A fractal fragmentation model for rockfalls

The impact-induced rock mass fragmentation in a rockfall is analyzed by comparing the in situ block size distribution (IBSD) of the rock mass detached from the cliff face and the resultant rockfall block size distribution (RBSD) of the rockfall fragments on the slope. The analysis of several inventoried rockfall events suggests that the volumes of the rockfall fragments can be characterized by a power law distribution. We propose the application of a three-parameter rockfall fractal fragmentation model (RFFM) for the transformation of the IBSD into the RBSD. A discrete fracture network model is used to simulate the discontinuity pattern of the detached rock mass and to generate the IBSD. Each block of the IBSD of the detached rock mass is an initiator. A survival rate is included to express the proportion of the unbroken blocks after the impact on the ground surface. The model was calibrated using the volume distribution of a rockfall event in Vilanova de Banat in the Cadí Sierra, Eastern Pyrenees, Spain. The RBSD was obtained directly in the field, by measuring the rock block fragments deposited on the slope. The IBSD and the RBSD were fitted by exponential and power law functions, respectively. The results show that the proposed fractal model can successfully generate the RBSD from the IBSD and indicate the model parameter values for the case study.     

Decomposing of mixed pattern of arsenic using fractal model in Gangdese belt,Tibet, China

Decomposing mixed geochemical patterns is a challenge in geochemical exploration and environmental assessment. In this paper, the spectrum–area technique (S–A) is used to decompose a mixed pattern of arsenic in Gangdese belt based on stream sediment data. S–A is a multifractal model based on power–law relationships between area of the set consisting of wave numbers with spectral energy density above S[A(>S)] on the 2D frequency domain. The original spatial distribution map of arsenic obtained by inverse distance weighted (IDW) shows a mixed pattern due to superposition of different geological processes or events and is converted into the frequency domain by means of Fourier transformation. Two components, including power spectrum density and phases, are obtained. The spectrum energy density (S) and the area (A) enclosed by the above-threshold spectrum energy density is plotted on a log–log scale. Two cutoff values determined by three straight lines define three filters which decompose the original map of arsenic into background, anomalous, and high frequency (noise) components. The areas with high anomaly of arsenic mainly are located surrounding known Cu deposits, indicating that arsenic anomalies may be related to Cu mineralization.     

钙质砂一维蠕变分形破碎特性宏微观试验研究

钙质砂是远洋地区港口、机场和民用建筑等构筑物的天然地基材料。通过钙质砂一维压缩蠕变试验和微观结构测试,发现了蠕变前后表面孔隙面积减小且呈分散分布的规律以及试验过程中试样瞬时变形、快速变形和衰减变形特征与粒径的高度相关性;利用基于分形理论改进的相对颗粒破碎率和质量分形维数描述了蠕变前后颗粒破碎程度,得到了分形维数和蠕变与时间的衰减形态曲线关系以及宏观质量分形维数和微观表面分形维数的线性关系,并在此基础上对单一粒径组钙质砂蠕变过程中的分形破碎行为进行了多尺度分析和宏微观跨尺度关联性研究,获得了蠕变过程中颗粒破碎发展以及微观孔隙变化规律,证明了钙质砂蠕变过程中的颗粒重组排列、破碎和研磨行为,揭示了钙质砂蠕变机制。     

H-V加筋黏性土的强度与变形特性

在提出非满布的H-V（水平－竖向）加筋的基础上,设计了非满布多层H-V加筋黏土的试验方案,以镀锌铁皮和有机玻璃为加筋材料进行了44组固结不排水三轴剪切试验。通过不同竖筋布置的加筋黏土三轴试验研究了加筋黏性土的应力-应变关系、强度特性及破坏形态,探讨了不同加筋高度、不同围压及不同筋材对加筋黏土强度的影响。试验结果表明：相对于无筋土及传统的水平加筋土而言,其峰值偏应力和抗剪强度均有大幅度提高。     

发泡塑料颗粒轻质土的强度、变形特性研究

发泡颗粒轻质土是一种比较新颖的土工材料,具有质量轻、强度高等特点。在道路、桥梁、建筑等领域有着广泛的应用前景。为了探讨轻质土的工程特性,利用室内试验及理论分析的方法对发泡颗粒轻质土的强度、变形特性以及影响因素进行了分析。根据分析探讨的结果,利用轻质土的构成特征所建立的两相体计算模型可以比较合理、可靠地分析轻质土的应力-应变特性,并在此基础上可方便地应用计算模型分析时间、轻质填充料含有率等因素对轻质土的强度、变形特性的影响,为轻质土的工程应用提供必要的理论依据。     

滨海相软土中搅拌桩强度特征分析

连临高速江苏段路基地层为滨海相软土,该软土层具有含水量、含盐量高及压缩性大的特点,路基采用水泥土搅拌桩进行加固。针对这一问题,对滨海相软土中水泥土搅拌桩的强度特征进行了研究。室内试验结果表明,该路基中水泥土强度随水泥掺量的增加而增大。在饱水状态下,28 d内水泥土强度有所增大,28 d后几乎不变,但水泥土强度随含水量的增大而减小,由于下部土层中含水量和含盐量高,导致桩身水泥土波速和强度具有上部大、下部小的特点,试验结果与现场钻探取样试验结果一致。     

Modeling of elastic and electrical properties of solid-liquid rock system with fractal microstructure

In the present paper we study the possibility of using joint quantitative interpretation of experimental electromagnetic and seismic data for lithospheric studies and to establish the situations in which the joint inversion of seismic and EM experimental data is possible. For this purpose a theoretical model of a solid-liquid rock mixture with fractal structure of grain-to-grain contact (Bahr, 1997; Spangenberg, 1998) was used to investigate dependence of elastic and electrical properties on rock microstructure. The electrical conductivity and seismic wave velocity were estimated by Monte-Carlo modeling for low porosity water-saturated crystalline rock and olivine-partially molten basalt system. It was shown that both elastic properties and conductivity of solid-liquid rock mixture depend non-linearly upon two main common factors, i.e. amount of liquid phase and fractal rock microstructure that is controlled by the degree of contact between grains. The dependence of rock physical macroproperties (seismic velocities, electrical conductivity and seismic and electrical anisotropy) upon these two main factors makes it possible to construct algorithms for joint quantitative interpretation of experimental seismic and electromagnetic data.     

Statistical self-affinity, fractal dimension, and geologic interpretation

Properties of statistical self-affinity are explored and explained. Semi-variogram analysis can be used for identifying statistical self-affine behavior. This is, however, not the only method available for such an analysis. Some error and interpretation is involved; therefore, estimating the Hurst dimension (and from this the fractal dimension) from the semi-variogram can be misleading. Simulations based on statistical self-affine properties are alternatively used to develop an empirical approach to assessing statistical self-affine behavior. Analyzing simulations using semi-variograms, and comparing these semi-variograms to those from actual data, offers an alternate and perhaps superior approach to the understanding of the statistical self-affine properties of a geologic phenomenon. This empirical approach offers a method of reverse modeling for verifying estimates of Hurst dimension from semi-variograms.     

土壤分形结构对其水力性质的指示作用

研究土壤的水力性质是进行生态水文模拟、农业水分管理和环境监测的关键,然而强烈的空间变异造成土壤的物性特征异常复杂,特别是水力性质测定困难,试验结果随机性强,耗费大量人力物力,却难以准确描述。本文在综合分析了国内外30余种量化土壤水力性质的研究方法的优劣后,系统总结了分形理论在土壤物性特征研究中的应用,剖析了分形理论与土壤水力性质之间的关系,旨在探讨土壤分形结构在水力性质领域的发展前景,以及在测定水力特性参数时所具备的优势。结果表明：(1)采用分形方法定量研究土壤结构具备可行性;(2)分形结构方法能够指示水力性质,并能为快速准确刻画不同尺度下的土壤水分分布特征提供科学依据;(3)利用已知土壤水力性质建立分形模型可以有效反演土壤结构。     

深部复合地层力学性质研究

为了研究深部复合地层在不同围压、不同软硬层厚度比条件下的力学性质,以水泥和纯白高岭土为原料,人工制作复合地层物理模拟样品进行单轴及三轴压缩力学试验,同时结合FLAC~(3D)数值模拟,研究不同围压、软硬层厚度比对复合地层力学性质的影响。研究表明,人工制作的复合地层可以满足强度差异要求;随着围压升高,复合地层会出现应变硬化,之后由于软硬岩不协调变形,应变硬化消失,软岩中的不规则裂纹增多;若不考虑结构面等因素,深部复合地层力学性质由占比多的岩性决定;数值模拟与试验得出的应力–应变曲线具有相似的趋势,都表明深部复合地层的变形主要发生在软岩部分。     

煤岩体采动裂隙网络的逾渗与分形特征关系研究

以平煤八矿己15-22060工作面为背景,引入逾渗和分形理论,分析了煤岩体裂隙网络的演化特征,得到了逾渗概率和分形维数随工作面推进度的变化规律及二者的变化关系。结果表明：逾渗概率的大小受横向离层裂隙和竖向破断裂隙的发育、贯通等因素影响,随工作面推进分阶段线性增大,且增幅有增大的趋势;随工作面推进煤岩体的裂隙网络逐步向工作面前方煤体和上覆岩层扩展,分形维数大小受裂隙的长度、宽度、数量、分布等因素控制,升维过程大致可分为3个阶段;煤岩体裂隙网络的逾渗概率与分形维数的关系可分段拟合为1个幂函数和2个线性函数,且具有很好的相关性,数学模型的建立可为研究煤岩体裂隙网络的等效渗透率奠定一定的基础。     

水泥加固红土的受力特性及其微结构特征

水泥加固红土的击实、剪切、压缩和渗透等受力特性及其微结构特征受到水泥加入比例和试样养护时间的影响。研究结果表明,水泥加固红土存在最佳击实制样时间,水泥加入越多,最大干密度越大、最优含水率越小。其抗剪强度和抗剪强度指标随水泥加入比例的增加和试样养护时间的延长逐渐增大,但增大的程度逐渐减慢,对粘聚力的影响大于对内摩擦角的影响;其压缩性和渗透性随水泥加入比例的增加和试样养护时间的延长显著减小,但减小的程度逐渐变缓;水泥加入比例的影响大于试样养护时间的影响。实质上,水泥的加入和试样的养护导致水泥加固红土呈现出包裹、填充和胶结的微结构特征,引起水泥加固红土的击实、剪切、压缩和渗透等力学特性的宏观变化。     

广西红粘土击实样强度特性与胀缩性能

通过对广西贵港红粘土重型击实样的室内试验研究,探讨了其力学特性、胀缩性能、孔径分布特征与含水量之间的关系。结果表明：干密度指标总体上能反映红粘土击实样的强度规律,但非饱和击实样强度峰值对应的含水量因基质吸力作用而偏小,饱和后土体由于吸水膨胀与基质吸力的消失,使得强度峰值对应含水量较饱和前明显增大,红粘土在最优含水量下压实,虽可获得很高的压实度,但饱和后的强度并非最大;红粘土击实样的胀缩性能主要由含水量决定,同时,受到干密度的影响;孔隙主要以孔径在0.01～0.05μm范围内的小孔隙为主,为进一步掌握红粘土的工程力学特性提供了帮助。     

Numerical simulation of ultrasonic waves in reservoir rocks with patchy saturation and fractal petrophysical properties

We simulate the propagation of ultrasonic waves in heterogeneous poroviscoelastic media saturated by immiscible fluids. Our model takes into account capillary forces and viscous and mass coupling effects between the fluid phases under variable saturation and pore fluid pressure. The numerical problem is solved in the space–frequency domain using a finite element procedure and the time–domain solution is obtained by a numerical Fourier transform. Heterogeneities due to fluid distribution and rock porosity–permeability are modeled as stochastic fractals, whose spectral densities reproduce saturation an petrophysical variations similar to those observed in reservoir rocks. The numerical experiments are performed at a central frequency of 500 kHz, and show clearly the effects of the different heterogeneities on the amplitudes of shear and compressional waves and the importance of wave mode conversions at the different interfaces.     

矿石崩落块度的三维建模技术及块度预测

以金川集团Ⅲ矿区为研究对象,根据现场不连续面参数调查结果,利用Monte Carlo模拟方法,产生不连续面综合数据库。然后确定构成岩块的节理面数量、建立三维坐标系统中节理面方程、确定构成岩块的顶点和每个顶点的坐标,并计算岩块的体积、判别岩块的形状特征,从而对矿石崩落块度进行预测。矿石的崩落块度直接影响采场的底部结构设计、出矿设备的选择、二次破碎、炸药消耗的估算等。经过模拟得出的崩落块度预测结果为: 等效尺寸大于0.9 m的块体筛上累积体积百分比为38.2 %,大于1.3 m的块体筛上累积体积百分比为17.2 %。     

Independence,dependence and fragmentation in the South Pacific

Since the 1960s most island groups of the South Pacific have achieved independence and many new nations have been established; only the very smallest islands remain colonies. Most of the small nations are extremely small yet secession movements in many areas have resulted in fragmentation producing the break-up of the Gilbert and Ellice Islands and the disintegration of the Trust Territory of the Pacific Islands. This has emphasized the distinctive characteristics of the Pacific nations: their small size (in population and in area) and limited natural resources, their isolation from each other and from markets and fragmentation within multiple island countries. The extension of outside interests into the Pacific has brought rapid economic changes, the emergence of cash cropping and the decline of subsistence agriculture, increased dependence on imports (especially food, resulting in some nutritional problems) and rapid urbanization, producing growing dependence and inequality which regional ties between the Pacific nations have not been able to overcome. Outmigration from the smallest nations to USA and New Zealand is likely to be maintained and the unusual characteristics of these small island nations suggest that strategies of development that appear viable elsewhere have little chance of success in the Pacific.     

植物根系分布形态及含根复合土强度特性试验

根系空间分布形态对含根复合土体抗剪强度影响显著。近年来快速发展的透明土试验技术为非嵌入式可视化观测植物根系分布形态提供了技术支撑。基于Carbopol Ultrez 10制配成透明黏土材料,开展高羊茅、香根草两种植物根系生长过程中的分布形态观测研究;并与植物在天然砂土与天然黏土中的根系生长长度进行对比分析。继而,开展高羊茅植物根系分别在水平、竖直、倾斜、相交及混合等分布形态下含根复合土体的十字板剪切试验,探讨最优含根量、根系增强效应系数以及表层加筋效应等问题。试验结果表明,透明黏土材料中最优含根量约为0.35%,混合分布形态下根系增强效应最明显,根系增强效应系数约为1.4～1.5。     

垃圾填埋场污泥灰改性黏土衬垫的强度特性及微观结构

为评价污泥灰改性黏土作为填埋场衬垫防渗材料的可行性,分析污泥灰改性黏土强度特性及孔隙结构,针对受垃圾渗沥液腐蚀的纯黏土与污泥灰掺量为1%～5%的改性黏土,采用直接剪切试验分析其抗剪强度变化规律,采用低温氮气吸附试验分析剪切变形后试样的孔隙结构组成。结果表明,改性黏土属于VI型等温线,并存在H3型滞后环,且2～6 nm介孔的数量占比较大。受垃圾渗沥液腐蚀后,黏土抗剪强度大幅下降,黏聚力与内摩擦角分别下降60.12%和19.17%;黏土的最大氮气吸附量降低16.19%,且孔隙分布双肩峰发育不完全;随污泥灰添加量的增加,改性黏土抗剪强度增大,且孔隙分布逐渐恢复双肩峰形式,总孔容增大。     

Natural fracture profiles,fractal dimension and joint roughness coefficients

Summary Thirteen natural rock profiles (Barton and Choubey, 1977) are analyzed for their fractal properties. Most of the profiles were found to approximate fractal curves but some also showed features of specific wavelengths and amplitudes superimposed on fractal characteristics. The profiles showed fractal dimensions from 1.1 to 1.5 covering a range of selfsimilar and self-affine curves. The analysis results suggest a negative correlation between fractal dimension,D, and amplitude,A. Joint roughness coefficients (JRC) show a positive correlation with amplitude,A, and a negative correlation with fractal dimension,D. A numerical model of fracture closure is used to investigate the effects of different profile characteristics (D, A and sample size) on the nature of dilation and contact area, using the natural profiles and synthetic fractional Brownian motion profiles. Smooth profiles (low JRC, highD, lowA) display many small contact regions whereas rough fractures (high JRC, lowD, highA) display few large contact areas. The agreement with published experimental data supports the suggested correlations between JRC and the fractal parameters,A andD. It is suggested that observed scale effects in JRC and joint dilation can be explained by small differential strain discontinuities across fractures, which originate at the time of fracture formation.