Principal stress plays a critical role in the deformation and failure process of rock or rock-like materials.However,existing studies indicate that the construction of a damage model based on principal stresses for de...Principal stress plays a critical role in the deformation and failure process of rock or rock-like materials.However,existing studies indicate that the construction of a damage model based on principal stresses for describing the entire process of three-dimensional rock fracturing is subject to certain limitations and inadequacies.In this study,an innovative three-dimensional statistical damage constitutive model is developed by integrating the principal stress effect with the Gamma distribution function.This model effectively captures the complete damage evolution process of rock materials with initial defects through the introduction of a compaction correction coefficient and a residual strength correction term.Notably,the simulation accuracy is significantly enhanced in both the initial compaction stage and the post-peak residual strength stage.The parameter θ serves as an indicator of the material brittle-to-ductile transition,whereas the parameter k reflects the material's strength characteristics.The parameter calibration process consists of three steps:determining the θ value on the basis of the rock brittleness index,deriving the k parameter from the k value growth curve,and finally establishing the peak-residual strength prediction equation under given confining pressure conditions.Compared with the traditional statistical damage model based on the Weibull distribution,this model not only features clear physical significance and a simplified calculation procedure but also contributes to the advancement of the three-dimensional damage fracture theory system for rock mechanics.Moreover,it offers a robust framework for evaluating the mechanical response of rocks under varying confining pressures,which has significant implications for safe design and risk assessment in civil engineering or rock engineering.展开更多
Uniaxial compression tests combined with acoustic emission(AE)monitoring were conducted on the sandstone and concrete specimens to measure the physical and mechanical properties and analyze the damage evolution after ...Uniaxial compression tests combined with acoustic emission(AE)monitoring were conducted on the sandstone and concrete specimens to measure the physical and mechanical properties and analyze the damage evolution after heating test.A modified thermal-mechanical statistical damage constitutive model was established by K-means++clustering algorithm for determining the proportion of tensile and shear cracks in AE data and for defining the new tensile and shear mechanical damage factors of the Weibull distribution.This model is verified to be valid by good agreement with the experimental results.展开更多
Accurate assessment of coal brittleness is crucial in the design of coal seam drilling and underground coal mining operations.This study proposes a method for evaluating the brittleness of gas-bearing coal based on a ...Accurate assessment of coal brittleness is crucial in the design of coal seam drilling and underground coal mining operations.This study proposes a method for evaluating the brittleness of gas-bearing coal based on a statistical damage constitutive model and energy evolution mechanisms.Initially,integrating the principle of effective stress and the Hoek-Brown criterion,a statistical damage constitutive model for gas-bearing coal is established and validated through triaxial compression tests under different gas pressures to verify its accuracy and applicability.Subsequently,employing energy evolution mechanism,two energy characteristic parameters(elastic energy proportion and dissipated energy proportion)are analyzed.Based on the damage stress thresholds,the damage evolution characteristics of gas bearing coal were explored.Finally,by integrating energy characteristic parameters with damage parameters,a novel brittleness index is proposed.The results demonstrate that the theoretical curves derived from the statistical damage constitutive model closely align with the test curves,accurately reflecting the stress−strain characteristics of gas-bearing coal and revealing the stress drop and softening characteristics of coal in the post-peak stage.The shape parameter and scale parameter represent the brittleness and macroscopic strength of the coal,respectively.As gas pressure increases from 1 to 5 MPa,the shape parameter and the scale parameter decrease by 22.18%and 60.45%,respectively,indicating a reduction in both brittleness and strength of the coal.Parameters such as maximum damage rate and peak elastic energy storage limit positively correlate with coal brittleness.The brittleness index effectively captures the brittleness characteristics and reveals a decrease in brittleness and an increase in sensitivity to plastic deformation under higher gas pressure conditions.展开更多
Coral reef limestone(CRL)constitutes a distinctive marine carbonate formation with complex mechanical properties.This study investigates the multiscale damage and fracture mechanisms of CRL through integrated experime...Coral reef limestone(CRL)constitutes a distinctive marine carbonate formation with complex mechanical properties.This study investigates the multiscale damage and fracture mechanisms of CRL through integrated experimental testing,digital core technology,and theoretical modelling.Two CRL types with contrasting mesostructures were characterized across three scales.Macroscopically,CRL-I and CRL-II exhibited mean compressive strengths of 8.46 and 5.17 MPa,respectively.Mesoscopically,CRL-I featured small-scale highly interconnected pores,whilst CRL-II developed larger stratified pores with diminished connectivity.Microscopically,both CRL matrices demonstrated remarkable similarity in mineral composition and mechanical properties.A novel voxel average-based digital core scaling methodology was developed to facilitate numerical simulation of cross-scale damage processes,revealing network-progressive failure in CRL-I versus directional-brittle failure in CRL-II.Furthermore,a damage statistical constitutive model based on digital core technology and mesoscopic homogenisation theory established quantitative relationships between microelement strength distribution and macroscopic mechanical behavior.These findings illuminate the fundamental mechanisms through which mesoscopic structure governs the macroscopic mechanical properties of CRL.展开更多
Based on statistical damage mechanics,the constitutive model of a rock underthree-dimensional stress was established by the law that the statistical strength of rockmicro-element obeys Weibull distribution.The acousti...Based on statistical damage mechanics,the constitutive model of a rock underthree-dimensional stress was established by the law that the statistical strength of rockmicro-element obeys Weibull distribution.The acoustic emission (AE) evolution model ofrock failure was put forward according to the view that rock damage and AE were consistent.Moreover,in the failure process of rock under three-dimensional stress,the change inrelationship between stress condition parameter and the characteristic parameters of AE,such as the event number and its change rate,were studied.Also,the rock AE characteristicunder uniaxial compression was analyzed in theory and verified with examples.Theresults indicate that the cumulative event number and change rate of AE in rock failure aredetermined by stress state parameter F.Along with the gradual increase of F,first the cumulativeevent number increases gradually,then rapidly,and then slowly after the stresspeak.The form of change rate of an event by increasing F is consistent with the distributionform of rock micro-element strength.The model explained the phenomenon that a relativelyquiet period of AE appears before rock rupture that is observed by many researchersin experiments.Verification examples indicate that the AE evolution model is consistentwith the test results,so the model is reasonable and correct.展开更多
The interaction between soil and marine structures like submarine pipeline/pipe pile/suction caisson is a complicated geotechnical mechanism process.In this study,the interface is discretized into multiple mesoscopic ...The interaction between soil and marine structures like submarine pipeline/pipe pile/suction caisson is a complicated geotechnical mechanism process.In this study,the interface is discretized into multiple mesoscopic contact elements that are damaged randomly throughout the shearing process due to the natural heterogeneity.The evolution equation of damage variable is developed based on the Weibull function,which is able to cover a rather wide range of distribution shapes by only two parameters,making it applicable for varying scenarios.Accordingly,a statistical damage model is established by incorporating Mohr–Coulomb strength criterion,in which the interfacial residual strength is considered whereby the strain softening behavior can be described.A concept of“semi-softening”characteristic point on shear stress–displacement curve is proposed for effectively modeling the evolution of strain softening.Finally,a series of ring shear tests of the interfaces between fine sea sand and smoothough steel surfaces are conducted.The predicted results using the proposed model are compared with experimental data of this study as well as some results from existing literature,indicating that the model has a good performance in modeling the progressive failure and strain softening behavior for various types of soil–structure interfaces.展开更多
This paper developed a statistical damage constitutive model for deep rock by considering the effects of external load and thermal treatment temperature based on the distortion energy.The model parameters were determi...This paper developed a statistical damage constitutive model for deep rock by considering the effects of external load and thermal treatment temperature based on the distortion energy.The model parameters were determined through the extremum features of stress−strain curve.Subsequently,the model predictions were compared with experimental results of marble samples.It is found that when the treatment temperature rises,the coupling damage evolution curve shows an S-shape and the slope of ascending branch gradually decreases during the coupling damage evolution process.At a constant temperature,confining pressure can suppress the expansion of micro-fractures.As the confining pressure increases the rock exhibits ductility characteristics,and the shape of coupling damage curve changes from an S-shape into a quasi-parabolic shape.This model can well characterize the influence of high temperature on the mechanical properties of deep rock and its brittleness-ductility transition characteristics under confining pressure.Also,it is suitable for sandstone and granite,especially in predicting the pre-peak stage and peak stress of stress−strain curve under the coupling action of confining pressure and high temperature.The relevant results can provide a reference for further research on the constitutive relationship of rock-like materials and their engineering applications.展开更多
For the purpose of describing the deformation characteristics of rocks,the effect of volume changes on mechanical properties of rocks should be taken into account with relation to the development of constitutive model...For the purpose of describing the deformation characteristics of rocks,the effect of volume changes on mechanical properties of rocks should be taken into account with relation to the development of constitutive model.Firstly,rocks are divided into three parts,i.e.,voids,a damaged part and an undamaged part in the course of loading.The void ratio was applied to describing the changes of voids or pores during the deformation process.Then,using statistical damage theory,a constitutive model was developed for rocks to describe their strain softening and hardening on the basis of investigating the relationship between the net stress and apparent stress,in which the influence of volume changes on rock behavior was correctly taken into account,such as the initial phase of compaction and the latter stage of dilation.Thirdly,a method of determining model parameters was also presented.Finally,this model was used to compare the theoretical results with those observed from experiments under conventional triaxial loading conditions.展开更多
The damage evolution and dynamic performance of a cement asphalt(CA)mortar layer of slab track subjected to vehicle dynamic load is investigated in this paper.Initially,a statistical damage constitutive model for the ...The damage evolution and dynamic performance of a cement asphalt(CA)mortar layer of slab track subjected to vehicle dynamic load is investigated in this paper.Initially,a statistical damage constitutive model for the CA mortar layer is developed using continuous damage mechanics and probability theory.In this model,the strength of the CA mortar elements is treated as a random variable,which follows the Weibull distribution.The inclusion of strain rate dependence affords considering its influence on the damage development and the transition between viscosity and elasticity.Comparisons with experimental data support the reliability of the model.A three-dimensional finite element(FE)model of a slab track is then created with the commercial software ABAQUS,where the devised model for the CA mortar is implemented as a user-defined material subroutine.Finally,a vertical vehicle model is coupled with the FE model of the slab track,through the wheel-rail contact forces,based on the nonlinear Hertzian contact theory.The evolution of the damage and of the dynamic performance of the CA mortar layer with various initial damage is investigated under the train and track interaction.The analysis indicates that the proposed model is capable of predicting the damage evolution of the CA mortar layer exposed to vehicle dynamic load.The dynamic compressive strain,the strain rate,and the induced damage increase significantly with an increase in the initial damage,whereas the dynamic compressive stress exhibits a sharp decrease with the increasing initial damage.Also,it is found that the strain rate dependence significantly influences the damage evolution and the dynamic behavior of the CA mortar layer.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.52204092).
摘要Principal stress plays a critical role in the deformation and failure process of rock or rock-like materials.However,existing studies indicate that the construction of a damage model based on principal stresses for describing the entire process of three-dimensional rock fracturing is subject to certain limitations and inadequacies.In this study,an innovative three-dimensional statistical damage constitutive model is developed by integrating the principal stress effect with the Gamma distribution function.This model effectively captures the complete damage evolution process of rock materials with initial defects through the introduction of a compaction correction coefficient and a residual strength correction term.Notably,the simulation accuracy is significantly enhanced in both the initial compaction stage and the post-peak residual strength stage.The parameter θ serves as an indicator of the material brittle-to-ductile transition,whereas the parameter k reflects the material's strength characteristics.The parameter calibration process consists of three steps:determining the θ value on the basis of the rock brittleness index,deriving the k parameter from the k value growth curve,and finally establishing the peak-residual strength prediction equation under given confining pressure conditions.Compared with the traditional statistical damage model based on the Weibull distribution,this model not only features clear physical significance and a simplified calculation procedure but also contributes to the advancement of the three-dimensional damage fracture theory system for rock mechanics.Moreover,it offers a robust framework for evaluating the mechanical response of rocks under varying confining pressures,which has significant implications for safe design and risk assessment in civil engineering or rock engineering.
基金funded by the National Natural Science Foundation of China(No.52374109)the Science and Technology Research and Development Program Project of China Railway Group Limited(Major projects,No.2023-Major projects-07)the Hunan Provincial Innovation Foundation for Postgraduate,China(No.CX20230223)。
摘要Uniaxial compression tests combined with acoustic emission(AE)monitoring were conducted on the sandstone and concrete specimens to measure the physical and mechanical properties and analyze the damage evolution after heating test.A modified thermal-mechanical statistical damage constitutive model was established by K-means++clustering algorithm for determining the proportion of tensile and shear cracks in AE data and for defining the new tensile and shear mechanical damage factors of the Weibull distribution.This model is verified to be valid by good agreement with the experimental results.
基金Project(52274096)supported by the National Natural Science Foundation of ChinaProject(WS2023A03)supported by the State Key Laboratory Cultivation Base for Gas Geology and Gas Control,China。
摘要Accurate assessment of coal brittleness is crucial in the design of coal seam drilling and underground coal mining operations.This study proposes a method for evaluating the brittleness of gas-bearing coal based on a statistical damage constitutive model and energy evolution mechanisms.Initially,integrating the principle of effective stress and the Hoek-Brown criterion,a statistical damage constitutive model for gas-bearing coal is established and validated through triaxial compression tests under different gas pressures to verify its accuracy and applicability.Subsequently,employing energy evolution mechanism,two energy characteristic parameters(elastic energy proportion and dissipated energy proportion)are analyzed.Based on the damage stress thresholds,the damage evolution characteristics of gas bearing coal were explored.Finally,by integrating energy characteristic parameters with damage parameters,a novel brittleness index is proposed.The results demonstrate that the theoretical curves derived from the statistical damage constitutive model closely align with the test curves,accurately reflecting the stress−strain characteristics of gas-bearing coal and revealing the stress drop and softening characteristics of coal in the post-peak stage.The shape parameter and scale parameter represent the brittleness and macroscopic strength of the coal,respectively.As gas pressure increases from 1 to 5 MPa,the shape parameter and the scale parameter decrease by 22.18%and 60.45%,respectively,indicating a reduction in both brittleness and strength of the coal.Parameters such as maximum damage rate and peak elastic energy storage limit positively correlate with coal brittleness.The brittleness index effectively captures the brittleness characteristics and reveals a decrease in brittleness and an increase in sensitivity to plastic deformation under higher gas pressure conditions.
基金National Key Research and Development Program of China (No.2021YFC3100800)the National Natural Science Foundation of China (Nos.42407235 and 42271026)+1 种基金the Project of Sanya Yazhou Bay Science and Technology City (No.SCKJ-JYRC-2023-54)supported by the Hefei advanced computing center
摘要Coral reef limestone(CRL)constitutes a distinctive marine carbonate formation with complex mechanical properties.This study investigates the multiscale damage and fracture mechanisms of CRL through integrated experimental testing,digital core technology,and theoretical modelling.Two CRL types with contrasting mesostructures were characterized across three scales.Macroscopically,CRL-I and CRL-II exhibited mean compressive strengths of 8.46 and 5.17 MPa,respectively.Mesoscopically,CRL-I featured small-scale highly interconnected pores,whilst CRL-II developed larger stratified pores with diminished connectivity.Microscopically,both CRL matrices demonstrated remarkable similarity in mineral composition and mechanical properties.A novel voxel average-based digital core scaling methodology was developed to facilitate numerical simulation of cross-scale damage processes,revealing network-progressive failure in CRL-I versus directional-brittle failure in CRL-II.Furthermore,a damage statistical constitutive model based on digital core technology and mesoscopic homogenisation theory established quantitative relationships between microelement strength distribution and macroscopic mechanical behavior.These findings illuminate the fundamental mechanisms through which mesoscopic structure governs the macroscopic mechanical properties of CRL.
基金Supported by the Key Program of National Basic Research Program(973)of China(2005CB221505)the National Natural Science Foundation of China(2005E041503)
摘要Based on statistical damage mechanics,the constitutive model of a rock underthree-dimensional stress was established by the law that the statistical strength of rockmicro-element obeys Weibull distribution.The acoustic emission (AE) evolution model ofrock failure was put forward according to the view that rock damage and AE were consistent.Moreover,in the failure process of rock under three-dimensional stress,the change inrelationship between stress condition parameter and the characteristic parameters of AE,such as the event number and its change rate,were studied.Also,the rock AE characteristicunder uniaxial compression was analyzed in theory and verified with examples.Theresults indicate that the cumulative event number and change rate of AE in rock failure aredetermined by stress state parameter F.Along with the gradual increase of F,first the cumulativeevent number increases gradually,then rapidly,and then slowly after the stresspeak.The form of change rate of an event by increasing F is consistent with the distributionform of rock micro-element strength.The model explained the phenomenon that a relativelyquiet period of AE appears before rock rupture that is observed by many researchersin experiments.Verification examples indicate that the AE evolution model is consistentwith the test results,so the model is reasonable and correct.
基金financially supported by the China Postdoctoral Science Foundation(Grant No.2023M732997)the National Natural Science Foundation of China(Grant Nos.51890912,52008268)Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering,Hohai University(Grant No.2023007)。
摘要The interaction between soil and marine structures like submarine pipeline/pipe pile/suction caisson is a complicated geotechnical mechanism process.In this study,the interface is discretized into multiple mesoscopic contact elements that are damaged randomly throughout the shearing process due to the natural heterogeneity.The evolution equation of damage variable is developed based on the Weibull function,which is able to cover a rather wide range of distribution shapes by only two parameters,making it applicable for varying scenarios.Accordingly,a statistical damage model is established by incorporating Mohr–Coulomb strength criterion,in which the interfacial residual strength is considered whereby the strain softening behavior can be described.A concept of“semi-softening”characteristic point on shear stress–displacement curve is proposed for effectively modeling the evolution of strain softening.Finally,a series of ring shear tests of the interfaces between fine sea sand and smoothough steel surfaces are conducted.The predicted results using the proposed model are compared with experimental data of this study as well as some results from existing literature,indicating that the model has a good performance in modeling the progressive failure and strain softening behavior for various types of soil–structure interfaces.
基金Project(11272119)supported by the National Natural Science Foundation of China。
摘要This paper developed a statistical damage constitutive model for deep rock by considering the effects of external load and thermal treatment temperature based on the distortion energy.The model parameters were determined through the extremum features of stress−strain curve.Subsequently,the model predictions were compared with experimental results of marble samples.It is found that when the treatment temperature rises,the coupling damage evolution curve shows an S-shape and the slope of ascending branch gradually decreases during the coupling damage evolution process.At a constant temperature,confining pressure can suppress the expansion of micro-fractures.As the confining pressure increases the rock exhibits ductility characteristics,and the shape of coupling damage curve changes from an S-shape into a quasi-parabolic shape.This model can well characterize the influence of high temperature on the mechanical properties of deep rock and its brittleness-ductility transition characteristics under confining pressure.Also,it is suitable for sandstone and granite,especially in predicting the pre-peak stage and peak stress of stress−strain curve under the coupling action of confining pressure and high temperature.The relevant results can provide a reference for further research on the constitutive relationship of rock-like materials and their engineering applications.
基金Project(2006AA11Z104) supported by the National High-Tech Research and Development Program of China
摘要For the purpose of describing the deformation characteristics of rocks,the effect of volume changes on mechanical properties of rocks should be taken into account with relation to the development of constitutive model.Firstly,rocks are divided into three parts,i.e.,voids,a damaged part and an undamaged part in the course of loading.The void ratio was applied to describing the changes of voids or pores during the deformation process.Then,using statistical damage theory,a constitutive model was developed for rocks to describe their strain softening and hardening on the basis of investigating the relationship between the net stress and apparent stress,in which the influence of volume changes on rock behavior was correctly taken into account,such as the initial phase of compaction and the latter stage of dilation.Thirdly,a method of determining model parameters was also presented.Finally,this model was used to compare the theoretical results with those observed from experiments under conventional triaxial loading conditions.
基金supported by the National Basic Research Program of China("973"Project)(Grant Nos.2013CB036202,2013CB036200)the National Natural Science Foundation of China(Grant No.51008254)+3 种基金the Funds from the Key Laboratory for Precision&Non-traditional Machining of the Ministry of Education,Dalian University of Technology(Grant No.JMTZ201002)the Fundamental Research Funds for the Central Universities(Grant No.2682013CX029)the Funds from the China Scholarship Councilthe 2013 Cultivation Program for the Excellent Doctoral Dissertation of Southwest Jiaotong University
摘要The damage evolution and dynamic performance of a cement asphalt(CA)mortar layer of slab track subjected to vehicle dynamic load is investigated in this paper.Initially,a statistical damage constitutive model for the CA mortar layer is developed using continuous damage mechanics and probability theory.In this model,the strength of the CA mortar elements is treated as a random variable,which follows the Weibull distribution.The inclusion of strain rate dependence affords considering its influence on the damage development and the transition between viscosity and elasticity.Comparisons with experimental data support the reliability of the model.A three-dimensional finite element(FE)model of a slab track is then created with the commercial software ABAQUS,where the devised model for the CA mortar is implemented as a user-defined material subroutine.Finally,a vertical vehicle model is coupled with the FE model of the slab track,through the wheel-rail contact forces,based on the nonlinear Hertzian contact theory.The evolution of the damage and of the dynamic performance of the CA mortar layer with various initial damage is investigated under the train and track interaction.The analysis indicates that the proposed model is capable of predicting the damage evolution of the CA mortar layer exposed to vehicle dynamic load.The dynamic compressive strain,the strain rate,and the induced damage increase significantly with an increase in the initial damage,whereas the dynamic compressive stress exhibits a sharp decrease with the increasing initial damage.Also,it is found that the strain rate dependence significantly influences the damage evolution and the dynamic behavior of the CA mortar layer.