Phase-field study of grain boundary tracking behavior in crack-seal microstructures

In order to address the growth of crystals in veins, a multiphase-field model is used to capture the dynamics of crystals precipitating from a super-saturated solution. To gain a detailed understanding of the polycrystal growth phenomena in veins, we investigate the influence of various boundary conditions on crystal growth. In particular, we analyze the formation of vein microstructures resulting from the free growth of crystals as well as crack-sealing processes. We define the crystal symmetry by considering the anisotropy in surface energy to simulate crystals with flat facets and sharp corners. The resulting growth competition of crystals with different orientations is studied to deduce a consistent orientation selection rule in the free-growth regime. Using crack-sealing simulations, we correlate the grain boundary tracking behavior depending on the relative rate of crack opening, opening trajectory, initial grain size, and wall roughness. Further, we illustrate how these parameters induce the microstructural transition between blocky (crystals growing anisotropically) to fibrous morphology (isotropic) and formation of grain boundaries. The phase-field simulations of crystals in the free-growth regime (in 2D and 3D) indicate that the growth or consumption of a crystal is dependent on the orientation difference with neighboring crystals. The crack-sealing simulation results (in 2D and 3D) reveal that crystals grow isotropically and grain boundaries track the opening trajectory if the wall roughness is high, opening increments are small, and crystals touch the wall before the next crack increment starts. Further, we find that within the complete crack-seal regime, anisotropy in surface energy results in the formation of curved/oscillating grain boundaries (instead of straight) when the crack-opening velocity is increased and wall roughness is not sufficiently high. Additionally, the overall capability of phase-field method to simulate large-scale polycrystal growth in veins (in 3D) is demonstrated enumerating the main advantages of adopting the novel approach.     

Progress on Formation Mechanism of the Fibrous Veins in Mudstone and Its Implications to Hydrocarbon Migration

The fibrous mineral veins are widespread in mudstones. According to the different microscopic morphology of the minerals, the fibres can be divided into stretched crystals, elongate-blocky crystals and the very fibrous crystals. Veins can also be classified according to the growth direction of these crystals into stretched veins, syntaxial veins and antitaxial veins. The resulting texture in the vein depends on the morphology of the fracture surface, the width of the fracture and the growth habit of the vein forming mineral. The crack-seal mechanism can only interpret the formation of the stretched crystal veins and the elongate-blocky crystal veins, and the antitaxial well-developped fibrous veins form without fracturing and the growth competition is inhibited during the rock deformation, which implies that the nutrient transport is by diffusional flow transport. Horizontal crack is the primary condition of the formation of the antitaxial bedding-parallel fibrous calcite veins in muddy hydrocarbon source rocks. The formation of the horizontal crack which caused by the abnormal high pressure can enhance the hydrocarbon generation efficiency and has a great effect on the rate and direction of hydrocarbon migration in the local. The presence of the veins indicates the hydrocarbon fluid can migrate laterally along the layers. The antitaxial bedding-parallel fibrous calcite veins in muddy hydrocarbon source rocks can be the sign of the generation and migration of hydrocarbon under the abnormal high pressure condition in petroleum-bearing basins.     

Mixed mode fracture analysis of semi-circular bend (SCB) specimen: A numerical study based on extended finite element method

Previous studies are mainly concentrated on the use of the semi-circular bend (SCB) specimen for determining the entire mixed-mode I-II fracture toughness of rock, while less attention has been paid to its mixed-mode fracture process. In this situation, this study investigated mixed-mode fracture behavior of the SCB specimen using the extended finite element method (X-FEM). The crack growth trajectory, crack initiation angle and onset of fracture were discussed in detail. This paper is expected to provide a better understanding of mixed-mode fracture process of the SCB specimen occurring during fracture initiation and propagation.     

Modeling of dynamic cohesive fracture propagation in porous saturated media

In this paper, a mathematical model is presented for the analysis of dynamic fracture propagation in the saturated porous media. The solid behavior incorporates a discrete cohesive fracture model, coupled with the flow in porous media through the fracture network. The double‐nodded zero‐thickness cohesive interface element is employed for the mixed mode fracture behavior in tension and contact behavior in compression. The crack is automatically detected and propagated perpendicular to the maximum effective stress. The spatial discretization is continuously updated during the crack propagation. Numerical examples from the hydraulic fracturing test and the concrete gravity dam show the capability of the model to simulate dynamic fracture propagation. The comparison is performed between the quasi‐static and fully dynamic solutions, and the performance of two analyses is investigated on the values of crack length and crack mouth opening. Copyright © 2010 John Wiley & Sons, Ltd.     

侧向应力对裂隙渗透性的影响

目前不同试验者得出的侧向应力对裂隙渗透性影响的结果存在矛盾,其根本原因在于侧向应力对裂隙有多方面的影响。侧向应力引起裂隙开度增加、壁面磨损、充填物压缩。这些对裂隙渗透性有不同的影响。根据裂隙是否存充填物,建立了相应的三维应力对裂隙渗透性影响的表达式。当不存在充填物时,裂隙渗透性与侧向应力呈指数关系,当存在较多充填物时呈负指数关系。把两种情况写成统一的指数形式,认为裂隙存在少量充填或者裂隙壁面磨损时也是适合的。利用已有的试验成果对结果进行了验证,表明本文建立的表达式与试验结果符合得比较好。     

圆孔缺陷与I型运动裂纹相互作用的试验研究

为了研究运动裂纹与圆形孔缺陷的相互作用机制,采用数字激光动态焦散线方法进行了含圆形孔缺陷的冲击试验。结果表明：在冲击载荷下,I型运动裂纹在与圆形孔贯通前,断裂面光滑,扩展路径平直;运动裂纹从圆形孔上端起裂后,断裂面凹凸不平,扩展路径也更为弯曲。当运动裂纹朝向邻近的圆形孔扩展时,圆形孔对运动裂纹的扩展速度和动态应力强度因子有抑制作用,且随着圆形孔直径的增大,这种抑制作用不断增强。当运动裂纹与圆形孔缺陷汇聚后,圆形孔阻碍了裂纹的继续扩展,裂纹尖端被钝化,钝裂纹的起裂韧度较尖裂纹提高9.58%～13.87%,裂纹再次起裂时的扩展速度和动态应力强度因子存在明显的跳跃,表明钝裂纹更难起裂,需要消耗的能量更多。     

Experimental study of syntaxial vein growth during lateral fluid flow in transmitted light: first results

In-situ observations of transmitted-light experiments of syntaxial vein growth during lateral fluid flow in a simulated fracture show a decrease in growth rate towards the downstream end. As a consequence, the fracture is sealed at the inlet. Our observations show the rapid, non-linear growth competition of grains, which is a result of anisotropic growth kinetics and the complex fluid flow around the individual crystals.We compared our results with simulations based on a simplified numerical model, which builds on existing simulation techniques of this system. The model incorporates plug flow and a fluid-flow velocity dependent crystal growth rate law based on literature data. Simulations are in reasonable agreement with experimental results. A sensitivity analysis shows that a high fluid flow velocity and a low supersaturation increase the potential to seal a vein homogeneously, in agreement with previous work. Additionally, the effect of the initial crack shape is explored.     

动态载荷下大理岩断口形貌特征试验研究

为了探究动态载荷下大理岩的断口形貌特征,本文先利用分离式霍普金森压杆对岩样进行不同弹速下的冲击压缩和动态劈裂试验。接着,采用钨丝灯扫描电镜对岩样断口形貌进行细观观察,对比分析了不同试验条件下岩样的断裂模式。最后,引入分形维数定量表征了岩样断口细观形貌及其粗糙程度与冲击弹速间的内在关系。结果表明:在动态载荷下大理岩断口呈脆性特性,其基本断裂模式为沿晶断裂或穿晶断裂;高弹速冲击下,岩样断裂花样变小变密,表面附着岩粉趋多;相对于动态劈裂试验,动态压缩后岩样的破碎程度要高,断口花样中穿晶断裂形式所占的比重较大;随着弹速的增加,动态劈裂和动态压缩断裂模式均由耗能较低的沿晶断裂向耗能较高的穿晶断裂转变,分形维数值相应增大,但动态劈裂试验中分形维数值比动态压缩试验的应变率敏感性更加明显。     

The effects of fracture roughness on P-wave velocity

Artificial fractures were created on three different rock samples by sawing. The fracture surfaces were in turn grooved in different directions by sawing to simulate the fracture roughness. Four different roughness types were created and a fracture roughness coefficient (FRC) was defined for each type. Model experiments were carried out on the rock samples having different fracture roughness to investigate how the sound velocity varies with fracture roughness.

The test results were statistically analysed using the method of least squares regression and polynomial relationships with high correlation coefficient were found between the FRC values and the P-wave velocities. The P-wave velocity decreases with increasing the FRC values.     

砂岩断裂及其亚临界断裂的力学行为和细观机制

通过三点弯曲的SEM试验,详细研究了砂岩断裂的力学特征和细观机制。结果表明：砂岩断裂是一个复杂的过程,它不但与砂岩的物理成分、微缺陷等有关,还与砂岩中碎屑颗粒的分布密切相关,存在明显的亚临界断裂。亚临界断裂裂纹和断裂主裂纹形态相似。亚临界断裂裂纹较多的样品呈现延性断裂破坏的特征,而亚临界断裂裂纹较少的样品则呈现脆性断裂破坏的现象。     

On the role of joint roughness on the micromechanics of rock fracturing process: a numerical study

The deformation process and failure mechanism of rock mass with increased joint roughness subjected to unconfined compression are investigated in this study using discrete element method. A numerical model is developed using soft-bonded particle and validated to realistically replicate the mechanical response of the rock mass. The micro-parameters of the rock material are first determined, and the effects of the joint roughness on the macromechanical response and fracture growth mechanism are then investigated. Analyses are also performed to examine the tensile and shear crack distributions, acoustic emission (AE) characteristics, coordination number, and crack anisotropy to advance the current understanding of the role of joint roughness on the mechanical behavior and deformability of rock mass. The results show that strength and deformability of the jointed rocks are highly dependent on the joint orientation and roughness. Joint roughness is found to restrain the propagation and coalescence of microcracks and AE events from the interlocking of asperities. In addition, the spatial distribution of the contact forces allows for better understanding of the effect of joint inclination angle on the response of the investigated rock samples.

     

Self‐similar solution of a plane‐strain fracture driven by a power‐law fluid

This paper analyses the problem of a hydraulically driven fracture, propagating in an impermeable, linear elastic medium. The fracture is driven by injection of an incompressible, viscous fluid with power‐law rheology and behaviour index n?0. The opening of the fracture and the internal fluid pressure are related through the elastic singular integral equation, and the flow of fluid inside the crack is modelled using the lubrication theory. Under the additional assumptions of negligible toughness and no lag between the fluid front and the crack tip, the problem is reduced to self‐similar form. A solution that describes the crack length evolution, the fracture opening, the net fluid pressure and the fluid flow rate inside the crack is presented. This self‐similar solution is obtained by expanding the fracture opening in a series of Gegenbauer polynomials, with the series coefficients calculated using a numerical minimization procedure. The influence of the fluid index n in the crack propagation is also analysed. Copyright © 2002 John Wiley & Sons, Ltd.     

不同加载速率Ⅰ型预制裂纹花岗岩断裂特征研究

以CCD相机配合高速相机搭建试验变形观测系统,开展不同加载速率下含Ⅰ型预制裂纹花岗岩试件的三点弯试验。利用数字散斑相关方法对试验过程采集的数字散斑图像进行分析,对不同加载速率作用下含Ⅰ型预制裂纹花岗岩试件裂纹扩展过程中的变形演化特征、裂纹扩展速率、裂纹尖端张开位移、裂纹张开角以及初始断裂应力强度因子进行研究,研究结果表明：（1）花岗岩试件初始裂纹扩展速率随着加载速率的增加总体呈线性增加趋势;最大扩展速率随着加载速率增加呈现先较快增加后缓慢增加的变化趋势。（2）不同加载速率作用下,花岗岩试件预制裂纹尖端张开位移均呈现非线性缓慢增长-迅速增长-线性增长的变形趋势,且线性增长阶段曲线斜率随着加载速率的增加而增大。（3）随着加载速率的增加,花岗岩试件初始裂纹张开角先逐渐减小后稳定在0.1o～0.13o。（4）随着加载速率的增加,花岗岩试件初始断裂应力强度因子呈指数增长。     

Universal hydrofracturing algorithm for shear-thinning fluids: Particle velocity based simulation

A universal particle velocity based algorithm for simulating hydraulic fractures, previously proposed for Newtonian fluids, is extended to the class of shear-thinning fluids. The scheme is not limited to any particular elasticity operator or crack propagation regime. The computations are based on two dependent variables: the crack opening and the reduced particle velocity. The application of the latter facilitates utilization of the local condition of Stefan type (speed equation) to trace the fracture front. The condition is given in a general explicit form which relates the crack propagation speed (and the crack length) to the solution tip asymptotics. The utilization of a modular structure, and the adaptive character of its basic blocks, result in a flexible numerical scheme. The computational accuracy of the proposed algorithm is validated against a number of analytical benchmark solutions.     

Development of crystal morphology during unitaxial growth in a progressively widening vein: I. The numerical model

A two-dimensional numerical model for the simulation of the formation of microstructures in crack-seal veins is presented here. The grain aggregate in the vein is described by grain boundary nodes that link short, straight boundary segments. Growth of crystals into a crack takes place by many small incremental movements of nodes. The rate of growth depends on the chosen growth morphology of the vein-forming material. Different growth morphologies can be defined. For every user-defined number of steps, the wall rock is moved a user-defined distance and direction, which simulates the opening of a crack, after which sealing can proceed again. The shape of the crack-surface (e.g. smooth or with ridges) can be set by the user and can be made to match fracture surfaces found in real rocks. The model is capable of reproducing realistic crack-seal textures and can be used to systematically investigate the role of different parameters on the microstructures of veins. First applications of the model are presented in Part II of this paper (this volume).     

A laboratory simulation of fibrous veins: some first observations

Following work by Stephen Taber 80 years ago, we describe vein-like arrays of parallel, fibrous crystals that grow evaporatively between pairs of brine-soaked, porous ceramic substrates. Crystals of solute grow antitaxially from fixed sites on the substrate, forcing older parts of the crystals away from the growth site, without benefit of any long-range cracking parallel to the substrate. The nutrients for growth are fed to the growth site advectively or diffusively through the substrate blocks themselves, not along the plane of the vein. We call such crystallization Taber growth and suggest, as Taber did, that it might be an important mechanism for non-evaporative fibrous vein development in nature. The Taber growth model provides a ready explanation for the ability of fibers to track vein opening directions, and tracking is indeed the rule in our samples, though exceptions are also seen. Our results lend support to ideas already in the literature that fibrous veins are not necessarily products of a crack-seal process and that fibrous veins are not necessarily syntectonic. Our observations also raise questions about criteria for recognition of syntaxial fibrous veins and underscore the importance of finding new criteria for recognition of the younging direction along fibers.     

Three-dimensional analysis of hydraulic fracturing

The formulation, development, implementation and application of a complete three-dimensional hydraulic fracturing simulator, 3DHFRAC, is described. The simulator consists of two principal components: the first represents the solid deformation, crack opening and propagation, using a surface integral scheme, hybridised with finite-elements as needed, and a condition of critical stress-intensity-factor or energy-release-rate to track the motion of the fracture perimeter; the second captures the fluid flow along the open fracture, and into the reservoir. The simulator has been tested extensively by comparison to analytical results, simpler models and laboratory experiments for which good agreement is obtained. It is finally used to study the general growth of 3-D fracture propagation under different fluid and reservoir conditions.     

考虑倾角与开度的薄基岩裂隙溃沙特性研究

顶板溃沙是我国西部矿区浅埋煤层开采过程中面临的安全威胁之一。利用自行研制的裂隙溃沙试验系统,开展无水条件下风积沙溃沙过程的模拟试验,研究沙层厚度、裂隙倾角和裂隙开度对溃沙速率的影响,获得不同影响因素与裂隙中风积沙流动速率之间的定量关系。研究发现,沙层厚度的变化对溃沙速率几乎没有影响;裂隙倾角的变化对溃沙速率有明显的影响,在裂隙开度一定的情况下溃沙速率随着裂隙倾角的增大而增大,两者之间呈对数关系;裂隙开度对溃沙速率的影响较为显著,裂隙倾角一定时溃沙速率随着裂隙开度的增大而快速递增,两者之间符合指数关系;裂隙开度对溃沙速率的影响权重最大,而沙层厚度的影响权重可以忽略。该研究成果可为西部煤矿溃沙灾害的防治提供理论依据和科学指导。     

考虑三维形貌特征粗糙裂隙加卸载渗流规律研究

裂隙岩体在天然地质因素和人工扰动作用下处于加卸载环境是普遍存在的,裂隙面的几何特征和加卸载环境对裂隙渗流特性的影响在实际工程中不可忽视。采用试验和数值模拟相结合的方法,利用热-流-固三场耦合渗流试验系统,开展了应力加卸载作用下不同粗糙度裂隙岩芯试件的渗透试验,自主开发程序将激光扫描裂隙面的三维形貌信息导入到ABAQUS软件,模拟应力作用下的粗糙裂隙渗流。试验和数值模拟一致表明,粗糙裂隙的宽度和渗透率都随载荷的增加而减小,随着载荷的增加,裂隙接触刚度增大,裂隙的宽度和渗透率对载荷变化的敏感性降低;由于点接触产生的塑性变形不可恢复,卸载阶段的裂隙宽度和渗透率增加幅度减小,且小于加载阶段同载荷条件下的宽度和渗透率;裂隙渗透率、宽度与粗糙度呈正相关关系,且粗糙度越大,接触应力分布越不均匀;裂隙内流场符合群岛流,粗糙度越大群岛流现象越明显。     

基于扩展有限元的深部岩体分区破裂化现象初步数值模拟

通过轮廓法追踪岩石裂纹扩展轨迹,将其嵌入ABAQUS扩展有限元（EFE）平台,对单轴压力下裂隙试件受压过程进行了模拟验证,裂纹起裂扩展效果良好。以此为平台,将推导得到的弧形裂纹应力强度因子嵌入其中,以最大周向拉应力准则为开裂准则,认为当其大于岩体断裂韧度时,硐室围岩体内初始裂纹将开始扩展。在此基础上,以发现分区破裂现象的圆形隧道模型试验为背景开展了分区破裂的数值模拟试验。模拟结果发现,深部巷道围岩出现了3~4层破裂分区,证实深部巷道围岩存在分区破裂现象。将数值模拟结果与模型试验完成后模型围岩破坏状态对比,发现二者破裂区分布特征基本一致。数值模拟结果表明,EFEM方法在处理复杂岩体裂纹问题方面的有效性。