A revised displacement discontinuity method(DDM) program is developed for the simulation of rock joint propagation and dilatancy analysis. The non-linear joint model used in the program adopts Barton-Bandis normal def...A revised displacement discontinuity method(DDM) program is developed for the simulation of rock joint propagation and dilatancy analysis. The non-linear joint model used in the program adopts Barton-Bandis normal deformation model, Kulhaway shear deformation model and Mohr-Coulomb criterion. The joint propagation criterion is based on the equivalent stress intensity factor which can be obtained by regression analysis. The simulated rock joint propagation accords well with the existing knowledge. The closure and opening of joint is investigated by DDM, and it is shown that if the opening volume of propagated joint is larger than closure volume of the old joint, the joint dilatancy occurs. The dilatancy condition is mainly controlled by the normal stiffness of the rock joint. When the normal stiffness is larger than the critical value, joint dilatancy occurs. The critical normal stiffness of rock joint changes with the joint-load angle, and joint dilatancy is most possible to occur at 30°.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
The present research is focused on the numerical crack coalescence analysis of the micro-cracks and cracks produced during the cutting action of TBM disc cutters. The linear elastic fracture mechanics(LEFM) concepts a...The present research is focused on the numerical crack coalescence analysis of the micro-cracks and cracks produced during the cutting action of TBM disc cutters. The linear elastic fracture mechanics(LEFM) concepts and the maximum tangential stress criterion are used to investigate the micro crack propagation and its direction underneath the excavating discs. A higher order displacement discontinuity method with quadratic displacement discontinuity elements is used to estimate the stress intensity factors near the crack tips. Rock cutting mechanisms under single and double type discs are simulated by the proposed numerical method.The main purposes of the present modeling are to simulate the chip formation process of indented rocks by single and double discs.The effects of specific disc parameters(except speed) on the thrust force Ft, the rolling force Fr, and the specific energy ES are investigated. It has been shown that the specific energy(energy required to cut through a unit volume of rock) of the double disc is less than that of the single disc. Crack propagation in rocks under disc cutters is numerically modeled and the optimum ratio of disc spacing S to penetration depth Pd(i.e. S/Pd ratio) of about 10 is obtained, which is in good agreement with the theoretical and experimental results cited in the literature.展开更多
The higher order displacement discontinuity method(HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics(LEFM) problems. The paper has selected several example ...The higher order displacement discontinuity method(HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics(LEFM) problems. The paper has selected several example problems from the fracture mechanics literature(with available analytical solutions) including center slant crack in an infinite and finite body, single and double edge cracks, cracks emanating from a circular hole. The numerical values of Mode Ⅰ and Mode Ⅱ SIFs for these problems using HODDM are in excellent agreement with analytical results(reaching up to 0.001% deviation from their analytical results). The HODDM is also compared with the XFEM and a modified XFEM results. The results show that the HODDM needs a considerably lower computational effort(with less than 400 nodes) than the XFEM and the modified XFEM(which needs more than 10000 nodes) to reach a much higher accuracy. The proposed HODDM offers higher accuracy and lower computation effort for a wide range of problems in LEFM.展开更多
The displacement discontinuity method(DDM) is a kind of boundary element method aiming at modeling two-dimensional linear elastic crack problems. The singularity around the crack tip prevents the DDM from optimally co...The displacement discontinuity method(DDM) is a kind of boundary element method aiming at modeling two-dimensional linear elastic crack problems. The singularity around the crack tip prevents the DDM from optimally converging when the basis functions are polynomials of first order or higher. To overcome this issue,enlightened by the mapped finite element method(FEM) proposed in Ref. [13], we present an optimally convergent mapped DDM in this work, called the mapped DDM(MDDM). It is essentially based on approximating a much smoother function obtained by reformulating the problem with an appropriate auxiliary map. Two numerical examples of crack problems are presented in comparison with the conventional DDM. The results show that the proposed method improves the accuracy of the DDM; moreover, it yields an optimal convergence rate for quadratic interpolating polynomials.展开更多
The back analysis of initial stress is usually based on measured stress values, but the measuring of initial stress demands substantial investment. Therefore, amounts of underground engineering have no measured initia...The back analysis of initial stress is usually based on measured stress values, but the measuring of initial stress demands substantial investment. Therefore, amounts of underground engineering have no measured initial stress data, such as tunneling engineering. Focusing on this problem, a new back analysis method which does not need measured initial stress data is developed. The fault is assumed to be caused by initial load, the displacement discontinuity method (DDM) which considered non-linear fault is adopted to establish a numerical model of the engineering site, and the multivariable regression analysis of the initial stress field around the faults is carried out based on the fault throw. The result shows that the initial stress field around the faults is disturbed significantly, stress concentration appears in the tip zone, the regressive fault throw matches the measured values well, and the regressive initial stress field is reliable.展开更多
A 3D displacement discontinuity method is applied to solve the fracture mechanics problems of the mixed mode crack under compression.Friction between the surface of the closed crack is considered by establishing a sim...A 3D displacement discontinuity method is applied to solve the fracture mechanics problems of the mixed mode crack under compression.Friction between the surface of the closed crack is considered by establishing a simple and efficient iterative algorithm based on method of contact resistance mitigation.On the surfaces of the closed crack,the Mohr-coulomb rule is satisfied by iteration when the crack is in condition of sliding.The stress intensity factors are obtained using displacement fitting method.It is shown that the numerical results agree with the experimental results well and that friction plays an important role in resisting crack propagation.展开更多
An iterative algorithm for modeling of non-linear joint by the displacement discontinuity method (DDM) was described, and the effect of the non-linear joint on the in-situ stress field was investigated in this paper. ...An iterative algorithm for modeling of non-linear joint by the displacement discontinuity method (DDM) was described, and the effect of the non-linear joint on the in-situ stress field was investigated in this paper. The Barton-Bandis (BB) non-linear joint model and failure criterion were adopted in the new DDM program. Using this program, the stress field around the non-linear joint was obtained, the parameters analysis of the joint was carried out, and the deformation and stress distribution of the joint were studied. The simulation results show that: (1)the in-situ stress is significantly affected by the joint; (2)the increase of stiffness, friction angle, and thickness of the joint affect the stress concentration in different ways; (3)the influence distance of the joint changes with the angle of the joint; (4)the deformation and stress of the joint change with the point position.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 primary g...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
The main task of fracture mechanics of rock masses is the study on the propagating mechanism of fractures in rock masses , which can be efficiently conducted by discontinuty displacement (DD) numerical evaluation . Fi...The main task of fracture mechanics of rock masses is the study on the propagating mechanism of fractures in rock masses , which can be efficiently conducted by discontinuty displacement (DD) numerical evaluation . Firstly ,the element stress and displacement are analysed and the principle and steps of the numerical calculation of stress intensity factor and fracture extension force are introduced .The numerical results of parallel and echelon fracture systems ,which are compared with real field fractures .are presented. Finally . a simple engineering application example is presented .展开更多
A multi-casing structure in drilling engineering can be considered as an inhomogeneous body consisting of many different materials. The mechanical behavior of the inhomogeneous body in an infinite domain is very com- ...A multi-casing structure in drilling engineering can be considered as an inhomogeneous body consisting of many different materials. The mechanical behavior of the inhomogeneous body in an infinite domain is very com- plicated. In this paper, a detailed expression about the fictitious stress method of the boundary element method （BEM） is demonstrated for the inhomogeneous body. Then the fictitious stress method is deployed to investigate the stresses for the multi-casing structure under non-uniform loading conditions and an irregular wellbore. Three examples of the multi-casing structure in the borehole imply the high effectiveness of BEM for complex geometries related to the borehole in an infinite formation. The effects of casing eccentricity and the interfacial gap on the stress field are discussed. The eccentric casing takes the potential yield when the eccentric orientation is along the direction of Sh. Under different eccentric orientations, the yon Mises stress in the casing increases with increasing degree of eccentricity. The radial stress in the multi-casing structure is always continuous along the radius, but the circumferential stress is discontinuous at the interface. The radial stress decreases and the circumferential stress increases with the increasing of the interfacial gap between the adjacent materials.展开更多
This article examines the interaction of multiple cracks in an infinite plate by using a numerical method. The numerical method consists of the non-singular displacement discontinuity element presented by Crouch and S...This article examines the interaction of multiple cracks in an infinite plate by using a numerical method. The numerical method consists of the non-singular displacement discontinuity element presented by Crouch and Startled and the crack tip displacement discontinuity elements proposed by the author. In the numerical method implementation, the left or the right crack tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The numerical method is called a hybrid displacement discontinuity method. The following test examples of crack problems in an infinite plate under tension are included： “ center-inclined cracked plate”, “interaction of two collinear cracks with equal length”, “interaction of three collinear cracks with equal length”, “interaction of two parallel cracks with equal length”, and “interaction of one horizontal crack and one inclined crack”. The present numerical results show that the numerical method is simple yet very accurate for analyzing the interaction of multiple cracks in an infinite plate.展开更多
A multivariable regression analysis of the in-situ stress field, which considers the non-linear deformation behavior of faults in practical projects, is presented based on a newly developed three-dimensional displacem...A multivariable regression analysis of the in-situ stress field, which considers the non-linear deformation behavior of faults in practical projects, is presented based on a newly developed three-dimensional displacement discontinuity method （DDM） program. The Bar- ton-Bandis model and the Kulhaway model are adopted as the normal and the tangential deformation model of faults, respectively, where the Mohr-Coulomb failure criterion is satisfied. In practical projects, the values of the mechanical parameters of rock and faults are restricted in a bounded range for in-situ test, and the optimal mechanical parameters are obtained from this range by a loop. Comparing with the traditional finite element method （FEM）, the DDM regression results are more accurate.展开更多
This paper presents an integrated study from fracture propagation modeling to gas flow modeling and a correlation analysis to explore the key controlling factors of intensive volume fracturing.The fracture propagation...This paper presents an integrated study from fracture propagation modeling to gas flow modeling and a correlation analysis to explore the key controlling factors of intensive volume fracturing.The fracture propagation model takes into account the interaction between hydraulic fracture and natural fracture by means of the displacement discontinuity method(DDM)and the Picard iterative method.The shale gas flow considers multiple transport mechanisms,and the flow in the fracture network is handled by the embedded discrete fracture model(EDFM).A series of numerical simulations are conducted to analyze the effects of the cluster number,stage spacing,stress difference coefficient,and natural fracture distribution on the stimulated fracture area,fractal dimension,and cumulative gas production,and their correlation coefficients are obtained.The results show that the most influential factors to the stimulated fracture area are the stress difference ratio,stage spacing,and natural fracture density,while those to the cumulative gas production are the stress difference ratio,natural fracture density,and cluster number.This indicates that the stress condition dominates the gas production,and employing intensive volume fracturing(by properly increasing the cluster number)is beneficial for improving the final cumulative gas production.展开更多
In this paper, the three-dimensional(3D) interfacial fracture is analyzed in a one-dimensional(1D) hexagonal quasicrystal(QC) coating structure under mechanical loading. A planar interface crack with arbitrary shape i...In this paper, the three-dimensional(3D) interfacial fracture is analyzed in a one-dimensional(1D) hexagonal quasicrystal(QC) coating structure under mechanical loading. A planar interface crack with arbitrary shape is studied by a displacement discontinuity method. Fundamental solutions of interfacial concentrated displacement discontinuities are obtained by the Hankel transform technique, and the corresponding boundary integral-differential equations are constructed with the superposition principle.Green’s functions of constant interfacial displacement discontinuities within a rectangular element are derived, and a boundary element method is proposed for numerical simulation.The singularity of stresses near the crack front is investigated, and the stress intensity factors(SIFs) as well as energy release rates(ERRs) are determined. Finally, relevant influencing factors on the fracture behavior are discussed.展开更多
Based on the idea of the developed 3D-FSM.DDM boundary element method, the field with muti-medium was formulized firstly, then connected at the interface of two fields according to the continuous conditions of stress ...Based on the idea of the developed 3D-FSM.DDM boundary element method, the field with muti-medium was formulized firstly, then connected at the interface of two fields according to the continuous conditions of stress and displacement, after that, a boundary value problem with unified model was formed and solved. Ultimately, an applied numerical simulation system was developed. It was compared with the model having analytical solution for verifying the applicability and the calculating precision.展开更多
In order to investigate propagation regularity of hydraulic fractures in the mode of multi-well pads, numerical modeling of simultaneous hydraulic fracturing of multiple wells was conducted. The mathematical model was...In order to investigate propagation regularity of hydraulic fractures in the mode of multi-well pads, numerical modeling of simultaneous hydraulic fracturing of multiple wells was conducted. The mathematical model was established coupling rock deformation with fluid flow in the fractures and wellbores. And then the model was solved by displacement discontinuity method coupling with implicit level set method. The implicit method was based on fracture tip asymptotical solution and used to determine fracture growth length. Simulation results showed that when multiple wells were fractured simultaneously, adjacent fractures might propagate towards each other, showing an effect of attraction other than repulsion. Fracture spacing and well spacing had significant influence on the propagation path and geometry of multiple fractures. Furthermore, when multiple wells were fractured simultaneously, stress reversal regions had a large area, and stress reversal regions were distributed not only in the area between fractures but also on the outside of them. The area of stress reversal regions was related to fracture spacing and well spacing. Results indicated that multi-well fracturing induced larger area of stress reversal regions than one-well fracturing, which was beneficial to generating complex fracture network in unconventional reservoirs.展开更多
基金Project(2009318000046) supported by the Western Transport Technical Program of the Ministry of Transport,China
文摘A revised displacement discontinuity method(DDM) program is developed for the simulation of rock joint propagation and dilatancy analysis. The non-linear joint model used in the program adopts Barton-Bandis normal deformation model, Kulhaway shear deformation model and Mohr-Coulomb criterion. The joint propagation criterion is based on the equivalent stress intensity factor which can be obtained by regression analysis. The simulated rock joint propagation accords well with the existing knowledge. The closure and opening of joint is investigated by DDM, and it is shown that if the opening volume of propagated joint is larger than closure volume of the old joint, the joint dilatancy occurs. The dilatancy condition is mainly controlled by the normal stiffness of the rock joint. When the normal stiffness is larger than the critical value, joint dilatancy occurs. The critical normal stiffness of rock joint changes with the joint-load angle, and joint dilatancy is most possible to occur at 30°.
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.
文摘The present research is focused on the numerical crack coalescence analysis of the micro-cracks and cracks produced during the cutting action of TBM disc cutters. The linear elastic fracture mechanics(LEFM) concepts and the maximum tangential stress criterion are used to investigate the micro crack propagation and its direction underneath the excavating discs. A higher order displacement discontinuity method with quadratic displacement discontinuity elements is used to estimate the stress intensity factors near the crack tips. Rock cutting mechanisms under single and double type discs are simulated by the proposed numerical method.The main purposes of the present modeling are to simulate the chip formation process of indented rocks by single and double discs.The effects of specific disc parameters(except speed) on the thrust force Ft, the rolling force Fr, and the specific energy ES are investigated. It has been shown that the specific energy(energy required to cut through a unit volume of rock) of the double disc is less than that of the single disc. Crack propagation in rocks under disc cutters is numerically modeled and the optimum ratio of disc spacing S to penetration depth Pd(i.e. S/Pd ratio) of about 10 is obtained, which is in good agreement with the theoretical and experimental results cited in the literature.
文摘The higher order displacement discontinuity method(HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics(LEFM) problems. The paper has selected several example problems from the fracture mechanics literature(with available analytical solutions) including center slant crack in an infinite and finite body, single and double edge cracks, cracks emanating from a circular hole. The numerical values of Mode Ⅰ and Mode Ⅱ SIFs for these problems using HODDM are in excellent agreement with analytical results(reaching up to 0.001% deviation from their analytical results). The HODDM is also compared with the XFEM and a modified XFEM results. The results show that the HODDM needs a considerably lower computational effort(with less than 400 nodes) than the XFEM and the modified XFEM(which needs more than 10000 nodes) to reach a much higher accuracy. The proposed HODDM offers higher accuracy and lower computation effort for a wide range of problems in LEFM.
基金the National Natural Science Foundation of China(No.11402146)the Young 1000 Talent Program of China
文摘The displacement discontinuity method(DDM) is a kind of boundary element method aiming at modeling two-dimensional linear elastic crack problems. The singularity around the crack tip prevents the DDM from optimally converging when the basis functions are polynomials of first order or higher. To overcome this issue,enlightened by the mapped finite element method(FEM) proposed in Ref. [13], we present an optimally convergent mapped DDM in this work, called the mapped DDM(MDDM). It is essentially based on approximating a much smoother function obtained by reformulating the problem with an appropriate auxiliary map. Two numerical examples of crack problems are presented in comparison with the conventional DDM. The results show that the proposed method improves the accuracy of the DDM; moreover, it yields an optimal convergence rate for quadratic interpolating polynomials.
基金the Western Transport Construction Science and Technology Project of the Ministry of Transport of the People's Republic of China(No.2009318000046)
文摘The back analysis of initial stress is usually based on measured stress values, but the measuring of initial stress demands substantial investment. Therefore, amounts of underground engineering have no measured initial stress data, such as tunneling engineering. Focusing on this problem, a new back analysis method which does not need measured initial stress data is developed. The fault is assumed to be caused by initial load, the displacement discontinuity method (DDM) which considered non-linear fault is adopted to establish a numerical model of the engineering site, and the multivariable regression analysis of the initial stress field around the faults is carried out based on the fault throw. The result shows that the initial stress field around the faults is disturbed significantly, stress concentration appears in the tip zone, the regressive fault throw matches the measured values well, and the regressive initial stress field is reliable.
文摘A 3D displacement discontinuity method is applied to solve the fracture mechanics problems of the mixed mode crack under compression.Friction between the surface of the closed crack is considered by establishing a simple and efficient iterative algorithm based on method of contact resistance mitigation.On the surfaces of the closed crack,the Mohr-coulomb rule is satisfied by iteration when the crack is in condition of sliding.The stress intensity factors are obtained using displacement fitting method.It is shown that the numerical results agree with the experimental results well and that friction plays an important role in resisting crack propagation.
基金Western Transport Construction Science and Technology Project of the Ministry of Transport of China ( No. 2009318000046)
文摘An iterative algorithm for modeling of non-linear joint by the displacement discontinuity method (DDM) was described, and the effect of the non-linear joint on the in-situ stress field was investigated in this paper. The Barton-Bandis (BB) non-linear joint model and failure criterion were adopted in the new DDM program. Using this program, the stress field around the non-linear joint was obtained, the parameters analysis of the joint was carried out, and the deformation and stress distribution of the joint were studied. The simulation results show that: (1)the in-situ stress is significantly affected by the joint; (2)the increase of stiffness, friction angle, and thickness of the joint affect the stress concentration in different ways; (3)the influence distance of the joint changes with the angle of the joint; (4)the deformation and stress of the joint change with the point position.
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 research is supported by the National Nature Science Foundation of China
文摘The main task of fracture mechanics of rock masses is the study on the propagating mechanism of fractures in rock masses , which can be efficiently conducted by discontinuty displacement (DD) numerical evaluation . Firstly ,the element stress and displacement are analysed and the principle and steps of the numerical calculation of stress intensity factor and fracture extension force are introduced .The numerical results of parallel and echelon fracture systems ,which are compared with real field fractures .are presented. Finally . a simple engineering application example is presented .
基金supported by the China National High Technology Research and Development Program 863 (Grant No. 2013AA064503)The China Scholarship Council
文摘A multi-casing structure in drilling engineering can be considered as an inhomogeneous body consisting of many different materials. The mechanical behavior of the inhomogeneous body in an infinite domain is very com- plicated. In this paper, a detailed expression about the fictitious stress method of the boundary element method （BEM） is demonstrated for the inhomogeneous body. Then the fictitious stress method is deployed to investigate the stresses for the multi-casing structure under non-uniform loading conditions and an irregular wellbore. Three examples of the multi-casing structure in the borehole imply the high effectiveness of BEM for complex geometries related to the borehole in an infinite formation. The effects of casing eccentricity and the interfacial gap on the stress field are discussed. The eccentric casing takes the potential yield when the eccentric orientation is along the direction of Sh. Under different eccentric orientations, the yon Mises stress in the casing increases with increasing degree of eccentricity. The radial stress in the multi-casing structure is always continuous along the radius, but the circumferential stress is discontinuous at the interface. The radial stress decreases and the circumferential stress increases with the increasing of the interfacial gap between the adjacent materials.
文摘This article examines the interaction of multiple cracks in an infinite plate by using a numerical method. The numerical method consists of the non-singular displacement discontinuity element presented by Crouch and Startled and the crack tip displacement discontinuity elements proposed by the author. In the numerical method implementation, the left or the right crack tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The numerical method is called a hybrid displacement discontinuity method. The following test examples of crack problems in an infinite plate under tension are included： “ center-inclined cracked plate”, “interaction of two collinear cracks with equal length”, “interaction of three collinear cracks with equal length”, “interaction of two parallel cracks with equal length”, and “interaction of one horizontal crack and one inclined crack”. The present numerical results show that the numerical method is simple yet very accurate for analyzing the interaction of multiple cracks in an infinite plate.
基金financially supported by the Western Transport Technical Project of the Ministry of Transport, China (No. 2009318000046)
文摘A multivariable regression analysis of the in-situ stress field, which considers the non-linear deformation behavior of faults in practical projects, is presented based on a newly developed three-dimensional displacement discontinuity method （DDM） program. The Bar- ton-Bandis model and the Kulhaway model are adopted as the normal and the tangential deformation model of faults, respectively, where the Mohr-Coulomb failure criterion is satisfied. In practical projects, the values of the mechanical parameters of rock and faults are restricted in a bounded range for in-situ test, and the optimal mechanical parameters are obtained from this range by a loop. Comparing with the traditional finite element method （FEM）, the DDM regression results are more accurate.
基金supported by the National Natural Science Foundation of China(Nos.52274038,5203401042174143)+1 种基金the Taishan Scholars Project(No.tsqnz20221140)the Open Fund of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation(Southwest Petroleum University)of China(No.PLN2020-5)。
文摘This paper presents an integrated study from fracture propagation modeling to gas flow modeling and a correlation analysis to explore the key controlling factors of intensive volume fracturing.The fracture propagation model takes into account the interaction between hydraulic fracture and natural fracture by means of the displacement discontinuity method(DDM)and the Picard iterative method.The shale gas flow considers multiple transport mechanisms,and the flow in the fracture network is handled by the embedded discrete fracture model(EDFM).A series of numerical simulations are conducted to analyze the effects of the cluster number,stage spacing,stress difference coefficient,and natural fracture distribution on the stimulated fracture area,fractal dimension,and cumulative gas production,and their correlation coefficients are obtained.The results show that the most influential factors to the stimulated fracture area are the stress difference ratio,stage spacing,and natural fracture density,while those to the cumulative gas production are the stress difference ratio,natural fracture density,and cluster number.This indicates that the stress condition dominates the gas production,and employing intensive volume fracturing(by properly increasing the cluster number)is beneficial for improving the final cumulative gas production.
基金Project supported by the National Natural Science Foundation of China (Nos. 11572289, 1171407,11702252, and 11902293)the China Postdoctoral Science Foundation (No. 2019M652563)。
文摘In this paper, the three-dimensional(3D) interfacial fracture is analyzed in a one-dimensional(1D) hexagonal quasicrystal(QC) coating structure under mechanical loading. A planar interface crack with arbitrary shape is studied by a displacement discontinuity method. Fundamental solutions of interfacial concentrated displacement discontinuities are obtained by the Hankel transform technique, and the corresponding boundary integral-differential equations are constructed with the superposition principle.Green’s functions of constant interfacial displacement discontinuities within a rectangular element are derived, and a boundary element method is proposed for numerical simulation.The singularity of stresses near the crack front is investigated, and the stress intensity factors(SIFs) as well as energy release rates(ERRs) are determined. Finally, relevant influencing factors on the fracture behavior are discussed.
文摘Based on the idea of the developed 3D-FSM.DDM boundary element method, the field with muti-medium was formulized firstly, then connected at the interface of two fields according to the continuous conditions of stress and displacement, after that, a boundary value problem with unified model was formed and solved. Ultimately, an applied numerical simulation system was developed. It was compared with the model having analytical solution for verifying the applicability and the calculating precision.
基金supported by the National Natural Science Foundation of China(Grant Nos.51234007&51490654)the National Science Foundation for Young Scientists of China(Grant No.51404291)+1 种基金Fundamental Research Funds for Central Universities(Grant Nos.14CX05024A&14CX02045A)Shandong Provincial Natural Science Foundation(Grant No.ZR2014EEQ010)
文摘In order to investigate propagation regularity of hydraulic fractures in the mode of multi-well pads, numerical modeling of simultaneous hydraulic fracturing of multiple wells was conducted. The mathematical model was established coupling rock deformation with fluid flow in the fractures and wellbores. And then the model was solved by displacement discontinuity method coupling with implicit level set method. The implicit method was based on fracture tip asymptotical solution and used to determine fracture growth length. Simulation results showed that when multiple wells were fractured simultaneously, adjacent fractures might propagate towards each other, showing an effect of attraction other than repulsion. Fracture spacing and well spacing had significant influence on the propagation path and geometry of multiple fractures. Furthermore, when multiple wells were fractured simultaneously, stress reversal regions had a large area, and stress reversal regions were distributed not only in the area between fractures but also on the outside of them. The area of stress reversal regions was related to fracture spacing and well spacing. Results indicated that multi-well fracturing induced larger area of stress reversal regions than one-well fracturing, which was beneficial to generating complex fracture network in unconventional reservoirs.
