A wave equation of rock under axial static stress is established using the equivalent medium method by modifying the Kelvin-Voigt model.The analytical formulas of longitudinal velocity,space and time attenuation coeff...A wave equation of rock under axial static stress is established using the equivalent medium method by modifying the Kelvin-Voigt model.The analytical formulas of longitudinal velocity,space and time attenuation coefficients and response frequency are obtained by solving the equation using the harmonic method.A series of experiments on stress wave propagation through rock under different axial static stresses have been conducted.The proposed models of stress wave propagation are then verified by comparing experimental results with theoretical solutions.Based on the verified theoretical models,the influences of axial static stress on longitudinal velocity,space and time attenuation coefficients and response frequency are investigated by detailed parametric studies.The results show that the proposed theoretical models can be used to effectively investigate the effects of axial static stress on the stress wave propagation in rock.The axial static stress influences stress wave propagation characteristics of porous rock by varying the level of rock porosity and damage.Moreover,the initial porosity,initial elastic modulus of the rock voids and skeleton,viscous coefficient and vibration frequency have significant effects on the P-wave velocity,attenuation characteristics and response frequency of the stress wave in porous rock under axial static stress.展开更多
An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primar...An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as 'macro-joints',while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as 'micro-defects'.The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass (ERM) from the conventional displacement discontinuity method (CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored.展开更多
Water-bearing rocks exposed to freezing temperature can be subjected to freezeethaw cycles leading tocrack initiation and propagation, which are the main causes of frost damage to rocks. Based on theGriffith theory of...Water-bearing rocks exposed to freezing temperature can be subjected to freezeethaw cycles leading tocrack initiation and propagation, which are the main causes of frost damage to rocks. Based on theGriffith theory of brittle fracture mechanics, the crack initiation criterion, propagation direction, andcrack length under freezing pressure and far-field stress are analyzed. Furthermore, a calculation methodis proposed for the stress intensity factor （SIF） of the crack tip under non-uniformly distributed freezingpressure. The formulae for the crack/fracture propagation direction and length of the wing crack underfreezing pressure are obtained, and the mechanism for coalescence of adjacent cracks is investigated.In addition, the necessary conditions for different coalescence modes of cracks are studied. Using thetopology theory, a new algorithm for frost crack propagation is proposed, which has the capability todefine the crack growth path and identify and update the cracked elements. A model that incorporatesmultiple cracks is built by ANSYS and then imported into FLAC3D. The SIFs are then calculated using aFISH procedure, and the growth path of the freezing cracks after several calculation steps is demonstratedusing the new algorithm. The proposed method can be applied to rocks containing fillings such asdetritus and slurry. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.展开更多
Using molecular dynamics （MD） simulation, we study the thermal shock behavior of tungsten （W）, which has been used for the plasma facing material （PFM） of tokamaks. The thermo-elastic stress wave, corresponding ...Using molecular dynamics （MD） simulation, we study the thermal shock behavior of tungsten （W）, which has been used for the plasma facing material （PFM） of tokamaks. The thermo-elastic stress wave, corresponding to the collective displacement of atoms, is analyzed with the Lagrangian atomic stress method, of which the reliability is also analyzed. The stress wave velocity corresponds to the speed of sound in the material, which is not dependent on the thermal shock energy. The peak pressure of a normal stress wave increases with the increase of thermal shock energy. We analyze the temperature evolution of the thermal shock region according to the Fourier transformation. It can be seen that the “obvious” velocity of heat propagation is less than the velocity of the stress wave; further, that the thermo-elastic stress wave may contribute little to the transport of kinetic energy. The heat propagation can be described properly by the heat conduction equation. These results may be useful for understanding the process of the thermal shock of tungsten.展开更多
This paper studies the stress-sirain field near crack tip in a pure bending beam ofrectangular section with one-sided mode I crack by the analytic method of Rej [1],then it gives the stress and strain components at th...This paper studies the stress-sirain field near crack tip in a pure bending beam ofrectangular section with one-sided mode I crack by the analytic method of Rej [1],then it gives the stress and strain components at the crack tip when the crackpropagates and further it obtains the formulas of calculating the elastic deformed areawidth, the deformed intensity, area width and the equation groups of calculating thecritical stress of crack propagation, last the equation group of calculating criticalstress of crack propagation is verified by calculating instance. The maximum error is0. 18%.展开更多
Complex weak structural planes and fault zones induce significant heterogeneity,discontinuity,and nonlinear characteristics of a rock mass.When an earthquake occurs,these characteristics lead to extremely complex seis...Complex weak structural planes and fault zones induce significant heterogeneity,discontinuity,and nonlinear characteristics of a rock mass.When an earthquake occurs,these characteristics lead to extremely complex seismic wave propagation and vibrational behaviors and thus pose a huge threat to the safety and stability of deep buried tunnels.To investigate the wave propagation in a rock mass with different structural planes and fault zones,this study first introduced the theory of elastic wave propagation and elastodynamic principles and used the Zoeppritz equation to describe wave field decomposition and develop a seismic wave response model accordingly.Then,a physical wave propagation model was constructed to investigate seismic waves passing through a fault,and dynamic damage was analyzed by using shaking table tests.Finally,stress wave attenuation and dynamic incompatible deformation mechanisms in a rock mass with fault zones were explored.The results indicate that under the action of weak structural planes,stress waves appear as a complex wave field decomposition phenomenon.When a stress wave spreads to a weak structural plane,its scattering may transform into a tensile wave,generating tensile stress and destabilizing the rock mass;wave dynamic energy is absorbed by a low-strength rock through wave scattering,which significantly weakens the seismic load.Wave propagation accelerates the initiation and expansion of internal defects in the rock mass and leads to a dynamic incompatible deformation.This is one of the main causes for large deformation and even instability within rock masses.These findings provide an important reference and guide with respect to stability analysis of rock mass with weak structural planes and fault zones.展开更多
Elastic wave refraction at the air-solid interface and wave propagations in the vicinity of the air-solid interface are numerically studied.The modified ghost fluid method(MGFM)and isobaric fix methods are combined to...Elastic wave refraction at the air-solid interface and wave propagations in the vicinity of the air-solid interface are numerically studied.The modified ghost fluid method(MGFM)and isobaric fix methods are combined to solve the fluid and solid statuses at the air-solid interface and construct a continuous boundary condition for the air-solid interface.The states in the ghost domain are evaluated by the MGFM-algorithm.The solid governing equations are solved with second order spatial discretization.Numerical tests verify the correctness of the presented continuous boundary condition and show that the combined method is convergent in the vicinity of the air-solid interface.The 3D numerical results by the combined method are close to those of the ArbitraryLagrangian-Eulerian(ALE)method.The combined method is robust when applied for multi-dimensional problems.A compression stress wave impacting on the air-solid interface result in a compression wave in air.A tension stress wave impacting on the air-solid interface result in an expansion wave in air.展开更多
Under the condition that any perfeetly plastic stress components at a crack tip are nothing but the Junctions of 0 only, making use of equilibriumequations,Hill ani.sutropic yield condition and unloading stress-strain...Under the condition that any perfeetly plastic stress components at a crack tip are nothing but the Junctions of 0 only, making use of equilibriumequations,Hill ani.sutropic yield condition and unloading stress-strain relations, in this paper, we derive the general analytical expressions of anisotropic plastiestress Jields at the slowly steadyhe slowly steady propagatin tips of plane and anti-phane strain,Applying these general analytical expressions to the concrete cracks the attchvtical expressions of anisotropie plastic stress fields at the slowly steady propagating tips of Motle I and Motle III cracks are obtained. For the isolropic plastic material, the anisotropic plastic stress fields at a slowly propagating crack tip become the perfeeby plastic mress fields展开更多
The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special fe...The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.展开更多
The full-field strain of rock material under dynamic compression load was studied using the high-speed three dimensional digital image correlation(3D-DIC)method.The dynamic test was conducted on Laizhou granite using ...The full-field strain of rock material under dynamic compression load was studied using the high-speed three dimensional digital image correlation(3D-DIC)method.The dynamic test was conducted on Laizhou granite using a split Hopkinson pressure bar(SHPB)method.Wave propagation,dispersion and radial inertial effect on the specimen were found by DIC results.A recovery of strain in the post-peak stage was detected on the specimen by DIC,which was unrevealed in the traditional one-dimensional theory method.It can be found that the strain measured by strain gauge was a calculated average one,whereas the strain measured by 3D-DIC could reflect more variation details.Specifically,the testing principle with impact loads and rock dynamic behavior was re-examined using stress wave propagation theory.The theoretical results showed that the specimen reached equilibrium after a series of wave reflections and transmissions and its stress was infinitely close to the initial value of 109.2 MPa.Moreover,the specimen had the calculated maximum strain of 0.52% and strain rate of 15.11 s^(-1),improving the reasonable agreement with the experimental results and requirements of rock mechanical properties measured by SHPB technology.展开更多
Numerical simulations of longitudinal wave propagation in a rock bar with microcracks are conducted by using the numerical manifold method which has great advantages in the simulation of discontinuities.Firstly,valida...Numerical simulations of longitudinal wave propagation in a rock bar with microcracks are conducted by using the numerical manifold method which has great advantages in the simulation of discontinuities.Firstly,validation of the numerical manifold method is carried out by simulations of a longitudinal stress wave propagating through intact and cracked rock bars.The behavior of the stress wave traveling in a one-dimensional rock bar with randomly distributed microcracks is subsequently studied.It is revealed that the highly defected rock bar has significant viscoelasticity to the stress wave propagation.Wave attenuation as well as time delay is affected by the length,quantity,specific stiffness of the distributed microcracks as well as the incident stress wave frequency.The storage and loss moduli of the defected rock are also affected by the microcrack properties;however,they are independent of incident stress wave frequency.展开更多
基金Projects(51664017,51964015)supported by the National Natural Science Foundation of ChinaProject(JXUSTQJBJ2017007)supported by the Program of Qingjiang Excellent Young Talents of Jiangxi University of Science and Technology,ChinaProjects(GJJ160616,GJJ171490)supported by Science and Technology Project of Jiangxi Provincial Department of Education,China
文摘A wave equation of rock under axial static stress is established using the equivalent medium method by modifying the Kelvin-Voigt model.The analytical formulas of longitudinal velocity,space and time attenuation coefficients and response frequency are obtained by solving the equation using the harmonic method.A series of experiments on stress wave propagation through rock under different axial static stresses have been conducted.The proposed models of stress wave propagation are then verified by comparing experimental results with theoretical solutions.Based on the verified theoretical models,the influences of axial static stress on longitudinal velocity,space and time attenuation coefficients and response frequency are investigated by detailed parametric studies.The results show that the proposed theoretical models can be used to effectively investigate the effects of axial static stress on the stress wave propagation in rock.The axial static stress influences stress wave propagation characteristics of porous rock by varying the level of rock porosity and damage.Moreover,the initial porosity,initial elastic modulus of the rock voids and skeleton,viscous coefficient and vibration frequency have significant effects on the P-wave velocity,attenuation characteristics and response frequency of the stress wave in porous rock under axial static stress.
文摘An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as 'macro-joints',while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as 'micro-defects'.The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass (ERM) from the conventional displacement discontinuity method (CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored.
基金the financial support from the National Natural Science Foundation of China (Grant Nos.41302237 and 41130742)the State Key Development Program for Basic Research of China (Grant No.2014CB046900)
文摘Water-bearing rocks exposed to freezing temperature can be subjected to freezeethaw cycles leading tocrack initiation and propagation, which are the main causes of frost damage to rocks. Based on theGriffith theory of brittle fracture mechanics, the crack initiation criterion, propagation direction, andcrack length under freezing pressure and far-field stress are analyzed. Furthermore, a calculation methodis proposed for the stress intensity factor （SIF） of the crack tip under non-uniformly distributed freezingpressure. The formulae for the crack/fracture propagation direction and length of the wing crack underfreezing pressure are obtained, and the mechanism for coalescence of adjacent cracks is investigated.In addition, the necessary conditions for different coalescence modes of cracks are studied. Using thetopology theory, a new algorithm for frost crack propagation is proposed, which has the capability todefine the crack growth path and identify and update the cracked elements. A model that incorporatesmultiple cracks is built by ANSYS and then imported into FLAC3D. The SIFs are then calculated using aFISH procedure, and the growth path of the freezing cracks after several calculation steps is demonstratedusing the new algorithm. The proposed method can be applied to rocks containing fillings such asdetritus and slurry. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.
基金Project supported by the National Magnetic Confinement Fusion Science Program of China(Grant No.2013GB109004)the National Natural Science Foundation of China(Grant Nos.51071095 and 50971077)
文摘Using molecular dynamics （MD） simulation, we study the thermal shock behavior of tungsten （W）, which has been used for the plasma facing material （PFM） of tokamaks. The thermo-elastic stress wave, corresponding to the collective displacement of atoms, is analyzed with the Lagrangian atomic stress method, of which the reliability is also analyzed. The stress wave velocity corresponds to the speed of sound in the material, which is not dependent on the thermal shock energy. The peak pressure of a normal stress wave increases with the increase of thermal shock energy. We analyze the temperature evolution of the thermal shock region according to the Fourier transformation. It can be seen that the “obvious” velocity of heat propagation is less than the velocity of the stress wave; further, that the thermo-elastic stress wave may contribute little to the transport of kinetic energy. The heat propagation can be described properly by the heat conduction equation. These results may be useful for understanding the process of the thermal shock of tungsten.
文摘This paper studies the stress-sirain field near crack tip in a pure bending beam ofrectangular section with one-sided mode I crack by the analytic method of Rej [1],then it gives the stress and strain components at the crack tip when the crackpropagates and further it obtains the formulas of calculating the elastic deformed areawidth, the deformed intensity, area width and the equation groups of calculating thecritical stress of crack propagation, last the equation group of calculating criticalstress of crack propagation is verified by calculating instance. The maximum error is0. 18%.
基金Fundamental Research Funds for the Central Universities,Grant/Award Number:B220202058National Natural Science Foundation of China,Grant/Award Number:41831278+1 种基金National Basic Research Program of China(973 Program),Grant/Award Number:2015CB057903ARC Future Fellowship,Grant/Award Number:FT140100019。
文摘Complex weak structural planes and fault zones induce significant heterogeneity,discontinuity,and nonlinear characteristics of a rock mass.When an earthquake occurs,these characteristics lead to extremely complex seismic wave propagation and vibrational behaviors and thus pose a huge threat to the safety and stability of deep buried tunnels.To investigate the wave propagation in a rock mass with different structural planes and fault zones,this study first introduced the theory of elastic wave propagation and elastodynamic principles and used the Zoeppritz equation to describe wave field decomposition and develop a seismic wave response model accordingly.Then,a physical wave propagation model was constructed to investigate seismic waves passing through a fault,and dynamic damage was analyzed by using shaking table tests.Finally,stress wave attenuation and dynamic incompatible deformation mechanisms in a rock mass with fault zones were explored.The results indicate that under the action of weak structural planes,stress waves appear as a complex wave field decomposition phenomenon.When a stress wave spreads to a weak structural plane,its scattering may transform into a tensile wave,generating tensile stress and destabilizing the rock mass;wave dynamic energy is absorbed by a low-strength rock through wave scattering,which significantly weakens the seismic load.Wave propagation accelerates the initiation and expansion of internal defects in the rock mass and leads to a dynamic incompatible deformation.This is one of the main causes for large deformation and even instability within rock masses.These findings provide an important reference and guide with respect to stability analysis of rock mass with weak structural planes and fault zones.
基金Supported by Science Foundation of Huaihai Institute of Technology(Z2016014)Initial Funding for Doctoral Research of Huaihai Institute of Technology(2016000011)+1 种基金Lianyungang Postdoctoral Research Project Foundation(188903)the National Natural Science Foundation of China(11802140)。
文摘Elastic wave refraction at the air-solid interface and wave propagations in the vicinity of the air-solid interface are numerically studied.The modified ghost fluid method(MGFM)and isobaric fix methods are combined to solve the fluid and solid statuses at the air-solid interface and construct a continuous boundary condition for the air-solid interface.The states in the ghost domain are evaluated by the MGFM-algorithm.The solid governing equations are solved with second order spatial discretization.Numerical tests verify the correctness of the presented continuous boundary condition and show that the combined method is convergent in the vicinity of the air-solid interface.The 3D numerical results by the combined method are close to those of the ArbitraryLagrangian-Eulerian(ALE)method.The combined method is robust when applied for multi-dimensional problems.A compression stress wave impacting on the air-solid interface result in a compression wave in air.A tension stress wave impacting on the air-solid interface result in an expansion wave in air.
文摘Under the condition that any perfeetly plastic stress components at a crack tip are nothing but the Junctions of 0 only, making use of equilibriumequations,Hill ani.sutropic yield condition and unloading stress-strain relations, in this paper, we derive the general analytical expressions of anisotropic plastiestress Jields at the slowly steadyhe slowly steady propagatin tips of plane and anti-phane strain,Applying these general analytical expressions to the concrete cracks the attchvtical expressions of anisotropie plastic stress fields at the slowly steady propagating tips of Motle I and Motle III cracks are obtained. For the isolropic plastic material, the anisotropic plastic stress fields at a slowly propagating crack tip become the perfeeby plastic mress fields
基金The project supported by the National Natural Science Foundation of China (50579081)the Australian Research Council (DP0452681)The English text was polished by Keren Wang
文摘The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.
基金the Key Project of National Natural Science Foundation of China(No.51574248)the National Natural Science Foundation of China(Grant Nos.52074300 and 51704120)+1 种基金the National Key Research and Development Program of China(Grant No.2016YFC0600901)the Fundamental Research Funds for the Central Universities(2021YJSSB11).
文摘The full-field strain of rock material under dynamic compression load was studied using the high-speed three dimensional digital image correlation(3D-DIC)method.The dynamic test was conducted on Laizhou granite using a split Hopkinson pressure bar(SHPB)method.Wave propagation,dispersion and radial inertial effect on the specimen were found by DIC results.A recovery of strain in the post-peak stage was detected on the specimen by DIC,which was unrevealed in the traditional one-dimensional theory method.It can be found that the strain measured by strain gauge was a calculated average one,whereas the strain measured by 3D-DIC could reflect more variation details.Specifically,the testing principle with impact loads and rock dynamic behavior was re-examined using stress wave propagation theory.The theoretical results showed that the specimen reached equilibrium after a series of wave reflections and transmissions and its stress was infinitely close to the initial value of 109.2 MPa.Moreover,the specimen had the calculated maximum strain of 0.52% and strain rate of 15.11 s^(-1),improving the reasonable agreement with the experimental results and requirements of rock mechanical properties measured by SHPB technology.
文摘Numerical simulations of longitudinal wave propagation in a rock bar with microcracks are conducted by using the numerical manifold method which has great advantages in the simulation of discontinuities.Firstly,validation of the numerical manifold method is carried out by simulations of a longitudinal stress wave propagating through intact and cracked rock bars.The behavior of the stress wave traveling in a one-dimensional rock bar with randomly distributed microcracks is subsequently studied.It is revealed that the highly defected rock bar has significant viscoelasticity to the stress wave propagation.Wave attenuation as well as time delay is affected by the length,quantity,specific stiffness of the distributed microcracks as well as the incident stress wave frequency.The storage and loss moduli of the defected rock are also affected by the microcrack properties;however,they are independent of incident stress wave frequency.
