferential crack is the highest under aerodynamic shockwaves.(3)The influence of train speed on the SIF of the circumferential crack is more than 40%.When the train speed,crack depth,and crack length change,the change of pressure in the crack is the direct cause of the change of SIF.展开更多
The near crack line analysis method was used to investigate a crack loaded by a pair of point shear forces in an infinite plate in an elastic-perfectly plastic solid. The analytical solution was obtained, that is the ...The near crack line analysis method was used to investigate a crack loaded by a pair of point shear forces in an infinite plate in an elastic-perfectly plastic solid. The analytical solution was obtained, that is the elastic-plastic fields near crack line and law that the length of the plastic zone along the crack line is varied with external loads. The results are sufficiently precise near the crack line and are not confined by small scale yielding conditions.展开更多
Crack line analysis is an effective way to solve elastic-plastic crack problems. Application of the method does not need the traditional small-scale yielding conditions and can obtain sufficiently accurate solutions n...Crack line analysis is an effective way to solve elastic-plastic crack problems. Application of the method does not need the traditional small-scale yielding conditions and can obtain sufficiently accurate solutions near the crack line. To address mode- Ⅲ crack problems under the perfect elastic-plastic condition, matching procedures of the crack line analysis method axe summarized and refined to give general forms and formulation steps of plastic field, elastic-plastic boundary, and elastic-plastic matching equations near the crack line. The research unifies mode-III crack problems under different conditions into a problem of determining four integral constants with four matching equations. An example is given to verify correctness, conciseness, and generality of the procedure.展开更多
In this paper, the improved near crack line analysis method proposed in Refs. [1]and [2] is used to investigate a mode Ⅲ crack loaded by antiplane point forces in aninfinite plate in an elastic-perfectly plastic sol...In this paper, the improved near crack line analysis method proposed in Refs. [1]and [2] is used to investigate a mode Ⅲ crack loaded by antiplane point forces in aninfinite plate in an elastic-perfectly plastic solid. The solutions of this paper aresufficiently precise near the crack line region because. the assumptions of the smallscale yielding theory have not been used and no other assumptions have been taken.展开更多
The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be u...The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσy, and σsy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σs is different.展开更多
The improved near crack line analysis method was used to investigate an eccentric cracked plate loaded by two pairs of anti_plane point forces at the crack surface in an elastic_perfectly plastic solid. The analytical...The improved near crack line analysis method was used to investigate an eccentric cracked plate loaded by two pairs of anti_plane point forces at the crack surface in an elastic_perfectly plastic solid. The analytical solutions of the elastic_plastic stress fields and displacements near the crack line have been found without the assumptions of the small scale yielding. The law that the length of the plastic zone along the crack line is varied with an external loads and the bearing capacity of an eccentric cracked plate are obtained.展开更多
The three-dimensional finite element method of lines is presented, and the basic processing description of 3D FEMOL in cracking questions is given in detail. Applications to 3D bodies with cracks indicate that good ac...The three-dimensional finite element method of lines is presented, and the basic processing description of 3D FEMOL in cracking questions is given in detail. Applications to 3D bodies with cracks indicate that good accuracy can be obtained with relatively coarse girds. In particular, application to the tension specimen shows very good agreement with the evaluation of stress intensity factors, which is better than the results of other methods. This implies a considerable potential for using this method in the 3D analysis of finite geometry solids and suggests a possible extension of this technique to nonlinear material behavior.展开更多
The Finite Element Method of Lines （FEMOL） is a semi-analytic approach and takes a position between FEM and analytic methods. First, FEMOL in Fracture Mechanics is presented in detail. Then, the method is applied to...The Finite Element Method of Lines （FEMOL） is a semi-analytic approach and takes a position between FEM and analytic methods. First, FEMOL in Fracture Mechanics is presented in detail. Then, the method is applied to a set of examples such as edge-crack plate, the central-crack plate, the plate with cracks emanating from a hole under tensile or under combination loads of tensile and bending. Their dimensionless stress distribution, the stress intensify factor （SIF） and crack opening displacement （COD） are obtained, and comparison with known solutions by other methods are reported. It is found that a good accuracy is achieved by FEMOL. The method is successfully modified to remarkably increase the accuracy and reduce convergence difficulties. So it is a very useful and new tool in studying fracture mechanics problems.展开更多
The near crack line field analysis method has been used to investigate into Mode III quasistatically propagating crack in an elastic-perfectly plastic material.The significance of this paper is that the usual small sc...The near crack line field analysis method has been used to investigate into Mode III quasistatically propagating crack in an elastic-perfectly plastic material.The significance of this paper is that the usual small scale yielding theory has been broken through.By obtaining the general solutions of the stresses and the displacement rate of the near crack line plastic region,and by matching the general solutions with the precise elastic fields(not the usual elastic K-dominant fields)at the elastic-plastic boundary,the precise and new solutions of the stress and deformation fields,the size of the plastic region and the unit normal vector of the elastic-plastic boundary have been obtained near the crack line.The solutions of this paper are sufficiently precise near the crack line region because the roughly qualitative assumptions of the small scale yielding theory have not been used and no other roughly qualitative assumptions have been taken,either.The analysis of this paper shows that the assumingly'steady-state case'for stable crack growth,which has been discussed attentively in previous works,do not exist,and the plastic strains near the crack line do not have singularities,Two most important cases for stable crack growth have been discussed.展开更多
The near crack line field analysis method has been used io investigate into theexact elastic-plastic solutions of a mode II crack under plane stress condilion in anelastic-perfectly plastic solid. The assumptions of t...The near crack line field analysis method has been used io investigate into theexact elastic-plastic solutions of a mode II crack under plane stress condilion in anelastic-perfectly plastic solid. The assumptions of the usual small scale yielding theory.hare been completely. dbandoned and the correct formulations of matching conditionsat the elaslic-plastic boundary. have been given. By, matching the general solution ofthe plastic slress field (bul not the special solution used to be adopted) with the exactelastic stress field (but not the crack tip K-dominant field) at the elastic-plasticboundary, near the crack line, the plastic stresses. the length of the plastic =one and theunit normal vector of the elastic-plastic boundary.which are sufficiently precise near the crack line region ,have been given.展开更多
The near crack line field analysis method has been used to investigate into the exact elastic-plastic solutions of a mode Ⅱ crack under plane stress condition in anelastic-perfectly plastic solid. The assumptions of ...The near crack line field analysis method has been used to investigate into the exact elastic-plastic solutions of a mode Ⅱ crack under plane stress condition in anelastic-perfectly plastic solid. The assumptions of the usual small scale yielding theoryhave been completely. dbandoned and the correct .formulations of matching conditionsat the elastic-plastic boundary have been given. By matching the general solution of the plastic stress field (but not the special solution used to be adopted) will the exactelastic stress field (but not the crack tip K-dominant field) at the elastic-plasticboundary. near the crack line, the plastic .stresses, the length of the plastic zone and theunit normal vector of the elaslic-plastic boundary. which sufficiently precise nearthe crack line region, hare been given.展开更多
In this paper, the improved near crack line analysis method proposed in Refs. [1] and [2] is used to investigate a center crack loaded by two pairs of antiplane point forces in a finite plate in an elastic-perfectly p...In this paper, the improved near crack line analysis method proposed in Refs. [1] and [2] is used to investigate a center crack loaded by two pairs of antiplane point forces in a finite plate in an elastic-perfectly plastic solid. And the analytical solutions are obtained, that is elastic-plastic stress fields near the crack line and the law that the length of the plastic zone along the crack line is varied with an external loads tr,ld the bearing capacity of a finite plate with a center crack. The results of this paper are sufficiently precise near the crack line, because the assumptions of the small scale yielding theory have not been used and no other assumptions have been taken.展开更多
The stick-slip action of strike-slip faults poses a significant threat to the safety and stability of underground structures.In this study,the north-east area of the Longmenshan fault,Sichuan,provides the geological b...The stick-slip action of strike-slip faults poses a significant threat to the safety and stability of underground structures.In this study,the north-east area of the Longmenshan fault,Sichuan,provides the geological background;the rheological characteristics of the crustal lithosphere and the nonlinear interactions between plates are described by Burger’s viscoelastic constitutive model and the friction constitutive model,respectively.A large-scale global numerical model for plate squeezing analysis is established,and the seemingly periodic stick-slip action of faults at different crust depths is simulated.For a second model at a smaller scale,a local finite element model(sub-model),the time history of displacement at a ground level location on the Longmenshan fault plane in a stick-slip action is considered as the displacement loading.The integration of these models,creating a multi-scale modeling method,is used to evaluate the crack propagation and mechanical response of a tunnel subjected to strike-slip faulting.The determinations of the recurrence interval of stick-slip action and the cracking characteristics of the tunnel are in substantial agreement with the previous field investigation and experimental results,validating the multi-scale modeling method.It can be concluded that,regardless of stratum stiffness,initial cracks first occur at the inverted arch of the tunnel in the footwall,on the squeezed side under strike-slip faulting.The smaller the stratum stiffness is,the smaller the included angle between the crack expansion and longitudinal direction of the tunnel,and the more extensive the crack expansion range.For the tunnel in a high stiffness stratum,both shear and bending failures occur on the lining under strike-slip faulting,while for that in the low stiffness stratum,only bending failure occurs on the lining.展开更多
基金supported by the National Science Foundation of China(Grant No.51908557,52278421)the Natural Science Foundation of Hunan Province,China(Grant No.2020JJ4743)+1 种基金the Research Innovation Project for Postgraduate of Central South University(Grant No.1053320213484)the Hunan Tieyuan Civil Engineering Testing Co.,Ltd(HNTY2021K06).
文摘Aiming at solving the challenges of insufficient data samples and low detection efficiency in tunnel lining crack detection methods based on deep learning,a novel detection approach for tunnel lining crack was proposed,which is based on pruned You Look Only Once v4(YOLOv4)and Wasserstein Generative Adversarial Network enhanced by Residual Block and Efficient Channel Attention Module(WGAN-RE).In this study,a data augmentation method named WGAN-RE was proposed,which can achieve the automatic generation of crack images to enrich data set.Furthermore,YOLOv4 was selected as the basic model for training,and a pruning algo-rithm was introduced to lighten the model size,thereby effectively improving the detection speed.Average Precision(AP),F1 Score(F1),model size,and Frames Per Second(FPS)were selected as evaluation indexes of the model performance.Results indicate that the storage space of the pruned YOLOv4 model is only 49.16 MB,which is 80%compressed compared with the model before pruning.In addition,the FPS of the model reaches 40.58f/s,which provides a basis for the real-time detection of tunnel lining cracks.Findings also demon-strate that the F1 score and AP of the pruned YOLOv4 are only 0.77%and 0.50%lower than that before pruning,respectively.Besides,the pruned YOLOv4 is superior in both model accuracy and efficiency compared with YOLOv3,SSD,and Faster RCNN,which indi-cated that the pruned YOLOv4 model can realize the accurate,fast and intelligent detection of tunnel lining cracks in practical tunnel engineering.
基金supported by the National Natural Science Foundation of China (52079128).
文摘The numerical simulation results utilizing the Peridynamics(PD)method reveal that the initial crack and crack propagation of the tunnel concrete lining structure agree with the experimental data compared to the Japanese prototype lining test.The load structure model takes into account the cracking process and distribution of the lining segment under the influence of local bias pressure and lining thickness.In addition,the influence of preset cracks and lining section formon the crack propagation of the concrete lining model is studied.This study evaluates the stability and sustainability of tunnel structure by the Peridynamics method,which provides a reference for the analysis of the causes of lining cracks,and also lays a foundation for the prevention,reinforcement and repair of tunnel lining cracks.
基金funded by the National Natural Science Foundation of China(Grant Nos.51978670 and 52308419)the Science and Technology Research and Development Program of China railway group limited(Grant Nos.2021-Major-01 and 2022-Key-22)+3 种基金the Fundamental Research Funds for the Central Universities of Central South University(Grant No.2023ZZTS0369)the Guangdong Basic and Applied Basic Research Foundation Project(Grant No.2021B1515130006)the Innovation and Technology Commission of Hong Kong,China(Grant No.K-BBY1)the Hong Kong Polytechnic University’s Postdoc Matching Fund Scheme(Grant No.1-W21Q).
文摘High-speed railway tunnels in various countries have continuously reported accidents of vault falling concrete blocks.Once the concrete block falling occurs,serious consequences follow,and traffic safety may be endangered.The aerodynamic shockwave evolves from the initial compression wave may be an important inducement causing the tunnel lining cracks to grow and form falling concrete blocks.A joint calculation framework is established based on ANSYS Fluent,ABAQUS,and FRANC3D for calculating the crack tip field under the aerodynamic shockwave.The intensification effect of aerodynamic shockwaves in the crack is revealed,and the evolution characteristics of the crack tip field and the influence factors of stress intensity factor(SIF)are analyzed.Results show that(1)the aerodynamic shockwave intensifies after entering the crack,resulting in more significant pressure in the crack than the input pressure.The maximum pressure of the inclined and longitudinal cracks is higher than the corresponding values of the circumferential crack,respectively.(2)The maximum SIF of the circumferential,inclined,and longitudinal crack appears at 0.5,0.68,and 0.78 times the crack front length.The maximum SIF of the circumferential crack is higher than that of the inclined and longitudinal crack.The possibility of crack growth of the circumferential crack is the highest under aerodynamic shockwaves.(3)The influence of train speed on the SIF of the circumferential crack is more than 40%.When the train speed,crack depth,and crack length change,the change of pressure in the crack is the direct cause of the change of SIF.
基金National Natural Science Foundation ofChina( No.5 98790 12 )
文摘The near crack line analysis method was used to investigate a crack loaded by a pair of point shear forces in an infinite plate in an elastic-perfectly plastic solid. The analytical solution was obtained, that is the elastic-plastic fields near crack line and law that the length of the plastic zone along the crack line is varied with external loads. The results are sufficiently precise near the crack line and are not confined by small scale yielding conditions.
基金supported by the National Natural Science Foundation of China (No.10672196)
文摘Crack line analysis is an effective way to solve elastic-plastic crack problems. Application of the method does not need the traditional small-scale yielding conditions and can obtain sufficiently accurate solutions near the crack line. To address mode- Ⅲ crack problems under the perfect elastic-plastic condition, matching procedures of the crack line analysis method axe summarized and refined to give general forms and formulation steps of plastic field, elastic-plastic boundary, and elastic-plastic matching equations near the crack line. The research unifies mode-III crack problems under different conditions into a problem of determining four integral constants with four matching equations. An example is given to verify correctness, conciseness, and generality of the procedure.
文摘In this paper, the improved near crack line analysis method proposed in Refs. [1]and [2] is used to investigate a mode Ⅲ crack loaded by antiplane point forces in aninfinite plate in an elastic-perfectly plastic solid. The solutions of this paper aresufficiently precise near the crack line region because. the assumptions of the smallscale yielding theory have not been used and no other assumptions have been taken.
文摘The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσy, and σsy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σs is different.
文摘The improved near crack line analysis method was used to investigate an eccentric cracked plate loaded by two pairs of anti_plane point forces at the crack surface in an elastic_perfectly plastic solid. The analytical solutions of the elastic_plastic stress fields and displacements near the crack line have been found without the assumptions of the small scale yielding. The law that the length of the plastic zone along the crack line is varied with an external loads and the bearing capacity of an eccentric cracked plate are obtained.
文摘The three-dimensional finite element method of lines is presented, and the basic processing description of 3D FEMOL in cracking questions is given in detail. Applications to 3D bodies with cracks indicate that good accuracy can be obtained with relatively coarse girds. In particular, application to the tension specimen shows very good agreement with the evaluation of stress intensity factors, which is better than the results of other methods. This implies a considerable potential for using this method in the 3D analysis of finite geometry solids and suggests a possible extension of this technique to nonlinear material behavior.
文摘The Finite Element Method of Lines （FEMOL） is a semi-analytic approach and takes a position between FEM and analytic methods. First, FEMOL in Fracture Mechanics is presented in detail. Then, the method is applied to a set of examples such as edge-crack plate, the central-crack plate, the plate with cracks emanating from a hole under tensile or under combination loads of tensile and bending. Their dimensionless stress distribution, the stress intensify factor （SIF） and crack opening displacement （COD） are obtained, and comparison with known solutions by other methods are reported. It is found that a good accuracy is achieved by FEMOL. The method is successfully modified to remarkably increase the accuracy and reduce convergence difficulties. So it is a very useful and new tool in studying fracture mechanics problems.
文摘The near crack line field analysis method has been used to investigate into Mode III quasistatically propagating crack in an elastic-perfectly plastic material.The significance of this paper is that the usual small scale yielding theory has been broken through.By obtaining the general solutions of the stresses and the displacement rate of the near crack line plastic region,and by matching the general solutions with the precise elastic fields(not the usual elastic K-dominant fields)at the elastic-plastic boundary,the precise and new solutions of the stress and deformation fields,the size of the plastic region and the unit normal vector of the elastic-plastic boundary have been obtained near the crack line.The solutions of this paper are sufficiently precise near the crack line region because the roughly qualitative assumptions of the small scale yielding theory have not been used and no other roughly qualitative assumptions have been taken,either.The analysis of this paper shows that the assumingly'steady-state case'for stable crack growth,which has been discussed attentively in previous works,do not exist,and the plastic strains near the crack line do not have singularities,Two most important cases for stable crack growth have been discussed.
文摘The near crack line field analysis method has been used io investigate into theexact elastic-plastic solutions of a mode II crack under plane stress condilion in anelastic-perfectly plastic solid. The assumptions of the usual small scale yielding theory.hare been completely. dbandoned and the correct formulations of matching conditionsat the elaslic-plastic boundary. have been given. By, matching the general solution ofthe plastic slress field (bul not the special solution used to be adopted) with the exactelastic stress field (but not the crack tip K-dominant field) at the elastic-plasticboundary, near the crack line, the plastic stresses. the length of the plastic =one and theunit normal vector of the elastic-plastic boundary.which are sufficiently precise near the crack line region ,have been given.
文摘The near crack line field analysis method has been used to investigate into the exact elastic-plastic solutions of a mode Ⅱ crack under plane stress condition in anelastic-perfectly plastic solid. The assumptions of the usual small scale yielding theoryhave been completely. dbandoned and the correct .formulations of matching conditionsat the elastic-plastic boundary have been given. By matching the general solution of the plastic stress field (but not the special solution used to be adopted) will the exactelastic stress field (but not the crack tip K-dominant field) at the elastic-plasticboundary. near the crack line, the plastic .stresses, the length of the plastic zone and theunit normal vector of the elaslic-plastic boundary. which sufficiently precise nearthe crack line region, hare been given.
文摘In this paper, the improved near crack line analysis method proposed in Refs. [1] and [2] is used to investigate a center crack loaded by two pairs of antiplane point forces in a finite plate in an elastic-perfectly plastic solid. And the analytical solutions are obtained, that is elastic-plastic stress fields near the crack line and the law that the length of the plastic zone along the crack line is varied with an external loads tr,ld the bearing capacity of a finite plate with a center crack. The results of this paper are sufficiently precise near the crack line, because the assumptions of the small scale yielding theory have not been used and no other assumptions have been taken.
基金supported by the Key Projects for International Science and Technology Innovation Cooperation between Governments(No.2022YFE0104300)National Natural Science Foundation of China(Grant No.52130808)+1 种基金Scientific and Technical Exploitation Program of China Railway Design Corporation(No.2020YY240610)Scientific and Technical Exploitation Program of China Railway(No.K2020G033).
文摘The stick-slip action of strike-slip faults poses a significant threat to the safety and stability of underground structures.In this study,the north-east area of the Longmenshan fault,Sichuan,provides the geological background;the rheological characteristics of the crustal lithosphere and the nonlinear interactions between plates are described by Burger’s viscoelastic constitutive model and the friction constitutive model,respectively.A large-scale global numerical model for plate squeezing analysis is established,and the seemingly periodic stick-slip action of faults at different crust depths is simulated.For a second model at a smaller scale,a local finite element model(sub-model),the time history of displacement at a ground level location on the Longmenshan fault plane in a stick-slip action is considered as the displacement loading.The integration of these models,creating a multi-scale modeling method,is used to evaluate the crack propagation and mechanical response of a tunnel subjected to strike-slip faulting.The determinations of the recurrence interval of stick-slip action and the cracking characteristics of the tunnel are in substantial agreement with the previous field investigation and experimental results,validating the multi-scale modeling method.It can be concluded that,regardless of stratum stiffness,initial cracks first occur at the inverted arch of the tunnel in the footwall,on the squeezed side under strike-slip faulting.The smaller the stratum stiffness is,the smaller the included angle between the crack expansion and longitudinal direction of the tunnel,and the more extensive the crack expansion range.For the tunnel in a high stiffness stratum,both shear and bending failures occur on the lining under strike-slip faulting,while for that in the low stiffness stratum,only bending failure occurs on the lining.
