Estimating probability curves of rock variables using orthogonai polynomials and sample moments

A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. Orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve.     

当联合概率密度未知时随机结构可靠性分析的随机有限元法

建立了在基本随机变量的联合概率密度未知的情况下随机结构可靠性分析的随机有限元法,阐述了受有随机载荷的多随机参数结构的失败概率的计算方法,应用已知的基本随机变量的前两阶矩和边缘概率分布函数对随机结构的可靠性进行了分析。     

灰色预测模型下隧道围岩稳定性的模糊概率分析

现阶段预测围岩的稳定性多是运用定值判断法,但影响围岩变形的因素繁多且相互制约,要确定一个准确的定值十分困难。为了避免定值判断法中定值确定的问题,本文采用灰色理论预测结合模糊概率法对隧道围岩的稳定性和稳定概率进行分析计算,将稳定性问题数学化,能准确地反映围岩的稳定状况。研究结果表明:灰色预测模型下隧道围岩稳定性的模糊概率法预测围岩的最终变形情况准确,分析围岩的稳定性合理,能及时提供围岩的稳定程度和结构可靠性的安全信息,预见事故和险情,且其计算过程简便,方便在工程中采用。     

Reliability analysis of supporting pressure in tunnels based on three-dimensional failure mechanism

Based on nonlinear failure criterion,a three-dimensional failure mechanism of the possible collapse of deep tunnel is presented with limit analysis theory.Support pressure is taken into consideration in the virtual work equation performed under the upper bound theorem.It is necessary to point out that the properties of surrounding rock mass plays a vital role in the shape of collapsing rock mass.The first order reliability method and Monte Carlo simulation method are then employed to analyze the stability of presented mechanism.Different rock parameters are considered random variables to value the corresponding reliability index with an increasing applied support pressure.The reliability indexes calculated by two methods are in good agreement.Sensitivity analysis was performed and the influence of coefficient variation of rock parameters was discussed.It is shown that the tensile strength plays a much more important role in reliability index than dimensionless parameter,and that small changes occurring in the coefficient of variation would make great influence of reliability index.Thus,significant attention should be paid to the properties of surrounding rock mass and the applied support pressure to maintain the stability of tunnel can be determined for a given reliability index.     

岩体等效抗剪强度概率特征值评估在边坡稳定性可靠度分析中的应用

为消除因采用Hock-Brown准则中间变量而导致评估等效抗剪强度参数概率特征时产生累积误差,针对Hoek-Brown准则各变量具可变性和不确定性,提出应直接由基本变量人手来评估.在简要介绍Hoek-Brown准则基础上,选用了Rosenblueth点估计法和Monte-Carlo抽样法对边坡岩体的等效抗剪强度概率特征值以及边坡稳定性可靠度和破坏概率进行了对比计算分析.尽管2种方法计算结果差异很小,但是与Monte-Carlo抽样法相比,Roseriblueth点估计法计算量明显减小.而Rosenbheth点估计法较为简单,因此工程中可以用它来估计岩体有关参数概率特征值、稳定性可靠度和破坏概率.     

含相关非正态变量边坡可靠度分析的子集模拟方法

提出了分析含相关非正态变量高维小失效概率可靠度问题的子集模拟方法,采用Nataf变换方法成功地解决了输入变量相关时子集模拟方法样本点的模拟问题.编写了基于MATLAB语言的计算程序SUBSETREL,并以岩质边坡稳定可靠度问题为例证明了所提方法的有效性.结果表明:该子集模拟方法能够有效地分析含相关非正态变量高维小失效概率的边坡可靠度问题.子集模拟方法的计算精度和蒙特卡洛模拟方法相当,计算效率远远高于传统的蒙特卡洛模拟方法.此外,该方法在分析含有复杂的隐式及非线性功能函数的边坡可靠度问题方面体现出明显的优越性.研究成果极大地拓展了子集模拟方法在边坡可靠度分析中的应用.     

单矢量传感器的互谱估计与方位估计

单矢量传感器的互谱估计,将时域随机过程变换成了频域随机变量.该变量的统计特性,使得各向同性噪声场影响具有更加明确的物理解释.给出了互谱估计一、二阶矩和一维概率密度函数.由于拾取了振速信息,单个矢量传感器便能获得目标方位的最大似然估计.基于互谱估计的统计特性,给出了方位估计概率密度函数的通解形式,在纯噪声和高信噪比两种极端情况下推导了方位估计的数字特征.对低信噪比的方位有偏现象做出了解释,对高信噪比的判别条件给出了定量描述.理论分析与仿真结果一致,从而为湖海实验研究预备了统计知识.     

Bolt support mechanism based on elastic theory

Mechanical model of anchorage surrounding rock considering tray effect was established based on elastic theory, in order to study the mechanism of bolt supporting. Elastic solutions of normal force at point in the interior of a semi-infinite solid were obtained by means of classical displacement function method in elasticity. The factors which influence stress of bolted surrounding rock, such as the length of bolt and tray effect, were analyzed. The absolute value of stress along bolt axes decreased rapidly with an increase in radical distance and the maximum appeared near ends of bolt. With increasing radical distance, the value of radical stress changed from positive to negative roughly and then increased to zero, with maximum at the middle of bolt. The evolution of hoop stress as radical distance increasing was similar with stress along bolt axes. With an increase in depth, the radical effect ranges of all normal stress components were reduced. These suggest that the effect from tray on stress along bolt axes of bolted surrounding rock could be neglected, except near surface of surrounding rock.     

地下大跨度破碎站硐室稳定性可靠度分析

根据叠加压缩拱承载结构和围岩耦合的力学特点,基于极限平衡理论建立了高应力矿区大跨度硐室工程的可靠度分析模型,利用FOSM法确定了高应力大跨度硐室的可靠度指标。通过对金川矿区破碎站硐室施工特点、地质调查和岩石力学3方面变异参数的均值及方差的计算,得到适合该矿区的可靠度指标计算式,并对金川Ⅲ矿区破碎站硐室的可靠度指标计算,其最小值为1.137。假设影响破碎站硐室稳定性的随机变量服从正态分布,则可靠度指标和失效概率存在确定的关系。根据标准正态分布函数关系式可以计算得到硐室结构的失稳风险概率小于5.87%,即该硐室稳定性可靠度大于94.13%满足硐室稳定性要求。     

概率方法证明级数不等式

计算服从级数分布的随机变量及其函数的原点矩，证明了三个级数不等式，进而讨论了各自的了些特殊情况，并说明一些级数不等式可用概率方法给出了证明。     

水下爆炸载荷作用下圆筒的可靠性研究

为了研究板壳结构系统在爆炸载荷作用下的可靠性问题,基于响应面法(RSM)和有限单元法(FEM)计算了圆筒结构在水下爆炸载荷作用下的可靠性指标.将炸药参数和结构材料参数作为基本随机变量,然后利用有限元数值模拟得到试验点上的结构动响应;通过回归分析拟合出结构动响应函数,并在此基础上建立了圆筒结构功能函数;最后以验算点法计算了圆筒结构的可靠性指标.最终的可靠度计算结果表明了该方法的可行性,并为工程应用提供了有益的参考价值.     

Probabilistic density function estimation of geotechnical shear strength parameters using the second Chebyshev orthogonal polynomial

A method to estimate the probabilistic density function （PDF） of shear strength parameters was proposed. The second Chebyshev orthogonal polynomial（SCOP） combined with sample moments （the origin moments） was used to approximate the PDF of parameters. X^2 test was adopted to verify the availability of the method. It is distribution-free because no classical theoretical distributions were assumed in advance and the inference result provides a universal form of probability density curves. Six most commonly-used theoretical distributions named normal, lognormal, extreme value Ⅰ , gama, beta and Weibull distributions were used to verify SCOP method. An example from the observed data of cohesion c of a kind of silt clay was presented for illustrative purpose. The results show that the acceptance levels in SCOP are all smaller than those in the classical finite comparative method and the SCOP function is more accurate and effective in the reliability analysis of geotechnical engineering.     

大变形隧洞稳定性模糊概率分析

为了分析大变形隧洞工程中存在的不确定性,用模糊概率法研究高地应力下大变形隧洞的稳定概率.采用模糊随机方法,推导出大变形隧洞稳定的模糊概率模型,模型中将围岩容许变形量作为随机变量,并假设随机变量服从正态分布,隶属函数取简化的线性分布.结合乌鞘岭隧洞F7断层带软岩隧洞工程,利用曲线回归和模糊概率对隧洞围岩稳定性进行计算分析.计算结果表明,开挖后第18天,左线隧洞,边墙稳定概率为15.2%,拱部稳定概率为99.1%,倾向于失稳状态;右线隧洞,边墙稳定概率为95.5%,拱部稳定概率为100%,隧洞比较稳定.模糊概率法考虑到工程中的随机性和模糊性,较确定性方法更加合理,有助于反映隧洞稳定性发展趋势.     

径流独立随机序列的电算分析

本文讨论了皮Ⅲ型曲线作为月径流理论频率曲线的适用性。文中分别用矩法和极大似然率法计算皮Ⅲ型的分布参数和理论频率曲肌线。X~2——检验被用于假设线型的分布检验。计算实例显示了由算分析的有效性。     

结构的非线性随机地震响应分析

提出了一种基于广义高斯分布的结构非线性随机地震响应分析方法,该方法采用广义高斯分布来预测结构非线性随机地震响应的边缘分布,采用Nataf分布预测结构非线性随机地震响应的联合分布,而预测模型的参数由非线性响应的一阶和二阶绝对矩来估计。采用发展的方法,分析了Kanai-Tajimi地面运动加速度作用下六层剪切型框架结构的非线性随机响应,分析结果表明该方法具有较高的数值精度和计算效率。     

Reliability analysis of multi-degree-of-freedom nonlinear random structure vibration systems with correlation failure modes

The safety of engineering structures is one of the major objectives of structure design. Uncertainties in material properties and structural geometry are due to the manufacturing error, measurement inaccuracies or structure complexities. The uncertainties may be materialized by the randomness of the structural parameters, such as mass, damping and stiffness. Inherent uncertainties in material properties and structural geometry certainly bring about randomness of the mass and stiffness. Structu…     

公路隧道正交下穿边坡与软弱夹层围岩稳定性分析

为分析山岭地区公路隧道-正交体系下，围岩内含软弱夹层导致施工过程易发生衬砌变形开裂甚至隧道塌方等问题，以某隧道边坡拟扩建公路为工程背景，基于抗拉剪强度折减法理论，采用FLAC^3D有限差分软件，研究不同边坡坡度和隧道埋深对该隧道-边坡围岩稳定性和安全系数的变化规律。结果表明：随着边坡坡度的不断增大，围岩最大剪切应变数值和分布范围逐渐增大，塑性区范围不断增大，围岩稳定性安全系数不断减小。随着隧道埋深的增大，围岩最大剪切应变数值先增大再减小后增大，但剪切应变范围不断增大，塑性区范围不断增大，围岩稳定性安全系数呈现先减小再增大。当无软弱夹层时计算的安全系数最大，当存在软弱夹层时，采用非同步折减法理论计算的安全系数比同步折减法较高。     

基于改进熵权-突变级数法的岩爆等级评判

为能够准确预测岩爆等级,从岩性、应力、围岩三方面选取岩爆发生的五个因素作为预测评价指标,通过改进后的熵权公式来计算评价指标的重要程度;结合突变级数法中多维的印第安人茅舍模型对无量纲处理后的岩爆样本数据进行归一化计算得到突变级数值,并划分岩爆等级区间。最后将此方法应用在江边水电站隧道岩爆预测中。结果表明:利用该方法评判岩爆等级,模型维数较多,评判结果客观、准确,和实际工程情况一致,与其他方面相比具有一定优势。     

基于OD反推的路网承载能力分析及应用

结合随机均衡（SUE）分配模型和OD反推技术,提出了运用TransCAD的OD Matrix Estimationt功能模块对拟建项目周边路网承载能力进行分析的方法,并以重庆寸滩三期工程为例,对其周边路网的承载能力进行分析,验证了该方法的有效性,最后基于分析结果,提出了一些解决瓶颈路段的措施。     

含裂结构脆性断裂的失效概率计算

采用随机有限元法研究结构脆性断裂的失效概率问题借助于能描述裂尖奇异应变场的裂尖元,将随机有限元法扩展到概率断裂力学的研究领域,简化了应力强度因子对各随机变量的求导过程,针对各随机变量的不确定性,计算了应力强度因子的统计矩,并利用优化确定了可靠性指标,采用一阶可靠性方法给出脆性断裂的失效概率,I型断裂的算例表明了计算模型和方法的有效性。