蒙特卡罗模拟在区域地震滑坡灾害评价中应用

2004年10月23日,日本新泻中越地区发生史上最强地震之一,震级达到Mw6.6。这次地震诱发上千个规模大小不一、形式各样的滑坡,造成一定的灾害损失和人员伤亡。因此,为了有效地避免和减轻这方面的灾害,有必要有效地、科学地预测和评价地震诱发滑坡的空间发生规律。为此以一定的地区作为研究对象,提出了蒙特卡罗随机模拟和Newmark滑动体位移分析法在区域地震斜坡失稳概率分析中的应用。该法充分考虑到岩土参数和相关地震参数空间变异性,结合地理信息系统空间分析的优势,以网格模型为基础,分析该区斜坡滑动体位移分布规律,并以2cm为失稳临界值探讨网格斜坡破坏的概率。实例证明,所提出的模型有效地预测了滑坡发生的空间分布规律。     

Spatial probabilistic modeling of slope failure using an integrated GIS Monte Carlo simulation approach

Spatial probabilistic modeling of slope failure using a combined Geographic Information System (GIS), infinite-slope stability model and Monte Carlo simulation approach is proposed and applied in the landslide-prone area of Sasebo city, southern Japan. A digital elevation model (DEM) for the study area has been created at a scale of 1/2500. Calculated results of slope angle and slope aspect derived from the DEM are discussed. Through the spatial interpolation of the identified stream network, the thickness distribution of the colluvium above Tertiary strata is determined with precision. Finally, by integrating an infinite-slope stability model and Monte Carlo simulation with GIS, and applying spatial processing, a slope failure probability distribution map is obtained for the case of both low and high water levels.     

Inverse trishear modeling of bedding dip data using Markov chain Monte Carlo methods

We present a method for fitting trishear models to surface profile data, by restoring bedding dip data and inverting for model parameters using a Markov chain Monte Carlo method. Trishear is a widely-used kinematic model for fault-propagation folds. It lacks an analytic solution, but a variety of data inversion techniques can be used to fit trishear models to data. Where the geometry of an entire folded bed is known, models can be tested by restoring the bed to its pre-folding orientation. When data include bedding attitudes, however, previous approaches have relied on computationally-intensive forward modeling. This paper presents an equation for the rate of change of dip in the trishear zone, which can be used to restore dips directly to their pre-folding values. The resulting error can be used to calculate a probability for each model, which allows solution by Markov chain Monte Carlo methods and inversion of datasets that combine dips and contact locations. These methods are tested using synthetic and real datasets. Results are used to approximate multimodal probability density functions and to estimate uncertainty in model parameters. The relative value of dips and contacts in constraining parameters and the effects of uncertainty in the data are investigated.     

Analyzing reproduction of correlations in Monte Carlo simulations: application to mine project valuation

Monte Carlo (MC) simulations are extensively used to assess risk in mining ventures; however, the correlation between the inputs used to build the models is often overlooked. We observed how value-at-risk (VaR) of a mining venture was affected by running MC simulations, using two different input correlation methods: Spearman's rank correlation and copulas using Kendall's tau. The goal was to compare different correlation approaches on risk analysis associated with uncertain parameters of mining ventures and uncover which one would yield the most accurate result. Three case studies were carried out to compare correlation structures. Modelling the input variable correlations was better achieved using copulas since they were able to capture a wider range of correlations that did not make any linearity assumptions. In the case study based on MC simulations, the impact of the input correlation choice on the VaR was rather severe with an approximate 9% difference between the results obtained with Spearman's correlations and the Normal copula correlations.     

基于MCMC法的非饱和土渗流参数随机反分析

基于贝叶斯理论,以马尔可夫链蒙特卡罗方法（Markov chain Monte Carlo Simulation, MCMC法）的自适应差分演化Metropolis算法为参数后验分布抽样计算方法,建立利用时变测试数据的参数随机反分析及模型预测方法。以香港东涌某天然坡地降雨入渗测试为算例,采用自适应差分演化Metropolis算法对时变降雨条件下非饱和土一维渗流模型参数进行随机反分析,研究参数后验分布的统计特性,并分别对校准期和验证期内模型预测孔压和实测值进行比较。研究结果表明,DREAM算法得到的各随机变量后验分布标准差较先验分布均显著减小;经过实测孔压数据的校准,模型计算精度很高,校准期内95%总置信区间的覆盖率达到0.964;验证期第2～4个阶段95%总置信区间的覆盖率分别为0.52、0.79和0.79,模型预测结果与实测值吻合程度较高。     

A Hazard Assessment Method for Potential Earthquake-Induced Landslides – A Case Study in Huaxian County, Shaanxi Province

The hazard assessment of potential earthquake-induced landslides is an important aspect of the study of earthquake-induced landslides. In this study, we assessed the hazard of potential earthquake-induced landslides in Huaxian County with a new hazard assessment method. This method is based on probabilistic seismic hazard analysis and the Newmark cumulative displacement assessment model. The model considers a comprehensive suite of information, including the seismic activities and engineering geological conditions in the study area, and simulates the uncertainty of the intensity parameters of the engineering geological rock groups using the Monte Carlo method. Unlike previous assessment studies on ground motions with a given exceedance probability level, the hazard of earthquake-induced landslides obtained by the method presented in this study allows for the possibility of earthquake-induced landslides in different parts of the study area in the future. The assessment of the hazard of earthquake-induced landslides in this study showed good agreement with the historical distribution of earthquake-induced landslides. This indicates that the assessment properly reflects the macroscopic rules for the development of earthquake-induced landslides in the study area, and can provide a reference framework for the management of the risk of earthquake-induced landslides and land planning.     

降雨型滑坡危险性区划方法

降雨诱发的滑坡等地质灾害分布广、危害大,开展地质灾害危险性区划是减轻地质灾害损失的有效途径之一。以湖南省为例,根据地质灾害调查成果,选取3 412处滑坡,分析了区域降雨型滑坡的发育特点和分布规律,建立了危险性区划指标体系,利用不确定性推理中的确定性系数法,对滑坡与工程地质岩组、坡度、坡向、植被和年均降水量5个评价因子进行了相关性分析,建立了Logistic多元回归模型;采用不规则网格单元划分方法,形成了湖南省滑坡灾害危险性区划图。     

基于Monte Carlo和Rosenblueth方法的边坡可靠性分析及其在工程实践中的应用

传统上常以安全系数作为边坡稳定性的评价指标,但是安全系数只是由一种确定的方法计算所得的一个定值,没有考虑设计参数的变异性,因此安全系数很难表征边坡的安全程度,为此本文引入了可靠度的概念,并运用基于概率论和数理统计学的蒙特卡洛法（Monte Carlo）和Rosenblueth法进行边坡可靠性分析,有效的弥补了边坡传统评...     

Microsommite: crystal chemistry, phase transitions, Ising model and Monte Carlo simulations

Microsommite, ideal formula [Na₄K₂(SO₄)] [Ca₂Cl₂][Si₆Al₆O₂₄], is a rare feldspathoid that occurs in volcanic products of Vesuvius. It belongs to the cancrinite–davyne group of minerals, presenting an ABAB… stacking sequence of layers that contain six-membered rings of tetrahedra, with Si and Al cations regularly alternating in the tetrahedral sites. The structure was refined in space group P6₃ to R=0.053 by means of single-crystal X-ray diffraction data. The cell parameters are a=22.161?Å=√3a _dav, c=5.358?Å=c _dav; Z=3. The superstructure arises due to the long-range ordering of extra-framework ions within the channels of the structure. This ordering progressively decreases with rising temperature until it is completely lost and microsommite transforms into davyne. The order–disorder transformation has been monitored in several crystals by means of X-ray superstructure reflections and the critical parameters T _c?≈?750?°C and β?≈?0.12 were obtained. The kinetics of the ordering process were followed at different temperatures and the activation energy was determined to be about 125?kJ?mol^?1. The continuous order–disorder phase transition in microsommite has been discussed on the basis of a two-dimensional Ising model in a triangular lattice with nn (nearest neighbours) and nnn (next-nearest neighbours) interactions. Such a model was simulated using a Monte Carlo technique. The theoretical model well matches the experimental data; two phase transitions were indicated by the simulated runs: at low temperature only one of the three sublattices begins to disorder, whereas the second transition involves all three sublattices.     

用Monte Carlo方法模拟砂土的自然堆积过程

用MonteCarlo随机模拟方法模拟砂土颗粒在重力作用下,在圆柱与长方体容器中的自然堆积过程。首先用参考网格法生成一个砂土颗粒的松散结构,松散结构中粒子与粒子、粒子与边界间不存在任何接触;然后启动MonteCarlo随机模拟算法,即给处于松散结构中的每个粒子施加随机位移,得到新构形,如果新构形中粒子间或粒子与边界间发生重叠,则放弃这个构形;如果没有重叠存在,则判别粒子体系的势能变化,运用Metropolis准则来判别这个构形是否被接受,重复这个过程可以得到砂土的密集堆积结构。采用Schinner建议的接触发现算法判别粒子间是否存在重叠,同时详细介绍了粒子与边界间的接触发现算法。模拟结果表明,用MonteCarlo方法模拟砂土的自然堆积结构是非常有效的,可以为砂土的流动、压实等的数值模拟工作提供初始构形。     

Safety assessment of infrastructures using a new Bayesian Monte Carlo method

A recently developed Bayesian Monte Carlo (BMC) method and its application to safety assessment of structures are described in this paper. We use a one-dimensional BMC method that was proposed in 2009 by Rajabalinejad in order to develop a weighted logical dependence between successive Monte Carlo simulations. Our main objective in this research is to show that the extended BMC can dramatically improve simulation efficiency by using prior information from modelling and outcomes of preceding simulations. We provide theory and numerical algorithms for an extended BMC method for multi-dimensional problems, integrate it with a probabilistic finite element model and apply these coupled models to assessment of reliability of a flood defence for the 17th Street Flood Wall system in New Orleans. This is the first successful demonstration of the BMC method to a complex system. We provide a comparison of the numerical efficiency for the BMC, Monte Carlo (MC) and Dynamic Bounds methods that are used in reliability assessment of complex infrastructures.     

Probabilistic analysis of reinforced slopes using RFEM and considering spatial variability of frictional soil properties due to compaction

Probabilistic stability analyses of constructed wrapped-face reinforced slopes (or embankments) using frictional soils were carried out using the random finite element method (RFEM). Soil properties reported in the literature for unsaturated frictional fills compacted to different densities were used in the simulations. Bar elements were added to the RFEM code to simulate extensible geosynthetic reinforcement layers and the Davis approach was used to improve numerical stability for purely frictional soil slopes at collapse. The influence of isotropic and anisotropic spatially variable soil strength was investigated and shown to have a large influence on the variation of maximum mobilised tensile forces in reinforcement layers for the steep 5 m-high slopes in the study. The influence of fill placed at different layer thickness and compacted to different levels was simulated by adjusting the soil strength and unit weight, and the vertical strength correlation length in the anisotropic spatially variable strength field used in each slope realisation. Numerical results showed that vertical strength correlation lengths approaching the magnitude of fill lift heights can control the probability of failure for reinforced slopes constructed with weak fills placed in lift heights close to but less than the wrapped reinforcement spacing used in the study.     

基于MATLAB的均质土坡稳定可靠度的蒙特卡罗模拟

根据Bishop条分法建立均质土坡的可靠度计算模型,利用MATLAB进行蒙特卡罗方法模拟的程序实现,进行均质土坡的可靠度模拟计算.结果表明土性参数c、ψ在正态分布或对数正态分布情况下,对于边坡可靠度基本没有影响.并将其应用于工程实例分析,取得良好效果,说明可靠度分析方法是对传统的确定性分析方法的有益补充.     

Physically-based landslide susceptibility analysis using Monte Carlo simulation in a tropical mountain basin

ABSTRACT

Physically-based distributed models are implemented for landslide susceptibility and hazard assessment around the world. Probabilistic methodologies are considered appropriate to study and quantify the uncertainties derived from the input parameters of these models. In this paper, three sets of Monte Carlo simulations, each one with 10,000 iterations, were applied for a slope stability analysis in a small basin of Envigado (Colombia), using the TRIGRS model, to characterise the uncertainty in the landslide assessment. Different parameters to determine the minimum number of realizations required to ensure a small variation in the failure probability were proposed and analyzed. The quality of the landslide susceptibility assessment was studied. Unexpected and probably erroneous results that may be common in the maps generated using this and other similar methodologies were identified and explained. Additionally, the distribution of the factor of safety was calculated for different grid cells of the basin, showing that the probability density function with the best adjustment to the frequency histogram of the factor of safety can vary between grid cells. The assumption of a normal distribution for the factor of safety would be inappropriate and would lead to miscalculations in this case study.     

Efficient system reliability analysis of soil slopes using multivariate adaptive regression splines-based Monte Carlo simulation

System effects should be considered in the probabilistic analysis of a layered soil slope due to the potential existence of multiple failure modes. This paper presents a system reliability analysis approach for layered soil slopes based on multivariate adaptive regression splines (MARS) and Monte Carlo simulation (MCS). The proposed approach is achieved in a two-phase process. First, MARS is constructed based on a group of training samples that are generated by Latin hypercube sampling (LHS). MARS is validated by a specific number of testing samples which are randomly generated per the underlying distributions. Second, the established MARS is integrated with MCS to estimate the system failure probability of slopes. Two types of multi-layered soil slopes (cohesive slope and c–φ slope) are examined to assess the capability and validity of the proposed approach. Each type of slope includes two examples with different statistics and system failure probability levels. The proposed approach can provide an accurate estimation of the system failure probability of a soil slope. In addition, the proposed approach is more accurate than the quadratic response surface method (QRSM) and the second-order stochastic response surface method (SRSM) for slopes with highly nonlinear limit state functions (LSFs). The results show that the proposed MARS-based MCS is a favorable and useful tool for the system reliability analysis of soil slopes.     

随机误差传递与合成的蒙特卡罗模拟

对分析测试过程中随机误差的传递与合成进行了蒙卡罗模拟,并偏制了ＢＡＳＩＣ程序。该方法解决了当被合成误差不相互独立时泰勒级数公式所遇到的困难,当被合成误差相互独立时,与泰勒公式计算结果一致。     

Probabilistic analysis of rock slope stability and random properties of discontinuity parameters, Interstate Highway 40, Western North Carolina, USA

Probabilistic analysis has been used as an effective tool to evaluate uncertainty so prevalent in variables governing rock slope stability. In this study a probabilistic analysis procedure and related algorithms were developed by extending the Monte Carlo simulation. The approach was used to analyze rock slope stability for Interstate Highway 40 (I-40), North Carolina, USA. This probabilistic approach consists of two parts: analysis of available geotechnical data to obtain random properties of discontinuity parameters; and probabilistic analysis of slope stability based on parameters with random properties. Random geometric and strength parameters for discontinuities were derived from field measurements and analysis using the statistical inference method or obtained from experience and engineering judgment of parameters. Specifically, this study shows that a certain amount of experience and engineering judgment can be utilized to determine random properties of discontinuity parameters. Probabilistic stability analysis is accomplished using statistical parameters and probability density functions for each discontinuity parameter. Then, the two requisite conditions, kinematic and kinetic instability for evaluating rock slope stability, are determined and evaluated separately, and subsequently the two probabilities are combined to provide an overall stability measure. Following the probabilistic analysis to account for variation in parameters, results of the probabilistic analyses were compared to those of a deterministic analysis, illustrating deficiencies in the latter procedure. Two geometries for the cut slopes on I-40 were evaluated, the original 75° slope and the 50° slope which has developed over the past 40 years of weathering.     

Markov Chain Monte Carlo Implementation of Rock Fracture Modelling

This paper deals with the problem of estimating fracture planes, given only the data at borehole intersections with fractures. We formulate an appropriate model for the problem and give a solution to fitting the planes using a Markov chain Monte Carlo (MCMC) implementation. The basics of MCMC are presented, with particular emphasis given to reversible jump, which is required for changing dimensions. We also give a detailed worked example of the MCMC implementation with reversible jump since our implementation relies heavily on this new methodology. The methods are tested on both simulated and real data. The latter is a unique data set in the form of a granite block, which was sectioned into slices. All joints were located and recorded, and the joint planes obtained by stacking strike lines. This work is important in the risk assessment for the underground storage of hazardous waste. Problems and extensions are discussed.     

基于NSMC方法的某核工程场地裂隙地下水数值模拟不确定分析

裂隙介质渗透结构表现为高度的非均质性与各项异性。为了科学有效地预测某核工程场地裂隙地下水的流动规律,揭示裂隙岩体地下水的渗流特性,笔者等采用Pilot Point调参方法与null space Monte Carlo方法(NSMC),开展了裂隙岩体渗透结构的不确定性分析研究,构建了符合实际水文地质条件的多个渗流数值模型集合。结果表明：该方法获得的各个实现地下水位模拟结果能够与实际观测数据较好吻合,可反映工程场地裂隙地下水动力特征与流动趋势;各个实现的参数化渗透结构在空间上存在一定的差异性,但整体变化趋势是保持一致的,渗透参数的不确定性表现为在实测数据分布区域相对较低,钻孔空白区域相对较高;该方法可以弥补单一、确定性模拟结果在表征裂隙介质渗透结构方面的局限性,有效地降低模型参数的不确定性与随机性。此方法对进一步提升裂隙岩体渗流模拟精度与预测能力,深化裂隙地下水迁移规律的认识具有重要的意义。