Analytical solution to 1D coupled water infiltration and deformation in two‐layer unsaturated soils

An analytical solution to 1D coupled water infiltration and deformation in layered soils is derived using a Laplace transformation. Coupling between seepage and deformation, and initial conditions defined by arbitrary continuous pore‐water pressure distributions are considered. The analytical solutions describe the transient pore‐water pressure distributions during 1D, vertical infiltration toward the water table through two‐layer unsaturated soils. The nonlinear coupled formulations are first linearized and transformed into a form that is solvable using a Laplace transformation. The solutions provide a reliable means of comparing the accuracy of various numerical methods. Parameters considered in the coupled analysis include the saturated permeability (k_s), desaturation coefficient (α), and saturated volumetric water content (θ_s) of each soil layer, and antecedent and subsequent rainfall infiltration rates. The analytical solution demonstrates that the coupling of seepage and deformation plays an important role in water infiltration in layered unsaturated soils. A smaller value of α or a smaller absolute value of the elastic modulus of the soil with respect to a change in soil suction (H) for layered unsaturated soils means more marked coupling effect. A smaller absolute value of H of the upper layer soil also tends to cause more marked coupling effect. A large difference between the saturated coefficients of permeability for the top and bottom soil layers leads to reduced rainfall infiltration into the deep soil layer. The initial conditions also play a significant role in the pore‐water pressure redistribution and coupling effect. Copyright © 2011 John Wiley & Sons, Ltd.     

水资源和环境工程中水平井研究简介

简单介绍了水平井在水资源和环境工程中的近期研究进展, 重点介绍了在不同含水层(如承压含水层、潜水含水层、越流含水层及河下含水层) 中, 水平井抽水条件下降深的半解析解, 同时分析了降深随抽水时间变化的标准曲线和微分标准曲线.这些半解析解可用于分析小流量水平井在中长时段的降深特性.分析了用于排水和供水的大流量水平井的水力学特征, 并介绍了求解渗流-管流耦合井流系统的一种新方法.同时介绍了在非饱和含水层中水平井抽取气体的动力学特征, 并分析了地面覆盖和未覆盖2种情况下的气体清除效率, 报告了在不同饱和含水层条件下水平井的捕获区和捕获时间的计算.      

非均质土壤中二维非饱和土壤水分运动的随机分析

以一水平向具有空间变异而垂直向为均质的二维非饱和流动区域中的均匀入渗问题为例,应用Monte Carlo随机模拟方法分析了土壤水分变量的随机统计特性及其一、二阶矩的时空分布规律。在随机分析过程中,将所研究的流动区域土壤水力特性的空间变异性以随空间位置变化的标定参数δ(x)表示,并将标定参数δ(x)视为一维随机空间函数的实现,应用随机生成模型来生成参数δ(x)的随机样本。通过随机模拟分析得到:垂直方向上负压水头方差与平均负压水头近似呈一线性关系;随入渗时间的延长,不同深度处表征负压水头空间变异结构的自相关函数趋于一稳定结构。     

混合型缓冲回填材料非饱和水分扩散试验研究

设计了专门的浸水试验装置,测定了膨润土-石英砂混合物在非膨胀条件下吸水引起的水分分布及膨胀应力变化,研究了混合型缓冲回填材料非饱和水力学性质。试验结果表明,干密度约1.70 g/cmP3、掺砂率为30%的GMZ001膨润土-砂混合物的水分扩散系数与含水率的关系呈U型变化,即随着含水率增加,汽态水分扩散系数减小,液态水分扩散系数增大。根据理论推导建立非饱和导水率估算方程。计算发现,混合物的非饱和导水率随含水率的增大而增大。其中,汽态水分非饱和导水率先增大后略有减小,液态水非饱和导水率始终增大。试验发现,试样吸水后干密度趋于均匀化,试样内部不同位置的应力发展与水分迁移过程密切相关：渗入端的应力在入渗初期增长很快,随后减慢;渗出端的应力持续稳定增长;入渗96 h后,两端应力趋于一致。估算出的水分扩散系数及非饱和导水率,可用于评价混合型缓冲回填材料阻隔核素迁移安全性。     

考虑淤泥层弹性储水的滨海承压含水层中海潮引起的地下水头波动

综合考虑了海底淤泥层的弹性储水系数、海潮荷载效应和渗透性,对海底露头处具有淤泥层的滨海承压含水层系统中海潮引起的水头波动进行分析,给出了相应的数学模型,并推导出其解析解,讨论了淤泥层弹性储水对于水头波动的影响.分析表明,当淤泥层的厚度或弹性储水系数较小时,或者其渗透性较好时,可以忽略其弹性储水效应,从而把整个淤泥层简化为第三类边界条件来处理.文章还考虑了承压含水层和淤泥层中可能存在的垂向流动,对垂向剖面二维地下水流动方程进行了数值模拟,将二维数值解与忽略垂向流动的一维解析解进行了比较,结果表明该含水层系统的垂向流动是可以被忽略的.     

非饱和土拟二维平面应变固结问题的解析计算方法

基于Fredlund非饱和土一维固结理论,建立了二维平面应变条件下的固结方程组,并得到了单层非饱和土平面应变条件下的解析解。基于相关理论,假设体变系数和渗透系数都为常量,同时考虑到瞬时加载条件下,沿着土体深度方向上产生均匀或者线性分布的初始超孔隙压力,建立了二阶二元偏微分方程组。求解时,引入函数方法来降低方程的阶数,然后通过分离变量法获得方程的通解。在此基础上,结合一个针对单面排水条件下二维平面应变问题案例,通过与数值解对比,验证了所提方法的正确性。并采用所提方法计算获得了二维平面下超孔隙水压力、气压力沿垂直和水平方向消散的等时线,通过计算对比,分析了不同线性分布情况下,初始超孔隙压力对固结消散过程的影响。研究结果表明：初始超孔隙压力的不同分布对超孔隙气压力消散的影响几乎可以忽略,而对超孔隙水压力消散的影响更大。     

A closed form analytical solution for two‐dimensional plane strain consolidation of unsaturated soil stratum

This paper discusses the excess pore‐air and pore‐water pressure dissipations and the average degree of consolidation in the 2D plane strain consolidation of an unsaturated soil stratum using eigenfunction expansion and Laplace transformation techniques. In this study, the application of a constant external loading on a soil surface is assumed to immediately generate uniformly or linearly distributed initial excess pore pressures. The general solutions consisting of eigenfunctions and eigenvalues are first proposed. The Laplace transform is then applied to convert the time variable t in partial differential equations into the Laplace complex argument s. Once the domain is obtained, a simplified set of equations with variable s can be achieved. The final analytical solutions can be computed by taking a Laplace inverse. The proposed equations predict the two‐dimensional consolidation behaviour of an unsaturated soil stratum capturing the uniformly and linearly distributed initial excess pore pressures. This study investigates the effects of isotropic and anisotropic permeability conditions on variations of excess pore pressures and the average degree of consolidation. Additionally, isochrones of excess pore pressures along vertical and horizontal directions are presented. It is found that the initial distribution of pore pressures, varying with depth, results in considerable effects on the pore‐water pressure dissipation rate whilst it has insignificant effects on the excess pore‐air pressure dissipation rate. Copyright © 2015 John Wiley & Sons, Ltd.     

晚更新世黄土渗透性的各向异性及其机制研究

非饱和黄土的渗透性是非饱和黄土性质的重要组成部分。研究黄土不同方向的渗透性对确定其湿陷范围和由于水的渗透引起的黄土滑坡具有很重要的理论意义。研究了黄土渗透性的各向异性特征及其机制。以具有明显各向异性的西安Q3原状黄土为研究对象,用TEN型张力计测量了黄土试样不同方向的、不同含水率下的吸力;用变水头渗透试验测量了黄土竖直和水平方向的饱和渗透系数。结果表明,当体积含水率在23%～41%时,张力计沿不同方向插入土样所测吸力相差不大;竖直方向的饱和渗透系数是水平方向的4.02倍。在吸力测量的基础上,根据土-水特征曲线,确定了竖直和水平方向的非饱和黄土的渗透系数。得出在黄土不同方向,随着吸力的增大或减小,渗透系数减小或增大;竖直方向的渗透系数普遍地大于水平方向的渗透系数;当吸力小于57 kPa时,随着吸力的增大,竖向渗透系数与水平向渗透系数的差值减小。通过观测黄土的结构,得出黄土结构对其渗透性有重要影响。     

低温水入渗条件下土壤水分温度动态变化

自制土槽试验装置,室内模拟低温水在河岸带土壤中非饱和入渗的过程。以填装中细砂为研究对象,进行了3种不同水头下的低温水入渗试验,对低温水在土壤中的入渗过程和水分、温度时空动态作了连续监测,分析了水头对入渗参数、水分场与温度场的影响规律。试验结果表明:在相同时间内,入渗水头越高,湿润锋垂直(水平)运移距离越大,垂直湿润锋的运移速度随入渗时间的增加有逐渐减少的趋势,最后逐渐趋于稳定;水头5 cm作用时入渗率波动较大,稳定时间大于水头25 cm和45 cm作用时土壤达到稳定入渗率所需的时间;入渗水头越高,平均温度下降越快,温度场也更快地达到相对稳态,水头25 cm在低温水入渗420 min后基本上达到稳态,水头45 cm在240 min后基本达到稳态。     

非饱和土中水平入渗方程显式求解

在求解非饱和态土中水分入渗问题时,水力函数是体积含水率或者吸力的函数,致使其控制方程呈现出强非线性的特征,进而使得其求解变得十分困难。基于水分在土体介质中流动耗时取极值路径的选择这一假定,引入时间泛函,基于变分法原理将水平入渗问题转化为泛函极值问题。通过求解Euler–Lagrange方程,结合边界条件,得到非线性瞬态水平入渗问题的显式解析解。结合Brooks-Corey型水力函数,显式地求解出该类型非饱和态土的体积含水率发展分布规律。通过计算4种不同类型土体的水平入渗规律,将求解结果与已有结果以及数值结果进行对比,验证了该方法的有效性。结果表明:体积含水率分布与位置距离和湿润峰距离比值呈幂函数关系,指数取决于土-水特征曲线的形状参数;初始条件与边界条件会对体积含水率分布造成不同程度的影响。     

Calculation of groundwater head distribution with a close barrier during excavation dewatering in confined aquifer

When pumping is conducted in confined aquifer inside excavation pit(waterproof curtain),the direction of the groundwater seepage outside the excavation changes from horizontal to vertical owing to the existence of the curtain barrier.There is no analytical calculation method for the groundwater head distribution induced by dewatering inside excavation.This paper first analyses the mechanism of the blocking effects from a close barrier in confined aquifer.Then,a simple equation based on analytical solution is proposed to calculate groundwater heads inside and outside of the excavation pit with waterproof curtain(hereafter refer to close barrier)in a confined aquifer.The distribution of groundwater head is derived according to two conditions:(i)pumping with a constant water head,and(ii)pumping with a constant flow rate.The proposed calculation equation is verified by both numerical simulation and experimental results.The comparisons demonstrate that the proposed model can be applied in engineering practice of excavation.     

渗透各向异性圆形围堰稳态渗流场解析解

对渗透各向异性土层中的圆形围堰渗流场进行解析研究。将圆形围堰周围渗流场分为3个区域,通过坐标变换以及将边界条件齐次化后,用分离变量法分别得到柱坐标系下3个区域的水头分布级数解形式,结合区域间的连续条件,并利用贝塞尔函数正交性得到渗透各向异性土层中圆形围堰稳态渗流场的显式解析解,与Plaxis2D软件的计算结果进行对比,验证了解析解的正确性。基于解析解,进一步推导出了涌水量、出逸比降公式,并与不同方法的计算结果作了对比,最后对稳态渗流情况下的水压力进行了计算分析。结果表明：相比于其他近似法,解析解求取的流量、出逸比降以及渗流情况下水压力与数值计算结果高度吻合;渗流水压力会随着围堰半径、纵横向渗透系数比值的增大而减小,而后逐渐趋近于一个稳定值。     

Analytical solution to 1D coupled water infiltration and deformation in unsaturated soils

An analytical solution to 1D coupled water infiltration and deformation is derived using a Fourier integral transform. Exponential functional forms are used to represent the hydraulic conductivity–pore‐water pressure relationship and the soil‐water characteristic curve. Fredlund's incremental‐linear constitutive model for unsaturated soils is adopted. The analytical solution considers arbitrary initial pore‐water pressure distributions and flux and pressure boundary conditions. The corresponding analytical solutions to coupled steady‐state problems are also obtained. The analytical solutions demonstrate that the coupling of seepage and deformation plays an important role in water infiltration in unsaturated soils. In the early stages of infiltration, the difference between uncoupled and coupled conditions becomes marked over time, and in late stages, the difference caused by the coupling effects diminishes toward the steady state. The difference between the uncoupled and coupled conditions increases with decreasing desaturation coefficient (α). Pore‐water pressure or deformation changes caused by the coupling effects are mainly controlled by the degree of soil volume change due to a change in soil suction (H). The smaller the absolute value of H, the greater the effect of coupling on the infiltration and deformation. The ratio of rainfall intensity to saturated permeability (q/k_s) also has a strong influence on the coupled seepage and deformation. Copyright © 2008 John Wiley & Sons, Ltd.     

Seepage characteristics and mechanical response of shield tunnels under localized leakage and exosmosisEI北大核心

针对有压盾构隧道中接缝水力劣化所引发的内外水力交互渗流问题,基于水力开度理论,通过数值和解析方法研究局部渗流下隧道衬砌与周围地层的渗流特性和力学响应。结果表明:基于镜像法推导的衬砌隧洞多点渗漏下渗流场解析解与数值解吻合良好,验证了给出的局部渗漏数值模型的有效性;局部外水内渗与内水外渗诱发的衬砌与地层共同作用存在较大差异,前者导致局部孔隙水压力降低引起土体挤压衬砌,衬砌轴力减小而弯矩增大从而产生衬砌外凸,后者则相反;多点局部渗漏对渗流场和衬砌响应的影响存在耦合作用,当内水压接近地层水头时可能出现外水内渗与内水外渗并存的特殊水力交互情况;地层渗透系数对局部渗漏行为的影响较大,复合地层下当局部渗漏发生于高渗透性地层时,其诱发的衬砌响应不显著,当渗漏处于下部低渗透性地层时,在地层交界面存在渗流折射现象,上部高渗透性地层起到补(排)水作用。     

Sinusoidal oscillations radiating from a cylindrical source in thermal conduction or groundwater flow: Closed‐form solutions

The diffusion equation governs thermal conduction and groundwater flow phenomena. In this paper, we study the two‐dimensional radial propagation of a sinusoidal perturbation radiating from a cylindrical source within an infinite slab of homogeneous material. The solution of this problem has several applications. For instance, it can be used to determine the hydraulic diffusivity of the subsurface based on measurements of the hydraulic head around a vertical well during its development. For thermal problems, it can be used to determine the thermal diffusivity based on measurements of the temperature distribution around a cylindrical heat source generating a sinusoidal power per unit length. In this paper, we present a comprehensive analytical solution of this problem and we compare these solutions with numerical solutions. Two approximate analytical solutions, which can be relevant in practice, are also presented. Finally, we give an upper bound for the survival time of the transient part of the solution and we provide an estimate of the radius of influence of the sinusoidal solicitation. Copyright © 2010 John Wiley & Sons, Ltd.     

Semi‐analytical solution to one‐dimensional consolidation for unsaturated soils with semi‐permeable drainage boundary under time‐dependent loading

This paper presents semi‐analytical solutions to Fredlund and Hasan's one‐dimensional consolidation of unsaturated soils with semi‐permeable drainage boundary under time‐dependent loadings. Two variables are introduced to transform two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. The pore‐water pressure, pore‐air pressure and settlement are obtained in the Laplace domain. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi‐analytical solutions in time domain. It is shown that the present solutions are more general and have a good agreement with the existing solutions from literatures. Furthermore, the current solutions can also be degenerated into conventional solutions to one‐dimensional consolidation of unsaturated soils with homogeneous boundaries. Finally, several numerical examples are provided to illustrate consolidation behavior of unsaturated soils under four types of time‐dependent loadings, including instantaneous loading, ramp loading, exponential loading and sinusoidal loading. Parametric studies are illustrated by variations of pore‐air pressure, pore‐water pressure and settlement at different values of the ratio of air–water permeability coefficient, depth and loading parameters. Copyright © 2017 John Wiley & Sons, Ltd.     

A simple analytical solution to one‐dimensional consolidation for unsaturated soils

This paper presents a simple analytical solution to Fredlund and Hasan's one‐dimensional (1‐D) consolidation theory for unsaturated soils. The coefficients of permeability and volume change for unsaturated soils are assumed to remain constant throughout the consolidation process. The mathematical expression of the present solution is much simpler compared with the previous available solutions in the literature. Two new variables are introduced to transform the two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved with standard mathematical formulas. It is shown that the present analytical solution can be degenerated into that of Terzaghi consolidation for fully saturated condition. The analytical solutions to 1‐D consolidation of an unsaturated soil subjected to instantaneous loading, ramp loading, and exponential loading, for different drainage conditions and initial pore pressure conditions, are summarized in tables for ease of use by practical engineers. In the case studies, the analytical results show good agreement with the available analytical solution in the literature. The consolidation behaviors of unsaturated soils are investigated. The average degree of consolidation at different loading patterns and drainage conditions is presented. The pore‐water pressure isochrones for two different drainage conditions and three initial pore pressure distributions are presented and discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

FINITE ELEMENT MODELLING FOR LAND DISPLACEMENTS DUE TO PUMPING

Equations of equilibrium (force balance) and flow in multidimensions were coupled in this paper to describe land displacements due to pressure decline in aquifers. A Galerkin finite element model based on these equations was developed. The saturated/unsaturated behaviour and the isotropic/anisotropic properties of permeability and elasticity were considered when the model was formulated. This model was verified by comparing its simulation results with those of known analytical solutions for simplified cases. The simulation of displacements due to pressure decline in unsaturated media was also performed. Those results demonstrated that the choice of boundary ranges for an aquifer with infinite domain may significantly affect the estimated horizontal and vertical displacements. To obtain a good estimation of land displacements, the boundary ranges should be carefully chosen. The displacements occurring in unconfined aquifers are caused by the drop of the water table and the change in body force in the dewatering zone. Simulation results also indicated that the change in body force should be considered once an unconfined aquifer has been pumped. Otherwise, the horizontal and vertical displacements in unconfined aquifers would be overestimated and underestimated, respectively. The behaviour of land displacements due to pumping was shown to be affected by changes in the total stresses in aquifers.     

融雪入渗条件下边坡渗流计算及稳定性分析

本文利用饱和非饱和渗流有限元方法,参考积雪厚度、温度变化与融雪入渗关系统计资料,对积雪深度、气温变化以及坡度等不同条件进行了边坡融雪入渗渗流计算及稳定性分析。本文条件下计算结果表明:同一坡度下融雪入渗系数和坡面一定范围内的含水量及压力水头随积雪深度增加而增加,积雪深度达1.0m时,融雪入渗垂直影响范围为30.0m,边坡暂态饱和水位升高13m;相同积雪深度条件下,坡度越大,融雪入渗系数越小,坡内压力水头及含水量变化越小,30°边坡融雪入渗垂直影响范围最大为30.0m;同一积雪深度和坡度下,融雪入渗系数及坡面附近压力水头均与气温变化幅度呈正相关关系。根据极限平衡计算,边坡的稳定系数随着融雪过程的持续而降低,积雪深度、边坡坡度或温度变化越大,安全系数降低幅度越大;其中,坡度因子对边坡安全系数的影响最为显著,60°边坡受融雪影响安全系数降幅达9.7%。     

压实黄土水分入渗规律及渗透性试验研究

为了研究压实黄土中的水分垂直入渗规律和非饱和渗透系数函数,在实验室内利用一维土柱垂直入渗模型试验装置,对两组压实黄土土柱试样分别进行了常水头入渗和降雨入渗试验。得到主要结论如下:（1）常水头入渗试验中,累积入渗量和湿润锋前进距离都随入渗时间呈幂函数形式增长,累积入渗量和湿润锋前进距离之间存在线性关系。入渗率在入渗初期最大,之后随入渗时间而快速降低,并在土柱试样底部出水以后达到稳定,且与湿润锋前进距离呈反比关系。（2）降雨入渗试验中,得到两组试样入渗过程中土-水特征曲线数据,分别用van Genuchten模型和Fredlund-Xing模型对两组试样进行了特征曲线拟合。并利用瞬时剖面法处理了入渗过程中水分和水势传感器的监测数据,得到两组试样的非饱和渗透系数,并拟合得到非饱和渗透系数与体积含水率之间的指数函数关系式。同时,采用van Genuchten和Fredlund等渗透系数模型分别对两组试样的非饱和渗透系数进行预测,通过对比模型预测结果和瞬时剖面法实测值,发现van Genuchten渗透系数模型预测结果更接近实测值。