基于Monte Carlo方法的由GPS观测计算地应变率的误差分析

在利用GPS观测计算地应变率中，应变率的误差分布在地球动力学研究中非常重要. 为解决这一问题，文中提出基于Monte Carlo技术，利用GPS观测的速度计算地应变率进行误差分析的方法；以青藏高原地区为例，利用带有误差的GPS观测数据进行了大量、独立的应变率重复计算，然后运用统计方法给出了应变率分量及其误差的分布. 结果显示青藏高原的喜马拉雅及中东部地区地应变率的东西向、南北向及剪应变率分量的误差相对较大，但整个青藏高原及附近地区应变率结果稳定可靠；研究结果进一步表明，由GPS观测计算应变率的误差主要决定于GPS观测速度的误差， 在变形小的区域（如中国东部地区），目前GPS的观测精度还不能完全满足地应变率计算的要求.     

Gibbs sampler by sampling-importance-resampling

Among the Markov chain Monte Carlo methods, the Gibbs sampler has the advantage that it samples from the conditional distributions for each unknown parameter, thus decomposing the sample space. In the case the conditional distributions are not tractable, the Gibbs sampler by means of sampling-importance-resampling is presented here. It uses the prior density function of a Bayesian analysis as the importance sampling distribution. This leads to a fast convergence of the Gibbs sampler as demonstrated by the smoothing with preserving the edges of 3D images of emission tomography.     

An Improved Perturbation Mechanism for Simulated Annealing Simulation

Simulated annealing (SA) is being increasingly used for the generation of stochastic models of spatial phenomena because of its flexibility to integrate data of diverse types and scales. The major shortcoming of SA is the extensive CPU requirements. We present a perturbation mechanism that significantly improves the CPU speed. Two conventional perturbation mechanisms are to (1) randomly select two locations and swap their attribute values, or (2) visit a randomly selected location and draw a new value from the global histogram. The proposed perturbation mechanism is a modification of option 2: each candidate value is drawn from a local conditional distribution built with a template of kriging weights rather than from the global distribution. This results in accepting more perturbations and in perturbations that improve the variogram reproduction for short scale lags. We document the new method, the increased convergence speed, and the improved variogram reproduction. Implementation details of the method such as the size of the local neighborhood are considered.     

Shallow landslides in deeply weathered slates of the Sierra de Collcerola (Catalonian Coastal Range, Spain)

Stability conditions in an area located NW of Barcelona (Spain) are discussed. Here, several mass movements were observed, mainly affecting weathered Paleozoic slates. Many of these failures involved slopes cut along recent infrastructures: debris flows, wedge and plane failures, generally surficial, occurred more frequently. After a detailed geological and geomorphologic survey, geomechanic characterization was carried out, according to RMR and SMR classifications. This rating gave a prediction of slope behaviour, in fairly good agreement with the real observed one.

Stability numerical analysis was carried out for the main cut slopes, based upon the Limit Equilibrium Method. First of all, the deterministic factor of safety was computed using the mean values of parameters. After that, a simulation technique based upon the Monte Carlo Method was applied in order to obtain factor of safety distributions. The probability of failure was estimated as P(F<1).

Finally, results from deterministic and probabilistic approaches were compared. The effectiveness of different possible remedial measures was highlighted by means of a sensitivity analysis, which showed that the more important parameters in the study area are the geometrical ones (height, slope and failure plane angles). The final technical solutions adopted are briefly outlined.     

铁路岩质边坡的RQD研究

以宝成铁路略阳站前后一段铁路工程边坡为例,采用蒙特卡洛原理和方法,计算模拟铁路边结构面概率参数,利用统计结果估算边坡岩体的岩石质量指标ＲＱＤ,提出方向ＲＱＤ的概念,初探方向ＲＱＤ值在铁路工程边坡中的应用及铁路开挖工程活动与自然地质环境间的相互影响。     

Effect of spatial variability of cross‐correlated soil properties on bearing capacity of strip footing

Geotechnical engineering problems are characterized by many sources of uncertainty. Some of these sources are connected to the uncertainties of soil properties involved in the analysis. In this paper, a numerical procedure for a probabilistic analysis that considers the spatial variability of cross‐correlated soil properties is presented and applied to study the bearing capacity of spatially random soil with different autocorrelation distances in the vertical and horizontal directions. The approach integrates a commercial finite difference method and random field theory into the framework of a probabilistic analysis. Two‐dimensional cross‐correlated non‐Gaussian random fields are generated based on a Karhunen–Loève expansion in a manner consistent with a specified marginal distribution function, an autocorrelation function, and cross‐correlation coefficients. A Monte Carlo simulation is then used to determine the statistical response based on the random fields. A series of analyses was performed to study the effects of uncertainty due to the spatial heterogeneity on the bearing capacity of a rough strip footing. The simulations provide insight into the application of uncertainty treatment to geotechnical problems and show the importance of the spatial variability of soil properties with regard to the outcome of a probabilistic assessment. Copyright © 2009 John Wiley & Sons, Ltd.     

金融领域的随机建模与基于软件R的Monte Carlo模拟(4):随机微分方程模型

主要研究线性随机微分方程模型,为此定义Itô随机微积分,建立Itô公式.鉴于研究的重点是利用R软件进行数值模拟,所以详细讨论了过去10多年来随机微分方程数值解的研究.     

地基承载力上限分析中的Monte Carlo搜索技术

Greco提出的临界滑裂面搜寻的Monte Carlo搜索技术具有原理简单、适应性强、搜索性能好及容易编程实现等优点,目前该类方法已在边坡稳定的优化计算中有许多成功的应用。为能够在多块体上限法求解地基极限承载力的优化计算中应用Monte Carlo搜索技术,基于上限法相容速度场的要求及地基承载力问题的特点,对Monte Carlo搜索技术实现中的目标函数、几何约束条件、初始破坏面的产生以及收敛准则等重新进行了设置。由于Monte Carlo搜索技术随机性的特点,某一次的搜索优化往往存在陷入局部极值的危险,为解决这一不足,采取了随机设置多次初始破坏面分别进行搜索优化的办法,计算表明,优化效果很好。通过对实际问题的计算以及对比发现,Monte Carlo搜索技术在此处多块体上限法求解地基承载力问题中的优化应用是相当成功的。此外,由于此处的优化是以破坏面上的节点为对象的,因此,不但可以方便地考虑三角形块体的优化,而且也可以方便地考虑四边形块体的优化问题,其适用性更强。     

Reliability analysis of piles in spatially varying soils considering multiple failure modes

In most limit state design codes, the serviceability limit checks for drilled shafts still use deterministic approaches. Moreover, different limit states are usually considered separately. This paper develops a probabilistic framework to assess the serviceability performance with the consideration of soil spatial variability in reliability analysis. Specifically, the performance of a drilled shaft is defined in terms of the vertical settlement, lateral deflection, and angular distortion at the top of the shaft, corresponding to three limit states in the reliability analysis. Failure is defined as the event that the displacements exceed the corresponding tolerable displacements. The spatial variability of soil properties is considered using random field modeling. To illustrate the proposed framework, this study assesses the reliability of each limit state and the system reliability of a numerical example of a drilled shaft. The results show the system reliability should be considered for the serviceability performance. The importance measures of the random variables indicate that the external loads, the performance criteria, the model errors of load transfer curves and soil strength parameter are the most important factors in reliability analysis. Moreover, it is shown that the correlation length and coefficient of variation of soil strength can exert significant impacts on the calculated failure probability.     

基于岩体精细化描述的围岩分类及力学参数概率分布特征分析

针对目前水电站地下厂房工程中不同围岩分类方法存在评价结果不一致、围岩力学参数存在室内试验值与实际情况不吻合的现象,现推荐采用岩体精细化描述体系对围岩岩体结构进行定量化评价。将常用围岩分类方法(RMR、Q、RMi、GSI、BQ、HC)评价指标予以归纳分组,并通过各组内不同指标对比分析获得围岩分类方法中的基础评价指标。以大岗山水电站主厂房某区段为分析对象,采取现场岩体精细化地质素描与后期数据挖掘、拟合相结合方法,并依据评价指标间的关联关系,获得了基础、非基础评价指标的分布概型及对应参数,实现对该段围岩岩体精细化描述认知;基于精细化描述结果,应用Monte Carlo法生成符合各评价指标分布概型的大量随机数,而后参照各分类方法评价思路与评分流程,得到评价指标在各分类方法对应的大量随机评分值,通过归纳统计获得不同围岩分类方法评价结果的分布概型;基于各围岩分类方法评价结果与力学参数值之间的关联关系实现对力学参数概率特征分析。该分析方法与思路可为类似工程围岩质量及力学参数的精确确定提供一定借鉴,并可为实现围岩支护极限状态设计提供必要的原始参数支持。