In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hy...In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.展开更多
为研究冻胀荷载对双裂隙岩体裂纹扩展及贯通机制的影响,文章基于扩展有限元法(extended finite element method,XFEM),分析冻胀力作用下不同岩桥参数双裂隙试样的裂纹扩展特征和破坏形式,探究在冻胀力和侧向卸荷共同作用下双裂隙试样的...为研究冻胀荷载对双裂隙岩体裂纹扩展及贯通机制的影响,文章基于扩展有限元法(extended finite element method,XFEM),分析冻胀力作用下不同岩桥参数双裂隙试样的裂纹扩展特征和破坏形式,探究在冻胀力和侧向卸荷共同作用下双裂隙试样的裂纹扩展贯通规律。结果表明:基于XFEM的数值模拟结果与试验中的裂纹扩展路径基本吻合,验证了XFEM能够有效地应用于双裂隙岩体的裂纹扩展模拟;非岩桥区冻胀裂纹的扩展方向与预制裂隙走向相同,而岩桥区裂纹的扩展方向受到冻胀应力的影响,裂纹扩展方向偏向于另一条预制裂隙位置;冻胀裂纹的扩展模式受到围压的影响,随着围压增加,侧向卸荷过程中裂纹扩展模式由拉张模式变成拉剪混合模式,裂纹扩展方向也发生偏转。研究方法和结果可为低温裂隙岩体裂纹扩展相关研究提供参考。展开更多
A unit cell including the matrix, precipitation free zone(PFZ) and grain boundary was prepared, and the crystal plasticity finite element method(CPFEM) and extended finite element method(XFEM) were used to simulate th...A unit cell including the matrix, precipitation free zone(PFZ) and grain boundary was prepared, and the crystal plasticity finite element method(CPFEM) and extended finite element method(XFEM) were used to simulate the propagation of cracks at grain boundary. Simulation results show that the crystallographic orientation of PFZ has significant influence on crack propagation, which includes the crack growth direction and crack growth velocity. The fracture strain of soft orientation is larger than that of hard orientation due to the role of reducing the stress intensity at grain boundary in intergranular brittle fracture. But in intergranular ductile fracture, the fracture strain of soft orientation may be smaller than that of hard orientation due to the roles of deformation localization.展开更多
In this paper, the extended finite element method (XFEM) is adopted to analyze the interaction between a single macroscopic inclusion and a single macroscopic crack as well as that between multiple macroscopic or micr...In this paper, the extended finite element method (XFEM) is adopted to analyze the interaction between a single macroscopic inclusion and a single macroscopic crack as well as that between multiple macroscopic or microscopic defects under thermal/mechanical load. The effects of different shapes of multiple inclusions on the material thermomechanical response are investigated, and the level set method is coupled with XFEM to analyze the interaction of multiple defects. Further, the discretized extended finite element approximations in relation to thermoelastic problems of multiple defects under displacement or temperature field are given. Also, the interfaces of cracks or materials are represented by level set functions, which allow the mesh assignment not to conform to crack or material interfaces. Moreover, stress intensity factors of cracks are obtained by the interaction integral method or the M-integral method, and the stress/strain/stiffness fields are simulated in the case of multiple cracks or multiple inclusions. Finally, some numerical examples are provided to demonstrate the accuracy of our proposed method.展开更多
Extended finite element method （XFEM） implementation of the interaction integral methodology for evaluating the stress intensity factors （SIF） of the mixed-mode crack problem is presented. A discontinuous function...Extended finite element method （XFEM） implementation of the interaction integral methodology for evaluating the stress intensity factors （SIF） of the mixed-mode crack problem is presented. A discontinuous function and the near-tip asymptotic function are added to the classic finite element approximation to model the crack behavior. Two-state integral by the superposition of actual and auxiliary fields is derived to calculate the SIFs. Applications of the proposed technique to the inclined centre crack plate with inclined angle from 0° to 90° and slant edge crack plate with slant angle 45°, 67.5° and 90° are presented, and comparisons are made with closed form solutions. The results show that the proposed method is convenient, accurate and computationallv efficient.展开更多
为研究水中高压电脉冲作用下页岩多条预制裂纹同步扩展应力干扰作用对裂纹扩展影响,通过裂纹扩展轨迹、扩展长度、平均宽度、偏转角度和裂纹间等效应力分布的变化规律,综合考虑裂纹夹角、裂纹数量、水平地应力差等因素对裂纹起裂、扩展...为研究水中高压电脉冲作用下页岩多条预制裂纹同步扩展应力干扰作用对裂纹扩展影响,通过裂纹扩展轨迹、扩展长度、平均宽度、偏转角度和裂纹间等效应力分布的变化规律,综合考虑裂纹夹角、裂纹数量、水平地应力差等因素对裂纹起裂、扩展的影响。采用真三轴高压脉冲水力压裂试验平台进行实验室压裂试验和扩展有限元法(extended finite element method, XFEM)数值模拟计算,利用PCAS(pore and cracks analysis system)裂隙分析软件分析裂纹几何形态特征。结果表明:水中高压电脉冲作用下,预制裂纹可沿径向及轴向起裂、扩展;径向双裂纹间夹角越大,缝间干扰作用越弱,裂纹扩展曲折程度越好,扩展效果越好;等夹角径向三裂纹扩展,中间裂纹受应力干扰、受抑制作用最大,不等夹角径向三裂纹扩展,远离中间裂纹的右侧裂纹受干扰最小,扩展效果最好;随着水平地应力差增加,裂纹间应力干扰作用增强,裂纹扩展效果逐渐减弱。研究成果可为分析水中高压电脉冲作用下页岩多预制裂纹扩展过程和规律提供一定的参考。展开更多
文摘In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.
文摘为研究冻胀荷载对双裂隙岩体裂纹扩展及贯通机制的影响,文章基于扩展有限元法(extended finite element method,XFEM),分析冻胀力作用下不同岩桥参数双裂隙试样的裂纹扩展特征和破坏形式,探究在冻胀力和侧向卸荷共同作用下双裂隙试样的裂纹扩展贯通规律。结果表明:基于XFEM的数值模拟结果与试验中的裂纹扩展路径基本吻合,验证了XFEM能够有效地应用于双裂隙岩体的裂纹扩展模拟;非岩桥区冻胀裂纹的扩展方向与预制裂隙走向相同,而岩桥区裂纹的扩展方向受到冻胀应力的影响,裂纹扩展方向偏向于另一条预制裂隙位置;冻胀裂纹的扩展模式受到围压的影响,随着围压增加,侧向卸荷过程中裂纹扩展模式由拉张模式变成拉剪混合模式,裂纹扩展方向也发生偏转。研究方法和结果可为低温裂隙岩体裂纹扩展相关研究提供参考。
基金Projects(51475162,51405153)supported by the National Natural Science Foundation of ChinaProject(14JJ5015)supported by the Hunan Provincial Natural Science Foundation,China
文摘A unit cell including the matrix, precipitation free zone(PFZ) and grain boundary was prepared, and the crystal plasticity finite element method(CPFEM) and extended finite element method(XFEM) were used to simulate the propagation of cracks at grain boundary. Simulation results show that the crystallographic orientation of PFZ has significant influence on crack propagation, which includes the crack growth direction and crack growth velocity. The fracture strain of soft orientation is larger than that of hard orientation due to the role of reducing the stress intensity at grain boundary in intergranular brittle fracture. But in intergranular ductile fracture, the fracture strain of soft orientation may be smaller than that of hard orientation due to the roles of deformation localization.
基金supported by the National Natural Science Foundation of China (Grants 11471262, 50976003, 51136005)
文摘In this paper, the extended finite element method (XFEM) is adopted to analyze the interaction between a single macroscopic inclusion and a single macroscopic crack as well as that between multiple macroscopic or microscopic defects under thermal/mechanical load. The effects of different shapes of multiple inclusions on the material thermomechanical response are investigated, and the level set method is coupled with XFEM to analyze the interaction of multiple defects. Further, the discretized extended finite element approximations in relation to thermoelastic problems of multiple defects under displacement or temperature field are given. Also, the interfaces of cracks or materials are represented by level set functions, which allow the mesh assignment not to conform to crack or material interfaces. Moreover, stress intensity factors of cracks are obtained by the interaction integral method or the M-integral method, and the stress/strain/stiffness fields are simulated in the case of multiple cracks or multiple inclusions. Finally, some numerical examples are provided to demonstrate the accuracy of our proposed method.
基金Projects(41172244,41072224) supported by the National Natural Science Foundation of ChinaProject(2009GGJS-037) supported by the Foundation of Youths Key Teacher by the Henan Educational Committee,China
文摘Extended finite element method （XFEM） implementation of the interaction integral methodology for evaluating the stress intensity factors （SIF） of the mixed-mode crack problem is presented. A discontinuous function and the near-tip asymptotic function are added to the classic finite element approximation to model the crack behavior. Two-state integral by the superposition of actual and auxiliary fields is derived to calculate the SIFs. Applications of the proposed technique to the inclined centre crack plate with inclined angle from 0° to 90° and slant edge crack plate with slant angle 45°, 67.5° and 90° are presented, and comparisons are made with closed form solutions. The results show that the proposed method is convenient, accurate and computationallv efficient.
文摘为研究水中高压电脉冲作用下页岩多条预制裂纹同步扩展应力干扰作用对裂纹扩展影响,通过裂纹扩展轨迹、扩展长度、平均宽度、偏转角度和裂纹间等效应力分布的变化规律,综合考虑裂纹夹角、裂纹数量、水平地应力差等因素对裂纹起裂、扩展的影响。采用真三轴高压脉冲水力压裂试验平台进行实验室压裂试验和扩展有限元法(extended finite element method, XFEM)数值模拟计算,利用PCAS(pore and cracks analysis system)裂隙分析软件分析裂纹几何形态特征。结果表明:水中高压电脉冲作用下,预制裂纹可沿径向及轴向起裂、扩展;径向双裂纹间夹角越大,缝间干扰作用越弱,裂纹扩展曲折程度越好,扩展效果越好;等夹角径向三裂纹扩展,中间裂纹受应力干扰、受抑制作用最大,不等夹角径向三裂纹扩展,远离中间裂纹的右侧裂纹受干扰最小,扩展效果最好;随着水平地应力差增加,裂纹间应力干扰作用增强,裂纹扩展效果逐渐减弱。研究成果可为分析水中高压电脉冲作用下页岩多预制裂纹扩展过程和规律提供一定的参考。
