非饱和土壤Richards方程入渗求解探讨

根据理查兹(Richards)方程求解非饱和土壤垂直一维入渗率历时规律,因缺乏土壤水分特性函数K(θ)、D(θ)的一般有效公式,而采用与实际相差甚远的定值或线性函数假设,使成果隐含过多经验成分或需要反复迭代计算.笔者在文献[1]中提出的非饱和土壤水分特性函数的一般有效基础公式,用分离变量法直接求解Richards方程,用土壤水动力学方法分别导出了含有渗前土湿因子的新入渗公式.它摆脱了同类入渗公式对水分函数过于简单的概化假设和经验成分.为放弃迄今水文学产流计算中惯用的下渗容量曲线"截首留尾"的经验做法,以直接使用含有渗前土湿因子的下渗公式提供了理论依据,从而将有利于产流计算方法的改进和计算精度的提高.     

非饱和土入渗的数值模拟

入渗引起土中孔隙水压力的变化,是影响非饱和土性状的最重要的原因之一。因此,正确地分析和模拟非饱和土入渗过程具有重要意义。通过对一维和二维降雨入渗问题的研究,展示了湿润锋面、地下水位面及孔隙水压力分布随时间的变化,使得对入渗问题的认识更加直观和清楚。     

非饱和土壤水分函数解析与Richards方程入渗新解

从土壤微观统计学角度出发，用各向均一无结构土壤“切片”孔径级配函数构建的统计毛管束模型和土壤水分分布依赖的力学原理，论证了理查兹方程中导水率、基质势、扩散率等水分函数和入渗率随充水度，土壤基质而变的机理、规律以及两者之间的内在联系，给出了相应的计算公式和可操作的参数确定方法。把迄今水分函数研究的纯经验相关现状提高到理论分析水平，使建立理论公式成为现实。     

鄂西恩施地区非饱和土降雨入渗规律

在分析鄂西恩施地区降雨特征的基础上,选取6组典型降雨条件,设计并进行了室内人工降雨土柱非饱和入渗试验。通过实测土体体积含水率,揭示了鄂西恩施地区非饱和土降雨入渗规律,获得了降雨入渗影响区体积含水率变化规律、入渗前锋运移规律以及降雨强度和历时对入渗的影响规律。通过GeoStudio软件对室内降雨试验进行了数值模拟,数值模拟结果与试验结果基本相同,进一步验证了降雨入渗规律。同时依据实测结果,分析了数值模拟的不足之处,为通过数值模拟方法研究非饱和土降雨入渗奠定了基础。     

降雨入渗对非饱和土边坡稳定性的影响

降雨往往是引起边坡失稳的主要促发因素.根据某算例,采用极限平衡分析方法,讨论了土体的初始体积含水率、降雨的强度、降雨时间对边坡稳定性的影响程度.     

考虑裂隙非饱和膨胀土边坡入渗模型与数值模拟

包含裂隙的非饱和膨胀土中的渗流具有随时间变化的特性。采用常规试验测定非饱和膨胀土膨胀时程曲线,定量地描述了膨胀土中裂隙在入渗过程中逐渐愈合的特征, 建立了考虑裂隙的非饱和膨胀土边坡入渗的数学模型;用有限元数值模拟方法分析了边坡地形、裂隙位置、裂隙开展深度及裂隙渗透特性等对边坡降雨入渗的影响。结果表明, 坡上位置的裂隙对边坡入渗影响较大;裂隙对边坡入渗的影响随裂隙深度的增大而增大,且存在一最大的影响程度;裂隙的存在加快了膨胀土的入渗速率;考虑裂隙随入渗而愈合时, 入渗达到平衡的时间有所延长。     

降雨入渗条件下非饱和土朗肯土压力分析

传统的土压力分析仅考虑了土体饱和强度对土压力产生的贡献,忽略了基质吸力及其变化对土压力的影响。运用非饱和土有效应力原理和饱和土朗肯土压力公式推导了非饱和土朗肯土压力公式,结合Iverson降雨入渗解析解,推导出降雨入渗条件下非饱和土压力公式。该公式将降雨入渗时的非饱和土压力表示为时间和深度的函数,更符合实际情况。研究结果表明：采用该方法计算得到的土压力值相对于传统计算结果偏大,作用点偏高;此外,随着降雨的发生、入渗和停止,主动土压力呈现“减小-增大-减小-稳定”趋势,被动土压力呈现“增大-减小-增大-稳定”趋势,该现象由降雨过程中基质吸力改变所致。由该公式获得的土压力分布及变化规律可用于挡土工程结构的设计。     

降雨入渗条件下非饱和土边坡稳定分析

针对降雨入渗土坡的稳定问题,建立一个考虑水力渗透系数特征曲线、土-水特征曲线以及修正的Mohr-Coulomb破坏准则的非饱和土流固耦合有限元计算模型,进行雨水入渗下非饱和土边坡渗流场和应力场耦合的数值模拟,得到非饱和土边坡变形与应力的若干重要规律。研究成果为降雨入渗条件下非饱和土边坡的稳定分析提供了基础。     

确定Brooks-Corey土壤水力特性模型参数的垂直入渗方法

在水平入渗方法的基础上,提出了一种不需测定饱和导水率,仅利用一维垂直入渗试验即可确定Brooks-Co-rey模型参数的新方法.利用封丘县两种质地土壤的入渗资料,对所提出的方法进行了检验.结果表明,只要入渗历时足够长,基质势和重力势作用相当,垂直入渗方法确定的土壤水力参数与水平吸渗方法的预测结果相近;利用预测的参数,数...     

降雨入渗条件下非饱和膨胀土边坡原位监测

为了对降雨诱发的非饱和膨胀土边坡失稳的机理有较深入的了解,在湖北枣阳选取了一个11 m高的典型的非饱和膨胀土挖方边坡进行人工降雨模拟试验和原位综合监测。监测成果表明：降雨入渗造成2 m深度以内土层中孔隙水压力和含水量大幅度增加,致使膨胀土体的抗剪强度由于有效应力的减少及土体吸水膨胀软化而降低;同时,降雨入渗造成土体中水平应力与竖向应力比显著增加,并接近理论的极限状态应力比,以致软化的土体有可能沿着裂隙面发生局部被动破坏,此破裂面在一定条件下（如持续降雨条件下）可能会逐渐扩展,最后发展成为膨胀土中常见的渐进式滑坡。     

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.     

An efficient iterative method for solving the governing equation of water infiltration problems in unsaturated soils

One of the significant problems in geo-environmental and geotechnical engineering is the unsaturated flow of soil in unsaturated soils. The model of this phenomenon in porous media is governed by the Richards equation. In this paper a new, efficient, iterative method is used to handle the Richards equation. This new technique is obtained from the variational iteration method by a simple reconstruction that is the Laplace iteration method (LIM). In order to evaluate the efficiency and accuracy of the solutions obtained by the proposed method, two representative examples were investigated. The obtained results show that the Laplace iteration method is a very effective method, simplifies the difficulty of classical techniques and is quite accurate for systems of partial differential equations.     

New class of solutions for water infiltration problems in unsaturated soils

This paper presents the results of approximate analytical solutions to Richards' equation, which governs the problem of unsaturated flow in porous media. The existing methods generally fall within the category of numerical and analytical methods, often having many restrictions for practical situations. In the present study, two approximate analytical methods known as the differential transform method (DTM) and homotopy perturbation method (HPM) were employed to find analytical solutions to Richards' equation. The methods were found to be robust in finding solutions practically identical to those from the existing analytical and numerical methods. Two representative examples were considered in order to evaluate the accuracy of the solutions obtained by DTM and HPM, revealing high level of accuracy in both cases.     

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.     

考虑非饱和浸润区的改进Green-Ampt模型

经典Green-Ampt入渗模型计算简单,广泛应用于土壤入渗问题的研究,但在湿润锋处理上采用明显的干湿分离界面,存在一定的理论假设。鉴于此,基于饱和区−非饱和浸润区分层模型,结合达西定律,推导出入渗过程中饱和区厚度与非饱和浸润区厚度关系的理论公式,提出了水分剖面理论模型,消除了饱和区厚度和浸润区厚度的关系假设。在此基础上,建立了考虑土壤水分剖面形状和非饱和浸润区等效参数的改进Green-Ampt模型,并采用试验和有限元数值仿真对该模型进行了验证,结果表明：该模型有很高的精度,对不同类型的土有很好的适应性。同时该模型求解简单,参数物理意义明确,便于工程应用。     

A generalized approximate analytical solution of horizontal infiltration in unsaturated soil

A generalized analytical solution for one-dimensional nonlinear horizontal infiltration in unsaturated soil is presented. The solution is an improved functional extremum method based on the principle of stationary action. Any prior assumption about the form of moisture diffusion functions is not implemented in the method. By considering a function of time, the water content type governing equation in the horizontal infiltration process is transformed into a function extremum problem. After solving the Euler–Lagrange equation, combined with boundary conditions, a linear relationship between the moisture diffusion function and the ratio of spatial location to the wetting-front distance is proposed. Furthermore, by using the square relationship between the wetting front and time, the spatial and temporal distribution characteristics of the water content profile are finally expressed. In contrast to most other work, the physical meanings of the parameters in this study are clear and can be derived explicitly. By utilizing the simultaneous Brooks–Corey moisture diffusion function, the development and distribution law of the water content profile was explicitly presented. The results of the solution matched well with the existing theoretical results of the four different soil samples. Owing to the high nonlinearity of the van Genuchten moisture diffusion function, the distribution of the water content profile was implicitly found based on the study method. The results obtained using this method were also consistent with the MATLAB routine, pdepe, numerical solutions for different types of soil properties.

     

基于最小作用原理的Richards方程变分解

经典的Richards入渗控制方程属于偏微分方程,具有强烈的非线性,难以求得解析解。以入渗时间为最小作用量,基于Richards方程建立关于入渗路径的时间泛函,将考虑重力项的非饱和土垂直入渗问题转化为泛函极值问题,并构造等价的Euler-Lagrange方程进行求解。计算结果表明,扩散系数D（?）与概化湿润锋距离具有函数关系,当扩散系数D（?）形式已知时,可求得最优路径下湿润锋处含水率、较远处湿润锋最小含水率、土壤含水率最大熵分布3个问题,并基于最优路径检验了本研究条件下,Boltzmann变换和线性变换求解Richards方程的精度。求解过程未引进新变量化简Richards方程,不改变原方程结构,因此其解具有普遍性,可作为非饱和土力学计算的一个补充。     

成层非饱和土渗流的耦合解析解

成层土在工程中很常见,研究降雨过程中成层非饱和土的渗流-变形耦合对非饱和土土力学的发展具有重要的意义。由流体质量守恒,Darcy定律和Lloret等的非饱和土本构模型可得成层非饱和土渗流-变形耦合的控制方程。采用Gardner的非饱和土的渗透系数公式以及Boltzman模型,基于Laplace变换得到耦合方程的解析解。解析及其参数分析表明,渗流和变形耦合是具有时间效应的。与吸力变化相关的土的模量F,对成层土的孔隙水压力分布有明显影响。两层土的F差异越大,孔隙水压力消散得越慢,耦合效应越不显著。增大表层土的F值有利于降低耦合效应。成层土饱和体积含水率变化对吸力变化产生有限的影响