水利水电工程岩基抗剪强度参数二维分布模型构造的Copula方法

基于国内103个水利水电工程1 174组岩基抗剪强度试验数据,采用Copula函数研究岩基抗剪强度参数联合分布模型,探讨水利水电工程中岩基抗剪强度参数联合分布模型构建方法。利用最小二乘法求出岩基抗剪强度参数试验数据的相关统计参数,基于AIC准则识别出岩基抗剪强度参数边缘分布。选择4种Copula函数构造岩基抗剪强度参数二维分布模型,探讨了基于Copula函数的岩基抗剪强度参数二维分布模型的优越性。结果表明：水利水电工程岩基抗剪强度参数存在明显的统计负相关性。Copula方法能够构造具有任意边缘分布和任意相关结构的岩基抗剪强度参数联合分布模型,它为构造抗剪强度参数联合分布模型提供了一种简便的工具。已知岩基抗剪强度参数的边缘分布函数和相关系数不能唯一确定岩基抗剪强度参数的联合概率分布模型,在抗剪强度参数边缘分布函数和相关系数完全相同的前提下,不同Copula函数建立的抗剪强度参数联合概率分布模型差异显著。与常用的抗剪强度参数二维正态分布模型相比,基于Copula函数的抗剪强度参数二维分布模型具有较强的灵活性,它能更好地拟合原始观测数据。水利水电工程中惯用小值平均法确定标准值,当摩擦系数取较小值时,不同Copula函数构造的黏聚力的条件累积分布函数差异显著,这将对抗剪强度参数标准值的选取以及相应的设计方案具有明显的影响。     

岩体结构面间距的双参数负指数分布研究

通过对负指数分布模型函数的分析,推导了负指数分布的极大值函数,证明在岩体结构面实测数据的回归分析中,负指数分布存在局限性。改用双参数负指数分布作为模型函数后,能克服负指数分布的缺点,继承其优点,提高回归分析的拟合度。回归分析的方法使用最小二乘法曲线回归方法。在云南小湾水电站坝基槽边坡结构面的统计中,双参数负指数分布作为回归分析的模型函数得到了成功运用。     

三峡库区岩体天然结构面抗剪性能试验研究

采用自制的试验装置对取自三峡库区的含天然结构面的岩块试件进行压剪试验,通过对4组试件进行不同正压力及不同含水量(天然状态与饱水状态)下的剪切试验,绘制出其相应的变形和强度曲线,并对这几组曲线进行了对比分析。试验结果表明：岩块中结构面的抗剪强度不仅与岩块所受法向应力的大小有关,而且与岩块含水量的大小有关,即结构面抗剪强度的大小随着法向应力的增大而增大,又随着含水量的增大而减小;最后,运用最小二乘法对该结构面的抗剪参数进行了求解,且与推荐值进行了比较,对比发现二者基本吻合,说明该试验装置与试验方法在实际工程应用中是可行、有效的。     

基于原生裂隙重张试验确定围岩块体边界法向应力分布规律研究

由于地下工程处于一定水平的地应力环境中,块体边界法向应力概化的正确与否直接关系到块体的稳定性分析结果,现通过实测途径确定块体边界法向应力的研究还较少。基于大型地下厂房块体稳定性分析,通过在块体范围及邻区不同方向布置多个钻孔,首次将原生裂隙重张试验引入到块体边界法向应力的测定,对开挖后与块体主要边界产状相近的所有原生裂隙的法向应力进行了测试,成功取得了块体边界上的法向应力状态及其空间变化规律。研究结果表明：洞室开挖完成后,块体边界应力分布不均匀,但具一定规律,垂直向表现为从浅部到深部结构面的法向应力依次增大,在水平向上,随与洞室开挖面距离的增大而增大;结构面的法向应力实测值稍小于基于围岩应力的估算值,但总体一致。该成果可为确定围岩块体的边界力学状态和应力模型简化提供参考和依据。     

岩土强度参数概率分布拟合及贝叶斯优化

岩土强度参数是工程设计以及工程核算中十分重要的参数,但在实际工程中,由于条件有限,从室内外试验中得到的试验数据难以确定工程中应采用的设计值。利用贝叶斯公式可以参考以往工程中积累的工程经验对实际工程中得到的岩土强度参数进行优化。论述了强度参数的单独以及联合分布的概率分布拟合、检验以及贝叶斯方法优化,提出了相关的贝叶斯优化公式。通过锦屏一级水电站左岸坝肩处近SW向结构面强度参数的优化,验证了该方法的可行性和有效性。     

基于岩体结构面分布分形维的岩体质量评价

尽管岩体结构面具有空间上的不规则性和结构网络上的复杂性,但由于它又具有自相似的特征,可以运用分形理论来对其进行研究。运用盒计维数法对某矿山巷道围岩体结构面分布的分维数进行计算,验证了岩体结构面分布的分形特征。通过对岩体结构面分布分形维值分布规律的分析发现,分形维数越大、结构面分布越密集,结构面迹线越长,岩体质量越差,表明可将岩体结构面分布的分形维作为岩体质量评价的指标。将计算所得的岩体结构面分布的分维数与按工程岩体分级标准对相应岩体分级所得的岩体质量等级进行对比,提出了一个以岩体结构面分布的分形维作为分级指标的岩体质量评价方案。     

Scaling of geological discontinuity normal load–deformation response using fractal geometry

The mechanical behaviour of discontinuities in rock, such as joints, is known to be size‐dependent. It is also suspected that the behaviour of larger size features, such as faults, is also size‐dependent. This size dependence has serious implications for performing numerical response simulations of geological media. In this paper, we develop a new mathematical theory for scaling of one particular discontinuity property, namely the interface normal stiffness. To accomplish this, we idealize an interface to have fractal geometry, and we develop analytical relations which show that the interface normal stiffness, which is commonly thought to be a size‐independent property, is in fact a size‐dependent property and has fractal characteristics that may be exploited to develop a fundamental theory for scaling. Copyright © 2001 John Wiley & Sons, Ltd.     

基于正态分布的岩石损伤统计本构模型及其参数确定方法研究

根据岩石微元强度服从正态分布的特点,引进能合理描述岩石微元强度的参量,基于岩石三轴应力应变试验曲线建立了反映岩石破裂全过程的统计损伤本构模型.在此基础上,重点探讨了正态分布参数对岩石损伤本构模型的影响,据此对岩石统计损伤模型进行了合理修正,从而建立了反映岩石破裂全过程的三维统计损伤本构模型,与试验结果及现有研究结果进行比较显示了该模型的合理性,具有广泛的应用前景.     

基于对数正态分布的井下疏放水钻孔水量分析

为了研究煤矿井下疏放水钻孔水量的分布规律,利用直方图、Q-Q图和非参数检验法对典型工作面疏放水钻孔水量进行了对数正态分布模型的检验,并进行了非线性回归模型的拟合,结合工作面水文地质条件,对模型中的参数进行了分析。结果表明：工作面井下疏放水钻孔水量服从对数正态分布,模型中典型工作面疏放水钻孔水量对数的均值和标准差与所属井田含水层单位涌水量的均值和标准差呈线性相关,分布曲线中的偏度和峰度主要受顶板含水层富水性及其均一程度控制,同井田内相邻多工作面疏放水钻孔水量也服从对数正态分布。研究成果可以为顶板水疏放钻孔和排水系统的设计提供参考。     

基于偏正态概率分布的粒度分布次总体分离及其沉积环境指示意义

沉积物颗粒是某种沉积环境和水动力条件下多个沉积过程的最终产物。粒度分布是原始沉积信息的载体,是来自不同沉积过程的多个次总体的叠加,频率曲线可能表现为双峰或者多峰特征。传统的沉积学粒度分析方法并未深入研究次总体;常见的概率分布模型在分离次总体后无法全面计算统计参数。本文以214份鄱阳湖现代沉积物的粒度分布数据为例,利用偏正态概率分布模型共分离提取977个次总体,计算各个次总体的统计参数,并对比分析了不同沉积环境中次总体参数的异同。结果表明：① 次总体均值、方差、偏度、峰度、所占百分比和最大频率等参数规律明显;② 从曲流河河道到河流末端、在河流末端顺流方向上和河道左右两侧远离河道方向上,粒度分布中主要次总体粒度均值逐渐减小,河道间洼地和湖区沉积物粒度分布的各个次总体占比接近;③ 江心洲的河道砂和河漫滩细粒粒度分布分别由3种和5种不同类型次总体组成。该方法可为沉积环境的定量判断和沉积过程的定量研究提供参考。     

基于正态分布时间函数地表动态沉陷预测研究

为了研究地表动态沉陷规律,基于正态分布时间函数,结合地表沉陷预测公式,构建了能够进行任意点任意时刻地表动态沉陷预测的函数模型,分析曲线形态系数对时间函数和计算误差的影响,讨论正态分布时间函数的时空完备性,建立了基于时间函数的地表动态下沉计算公式。以辛置煤矿五采区开采为例,利用空间曲面拟合方法求取了地表动态沉陷预测参数,并对特征点的下沉趋势进行了预测。结果表明,地表沉陷预测时曲线形态系数δ > 2为其合理取值,理论预测相对中误差不会超过±4.55%,且随着δ的增大,预测误差逐渐减小;正态分布时间函数在地表下沉、下沉速度以及加速度方面均体现了地表沉陷时空分布的完备性。基于叠加原理的空间曲面拟合求参方法能够进行预测参数的自动求取,地表特征点下沉趋势预测最大中误差为±64 mm,相对中误差为±5.7%,理论值与实测值相吻合,基于正态分布时间函数的预测模型能够体现地表动态下沉的时空分布特征。     

An improved Monte Carlo simulation method for discontinuity orientations based on Fisher distribution and its program implementation

Fisher distribution is the most commonly used probability density function for discontinuity orientations. Based on Fisher distribution, Monte Carlo simulation method for discontinuity orientations was reviewed and improved. Those orientations extending beyond the edge of an upper hemisphere projection (OEBEUHP) often have an important influence on both the mean orientation and Fisher constant K, thus affecting simulation results. The detailed algorithms for identifying and adjusting those OEBEUHP were developed in this paper. Based on the improved method, a program for generating discontinuity orientations and plotting their stereographic projection maps, named as MCSDO, was developed. Due to the aforementioned adjustment, the generated orientations by MCSDO are close to the original discontinuity orientations, which were mapped in field, and satisfactory. Only the original orientations and target number of generated orientations need to be input. By running the program we can directly obtain the follows: orientations of generated discontinuities, mean orientations of both original and generated discontinuities, Fisher constant K of both original and generated discontinuities, and stereographic projection maps of both original and generated discontinuities. MCSDO is a freeware designed for researchers and practicing engineers, and can be easily mastered with a little computer knowledge.     

结构面在剪切状态下的力学特性研究

文章通过规则齿形结构面在不同法向应力下的剪切试验,对其力学特性进行了基础性研究,阐述了规则齿形结构面在剪切条件下力学特性的主要特征及其力学特性的主要规律。通过对试验数据的分析,对结构面在剪切力作用下的强度特性以及结构面在剪切条件下的粗糙度特性进行了研究,在此基础上提出了结构面剪切刚度计算模型以及结构面爬坡角与粗糙度系数之间的经验关系,同时对结构面的剪切位移曲线特征进行了描述,并对现象做出了解释。     

The Gubbio normal fault (Central Italy): geometry, displacement distribution and tectonic evolution

Normal faults within orogenic belts can be pre-, syn- or post-orogenic features. We studied the Gubbio normal fault (central Italy), which is an example of a pre-orogenic fault reactivated in a post-orogenic stage. The Gubbio Fault is a 22-km-long fault bordering a Quaternary basin and part of an active faults system in the Umbria–Marche region (Central Italy). The interpretation of a set of seismic profiles enables us to reconstruct the fault geometry in detail and to measure displacement and throw distributions along the fault strike. Seismic data indicate that the Gubbio Fault represents an example of multiple reactivation: at least a portion of the fault was active in the Miocene and only a part of the total displacement was achieved in the Quaternary. The reconstruction of the fault geometry at depth shows that the fault is characterised by listric geometry. The fault is also characterised by a bend along strike and structure contours show that this geometry is maintained at depth. As the fault is commonly addressed as presently active, the maximum fault dimensions are correlated to the maximum expected earthquake, and the presence of the fault bend is discussed as a possible barrier to seismic ruptures propagation.     

A mathematical model for orientation data from macroscopic conical folds

Statistical techniques are developed to classify folds into one of three classes: cylindrical, conical, or neither. A translated version of Bingham's distribution on the sphere is applied to orientation data fron conical folds. Iterative least-squares techniques are used to determine the best-fitting small circle (or cone), and confidence intervals for the cone axis and half apical angle are developed. Examples of a cylindrical and a conical fold are given. Another fold is neither cylindrical nor conical and is classified as pseudoconical. Relationships between the Bingham and Fisher distributions are presented.     

边坡滑面正应力构成及分布模式选择

通过假定滑面的正应力分布来计算边坡安全系数,这是近年来极限平衡理论研究的一个突破,讨论滑面正应力的组成及合理假设模式对获得可靠、可信的安全系数具有重要意义。根据土条的力平衡条件得到滑面正应力是由滑体体积力（含坡面外力）和土条间作用力这两部分所贡献的,通过算例分析了不同条间力假设模式下的滑面正应力及其两个贡献分量的分布。研究表明：滑体体积力（含坡面外力）贡献分量占主导地位,而土条间作用力的贡献分量较小。安全系数对滑面正应力分布不敏感。因此,在滑面正应力分布函数的构造上无需过分追求与真实分布之间的吻合度,可采用以占主导贡献地位的滑体体积力（含坡面外力）贡献分量为核心函数,选用含两个待定参数的修正函数来逼近土条间作用力贡献分量的分布。研究成果规范了滑面正应力的假设模式,具有一定的理论和应用价值。     

Computational methods for fitting statistical distribution models of multi-site binding equilibria

Statistical distribution models of multi-site binding equilibria have potential applicability in the study of acid-base and metal complexation chemistry of humic substances in soils, sediments, and natural waters. A mathematical derivation is presented for the general continuous model for the case of proton binding; computational methods are described for fitting numerically the parameters in such models. Among models considered are those based on nontruncated, truncated, and bimodal (mixed) distributions. Specific emphasis is placed on Gaussian distribution models.     

On the character of distribution of chemical elements in nature

Distribution of chemical elements in nature is controlled by the general physical-chemical state of natural processes, a result of the effort to reach thermodynamic equilibrium. Natural processes, forming geologic objects (e.g., rocks, ores) usually do not reach total chemical equilibrium. This is reflected in distributions of chemical elements in nature. We recognize symmetric as well as asymmetric distributions. The question arises, what distribution in nature is most commonly followed? Evidently, this should be a distribution of chemical elements in thermodynamic equilibrium throughout the system, thus with maximum entropy. This paper notes that Gauss's normal distribution may be derived from statistic explanation of entropy as a function of contnt of chemical elements in a system with application of Einstein's formula.     

基于岩体结构面统计与分维数的岩体质量评价及其在矿山工程中的应用

以三山岛金矿-510中段和-555中段为例,基于结构面实测数据,利用Matlab对结构面特征进行统计模型,进而实现了岩体裂隙网络Monte-Carlo模拟。然后结合分形理论确定了岩体质量的分维值。研究表明,-510中段和-555中段F3以北的岩体稳定性要好于F3以南的岩体稳定性,从定性和定量的角度对岩体质量进行了分析,为矿山的安全生产提供了一定的依据。