基于数字图像灰度相关性的类岩石材料损伤分形特征研究

通过类岩石材料石膏试件单轴压缩试验,获得材料在荷载作用下从损伤到破坏的整个时间序列的数字图像。以试件表面数字图像的灰度相关性的变化为依据,建立损伤量度来表征材料表面损伤和破坏的发展。通过图像处理,建立损伤演化的二值图,并采用分形和多重分形谱理论对材料表面损伤的演化进行描述。研究结果表明,图像灰度相关性系数分布的演化与试件表面的变形局部化在空间和时间上都存在对应关系。随着试件表面损伤量增加,分形维数与应变之间有很好的线性关系,多重分形谱图的曲线形状从开始的对称光滑单峰形式,逐渐向左侧集中发展,其谱宽逐渐减小。     

红层软岩遇水作用的孔隙结构多重分形特征

红层软岩内部孔隙具有随机、多样化的分布特点,孔隙结构的变化是影响其宏观力学性能的关键所在。由SEM扫描电镜获取岩样不同饱水时间下的细观结构图像,根据盒维数法计算出孔隙的分形维数,发现随着饱水时间的加长,孔隙的分形维数呈现增大趋势。同时对孔隙的数量、大小进行统计分析,得出不同饱水时间下岩样内部孔隙的分布特征。基于多重分形理论,采用统计矩的方法对孔隙结构进行定量表征。结果表明,孔隙结构的分配函数与q阶次趋于线性关系,验证了该结构的自相似性与无标度性,由广义分形维数D(0)>D(1)>D(2)说明了孔隙具有多重分形特征,由多重分形谱参数分析了孔隙结构的不规则性与复杂程度,更好地表征孔隙大小各异的分布情况。结合孔隙结构的多重分形特征与岩样抗压强度,建立起孔隙结构变化与其力学性能的关联性,对研究红层软岩的损伤过程具有一定的指导意义。     

不同岩石破裂全过程的声发射序列分形特征试验研究

通过对不同岩性的岩石进行单轴压缩声发射试验,获取岩石破裂全过程中的载荷-轴向变形曲线及声发射参数,观察试件破裂失稳时的破坏情况,分析破坏过程的载荷变化关系。着重对比了不同岩石的不同力学性质、岩石声发射序列的时域特征和声发射序列的分形特征。研究结果表明,采用声发射率、能率可以很好地描述岩石破裂损伤的整个阶段;计算岩石声发射率、声发射能率的关联维数,可得出岩石破裂过程的声发射序列具有分形特征;岩石破裂过程的声发射分维值D反映了岩石内部微裂隙的统计演化规律;不同岩性的岩石破裂过程的声发射参数序列的分形特征具有一定的共性;归纳总结出岩体声发射序列分维曲线的演化模式,即波动→持续下降演化模式,提出可以将分维值的持续下降作为岩体破裂失稳的前兆。     

Changes in Frequency of Electromagnetic Radiation from Loaded Coal Rock

To understand the relationship between the frequency of electromagnetic radiation (EMR) emitted from loaded coal rock and the micro-crack structures inside it, and assess the stress state and the stability of coal rock by analyzing frequency changes in characteristics of its emitted EMR, we first experimentally studied the changes in time sequence and the frequency spectrum characteristics of EMR during uniaxial compression, then theoretically derived the relationship between the principal frequency of EMR signals and the mechanical parameters of coal crack and analyzed the major factors causing the changes in the principal frequency, and lastly verified the results at Nuodong Coal Mine, Guizhou Province, China. The experimental results showed that (1) EMR intensity increased with the applied stress on loaded coal rock during its deformation and failure and could qualitatively reflect the coal’s stress status; (2) with the applied stress increasing, the principal frequency gradually increased from near zero to about 60 kHz and then dropped to less than 20 kHz. During this period, coal rock first stepped into the linearly and elastically deformed stage and then ruptured around the peak load. Theoretical analysis showed that there was a negative correlation between the principle frequency and the size of internal cracks. Field detection showed that a lower principle frequency was generated from coal rock applied by a greater load, while a higher principal frequency was generated from coal rocks suffering a weaker load.     

流域地貌形态特征多重分形算法研究

为研究流域地貌形态特征的量化指标,提出基于高程分布概率的多重分形计算模型,结合大理河岔巴沟流域和大堡岔流域DEM数据进行多重分形计算,对流域地貌形态特征多重分形谱的表征意义进行了探讨。结果表明:流域地貌形态特征多重分形谱可以更加敏感、更加全面地对流域地貌形态的总体特征进行描述;多重分形谱的顶点对应简单分形的容量维,多重分形谱的宽度可以定量表征流域表面的起伏程度,多重分形谱的端点维数的差别可以间接地反映流域峰谷数目的比例;流域地貌形态特征多重分形谱能够分层次地刻画流域内部的精细结构,从而更加突出地表现异常局部地貌变化特征;流域地貌形态特征多重分形谱的无标度区间的合理范围,应该确定为DEM像元尺度到流域最大高程值的1.5倍左右最为合适。     

A cost–benefit analysis of mitigation options for optimal management of risks posed by flow-like phenomena

We analyzed the fractal and multifractal properties of the earthquake time series occurred around the Enguri dam in West Georgia by applying the methods of detrended fluctuation analysis and multifractal detrended fluctuation analysis. We examined the interevent time series in two periods: (1) 1960–1980, in which the investigated area was characterized by the natural seismicity; and (2) 1981–2012, in which the quasi-periodic change of the reservoir water level affected the earthquake generation. Our findings show that the water level variation may influence the fractal properties of earthquake temporal distribution in the local area around the Enguri dam. In particular, it is observed that the time distribution features of seismicity occurred in the second period are more persistent than the natural seismicity occurred in the first period. Furthermore, the seismic process of the second period shows a lower multifractal degree than that of the first period, indicating that the influence of quasi-periodic fluctuation of water level features the seismicity as more regular compared to the natural seismicity.     

Fractal approach in modelling of earthquakes

A model for an earthquake simulation is proposed with the use of a fractal approach. Multiple generation and coalescence of shear faults in stochastic brittle media (modelled as a 2d lattice) are considered to be a source of seismicity. Dynamics of local failure events are governed by accumulation of shear defects, described in terms of continuum damage mechanics. Fractal tree structure is used as an analogue for a stress redistribution process. Energy release, caused by the non-uniform failure, is studied for a non-conservative case. Effect of various types of rocks' properties stochasticity on energy release dynamics is analysed with a utilization of multifractal formalism. The latter is shown to be an additional method for seismicity characterization.     

分形理论与成矿作用

总结近年来分形理论在成矿作用研究中的应用及取得的主要成果 ,主要表现在 :矿床的空间分布具分形和多重分形性质 ,表明成矿作用在一定的空间范围内具标度不变性 ;钻孔中金属品位的频率分析表明品位的分布具分形和多重分形结构 ,其结构与品位高低有关 ,对预测深部矿体有指导意义 ;矿床的规模、品位的分布也具分形和多重分形结构 ,不同规模的矿床具有不同的分形结构 ,暗示不同规模的矿床具有不同的成矿地质背景和机制 ;元素在微观矿物表面及区域大面积的分布也具有分形和多重分形结构 ,其结构类型与其成因条件及机制有关。     

单轴加载煤体破坏特征与电荷规律研究及应用

为了完善电荷感应方法用于冲击地压的预测预报,利用自主研制的电荷监测系统开展了室内单轴压缩条件下煤样破裂电荷监测试验。重点分析了煤样的破坏类型、力学特性以及不同破坏类型下电荷时-频域信号规律,并对试验结果进行了工程验证。研究结果表明：煤样变形破坏特征可分为单剪型、共轭剪切型和破碎型;单剪型煤样电荷时域信号仅在峰后破坏初期,应力跌落至97% 左右时产生,前兆信息难以捕捉,信号具有孤立性,幅值较高,电荷频率分布离散,主频为250 Hz。此特征电荷信号预示着相应工程煤体可能发生局部化破坏,将集聚的能量瞬间释放,冲击危害程度较大;共轭剪切型煤样电荷时域信号在强化损伤后期,应力达到(85%～100%) 时开始产生,信号具有间隔突发性,主频为150 Hz。预示着煤体可能发生分区化破裂,能量间断释放,冲击危害程度次之;破碎型煤样电荷时域信号在强化损伤初期,应力达到(70%～85%) 时就开始产生,前兆信息易于捕捉,信号具有群发性,幅值较低,主频为0 Hz。预示着煤体可能发生均匀型破碎,能量缓慢释放,冲击危害程度较小。现场监测结果表明,在工作面煤体破碎区和发生煤炮时监测到的电荷信号特征,与试验室煤样发生均匀型破碎和单剪型破裂而产生的电荷信号特征具有高度相似性,验证了试验室结果的可靠性。     

Multifractal modeling and spatial statistics

In general, the multifractal model provides more information about measurements on spatial objects than a fractal model. It also results in mathematical equations for the covariance function and semivariogram in spatial statistics which are determined primarily by the second-order mass exponent. However, these equations can be approximated by power-law relations which are comparable directly to equations based on fractal modeling. The multifractal approach is used to describe the underlying spatial structure of De Wijs 's example of zinc values from a sphalerite-bearing quartz vein near Pulacayo, Bolivia. It is shown that these data are multifractal instead of fractal, and that the second-order mass exponent (=0.979±0.011 for the example) can be used in spatial statistical analysis.     

西太平洋海域海山地形分形特征研究

对太平洋麦哲伦海山区、威克—马尔库斯海山区、马绍尔群岛、中太平洋海山区及莱恩群岛5个海山区的平顶海山与尖顶海山地形进行分形研究,结果表明两种类型海山地形具有不同的分形特征。海山形态投影覆盖法揭示平顶海山具有单分形的大尺度构造分形,尖顶海山具有大尺度构造分形和小尺度结构分形的双分形结构。海山等高线尺度法分形结果显示,同一海山区平顶海山分维值小于尖顶海山的;同一海山不同高程段等高线分维值基本保持稳定,垂向上具有明显的分段性,可以参考并使用它进行地貌垂向分带。     

四川地区断层空间分布的多重分形特征

断层系统多重分形避免了容量维Ｄ０的不足，考虑了每一条断层对整体分维的贡献，反映了断层的空间分布特征。根据四川地区断层分布图，运用多重分形理论检验了断层空间分布的自相似性，分区计算了四川地区各带的多重分维值。结果表明，断层破裂系统为分形结构，具有很好的自相似性，相关系数均达０．９９。不同带分维值的较大差异，反映不同构造区域的断层分布特点。最后，对分维的含义进行了深入探讨，对油气勘探的有利区域进行了分析。     

高温预损伤下煤岩蠕变声发射及分形特征

为了研究高温条件下煤岩微裂缝发展及破坏规律，对煤样进行不同温度预损伤和三轴蠕变声发射实验，探讨煤岩在经历高温预损伤过后的力学行为特征。研究结果表明:随着温度升高，煤岩预损伤呈幂函数型递增；较低温（≤ 200℃）预损伤下，煤岩呈脆性破坏特征，加速蠕变特征不明显；较高温（>200℃）预损伤下，煤岩呈韧-脆性破坏特征，且加速蠕变特征较明显；稳态蠕变速率ε_s的对数值与预损伤D之间呈线性相关关系；温度越高，煤岩的声发射振铃计数率水平越小，呈低频低幅值变化，且蠕变3阶段越趋于"同频"发展，累计振铃计数N_m与预损伤D之间呈负指数型函数递减；分形维数值呈"减小-动态稳定-再次减小"3阶段变化，并与蠕变3阶段相对应，分形维数由稳态向减小转变的转折点可作为判断煤岩失稳破坏的依据；温度越高（预损伤值越大），分形维数d_f越大，岩样破坏越无序。研究成果对于揭示经历不同温度热解气化损伤后煤岩的长期力学行为具有重要意义。      

裂隙网络多标度分形计算机模拟

岩体裂隙网络是不均匀，非对称的复杂分形，用简单分数维不能刻画其特征，必须采用多标度分形来研究，才能全面客观地描述其本质。文中介质了隙网络多标度分形计算机模拟原理与方法。     

构造附加动力对煤变质过程的影响

本文从固体力学、构造物理化学的角度分析了煤岩所受应力的来源、性质以及应力在煤变质过程中的影响方式。作者在前人研究基础上,阐述了构造动力影响过程中煤岩能量的转换形式,分析了应力在烟煤分子团聚过程中的影响。研究认为,煤岩所受的各种应力(压应力、拉应力、剪应力)为地层压力与构造动力所造成的附加内力。这种附加内力可以分解为构造附加静水压力与偏应力两部分。构造附加静水压力主要影响煤岩的物理性质,如孔隙度、颗粒性质与瓦斯吸附特征,并对煤的化学煤化过程有缓慢促进作用。偏应力主要使煤岩发生变形和位移。煤化过程中,由构造运动所产生的动能转化为各种形式的热能、表面能、弹性变形能以及声、光、电、磁等形态能量。     

Markov Processes and Discrete Multifractals

Fractals and multifractals are a natural consequence of self-similarity resulting from scale-independent processes. Multifractals are spatially intertwined fractals which can be further grouped into two classes according to the characteristics of their fractal dimension spectra: continuous and discrete multifractals. The concept of multifractals emphasizes spatial associations between fractals and fractal spectra. Distinguishing discrete multifractals from continuous multifractals makes it possible to describe discrete physical processes from a multifractal point of view. It is shown that multiplicative cascade processes can generate continuous multifractals and that Markov processes result in discrete multifractals. The latter result provides not only theoretical evidence for existence of discrete multifractals but also a fundamental model illustrating the general properties of discrete multifractals. Classical prefractal examples are used to show how asymmetrical Markov process can be applied to generate prefractal sets and discrete multifractals. The discrete multifractal model based on Markov processes was applied to a dataset of gold deposits in the Great Basin, Nevada, USA. The gold deposits were regarded as discrete multifractals consisting of three spatially interrelated point sets (small, medium, and large deposits) yielding fractal dimensions of 0.541 for the small deposits (<25 tons Au), 0.296 for the medium deposits (25--500 tons Au), and 0.09 for the large deposits (>500 tons Au), respectively.     

Correlation Fractal and Multifractal Characteristics of Seismic Activity in the Taiwan Area, China

Based on the analysis of newly collected data of plate tectonics, distribution of active faults and crustal deformation, the Taiwan area is divided into two seismic regions and six seismic belts. Then, correlation fractal dimensions of all the regions and belts are calculated, and the fractal characteristics of hypocenteral distribution can be quantitatively analyzed. Finally, multifractal dimensions Dq and f(α) are calculated by using the earthquake catalog of the past 11 years in the Taiwan area. This study indicates that (1) there exists a favorable corresponding relationship between spatial images of seismic activity described with correlation fractal dimension analysis and tectonic settings; (2) the temporal structure of earthquakes is not single but multifractal fractal, and the pattern of Dq variation with time is a good indicator for predicting strong earthquake events.     

Discrete multifractals

The concept of multifractal modeling has been used intensively in various fields of science for characterizing measures with self- similarity. It has been shown that multifractal modeling provides powerful tools for characterizing patterns in the spatial distribution of geological quantities and objects. Existing multifractal models were proposed for the purpose of handling spatially intertwined fractals with continuous fractal spectrum f(α) (or continuous codimension function C(γ)). In this paper, these conventional multifractals are termed “continuous multifractals” whereas multifractals with discrete fractal dimensions are termed “discrete multifractals.” The properties of discrete multifractals are investigated. It is shown by various artificial examples and a case study of stratigraphy of Ocean Drilling Program (ODP) site 645 that spatially intertwined fractals/multifractals indeed can have discrete fractal dimensions. Histogram-and moment-based techniques are proposed for discrete multifractal modeling and illustrated using the artificial examples. The new concept of discrete multifractals and associated multifractal modeling yields not only techniques for characterizing multifractals with discrete fractal dimensions but it also provides insight into the relationships between fractals, bifractals, and multifractals.     

Discrete multifractals

The concept of multifractal modeling has been used intensively in various fields of science for characterizing measures with self- similarity. It has been shown that multifractal modeling provides powerful tools for characterizing patterns in the spatial distribution of geological quantities and objects. Existing multifractal models were proposed for the purpose of handling spatially intertwined fractals with continuous fractal spectrum f(α) (or continuous codimension function C(γ)). In this paper, these conventional multifractals are termed “continuous multifractals” whereas multifractals with discrete fractal dimensions are termed “discrete multifractals.” The properties of discrete multifractals are investigated. It is shown by various artificial examples and a case study of stratigraphy of Ocean Drilling Program (ODP) site 645 that spatially intertwined fractals/multifractals indeed can have discrete fractal dimensions. Histogram-and moment-based techniques are proposed for discrete multifractal modeling and illustrated using the artificial examples. The new concept of discrete multifractals and associated multifractal modeling yields not only techniques for characterizing multifractals with discrete fractal dimensions but it also provides insight into the relationships between fractals, bifractals, and multifractals.     

岩石破裂声发射关键特征信号优选方法

岩石破裂过程的声发射中大量的低能常规信号易将少量的高能关键信号特征规律淹没,不利于前兆特征分析和灾变预警。从岩石破裂失稳预警角度出发,以提取影响岩石结构稳定的关键破裂事件声发射信号为目标,提出了岩石破裂失稳关键特征信号的识别准则及其定义。构建了基于信号能量贡献率的岩石破裂关键事件声发射信号的优选方法,并针对花岗岩、大理岩、煤岩和粉砂岩进行了岩石破坏失稳的声发射监测试验验证。试验结果表明,新方法能有效提取岩石破裂过程中影响岩石整体稳定的关键声发射信号,具有一定的普适性。着重从声发射事件率突降、相对平静期和累计能量急升跃阶等前兆特征对优选后岩石破裂关键特征信号进行了一致性检验。检验结果表明,优选后的关键特征信号与上述前兆特征高度一致,并能够有效地提高后期声发射特征参数计算效率,方法有效可行。