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1.
Peng-Zhi Pan Jonny Rutqvist Xia-Ting Feng Fei Yan Quan Jiang 《Rock Mechanics and Rock Engineering》2014,47(6):2183-2198
We present a formulation of a discontinuous cellular automaton method for modeling of rock fluid pressure induced fracture propagation and coalescence without the need for remeshing. Using this method, modelers discretize a discontinuous rock-mass domain into a system composed of cell elements in which the numerical grid and crack geometry are independent of each other. The level set method, which defines the relationship between cracks and the numerical grid, is used for tracking the crack location and its propagation path. As a result, no explicit meshing for crack surfaces and no remeshing for crack growth are needed. Discontinuous displacement functions, i.e., the Heaviside functions for crack surfaces and asymptotic crack-tip displacement fields, are introduced to represent complex discontinuities. When two cracks intersect, the tip enrichment of the approaching crack is annihilated and is replaced by a Heaviside enrichment. We use the “partition of unity” concept to improve the integral precision for elements, including crack surfaces and crack tips. From this, we develop a cellular automaton updating rule to calculate the stress field induced by fluid pressure. Then, the stress is substituted into a mixed-mode fracture criterion. The cracking direction is determined from the stress analysis around the crack tips, where fracture fluid is assumed to penetrate into the newly developed crack, leading to a continuous crack propagation. Finally, we performed verification against independent numerical models and analytic solutions and conducted a number of simulations with different crack geometries and crack arrangements to show the robustness and applicability of this method. 相似文献
2.
This paper describes the application of symmetric Galerkin boundary element methods (SGBEM) for the analysis of a 2D crack propagation problem. The sub-domain SGBEM for crack problem is derived. The coefficient matrix is completely symmetric. Cohesive crack model is used to simulate crack propagation. The increment control method for crack propagation and the method for unknown crack propagation path have been derived for high-order element. Two-stage interpolation method called the ‘quasi-higher order element method’ (QHOEM) is then proposed to solve the double integrals. In the initial stage, it uses higher order elements to interpolate the field variables, and for the numerical integration involved, it further uses interpolation functions to decompose the higher order elements into lower order elements so that the existing analytical integration can be applied. A finite rectangular plate containing a centre crack growth and four-points bending beam problem have been analysed to check the accuracy of the proposed method. For actual application, a dam buttress with an edge crack has been analysed and the results are found to be in agreement with the other numerical and experimental results. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
3.
含多裂纹沥青路面开裂机制及扩展分析 总被引：1，自引：1，他引：0
基于断裂力学基本理论,通过有限元数值模拟方法,研究了同时存在表面裂纹和反射裂纹的沥青路面在交通荷载作用下表面裂纹和反射裂纹开裂机制及扩展路径,深入讨论了路面材料和结构对裂纹扩展路径的影响,分析了表面裂纹的位置对反射裂纹扩展路径的影响,采用多裂纹小梁弯曲试验验证了多裂纹的扩展行为。结果表明：在交通荷载作用下,表面裂纹向着偏离载荷的方向扩展,且扩展路径几乎为直线,反射裂纹则沿着“Z”字形向上扩展;路面结构层模量和厚度的改变能够影响裂纹的扩展路径;反射裂纹总是向着存在表面裂纹的一侧扩展;小梁弯曲试验得到裂纹扩展行为与数值模拟结果一致。 相似文献
4.
水力压裂作为煤层强化增透技术的一种,其应力演化特征及裂隙形态与扩展范围的判断尤为重要。采用离散元数值方法,以导向压裂为背景,建立水力压裂流固耦合模型;通过应力路径、裂纹热点图等手段,探究水力压裂过程中压裂排量、泊松比、天然裂隙密度对应力演化和裂隙演化的影响及其细观规律。结果表明:不同压裂排量下的应力演化方向及最终应力路径曲线形状有着明显的不同,低排量下裂隙附近的应力比值逐渐增大,而在高排量下先增大后减小;煤层泊松比越大,平均压裂半径越低,但对起裂时间及裂隙的扩展形态影响不明显;天然裂隙的发育情况对水力裂隙的扩展起着关键性作用,高裂隙发育煤层水力裂隙扩展的方向性无法预测,应力演化方向会出现反转现象;压裂过程中不同区域的应力演化特征能够反映出裂隙的扩展状态,现场可通过监测压裂区域附近应力变化,判断水力压裂缝网的扩展范围。 相似文献
5.
提出了一种模拟裂纹扩展的水平集和无网格耦合方法。由于水平集和无网格方法都是建立在离散节点上,因而可以很自然地实现耦合。在该方法中,两个在裂尖处相互正交的水平集不仅用于描述裂纹的几何形态和裂尖位置,而且用于建立无网格伽辽金法（简称EFGM）不连续近似函数中的Heaviside跳跃项和裂尖处的Westergaard扩展项。当裂纹扩展时,则由水平集更新算法确定新裂纹的位置。水平集和无网格耦合法无需使用可视法、衍射法或透明法,克服了这些方法在裂尖处人为引入的不连续且能很好地再生 奇异场;而且节点影响域不受裂纹线切割的影响,在计算中往往使用较小的影响域,保持了整体刚度矩阵的带状、稀疏性;另外,水平集简化了扩展节点的选取和附加函数的建立,其更新过程无需求解演化方程,实现简单且易于编程。数值算例表明本文方法具有较高的计算精度,其模拟的裂纹扩展路径与试验结果吻合得很好,从而验证了本文方法的正确性和可行性。 相似文献
6.
模拟岩石破裂过程的块体单元离散弹簧模型 总被引：2，自引：0，他引：2
在变形体离散元的基础上建立块体单元离散弹簧模型,并应用于岩石破裂过程的数值模拟研究。该模型以连续介质力学理论为基础,将块体单元离散为具有明确物理意义的弹簧系统,通过对弹簧系统的能量泛函求变分获得各弹簧的刚度系数,进而可以直接利用弹簧刚度求解单元的变形和应力,提高计算效率。以重力作用下的岩质边坡计算为例,通过与传统的有限元进行对比,验证该模型弹性计算结果的正确性。在该基础上,引入Mohr-Coulomb与最大拉应力的复合破坏准则,判断单元的破坏状态及破裂方向。当单元的内部破坏面确定后,则通过块体切割的方式实现单元破坏,并建立单元边界和单元内部的双重破裂机制,实现块体由连续到非连续的破裂过程,进而显示的模拟裂纹的形成和扩展。最后,以巴西圆盘劈裂、单轴压缩破裂以及三点弯曲梁等典型算例验证该方法,结果表明该方法可以较好地模拟拉伸、压剪等应力状态下裂纹的形成和扩展,从而可模拟岩石介质由连续到非连续的破裂过程。 相似文献
7.
Capturing the two‐way hydromechanical coupling effect on fluid‐driven fracture in a dual‐graph lattice beam model 
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下载免费PDF全文 Fluid‐driven fractures of brittle rock is simulated via a dual‐graph lattice model. The new discrete hydromechanical model incorporates a two‐way coupling mechanism between the discrete element model and the flow network. By adopting an operator‐split algorithm, the coupling model is able to replicate the transient poroelasticity coupling mechanism and the resultant Mandel‐Cryer hydromechanical coupling effect in a discrete mechanics framework. As crack propagation, coalescence and branching are all path‐dependent and irreversible processes, capturing this transient coupling effect is important for capturing the essence of the fluid‐driven fracture in simulations. Injection simulations indicate that the onset and propagation of fractures is highly sensitive to the ratio between the injection rate and the effective permeability. Furthermore, we show that in a permeable rock, the borehole breakdown pressure, the pressure at which fractures start to grow from the borehole, depends on both the given ratio between injection rate and permeability and the Biot coefficient. 相似文献
8.
开挖卸荷作用下裂隙岩体边坡的破坏模式与路径分析是边坡工程灾害研究的热点之一,准确识别边坡的潜在破裂路径对工程安全施工和支护优化设计具有重要意义。依据断裂扩展分析方法,将裂隙扩展判别的理论方法开发并应用于数值模拟分析中,通过裂隙尖端应力强度因子计算、裂隙扩展模式识别、裂隙起裂角演算、裂隙扩展交汇等技术实现了岩体中断续裂隙的起裂、扩展与贯通演化过程的快速模拟;以某高速公路沿线裂隙岩体路堑边坡为对象,采用提出的模拟方法分析了多级开挖卸荷作用下坡体裂隙的扩展机制与边坡的破坏路径。结果表明：裂隙岩体边坡从上至下多级开挖过程中,坡肩裂隙首先起裂,并通过拉张型扩展逐渐发展为优势裂隙;随着边坡下挖,优势裂隙沿坡面向下逐步发生拉张/剪切混合型扩展并与既有裂隙交汇,在边坡中上部形成阶梯状扩展破坏路径;裂隙扩展至边坡下部及坡脚后扩展模式由拉张/剪切混合型转化为剪切型,并最终以弧形剪切面从坡脚出露。研究揭示了裂隙岩体边坡多级开挖卸荷作用下上部阶梯状拉张/剪切混合型破裂-下部弧形剪切型破裂的复合破坏模式,可为边坡工程支护设计和施工稳定性控制提供新思路。 相似文献
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The details of the Element Free Galerkin (EFG) method are presented with the method being applied to a study on hydraulic fracturing initiation and propagation process in a saturated porous medium using coupled hydro-mechanical numerical modelling. In this EFG method, interpolation (approximation) is based on nodes without using elements and hence an arbitrary discrete fracture path can be modelled.The numerical approach is based upon solving two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Displacement increment and pore water pressure increment are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system of equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on the penalty method. In order to model discrete fractures, the so-called diffraction method is used.Examples are presented and the results are compared to some closed-form solutions and FEM approximations in order to demonstrate the validity of the developed model and its capabilities. The model is able to take the anisotropy and inhomogeneity of the material into account. The applicability of the model is examined by simulating hydraulic fracture initiation and propagation process from a borehole by injection of fluid. The maximum tensile strength criterion and Mohr–Coulomb shear criterion are used for modelling tensile and shear fracture, respectively. The model successfully simulates the leak-off of fluid from the fracture into the surrounding material. The results indicate the importance of pore fluid pressure in the initiation and propagation pattern of fracture in saturated soils. 相似文献
10.
在岩土工程分析中求解精度控制常常是必需的,在数值流形法中可以通过控制数学覆盖网格的稀疏和覆盖位移的阶数来达到精度的要求。提出了基于等几何分析的数值流形方法,定义了相应的数学覆盖的构造形式,推导了基于二次B样条的9节点数值流形方法分析格式;针对基于Lagrange插值函数的4节点数值流形方法提出了基于T样条思想的数学覆盖网格的局部加密方法。算例计算结果表明,相对于4节点的数值流形方法,基于非均匀有理B样条的9节点数值流形方法具有更高的精度;基于T样条思想的加密网格在保持计算精度的前提下降低了自由度的数量,表明T样条加密是一种自然的局部加密算法。 相似文献
11.
The analysis of the wave propagation in layered rocks masses with periodic fractures is tackled via a two-scale approach in order to consider shape and size of the rock inhomogeneities. To match the displacement fields at the two scales, an approximation of the micro-displacement field is assumed that depends on the first and second gradients of the macro-displacement through micro-fluctuation displacement functions obtained by the finite element solution of cell problems derived by the classical asymptotic homogenization. The resulting equations of motion of the equivalent continuum at the macro-scale result to be not local in space, thus a dispersive wave propagation is obtained from the model. The simplifying hypotheses assumed in the multi-scale kinematics limit the validity of the model to the first dispersive branch in the frequency spectrum corresponding to the lowest modes.Although the homogenization procedure is developed to study the macro-scale wave propagation in rock masses with bounded domain, the reliability of the proposed method has been evaluated in the examples by considering unbounded rock masses and by comparing the dispersion curves provided by the rigorous process of Floquet–Bloch with those obtained by the method presented. The accuracy of the method is analyzed for compressional and shear waves propagating in the intact-layered rocks along the orthotropic axes. Therefore, the influence of crack density in the layered rock mass has been analyzed. Vertical cracks have been considered, periodically located in the stiffer layer, and two different crack densities have been analyzed, which are differentiated in the crack spacing. A good agreement is obtained in case of compressional waves travelling along the layering direction and in case of both shear and compressional waves normal to the layering. The comparison between two crack systems with different spacing has shown this aspect to have a remarkable effect on waves travelling along the direction of layering, and limited in the case of waves propagating normal to the layers.The equivalent continuous model obtained through the dynamic homogenization technique here presented may be applied to the computational analysis of non-stationary wave propagation in rock masses of finite size, also consisting of sub-domains with different macro-mechanical characteristics. This avoids the use of computational models represented at the scale of the heterogeneities, which may be too burdensome or even unfeasible. 相似文献
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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. 相似文献
13.
This paper presents a boundary element method (BEM) procedure for a linear elastic fracture mechanics analysis in two‐dimensional anisotropic bimaterials. In this formulation, a displacement integral equation is only collocated on the uncracked boundary, and a traction integral equation is only collocated on one side of the crack surface. A fundamental solution (Green's function) for anisotropic bimaterials is also derived and implemented into the boundary integral formulation so that except for the interfacial crack part, the discretization along the interface can be avoided. A special crack‐tip element is introduced to capture the exact crack‐tip behavior. A computer program using FORTRAN has been developed to effectively calculate the stress intensity factors of an anisotropic bimaterial. This BEM program has been verified to have a good accuracy with previous studies. In addition, a central cracked bimaterial Brazilian specimen constituting cement and gypsum is prepared to conduct the Brazilian test under diametral loading. The result shows that the numerical analysis can predict relatively well the direction of crack initiation and the path of crack propagation. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
14.
通过对岩石边坡中的裂隙水对岩石边坡裂隙作用的力学原理进行分析的基础上,提出了数值流形方法中对裂隙水渗流作用的计算方法,并在原有考虑裂纹扩展的数值流形方法程序中加入了考虑裂隙渗流的子程序。最后利用综合考虑渗流与断裂的数值流形方法程序对含初始裂隙的岩石边坡在渗流作用下的破坏过程进行了模拟。模拟结果再现了原始裂隙在渗流作用下的扩展路径及所形成的切割块体在自重作用下的运动过程,与边坡的实际破坏模式基本一致。 相似文献
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A relationship between tensile strength and loading stress governing the onset of mode I crack propagation obtained via numerical investigations using a bonded particle model 下载免费PDF全文
下载免费PDF全文 Numerical models based on the discrete element method are used to study the fracturing process in brittle rock‐like materials under direct and indirect tension. The results demonstrate the capacity of the model to capture the essential characteristics of fracture including the onset of crack propagation, stable and unstable crack growth, arrest and reinitiation of fracturing, and crack branching. Simulations of Brazilian indirect tension tests serve to calibrate the numerical model, relating macroscopic tensile strength of specimens to their micromechanical breakage parameters. A second suite of simulations reveals a linear relationship between the tensile strength of specimens and the loading stress for which mode I tensile crack propagation ensues. Based on these results, a crack initiation criterion for brittle materials is proposed, prescribing the stressing conditions required to induce tensile failure. Such a criterion, if broadly applicable, provides a practical means to rapidly assess the failure potential of brittle materials under tensile loads. 相似文献
17.
为了有效地模拟连续介质向非连续介质的转化,发展了一种拉格朗日元方法、变形体离散元方法及虚拟裂纹模型耦合且考虑四边形单元沿对角线开裂的连续—非连续方法。利用该方法,模拟了不同围压时含孔洞模型的变形—开裂过程,统计了拉裂缝及剪裂缝区段数目,监测了一些单元的最大主应力。研究结果表明:当围压较小时,初始拉裂缝首先出现在孔洞的顶、底部,然后向模型的上、下端扩展,在初始拉裂缝的左、右两侧的拉应力集中区中产生远场拉裂缝,随后在孔洞的左、右两侧出现剪裂缝,最后,剪裂缝贯穿模型;当围压较大时,远场拉裂缝数量较少,未充分发展,远场拉裂缝与剪裂缝的发展阶段的界限不分明。含孔洞模型的最大承载力的下降是由于孔洞左、右两侧的剪裂缝向外扩展造成的。随着围压的增加,开始出现初始拉裂缝的时步数目增大,初始拉裂缝两侧的远场拉裂缝数目变少、出现变晚。 相似文献
18.
接触裂纹问题在工程结构中较为常见。结合数值流形法在裂纹处理上的优势,分析了压剪荷载作用下的接触裂纹问题,模拟了压剪裂纹渐进扩展过程。为了减少由于裂纹尖端位置不同而产生的误差,对裂纹尖端附近一定范围内的每一个物理覆盖附加奇异覆盖函数项,并根据裂纹尖端位置和单元含奇异物理覆盖的数目进行分区积分。选取一个压剪破坏算例,分析了法向接触力对应力强度因子计算结果的影响,并模拟了其渐进破坏过程。计算结果表明,所提方法在压剪裂纹问题方面的可行性,与未细化和覆盖细化方法得到的结果相比,更能准确地描述裂纹扩展路径。法向接触力对II型应力强度因子的贡献为0,对I型应力强度因子的影响较大,相对误差随网格密度变化明显,且法向接触力对I型应力强度因子的影响要比直接施加内压时的影响大。 相似文献
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为精准获得岩石I型裂纹扩展演化全过程,采用一种简易裂纹定向扩展装置开展了不同岩性试样裂纹扩展试验研究,借助声发射及数字散斑技术对裂纹扩展全过程进行了监测,建立了裂纹定向扩展力学模型,分析了裂纹扩展过程中声发射及变形场的演化规律,提出了评价岩石I型裂纹扩展难易程度的能量指标CE,探讨了I型裂纹定向起裂扩展机制。结果表明：该简易裂纹定向扩展装置能够有效实现I型裂纹沿预定方向稳定扩展,其起裂角均小于10º,同时通过简化力学模型计算得到白砂岩、灰砂岩的裂纹扩展峰值强度与巴西劈裂抗拉强度相比偏差分别为22.76%、7.53%;根据变形场演化规律,可将裂纹扩展分为微裂隙发育（散斑变形场分区不明显）、主控裂纹孕育（散斑变形场出现分区现象）和主控裂纹扩展3个阶段;声发射演化过程可分为平静期、缓增期、急增期和降低期4个阶段,由于灰砂岩相较于白砂岩质地更致密、更坚硬,导致其声发射平静期长,而后3个阶段持续时间短;将载荷−位移曲线峰前与峰后的面积之比定义为评价岩石I型裂纹扩展难易程度的能量指标CE,计算得到灰砂岩、白砂岩的CE分别为13～16、1～2,表明CE可有效评价岩石I型裂纹扩展难易程度;岩石I型裂纹起裂扩展机制可概况为：在加载峰值前裂隙尖端受最大拉应力作用,存储的弹性能快速增加、耗散能缓慢增加,但在加载峰值后裂隙尖端存储弹性能超过其储能极限迅速释放,此时输入能大部分转化为耗散能促进主控裂纹快速扩展。后续将对裂纹定向扩展试验装置进一步优化改进,以期为裂纹扩展机制、岩石破坏前兆信息、裂纹止裂原理等研究提供一种新方法,同时为工程现场煤岩层定向爆破、压裂、止裂等相关技术优化提供理论指导。 相似文献
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运用三维数值流形法（3D NMM）进行三维裂纹扩展分析,并采用C++语言编写了相应的程序。充分利用三维数值流形法模拟裂纹扩展的优势,只需要更新裂纹尖端线附近的边界环路和流形单元,不需要使用阶跃函数。根据三维数值流形法计算得到的应力结果,应用非局部求迹方法分析每个裂纹尖端的破坏状态,如果发生破坏则沿垂直于其最大主应力方向扩展。针对裂纹扩展后的不同状况,采用四边形或三角形推进法。裂纹扩展后为了使变形后的面保持平面,必须对新生成的面进行三角化分割。对诸如单边裂纹、平行钱币型裂纹和倾斜钱币型裂纹扩展问题进行数值模拟。计算结果表明,采用三维数值流形法进行裂纹扩展模拟是可行的,文中方法对裂纹尖端线非闭合和闭合的情形均适用,且文中方法对于裂纹尖端线位于单元内部的非平面裂纹扩展也是有效的。 相似文献