Simulating a lake as a high-conductivity variably saturated porous medium

One approach for simulating ground water–lake interactions is to incorporate the lake into the ground water solution domain as a high-conductivity region. Previous studies have developed this approach using fully saturated models. This study extends this approach to variably saturated models, so that ground water–lake interactions may be more easily simulated with commonly used or public domain variably saturated codes that do not explicitly support coupled lake–water balance modeling. General guidelines are developed for the choices of saturated hydraulic conductivity and moisture retention and relative permeability curves for the lake region. When applied to an example ground water–lake system, model results are very similar to those from a model in which the lake is represented as a specified head boundary continuously updated by a lake mass balance. The high-conductivity region approach is most suitable for relatively simple geometries and lakes with slower and smaller fluctuations when the overall flow pattern and system fluxes, rather than the detailed flow pattern around the intersection of the lake and land surfaces, are of interest.     

MRCON: COMPUTER PROGRAM FOR ESTIMATING SOIL MOISTURE RETENTION AND UNSATURATED HYDRAULIC CONDUCTIVITY

Abstract. MRCON is an interactive computer program designed to approximate soil moisture retention ( Θ-Ψ ) and/or unsaturated hydraulic conductivity (K- Θ ) for soils. MRCON, which is written in BASIC, uses empirical methods obtained from the literature to calculate K- Θ and a modified method to calculate Θ-Ψ . Input data for the program consist of a saturated moisture content and a minimum of three values of Θ-Ψ . A measured value of saturated hydraulic conductivity can be used as input to better approximate the K -Θ curves to field conditions.     

A two‐dimensional model of hydraulic performance of stormwater infiltration systems

Stormwater infiltration systems are a popular method for urban stormwater control. They are often designed using an assumption of one‐dimensional saturated outflow, although this is not very accurate for many typical designs where two‐dimensional (2D) flows into unsaturated soils occur. Available 2D variably saturated flow models are not commonly used for design because of their complexity and difficulties with the required boundary conditions. A purpose‐built stormwater infiltration system model was thus developed for the simulation of 2D flow from a porous storage. The model combines a soil moisture–based model for unsaturated soils with a ponded storage model and uses a wetting front‐tracking approach for saturated flows. The model represents the main physical processes while minimizing input data requirements. The model was calibrated and validated using data from laboratory 2D stormwater infiltration trench experiments. Calibrations were undertaken using five different combinations of calibration data to examine calibration data requirements. It was found that storage water levels could be satisfactorily predicted using parameters calibrated with either data from laboratory soils tests or observed water level data, whereas the prediction of soil moistures was improved through the addition of observed soil moisture data to the calibration data set. Copyright © 2012 John Wiley & Sons, Ltd.     

Hydraulic properties of peat soils along a bulk density gradient—A meta study

Our understanding of hydraulic properties of peat soils is limited compared with that of mineral substrates. In this study, we aimed to deduce possible alterations of hydraulic properties of peat soils following degradation resulting from peat drainage and aeration. A data set of peat hydraulic properties (188 soil water retention curves [SWRCs], 71 unsaturated hydraulic conductivity curves [UHCs], and 256 saturated hydraulic conductivity [K_s] values) was assembled from the literature; the obtained data originated from peat samples with an organic matter (OM) content ranging from 23 to 97 wt% (weight percent; and according variation in bulk density) representing various degrees of peat degradation. The Mualem‐van Genuchten model was employed to describe the SWRCs and UHCs. The results show that the hydraulic parameters of peat soils vary over a wide range confirming the pronounced diversity of peat. Peat decomposition significantly modifies all hydraulic parameters. A bulk density of approximately 0.2 g cm^?3 was identified as a critical threshold point; above and below this value, macroporosity and hydraulic parameters follow different functions with bulk density. Pedotransfer functions based on physical peat properties (e.g., bulk density and soil depth) separately computed for bog and fen peat have significantly lower mean square errors than functions obtained from the complete data set, which indicates that not only the status of peat decomposition but also the peat‐forming plants have a large effect on hydraulic properties. The SWRCs of samples with a bulk density of less than 0.2 g cm^?3 could be grouped into two to five classes for each peat type (botanical composition). The remaining SWRCs originating from samples with a bulk density of larger than 0.2 g cm^?3 could be classified into one group. The Mualem‐van Genuchten parameter values of α can be used to estimate K_s if no K_s data are available. In conclusion, the derived pedotransfer functions provide a solid instrument to derive hydraulic parameter values from easily measurable quantities; however, additional research is required to reduce uncertainty.     

A new saturated/unsaturated model for stormwater infiltration systems

Infiltration systems are widely used as an effective urban stormwater control measure. Most design methods and models roughly approximate the complex physical flow processes in these systems using empirical equations and fixed infiltration rates to calculate emptying times from full. Sophisticated variably saturated flow models are available, but rarely applied owing to their complexity. This paper describes the development and testing of an integrated one‐dimensional model of flow through the porous storage of a typical infiltration system and surrounding soils. The model accounts for the depth in the storage, surrounding soil moisture conditions and the interaction between the storage and surrounding soil. It is a front‐tracking model that innovatively combines a soil‐moisture‐based solution of Richard's equation for unsaturated flow with piston flow through a saturated zone as well as a reservoir equation for flow through a porous storage. This allows the use of a simple non‐iterative numerical solution that can handle ponded infiltration into dry soils. The model is more rigorous than approximate stormwater infiltration system models and could therefore be valuable in everyday practice. A range of test cases commonly used to test soil water flow models for infiltration in unsaturated conditions, drainage from saturation and infiltration under ponded conditions were used to test the model along with an experiment with variable depth in a porous storage over saturated conditions. Results show that the model produces a good fit to the observed data, analytical solutions and Hydrus. Copyright © 2008 John Wiley & Sons, Ltd.     

Fully fluid-solid coupling dynamic model for seismic response of underground structures in saturated soils

The seismic response characteristics of underground structures in saturated soils are investigated. A fully fluid-solid coupling dynamic model is developed and implemented into ABAQUS with a user-defined element to simulate the dynamic behavior of saturated soils. The accuracy of the model is validated using a classic example in literature. The performance of the model is verified by its application on simulating the seismic response characteristics of a subway station built in saturated soils. The merits of the model are demonstrated by comparing the difference of the seismic response of an underground structure in saturated soils between using the fully coupling model and a single-phase medium model. The study finds that the fully coupling model developed herein can simulate the dynamic response characteristics of the underground structures in saturated soils with high accuracy. The seismic response of the underground structure tends to be underestimated by using the single-phase medium model compared with using the fully coupling model, which provides a weaker confining action to the underground structure.     

A comparative study of closed-form hydraulic conductivity prediction models

The Mualem and the Burdine hydraulic conductivity prediction models are considered in combination with the van Genuchten analytical retention curve, as well as the Brooks and Corey prediction model. An equivalence is presented between the retention curves of these models. A comparative study follows between hydraulic conductivities that are based on equivalent retention curves. A unified presentation of prediction models provides a framework for the whole analysis. The treatment of the equivalence problem consists in a minimization procedure characterized by uncoupling of the parameters and analytical evaluation of the objective function. Exact analytical equivalence relations are given for significant parts of the parameter ranges, and, for the remaining parts, analytical approximations are proposed. The comparisons between hydraulic conductivities are carried out via an inequality analysis. It is shown that the hydraulic conductivity of the Burdine model is less than that of the other models for extended ranges of equivalent parameters.     

Estimation of water saturation dependence of dispersion in unsaturated porous media: experiments and modelling analysis

In the dispersion theory, a linear relationship has been verified between the coefficient of hydrodynamic dispersion and water velocity, both in saturated and in unsaturated porous media. But for unsaturated soils the variability of flow directions and microscopic velocities can be larger than in saturated soils because of the lower degree of water saturation. This leads to an increased dispersion. Therefore, relationships between water content and relative water velocity fluctuations and water content together with the coefficient of dispersivity in unsaturated porous media respectively have been investigated systematically by displacement experiments in glass beads and coarse-textured sandy soil columns. The breakthrough curves (BTCs) of chloride showed that an increase of solute mixing with a decrease of water content was caused by an increase of flow velocity fluctuations for different pathways. In order to explain the observed tailing effect in unsaturated flow, two mathematical models were used to fit theoretically derived nonlinear functions of water content dependent dispersivities for both porous media. The close agreement between the observed and computed results suggests that the theoretical model of hydrodynamic dispersion can be extended to transport in unsaturated porous media, providing that BTCs of the effluent water are used to estimate representative dispersivity parameters of soils.     

Mathematical models of groundwater flow with a horizontal drain

An analytical review is given to drainage theory, the foundation of which was laid down by researchers in our country in the first half of the 20th century. Later the author of this paper developed and thoroughly studied a complex of mathematical models describing two-dimensional groundwater flow in drained soils based on the boundary problems of the theory of analytical functions. These models were used to provide a hydrodynamic substantiation for the regularities in subsoil water dynamics that were established by ameliorators in relation to the leaching of salts from soils; to identify the specific features of groundwater flow with drainage in the presence in the flow of one or two unknown free boundaries; and to develop approaches to the analysis of such flows in a direct formulation.     

An analytical solution for predicting the transient seepage from a subsurface drainage system

Subsurface drainage systems have been widely used to deal with soil salinization and waterlogging problems around the world. In this paper, a mathematical model was introduced to quantify the transient behavior of the groundwater table and the seepage from a subsurface drainage system. Based on the assumption of a hydrostatic pressure distribution, the model considered the pore-water flow in both the phreatic and vadose soil zones. An approximate analytical solution for the model was derived to quantify the drainage of soils which were initially water-saturated. The analytical solution was validated against laboratory experiments and a 2-D Richards equation-based model, and found to predict well the transient water seepage from the subsurface drainage system. A saturated flow-based model was also tested and found to over-predict the time required for drainage and the total water seepage by nearly one order of magnitude, in comparison with the experimental results and the present analytical solution. During drainage, a vadose zone with a significant water storage capacity developed above the phreatic surface. A considerable amount of water still remained in the vadose zone at the steady state with the water table situated at the drain bottom. Sensitivity analyses demonstrated that effects of the vadose zone were intensified with an increased thickness of capillary fringe, capillary rise and/or burying depth of drains, in terms of the required drainage time and total water seepage. The analytical solution provides guidance for assessing the capillary effects on the effectiveness and efficiency of subsurface drainage systems for combating soil salinization and waterlogging problems.     

Free surface and saturated-unsaturated analyses of borehole infiltration tests above the water table

Constant head borehole infiltration tests are widely used for the in situ evaluation of saturated hydraulic conductivities of unsaturated soils above the water table. The formulae employed in analysing the results of such tests disregard the fact that some of the infiltrating water may flow under unsaturated conditions. Instead, these formulae are based on various approximations of the classical free surface theory which treats the flow region as if it were fully saturated and enclosed within a distinct envelope, the so-called ‘free surface’. A finite element model capable of solving free surface problems is used to examine the mathematical accuracy of the borehole infiltration formulae. The results show that in the hypothetical case where unsaturated flow does not exist, the approximate formulae are reasonably accurate within·a practical range of borehole conditions. To see what happens under conditions closer to those actually encountered in the field, the effect of unsaturated flow on borehole infiltration is investigated by means of two different numerical models: a mixed explicit-implicit finite element model, and a mixed explicit-implicit integrated finite difference model. Both of these models give nearly identical results; however, the integrated finite difference model is considerably faster than the finite element model. The relatively low computational efficiency of the finite element scheme is attributed to the large number of operations required in order to re-evaluate the conductivity (stiffness) matrix at each iteration in this highly non-linear saturated-unsaturated flow problem. The saturated-unsaturated analysis demonstrates that the classical free surface approach provides a distorted picture of the flow pattern in the soil. Contrary to what one would expect on the basis of this theory, only a finite region of the soil in the immediate vicinity of the borehole is saturated, whereas a significant percentage of the flow takes place under unsaturated conditions. As a consequence of disregarding unsaturated flow, the available formulae may underestimate the saturated hydraulic conductivity of fine grained soils by a factor of two, three, or more. Our saturated-unsaturated analysis leads to an improved design of borehole infiltration tests and a more accurate method for interpreting the results of such tests. The analysis also shows how one can predict the steady state rate of infiltration from data collected during the early transient period of the test.     

Finite-element analysis of the transport of water and solutes in title-drained soils

The finite-element method based on a Galerkin technique was used to formulate the problem of simulating the two-dimensional (cross-sectional) transient movement of water and solute in saturated or partially saturated nonuniform porous media. The numerical model utilizes linear triangular elements. Nonreactive, as well as reactive solutes whose behaviour can be described by a distribution coefficient or first-order reaction term were considered. The flow portion of the model was tested by comparison of the model results with experimental and finite-difference results for transient flow in an unsaturated sand column and the solute transport portion of the model was tested by comparison with analytical solution results. The model was applied to a hypothetical case involving movement of water and solutes in tile-drained soils. The simulation results showed the development of distinct solute leaching patterns in the soil as drainage proceeded. Although applied to a tile drainage problem in this study, the model should be equally useful in the study of a wide range of two-dimensional water and solute migration problems.     

Drainage in heterogeneous sand columns with different geometric structures

This paper discusses multi-step drainage experiments in two heterogeneously packed sand columns (10 × 10 × 20 cm³). Different packing structures were generated using two different sand types. One purpose of the study was to test the influence of packing structures on the movement of water. The second purpose was to assess the quality of predictions for the outflow curves in both columns made with an upscaled model. The heterogeneous structures of the columns can be considered as two opposing extremes. The first column was packed with a random arrangement of two sand types that is not stochastically homogeneous and where a cluster running through the column exists for both materials. The second column was packed with a periodic pattern of coarse-sand inclusions in a fine-sand background and has a clearly defined unit cell. The depth-averaged (2D) spatial distribution of the water content in the columns was monitored during the whole multi-step outflow experiment using neutron radiography. The 3D water content was measured at the steady states by neutron tomography. The experimental results are compared with the model predictions of an upscaled model derived with the homogenization theory. The parameters for the upscaled model are calculated from the hydraulic parameters of the two sand types. These hydraulic parameters were first identified in independent measurements on samples of the two individual sand types, separately. Additionally, the hydraulic parameters of both sands were identified by fitting a numerical model to the measured outflow curves. The different column structures showed a significant effect on water retention and the effective retention function, as water was trapped in the coarse-sand inclusions of the periodic structure. We included this trapping effect in the effective retention function of the upscaled model with an apparent air entry pressure. Contrary to the retention, the different packing structures had no large effect on the dynamic behavior of the outflow. The effective conductivity of the columns is therefore not significantly influenced by the structure. The upscaled models predicted the movement of the averaged water content in the two columns well. This confirms the applicability of upscaled models even if the underlying requirements are not strictly met.     

A practical numerical method for large strain liquefaction analysis of saturated soils

Accurate prediction of the liquefaction of saturated soils is based on strong coupling between the pore fluid phase and soil skeleton. A practical numerical method for large strain dynamic analysis of saturated soils is presented. The u–p formulation is used for the governing equations that describe the coupled problem in terms of soil skeleton displacement and excess pore pressure. A mixed finite element and finite difference scheme related to large strain analysis of saturated soils based on the updated Lagrangian method is given. The equilibrium equation of fluid-saturated soils is spatially discretized by the finite element method, whereas terms associated with excess pore pressure in the continuity equation are spatially discretized by the finite difference method. An effective cyclic elasto-plastic constitutive model is adopted to simulate the non-linear behavior of saturated soils under dynamic loading. Several numerical examples that include a saturated soil column and caisson-type quay wall are presented to verify the accuracy of the method and its usefulness and applicability to solutions of large strain liquefaction analysis of saturated soils in practical problems.     

Wave-induced dynamic response of saturated multi-layer porous media: Analytical solutions and validity regions of various formulations in non-dimensional parametric space

In this paper, dynamic response of saturated-layered porous media under harmonic waves is evaluated through a semi-analytical solution. The coupled differential equations governing the dynamics of saturated or nearly saturated porous media such as soils containing all the inertial terms of solid and fluid phases are presented for a multi-layer system. Possible simplifications of the equations which are called formulations are introduced based upon the presence of inertial terms associated with the phases. The semi-analytical solutions to the response of multiple layers for all the formulations are presented in terms of pore water pressure and stress variations considering a set of non-dimensional parameters and their respective ratios. Validity of the formulations is presented in a non-dimensional parametric space. The maximum discrepancies in the pore pressure response of the formulations leading to validity regions are illustrated for typical dynamic problems. Subsequently, the effects of layering and drainage conditions on these regions are also presented. The proposed semi-analytical solution may be served as a benchmark one for validating the coupled numerical solutions, which can be used to deal with real scientific and geo-engineering problems in the emerging field of computational geomechanics.     

等吸力三轴剪切试验中非饱和黄土强度变形及水量变化特性

通过饱和原状黄土常规三轴试验和非饱和原状黄土等吸力三轴试验研究吸力和净围压对非饱和黄土强度变形的影响,并用HUANG等、胡冉等和方祥位等提出的土水特征曲线模型分析剪切过程中排水规律。研究结果表明：等吸力下原状土样固结剪切体积变形随净围压增大而增大;等净围压下原状土样固结剪切体积变形量随吸力的增大基本呈减小趋势。p-q平面内饱和土CSL线逐渐超过低吸力下非饱和土CSL线,原因在于随着p值增大,相对于非饱和土,饱和土孔隙比越来越小,较小孔隙比对抗剪强度的贡献逐渐大于非饱和土吸力对抗剪强度的贡献。应用固结稳定的数据拟合出HUANG等和胡冉等提出的模型参数,并预测剪切过程中的排水量,发现剪切速率对排水量有影响,这两种模型适用于剪切速率慢,排水充分的情况,而方祥位等提出的模型对不同剪切速率会拟合出不同的参数。     

Simulation of field‐scale water flow and bromide transport in a cracked clay soil

Single domain models may seriously underestimate leaching of nutrients and pesticides to groundwater in clay soils with shrinkage cracks. Various two‐domain models have been developed, either empirical or physically based, which take into account the effects of cracks on water flow and solute transport. This paper presents a model concept that uses the clay shrinkage characteristics to derive crack volume and crack depth under transient field conditions. The concept has been developed to simulate field average behaviour of a field with cracks, rather than flow and transport at a small plot. Water flow and solute transport are described with basic physics, which allow process and scenario analysis. The model concept is part of the more general agrohydrological model SWAP, and is applied to a field experiment on a cracked clay soil, at which water flow and bromide transport were measured during 572 days. A single domain model was not able to mimic the field‐average water flow and solute transport. Incorporation of the crack concept considerably improved the simulation of water content and bromide leaching to the groundwater. Still deviations existed between the measured and simulated bromide concentration profiles. The model did not reproduce the observed bromide retardation in the top layer and the high bromide dispersion resulting from water infiltration at various soil depths. A sensitivity analysis showed that the amounts of bromide leached were especially sensitive to the saturated hydraulic conductivity of the top layer, the solute transfer from the soil matrix to crack water flow and the mean residence time of rapid drainage. The shrinkage characteristic and the soil hydraulic properties of the clay matrix showed a low sensitivity. Copyright © 2000 John Wiley & Sons, Ltd.     

SV波在饱和土体自由表面的反射

基于饱和两相介质弹性波动方程分析SV波在饱和土体自由表面的反射问题,引入波动方程的势函数解答,求解出二维问题中SV波入射情况下饱和土体自由场的位移、速度、加速度和应力响应。在饱和土体自由场响应解析解基础上,建立SV波入射下饱和土体自由场静、动力有限元模型。建模中考虑了如下几方面因素:(1)在不同分析步,对土体单元赋予不同材料本构。通过*model change命令进行单元生死设定,从而实现在初始应力场平衡的静力状态下采用DuncanChang本构模型,而地震波动输入时采用Davidenkov动力本构模型;(2)采用多孔介质黏弹性人工边界条件,在人工边界上分别施加固相和液相介质的弹簧和阻尼来模拟饱和土体中能量的传播;(3)将地震波转化为作用在人工边界上的等效地震荷载,施加到人工边界节点上;(4)土体单元采用4结点平面应变孔压单元(CPE4P)。有限元计算与解析解比较结果表明:SV波在垂直入射和掠入射时,竖向位移响应为零;在45°左右入射时,水平位移响应最大;60°左右入射时,竖向位移响应最大。这些结论与解析解吻合较好,本文模型为建立土-结构动力相互作用模型打下良好的基础。     

Impact of land use on the hydraulic properties of the topsoil in a small French catchment

The hydraulic properties of the topsoil control the partition of rainfall into infiltration and runoff at the soil surface. They must be characterized for distributed hydrological modelling. This study presents the results of a field campaign documenting topsoil hydraulic properties in a small French suburban catchment (7 km²) located near Lyon, France. Two types of infiltration tests were performed: single ring infiltration tests under positive head and tension‐disk infiltration using a mini‐disk. Both categories were processed using the BEST—Beerkan Estimation of Soil Transfer parameters—method to derive parameters describing the retention and hydraulic conductivity curves. Dry bulk density and particle size data were also sampled. Almost all the topsoils were found to belong to the sandy loam soil class. No significant differences in hydraulic properties were found in terms of pedologic units, but the results showed a high impact of land use on these properties. The lowest dry bulk density values were obtained in forested soils with the highest organic matter content. Permanent pasture soils showed intermediate values, whereas the highest values were encountered in cultivated lands. For saturated hydraulic conductivity, the highest values were found in broad‐leaved forests and small woods. The complementary use of tension‐disk and positive head infiltration tests highlighted a sharp increase of hydraulic conductivity between near saturation and saturated conditions, attributed to macroporosity effect. The ratio of median saturated hydraulic conductivity to median hydraulic conductivity at a pressure of − 20 mm of water was about 50. The study suggests that soil texture, such as used in most pedo‐transfer functions, might not be sufficient to properly map the variability of soil hydraulic properties. Land use information should be considered in the parameterizations of topsoil within hydrological models to better represent in situ conditions, as illustrated in the paper. Copyright © 2010 John Wiley & Sons, Ltd.     

Effects of macro-pores on water flow in coastal subsurface drainage systems

Leaching through subsurface drainage systems has been widely adopted to ameliorate saline soils. The application of this method to remove salt from reclaimed lands in the coastal zone, however, may be impacted by macro-pores such as crab burrows, which are commonly distributed in the soils. We developed a three-dimensional model to investigate water flow in subsurface drainage systems affected by macro-pores distributed deterministically and randomly through Monte Carlo simulations. The results showed that, for subsurface drainage systems under the condition of continuous surface ponding, macro-pores increased the hydraulic head in the deep soil, which in turn reduced the hydraulic gradient between the surface and deep soil. As a consequence, water infiltration across the soil surface was inhibited. Since salt transport in the soil is dominated by advection, the flow simulation results indicated that macro-pores decreased the efficiency of salt leaching by one order of magnitude, in terms of both the elapsed time and the amount of water required to remove salt over the designed soil leaching depth (0.6 m). The reduction of the leaching efficiency was even greater in drainage systems with a layered soil stratigraphy. Sensitivity analyses demonstrated that with an increased penetration depth or density of macro-pores, the leaching efficiency decreased further. The revealed impact of macro-pores on water flow represents a significant shortcoming of the salt leaching technique when applied to coastal saline soils. Future designs of soil amelioration schemes in the coastal zone should consider and aim to minimize the bypassing effect caused by macro-pores.