堤防工程三维随机渗流场理论及研究

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。     

基于蒙特卡罗随机有限元法的三维随机渗流场研究

通过建立改进Latin超立方抽样和对偶抽样相结合的复合抽样法,以提高Monte Carlo方法的计算效率,并将其引入Monte Carlo随机有限元（MSFEM）。基于三维有限元模型,采用MCSFEM对山坪土石坝进行随机渗流场分析,研究渗透系数和水头边界条件的随机特性对渗流场的干扰,进行变异系数和抽样次数的敏感性分析。最后,对渗流场的求解量进行概型分析。研究表明：总水头势、流速及渗透体积力的变异性随着渗透系数随机性的增强而变大;复合抽样法既能有效加快Monte Carlo的收敛速度,又能降低样本间的统计相关性,说明了该方法的实用性与有效性;当渗透系数服从正态分布时,渗流场中所取结点的水头和坡降也服从正态分布。     

岩土材料导热系数与孔隙率关系的数值模拟分析

采用有限元方法数值,模拟了岩土材料的导热系数与孔隙率之间的非线性关系。有限元模型中的固体骨架和孔隙根据孔隙率的大小随机生成,模型中的材料参数和单元属性用ANSYS中的APDL参数化语言赋值。根据有限元随机模拟断面的热流密度分布和稳态热传导傅立叶定律,计算在不同孔隙率条件下的等效导热系数。研究表明,岩土材料模型等效导热系数随着孔隙的增加而减小;并且当孔隙率大于逾渗值后,等效导热系数的减小梯度明显降低;含孔隙岩土材料的热传导特性与渗流一样具有逾渗特性。     

Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis

In recent years, spatial variability modeling of soil parameters using random field theory has gained distinct importance in geotechnical analysis. In the present study, commercially available finite difference numerical code FLAC 5.0 is used for modeling the permeability parameter as spatially correlated log-normally distributed random variable and its influence on the steady state seepage flow and on the slope stability analysis are studied. Considering the case of a 5.0 m high cohesive–frictional soil slope of 30°, a range of coefficients of variation (CoV%) from 60 to 90% in the permeability values, and taking different values of correlation distance in the range of 0.5–15 m, parametric studies, using Monte Carlo simulations, are performed to study the following three aspects, i.e., (i) effect of stochastic soil permeability on the statistics of seepage flow in comparison to the analytic (Dupuit′s) solution available for the uniformly constant permeability property; (ii) strain and deformation pattern, and (iii) stability of the given slope assessed in terms of factor of safety (FS). The results obtained in this study are useful to understand the role of permeability variations in slope stability analysis under different slope conditions and material properties.     

Reliability updating in geotechnical engineering including spatial variability of soil

At geotechnical sites, deformation measurements are routinely performed during the construction process. In this paper, it is shown how information from such measurements can be utilized to update the reliability estimate of the geotechnical site at future construction stages. A recently proposed method for Bayesian updating of the reliability is successfully applied in conjunction with a stochastic nonlinear geotechnical finite element model. Therein, uncertainty in the soil material properties is modelled by non-Gaussian random fields. The structural reliability evaluations required for the Bayesian updating are carried out by means of subset simulation, an efficient adaptive Monte Carlo method. The approach is demonstrated through an application to a sheet pile wall at a deformation-sensitive geotechnical construction site.     

Stochastic finite element modelling of water flow in variably saturated heterogeneous soils

Water flow is greatly influenced by the characteristics of the domain through which the process occurs. It is generally accepted that earth materials have extreme variations from point to point in space. Consequently, this heterogeneity results in high variation in hydraulic properties of soil. In order to develop an accurate predictive model for transport processes in soil, the effects of this variability should be considered. In this study a two‐dimensional stochastic finite element flow model was developed for simulation of water flow through unsaturated soils. In this model, the stochastic partial differential governing equation of water flow, obtained from implementation of the perturbation‐spectral stochastic method on classical Richard's equation, was solved using a finite element method in the space domain and a finite difference scheme in the time domain. The effective hydrological parameters embedded in the mathematical model depend on time derivatives of capillary tension head; this makes possible to consider the hysteresis due to large‐scale variability of soil hydrological properties. The model is also capable of simulating infiltration and evaporation events and rapid change in the land surface boundary condition from one type event to another, based on a scheme used in the model for implementation of land surface boundary condition. The model was validated with the data obtained from a layered lysimeter test. The model was also used to simulate water flow under a long irrigation furrow. The results obtained with this model show better agreement with experimental measurements in comparison with a deterministic model. The possible reason for this agreement is that in the developed model, the influence of the variability of the properties of soil and effects of parameter hysteresis on water flow and water content redistribution are considered. Copyright © 2010 John Wiley & Sons, Ltd.     

Identifying variably saturated water-flow patterns in a steep hillslope under intermittent heavy rainfall

The objective of this paper is to identify water-flow patterns in part of an active landslide, through the use of numerical simulations and data obtained during a field study. The approaches adopted include measuring rainfall events and pore-pressure responses in both saturated and unsaturated soils at the site. To account for soil variability, the Richards equation is solved within deterministic and stochastic frameworks. The deterministic simulations considered average water-retention data, adjusted retention data to account for stones or cobbles, retention functions for a heterogeneous pore structure, and continuous retention functions for preferential flow. The stochastic simulations applied the Monte Carlo approach which considers statistical distribution and autocorrelation of the saturated conductivity and its cross correlation with the retention function. Although none of the models is capable of accurately predicting field measurements, appreciable improvement in accuracy was attained using stochastic, preferential flow, and heterogeneous pore-structure models. For the current study, continuum-flow models provide reasonable accuracy for practical purposes, although they are expected to be less accurate than multi-domain preferential flow models. Electronic Publication     

Stochastic Modeling of Variably Saturated Transient Flow in Fractal Porous Media

This work presents the application of a Monte Carlo simulation method to perform an statistical analysis of transient variably saturated flow in an hypothetical random porous media. For each realization of the stochastic soil parameters entering as coefficients in Richards' flow equation, the pressure head and the flow field are computed using a mixed finite element procedure for the spatial discretization combined with a backward Euler and a modified Picard iteration in time. The hybridization of the mixed method provides a novel way for evaluating hydraulic conductivity on interelement boundaries. The proposed methodology can handle both large variability and fractal structure in the hydraulic parameters. The saturated conductivity K _s and the shape parameter _vg in the van Genuchten model are treated as stochastic fractal functions known as fractional Brownian motion (fBm) or fractional Gaussian noise (fGn). The statistical moments of the pressure head, water content, and flow components are obtained by averaging realizations of the fractal parameters in Monte Carlo fashion. A numerical example showing the application of the proposed methodology to characterize groundwater flow in highly heterogeneous soils is presented.     

基于随机有限元的堤防渗透失稳概率分析

基于随机有限元理论进行了堤防渗透失稳概率分析,探讨了渗透系数变异性、洪水位变化、堤防几何尺寸变化对渗透失稳概率的影响。结果表明,随着渗透变异系数的增加,渗透失稳概率基本呈线性增长,当变异系数增大到一定程度时渗透失稳概率保持不变,随后略有下降;随着汛期水位的升高,堤防渗透失稳的概率不断变大;渗透失稳概率随着堤防坡度变陡而不断地增加,尤其是在堤防坡比大于1：2.5时,其渗透失稳概率增加得非常快。     

Influence of random heterogeneity of the friction angle on bearing capacity factor Nγ

ABSTRACT

Probabilistic methods in geotechnical engineering have received a lot of attention during the last decade and different methodologies are used to capture the inherent variability of soil in different geotechnical engineering problems. In this paper, numerical simulations are conducted to obtain the bearing capacity factor, N_γ, for a purely frictional heterogenous soil where the friction angle is modelled as randomly distributed throughout the domain and the effect of its spatial variability on N_γ is investigated. A finite element method, based on the upper bound limit analysis was combined with random field theory and linear programming to develop a probabilistic analysis. Monte Carlo simulations were performed and the effect of the variability of the friction angle defined by statistical parameters on the bearing capacity factor was investigated. Results show that the mean bearing capacity factor N_γ of a footing on a spatially variable cohesionless soil is generally higher than the deterministic N_γ obtained from a constant mean value. Increasing the heterogeneity of the friction angle by an increase in the coefficient of variation generally increases this deviation. This can be explained by the nonlinearity of the relationship between N_γ and the friction angle.     

河流冲刷对堤岸渗流和变形的影响研究

通过理论分析和有限元技术,建立了综合考虑河流冲刷力、渗透力、自重应力耦合力系下的堤岸（水上、水下）与河床的整体分析模型,直接分析河流冲刷作用对堤岸渗流和变形的影响,并结合强度折减有限元法分析河流冲刷对堤岸边坡整体稳定性的影响。结果表明,渗透流速的最大值出现在堤脚,冲刷作用使堤岸的渗透流速有所提高,并使堤岸坡脚沿外江方向的水平位移明显增加,愈靠近坡脚,外江方向水平位移增加的幅度愈大,在不同水位下堤脚都是最易受到渗流和冲刷影响的地方;河流冲刷进一步加大了堤岸和河床塑性区范围,堤岸的安全系数降低;河流冲刷对堤岸渗流和变形产生的影响随着河水位的上升而加剧,河水位越高,冲刷作用使堤岸稳定性降低的幅度越大。     

Influence of spatial variability of soil friction angle on sheet pile walls’ structural behaviour

The uncertainty in terms of soil characterisation is studied to assess its effect on the structural behaviour of extended structures as sheet pile walls. A finite element model is used. This integrates a numerical model of the soil–structure interaction together with a stochastic model that allows characterising the soil variability. The model serves in propagating the variability and the system parameter uncertainties. Discussion is mainly focused on two points: (1) testing the sensitivity of the structural behaviour of a sheet pile wall to different geotechnical parameters and (2) assessing the influence of spatial variability of soil properties on the structural behaviour by identifying the most sensitive geotechnical parameter and the most significant correlation length values. The findings showed that in assessing the sheet pile wall’s structural behaviour, there are spatial variability parameters that cannot be considered negligible. In this study, soil friction angle is found to be an important parameter.     

水位下降条件下黏性土边坡稳定性的图表法

库（河）岸边坡由于坡体迎水面水位下降经常造成坡体稳定性降低,建立快速评估水位变化条件下的边坡稳定性分析方法具有重要的工程实用价值。基于库（河）水位下降过程及坡体内非稳定渗流条件,通过对ABAQUS程序进行二次开发,发展了考虑地表水-地下水联动作用下的黏性土边坡强度折减有限元分析方法;在分析边坡土性参数、相对渗透比值、边界条件对边坡稳定性影响的基础上,建立了考虑土性参数、相对渗透比值、库水位下降比、坡角等一体化的相对稳定安全系数综合图表表示方法。该方法能够简便、快捷地查出实际涉水边坡在不同工况下的稳定安全系数及设计边坡坡比,可作为现有图表法的有益补充。     

三相耦合渗流侵蚀管涌机制研究及有限元模拟

管涌的发生、发展过程是土骨架相在渗流作用下侵蚀为可动细颗粒相,并随水相在孔隙通道中运移流失的过程。在该过程中,渗流与侵蚀相互耦合,相互促进,水相、土相、可动细颗粒相互作用,因此,管涌过程是一个多场、多相耦合的高度非线性的动态过程。现有的管涌试验结果表明,只有当水力梯度大于起始水力梯度时,细颗粒相才会随水相从土体中运移流失,土体才会发生管涌侵蚀,且管涌稳定后土体的孔隙率（稳定孔隙率）和水力梯度之间存在对应关系,根据该结果,提出管涌稳定孔隙率的概念,修正传统的渗流侵蚀本构方程,建立多孔介质中三相耦合的修正的渗流侵蚀管涌控制方程。最后,针对特定应力状态下的土体建立稳定孔隙率和水力梯度之间的对应关系。基于Galerkin有限元法编制有限元程序,在轴对称情况下对该土体的管涌过程进行数值模拟。结果表明,修正后的管涌控制方程能更全面地描述管涌发生、发展直至稳定状态的特性。     

基于饱和渗透系数空间变异结构的斜坡渗流及失稳特征

以往研究一般采用单随机变量方法（SRV）或基于水平或垂直方向波动范围生成的空间变异随机场来模拟岩土参数的空间变异性,对具有倾斜定向特征的空间变异随机场未有涉及.基于条件模拟相关理论和非侵入式随机有限元的理论框架,提出了利用序贯高斯模拟方法进行斜坡参数条件随机场模拟并运用有限元方法进行斜坡渗流和稳定性分析的方法.针对理想边坡,对各向同性和几何各向异性的共7种空间变异结构的饱和渗透系数（K_s）各进行了200次条件随机场模拟,基于条件随机场模拟结果进行了有限元渗流和稳定性计算,对每种空间变异结构多次计算结果进行了统计分析.结果表明:本文所提出的方法不仅再现了研究区域参数的空间二阶统计特性,通过设定变异函数参数进行不同空间变异类型、变异程度、变异定向性的随机场模拟,同时利用现场观测数据对随机场模拟结果进行条件限制,从而提高了随机场的赋值精度;K_s的空间变异结构对孔隙水压力的分布规律、地下水位线变化范围、稳定性系数和最危险滑动面分布特征均有一定程度的影响.本研究为库岸斜坡稳定性评价提供方法支撑.      

心墙堆石坝渗透稳定可靠性分析的随机响应面法

将大规模渗流有限元计算与随机响应面法相结合,对双江口心墙堆石坝进行渗透稳定可靠性分析。在基于随机响应面法的可靠度分析框架内,堆石坝稳定渗流有限元计算过程和可靠度分析过程分开独立进行,通过对心墙渗透坡降较大区域的节点建立统一的渗透稳定功能函数,采用渗流有限元分析方法和随机响应面法,计算出该区域每个节点处的渗透破坏失效概率,并将最大失效概率作为心墙的失效概率。最后,分析了心墙渗透系数、覆盖层渗透系数、上游水位与心墙具有最大失效概率节点处渗透坡降的相关关系,以及心墙渗透系数和上游水位的变异性对心墙渗透破坏失效概率的影响。计算结果表明,随机响应面法3阶Hermite展开就能够保证良好的计算精度,且计算耗时较小;双江口堆石坝心墙具有最大失效概率节点处的渗透坡降与上游水位密切相关,而与心墙本身的渗透系数呈弱负相关关系,与覆盖层渗透系数的相关性不显著;随着上游水位变异性的增大,心墙失效概率急剧增大,而这种效应对于心墙渗透系数并不明显。研究成果为随机响应面法在实际工程中的应用奠定了一定的基础。     

渗流对多年冻土区路基温度场影响的数值模拟

运用传热学理论和渗流理论导出了路堤侧向有地表积水入渗情形下,多年冻土区路基温度场渗流场耦合作用的控制微分方程,然后以现场观测资料为基础,用Ｇａｌｅｒｋｉｎ有限元方法对青康公路（２１４国道）花石峡冻土研究站１号试验路段路基温度场未来可能的变化状态进行了数值预报。结果表明,若无渗流作用,５ａ后路堤左侧天然地表、路堤堤身和路堤右侧天然地表的最大季节融深分别为１．４ｍ,３．２ｍ和１．４ｍ;若有渗流作用,则     

Foundation settlement statistics via finite element analysis

The dispersion observed in soil data comes both from the spatial variability which greatly influences the behavior of large structures and from errors in testing. Thus, the geotechnical engineering deals with uncertainties for which deterministic approaches are not suitable. The resort to probabilistic techniques, enables modeling uncertainties by analyzing their dispersion effect on the global behavior of the structure. The scope of this paper is analyzing settlement and differential settlement variability of a pair of foundations on random heterogeneous medium. The random soil properties of interest are the elastic modulus, and the Poisson ratio. The elastic modulus is modeled as a spatially random field by adopting the lognormal distribution, which enables analyzing its large variability. Because soil Poisson ratio is bounded in practice between two extreme values, its random field is obtained by using the Beta distribution. In this study, one proposes for the Beta field determination, a mapping technique on the probability distribution function diagram, by solving a non-linear equation. However, the mean and variance are unchanged through the mapping operation. Because the soil Poisson ratio is a positive parameter, one prefers to perform the mapping operation with the probability function of the lognormal distribution. Also, the proposed technique can be used for other bounded soil properties such as the porosity. In this paper, settlement and differential settlement statistics prediction are carried out using Monte Carlo simulations combined with deterministic finite element method (DFEM). A performed parametric study shows the following: (i) as the variability of the elastic modulus increases as settlement and differential settlement statistics are important, also, settlement statistics decreases as the Poisson ratio variability increases, and differential settlement statistics do not seem be affected by its variability. (ii) settlement and differential settlement statistics are important for positive inter-property correlation. (iii) a great influence of the correlation lengths on settlement and differential settlement statistics.     

Reliability-based semi-analytical solution for ground improvement by PVDs incorporating inherent (spatial) variability of soil

The design of soil consolidation via prefabricated vertical drains (PVDs) has been traditionally carried out deterministically and thus can be misleading due to the ignorance of the uncertainty associated with the inherent (spatial) variation of soil properties. To treat such uncertainty in the design process of soil consolidation by PVDs, stochastic approaches that combine the finite element method with the Monte Carlo technique (FEMC) have been usually used. However, such approaches are complex, computationally intensive and time consuming. In this paper, a simpler reliability-based semi-analytical (RBSA) method is proposed as an alternative tool to the complex FEMC approach for soil consolidation by PVDs, considering soil spatial variability. The RBSA method is found to give similar results to those obtained from the FEMC approach and can thus be used with confidence in practice.     

边坡可靠度分析的非侵入式随机有限元法

提出基于非侵入式随机有限元法的边坡可靠度分析方法,并编写计算程序NISFEM。采用有限元滑面应力法计算边坡安全系数,将Hermite随机多项式展开与SIGMA/W和SLOPE/W模块有机结合实现边坡可靠度非侵入式随机分析。根据随机多项式展开系数,给出边坡安全系数前4阶统计矩（均值、标准差、偏度和峰度）和Sobol指标解析表达式,并采用Sobol指标进行边坡可靠度参数敏感性分析。最后,以均质土坡可靠度问题为例,证明该方法在边坡可靠度分析中的有效性。结果表明,边坡可靠度分析的非侵入式随机有限元法能够有效地考虑边坡变形对边坡可靠度的影响,计算效率远远高于蒙特卡罗模拟方法（MCS）,是解决复杂边坡可靠度问题一种有效地分析手段;黏聚力和内摩擦角变异性对边坡安全系数前四阶统计矩具有明显的影响,重度变异性对安全系数前4阶统计矩几乎没有影响;抗剪强度参数间负相关性对边坡安全系数均值几乎没有影响,但对安全系数标准差、偏度和峰度均有明显的影响。此外,随着抗剪强度参数间负相关性的增加,边坡安全系数由近似正态分布逐渐变为明显的非正态分布。