含孔多裂隙岩石力学特性与破裂分形维数相关性研究

为研究含孔多裂隙岩石破裂及分形特征,制备含孔多裂隙岩石试件并对其进行单轴压缩试验,运用RFPA2D软件数值研究破裂过程,构建悬臂梁和结构面力学模型解释拉伸裂纹的形成机制以及裂隙倾角对试件抗压强度的影响效应。此外,引入盒维数法计算分形维数,以此定量表征最终破坏后的物理、数值模型试件裂纹的几何分布特征及其与破裂特性的相关性。研究结果表明:(1)试件破坏模式可划分为穿切裂隙剪切破坏(I型)和沿裂隙剪切破坏(II型)2类,试验与数值模拟结果吻合;(2)孔洞两侧的岩桥可简化为悬臂梁模型,由于非几何对称部位作用的弯矩较大,导致孔洞周边出现较多的拉伸裂纹;(3)预制多裂隙显著弱化了试件的抗压强度,随着裂隙倾角的增大,抗压强度呈先减小后增大的趋势,弱化系数W的变化规律与之相反,与结构面力学模型的解释一致;(4)最终破坏后的含孔多裂隙岩石新生裂纹几何分布的分形维数D与破坏特性密切相关;相比于II型破坏,发生I型破坏的试件抗压强度更大,受力过程中出现的宏观裂纹更多且扩展更充分,导致分形维数更大,数据拟合进一步证明抗压强度与分形维数近似服从正相关关系。     

分形几何方法模拟混凝土材料的裂纹扩展

假设裂纹顶端沿分形轨迹运动，开裂路径垂直于最大主应力方向，由此建立了描述裂纹非规则扩展的分形几何模型．给出了用Ｃ语言开发模拟混凝土简支梁在集中荷载下裂纹生成与扩展的例子．     

水力致裂法测定分形裂纹下岩石的断裂韧性

 引入分形几何理论,应用分形方法来描述岩石断裂裂纹的曲折形态,进而建立分形裂纹下的岩石断裂韧性理论模型。在此基础上,应用自主研制的内压法岩样断裂韧性测试系统对不同假设条件下的岩石断裂韧性进行测定。结果表明,分形裂纹模型测试得到的岩石断裂韧性大于直线模型的断裂韧性,这也从理论上证实了目前水力压裂作业中理论计算值常低于施工压力的结论,说明应用该文的模型计算结果更接近实际情况。     

混凝土损伤力学中的分形应用研究

利用分形几何的原理,通过对混凝土骨料进行研究得出骨料分维数和级配关系,进而讨论了混凝土断面分形测量方法的优缺点,并给出了相关裂纹扩展的分形几何模型。     

三轴应力下致密砂岩裂纹展布规律及表征方法

利用三轴试验机和CT扫描设备,开展了多组不同围压作用下的致密砂岩三轴压缩试验及CT扫描试验,得到了不同三轴应力条件下砂岩破坏裂纹的CT图像;利用图像处理技术和统计学原理提取了裂纹展布的几何形态。引入裂纹的宽度、长度、面积和分形维数等几何参数描述了破坏裂纹的空间形貌,分析了不同围压条件下岩石破坏裂纹面积、长度、宽度和分形维数的分布特征,揭示了围压应力对上述裂纹几何特征的影响规律。研究表明：围压应力对破坏裂纹的面积、长度、宽度和分形等几何特征有显著的影响,低围压条件下,裂纹的面积、长度和宽度都较小,随着围压的增加裂纹的面积、长度和宽度也增大,且概率密度分布函数有了明显的差异;破坏裂纹的分形维数随着围压的增大呈指数递减趋势,低围压条件下裂纹的分形维数大,说明裂纹形态复杂,曲线边界粗糙,产生的小裂纹较多,且相互交错分布,形成的裂纹网络结构占据了整个试件二维横截面图。随着围压的增大,破坏裂纹的分形维数减小,说明裂纹形态趋于规则,小裂纹减少,形成了近似直线的光滑主裂纹。     

分形理论在岩石孔隙结构研究中的应用

岩石的孔隙空间具有良好的分形特征,孔隙结构的分形维数可以定量描述孔隙结构的复杂程度和非均质性.应用分形几何的原理,研究了低渗透储层岩石的孔隙结构,建立了毛细管压力和孔隙大小概率密度分布的分形几何模型.并根据毛细管压力曲线资料计算了孔隙结构的分形维数和孔径大小的概率密度分布.计算结果表明,用该方法研究孔隙结构不仅简单易行,而且精度很高.     

探讨分形几何在图案造型设计中的应用

当代社会,分形几何被应用到图案造型设计中的频率以及范围越来越多。分形几何简单来说就是研究无限复杂,同时在无限复杂的基础上,具有一定意义的自相似图形和结构几何学,从某种意义上来说,分形几何揭示了大自然的本质。正因如此,越来越多的领域应用了分形几何学来进行图案设计、造型设计,比如说美术、房屋设计、服装设计等方面,可以说分形几何为这些领域注入了一种新的元素与活力。本文主要是研究与分析分形图案造型设计,以此促进分形几何在图案设计应用的发展。     

节理岩体结构的分形几何研究

在岩体结构宏观分区的基础上,应用分形几何的观点从三维角度对分区内的岩体结构进行了研究。应用随机不连续面三维网络模拟技术建立岩体结构统计均质区内不连续面的概化模型,借助计算机模拟再现岩体结构;从岩体结构网络图中抽取“样本”,通过计算二维、三维样本的分形维数,表明三维分形维数等于二维分形维数加1,从三维角度表明统计均质区内岩体结构具有统计自相似性。     

预制雁型裂纹岩石巴西圆盘劈裂过程的数值模拟研究

本文采用真实破坏过程分析软件(RFPA)针对预制两条雁型裂纹岩石巴西圆盘劈裂过程进行了数值模拟,分析结果表明:(1)最大剪应力主要集中在试件与加载板接触位置及雁型裂纹尖端位置附近,岩石的宏观裂纹亦是从该区域开始并不断贯通的,雁型裂纹对岩石试件的宏观破裂起到了引导作用。(2)岩石试件在加载过程中声发射的位置与最大剪应力出现的位置大体上是一致的。加载初期和加载末期声发射事件个数和所释放的能量均较小,而加载中期声发射事件个数较多且能量释放相对较大,预制雁型裂纹的岩石巴西盘在受荷过程中期胶结物发生断裂最为集中。     

混凝土的分形性及其单轴应力下裂纹演化的混沌效应

基于分形几何、损伤力学和混沌理论研究混凝土的复杂结构和功能及其在单轴应力作用下其内部微裂纹动态演化规律和破坏特征。首先从唯象和分形角度描述混凝土裂纹的产生和扩展过程,然后,推导了混凝土损伤演化方程,划规为统一形式并检验其混沌特征,进而分析了混凝土裂纹演化的混沌效应;同时,利用混沌理论解释了单轴受压混凝土构件的破坏特征。通过研究混凝土裂纹演化的混沌效应,为混凝土破坏机理研究提供新的手段,也为混凝土结构设计和维护提供理论依据。     

基于分形理论的裂隙岩体地下水溶质运移模拟

岩体裂隙面是粗糙不平的，具有分形特征。裂隙本身可以看成由上下两裂隙面叠合而成的，可以应用分形几何理论来模拟粗糙裂隙面和裂隙张开度的分布情况。在用分形理论模拟裂隙面及裂隙张开度的基础上，用特征有限元方法对粗糙裂隙中的溶质运移进行了模拟。模拟结果显示，考虑裂隙面的粗糙度，模拟其中的溶质运移更符合实际情况。与平均张开度下光滑裂隙中的溶质运移相比，粗糙裂隙中的浓度锋面更落后，而且存在不均匀性和各向异性的特点。     

Topography of natural and artificial fractures in granitic rocks: Implications for studies of rock friction and fluid migration

The topography of fractures and joints has a strong influence on their frictional strength and fracture permeability. Important aspects of the surfaces are the size, distribution and density of contact spots between the surfaces, which can be calculated using topographic data. For a variety of tensile fracture surfaces in granite, including both natural joints and man-made fractures, spectral and statistical properties are similar, suggesting that man-made fractures in granites can be acceptable substitutes for natural fractures in some experimental situations. The topographic data indicate that fracture surfaces at scales from 0.1 to 200 mm are approximately fractal and statistically self-affine. A log-log plot of power spectral density vs spatial frequency, calculated from the fracture surfaces indicates a spectral slope of −2.3 ± 0.2, yielding a fractal dimension D between 2.25 and 2.45. Shear fracture surfaces are also fractal, but have anisotropic roughness, which develops during the fracture initiation process. The amount of anisotropy that develops on the shear fracture surfaces is small in comparison to that exhibited by natural fault surfaces, which include anisotropy that results from post failure wear and from surface evolution. For fractures like those measured in this study, simple simulations indicate that the aperture, size and number density of wall-to-wall contacts between the surfaces change non-linearly with relative shear displacement of the surfaces. It is possible to make preliminary estimates of how the permeability and frictional properties of fractures and joints depend on the size, distribution and character of the contact spots. Furthermore, given that artificial fractures can be generated numerically with statistical properties similar to those of natural or man-made fractures, it is reasonable for systematic studies of the effects of roughness on friction and fluid flow to use computer designed surfaces to provide a range of variability that is not easily accessible in the laboratory.     

单轴压缩条件下三峡坝基岩石破裂的分形特征

基于分形理论,研究了单轴压缩状态下三峡坝基岩石破裂的分形结构,结果表明,在单轴受压时,岩石破裂系和主破裂均表现出很好的分形性质,分维随着压力增加而上升。分维和为描述岩石破裂过程的参数,同岩石抗压强度和风化程度有很好的相关性,表征了岩石裂隙的形成演化特征。     

Numerical manifold method modeling of coupled processes in fractured geological media at multiple scales

The greatest challenges of rigorously modeling coupled hydro-mechanical(HM) processes in fractured geological media at different scales are associated with computational geometry.These challenges include dynamic shearing and opening of intersecting fractures at discrete fracture scales as a result of coupled processes,and contact alteration along rough fracture surfaces that triggers structural and physical changes of fractures at micro-asperity scale.In this paper,these challenges are tackled by developing a comprehensive modeling approach for coupled processes in fractured geological media based on numerical manifold method(NMM) at multiple scales.Based on their distinct geometric features,fractures are categorized into three different scales:dominant fracture,discrete fracture,and discontinuum asperity scales.Here the scale is relative,that of the fracture relative to that of the research interest or domain.Different geometric representations of fractures at different scales are used,and different governing equations and constitutive relationships are applied.For dominant fractures,a finite thickness zone model is developed to treat a fracture as a porous nonlinear domain.Nonlinear fracture mechanical behavior is accurately modeled with an implicit approach based on strain energy.For discrete fractures,a zero-dimensional model was developed for analyzing fluid flow and mechanics in fractures that are geometrically treated as boundaries of the rock matrix.With the zero-dimensional model,these fractures can be modeled with arbitrary orientations and intersections.They can be fluid conduits or seals,and can be open,bonded or sliding.For the discontinuum asperity scale,the geometry of rough fracture surfaces is explicitly represented and contacts involving dynamic alteration of contacts among asperities are rigorously calculated.Using this approach,fracture alteration caused by deformation,re-arrangement and sliding of rough surfaces can be captured.Our comprehensive model is able to handle the computational challenges with accurate representation of intersections and shearing of fractures at the discrete fracture scale and rigorously treats contacts along rough fracture surfaces at the discontinuum asperity scale.With future development of three-dimensional(3 D) geometric representation of discrete fracture networks in porous rock and contacts among multi-body systems,this model is promising as a basis of 3 D fully coupled analysis of fractures at multiple scales,for advancing understanding and optimizing energy recovery and storage in fractured geological media.     

THE FRACTAL CHARACTERISTICS OF ROCK FRACTURE IN DAM FOUNDATION OF THE THREE GORGES PROJECT UNDER UNIAXIAL COMPRESSION

The fractal structure of rock fracture in dam founda ti on of the Three Gorges Project under uniaxial compression is studied based on fr actal theory. The results show that the fracture system and the main fractures of rock under uniaxial compression tests are of highly self-similar characteris tic in statistics. The fractal dimension values of rock fracture raise with incr ease of pressure. The fractal dimension can be taken as a parameter to describe the process of rock fracture and there are good correlation among fractal dimens ion of rock fracture, uniaxial compressive strength and rock weathering deg ree. The fractal dimensions reflect the formational and evolutional features of rock fractures and the difference of rock weathering.     

混凝土材料声发射过程分形特征及其在断裂分析中的应用

为了寻求混凝土材料声发射过程与断裂演化之间的关系,从实验入手,首先给出了声发射过程关联分维函数的概念,并通过实验,证明了声发射过程分形特征的存在。然后,通过混凝土试块的三点弯曲实验,分析了材料断裂过程中声发射关联数的变化规律。进而确定了混凝土试块在临界断裂时的分形特征识别模式。研究结果表明,混凝土材料的声发射过程不仅具有明显的分形特征,而且在临界状态下,知声发射分形特征参数都表现出一定的异常“模式”,这种识别模式可以作为材料出现临界断裂的识别特征。     

扰动岩体裂隙网络分形性质分析

应用相似材料试验模型,研究扰动岩体裂隙网络的演化特征和规律,借助分形几何方法计算分析了扰动岩体裂隙网络的分形维数和分形演化特征,展望了研究覆岩力学性质与裂隙网络演化的依赖关系,对评价采动覆岩变形过程、力学行为和渗流性质具有重要意义.     

Fractal behaviour of the microseismic energy associated with immediate rockbursts in deep,hard rock tunnels

Rockbursts in tunnels can be a significant hazard. During the development of immediate rockbursts, a series of fractures is generated which can be monitored using microseismic events. A fractal calculation method has been proposed to study the self-similarity of the energy distribution of microseismic events during the development of immediate rockbursts. The proposed method was used to study the fractal behaviour of the energy distribution of microseismic events during the development of immediate rockbursts that occurred in four deep headrace tunnels and one drainage tunnel at the Jinping II hydropower project, China. The overburden of the studied tunnels, which are excavated in marble, is between 1900 m and 2525 m. The tunnels have a total length of 12.4 km. The results indicated that the energy distribution of microseismic events during the development of immediate rockbursts has a fractal structure. The fractal behaviour of microseismic energy during the development of immediate strainbursts and immediate strain-structure slip rockbursts are distinguishable. The energy fractal dimensions of immediate strainbursts were larger than 0.2 but those of immediate strain-structure slip rockbursts were less than 0.2. For both immediate strainbursts and immediate strain-structure slip rockbursts, if the intensity was higher, the energy fractal dimensions were larger. The daily energy fractal dimension for microseismic events increased as approach of the immediate rockbursts. The energy fractal behaviour was used as a guide to establish a dynamic warning system based on the evolution of microseismic events to reduce the risk of immediate rockbursts during excavation of deep, hard-rock tunnels.     

Numerical simulations examining the relationship between wall-roughness and fluid flow in rock fractures

Understanding how fracture wall-roughness affects fluid flow is important when modeling many subsurface transport problems. Computed tomography scanning provides a unique view of rock fractures, allowing the measurement of fracture wall-roughness, without destroying the initial rock sample. For this computational fluid dynamics study, we used several different methods to obtain three-dimensional meshes of a computed tomography scanned fracture in Berea sandstone. These volumetric meshes had different wall-roughnesses, which we characterized using the Joint Roughness Coefficient and the fractal dimension of the fracture profiles. We then related these macroscopic roughness parameters to the effective flow through the fractures, as determined from Navier–Stokes numerical models. Thus, we used our fracture meshes to develop relationships between the observed roughness properties of the fracture geometries and flow parameters that are of importance for modeling flow through fractures in field scale models. Fractures with high Joint Roughness Coefficients and fractal dimensions were shown to exhibit tortuous flow paths, be poorly characterized by the mean geometric aperture, and have a fracture transmissivity 35 times smaller than the smoother modeled fracture flows.     

含裂隙水围岩巷道变形破坏数值模拟

巷道围岩在地下水渗透作用下慢慢软化,使得围岩内部的裂隙不断发生扩展,在这些裂隙达到贯通或者通过损伤演化扩展形成新的裂隙后,就成为了宏观状态下的裂缝,当这些裂缝不断的发生积累演化,最后导致岩体失稳破坏。这种失稳破坏改变了围岩应力分布状态,影响到围岩位移场分布及破坏范围,从而大大降低了围岩的稳定性,给煤矿的安全生产带来了隐患。结合断裂力学和损伤力学的相关理论,笔者建立了FLAC3D二次开发模型并进行了验证,将此模型应用于工程实践的稳定性分析。