Understanding the anisotropic fracture behavior and the characteristics of the fracture process zone(FPZ)under size effects in laminated rocks,as well as its role in rock fracturing,is crucial for various engineering ...Understanding the anisotropic fracture behavior and the characteristics of the fracture process zone(FPZ)under size effects in laminated rocks,as well as its role in rock fracturing,is crucial for various engineering applications.In this study,three-point bending tests were conducted on shale specimens with varying bedding angles and sizes.The anisotropic characteristics and size effects of fracture parameters were revealed.A comparative analysis was performed on the evolutions of FPZs computed using size effect theory,digital image correlation(DIC),and linear elastic fracture mechanics.The results divulged that:(i)With increasing bedding angles,there is a noticeable decrease in apparent fracture toughness(KICA),apparent fracture energy(GICA),and nominal strength(σ_(Nu)).When the bedding angle of shale is less than 45°,the crack propagation and fracture parameters are mainly influenced by the matrix.Contrary,shale with bedding angles greater than 60°,the crack propagation and fracture parameters are mainly controlled by the bedding.When the bedding angle is between 45°and 60°,the fracture propagation evolves from permeating the matrix to extending along the bedding;(ii)The fracture parameters exhibit significant size dependent behavior,as KICA and GICA rise with increasing specimen size,butσNu falls with increasing specimen sizes.The fracture parameters align with the theoretical predictions of Bažant size effect law;and(iii)The lengths of DIC-based FPZ,effective FPZ,and inelastic zone follow W-shape variations with bedding angle.The dimensionless sizes of FPZ and inelastic zone decrease with specimen size,indicating a size effect.Furthermore,there is a negative relation between KICA and the dimensionless size of the FPZ,whileσNu is positively correlated to the dimensionless size of the FPZ.This highlights the essential role of the FPZ in the size effect of rock fracture.The bedding angle exerts an influence on the FPZ,subsequently affecting the anisotropic fracture and size-dependent behavior of shale.展开更多
An analytical expression for the prediction of shear-compressive fracture process zone(SCFPZ) is derived by using a proposed local strain energy density criterion, in which the strain energy density is separated into ...An analytical expression for the prediction of shear-compressive fracture process zone(SCFPZ) is derived by using a proposed local strain energy density criterion, in which the strain energy density is separated into the dilatational and distortional strain energy density, only the former is considered to contribute to the brittle fracture of rock in different loading cases. The theoretical prediction by this criterion shows that the SCFPZ is of asymmetric mulberry leaf in shape, which forms a shear-compression fracture kern. Dilatational strain energy density along the boundary of SCFPZ reaches its maximum value. The dimension of SCFPZ is governed by the ratio of K_Ⅱ to (K_Ⅰ.) The analytical results are then compared with those from literatures and the tests conducted on double edge cracked Brazilian disk subjected to diametrical compression. The obtained results are useful to the prediction of crack extension and to nonlinear analysis of shear-compressive fracture of brittle rock.展开更多
On the basis of that rock material usually has a larger fracture process zone,a new fracture criterion which is different from that of linear elastic fracture theory was presented.On this basis,the fracture behavior a...On the basis of that rock material usually has a larger fracture process zone,a new fracture criterion which is different from that of linear elastic fracture theory was presented.On this basis,the fracture behavior and influencing factors under modeⅡor compressive shear loading were investigated.展开更多
This study investigates the fracture characteristics and the fracture process zone(FPZ)of mode I fracture in sandstone,aiming to analyze the propagation behaviors of mode I crack under different freeze-thaw cycles.Sem...This study investigates the fracture characteristics and the fracture process zone(FPZ)of mode I fracture in sandstone,aiming to analyze the propagation behaviors of mode I crack under different freeze-thaw cycles.Semicircular bending tests(SCB)were conducted using different freeze-thaw cycles to evaluate mode I fracture toughness,FPZ dynamics,and macroscopic microscopic features.Digital image correlation(DIC)and scanning electron microscopy(SEM)techniques were employed for detailed analysis.Experimental results reveal that freeze-thaw cycling leads to the widening of both preexisting and newly formed microcracks between internal particles.Under external loading,crack propagation deviates from prefabricated paths,forming serrated crack patterns.The FPZ initiates at the prefabricated crack tip and extends toward the loading end,exhibiting an arcshaped tip shape.The FPZ length increases with loading but decreases after reaching a peak value.With additional freeze-thaw cycles,the maximum FPZ length first increases and then diminishes.展开更多
The development of geological lamination in shale reservoirs influences fracture propagation during hydraulic stimulation,and the fracture generation mechanism as it propagates through the laminated interface is close...The development of geological lamination in shale reservoirs influences fracture propagation during hydraulic stimulation,and the fracture generation mechanism as it propagates through the laminated interface is closely related to fracturing effects.In this paper,the laminated shale was selected to conduct three-point bending experiments using digital image correlation(DIC)and acoustic emission(AE)techniques,which revealed that the propagation path of cross-layer fractures exhibits dislocation features.The cohesive fracture mechanism of cross-layer fractures is investigated from the viewpoint of the fracture process zone(FPZ),which displays the characteristics of intermittence and dislocation during fracture development.A computational criterion for predicting the dislocation of cross-layer fracture at the interface is proposed,which shows that the maximum dislocation range does not exceed 72%of the FPZ length.Considering the mechanical differences between adjacent layers of laminated shale,the cohesive zone model of cross-layer fracture is discussed,from which the constitutive relationship and fracture energy during FPZ development are characterized,and the discontinuous nature of the constitutive relationship is found.This study improves the understanding of the geometry and cohesive fracture mechanism of the cross-layer fracture and provides valuable insights for field fracturing in shale reservoirs.展开更多
This study investigates the fracture behavior of clay-rich mudstone under varying temperature and pressure conditions,which is crucial for the safety of geological structures.It focuses on three fracture types:pure mo...This study investigates the fracture behavior of clay-rich mudstone under varying temperature and pressure conditions,which is crucial for the safety of geological structures.It focuses on three fracture types:pure mode I tensile fractures,pure mode II tensile fractures,and shear fractures,examining specimens at room temperature(RT)and after thermal treatments at 250 and 500℃.The findings reveal that increasing temperatures makes the mudstone more brittle,enhancing fracture velocity,toughness,load-bearing capacity,roughness,and the fracture process zone(FPZ)radius.Notably,tensile fractures induced under pure mode II displayed the highest velocities,while shear fractures exhibited the lowest velocities,smoothest surfaces,and greatest resistance to failure.The application of a confining pressure of 4 MPa significantly improved shear fracture toughness by 119.7%,98.5%and 71.9%at RT,250℃and 500℃,respectively,and reduced roughness by 8.2%,22.4%and 30.4%.This research offers a novel,comprehensive view of how temperature and pressure impact fractures in mudstone sensitive to temperature due to its high clay content and water affinity.The findings provide valuable insights applicable to geothermal energy,oil and gas exploration,and underground construction,thereby enhancing the understanding of fracture mechanics in geological contexts.展开更多
Evaluating the fracture resistance of rocks is essential for predicting and preventing catastrophic failure of cracked structures in rock engineering.This investigation developed a brittle fracture model to predict te...Evaluating the fracture resistance of rocks is essential for predicting and preventing catastrophic failure of cracked structures in rock engineering.This investigation developed a brittle fracture model to predict tensile mode(mode I)failure loads of cracked rocks.The basic principle of the model is to estimate the reference crack corresponding to the fracture process zone(FPZ)based on the maximum normal strain(MNSN)ahead of the crack tip,and then use the effective crack to calculate the fracture toughness.We emphasize that the non-singular stress/strain terms should be considered in the description of the MNSN.In this way,the FPZ,non-singular terms and the biaxial stress state at the crack tip are simul-taneously considered.The principle of the model is explicit and easy to apply.To verify the proposed model,laboratory experiments were performed on a rock material using six groups of specimens.The model predicted the specimen geometry dependence of the measured fracture toughness well.More-over,the potential of the model in analyzing the size effect of apparent fracture toughness was discussed and validated through experimental data reported in the literature.The model was demonstrated su-perior to some commonly used fracture models and is an excellent tool for the safety assessment of cracked rock structures.展开更多
Based on the parallel bar system, combining with the synergetic method, the catastrophe theory and the acoustic emission test, a new motivated statistical damage model for quasi-brittle solid was developed. Taking con...Based on the parallel bar system, combining with the synergetic method, the catastrophe theory and the acoustic emission test, a new motivated statistical damage model for quasi-brittle solid was developed. Taking concrete for instances, the rationality and the flexibility of this model and its parameters-determining method were identified by the comparative analyses between theoretical and experimental curves. The results show that the model can simulate the whole damage and fracture process in the fracture process zone of material when the materials arc exposed to quasi-static uniaxial tensile traction. The influence of the mesoscopic damage mechanism on the macroscopic mechanical properties of quasi-brittle materials is summarized into two aspects, rupture damage and yield damage. The whole damage course is divided into the statistical even damage phase and the local breach phase, corresponding to the two stages described by the catastrophe theory. The two characteristic states, the peak nominal stress state and the critical state are distinguished, and the critical state plays a key role during the whole damage evolution course.展开更多
Changes of the material fracture toughness with crack propagation can be described by a crack extension resistance curve,one of the fundamental fracture criteria in crack mechanics.Recently,experimental observation of...Changes of the material fracture toughness with crack propagation can be described by a crack extension resistance curve,one of the fundamental fracture criteria in crack mechanics.Recently,experimental observation of the fracture behavior in concrete was used to develop a new fracture criterion,the crack extension GR resistance curve,to analyze crack propagation during the entire concrete fracture process.The variation of the crack extension resistance is mainly associated with the energy consumption in the fracture process zone ahead of the stress-free crack tip.The crack extension resistance is then a function of the softening curve,which is a basic mechanical property in the fracture process zone.The relationship between the softening curve and the crack extension GR resistance curve is then analyzed based on results of three-point bending beams tests.The results indicate that the characteristic points of the crack extension resistance GR curve is closely related to the characteristic point on used tension softening curve.展开更多
基金funded by the National Natural Science Foundation of China(Grant Nos.12172230,U22A20166)the Department of Science and Technology of Guangdong Province(Grant No.2019ZT08G315).
文摘Understanding the anisotropic fracture behavior and the characteristics of the fracture process zone(FPZ)under size effects in laminated rocks,as well as its role in rock fracturing,is crucial for various engineering applications.In this study,three-point bending tests were conducted on shale specimens with varying bedding angles and sizes.The anisotropic characteristics and size effects of fracture parameters were revealed.A comparative analysis was performed on the evolutions of FPZs computed using size effect theory,digital image correlation(DIC),and linear elastic fracture mechanics.The results divulged that:(i)With increasing bedding angles,there is a noticeable decrease in apparent fracture toughness(KICA),apparent fracture energy(GICA),and nominal strength(σ_(Nu)).When the bedding angle of shale is less than 45°,the crack propagation and fracture parameters are mainly influenced by the matrix.Contrary,shale with bedding angles greater than 60°,the crack propagation and fracture parameters are mainly controlled by the bedding.When the bedding angle is between 45°and 60°,the fracture propagation evolves from permeating the matrix to extending along the bedding;(ii)The fracture parameters exhibit significant size dependent behavior,as KICA and GICA rise with increasing specimen size,butσNu falls with increasing specimen sizes.The fracture parameters align with the theoretical predictions of Bažant size effect law;and(iii)The lengths of DIC-based FPZ,effective FPZ,and inelastic zone follow W-shape variations with bedding angle.The dimensionless sizes of FPZ and inelastic zone decrease with specimen size,indicating a size effect.Furthermore,there is a negative relation between KICA and the dimensionless size of the FPZ,whileσNu is positively correlated to the dimensionless size of the FPZ.This highlights the essential role of the FPZ in the size effect of rock fracture.The bedding angle exerts an influence on the FPZ,subsequently affecting the anisotropic fracture and size-dependent behavior of shale.
基金Project(50274074) supported by the National Natural Science Foundation of China project(04JJ6030) supported by theNatural Science Foundation of Hunan Province
文摘An analytical expression for the prediction of shear-compressive fracture process zone(SCFPZ) is derived by using a proposed local strain energy density criterion, in which the strain energy density is separated into the dilatational and distortional strain energy density, only the former is considered to contribute to the brittle fracture of rock in different loading cases. The theoretical prediction by this criterion shows that the SCFPZ is of asymmetric mulberry leaf in shape, which forms a shear-compression fracture kern. Dilatational strain energy density along the boundary of SCFPZ reaches its maximum value. The dimension of SCFPZ is governed by the ratio of K_Ⅱ to (K_Ⅰ.) The analytical results are then compared with those from literatures and the tests conducted on double edge cracked Brazilian disk subjected to diametrical compression. The obtained results are useful to the prediction of crack extension and to nonlinear analysis of shear-compressive fracture of brittle rock.
文摘On the basis of that rock material usually has a larger fracture process zone,a new fracture criterion which is different from that of linear elastic fracture theory was presented.On this basis,the fracture behavior and influencing factors under modeⅡor compressive shear loading were investigated.
基金supported by the projects(Grant No.:52304118)supported by National Natural Science Foundation of China,the Scientific Research Foundation for High-level Talents of Anhui University of Science and Technology(2023yjrc18)the Open Fund of the State Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mine(Grant No.:SKLMRDPC23KF08).
文摘This study investigates the fracture characteristics and the fracture process zone(FPZ)of mode I fracture in sandstone,aiming to analyze the propagation behaviors of mode I crack under different freeze-thaw cycles.Semicircular bending tests(SCB)were conducted using different freeze-thaw cycles to evaluate mode I fracture toughness,FPZ dynamics,and macroscopic microscopic features.Digital image correlation(DIC)and scanning electron microscopy(SEM)techniques were employed for detailed analysis.Experimental results reveal that freeze-thaw cycling leads to the widening of both preexisting and newly formed microcracks between internal particles.Under external loading,crack propagation deviates from prefabricated paths,forming serrated crack patterns.The FPZ initiates at the prefabricated crack tip and extends toward the loading end,exhibiting an arcshaped tip shape.The FPZ length increases with loading but decreases after reaching a peak value.With additional freeze-thaw cycles,the maximum FPZ length first increases and then diminishes.
基金financiallysupported by the Excellent Young Fund of Sinopec Petroleum Exploration and Production Research Institute(Grant No.YK2024009)the National Natural Science Foundation of China(Grant Nos.U23B6004 and 51925405).
文摘The development of geological lamination in shale reservoirs influences fracture propagation during hydraulic stimulation,and the fracture generation mechanism as it propagates through the laminated interface is closely related to fracturing effects.In this paper,the laminated shale was selected to conduct three-point bending experiments using digital image correlation(DIC)and acoustic emission(AE)techniques,which revealed that the propagation path of cross-layer fractures exhibits dislocation features.The cohesive fracture mechanism of cross-layer fractures is investigated from the viewpoint of the fracture process zone(FPZ),which displays the characteristics of intermittence and dislocation during fracture development.A computational criterion for predicting the dislocation of cross-layer fracture at the interface is proposed,which shows that the maximum dislocation range does not exceed 72%of the FPZ length.Considering the mechanical differences between adjacent layers of laminated shale,the cohesive zone model of cross-layer fracture is discussed,from which the constitutive relationship and fracture energy during FPZ development are characterized,and the discontinuous nature of the constitutive relationship is found.This study improves the understanding of the geometry and cohesive fracture mechanism of the cross-layer fracture and provides valuable insights for field fracturing in shale reservoirs.
基金Projects(19300604,19300751)supported by the ORSP at Abu Dhabi University,UAE。
文摘This study investigates the fracture behavior of clay-rich mudstone under varying temperature and pressure conditions,which is crucial for the safety of geological structures.It focuses on three fracture types:pure mode I tensile fractures,pure mode II tensile fractures,and shear fractures,examining specimens at room temperature(RT)and after thermal treatments at 250 and 500℃.The findings reveal that increasing temperatures makes the mudstone more brittle,enhancing fracture velocity,toughness,load-bearing capacity,roughness,and the fracture process zone(FPZ)radius.Notably,tensile fractures induced under pure mode II displayed the highest velocities,while shear fractures exhibited the lowest velocities,smoothest surfaces,and greatest resistance to failure.The application of a confining pressure of 4 MPa significantly improved shear fracture toughness by 119.7%,98.5%and 71.9%at RT,250℃and 500℃,respectively,and reduced roughness by 8.2%,22.4%and 30.4%.This research offers a novel,comprehensive view of how temperature and pressure impact fractures in mudstone sensitive to temperature due to its high clay content and water affinity.The findings provide valuable insights applicable to geothermal energy,oil and gas exploration,and underground construction,thereby enhancing the understanding of fracture mechanics in geological contexts.
基金he authors thank the financial support fromthe Key Program of National Natural Science Foundation of China(GrantNo.52039007)the Youth Science and Technology Innovation Research Team Fund of Sichuan Province(Grant No.2020JDTD0001).
文摘Evaluating the fracture resistance of rocks is essential for predicting and preventing catastrophic failure of cracked structures in rock engineering.This investigation developed a brittle fracture model to predict tensile mode(mode I)failure loads of cracked rocks.The basic principle of the model is to estimate the reference crack corresponding to the fracture process zone(FPZ)based on the maximum normal strain(MNSN)ahead of the crack tip,and then use the effective crack to calculate the fracture toughness.We emphasize that the non-singular stress/strain terms should be considered in the description of the MNSN.In this way,the FPZ,non-singular terms and the biaxial stress state at the crack tip are simul-taneously considered.The principle of the model is explicit and easy to apply.To verify the proposed model,laboratory experiments were performed on a rock material using six groups of specimens.The model predicted the specimen geometry dependence of the measured fracture toughness well.More-over,the potential of the model in analyzing the size effect of apparent fracture toughness was discussed and validated through experimental data reported in the literature.The model was demonstrated su-perior to some commonly used fracture models and is an excellent tool for the safety assessment of cracked rock structures.
基金Projects(90510018, 50679006) supported by the National Natural Science Foundation of ChinaProject(NCET-05-0413) support by the Program for New Century Excellent Talents in University
文摘Based on the parallel bar system, combining with the synergetic method, the catastrophe theory and the acoustic emission test, a new motivated statistical damage model for quasi-brittle solid was developed. Taking concrete for instances, the rationality and the flexibility of this model and its parameters-determining method were identified by the comparative analyses between theoretical and experimental curves. The results show that the model can simulate the whole damage and fracture process in the fracture process zone of material when the materials arc exposed to quasi-static uniaxial tensile traction. The influence of the mesoscopic damage mechanism on the macroscopic mechanical properties of quasi-brittle materials is summarized into two aspects, rupture damage and yield damage. The whole damage course is divided into the statistical even damage phase and the local breach phase, corresponding to the two stages described by the catastrophe theory. The two characteristic states, the peak nominal stress state and the critical state are distinguished, and the critical state plays a key role during the whole damage evolution course.
基金This paper was financially supported by the National Natural Science Foundation of China(Grant No.50438010).
文摘Changes of the material fracture toughness with crack propagation can be described by a crack extension resistance curve,one of the fundamental fracture criteria in crack mechanics.Recently,experimental observation of the fracture behavior in concrete was used to develop a new fracture criterion,the crack extension GR resistance curve,to analyze crack propagation during the entire concrete fracture process.The variation of the crack extension resistance is mainly associated with the energy consumption in the fracture process zone ahead of the stress-free crack tip.The crack extension resistance is then a function of the softening curve,which is a basic mechanical property in the fracture process zone.The relationship between the softening curve and the crack extension GR resistance curve is then analyzed based on results of three-point bending beams tests.The results indicate that the characteristic points of the crack extension resistance GR curve is closely related to the characteristic point on used tension softening curve.
