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。     

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.     

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.     

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。     

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。     

应用力学机理的网络模拟预测隧洞超挖问题

概述了结构面的网络模拟技术的基本原理、方法和现状。在充分考虑岩石破裂的力学机理的基础上,结合野外测得的结构面特征参数,提出了一种基于力学机理分析的网络模拟技术,并把该技术运用到地下洞室的超挖预测中。通过某工程实例验证结果的准确性,预测的结果表明：考虑岩石破坏机理的网络模拟技术,能充分反映岩体结构面的几何特征,合理地预测地下洞室中的超挖问题。     

运用概率分布函数确定特高品位

地质品位是评价矿石质量的重要依据。样品的品位与频率的曲线为不对称的正态曲线时,通过对样品品位的数率统计,用正态分布积分函数计算某测定品位以上的样品在样本总体内允许出现的数量,确定其是否为特高品位。     

大样本岩土参数概率分布的正态信息扩散推断

在重要的岩土工程中,确定大样本岩土参数的概率分布对岩土工程稳定性和可靠性分析有着极其重要的意义。为此,基于积分均方误差最小计算得到的最优窗宽,提出了推断大样本岩土参数概率密度函数的正态信息扩散法。该方法基于信息扩散原理,从试验样本和信息论的角度出发,充分利用样本提供的数据信息,而不是先假定成经典的概率分布曲线拟合检验,数学意义和物理意义更加充分和严密。以推断压缩指数Cc的概率密度函数为例,分析了窗宽对信息扩散估计结果的影响规律,说明了该方法在大样本岩土参数概率密度函数推断方面的合理性。用该方法推断了大样本岩土抗剪强度参数的概率密度函数,通过K-S检验,验证了该方法的正确性和实用性。     

A mathematical model for orientation data from macroscopic cylindrical folds

An asymptotic form of Bingham's distribution on the sphere is applied to orientation data from cylindrical folds. Data from cylindrical folds typically form two clusters, one cluster for each fold limb. A bimodal distribution is obtained by fitting a unimodal distribution to each cluster. One parameter of the distribution gives the fold axis, another parameter is directly related to the curvature of the fold limb. Certain tests of hypotheses based on this distribution are the same as tests based on the Dimroth—Watson (symmetric girdle)distribution. One such is the test of whether two folds have the same fold axis.     

GPS高程拟合方法精度分析

近年来人们往往利用GPS数据来确定大地高,但大地高不同于正常高,为此,利用多项式拟合与地球重力场模型相结合的数学方法,使GPS所测大地高通过这些数学模型直接转换为具有厘米精度的正常高,将该方法得到的正常高与单独利用多项式拟合和地球重力场模型得到的结果进行了比较,其差值的标准差为±38 cm。