基于响应面法的边坡稳定二阶可靠度分析

提出了基于响应面法的边坡稳定二阶可靠度分析的实用算法。选择U空间中的随机变量,通过空间变换和相关矩阵分解,计算试验点的功能函数;通过迭代算法构造响应面、以确保通过最小的计算量获得最优精度,并在此基础上进行FORM/SORM计算。以一岩石边坡的平面滑动问题为例,通过与蒙特卡洛模拟、FORM及随机响应面法的比较,证明了该方法的准确性和高效性。分析了参数的相关性及试验点取值范围对计算结果的影响,讨论了可靠度分析结果中参数敏感性和物理属性问题。该方法可为实际边坡问题的可靠度分析提供参考,并可以用来进行基于可靠度分析的加固设计。     

地震动群延时不确定性对反应谱的影响研究

为了考察外部激励群延时对反应谱的影响,分别从确定性的角度和统计的角度分析了群延时对线性单自由度结构体系位移响应最大值的影响。推导出了对应于给定单自由度结构体系在任意外部激励作用下最大位移响应的群延时。据此可以利用任意外部激励的群延时与结构体系的最大位移响应群延时的关系评估体系在该外部激励作用下位移响应峰值的大小。统计分析的结果表明:激励群延时的均值和方差对结构体系位移响应最大值的影响具有明显的规律性;激励群延时的分布频数与结构体系最大位移响应之间也存在着显著的关系。     

A Fractal Interaction Model for Winding Paths through Complex Distributions: Application to Soil Drainage Networks

Water interacts with soil through pore channels putting mineral constituents and pollutants into solution. The irregularity of pore boundaries and the heterogeneity of distribution of soil minerals and contaminants are, among others, two factors influencing that interaction and, consequently, the leaching of chemicals and the dispersion of solute throughout the soil. This paper deals with the interaction of irregular winding dragging paths through soil complex distributions. A mathematical modelling of the interplay between multifractal distributions of mineral/pollutants in soil and fractal pore networks is presented. A Hölder path is used as a model of soil pore network and a multifractal measure as a model of soil complex distribution, obtaining a mathematical result which shows that the Hölder exponent of the path and the entropy dimension of the distribution may be used to quantify such interplay. Practical interpretation and potential applications of the above result in the context of soil are discussed. Since estimates of the value of both parameters can be obtained from field and laboratory data, hopefully this mathematical modelling might prove useful in the study of solute dispersion processes in soil.     

Non-linear Bayesian joint inversion of seismic reflection coefficients

Inversion of seismic reflection coefficients is formulated in a Bayesian framework. Measured reflection coefficients and model parameters are assigned statistical distributions based on information known prior to the inversion, and together with the forward model uncertainties are propagated into the final result. This enables a quantification of the reliability of the inversion. Quadratic approximations to the Zoeppritz equations are used as the forward model. Compared with the linear approximations the bias is reduced and the uncertainty estimate is more reliable. The differences when using the quadratic approximations and the exact expressions are minor. The solution algorithm is sampling based, and because of the non-linear forward model, the Metropolis–Hastings algorithm is used. To achieve convergence it is important to keep strict control of the acceptance probability in the algorithm. Joint inversion using information from both reflected PP waves and converted PS waves yields smaller bias and reduced uncertainty compared to using only reflected PP waves.     

Analysis of extreme rainfall using the log logistic distribution

Computer-intensive methods are used to examine the fit of the log logistic distribution to annual maxima of Irish rainfall. The characteristics of the L-moment solutions are examined by using the conventional bootstrap on the data and by random sampling within the ellipse of concentration of the parameter estimates. A statistical method of examining uncertainty is provided by the maximum product of spacings solution. Factors derived from random division of an interval are proposed for estimation of short-duration falls for which no data are available.     

Unified scaling theory for distributions of temporal and spatial characteristics in seismology

The paper describes the unified scaling theory for distribution functions of temporal and spatial characteristics in seismology. It is based on the scaling of seismological characteristics calculated for various energy–spatial–temporal intervals. The common mathematical methods for the scaling of distribution functions are developed. The means to test possibility of such scaling are found as well. The relationship between the unified scaling theory and other present scaling approaches is determined. The theory is applied to two characteristics of different seismoactive regions. The first characteristic is the waiting time between earthquakes ΔT, the second one is a new space parameter ΔD_min, which is the minimum distance of a current seismic event to the nearest (in space) neighbor in an energy–spatial–temporal interval. The distribution of the characteristics ΔT and ΔD_min allows estimating the time interval to the next earthquake and the distance of the following earthquake from previous earthquakes. Thus, these characteristics are very important for seismic hazard estimations. Scaling of distributions functions is proven to be successful for ΔD_min in all energy–spatial–temporal intervals and for ΔT with variations of energy/magnitude range. The distribution function of ΔT for various time domains was stable in only 60% of the cases, and near to unstable for spatial variations.