The three-dimensional （3D） crack propagation is a hot issue in rock mechanics. To properly simulate 3D crack propagation, a modified maximum tangential tensile stress criterion is proposed. In this modified criterio...The three-dimensional （3D） crack propagation is a hot issue in rock mechanics. To properly simulate 3D crack propagation, a modified maximum tangential tensile stress criterion is proposed. In this modified criterion, it is supposed that cracks propagate only at crack front in the principal normal plane. The tangential tensile stress at crack front in the principal normal plane in local coordinates is employed to determine crack propagation, which is calculated through coordinate transformation from global to local coordinates. New cracks will propagate when the maximum tangential tensile stress at crack front in the principal normal plane reaches the tensile strength of rock-like materials. Compared with the previous crack propagation criteria, the modified crack propagation criterion is helpful in calculating 3D crack stress intensity factor, and can overcome the limitations of propagation step determined by individual experiences in previous studies. Finally, the 3D crack propagation process is traced by element-free Galerkin method. The numerical results agree well with the experimental ones for a frozen resin sample with prefabricated 3D cracks.展开更多
A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the ...A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the two contacted surfaces of the crack must be satisfied.A simple iterative method was adopted in order to consider three different states of cracks.Under the assumption that the advance of the point on the crack front would occur only in the normal plane which is through this edge point,the maximum energy release rate criterion is modified to be used as the criterion for the crack growth.With discretization,the process of crack propagation can be seen as the advance of the vertices of the crack front.The program MCP3D was developed based on these theories to simulate the 3D quasi-static crack propagation.A numerical example of a penny-shaped crack subject to tension and compression in an infinite elastic media was analyzed with MCP3D,and the results in comparison with others' show that the present method for 3D crack propagation is effective.展开更多
Soil-rock mixture （SRM） is a unique type of geomaterial characterized by a heterogeneous composition and a complicated structure. It is intractable for the continuum-based soil and rock mechanics theories to accurat...Soil-rock mixture （SRM） is a unique type of geomaterial characterized by a heterogeneous composition and a complicated structure. It is intractable for the continuum-based soil and rock mechanics theories to accurately characterize and predict the SRM＇s mechanical properties. This study reports a novel numerical method incorporating microfocus computed tomography and PFC3D codes to probe the deformation and failure processes of SRM. The three-dimensional （3D） PFC models that represent the SRM＇s complex structures were built. By simulating the entire failure process in PFC3D, the SRM＇s strength, elastic modulus and crack growth were obtained. The influence of rock ratios on the SRM＇s strength, deformation and failure processes, as well as its internal mesoscale mechanism, were analyzed. By comparing simulation results with experimental data, it was verified that the 3D PFC models were in good agreement with SRM＇s real structure and the SRM＇s compression process, deformation and failure patterns; its intrinsic mesomechanism can be effectively analyzed based on such 3D PFC models.展开更多
The prediction on small disturbance propagation in complex three-dimensional(3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the lin...The prediction on small disturbance propagation in complex three-dimensional(3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory(LST) with the equivalent spanwise wavenumber correction(ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.展开更多
J-integral has served as a powerful tool in characterizing crack tip status. The main feature, i.e. path- independence, makes it one of the foremost fracture parameters. In order to remain the path- independence for f...J-integral has served as a powerful tool in characterizing crack tip status. The main feature, i.e. path- independence, makes it one of the foremost fracture parameters. In order to remain the path- independence for fluid-driven cracks, J-integral is revised. In this paper, we present an extended J-in- tegral explicitly for fluid-driven cracks, e.g. hydraulically induced fractures in petroleum reservoirs, for three-dimensional （3D） problems. Particularly, point-wise 3D extended J-integral is proposed to char- acterize the state of a point along crack front. Besides, applications of the extended J-integral to porous media and thermally induced stress conditions are explored. Numerical results show that the extended J- integral is indeed path-independent, and they are in good agreement with those of equivalent domain integral under linear elastic and elastoplastic conditions. In addition, two distance-independent circular integrals in the K-dominance zone are established, which can be used to calculate the stress intensity factor （SIF）.展开更多
In this work, a novel numerical method is developed for simulating arbitrary crack growth in pipes with the idea of enriched shape functions which can represent the discontinuity independent of the mesh. The concept o...In this work, a novel numerical method is developed for simulating arbitrary crack growth in pipes with the idea of enriched shape functions which can represent the discontinuity independent of the mesh. The concept of the enriched shape functions is introduced into the continuum-based (CB) shell element. Due to the advantage of CB shell element, the shell thickness varia- tion and surface connection can be concerned during the deformation. The stress intensity factors of the crack in the CB shell element are calculated by using the 'equivalent domain integral' method for 3D arbitrary non-planar crack. The maximum en- ergy release rate is used as a propagation criterion. This method is proved able to capture arbitrary crack growth path in pipes which is independent of the element mesh. Numerical examples of different fracture patterns in pipes are presented here.展开更多
The study of rock crack propagation by multi-scale method is of great significance to comprehensively and accurately understand the law of rock crack evolution.In this paper,the theoretical,experimental and numerical ...The study of rock crack propagation by multi-scale method is of great significance to comprehensively and accurately understand the law of rock crack evolution.In this paper,the theoretical,experimental and numerical methods from macroscale,mesoscale and microscale used for crack propagation in recent years are summarized and analyzed.Firstly,the evolution mechanism of the crack and the related research status are analyzed from a single scale.Secondly,multi-scale theory,modeling,meshing algorithm and macro-mesoscopic parameters are reviewed in the multi-scale coupling method.Through the analysis of the results published in recent years,it is considered that the following aspects need to be further studied:the characteristic parameters of the rock are different at different scales,so the extraction of the characteristic parameters under different scales is essential to modeling and coupling;the heterogeneity of rock and the prefabrication of cracks are greatly affected by human factors,so that 3D printing will be a good breakthrough to build the model of crack owing to its accurate control on the distribution and the size of cracks.The internal stress field of the rock is complex and varied,and the generation and expansion of the microcracks in the process of crack propagation are closely related to the surrounding environment.Therefore,it is of great importance to combine theoretical,experimental and numerical research with practical engineering.展开更多
基金Supported by the National Natural Science Foundation of China (50979052,40872203, 41072234)the Provincial Natural Science Foundation of Shandong (ZR2009FM041,ZR2010EM032,ZR2009AZ001)
文摘The three-dimensional （3D） crack propagation is a hot issue in rock mechanics. To properly simulate 3D crack propagation, a modified maximum tangential tensile stress criterion is proposed. In this modified criterion, it is supposed that cracks propagate only at crack front in the principal normal plane. The tangential tensile stress at crack front in the principal normal plane in local coordinates is employed to determine crack propagation, which is calculated through coordinate transformation from global to local coordinates. New cracks will propagate when the maximum tangential tensile stress at crack front in the principal normal plane reaches the tensile strength of rock-like materials. Compared with the previous crack propagation criteria, the modified crack propagation criterion is helpful in calculating 3D crack stress intensity factor, and can overcome the limitations of propagation step determined by individual experiences in previous studies. Finally, the 3D crack propagation process is traced by element-free Galerkin method. The numerical results agree well with the experimental ones for a frozen resin sample with prefabricated 3D cracks.
文摘A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the two contacted surfaces of the crack must be satisfied.A simple iterative method was adopted in order to consider three different states of cracks.Under the assumption that the advance of the point on the crack front would occur only in the normal plane which is through this edge point,the maximum energy release rate criterion is modified to be used as the criterion for the crack growth.With discretization,the process of crack propagation can be seen as the advance of the vertices of the crack front.The program MCP3D was developed based on these theories to simulate the 3D quasi-static crack propagation.A numerical example of a penny-shaped crack subject to tension and compression in an infinite elastic media was analyzed with MCP3D,and the results in comparison with others' show that the present method for 3D crack propagation is effective.
基金Acknowledgements The authors gratefully acknowledge the financial support from the State Key Research Development Program of China （Grant No. 2016YFC0600705）, the National Natural Science Foundation of China （Grant Nos. 51674251, 51727807, 51374213）, the National Natural Science Foundation for Distinguished Young Scholars of China （Grant No. 51125017）, the Fund for Creative Research and Development Group Program of Jiangsu Province （Grant No. 2014-27）, and the Priority Academic Program Development of Jiangsu Higher Education Institutions （Grant No. PAPD2014）, and an open project sponsored by the State Key Labo- ratory for Geomechanics and Deep Underground Engineering （Grant SKLGDUE K1318） for their financial support.
文摘Soil-rock mixture （SRM） is a unique type of geomaterial characterized by a heterogeneous composition and a complicated structure. It is intractable for the continuum-based soil and rock mechanics theories to accurately characterize and predict the SRM＇s mechanical properties. This study reports a novel numerical method incorporating microfocus computed tomography and PFC3D codes to probe the deformation and failure processes of SRM. The three-dimensional （3D） PFC models that represent the SRM＇s complex structures were built. By simulating the entire failure process in PFC3D, the SRM＇s strength, elastic modulus and crack growth were obtained. The influence of rock ratios on the SRM＇s strength, deformation and failure processes, as well as its internal mesoscale mechanism, were analyzed. By comparing simulation results with experimental data, it was verified that the 3D PFC models were in good agreement with SRM＇s real structure and the SRM＇s compression process, deformation and failure patterns; its intrinsic mesomechanism can be effectively analyzed based on such 3D PFC models.
基金Project supported by the National Key Research and Development(R&D)Program of China(No.2016YFA0401200)the National Natural Science Foundation of China(Nos.11402167,11332007,11672204,11672205,and 11732011)
文摘The prediction on small disturbance propagation in complex three-dimensional(3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory(LST) with the equivalent spanwise wavenumber correction(ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.
文摘J-integral has served as a powerful tool in characterizing crack tip status. The main feature, i.e. path- independence, makes it one of the foremost fracture parameters. In order to remain the path- independence for fluid-driven cracks, J-integral is revised. In this paper, we present an extended J-in- tegral explicitly for fluid-driven cracks, e.g. hydraulically induced fractures in petroleum reservoirs, for three-dimensional （3D） problems. Particularly, point-wise 3D extended J-integral is proposed to char- acterize the state of a point along crack front. Besides, applications of the extended J-integral to porous media and thermally induced stress conditions are explored. Numerical results show that the extended J- integral is indeed path-independent, and they are in good agreement with those of equivalent domain integral under linear elastic and elastoplastic conditions. In addition, two distance-independent circular integrals in the K-dominance zone are established, which can be used to calculate the stress intensity factor （SIF）.
基金supported by the National Natural Science Foundation of China (Grant No. 11011140335)
文摘In this work, a novel numerical method is developed for simulating arbitrary crack growth in pipes with the idea of enriched shape functions which can represent the discontinuity independent of the mesh. The concept of the enriched shape functions is introduced into the continuum-based (CB) shell element. Due to the advantage of CB shell element, the shell thickness varia- tion and surface connection can be concerned during the deformation. The stress intensity factors of the crack in the CB shell element are calculated by using the 'equivalent domain integral' method for 3D arbitrary non-planar crack. The maximum en- ergy release rate is used as a propagation criterion. This method is proved able to capture arbitrary crack growth path in pipes which is independent of the element mesh. Numerical examples of different fracture patterns in pipes are presented here.
基金This paper is financially supported by National Science and Technology Major Project of China under Grant no.2017ZX 05013006.
文摘The study of rock crack propagation by multi-scale method is of great significance to comprehensively and accurately understand the law of rock crack evolution.In this paper,the theoretical,experimental and numerical methods from macroscale,mesoscale and microscale used for crack propagation in recent years are summarized and analyzed.Firstly,the evolution mechanism of the crack and the related research status are analyzed from a single scale.Secondly,multi-scale theory,modeling,meshing algorithm and macro-mesoscopic parameters are reviewed in the multi-scale coupling method.Through the analysis of the results published in recent years,it is considered that the following aspects need to be further studied:the characteristic parameters of the rock are different at different scales,so the extraction of the characteristic parameters under different scales is essential to modeling and coupling;the heterogeneity of rock and the prefabrication of cracks are greatly affected by human factors,so that 3D printing will be a good breakthrough to build the model of crack owing to its accurate control on the distribution and the size of cracks.The internal stress field of the rock is complex and varied,and the generation and expansion of the microcracks in the process of crack propagation are closely related to the surrounding environment.Therefore,it is of great importance to combine theoretical,experimental and numerical research with practical engineering.
