基于扩展有限元的页岩水力压裂数值模拟

考虑裂缝内流体流动和周围岩石应力变形,建立了页岩人工裂缝扩展的数学模型,分别采用有限元和扩展有限元求解裂缝流场和岩石应力场,并通过Picard迭代方法耦合求解,计算结果与经典模型结果吻合,验证了模型正确性.在此基础上,分析了岩石弹性模量、Poisson(泊松)比和注入速度对裂缝几何形态的影响以及水力裂缝任意角度逼近天然裂缝扩展动态.结果表明:弹性模量和注入速度对裂缝形态具有重要影响,而Poisson比对裂缝形态影响较小;随着页岩脆性增高,压裂裂缝趋于"长窄型"扩展;地应力差和逼近角越大,水力裂缝越易贯穿天然裂缝;水力裂缝与天然裂缝相交处裂缝宽度存在相对较大的降低;扩展有限元方法避免了计算过程中的网格重构与网格加密,减少了计算量,该模型可以为页岩压裂设计提供理论指导.     

基于光滑扩展有限元的平板裂纹参数不确定性反求

裂纹位置和尺寸等是工程监测需掌握的非常重要的信息.光滑扩展有限元是近年来发展起来的一种模拟裂纹的有效方法,即使采用极度不规则单元仍可获得精确的模拟结果,无需单元"质量"要求.因此在单元自动划分方面具有突出的优势,这一特点也使得该方法适用于裂纹反求过程的实时调用和含裂纹仿真模型的网格自动划分.研究基于光滑扩展有限元的不确定反求方法,用于识别平面弹性板中直裂纹位置和尺寸参数,即采用光滑扩展有限元法进行拉伸工况的正问题分析,通过测量平板边缘的节点位移建立优化模型,调用遗传算法实现裂纹参数的反求.反求过程中将材料的弹性模量和Poisson(泊松)比作为区间不确定变量,采用一阶Taylor(泰勒)公式实现了平板裂纹参数的不确定性反求.     

Ⅲ型弹粘塑性/刚性界面裂纹的定常扩展裂尖场

考虑裂纹尖端的奇异性和粘性效应,建立了双材料界面扩展裂纹尖端的弹粘塑性控制方程．引入界面裂纹尖端的位移势函数和边界条件,对刚性-弹粘塑性界面Ⅲ型界面裂纹进行了数值分析,求得了界面裂纹尖端应力应变场,并讨论了界面裂纹尖端场随各影响参数的变化规律．计算结果表明,粘性效应是研究界面扩展裂纹尖端场时的一个主要因素,界面裂纹尖端为弹粘性场,其场受材料的粘性系数、Mach数和奇异性指数控制．     

基于扩展有限元的页岩水平井多裂缝模拟研究

页岩储层水平井分段多簇压裂簇间距优选是压裂技术的关键,建立了水力压裂流固耦合数学模型,基于扩展有限单元法模拟多条裂缝的扩展过程,研究多条裂缝同时扩展的转向规律,以及应力干扰、水平主应力差、裂缝间距等因素与裂缝转向角度的关系.结果表明:应力干扰作用对裂缝宽度具有限制作用,单条裂缝张开宽度比两条裂缝的大;裂缝转角随应力差的减小而增大,随压裂时间的增加而增大.簇间距越小,应力干扰越强,转角越大,综合主缝均匀扩展、支撑剂填充以及复杂裂缝网络形成等条件,确定最优簇间距为30~40 m.多条裂缝同时扩展时,中间裂缝会受到两边裂缝的限制作用,簇间距越小,限制作用越强,裂缝发育时间越长,扩展速度越慢.     

三轴压缩下岩石/混凝土的三维细观损伤模型

考虑三轴压应力作用下的无限大体深埋椭圆形裂纹的变形场,给出了闭合椭圆形微裂纹的能量释放率.采用能量平衡方法分析了闭合椭圆形微裂纹的扩展条件,得到了代表性体积单元中具有任意空间取向的单个闭合椭圆形微裂纹及其扩展引起的附加柔度张量.分析了闭合椭圆形微裂纹的偏折扩展,得到了微裂纹偏折扩展引起的附加柔度张量.采用Taylor方法考虑微裂纹系统对代表性体积单元变形的影响,引入概率密度函数,得到了三轴压缩下岩石/混凝土的三维细观损伤模型.分析了混凝土的单轴压缩特性,结果表明该模型能够很好地描述实验现象.     

论非线性连续介质热-力耦合系统中的动力裂纹传播

在许多工程问题中,热-力耦合是重要的,而不能加以忽略.核反应堆工程就是这样的一个例子.本文讨论非线性连续介质的热-力耦合系统中的裂纹传播问题.各种的非线性介质,包括非线性弹性、弹塑性介质,被加以考虑,并且给出了相应情况下的各种路径无关积分.为了解释这些积分的物理含义,通过考虑一个缺口试件的裂纹传播,证明热-力耦合系统中的动力裂纹扩展力就等于这一路径无关积分.因此,就可利用这些积分来构作热-力耦合系统断裂动力学的非线性断裂准则.     

Ⅰ型动态扩展裂纹尖端的弹粘-理想塑性场

由于材料在扩展裂纹尖端的粘性效应的存在,考虑粘性效应并假设粘性系数与塑性等效应变率的幂次成反比,对理想塑性材料中平面应变扩展裂纹尖端场进行了弹粘塑性渐近分析,得到了不含间断的连续解,并讨论了Ⅰ型裂纹数值解的性质随各参数的变化规律．分析表明,应力和应变均具有幂奇异性,通过分析使尖端场的弹、粘、塑性可以合理匹配．对于Ⅰ型裂纹,裂尖场不含弹性卸载区．趋于极限情况时,裂纹尖端处于一种超粘性状态,并积聚了大量的能量,在各个受压应力状态下裂纹扩展．     

含分层损伤复合材料加筋层合板的分层扩展研究

建立了复合材料加筋结构的后屈曲和分层损伤扩展行为的数值模拟方法．基于Mindlin一阶剪切理论和von-Karman大挠度理论的层合板和层合梁单元，提出了含分层损伤复合材料加筋层合板分层扩展行为的有限元分析方法；利用虚裂纹闭合技术计算分层前缘的总能量释放率，并采用总能量释放率准则分层扩展判据，结合自适应网格移动技术，对在压缩载荷作用下的具有不同加筋形式，不同初始分层面积和形状的加筋板结构分层扩展行为进行了数值模拟研究，在分析中还考虑了加筋刚度、位置和分布，分层形状和大小、边界支撑强弱和分层前缘的接触效应对结构分层扩展行为的影响．本所提出的研究方法对工程界关于复合材料结构的设计具有重要意义．     

基于虚节点的多边形有限元法

虚节点法是一种新的基于单位分解理论的多边形有限元法.将虚节点法应用于求解弹性力学问题,并且通过大量数值实验测试虚节点法的计算效果.因为虚节点法具有多项式形式,所以有效地降低了传统多边形有限元法的积分误差.数值实验证明,在分片实验中虚节点法能得到比包括Wachspress法和mean value法在内的传统多边形有限元法更精确的数值结果.在收敛性试验中,虚节点法在相同节点数的条件下能取得比三角形一次单元更精确的数值结果.因为虚节点法能适应任意边数的多边形单元,所以对网格具有很强的适应性,在几何条件复杂、网格生成困难的问题中具有良好的应用价值.为了展示虚节点法潜在的应用价值,用虚节点法求解断裂力学应力强度因子和模拟裂纹扩展.同时,基于多边形单元的网格重划分技术和网格加密技术也应用于求解断裂力学应力强度因子和模拟裂纹扩展.     

非线性断裂动力学中的路径无关积分和断裂准则

本文考虑非线性断裂动力学中的路径无关积分和断裂准则.在讨论中计入了动力效应和裂纹的传播现象,考虑了裂纹在非线性弹性介质中的传播以及在弹塑性介质中的传播二种情况,作出了一些相应的路径无关积分.作为例子.讨论了裂纹的定常传播情况.最后,给出了这种路径无关积分的力学意义.说明它可用来作为非线性断裂动力学的一种断裂准则.     

Non-linear seismic response of concrete gravity dams to near-fault ground motions including dam-water-sediment-foundation interaction

This study focuses on non-linear seismic response of a concrete gravity dam subjected to near-fault and far-fault ground motions including dam-water-sediment-foundation rock interaction. The elasto-plastic behavior of the dam concrete is idealized using Drucker–Prager yield criterion based on associated flow rule assumption. Water in the reservoir is represented by 9-noded isoparametric quadrilateral fluid finite elements while the dam, the foundation rock and the sediment layer are modeled by using 8-noded isoparametric quadrilateral solid finite elements. The program NONSAP modified for elasto-plastic analysis of fluid-structure systems using the Lagrangian fluid finite element is employed in the response calculations. The fluid element includes the effects of surface waves and sloshing behavior of fluids. Non-linear seismic analyses of the selected concrete dam subjected to both near-fault and far-fault ground motions are performed. The results obtained from linear and non-linear analyses are compared with each other.     

A coupled NMM-SPH method for fluid-structure interaction problems

The main challenges in the numerical simulation of fluid–structure interaction (FSI) problems include the solid fracture, the free surface fluid flow, and the interactions between the solid and the fluid. Aiming to improve the treatment of these issues, a new coupled scheme is developed in this paper. For the solid structure, the Numerical Manifold Method (NMM) is adopted, in which the solid is allowed to change from continuum to discontinuum. The Smoothed Particle Hydrodynamics (SPH) method, which is suitable for free interface flow problem, is used to model the motion of fluids. A contact algorithm is then developed to handle the interaction between NMM elements and SPH particles. Three numerical examples are tested to validate the coupled NMM-SPH method, including the hydrostatic pressure test, dam-break simulation and crack propagation of a gravity dam under hydraulic pressure. Numerical modeling results indicate that the coupled NMM-SPH method can not only simulate the interaction of the solid structure and the fluid as in conventional methods, but also can predict the failure of the solid structure.     

Simulation of crack–propagation using embedded discontinuities

The transition from microscale damage phenomena to crack initiation and growth at the macroscale is an important mechanism which constrains the lifetime of concrete structures. Analysing crack growth using the finite element method without enhancement of the shape functions is possible only by continuously updating the corresponding meshes, which constitutes a significant computational effort. But even then the results can be substantially mesh–dependent and hard to interpret. The extended Finite Element Method (XFEM) uses additional discontinuous shape–functions and is one possibility to overcome these problems. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The pressure distribution around a growing crack

Exact solutions of the problem of the pressure distribution around an ideal hydraulic fracture are derived. The crack propagates in a permeable porous medium following a square-root growth law. The case of the penetration of the fracturing fluid into a reservoir is also considered.     

应用模糊综合评判方法优选水力压裂井

考虑到水力压裂井压裂效果影响因素之间的关系复杂,且各影响因素本身具有模糊性,这些因素很难用常规方法量化研究,尝试应用模糊综合评判的方法进行水力压裂井优选.通过对影响压裂效果的各个因素进行分析,优选出生产压差、含水率、压前增油量、孔隙度、渗透率、小层有效厚度、加砂量等7个主要因素,并应用层次分析法得到各个影响因素的权重,最后采用模糊综合评判方法对水力压裂井进行评估,最终判定其是否适合压裂并对压裂井进行优选,现场实际应用表明,该方法可以提高现场的工作效率和选井的客观性、准确性.     

Nonlinear finite element reliability analysis of Concrete-Faced Rockfill (CFR) dams under static effects

The response of concrete slab on Concrete-Faced Rockfill (CFR) dams is very important. This study investigates the reliability of the concrete slab on a CFR dam by the improved Rackwitz–Fiessler method under static loads. For this purpose, ANSYS finite element analysis software and FERUM reliability analysis program are combined with direct coupled method and response surface method. Reliability index and probability of failure of the concrete are computed in the all critical points of the concrete slab by dam height. This study is also expanded for the reliability of CFR dams including different concrete slab thickness. In addition to the linear behavior, geometrically and materially non-linear responses of the dam are considered in the finite element analysis which is performed with reliability analysis. The Drucker–Prager method and the multi linear kinematic hardening method are, respectively, used for concrete slab and for rockfill and foundation rock. Finite element model used in the analyses includes dam–reservoir–foundation interaction. Reservoir water is modeled by the Lagrangian approach. Welded and friction contact based on the Coulomb’s friction law are considered in the joints of the dam. One-dimensional two noded contact elements are used to define friction. The self-weight of the dam and the hydrostatic pressure of the reservoir water are considered in the numerical solutions. According to this study, hydrostatic pressure, nonlinear response of the rockfill and the decrease in the concrete slab thickness reduce the reliability of the concrete slab of the CFR dam. Besides, the CFR dam models including friction are safer than the models including welded contact in the joints.     

Discontinuous cellular automaton method for crack growth analysis without remeshing

A numerical technical of discontinuous cellular automaton method for crack growth analysis without remeshing is developed. In this method, the level set method is employed to track the crack location and its growth path, where the level set functions and calculation grids are independent, so no explicit meshing for crack surface and no remeshing for crack growth are needed. Then, the discontinuous enrichment shape functions which are enriched by the Heaviside function and the exact near-tip asymptotic field functions are constructed to model the discontinuity of cracks. Finally, a discontinuous cellular automaton theory is proposed, which are composed of cell, neighborhood and updating rules for discontinuous case. There is an advantage that the calculation is only applied on local cell, so no assembled stiffness matrix but only cell stiffness is needed, which can overcome the stiffness matrix assembling difficulty caused by unequal degrees of nodal freedom for different cells, and much easier to consider the local properties of cells. Besides, the present method requires much less computer memory than that of XFEM because of it local property.     

Hydraulic fracturing with a simplified fluid model and XFEM

In hydraulic fracturing, the pressure exerted by the fracking fluid onto the surrounding solid, is typically obtained from solving the Reynolds equation. This is not always robust and leads to a complex behaviour at the crack front (toughness or viscous regimes). In the presented work, the Reynolds equation is replaced by a simplified fluid model, where pre-defined pressure distributions are assumed which lead to a simpler and robust coupled problem. The surface integration of the fluid pressure onto the surrounding solid is outlined without any limitations on the distributions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)