岩石加速破裂行为的物理自相似律

掌握岩石变形破坏过程中体积膨胀点至峰值强度点之间加速破裂行为的演化规律,是实现地质灾害物理预测的关键.本文考虑裂纹张开和闭合两种情况,基于断裂力学建立了三轴应力作用下裂纹扩展临界尺度与等效应力的关系.对微元体破坏概率,分别采用以等效应力表达的Weibull分布函数和裂纹尺度分形函数,通过对比导出了形状参数m与裂纹分布分维D_f关系的表达式.一个有趣的发现是,岩石峰值强度点与体积膨胀点应变比仅与m或D_f有关.对岩石蠕变或准蠕变破坏,合理的m值范围为[1.0,4.0],在此范围内应变比近似为常数1.48,该常数是描述不同尺度岩石加速破裂规律的物理自相似常数.实例分析表明,基于岩石加速破裂规律构建的多锁固段脆性破裂理论,其适用性广,尤其在崩滑和大地震预测领域,具有良好应用前景.此外,本文给出了b值与m值定量关系,以解释b值的物理意义,并探讨将其用于地震预测的可行性.     

沂沭断裂带及其附近断裂的断层泥分形特征及其地震地质意义

利用岩石碎裂数目的分形理论，分析，计算了沂沭断裂带及其西侧北西向断裂的断层泥粒度成分的分维值，讨论了断层泥粒度成分分维的地震地质意义，研究结果表明，沂沭断裂带内的断裂活动的强度大于北西向断裂活动强度；Ｆ２是沂沭断裂带中活动最强的一条断裂，断层泥粒度成分分维值可作为表征断裂活动时代，破裂形式和断层泥形成斫代等的参量；分维值还与断层泥的母岩，厚度，粘土矿物含量和所处的断裂部位等相关。     

地震中的分形结构

岩石的破坏是一自相似的过程,破坏过程中微破裂事件的空间分布以及破坏后断裂带中不均匀体的分布(或结构)常常是分形的,本文综述了最近几年来在有关地震中的分形结构研究方面的进展,讨论了地震中广泛存在的分形结构的物理本质,发现孕震系统的降维过程与减熵过程是一致的,并推导出孕震过程中微震事件的分布分数维(D)与系统熵(S)之间的函数关系;我们还比较了各种不同的求取分形体的分数维的方法以及它们对结果的影响,并提出了计算有限角度分形体的分数维算法。     

二维分形参数与构造活动关系研究——以滇西南块体为例

构造地貌能够记录构造运动的长期积累,并能通过相关参数定量表达。但是,由于地貌还受到气候和岩性等因素的影响,所以如何利用相关参数来表达地貌与构造之间的关系是一个研究热点。文中利用水平分辨率为90m的SRTM数据,采用元分维模型,通过变差函数法计算了滇西南地区的二维分形参数。并对比了在不同岩性不同气候条件下分形参数的分布特征。结果显示,二维分形参数与岩性、气候因素相关性不强。而分维值与构造活动因素相关性很好,在构造活动强烈区域分维值较低,在构造活动不强烈区域分维值较高。这说明分维值能在一定程度上反映构造活动的强弱,为研究区域构造活动提供了一种新的手段。     

火星表面陨石坑的碎形特征

对2004年1月5日美国宇航局发布的火星轨道探测器拍摄的勇气号着陆点照片进行了研究,认为照片上的地形为陨石撞击火星表面留下的痕迹．详细计量了照片上陨石坑的数目和尺度．对陨石坑尺寸和数目之间的关系进行了研究．认为,火星陨石坑的分布具有碎形特征,并符合分形分布,分维数为1．7．和地球上其它岩石破碎相比,分维数较低．我们推测,撞击火星的陨石可能来源于同一块岩石的破碎。并且该岩石的破碎程度较低．其破碎过程应该和断层、断裂、节理以及风化等地质过程引起的破碎不同．     

一个能产生分形结构的地震活动性模型

本文提出了一个模拟地震活动性的层次结构模型，它所产生的地震活动性是分形的。根据该模型本文导出了Ｇｕｔｅｎｂｅｒｇ－Ｒｉｃｈｔｅｒ统计关系式，并建立了分维数Ｄ与ｂ值间的定量关系。同时还导出了不同震级地震间的平均震中距公式，该公式表明分形几何学在地震预报中有实际应用价值。     

地震活动的分形特征及其对地震预测的意义

岩石破裂是一个自相似过程,地震作为地壳岩石破裂的结果,它在时间和空间上的分布具有分形结构。基于系统科学和分形几何学的观点,本文采用标度变换法和嵌入空间法,分别研究了唐山7.8级、海城7.3级和松潘7.2级地震前后地震活动时、空分布的分维数,同时分析了宁夏灵武5.5级震群和澜沧5.0级前震序列的时间分维随时间的变化特征。初步结果表明:大震后余震的分维数明显增大,无标度区范围减小,展示了震后地震活动随机干扰背景增强！前兆性地震序列的时间分维数相对偏低,有序性增加。此外,文中还研究了单轴压缩下岩石破裂声发射序列的分形特征,结果表明,声发射序列亦具有自相似性,在岩石破坏过程中,声发射序列的分线数随时间的变化不是单调的。最后,籍助于“耗散结构理论”的基本概念,简要地探讨了地震时间、空间分维与地震活动熵的关系。提出了地震时、空分维作为表征地震孕育系统演化过程的序参量之一,应用于地震预测的可能途径及需要进一步研究的若干问题。     

逾渗与岩石破裂的计算机模拟研究

用计算机模拟方法研究了岩石破裂的逾渗模型，给出了在微裂隙随机分布情况下破裂集团的分布图象、破裂集团的大小分布规律、总破裂集团数、集团平均大小、ｂ值、逾渗分维Ｄ及临界情形。所得结果与其他模型和实验基本一致，表明通渗模型是描述岩石破裂扩展演化过程的一种较合适的模型。还发现了岩石破裂过程存在的两个转折点，深入研究这两个转折点附近岩石的宏观性质，可为探索地震孕育演化过程的前兆性质提供依据。     

甘肃中部及邻区水系分形研究结果与滑坡分布的关系

本文用分形几何学理论对甘肃中部及其邻近地区进行了水系分析，发现分维值的大小反映了研究区内发生滑坡灾害的程度。研究结果表明，不同区域水系的分维值与滑坡的分布数量非常吻合。由此可见，水系分形研究对区域性滑坡灾害的危险度判定有一定的实际意义。     

破裂的定标律

早期的一些论文在很宽的尺度范围内讨论了破裂的标度问题。种种统计幂函数关系常常可以成功地用来描述碎块的大小分布及其形状，表明破裂具有一种标度不变的过程。但是，这是建立破裂形状对碎块大小分布的分数维没有任意影响的条件之下。对于岩石破碎破裂能量的新定标律，可由分形几何学概念及Ｇｒｉｆｆｉｔｈ能量平衡准则导出。     

Fractal dimension of fault systems in Japan: Fractal structure in rock fracture geometry at various scales

Based on fault maps, whether or not the fracture geometry of rocks is self-similar, was examined by using a box-counting algorithm. The statistical self-similarity (fractal structure) of the fault fracture systems holds well at the scale of about 2 to 20 km. The fractal dimension in Japan varied from 1.05 to 1.60. The fractal dimension is about 1.5–1.6 at the central part of the Japan Arc, and decreases with distance from the center. At a smaller scale, the fractal structure also holds well in the rock fracture geometry. The fractal dimension of the North Izu Peninsula fault system (branching faults) is 1.49 at the scale of 0.625 to 10 km, the fractal dimension of rock fracture geometry at the scale order of 10^–1 to 10^–2 meters is about 1.49–1.61. The upper limit of the fractal dimension of rock fracture geometry is about 1.6, judging from the estimation of fractal dimension on actual fracture geometry of rocks. This value may impose a restraint on modeling of faulting and the fracture process of rocks.     

甘肃北山花岗岩裂隙几何学特征研究及岩石质量初探

文中以甘肃北山花岗岩中发育的构造裂隙(主要指节理)为研究对象,通过野外裂隙调查,应用传统的概率统计方法与分形几何学理论,利用Mapinfo,ArcGIS平台进行裂隙几何学参数(方位、长度、密度等)的统计、计算和裂隙网络的空间结构分析,研究花岗岩岩体中裂隙的几何学特征。并以此为基础,对甘肃北山花岗岩岩体质量优劣进行初步评价。结果表明:在10～200cm范围内,裂隙网络是分形的;5个测点裂隙网络的分维值分别是1.636,1.548,1.596,1.724,1.604。分维数D不仅能刻画岩体中结构面发育的数量,而且能反映结构面在岩体中分布的均匀程度和交切方式。因此,可以表征岩体的质量优劣,对岩体质量进行分级。按照分维所划分的岩体质量分级,北山花岗岩属于裂隙较发育、岩体质量等级一般的岩体     

岩石断面的分形测量及其分维的计算

在实验室内使岩石单轴压缩直至破裂,用位移传感器测量其断面高度,用显微镜观测断面切片的剖线,所得数据用尺度法计算其分维,各种岩石的不同曲线的分维在1.002-1.028之间,与野外断层主迹线分维值相同.用切岛法计算整个断面的分维约为2.05左右.有关分析和计算认为,分维的大小与岩石破裂时所受力的方向有关,与采样步长有关,而与岩石样品的大小无关.     

Fractal generation of surface area of porous media

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity, the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean, variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately 2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82. The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy assumed.     

Fractal generation of surface area of porous media

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity, the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean, variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately 2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82. The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy assumed.     

Fractal analysis of 2-D fracture networks of geothermal reservoirs in south-western Turkey

Natural fracture patterns of producing geothermal formations in south-western Turkey are mapped at different scales. The fractal dimensions of different fracture network properties, such as spatial distribution, density, connectivity, orientation, and length are measured by different methods. Analysis of the natural fracture patterns from giga to microscales identifies the descending behavior of box-counting fractal dimension with respect to the scale. It is observed that the fracture networks represent scale-invariant properties, but fractal dimensions might notably differ when the mass dimension is measured applying different methods. Anisotropic nature of fracture networks is also included in the fractal analysis.     

A theoretical derivation of the dilatancy equation for brittle rocks based on Maxwell model

In this paper, the micro-cracks in the brittle rocks are assumed to be penny shaped and evenly distributed; the damage and dilatancy of the brittle rocks is attributed to the growth and expansion of numerous micro-cracks under the local tensile stress. A single crack’s behaviour under the local tensile stress is generalized to all cracks based on the distributed damage mechanics. The relationship between the local tensile stress and the external loading is derived based on the Maxwell model. The damage factor corresponding to the external loading is represented using the p–alpha (p–α) model. A dilatancy equation that can build up a link between the external loading and the rock dilatancy is established. A test of dilatancy of a brittle rock under triaxial compression is conducted; the comparison between experimental results and our theoretical results shows good consistency.     

震后地下岩层分形渗透率的时间演化规律研究

天然地震发生后,地震波及区域内的地下岩层渗透率常常会发生显著改变,其变化曲线显示出独有的特征,造成这一现象的机理较为复杂,传统渗流理论尚不能给出合理解释.针对这一问题,从震后渗透率变化规律入手,深入分析了地下岩层裂缝体系对渗透率的影响,给出了裂缝结构参数与渗透率之间的定量关系.结合岩层黏弹特性以及天然地震所产生的地下岩层体应变特征,基于裂缝体系分维度正比于外部应力的实验事实,将黏弹体应力松弛机制引入该体系,对裂缝分形渗透率模型进行了含时推广,建立起震后地下岩层渗透率的时间演化模型,理论预测曲线与实验曲线吻合较好.在此基础上提出‘分形裂缝渗透率松弛效应’这一全新概念.本研究为震控流体运移研究提供了新思路,对于揭示震后断层恢复机制,探讨断层活动与孕震的关联有一定的理论价值和现实意义.