基于分形几何理论的DFN模型构建方法研究

以重庆梁-忠（梁平县-忠县）高速公路礼让隧道为工程研究背景,通过测线法调查现场节理,获得了节理产状分布概率密度函数,并从分形几何学的角度分析了节理间距及迹长的分形分布规律,推导出能反映节理间距及迹长分布状态的分形维数D及分形分布概率密度函数。在该基础上采用Matlab软件以及Monte-Carlo随机分析方法,产生节理参数随机数,结合3DEC中最新模块离散裂隙网络(DFN)技术,建立了能反映节理裂隙分布特征的离散裂隙网络模型并验证了模型的有效性,结果表明,分形分布比负指数分布包含更多的间距、迹长分布信息,更接近于实际分布;分形维数D反映了节理间距、迹长在其变化范围内的分布特征,分形维数的大小取决于小间距、小迹长部分数量在总节理数量中的比例,为节理裂隙岩体网络模型构建提供了一种新方法。     

含节理岩块单轴受压试验三维离散元数值模拟

采用三维离散元方法,模拟含节理岩块的单轴受压试验。并针对节理空间分布,给出了解析解与数值计算比较的结果,验证了数值模拟的正确性。当节理正交时,离散元与有限元的计算结果一致。计算结果定量地说明了岩体的各向异性和尺寸效应。     

节理岩体分形描述

研究了岩体节理产状、迹长、间距和节理数目对岩体节理网络分维的影响和节理几何参数的分维特征。结果表明,随节理发育方向、迹长、间距和节理数目的变化,岩体节理网络分维发生变化,节理间距和迹长的空间分布具有较好的分维特性,岩体节理网络分维可以作为岩体节理几何特征的定量描述指标。     

非贯通随机节理岩体的结构效应对地下洞室地震响应的影响

为研究非连通随机节理岩体的结构效应对地下洞室地震响应的影响,首先探讨了二维节理网络的生成原理,给出了结构效应影响的5个表征参数,即节理密度、节理倾角角度、节理倾角离散程度、节理迹长长度和节理迹长离散程度。以大岗山水电站主厂房洞室为背景工程,研究节理岩体结构效应对地下洞室地震响应的影响。结果表明,相同地震动水平下节理密度增加则洞室地震位移增加;节理角度在0°～80°范围内时,随节理倾角增加洞室的地震位移增加;节理离散程度较大时,随节理倾角离散程度减小洞室的地震位移减小,但当节理离散程度较小时则基本无影响;随节理迹长长度增加,洞室地震位移也增加;节理迹长的离散程度则对对洞室地震位移影响较小。结论可供节理岩体中地下洞室的抗震设计参考。     

基于钻孔电视的深部岩体节理三维网络模拟

为了准确模拟岩体节理的空间分布,评价高放废物地质处置库围岩的稳定性,先通过调查露头节理数据,运用概率统计理论进行节理几何特征模拟,再利用Monte-Carlo法来模拟节理空间分布特征,并以高放废物地质处置新疆预选区天湖地段花岗岩体为研究对象,通过钻孔电视调查不同深度节理几何特征,划分钻孔岩体结构均质区,提出钻孔节理产状、大小、密度的统计方法和计算公式,以均质区建立节理三维网络模型并通过数据对比法进行模型验证。结果表明：1）利用列联表卡方检验和重叠窗口法可将天湖钻孔岩体划分为0~90、120~240、270~360和390~600 m等4个均质区;2）利用SPSS软件以及基于节理直径、迹长和隙宽之间的数量关系得出节理产状服从正态分布,节理直径服从负指数分布;3）通过数据对比法得出模型统计和现场测量的节理平均产状数据相差±3°以内,平均直径相差±1 m以内,平均面密度相差±0.01 m^-2以内,从而验证了Monte-Carlo法建立的节理三维网络模拟的准确性。     

岩体表面节理迹长与节理真实长度尺寸的概率关系

空间节理长度不能直接进行测量,只能通过岩石暴露面上节理迹线长度来量测,但是节理迹线是节理面与岩面交切的结果,迹长在多大程度上能代表节理真实长度是值得研究的,本文利用计算机模拟的方法分析了迹长与节理真实长度的统计关系。     

秦山三期核电工程反应堆地段节理裂隙模拟

以秦山三期核电工程反应堆地段作为研究对象 ,针对节理裂隙在岩体中的分布具有随机性的特点 ,运用随机方法对其分布规律进行了研究。根据实测的节理裂隙产状、间距及迹线长度 ,推断节理裂隙概率分布特征。同时充分考虑到节理裂隙分布的不均匀性和方向性等特点 ,采用非平稳态随机过程模拟节理裂隙间距 ,通过 Monte- Carlo方法得到等效的节理裂隙网络。根据统计和拟合的结果 ,对反应堆地段岩体的节理裂隙进行了评价。     

节理迹线中点密度修正方法的探讨

节理迹线中点密度是描述岩体露头节理分布特征的重要指标。由于露头或测窗尺寸的限制、节理迹长的差异以及露头面和节理面夹角的变化,常规的迹线中点密度计算方法通常包含尺寸、截长和角度误差。本文首先介绍了截长、尺寸和角度误差的修正原理,继而将角度误差修正系数引入到关联点密度计算方法中,提出了凸面测窗条件下同时修正截长、尺寸和角度误差的迹线中点密度计算方法。利用三维节理网络建模技术,模拟生成不同方位、不同大小和不同形状的测窗,系统分析了尺寸、截长和角度误差对迹线中点密度的影响,验证了新方法的有效性。最后,针对我国高放废物地质处置北山坑探设施的硐口岩体露头,实现了节理迹线中点密度分析。上述算例和应用表明,新方法可以有效地修正截长、尺寸和角度误差,可以为估算岩体节理分布密度提供更为可靠的依据。     

基于有限元修正节理岩质边坡稳定性计算的解析解

采用有限元方法探讨在人工开挖或自然侵蚀环境下,岩质边坡体内应力场的变化及节理发育形成机理,并采用有限元强度折减法对后缘具有张节理边坡的稳定性影响因素进行敏感性对比分析,进而得出具有非贯通节理边坡稳定性计算的修正解析解。结果表明：卸荷及风化作用导致边坡体由表及里出现应力重分布及应力集中的现象,使边坡后缘由顶部向下发育一簇竖直向下或略向临空面倾斜的张节理,当张节理与下部的缓倾剪节理贯通时,边坡发生破坏;边坡稳定性最敏感的影响因素为受剪节理的倾角及贯通度,其次是节理的强度参数;可将工程中较难调查的节理贯通度转化为节理的强度参数来等效表达,并根据Mohr-Coulomb强度准则推导得到适用于具有非贯通节理的岩质边坡稳定性的修正解析解。     

基于钻孔摄像技术的岩体节理大小估算方法

目前,确定岩体节理大小通常是根据岩体暴露区域的节理迹长进行估算,往往因岩体暴露区域的局限性而影响估算结果。以钻孔内节理特性为研究对象,尝试进行岩体节理大小估算,首先通过钻孔摄像技术获取地质钻孔内节理的倾向和倾角信息,建立所研究深度范围内的节理平面方程,形成钻孔之间节理面的连通判断准则,从而确定节理面的迹线长度,同时构建出节理迹线均值函数,最后根据节理面迹长与大小之间的对应关系,估算出岩体节理的大小,从而形成一种利用钻孔内的节理特性来估算岩体节理大小的方法。将该方法应用于张家湾铁矿的地下采选联合工程,其估算结果准确可靠。     

Stereological and Other Methods Applied to Rock Joint Size Estimation—Does Crofton''s Theorem Apply?

A number of authors concerned with the analysis of rock jointing have used the idea that the joint areal or diametral distribution can be linked to the trace length distribution through a theorem attributed to Crofton. This brief paper seeks to demonstrate why Crofton's theorem need not be used to link moments of the trace length distribution captured by scan line or areal mapping to the moments of the diametral distribution of joints represented as disks and that it is incorrect to do so. The valid relationships for areal or scan line mapping between all the moments of the trace length distribution and those of the joint size distribution for joints modeled as disks are recalled and compared with those that might be applied were Crofton's theorem assumed to apply. For areal mapping, the relationship is fortuitously correct but incorrect for scan line mapping.     

On the Existence,Uniqueness and Correctness of the Fracture Diameter Distribution Given the Fracture Trace Length Distribution

Based on the fracture trace length distribution, conditions for the existence, uniqueness, and correctness of the fracture diameter distribution are given using Warburton’s fracture model. In particular, a solution for the fracture diameter distribution exists and is unique for all trace length probability density functions, h _A (y), such that \(h_{A}(y)/\sqrt{y^{2}-x^{2}}\) is Lebesgue integrable on [x,∞). This condition is met by the uniform, exponential, gamma, lognormal, and power-law trace length distributions as well as by the trace length distributions that arise from a deterministic fracture diameter or from a discontinuous fracture diameter length distribution. Exponential, gamma, lognormal, and power-law trace length distributions satisfy necessary conditions for the diameter distribution to be non-negative, and necessary and sufficient conditions for the distribution to have unit integral over the real line. Negative values of the fracture diameter distribution arise when the trace has a uniform distribution and the lower bound of the fracture trace is greater than zero.     

Maximum likelihood estimation of joint size from trace length measurements

Summary Usually, rock joints are observed in outcrops and excavation walls only as traces. Under some assumptions about the shapes of the joints and the nature of their size distributions, the underlying joint size distribution can be estimated from trace length measurements. However, the interpretation of trace length distributions from line mapping data should be approached with caution. The data are always length-biased and furthermore, the semi-trace length, the trace length, and the underlying joint size may have different distributional forms. Semi-trace length distributions are monotonic decreasing functions not sensitive to changes in the real trace length distributions. Experimental full trace length distributions are shown to have lognormal distributions and to be insensitive to major changes in the underlying joint size distributions. Under the assumptions of joint convexity and circularity a parametric model for the three-dimensional distribution of joint sizes is developed. A maximum likelihood estimation of the distribution of joint diameters, which best reflects the observed joint trace data, and corrects simultaneously for joint censoring, truncation and size bias, is developed. The theory is illustrated with numerical examples using data collected from five field sites.     

Estimation of joint trace length probability distribution function in igneous,sedimentary, and metamorphic rocks

To predict the behavior of structures in and on jointed rock masses, it is necessary to characterize the geomechanical properties of joints and intact rock. Among geometry properties of joints, trace length has a vital importance, because it affects rock mass strength and controls the stability of the rock structures in jointed rock masses. Since joint length has a range of values, it is useful to have an understanding of the distribution of these values in order to predict how the extreme values may be compared to the values obtained from a small sample. For this purpose, three datasets of joint systems from nine exposures of igneous, metamorphic, and sedimentary rocks are studied. Joint trace length is one of the most difficult properties to measure accurately, but it may be possible to record other geometrical properties of exposed joints accurately; thereby, support vector machine (SVM) model is used to predict the joint trace length. SVM is a novel machine learning method, which is a powerful tool used to solve the problem characterized by small sample and non-linearity with a good generalization performance. Consequently, goodness-of-fit (GOF) tests were applied on these data. According to these GOF tests, the lognormal distribution was found to be the best probability distribution function for representing a joint trace length distribution.     

Rock Mass Characteristics in Beishan, A Preselected Area for China’s High-Level Radioactive Waste Disposal

Geological and hydrological characteristics, joint geometric features, rock physical and mechanical properties and rock mass quality are studied in the Beishan area, preselected for China’s high-level radioactive waste (HLW) disposal engineering. A comprehensive survey method is developed to study joint geometric features in the outcrop and samples from borehole BS06 into the Xinchang rock mass were tested. The optimal joint sets are determined by rose diagrams and equal-area lower hemisphere plots of joint poles. Results show that: 1) the distribution of joint occurrence obeys a normal distribution, while the distribution of joint spacing obeys a negative exponential distribution; 2) concentric circular and tangent circular sampling windows are applied to study the trace length and the trace midpoint density. Results indicate that tangent circular sampling window is more stable and reasonable; 3) Beishan granite shows high density, low porosity and high strength based on many laboratory tests and the physical properties and mechanical properties are closely related; and 4) a synthesis index, Joint Structure Rating (JSR), is applied to evaluate the quality of rock mass. Through the research results of rock mass characteristics, the Xinchang rock mass in the Beishan preselected area has the favorable conditions for China’s HLW disposal repository site.     

Stereological and Other Methods Applied to Rock Joint Size Estimation—Does Crofton's Theorem Apply?

A number of authors concerned with the analysis of rock jointing have used the idea that the joint areal or diametral distribution can be linked to the trace length distribution through a theorem attributed to Crofton. This brief paper seeks to demonstrate why Crofton's theorem need not be used to link moments of the trace length distribution captured by scan line or areal mapping to the moments of the diametral distribution of joints represented as disks and that it is incorrect to do so. The valid relationships for areal or scan line mapping between all the moments of the trace length distribution and those of the joint size distribution for joints modeled as disks are recalled and compared with those that might be applied were Crofton's theorem assumed to apply. For areal mapping, the relationship is fortuitously correct but incorrect for scan line mapping.