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1.
给出分析各向异性非均质稳定随机渗流场问题的三维有限元模型;结合实际工程问题,统计分析长江荆南干堤士性参数的分布特征,通过Kolomogorov-Smirnov统计检验表明,渗透系数呈高斯分布假设可以接受;通过对长江荆南干堤随机渗流场的三维有限元统计模拟的数值分析,研究长江荆南干堤渗流场的各种随机特性,并进一步对随机模拟结果进行统计检验,验证模拟结果的合理性;在实际的分析研究中把上下游水位的随机波动引入三维有限元的随机分析模型,分析上下游水位的变异性对渗流场矢量的随机干扰和边界条件的随机性对随机渗流场分析结果变异性的影响。在此基础上进一步考虑施加诸如垂直截渗墙、下游导渗沟等抗渗措施后,它们作为复杂边界条件的扰动,在与场内土性参数的变异性共同影响下,对渗流场水头势分布的随机干扰特性,并与相应的确定性稳定渗流场问题的结果对比,证实随机渗流场研究的必要性、可行性及实用性。实现了对长江荆南干堤的三维渗流场的较为全面的随机场模拟及特性分析,分析得到的结论通过统计检验并结合实测工程数据对照证明是可靠的,所研制的程序是适用的。 相似文献
2.
渗流场随机性的随机有限元分析 总被引：3，自引：0，他引：3
基于一阶Taylor随机有限元法,推导出相应的渗流场随机分析中渗流响应量（水头和水力梯度）的随机响应公式,进而实现三维稳定渗流场随机有限元分析,并编制了相应的程序。在分析中,将渗流区域材料的渗透张量视为三维各向异性随机场,利用三维可分离向量随机场的局部平均法对随机场进行离散,根据参数选取的不同,可以离散出不同数量的随机变量。最后,给出一个算例,对离散出随机变量数量不同的情况分别进行随机分析,将分析结果和仅仅将渗透张量视为三维随机变量得到的结果对比,验证了所提方法的可行性。 相似文献
3.
Wang Mingyu The University of Arizona Tucson Arizona USA Department of Water Resources Environmental Engineering China University of Geosciences Beijing Chen Jinsong Wan Li Department of Water Resources Environmental Engineering 《中国地质大学学报(英文版)》2001,12(3)
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4.
Dynamic stochastic estimation of physical variables 总被引：1，自引：0，他引：1
A fundamental problem facing the physical sciences today is analysis of natural variations and mapping of spatiotemporal processes. Detailed maps describing the space/time distribution of groundwater contaminants, atmospheric pollutant deposition processes, rainfall intensity variables, external intermittency functions, etc. are tools whose importance in practical applications cannot be overestimated. Such maps are valuable inputs for numerous applications including, for example, solute transport, storm modeling, turbulent-nonturbulent flow characterization, weather prediction, and human exposure to hazardous substances. The approach considered here uses the spatiotemporal random field theory to study natural space/time variations and derive dynamic stochastic estimates of physical variables. The random field model is constructed in a space/time continuum that explicitly involves both spatial and temporal aspects and provides a rigorous representation of spatiotemporal variabilities and uncertainties. This has considerable advantages as regards analytical investigations of natural processes. The model is used to study natural space/time variations of springwater calcium ion data from the Dyle River catchment area, Belgium. This dataset is characterized by a spatially nonhomogeneous and temporally nonstationary variability that is quantified by random field parameters, such as orders of space/time continuity and random field increments. A rich class of covariance models is determined from the properties of the random field increments. The analysis leads to maps of continuity orders and covariances reflecting space/time calcium ion correlations and trends. Calcium ion estimates and the associated statistical errors are calculated at unmeasured locations/instants over the Dyle region using a space/time kriging algorithm. In practice, the interpretation of the results of the dynamic stochastic analysis should take into consideration the scale effects. 相似文献
5.
Digital simulation of multivariate two- and three-dimensional stochastic processes with a spectral turning bands method 总被引：3，自引：0，他引：3
Aristotelis Mantoglou 《Mathematical Geology》1987,19(2):129-149
The space domain version of the turning bands method can simulate multidimensional stochastic processes (random fields) having particular forms of covariance functions. To alleviate this limitation a spectral representation of the turning bands method in the two-dimensional case has shown that the spectral approach allows simulation of isotropic two-dimensional processes having any covariance or spectral density function. The present paper extends the spectral turning bands method (STBM) even further for simulation of much more general classes of multidimensional stochastic processes. Particular extensions include: (i) simulation of three-dimensional processes using STBM, (ii) simulation of anisotropic two- or three-dimensional stochastic processes, (iii) simulation of multivariate stochastic processes, and (iv) simulation of spatial averaged (integrated) processes. The turning bands method transforms the multidimensional simulation problem into a sum of a series of one-dimensional simulations. Explicit and simple expressions relating the cross-spectral density functions of the one-dimensional processes to the cross-spectral density function of the multidimensional process are derived. Using such expressions the one-dimensional processes can be simulated using a simple one-dimensional spectral method. Examples illustrating that the spectral turning bands method preserves the theoretical statistics are presented. The spectral turning bands method is inexpensive in terms of computer time compared to other multidimensional simulation methods. In fact, the cost of the turning bands method grows as the square root or the cubic root of the number of points simulated in the discretized random field, in the two- or three-dimensional case, respectively, whereas the cost of other multidimensional methods grows linearly with the number of simulated points. The spectral turning bands method currently is being used in hydrologic applications. This method is also applicable to other fields where multidimensional simulations are needed, e.g., mining, oil reservoir modeling, geophysics, remote sensing, etc. 相似文献
6.
Gradual Deformation and Iterative Calibration of Gaussian-Related Stochastic Models 总被引：11，自引：0，他引：11
Lin Y. Hu 《Mathematical Geology》2000,32(1):87-108
This paper describes a new method for gradually deforming realizations of Gaussian-related stochastic models while preserving their spatial variability. This method consists in building a stochastic process whose state space is the ensemble of the realizations of a spatial stochastic model. In particular, a stochastic process, built by combining independent Gaussian random functions, is proposed to perform the gradual deformation of realizations. Then, the gradual deformation algorithm is coupled with an optimization algorithm to calibrate realizations of stochastic models to nonlinear data. The method is applied to calibrate a continuous and a discrete synthetic permeability fields to well-test pressure data. The examples illustrate the efficiency of the proposed method. Furthermore, we present some extensions of this method (multidimensional gradual deformation, gradual deformation with respect to structural parameters, and local gradual deformation) that are useful in practice. Although the method described in this paper is operational only in the Gaussian framework (e.g., lognormal model, truncated Gaussian model, etc.), the idea of gradually deforming realizations through a stochastic process remains general and therefore promising even for calibrating non-Gaussian models. 相似文献
7.
地基固结沉降随机有限元计算和可靠度分析 总被引：4，自引：0，他引：4
基于比奥（Biot）固结理论，采用邓肯-张本构模型，考虑随机场的影响，首次给出了地基固结沉降随机有限元分析方法，并基于随机有限元对点固结沉降和差异固结沉降的可靠度进行了分析。 相似文献
8.
In this paper, a coupled constitutive model is proposed for anisotropic damage and permeability variation in brittle rocks under deviatoric compressive stresses. The formulation of the model is based on experimental evidences and main physical mechanisms involved in the scale of microcracks are taken into account. The proposed model is expressed in the macroscopic framework and can be easily implemented for engineering application. The macroscopic free enthalpy of cracked solid is first determined by approximating crack distribution by a second‐order damage tensor. The effective elastic properties of damaged material are then derived from the free enthalpy function. The damage evolution is related to the crack growth in multiple orientations. A pragmatic approach inspired from fracture mechanics is used for the formulation of the crack propagation criterion. Compressive stress induced crack opening is taken into account and leads to macroscopic volumetric dilatancy and permeability variation. The overall permeability tensor of cracked material is determined using a micro–macro averaging procedure. Darcy's law is used for fluid flow at the macroscopic scale whereas laminar flow is assumed at the microcrack scale. Hydraulic connectivity of cracks increases with crack growth. The proposed model is applied to the Lac du Bonnet granite. Generally, good agreement is observed between numerical simulations and experimental data. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
9.
10.
A numerical procedure to determine the equivalent permeability tensor of a fractured rock is presented, using a stochastic REV (Representative Elementary Volume) concept that uses multiple realizations of stochastic DFN (Discrete Fracture Network) models. Ten square DFN models are generated using the Monte Carlo simulations of the fracture system based on the data obtained from a site characterization program at Sellafield, Cumbria, UK. Smaller models with varying sizes of from 0.25 m×0.25 m to 10 m×10 m are extracted from the generated DFN models and are used as two-dimensional geometrical models for calculation of equivalent permeability tensor. The DFN models are also rotated in 30º intervals to evaluate the tensor characteristics of calculated directional permeability. Results show that the variance of the calculated permeability values decreases significantly as the side lengths of the DFN models increase, which justifies the existence of a REV. The REV side length found in this analysis is about 5 m and 8 m with 20% and 10% acceptable variations, respectively. The calculated directional permeability values at the REV size have tensor characteristic that is confirmed by a close approximation of an ellipse in a polar plot of the reciprocal of square roots of the directional permeability.
相似文献
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11.
Quasi-Stochastic Analysis of Uncertainty for Modelling Structurally Controlled Failures 总被引：1，自引：0，他引：1
In one approach to predicting the behaviour of rock masses, effort is being devoted to the use of probabilistic methods to model structures interior to a rock mass (sometimes referred to as ‘inferred’ or ‘stochastic’ structures). The physical properties of these structures (e.g. position, orientation, size) are modelled as random parameters, the statistical properties of which are derived from the measurements of a sample of the population (sometimes referred to as ‘deterministic’ structures). Relatively little attention has been devoted to the uncertainty associated with the deterministic structures. Typical geotechnical analyses rely on either an entirely stochastic analysis, or deterministic analyses representing the structures with a fixed shape (i.e. disc), position, size, and orientation. The simplifications assumed for this model introduce both epistemic and stochastic uncertainties. In this paper, it is shown that these uncertainties should be quantified and propagated to the predictions of behaviour derived from subsequent analyses. We demonstrate a methodology which we have termed quasi-stochastic analysis to perform this propagation. It is shown that relatively small levels of uncertainty can have large influence on the uncertainties associated with geotechnical analyses, such as predictions of block size and block stability, and therefore this methodology can provide the practitioner with a method for better interpretation of these results. 相似文献
12.
储层岩石物性应力敏感研究主要停留在实验测试与数据处理方法上,无法通过单一形状孔隙的理论模型从机理上得到解释;因此,本研究基于随机孔隙网络模型实现渗透率应力敏感感机理解释。以逾渗理论、水电相似原理、Kirchoff定律为理论基础,采用迭代法,基于QT Creator平台编程生成了三维随机孔隙网络模型,并对无因次半径与有效应力的关系进行了模拟。模拟结果表明:纵横比越小,无因次半径受到有效应力的影响越明显。因此,通过网络模型建立渗透率与有效应力关系,能够实现渗透率应力敏感的机理解释。 相似文献
13.
随机连续模型分析裂隙岩体耦合行为 总被引：2，自引：1，他引：1
利用能够反映岩体水力性质空间变异特性的随机连续模型对隧洞开挖过程中的裂隙岩体渗流-应力耦合过程进行了数值分析。随机渗透系数场通过顺序指示模拟方法生成。顺序指示法是一种非参数地质统计学技术,他允许输入任何形式的渗透系数概率分布而不需要对分布做任何假设。由随机模拟生成的渗透系数场被投影到有限元计算网格中进行耦合分析。力学响应使用基于连续介质的节理本构模型来反映岩体中软弱面的影响。结果表明,随机连续模型能够较好地预测裂隙岩体的稳定入渗率,水力性质的空间变异性对裂隙介质的耦合过程起着重要作用。在不排水条件下,隧洞每次开挖开始时,由于岩石应力重分布,孔隙水受到扰动,短时间内不能流动平衡,因此孔压会迅速上升,这对于围岩稳定是不利的。 相似文献
14.
Linda Werner Hartman 《Mathematical Geology》2006,38(2):113-133
Spatial datasets are common in the environmental sciences. In this study we suggest a hierarchical model for a spatial stochastic field. The main focus of this article is to approximate a stochastic field with a Gaussian Markov Random Field (GMRF) to exploit computational advantages of the Markov field, concerning predictions, etc. The variation of the stochastic field is modelled as a linear trend plus microvariation in the form of a GMRF defined on a lattice. To estimate model parameters we adopt a Bayesian perspective, and use Monte Carlo integration with samples from Markov Chain simulations. Our methods does not demand lattice, or near-lattice data, but are developed for a general spatial data-set, leaving the lattice to be specified by the modeller. The model selection problem that comes with the artificial grid is in this article addressed with cross-validation, but we also suggest other alternatives. From the application of the methods to a data set of elemental composition of forest soil, we obtained predictive distributions at arbitrary locations as well as estimates of model parameters. 相似文献
15.
针对确定性模型难以描述含水层非均质空间分布的问题,提出基于随机理论的地下水环境风险评价方法。以矩形场地地下水污染风险评价为例,采用蒙特卡罗法生成大量渗透系数随机场,模拟含水层参数各种可能的非均质空间分布,在此基础上建立场地地下水流模型与溶质运移模型,分别计算污染物在地下水中的迁移转化情况。统计大量随机模拟中污染事故发生的频率,当模拟次数足够多时,污染频率收敛于污染概率,污染风险即通过污染概率体现出来。该方法将模型参数设为满足一定分布特征的随机变量,避免了确定性方法得出的武断的评价结果,可为工厂的选址、水源地的选址等工作提供科学指导。 相似文献
16.
Analysis and Estimation of Natural Processes with Nonhomogeneous Spatial Variation Using Secondary Information 总被引：1，自引：0，他引：1
Natural processes encountered in mining, hydrogeologic, environmental, etc. applications usually are poorly known because of scarcity of data over the area of interest. Therefore, stochastic estimation techniques are the tool of choice for a careful accounting of the heterogeneity and uncertainty involved. Within such a framework, a better utilization of all available data concerning the process of interest and all other natural processes related to it, is of primary importance. Because many natural processes show complicated spatial trends, the hypothesis of spatial homogeneity cannot be invoked always, and the more general theory of intrinsic spatial random fields should be employed. Efficient use of secondary information in terms of the intrinsic model requires that suitable permissibility criteria for the generalized covariances and cross-covariances are satisfied. A set of permissibility criteria are presented for the situation of two intrinsic random fields. These criteria are more general and comprehensive than the ones currently available in the geostatistical literature. A constrained least-square technique is implemented for the inference of the generalized covariance and cross-covariance parameters, and a synthetic example is used to illustrate the methodology. The numerical results show that the use of secondary information can lead to significant reductions in the estimation errors. 相似文献
17.
Ji Yuan Iason Papaioannou Daniel Straub 《Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards》2019,13(1):20-33
Rainfall-induced landslides occur during or immediately after rainfall events in which the pore water pressure builds up, leading to shallow slope failure. Thereby, low permeability layers result in high gradients in pore water pressure. The spatial variability of the soil permeability influences the probability such low permeability layers, and hence the probability of slope failure. In this paper, we investigate the influence of the vertical variability of soil permeability on the slope reliability, accounting for the randomness of rainfall processes. We model the saturated hydraulic conductivity of the soil with a one-dimensional random field. The random rainfall events are characterised by their duration and intensity and are modelled through self-similar random processes. The transient infiltration process is represented by Richards equation, which is evaluated numerically. The reliability analysis of the infinite slope is based on the factor of safety concept for evaluating slope stability. To cope with the large number of random variables arising from the discretization of the random field and the rainfall process, we evaluate the slope reliability through Subset Simulation, which is an adaptive Monte Carlo method known to be especially efficient for reliability analysis of such high-dimensional problems. Numerical investigations show higher probability of slope failure with increased spatial variability of the saturated hydraulic conductivity and with more uniform rainfall patterns. 相似文献
18.
A probabilistic parametrization for geological uncertainty estimation using the ensemble Kalman filter (EnKF) 总被引：2，自引：0，他引：2
In the past years, many applications of history-matching methods in general and ensemble Kalman filter in particular have been proposed, especially in order to estimate fields that provide uncertainty in the stochastic process defined by the dynamical system of hydrocarbon recovery. Such fields can be permeability fields or porosity fields, but can also fields defined by the rock type (facies fields). The estimation of the boundaries of the geologic facies with ensemble Kalman filter (EnKF) was made, in different papers, with the aid of Gaussian random fields, which were truncated using various schemes and introduced in a history-matching process. In this paper, we estimate, in the frame of the EnKF process, the locations of three facies types that occur into a reservoir domain, with the property that each two could have a contact. The geological simulation model is a form of the general truncated plurigaussian method. The difference with other approaches consists in how the truncation scheme is introduced and in the observation operator of the facies types at the well locations. The projection from the continuous space of the Gaussian fields into the discrete space of the facies fields is realized through in an intermediary space (space with probabilities). This space connects the observation operator of the facies types at the well locations with the geological simulation model. We will test the model using a 2D reservoir which is connected with the EnKF method as a data assimilation technique. We will use different geostatistical properties for the Gaussian fields and different levels of the uncertainty introduced in the model parameters and also in the construction of the Gaussian fields. 相似文献
19.
Aquifer properties, for example permeability and porosity, vary in space and may be characterized by their distributions. The property distribution is not totally random but shows some correlation structure. Because most of the values are not known, some rational method is required to generate credible aquifer distribution properties for inclusion in fluid transport models. This paper presents a numerically efficient method of generating geostatistical random fields, by the source Point Method (SPM). The SPM is a very efficient method and requires little computer time and relatively small data storage, as compared to other methods of generating random fields. In addition, the SPM is modified to include any desired amount of anisotropy in the property distribution of a system. By using conditional covariances, a formula for a two-dimensional anisotropic field is derived to prespecify the desired correlation length in any direction. Results show that for an anisotropic medium the correlation length can be pre-specified in any specific direction. 相似文献
20.
Constraining stochastic models of reservoir properties such as porosity and permeability can be formulated as an optimization problem. While an optimization based on random search methods preserves the spatial variability of the stochastic model, it is prohibitively computer intensive. In contrast, gradient search methods may be very efficient but it does not preserve the spatial variability of the stochastic model. The gradual deformation method allows for modifying a reservoir model (i.e., realization of the stochastic model) from a small number of parameters while preserving its spatial variability. It can be considered as a first step towards the merger of random and gradient search methods. The gradual deformation method yields chains of reservoir models that can be investigated successively to identify an optimal reservoir model. The investigation of each chain is based on gradient computations, but the building of chains of reservoir models is random. In this paper, we propose an algorithm that further improves the efficiency of the gradual deformation method. Contrary to the previous gradual deformation method, we also use gradient information to build chains of reservoir models. The idea is to combine the initial reservoir model or the previously optimized reservoir model with a compound reservoir model. This compound model is a linear combination of a set of independent reservoir models. The combination coefficients are calculated so that the search direction from the initial model is as close as possible to the gradient search direction. This new gradual deformation scheme allows us for reducing the number of optimization parameters while selecting an optimal search direction. The numerical example compares the performance of the new gradual deformation scheme with that of the traditional one. 相似文献