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A virtual multidimensional internal bond (VMIB) model developed to simulate the propagation of hydraulic fractures using the finite‐element method is formulated within the framework of the virtual internal bond theory (VIB) that considers a solid as randomized material particles in the micro scale, and derives the macro constitutive relation from the cohesive law between the material particles with an implicit fracture criterion. Hydraulic pressure is applied using a new scheme that enables simulation of hydraulically driven cracks. When the model is applied to study hydraulic fracture propagation in the presence of a natural fracture, the results show the method to be very effective. It shows that although the in situ stress ratio is the dominant factor governing the propagation direction, a natural fault can also strongly influence the hydraulic fracture behavior. This influence is conditioned by the shear stiffness of the fault and the distance to the original hydraulic fracture. The model results show that when the fault is strong in shear, its impact on hydraulic fracture trajectory is weak and the hydraulic fracture will likely penetrate the fault. For a weak fault, however, the fracture tends to be arrested at the natural fault. The distance between the fault and the hydraulic fracture is also important; the fault influence increases with decreasing distance. The VMIB does not require selection of a fracture criterion and remeshing when the fracture propagates. Therefore, it is advantageous for modeling fracture initiation and propagation in naturally fractured rock. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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VMIB (Virtual Multi-dimensional Internal Bonds)模型是在VIB(Virtual Internal Bond) 模型基础上发展起来的一种多尺度力学模型。VIB认为,固体材料在微观上是由随机分布的质量微粒（Material particle）构成,微粒与微粒之间由一虚内键（virtual internal bond）连结,材料的宏观本构方程则直接由微粒之间的连结法则（Cohesive law）导出。而在VMIB中,微粒之间引入了切向效应,材料的宏观本构方程由虚内键刚度系数导出。由于考虑了微粒之间的切向效应,VMIB能够再现材料不同泊松比。依据VMIB,材料的宏观力学行为决定于微观虚内键的演化。岩石材料在围压条件下强度显著增强,破坏模式一般表现为剪切破坏,其微观机制在于虚内键的演化决定于自身的法向和切向变形,并且演化速度决定于连续层次上材料微元的应力状态。为描述这种微观虚内键的演化机制,提出了一种虚内键演化方程。通过该演化方程,可以宏观再现岩石材料在围压条件下的断裂破坏行为。作为初步应用,没有考虑材料的塑性变形机制,因此,还有待于进一步的理论完善。 相似文献
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In order to study the damage constitutive model of rock mass with non-persistent joints in engineering practice, the assumption that the rock mesoscopic elements strength obeys the Weibull distribution function of random, the Drucker–Prager criterion is used as a representation method to describe the strength of the mesoscopic elements, and mesoscopic damage variable is deduced. Combined with the energy principle and the fracture damage theory, the macroscopic damage variable formula is deduced considering the crack propagation length and the friction effect of joint closure in the rock mass. Finally, based on the strain equivalent hypothesis of Lemaitre and considering the coupling of macro and micro defects, the composite damage variables are derived. A macro–meso composite damage constitutive model of rock mass with non-persistent joints is established based on the Drucker–Prager criterion. The theoretical constitutive curves of the model are in good agreement with the experimental constitutive curves of the non-persistent jointed rock masses. The considering effects of crack propagation length and joint closure friction effect are compared with those without considering the crack propagation length and joint closure friction effect, which finds that the former is superior to the latter, and the rationality and validity of the model is verified. 相似文献
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Modeling 3D thermal fracture propagation by transient cooling using virtual multidimensional internal bonds 
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下载免费PDF全文 Thermal fracturing can play an important role in development of unconventional petroleum and geothermal resources. Thermal fractures can result from the nonlinear deformation of the rock in response to thermal stress related to cold water injection as well as heating. Before the rock reaches the final failure stage, material softening and bulk modulus degradation can cause changes in the thermo‐mechanical properties of the solid. In order to capture this aspect of the rock fracture, a virtual multidimensional internal bond‐based thermo‐mechanical model is derived to track elastic, softening, and the failure stages of the rock in response to the temporal changes of its temperature field. The variations in thermo‐mechanical properties of the rock are derived from a nonlinear constitutive model. To represent the thermo‐mechanical behavior of pre‐existing fractures, the element partition method is employed. Using the model, numerical simulation of 3D thermal fracture propagation in brittle rock is carried out. Results of numerical simulations provide evidence of model verification and illustrate nonlinear thermal response and fracture development in rock under uniform cooling. In addition, fracture coalescence in a cluster of fractures under thermal stress is illustrated, and the process of thermal fracturing from a wellbore is captured. Results underscore the importance of thermal stress in reservoir stimulation and show the effectiveness of the model to predict 3D thermal fracturing. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Propagation of fractures, especially those emanating from wellbores and closed natural fractures, often involves Mode I and Mode II, and at times Mode III, posing significant challenges to its numerical simulation. When an embedded inclined fracture is subjected to compression, the fracture edge is constrained by the surrounding materials so that its true propagation pattern cannot be simulated by 2D models. In this article, a virtual multidimensional internal bond (VMIB) model is presented to simulate three‐dimensional (3D) fracture propagation. The VMIB model bridges the processes of macro fracture and micro bond rupture. The macro 3D constitutive relation in VMIB is derived from the 1D bond in the micro scale and is implemented in a 3D finite element method. To represent the contact and friction between fracture surfaces, a 3D element partition method is employed. The model is applied to simulate fracture propagation and coalescence in typical laboratory experiments and is used to analyze the propagation of an embedded fracture. Simulation results for single and multiple fractures illustrate 3D features of the tensile and compressive fracture propagation, especially the propagation of a Mode III fracture. The results match well with the experimental observation, suggesting that the presented method can capture the main features of 3D fracture propagation and coalescence. Moreover, by developing an algorithm for applying pressure on the fracture surfaces, propagation of a natural fracture is also simulated. The result illustrates an interesting and important phenomenon of Mode III fracture propagation, namely the fracture front segmentation. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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Concrete cracking in reinforced concrete structures is governed by two mechanisms: the activation of bond forces at the steel–concrete interface and the bridge effects of the reinforcement crossing a macro‐crack. The computational modelling of these two mechanisms, acting at different scales, is the main objective of this paper. The starting point is the analysis of the micro‐mechanisms, leading to an appropriate choice of (measurable) state variables describing the energy state in the surface systems: on the one side the relative displacement between the steel and the concrete, modelling the bond activation; on the other hand, the crack opening governing the bridge effects. These displacement jumps are implemented in the constitutive model using thermodynamics of surfaces of discontinuity. On the computational side, the constitutive model is implemented in a discrete crack approach. A truss element with slip degrees of freedom is developed. This degree of freedom represents the relative displacement due to bond activation. In turn, the bridge effect is numerically taken into account by modifying the post‐cracking behaviour of the contact elements representing discrete concrete cracks crossed by a rebar. First simulation results obtained with this model show a good agreement in crack pattern and steel stress distribution with micro‐mechanical results and experimental results. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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裂隙的剪胀特性及扩展演化规律对岩体的渗流特性具有重要影响。为揭示裂隙剪胀及扩展演化对岩体渗流的影响,基于残余强度提出了一种能较好描述岩石硬化-软化特性的全剪切本构关系;结合剪切变形与裂隙开度的关系,利用最小势能原理和立方定律,建立了压剪作用下考虑裂隙剪胀特性的渗流应力耦合模型;假定压剪作用下裂隙发生Ⅰ型扩展,提出了伴有翼型裂纹的渗流模型,该模型不仅考虑了岩石的剪胀特性,更反映了裂隙扩展过程渗流的演化规律。对不同裂隙粗糙度的剪切应力-位移曲线进行分析,全剪切本构模型表现出较高的拟合精度。在剪切应力-位移关系基础上,通过剪切渗流试验数据对压剪作用下渗流模型进行验证,结果表明,该模型能较好地描述岩体剪胀阶段渗透性演化规律。利用等效裂隙简化裂隙网络,并通过试验数据进行验证,证实了裂隙扩展过程渗流-应力耦合模型的准确性与适用性。 相似文献
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外部荷载作用下的裂隙扩展在空间上一般是非均匀的,引起岩石材料的衍生各向异性。将材料离散成大量随机分布的由力键连结的物质点,基于力键的方向性,且将局部弹性张量离散成一定数量的方向张量,理论推导出力键模量与宏观弹性参数之间的关系。通过考虑力键断裂效应,建立了各向异性弹性损伤本构模型。为了模拟中等孔隙率岩石在常规三轴压缩试验中脆性向延性转变的力学行为,在力键断裂效应中引入损伤抑制函数。通过模拟Tennessee大理岩和Indiana石灰岩的常规三轴实验,并与试验数据对比,验证了模型的合理性和有效性。 相似文献
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We present a contribution on the risk of hydraulic fracturing in CO2 geological storage using an analytical model of hydraulic fracturing in weak formations. The work is based on a Mohr–Coulomb dislocation model that is extended to account for material with fracture toughness. The complete slip process that is distributed around the crack tip is replaced by superdislocations that are placed in the effective centers. The analytical model enables the identification of a dominant parameter, which defines the regimes of brittle to ductile propagation and the limit at which a mode‐1 fracture cannot advance. We examine also how the corrosive effect of CO2 on rock strength may affect hydraulic fracture propagation. We found that a hydraulically induced vertical fracture from CO2 injection is more likely to propagate horizontally than vertically, remaining contained in the storage zone. The horizontal fracture propagation will have a positive effect on the injectivity and storage capacity of the formation. The containment in the vertical direction will mitigate the risk of fracturing and migration of CO2 to upper layers and back to the atmosphere. Although the corrosive effect of CO2 is expected to decrease the rock toughness and the resistance to fracturing, the overall decrease of rock strength promotes ductile behavior with the energy dissipated in plastic deformation and hence mitigates the mode‐1 fracture propagation. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Rock is a heterogeneous medium that is composed of minerals of various sizes. Under the action of external loads, the generation, propagation and coalescence of microdefects in the rock mass determines the macroscopic deformation and fracture of rock. To understand the damage law of rock and to reveal the evolution of dynamic failure, a uniaxial compression model was established based on particle flow code. Acoustic emission and energy characteristics of rock damage were analyzed, and the damage constitutive models of rock were discussed. During rock uniaxial compression, acoustic-emission events undergo a relatively quiet, sudden increase and sharp decrease for three periods, which corresponds to the compaction and elastic deformation stage, yield stage and post-peak stage in the stress–strain curve. Before the yield stress is reached, the proportion of bond and strain energies is larger. Friction energy accounts for a small proportion of the total energy, and a reciprocal relationship exists between them. The constitutive model that is based on friction energy can better reflect the variation in stress and strain, then the constitutive model based on acoustic-emission parameters. 相似文献
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Computational model coupling mode II discrete fracture propagation with continuum damage zone evolution 下载免费PDF全文
下载免费PDF全文 We propose a numerical method that couples a cohesive zone model (CZM) and a finite element‐based continuum damage mechanics (CDM) model. The CZM represents a mode II macro‐fracture, and CDM finite elements (FE) represent the damage zone of the CZM. The coupled CZM/CDM model can capture the flow of energy that takes place between the bulk material that forms the matrix and the macroscopic fracture surfaces. The CDM model, which does not account for micro‐crack interaction, is calibrated against triaxial compression tests performed on Bakken shale, so as to reproduce the stress/strain curve before the failure peak. Based on a comparison with Kachanov's micro‐mechanical model, we confirm that the critical micro‐crack density value equal to 0.3 reflects the point at which crack interaction cannot be neglected. The CZM is assigned a pure mode II cohesive law that accounts for the dependence of the shear strength and energy release rate on confining pressure. The cohesive shear strength of the CZM is calibrated by calculating the shear stress necessary to reach a CDM damage of 0.3 during a direct shear test. We find that the shear cohesive strength of the CZM depends linearly on the confining pressure. Triaxial compression tests are simulated, in which the shale sample is modeled as an FE CDM continuum that contains a predefined thin cohesive zone representing the idealized shear fracture plane. The shear energy release rate of the CZM is fitted in order to match to the post‐peak stress/strain curves obtained during experimental tests performed on Bakken shale. We find that the energy release rate depends linearly on the shear cohesive strength. We then use the calibrated shale rheology to simulate the propagation of a meter‐scale mode II fracture. Under low confining pressure, the macroscopic crack (CZM) and its damaged zone (CDM) propagate simultaneously (i.e., during the same loading increments). Under high confining pressure, the fracture propagates in slip‐friction, that is, the debonding of the cohesive zone alternates with the propagation of continuum damage. The computational method is applicable to a range of geological injection problems including hydraulic fracturing and fluid storage and should be further enhanced by the addition of mode I and mixed mode (I+II+III) propagation. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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在全断面岩石掘进机（TBM）刀具破岩的颗粒元模拟中颗粒参数的选取至关重要,其中颗粒间平行黏结切向、法向强度是关键控制性参数之一,它们之间的比值关系直接决定所模拟试样的延脆性质,影响刀具破岩过程及其破岩效果。为探讨延脆性对刀具破岩模式的影响,（1）建立9种采用不同平行黏结强度比值的数值模型,分别进行单轴压缩及巴西劈裂模拟,研究不同延脆性试样的力学行为及破坏模式的变化。（2）对9种模型进行双刀破岩,并监控其裂缝的发展情况及刀具的受力状况。（3）为减小随机性对模拟结果的影响,通过改变随机数,每种模型重复模拟5次,综合分析5次的计算结果。模拟分析发现,随着切向和法向黏结强度比值( )的增大,试样的脆性增加,破坏模式逐渐从剪切破坏转变为脆性张拉破坏,刀具破岩压碎区范围减小,张拉裂缝更容易在刀具间贯通延伸从而切割出块体更大的岩渣;随着试样脆性的增加,归一化比能减小,刀具破岩的效率增加;平行黏结强度比值相同的条件下采用不同随机数种子生成的模型中,试样的具体破坏情况有一定的差别,但总体破坏模式相似。 相似文献
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Jiao Kaituo Han Dongxu Wang Daobing Chen Yujie Li Jingfa Gong Liang Bai Bofeng Yu Bo 《Computational Geosciences》2022,26(5):1167-1187
Thermal-hydro-mechanical (THM) coupled fracture propagation is common in underground engineering. Rock damage, as an inherent property of rock, significantly affects fracture propagation, but how it influences the THM coupled fracturing remains stubbornly unclear. A pore-scale THM coupling model is developed to study this problem, which combines the lattice Boltzmann method (LBM), the discrete element method (DEM), and rock damage development theory together for the first time. This model can more accurately calculate the exchanged THM information at the fluid-solid boundary and fluid conductivity dependent on fracture and rock damage. Based on the developed model, the synergistic effect of injected temperature difference (fluid temperature below rock temperature) and rock damage (characterized by the parameter “critical fracture energy”, abbreviated as “CFE”) on fracture propagation of shale are investigated particularly. It is found that: (1) the generation of branched cracks is closely related to the temperature response frontier, and the fracture process zone of single bond failure increases in higher CFE. (2) through the analysis of micro failure events, hydraulic fracturing is more pronounced in the low CFE, while thermal fracturing displays the opposite trend. The fluid conductivity of fractured rock increases with a higher injected temperature difference due to the more penetrated cracks and wider fracture aperture. However, this enhancement weakens when rock damage is significant. (3) in the multiple-layered rock with various CFEs, branched cracks propagating to adjacent layers are more difficult to form when the injection hole stays in the layer with significant rock damage than without rock damage.
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采用凝固过程中的混凝土模拟不同物理力学特性的锚固介质,用数值模拟和试验的方法研究了锚固锚杆中的波系及锚固锚杆中界面波的形成过程。数值模拟和试验模拟都表明随着锚固介质力学性质的改变锚杆中传播的波的特性发生改变。锚杆中传播的P波对锚固介质的力学特性非常敏感,随着锚固强度的增加,界面波产生,P波逐渐衰减消失。锚杆中传播的波由原来的P波占主导成为界面波占主导,波在锚固段的传播速度也由杆速度成为界面波波速。界面波的波速与锚固介质的力学性质相关,因此可以用界面波的波速来评价锚杆锚固质量以及计算锚杆锚固段长度。 相似文献
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借助损伤力学思想,基于统计强度理论,提出一种适用于深部工程破裂区破裂岩体的本构模型建立方法,并通过室内试验和数值试验进行了验证。将破裂岩体划分为无数微元立方体,微元立方体的强度与岩石破裂程度有关,且各立方体强度随机分布,故可用强度反映破裂岩体的破裂程度,据此提出一种破裂岩体本构模型建立方法。其中,根据岩石破裂面间的摩擦力做功等于材料破裂后释放的应变能,得到从力学角度定义的岩石破裂程度变量;另外,假定微元立方体强度分布服从Weibull分布,应力水平满足Hoek-Brown准则。利用泥质砂岩破裂岩体典型三轴试验结果,建立泥质砂岩破裂岩体本构模型,并进行了验证,结果表明模型计算曲线与试验曲线吻合度较好。利用离散元软件PFC进行了补充数值试验验证研究,证明了泥质砂岩破裂岩体理论模型的良好计算效果,进而证明提出的本构模型建立方法的可行性。 相似文献
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Modeling hydraulic fracturing in the presence of a natural fracture network is a challenging task, owing to the complex interactions between fluid, rock matrix, and rock interfaces, as well as the interactions between propagating fractures and existing natural interfaces. Understanding these complex interactions through numerical modeling is critical to the design of optimum stimulation strategies. In this paper, we present an explicitly integrated, fully coupled discrete‐finite element approach for the simulation of hydraulic fracturing in arbitrary fracture networks. The individual physical processes involved in hydraulic fracturing are identified and addressed as separate modules: a finite element approach for geomechanics in the rock matrix, a finite volume approach for resolving hydrodynamics, a geomechanical joint model for interfacial resolution, and an adaptive remeshing module. The model is verified against the Khristianovich–Geertsma–DeKlerk closed‐form solution for the propagation of a single hydraulic fracture and validated against laboratory testing results on the interaction between a propagating hydraulic fracture and an existing fracture. Preliminary results of simulating hydraulic fracturing in a natural fracture system consisting of multiple fractures are also presented. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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Studying the effect of non‐spherical micro‐particles on Hoek–Brown strength parameter mi using numerical true triaxial compressive tests 下载免费PDF全文
下载免费PDF全文 The strength parameter mi in the Hoek–Brown strength criterion is empirical and was developed by trial and error. To better understand the fundamental relationship between mi and the physical characteristics of intact rock, this paper presents a systematic study of mi by representing intact rock as a densely packed cemented particle material and simulating its mechanical behavior using particle flow modeling. Specifically, the three‐dimensional particle flow code (PFC3D) was used to conduct numerical true triaxial compression tests on intact rock and to investigate the effect of non‐spherical micro‐particle parameters on mi. To generate numerical intact rock specimens containing non‐spherical micro‐particles, a new genesis process was proposed, and a specific loop algorithm was used based on the efficiency of the process and the acceptability of generated specimens. Four main parameters—number, aspect ratio, size, and shape—of non‐spherical micro‐particles were studied, and the results indicated that they all have great effect on mi. The strength parameter mi increases when the number, aspect ratio, or size is larger or the shape becomes more irregular, mainly as a result of the higher level of interlocking between particles. This confirms the observations from engineering experience and laboratory experiments. To simulate the right strength parameter mi, it is important to use appropriate non‐spherical micro‐particles by controlling these four parameters. This is further demonstrated by the simulation of two widely studied rocks, Lac du Bonnet granite and Carrara marble. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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This work deals with the development of a constitutive law for fractured rocks. Fractures are considered as penny‐shaped inclusions, whose constitutive law is deduced from an interface law and a regularization procedure. Such a method is applied to linear and non‐linear interface behaviours in order to reproduce effects such as an increase in stiffness during fracture closing, dilatancy or asperity surface degradation. Then, considering the fractured rock as a composite material, we use a Mori–Tanaka method to estimate the homogenized properties of the rock. Numerical experiments illustrate the interest of the proposed homogenization procedure. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献