基于van Genuchten-Mualem模型的饱和-非饱和介质流动随机数值分析

基于van Genuchten-Mualem非饱和水分特征模型，联合运用Karhunen-Loeve展开法、混沌多项式展开以及摄动方法，对饱和-非饱和流问题进行随机数值分析。将土壤特性参数假定为协方差已知的随机函数，并按Karhunen-Loeve法分解，把压力水头表示为多项式。通过摄动方法得到一系列关于水头展开式的偏微分方程，用有限差分法进行求解，获得了压力水头的随机描述，并计算其均值和方差。应用本文的随机模型研究了二维非饱和以及饱和-非饱和介质流动的实例，结果与动量方法的计算结果一致，而且计算效率高于传统的动量方法。     

刘家坡滑坡非饱和渗流情况下的稳定分析

分析研究刘家坡滑坡在暴雨作用下的渗流场,通过正交实验确定饱和———非饱和渗流计算参数。并应用粘弹塑性有限单元法对滑坡在非饱和渗流场作用下的稳定性进行了分析评价。     

饱和-非饱和渗流计算参数分析

在饱和 非饱和渗流计算中,非饱和渗流参数的选择至关重要。通过开展非饱和渗流参数试验及非饱和渗流模型试验,用模型试验结果作为评判标准,研究了VG模型代入法和试验数据法之间的差距,提出了"双参数VG模型"的方法。结果表明,利用"双参数VG模型"代入数值计算中,计算结果可以较好地和试验结果相吻合。     

土石坝渗流热监测理论研究进展

对渗流热监测理论各发展阶段特点与相关研究作了评述,着重介绍了定量研究阶段考虑渗流场影响推求温度分布的正演分析,详述了各渗流场与温度场耦合数学模型的基本原理、模拟对象、耦合机理与模型计算方法,总结了渗流-温度场耦合模型研究的趋势与问题。介绍了耦合模型计算的2个部分(渗流场计算与温度场计算)的研究现状与发展重点,阐述了研究基于非饱和渗流双场耦合的必要性和建立模型涉及的基本理论。对未来的研究提出几点建议:考虑有关参数的温变特性,提高模型仿真精度;开展基于非饱和渗流的耦合模型研究,丰富复杂条件下渗流热监测理论;加强由温度场求解渗流场的反演分析研究。     

降雨作用下非饱和土边坡水力耦合过程分析

基于渗流理论、弹性理论及VG土-水特征曲线模型,建立了二维非饱和土渗流-变形耦合控制方程组。该控制方程突破了饱和时渗透系数是常数的局限,适用于任意初始条件和降雨条件的土坡稳定性分析。有限元软件COMSOL Multiphysics能根据已建好的非饱和土坡渗流-变形耦合模型开展分析。通过算例分析了非饱和土降雨入渗过程中渗流-变形的耦合效应,并探讨了考虑饱和渗透系数为变量情况以及不同的初始条件对渗流场和应力场的影响。结果表明:在非饱和土坡降雨入渗过程中渗流-变形的耦合效应是非常显著的,且与时间有关。对于湿陷性土,考虑耦合效应的压力水头变化总是慢于非耦合情况。饱和状态时渗透系数是应变的函数,其值的变化对非饱和土边坡渗流场有一定的影响,但对非饱和土边坡变形影响微弱。初始条件对渗流和变形的影响是非常大的。     

土石坝饱和—非饱和稳定渗流场影响分析

土石坝是当今最为常用的一种坝型,而防渗体系的构建对坝体稳定具有十分重要的作用,国内外的多起水利工程安全事故足以引起足够的重视。进行土石坝的渗流分析需要将渗流场定义为饱和和非饱和区的共同体,过去的经验已然证明二者的相辅相成。二者相比非饱和渗流的运动特性相对复杂,影响因子也较饱和渗流多。文章结合工程实例,运用有限元数值模拟出土石坝在饱和与非饱和渗流中渗流场的变化规律,得出正确合理的渗流场理论,研究成果在土石坝的防渗体系的构建上具有一定的参考价值。     

考虑非饱和区影响的土石坝渗流有限元计算

传统的有限元饱和渗流计算往往把渗透系数取作定值,而实际上非饱和土渗透系数呈非线性函数关系,与体积含水率、孔隙水压力密切相关.基于饱和-非饱和土渗流计算模型与原理,本文考虑渗流场非饱和区对堤坝渗流的影响,对某土石坝进行了渗流有限元计算与分析.算例结果表明,应用该思想与方法计算土石坝渗流,可以获得较为准确合理的渗流场计算结果.     

水位骤变下渠道衬砌边坡破坏问题研究

以某长距离调水工程为背景，在概述渠道典型断面及排水细部构造的基础上，对典型渠段衬砌边坡损毁情况展开实地调查，比较分析非饱和渗流对边坡稳定性影响后，对强降雨作用下渠道衬砌边坡饱和-非饱和渗流场进行了有限元分析；在概括调水渠道衬砌边坡破坏原因后，有针对性的提出处治工程措施，加固效果较为理想。     

考虑非饱和渗流的谷幅变形对高拱坝影响分析

蓄水初期谷幅变形对拱坝当前工作性态和长期安全状况的影响是坝工界和学术界面临的新课题。针对我国锦屏一级拱坝蓄水期间出现的谷幅收缩问题,基于非饱和渗流分析理论,采用非线性有限元数值分析方法,通过对裂隙岩体吸湿曲线进行敏感性分析,研究了非饱和渗流过程中的谷幅变形规律,并分析了谷幅变形对大坝位移和应力的影响。结果表明:在非饱和渗流场作用下,两岸边坡向河谷中心变形,且上游比下游的谷幅变形值大。随着水位的升高,谷幅变形值不断增大,当渗流场达到饱和时谷幅收缩值最大。在非饱和渗流过程中坝体位移和应力的分布规律基本保持不变,但随水位的升高坝体最大顺河向位移和最大主压应力略有减小,最大主拉应力略有增加。谷幅收缩对坝体产生挤压作用,导致坝体最大顺河向位移减小,最大主拉应力由坝踵向坝肩上游侧转移,下游面高压应力区向拱冠梁中部扩展,且饱和渗流场对拱坝位移和应力的影响比非饱和渗流场明显,但渗流场作用的谷幅变形对坝体位移和应力的改变有限,不会影响坝体的整体稳定性。     

堤坝饱和—非饱和渗流数值模拟

本文基于饱和－非饱和渗流数学模型，采用有限单元法对飞来峡水利枢纽工程纵向围堰典型剖面进行渗流数值模拟，分析降雨及非稳定渗流对渗流场的影响，简捷地得到了较全面、准确的参数分布。本文还提出一个简易的（Ｋｒ－Ψ－θ）曲线拟合方法从有限的观测试验中获取所需参数。本模型及程序可以不作特别的修改而应用到具有复杂地质分布和边界条件的各种实际渗流工程。     

非均质土体中渗流场的非平稳随机模拟

将渗透系数作为对数正态非平稳随机场,分解为确定性趋势和平稳性扰动两部分,采用基于随机场Karhunen Loeve展开和摄动分析的KLME随机数值方法,探讨参数场的连续型线性趋势和间断型趋势项对渗流场统计特征的影响。分析表明,水头均值和标准差的空间分布受到参数场趋势性变化的影响,随线性趋势的变化方向而呈不同分布,线性趋势的斜率增大,水头统计矩的二阶修正项的作用也增大,在参数场间断型趋势条件下,水头统计矩呈复杂的非规则空间分布。     

Three-dimensional stochastic seepage field for embankment engineering

Owing to the complexity of get-engineering seepage problems influenced by different random factors, three-dimensional simulation and analysis of the stochastic seepage field plays an important role in engineering applications. A three-dimensional anisotropic heterogeneous steady random seepage model was developed on the basis of the finite element method. A statistical analysis of the distribution characteristics of soil parameters sampled from the main embankment of the Yangtze River in the Southern Jingzhou zone of China was conducted. The Kolomogorov-Smimov test verified the statistical hypothesis that the permeability coefficient tensor has a Gaussian distribution. With the help of numerical analysis of the stochastic seepage field using the developed model, various statistical and random characteristics of the stochastic seepage field of the main embankment of the Yangtze River in the Southern Jingzhou zone of China were investigated. The model was also examined with statistical testing. Through the introduction of random variation of the upstream and downstream water levels into the model, the effects of the boundary randomness due to variation of the downstream and upstream water levels on the variation of simulated results presented with a vector series of the random seepage field were analyzed. Furthermore, the combined influence of the variation of the soil permeability coefficient and such seepage resistance measures as the cut-off wall and relief ditch on the hydraulic head distribution was analyzed and compared with the results obtained by determinate analysis. Meanwhile, sensitivities of the hydraulic gradient and downstream exit height to the variation of boundary water level were studied. The validity of the simulated results was verified by stochastic testing and measured data. The developed model provides more detail and a full stochastic algorithm to characterize and analyze three-dimensional stochastic seepage field problems.     

STOCHASTIC ANALYSIS OF WATER FLOW IN HETEROGENEOUS MEDIA

A stochastic model for saturated-unsaturated flow is developed based on the combination of the KarhunenLoeve expansion of the input random soil properties with a perturbation method. The saturated hydraulic conductivity ks(x) is assumed to be log-normal random functions, expressed by f(x). f(x) is decomposed as infinite series in a set of orthogonal normal random variables by the Karhunen-Loeve (KL) expansion and the pressure head is expand as polynomial chaos with the same set of orthogonal random variables. With these expansions, the stochastic saturated-unsaturated flow equation and the corresponding initial and boundary conditions are represented by a series of deterministic partial differential equations which can be solved subsequently by a suitable numerical method. Some examples are given to show the reliability and efficiency of the proposed method.     

QUALIFICATION OF UNCERTAINTY FOR SIMULATING SOLUTE TRANSPORT IN THE HETEROGENEOUS MEDIA WITH SPARSE GRID COLLOCATION METHOD

The sparse grid collocation method is discussed to qualify the uncertainty of solute transport. The Karhunen-Loeve (KL) expansion is employed to decompose the log transformed hydraulic conductivity. The head, velocity and concentration fields are represented by the Lagrange polynomial expansion. A sparse grid collocation method is then used to reduce the original stochastic partial differential equations to a set of deterministic equations which is collocated at selected interpolation (collocation) points. The collocation points are constructed by the Smolyak algorithm. The accuracy, efficiency and convergence property of sparse grid collocation method are investigated by numerical experiments. The analysis shows that stochastic collocation strategy helps to decouple stochastic computations, and all the numerical computation is possible to be implemented by existing deterministic finite element codes. The proposed method provides an efficient way to evaluate the uncertainty of the solute transport in the heterogeneous media.     

Stochastic simulation of fluid flow in porous media by the complex variable expression method

A stochastic simulation of fluid flow in porous media using a complex variable expression method (SFCM) is presented in this paper. Hydraulic conductivity is considered as a random variable and is then expressed in complex variable form, the real part of which is a deterministic value and the imaginary part is a variable value. The stochastic seepage flow is simulated with the SFCM and is compared with the results calculated with the Monte Carlo stochastic finite element method. In using the Monte Carlo method to simulate the stochastic seepage flow field, the hydraulic conductivity is assumed in three different probability distributions using random sampling method. The obtained seepage flow field is examined through skewness analysis, and the skewed distribution probability density function is given. The head mode value and the head comprehensive standard deviation are used to represent the statistics of calculation results obtained by the Monte Carlo method. The stochastic seepage flow field simulated by the SFCM is confirmed to be similar to that given by the Monte Carlo method from numerical aspects. The range of coefficient of variation of hydraulic conductivity in SFCM is larger than used previously in stochastic seepage flow field simulations, and the computation time is short. The results proved that the SFCM is a convenient calculating method for solving the complex problems.     

岩石节理非饱和渗流特性研究

根据岩石节理非饱和渗流试验所测定的节理排泄和吸湿过程，探讨了节理非饱和渗流机理，提出了基于节理概率分布的毛细压力与饱和度的解析模型以及节理非饱和水力传导度的理论表达式. 研究表明，单节理非饱和渗流特性与二维非均质多孔介质具有一定的相似性，本文提出的有关模型可作为确定岩石节理非饱和渗流参数的基本方法。     

Stochastic back analysis of permeability coefficient using generalized Bayesian method

Owing to the fact that the conventional deterministic back analysis of the permeability coefficient cannot reflect the uncertainties of parameters, including the hydraulic head at the boundary, the permeability coefficient and measured hydraulic head, a stochastic back analysis taking consideration of uncertainties of parameters was performed using the generalized Bayesian method. Based on the stochastic finite element method （SFEM） for a seepage field, the variable metric algorithm and the generalized Bayesian method, formulas for stochastic back analysis of the permeability coefficient were derived. A case study of seepage analysis of a sluice foundation was performed to illustrate the proposed method. The results indicate that, with the generalized Bayesian method that considers the uncertainties of measured hydraulic head, the permeability coefficient and the hydraulic head at the boundary, both the mean and standard deviation of the permeability coefficient can be obtained and the standard deviation is less than that obtained by the conventional Bayesian method. Therefore, the present method is valid and applicable.     

STOCHASTIC ANALYSIS OF GROUNDWATER FLOW SUBJECT TO RANDOM BOUNDARY CONDITIONS

A stochastic model was developed to simulate the flow in heterogeneous media subject to random boundary conditions. Approximate partial differential equations were derived based on the Karhunen-Loeve （KL） expansion and perturbation expansion. The effect of random boundary conditions on the two-dimensional flow was examined. It is shown that the proposed stochastic model is efficient to include the random boundary conditions. The random boundaries lead to the increase of head variance and velocity variance. The influence of the random boundary conditions on head uncertainty is exerted over the whole simulated region, while the randomness of the boundary conditions leads to the increase of the velocity variance in the vicinity of boundaries.     

饱和-非饱和非稳定渗流有限元分析方法的改进

对饱和-非饱和非稳定渗流分析的有限元计算方法加以改进,提出饱和度对渗透压力偏导数的修正公式,消除了饱和-非饱和非稳定渗流计算中存在的数值弥散现象和参数拟合不收敛现象,使迭代收敛速度提高了3倍。同时也消除了有限元迭代求解过程中的振荡现象。经实例证明,本文方法是有效可行的。