基于单轴压缩试验的不同风化程度花岗岩分形特征分析

风化花岗岩物理力学性质的弱化给工程稳定性带来很大影响,因此,研究不同风化程度花岗岩的破坏特性具有重要意义。利用河南五岳抽水蓄能电站库区采集的风化花岗岩,结合现场岩芯特征的定性描述及波速比定量评价指标,划分出了微、弱、强3种不同风化程度的花岗岩;对单轴压缩破坏后产生的碎屑进行质量和尺度的特征分析,在此基础上建立了碎屑分形维数值与波速比之间的对应关系,并利用MATLAB对花岗岩破坏后主破裂表面裂缝进行分形维数计算。结果表明：风化试样产生的碎屑以粗粒组为主,且随风化程度增强,粗粒组碎屑质量占比逐渐增大;强风化岩石碎屑长厚比分布范围小,块状碎屑占比低,破坏动力学特性不明显,其形状更单一,主要以板状为主;随着风化程度的降低,块状碎屑含量增多,岩石动力学破坏特征增强,碎屑分形维数随着表征风化程度波速比的增大而呈增大趋势;相较于碎屑质量、宽度和厚度,碎屑数量和长度是影响碎屑分形维数的主控因素,是反映不同风化程度花岗岩破碎分形特征的主要参量;强风化类组花岗岩表面裂缝分形随波速比变化不明显,而弱风化、微风化花岗岩的裂缝分形维数随波速比增大而呈显著增大趋势,说明其自相似程度更高,形状更复杂,而在裂缝形成过...     

断裂尺度的分形分布与其损伤演化的关系

借助于分形几何学和损伤力学的方法,重新考察和分析计算了有关的岩石断裂实验所提供的实验数据。分析计算结果表明:岩石断裂的损伤演化过程具有良好的统计自相似性,断裂尺度分布的分形维数能够很好地刻画岩石的损伤程度,并且在岩石断裂的损伤演化过程中,断裂尺度分布的分形维数(D_L)随外载荷(σ)呈线性增大。对断裂尺度分布的分形维数而言,损伤演化过程是一个增维过程。根据计算结果给出了分形维数(D_L)与损伤变量(ω)之间的经验关系。      

岩石结构分形维数与岩石压缩强度关系的探讨

运用分形几何学的理论和方法研究煤层顶板岩石的结构，发现岩石的粒度结构和孔隙结构均具有自相似性，粒度分形维数和孔隙分形维数与岩石压缩强度之间有良好的相关关系，故可以用岩石结构的分形维数定量表述岩石的压缩强度。     

大理岩冲击加载试验碎块的分形特征分析

应用分形几何的方法对冲击加载试验中大理岩破碎块度分布进行统计分析。结果表明,大理岩的冲击破碎块度分布具有分形特征,采用破碎分形维数对岩石破碎过程进行定量描述,可以合理地反映大理岩冲击破碎的程度;大理岩的平均破碎块度与冲击加载速率有着较强的相关性,随着加载速率的提高迅速减小;建立了能量吸收与破碎分维的关系,从能量吸收的角度可以较好地解释破碎分维的变化规律。破碎分维是评价岩石冲击破碎块度分布的理想指标,可较为全面地反映岩石冲击破碎的全过程。     

排土场散体岩石粒度分布与剪切强度的分形特征

应用分形理论研究了矿山排土场散体岩石粒度分布的分维规律,建立了分维数与排土场散体物料剪切强度参数的定量关系式。研究表明,排土场岩石块度分布具有良好的分形结构,分维数值大小随着排土场高度的增加而增加,但不超过3。当采样尺度范围一定时,分维数越大,散体中细颗粒含量越多,平均粒径也越小。分维数与散体岩石的剪切强度参数摩擦角?呈负指数关系。分维数值可用于排土场粒度资料的统计分析与剪切力学强度参数的预测。     

矿物微观结构的多重分形

分形与多重分形已广泛地应用于不同领域, 不同尺度下的各种分布特征研究更是受到广泛关注.以云南个旧松树脚矿田中2件含矿矽卡岩样品中黄铁矿颗粒为研究对象, 通过分形与多重分形方法研究了黄铁矿颗粒在二维空间上的分布特征.结果显示, 黄铁矿在微观尺度空间上的分布不均一, 具有明显的分形与多重分形分布特征.所选研究区外接触带黑绿色含硫化物矿石矽卡岩和接触带矽卡岩型块状硫化物矿石显微照片分析结果显示, 前者黄铁矿颗粒分布的盒子维数D₀、信息维数D₁、关联维数D₂及广义多重分形维数D_q的变化范围均较小, 而后者较大; 前者外接触带黑绿色含硫化物矿石矽卡岩含矿性相对较弱, 而后者矿石矿物相对富集.从这个意义上说, 分形与多重分形维数与样品含矿性有一定的对应关系, 因此, 分形与多重分形分析有望进一步为岩石含矿性的定量化评价提供微观尺度上的证据.      

岩石材料微、细、宏观断裂机理尺度效应的分形研究

基于同一现场不同尺度的岩石材料,从大量三轴MTS试验岩石断口边痕、试样切割面或磨光面的节理痕迹和现场断裂迹线3个尺度层次,进行了岩石材料微、细、宏观断裂机理尺度效应的分形研究。提出圆与正方形相耦合的分形维数算法,探讨了其优越性并应用于岩石断裂的分形特征研究,得到岩石材料的微、细、宏观断裂机理存在无标度区域。在无标度区0.002 mm～4 000 mm内,岩石断裂构造的分布规律具有自相似性,是岩石材料的微、细、宏观断裂机理内在联系的外在反映,为跨越尺度界限研究岩石节理裂隙的破坏机理提供了可行途径。     

饱和级配破碎泥岩压实与粒度分布分形特征试验研究

通过饱和级配破碎泥岩的压实试验,得到了不同级配下试样轴向位移和粒度分布分形维数随轴向应力变化曲线,分析了Talbol幂指数对饱和破碎泥岩压实变形与粒度分布的影响规律,建立了一种饱和破碎泥岩压缩模量与轴向应力的关系式。试验结果表明,饱和破碎泥岩的压实过程可分为2个阶段,即0~4 MPa的快速变形阶段和4 MPa后的缓慢变形阶段。其中,约80%的变形发生在快速变形阶段。轴向位移、压缩模量与粒度分布分形维数均可用轴向应力的指数函数拟合。相同轴向应力下,Talbol幂指数越大,试样轴向位移越大,粒度分布分形维数越小。轴向应力大于8 MPa后,各级配试样的粒度分布分形维数相差很小,且随着轴向应力的进一步增大,各级配试样的分形维数差异将继续减小,最终,分形维数将趋于一致。在加载初期,试样压实变形主要以岩石颗粒移位为主;而在加载后期,试样的压实变形则以颗粒破碎为主。     

北京沿河城地区东岭台组酸性火山碎屑流的碎屑分形特征及其成因

火山碎屑岩中的碎屑颗粒形态、分布和显微结构保存着岩浆房内岩浆的结晶状态、火山爆炸过程中的岩浆气泡化和碎裂作用以及火山碎屑堆积和变形过程的大量物理信息。为揭示北京西山沿河城地区东岭台组酸性火山碎屑流形成的物理过程,本文以东岭台组第三岩性段的酸性熔结火山碎屑岩的火山地质、岩相学研究为基础,应用分形理论和方法对酸性熔结火山碎屑岩中的碎屑形态的分形特征开展了定量研究。不同类型碎屑的表面和边界盒维数的数值范围大小具有一致性。玻屑变幅较大,石英晶屑和岩屑变幅较小,这说明碎屑的塑性和流变性对碎屑形态多样性的影响较大。在几类碎屑中,熔蚀石英的边界盒维数和周长-面积法获得的分形维数最大,说明熔蚀作用对石英斑晶边界形态复杂性的影响超过了其它机制对火山碎屑形态复杂性的影响。东岭台组酸性火山碎屑岩中的熔蚀石英、石英碎屑、长石碎屑、玻屑和岩屑的分形特征有明显差异,反映了火山喷发过程中围岩和岩浆性质、物理化学条件以及火山作用机制的差异。火山碎屑形态的分形特征和幂率规律,证明火山爆炸过程是一种自组织临界条件下发生的。     

碳封存砂岩储层的孔隙迂曲度分形特征研究

目前“双碳”减排的背景下,砂岩咸水层是最具潜力的二氧化碳封存介质,其孔隙结构特征决定了流体的运移及封存效率,对其进行研究具有重要的科学意义。分形维数常用于定量表征砂岩孔隙结构在三维空间中的分布规律,但以往对砂岩孔隙迂曲度分形特征进行研究时,多依赖于孔隙率、平均孔隙半径、平均迂曲度等特征值计算分形维数,并不能很好的反映岩石孔隙排列分布及孔隙连接的非均质性。文章将砂岩孔隙结构概化为具有迂曲度的毛细管,首先通过核磁共振成像（MRI）技术获取岩石片层图像,以盒维数法获得孔径分布分形维数;随后以孔径分布分形维数为目标值,结合不同迂曲度下的毛细管数量与孔径的分形标量关系,迭代计算迂曲度分形维数。与传统的分形维数计算方法相比,该研究确定的迂曲度分形维数更能体现岩石内部不同孔隙排列方式引起的迂曲度差异。     

Fractal Analysis of <Emphasis Type="Italic">In Situ</Emphasis> Host Rock Nepheline Syenite Xenoliths in a Micro-Shonkinite Dyke (The Elchuru Alkaline Complex,SE India)

Formation of the fragments of the wall-rock during dyking is one of the important manifestations of instantaneous magmatic events. This process is well documented at shallower depths of Earth’s crust but not at deeper levels. In this paper the in situ xenoliths of host rock nepheline syenite within a micro-shonkinite dyke emplaced at mid-crustal depths is described and the fractal theory applied to evaluate origin of the xenoliths. The nepheline syenite xenoliths are angular to oval shaped and sub-millimetre to ~50 cm long. The xenoliths are matrix supported with clasts and matrix being in equal proportions. Partly detached wall-rock fragments indicate incipient xenolith formation, which suggested that the model fragmentation processes is solely due to dyke emplacement. Fractal analytical techniques including clast size distribution, boundary roughness fractal dimension and clast circularity was carried out. The fractal data suggests that hydraulic (tensile) fracturing is the main process of host rock brecciation. However, the clast size and shape are further affected by postfragmentation processes including shear and thermal fracturing, and chemical erosion. The study demonstrates that dyking in an isotropic medium produces fractal size distributions of host rock xenoliths; however, post-fragmentation processes modify original fractal size distributions.     

大理岩断裂能与细观结构几何特征相关性

岩石在细观尺度上是由矿物颗粒胶结而成,除细观结构的力学特性外,其几何特征（颗粒界面网络结构和颗粒粒度分布）也对宏观断裂能具有一定的影响。为了探索这种几何特征与大理岩断裂能之间的相关性,从而进一步揭示岩石细观断裂机制,首先通过三点弯曲试验测定大理岩的断裂能,然后在试验后的三点弯试件断口处取岩石切片,进行电镜（SEM）扫描以获取岩石细观结构图像。利用图像处理技术获取岩石细观颗粒的界面网络图。通过对颗粒界面网络图分析,发现颗粒界面网络拓扑结构与颗粒粒度分布具有较强的分形特征。将二者分形维数与试件宏观断裂能相对比,发现它们之间具有很强的相关性。界面网络分形维数与宏观断裂能具有很强的二次相关性,而粒度分布维数与宏观断裂能之间具有较强的线性相关性。宏观断裂能随着两种分形维数的增大而增大。该研究结果揭示了宏观断裂能与岩石细观结构几何特征的相关性,加深了对宏观断裂能细观机制的理解。     

人工冻土破碎块度分布的分形性质

从分形几何的观点出发，通过对冻土模型的爆破试验，着重对试样爆后破块块度分析进行了统计分析。结果表明，冻土爆后块度分布是个分形，分形维数不仅是反映冻土破碎程度恰当的统计特征量，而且与试样冻结温度密切相关，还探讨了分维值与冻土抗压强度的关系。     

黑龙江镜泊湖地区蛤蟆塘火山空落堆积物形成机制研究

火山碎屑物的粒度、粒形和分布特征蕴含着其形成机制和喷发的环境信息。基于镜泊湖地区蛤蟆塘火山的一个空落堆积剖面的野外地质和岩相学,以粒度分析和分形理论定量研究了火山碎屑物的粒度分布、粒形几何及其分形特征。蛤蟆塘火山空落碎屑粒度分布均为单峰式,由岩浆爆炸形成的空落浮岩粒度峰值较小,而由射气岩浆喷发形成的含细花岗岩碎屑夹层的碎屑粒度峰值较大。空落浮岩颗粒的类球度、长宽比和凸度都小于含细花岗岩碎屑夹层的数值,表明空落浮岩颗粒相对不规则的特点。利用多段幂律方法拟合了蛤蟆塘火山空落碎屑颗粒分布规律,发现空落浮岩颗粒存在四个幂律分布段（即对应四个分形维数）,这是由于岩浆初始破碎、火山通道内的二次破碎以及风力筛选作用等造成的;含细花岗岩碎屑夹层的碎屑分布有两个幂律分布段（对应两个明显不同的分形维数）,即浮岩和花岗岩碎屑的形成是因不同破碎机制造成的。     

基于尺寸效应的粗粒土单颗粒破碎试验及数值模拟

在外荷载等因素作用下,粗粒土易发生颗粒破碎。对泥岩和砂岩颗粒进行了一系列的单颗粒破碎试验,基于尺寸效应和颗粒破碎分形模型,研究了单颗粒破碎强度、破碎能量及Weibull模量等与分形维数间的关系。利用PFC3D对单颗粒破碎过程进行分析,并与试验数据对比,验证了数值程序的可靠性;随后扩展到大颗粒粒径,分析了其单破碎强度及破碎能量。结果表明：在同类试验条件下,不同材料所得的分形维数是不同的;不同粒径砂岩的破碎程度均大于泥岩;单颗粒破碎强度具有明显的尺寸效应;单颗粒破碎强度与破碎能量均可通过分形维数与颗粒粒径预测得出;修正后的Weibull模量也可通过分形维数得出;数值模拟结果与试验结果及预测结果基本一致;大颗粒粒径单颗粒破碎强度模拟结果与预测结果基本一致,破碎能量稍有差异,需进一步试验验证。研究成果可为获取大粒径粗粒土的单颗粒强度与变形特性提供参考。     

Fractal analysis of the roughness and size distribution of granular materials

The roughness, i.e. general shape and surface irregularity, of particulate soil is an important characteristic that affects the mass behavior of the soil. Characterization of roughness has typically been limited to visual comparison of particles to standard charts, although other more quantitative methods such as Fourier analysis have also been used. Particle size distribution is another important mass-behavioral characteristic of granular soils, and similar to roughness, is defined within limited boundaries. Fractal geometry can be applied to irregular or fragmented patterns such as roughness and grain size distribution to provide quantifying and unique numerical values. This paper presents an evaluation of the applicability of fractal dimensioning techniques to the quantification of both physical particle roughness and grain size distribution of granular soil. The divider and the area-perimeter fractal dimensioning techniques are used to quantify roughness of planar profiles of individual sand grains. The characterization of the size distribution of granular material using fractal geometry is evaluated through Korcak's fragmentation theory. As shown herein, both the divider and the area-perimeter fractal dimensioning techniques are useful in characterizing soil particle roughness, and the results confirm the importance of differentiating between textural and structural aspects of roughness. Fractal geometry can also be used to quantify the size distribution of granular soils with relatively well-graded size distributions.     

Scanline Method to Determine the Fractal Nature of 2-D Fracture Networks

A previous method proposed to measure the fractal dimension of pore spaces is adapted and modified for 2-D fracture networks. The method relies on scanning a 2-D fracture network through successive straight lines from top to bottom and measuring the distance between two fractures. The fractal dimension is then obtained using the log–log plot of the feature size and the number of features for this particular size at different magnifications. It is shown in this study that the method proposed to measure the fractal dimension of porous structures can be applicable to 2-D fracture networks with some modifications after testing it on synthetic and natural fracture patterns. The method is simplified to be useful for practical applications in the fractal analysis of fracture networks. The results reveal that, on the basis of the direction of scanning lines, different fractal behavior and dimensions can be obtained indicating that 2-D fracture networks possess multifractal character. This approach takes into account the effect of fracture orientation on the fractal behavior and anisotropic nature of fracture networks as well as the fracture density, length, and spatial distribution.     

Fractal and Multifractal Properties of the Spatial Distribution of Natural Fractures--Analyses and Applications

The Cantor's dust theory is applied to investigate the scaling properites of the spatial distribution of natural fractures obtained from detailed scanline surveys of 27 field sites in the Appalachian Plateau of western New York, USA. The results obtained in this study indicate: 1) fracture spacing is characterized by fractal and multifractal properties. On small scales analyses yield an average fractal dimension of 0.15, which suggests a very high degree of clustering. In contrast, on large scales, fractures tend to be more regular and evenly distributed with an average fracture dimension of 0.52; 2) fractal dimension varies with different sets in different orientations, which can be attributed to interactions between pre-existing fractures and younger ones, as well as variations of the intensity of the stresses under which the fractures were formed; 3) a time sequence of fracture set formation can be proposed based on fractal and multifractal analyses, which consists of (from old to young): N-S, NW, ENE, and NE-striking sets. This time sequence is confirmed by the study of the abutting relationships of different fracture sets observed in the field.     

Fractal and Multifractal Propertiesof the Spatial Distribution of Natural Fractures——Analyses and Applications

The Cantor's dust theory is applied to investigate the scaling properties of the spatial distribution of natural fractures obtained from detailed scanline surveys of 27 field sites in the Appalachian Plateau of western New York, USA. The results obtained in this study indicate: 1) fracture spacing is characterized by fractal and multifractal properties. On small scales analyses yield an average fractal dimension of 0.15, which suggests a very high degree of clustering. In contrast, on large scales, fractures tend to be more regular and evenly distributed with an average fracture dimension of 0.52; 2) fractal dimension varies with different sets in different orientations, which can be attributed to interactions between pre-existing fractures and younger ones, as well as variations of the intensity of the stresses under which the fractures were formed; 3) a time sequence of fracture set formation can be proposed based on fractal and multifractal analyses, which consists of (from old to young): N-S, NW, EN