Flow In Unsaturated Soils Research Articles

Influence of the soil-atmosphere exchange on the hydric profile induced in soil-structure system

Abstract. Soil-atmosphere exchange leads to a moisture change in the soil. This can cause major damage to engineering structures due to the soil expansion and shrinkage. The soil-atmosphere exchange is related to several parameters, in particular the soil characteristics and climate conditions. The presence of an engineering structure causes a variation of the hydraulic profile in the soil, which can lead to heterogeneous soil movement and consequently to structural damage. This paper presents a coupled numerical model based on the consideration of both water flow in unsaturated soils and soil-atmosphere exchange. After the validation of the model, the paper presents its use for the analysis of the influence of the presence of structures on moisture change induced under climatic conditions recorded in a semi-arid region. Analysis shows that the presence of the structure leads to important change in the moisture distribution, in particular in the vicinity of the structure.

A DRBEM with a predictor–corrector scheme for steady infiltration from periodic channels with root-water uptake

Abstract Water flow in unsaturated soils that is induced by infiltration and root-water uptake processes is governed by Richard's equation. To study the governing equation more conveniently, it is transformed into a modified Helmholtz equation using the Kirchhoff transformation with dimensionless variables. In this study, we employ a dual reciprocity boundary element method (DRBEM) and the predictor–corrector method to numerically solve problems governed by the equation. The proposed method is tested on problems involving infiltration from periodic channels with root water uptake.

Inverse modeling of dynamic nonequilibrium in water flow with an effective approach

Observations of water flow in unsaturated soils often show “dynamic effects,” indicated by nonequilibrium between water contents and water potential, a phenomenon that cannot be modeled with the Richards equation. The objective of this article is to formulate an effective process description of dynamic nonequilibrium flow in variably saturated soil which is both flexible enough to match experimental observations and as parsimonious as possible to allow unique parameter estimation by inverse modeling. In the conceptual model, water content is partitioned into two fractions. Water in one fraction is in equilibrium with the pressure head, whereas water in the second fraction is in nonequilibrium, described by the kinetic equilibration approach of Ross and Smettem (2000). Between the two fractions an instantaneous equilibration of the pressure head is assumed. The new model, termed the dual‐fraction nonequilibrium model, requires only one additional parameter compared to the nonequilibrium approach of Ross and Smettem. We tested the model with experimental data from multistep outflow experiments conducted on two soils and compared it to the Richards equation, the nonequilibrium model of Ross and Smettem, and the dual‐porosity model of Philip (1968). The experimental data were evaluated by inverse modeling using a robust Markov chain Monte Carlo sampler. The results show that the proposed model is superior to the Richards equation and the Ross and Smettem model in describing dynamic nonequilibrium effects occurring in multistep outflow experiments. The three popular model selection criteria (Akaike information criterion, Bayesian information criterion, and deviance information criterion) all favored the new model because of its smaller number of parameters.

Invariant Solutions of Richards' Equation for Water Movement in Dissimilar Soils

Scaling methods allow a single solution to Richards' equation (RE) to suffice for numerous specific cases of water flow in unsaturated soils. During the past half‐century, many such methods were developed for similar soils. In this paper, a new method is proposed for scaling RE for a wide range of dissimilar soils. Exponential‐power (EP) functions are used to reduce the dependence of the scaled RE on the soil hydraulic properties. To evaluate the proposed method, the scaled RE was solved numerically considering two test cases: infiltration into relatively dry soils having initially uniform water content distributions, and gravity‐dominant drainage occurring from initially wet soil profiles. Although the results for four texturally different soils ranging from sand to heavy clay (adopted from the UNSODA database) showed that the scaled solution were invariant for a wide range of flow conditions, slight deviations were observed when the soil profile was initially wet in the infiltration case or deeply wet in the drainage case. The invariance of the scaled RE makes it possible to generalize a single solution of RE to many dissimilar soils and conditions. Such a procedure reduces the numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils.

土壤优先流的离子显色示踪技术与分形模型模拟方法研究

为获得优先流的非均匀运动模式、提高优先流模拟预测的精度，本文运用碘-淀粉显色示踪技术，将优先流流场从流动背景中显示出来，通过数字图像分析技术和采样分析，获得优先流流场及流场内的土壤含水率和溶质浓度的非均匀分布模式；在此基础上，分别运用活动流场模型和二域模型对试验条件下的水流运动和溶质运移结果展开模分析，并通过相对标准偏差分析定量评价活动流场模型和二域模型模拟预测优先流发展的有效性。相对标准偏差分析显示，相对于二域模型，活动流场模型对土壤水流运动和溶质运移的模拟预测精度均较高。研究结果表明，活动流场模型较好的捕捉到了土壤优先流的整体非均匀信息。 To capture the heterogeneous flow pattern and enhance the prediction accuracy of preferential flow in unsaturated soil, the iodine-starch staining method was applied to visualize the preferential flow pattern from the background in this research. The digital imaging procedure was conducted to obtain the heterogeneous distribution pattern of preferential flow paths, and soil sampling was conducted to obtain the heterogeneous distributions of soil water content and solute concentration in the preferential flow region. The measured distributions of soil water content and solute concentration resulted from preferential flow were simulated and predicted using the active region model (ARM) and the mobile-immobile region model (MIM). The modeling efficiency using ARM and MIM were quantitatively evaluated and compared using the relative root mean square error (RRMSE) analysis. The model evaluation and comparison revealed that, ARM produced more accurate infiltration depth, and soil water and solute concentration distributions predictions, showing the ARM captured the macroscopic behavior of preferential flow and transport well.

Effect of hydraulic hysteresis on seepage analysis for unsaturated soils

This paper describes a study into the effects of hysteresis on the hydraulic behaviour of unsaturated soil covers. The Richards equation is coupled with the hysteretic soil water characteristic curves (SWCCs), to describe water flow in unsaturated soils. A linear scanning curve on semi-logarithmic scales is used to describe the hydraulic behaviour within the main hysteretic loop in unsaturated seepage problems. The proposed approach is implemented for one-dimensional flow problems using the finite difference method. A comparison of predictions of the proposed hysteretic model with those of the traditional non-hysteretic model is carried out first. For the assumed scenario of a compacted clay cover, the non-hysteretic model using the main drying SWCC leads to significantly different results than the hysteretic model, further demonstrating the necessity of accounting for hysteresis in unsaturated seepage analysis. Moreover, three infiltration tests on layered soil columns are simulated with the proposed hysteretic model. Results show that hysteresis plays an important role in the seepage analysis of unsaturated soils subjected to cyclic drying and wetting. The hysteretic model is suggested for use in the design and evaluation of the hydraulic performance of soil covers.

Numerical analysis of air-water-heat flow in unsaturated soil: Is it necessary to consider airflow in land surface models?

[1] From a subsurface physical point of view, this paper discusses the necessity of considering the two-phase heat and mass transfer process in land surface models (LSMs). The potential-based equations of coupled mass and heat transport under constant air pressure form the basis of the proposed model. The model is developed considering dry air as a single phase, and including mechanical dispersion in the water vapor and dry air transfer. The adsorbed liquid flux due to thermal gradient is also taken into account. The set of equations for the two-phase heat and mass transfer is formulated fully considering diffusion, advection, and dispersion. The advantage of the proposed model over the traditional equation system is discussed. The accuracy of the proposed model is assessed through comparison with analytical work for coupled mass and heat transfer and experimental work for isothermal two-phase flow (moisture/air transfer). The influence adding airflow has on the coupled moisture and heat transfer is further investigated, clearly identifying the importance of including airflow in the coupled mass and heat transfer. How the isothermal two-phase flow is affected by considering heat flow is also evaluated, showing the influence of heat flow only to be significant if the air phase plays a significant role in solving the equations of the water phase. On the basis of a field experiment, the proposed model is compared with the measured soil moisture, temperature, and evaporation rate, the results showing clearly that it is necessary to consider the airflow mechanism in soil-atmosphere interaction studies.

Scaling to generalize a single solution of Richards' equation for soil water redistribution

Using scaling methods, a single solution of Richards' equation (RE) will suffice for numerous specific cases of water flow in unsaturated soils. In this study, a new method is developed to scale RE for the soil water redistribution process. Two similarity conditions are required: similarity in the shape of the soil water content profiles as well as of the water flux density curves. An advantage of this method is that it is not restricted to a specific soil hydraulic model - hence, all such models can be applied to RE. To evaluate the proposed method, various soil textures and initial conditions were considered. After the RE was solved numerically using the HYDRUS-1D model, the solutions were scaled. The scaled soil water content profiles were nearly invariant for medium- and fine-textured soils when the soil profile was not deeply wetted. The textural range of the soils in which the similarity conditions are held decreases as the initial conditions deal with a deeply wetted profile. Thus, the scaling performance was poor in such a condition. This limitation was more pronounced in the coarse-textured soils. Based on the scaling method, a procedure is suggested by which the solution of RE for a specific case can be used to approximate solutions for many other cases. Such a procedure reduces complicated numerical calculations and provides additional opportunities for solving the highly nonlinear RE as in the case of unsaturated water flow in soils.

Combined Transient Method for Determining Soil Hydraulic Properties in a Wide Pressure Head Range

Simulation of water flow in unsaturated soils requires knowledge of the soil hydraulic properties. Two standard methods for the simultaneous determination of the water retention and hydraulic conductivity function in the laboratory are the multistep-outflow and the evaporation method. The multistep-outflow method provides information primarily in the pressure head range corresponding to relatively moist conditions, whereas the evaporation method has its highest information content in the medium to dry range. In the moisture ranges not covered by the experiments, an extrapolation of the soil hydraulic functions leads to very uncertain and possibly incorrect estimations of hydraulic properties. To obtain reliable estimates of soil hydraulic properties in a wider range of soil moisture contents, we combined both methods in a successive manner. The combined experiment starts with a multistep-outflow experiment, which is directly followed by an evaporation experiment. We tested this experimental design using synthetic data and laboratory measurements evaluated by inverse modeling. In the evaluation of the combined experiment, data points for the retention and conductivity functions were calculated from the evaporation experiment and included in the objective function for the inverse simulation of the multistep-outflow experiment. The combined evaluation led to greatly improved estimates of the hydraulic properties in a wide moisture range, circumvented the unreliable extrapolation beyond the pressure head ranges of the separate experiments, and significantly reduced the model error caused by such extrapolations.

Model of Water-Air Two-Phase Flow in Saturated-Unsaturated Soil

For seepage in unsaturated soil, there are both air flow and water flow, which can be called the water-air two-phase flow. In order to simulate the water-air two-phase flow in soil when there is groundwater, a numerical model of water-air two-phase flow in saturated-unsaturated soil is established in this paper. By the model, the air-flow and water-flow in unsaturated soil are both considered in seepage calculation. And the mass transfer between air-phase and water-phase, change of phase states are considered in calculation. Capillary pressure is the most important factor for the water-air two-phase flow in unsaturated soil, and the calculation method of capillary pressure is also given in the paper. At last examples are given to verify the correctness of the numerical model and the calculation method.

Governing equations for modeling preferential flow in unsaturated soil based on fractal theory

Governing equations for modeling preferential flow in unsaturated soil based on fractal theory

Testing system for hydraulic properties of unsaturated nonwoven geotextiles

ABSTRACT: The water retention curve (WRC) of unsaturated nonwoven geotextiles is necessary for the prediction of transient water flow in unsaturated soil–geotextile systems. A test method is introduced in this study to measure the WRC of deformable, unsaturated nonwoven geotextiles. This test method combines the axis-translation technique with water flow control using a flow pump. Specifically, a nonwoven geotextile specimen is placed within a flexible wall permeameter atop a cellulose membrane having high air entry and low impedance, and the flow pump is used to impose upward or downward water flow across the membrane. A control loop is used to reach stable suction values at the boundary of the suction in order to ensure that points on the WRC are defined for equilibrium flow conditions. A piston is used to apply a vertical load on the nonwoven geotextile specimen in order to replicate field loading conditions, and was also useful for measurement of changes in specimen volume. The combination of flow control, suction stabilization, and height measurement allow this new approach to effectively consider the impact of normal stress and matric suction on the porosity of the geotextile during measurement of the WRC. Experimental results for typical tests indicate that this approach yields drying and rewetting WRC curves for a geotextile specimen consistent with those in the technical literature.

Analytical model of infiltration under constant‐concentration boundary conditions

Known integrable models for 1D flow in unsaturated soil have a rescaled soil water diffusivity that is either constant or proportional to C(C − 1)/(C − Θ)2, where Θ is the degree of saturation and C > 1 is constant. With a wider more realistic range of hydraulic conductivity functions than has been used in this context before, a formal series solution is developed for infiltration, subject to constant‐concentration boundary conditions. A readily programmed iteration algorithm, applicable for any value of C, is used to construct many coefficients of the infiltration series without requiring any numerical integration. In particular, for either C − 1 small or 1/C small, several infiltration series coefficients are constructed as formal power series in C − 1 or in 1/C, for which we construct a number of terms explicitly. In the limit as the diffusivity approaches a delta function, the infiltration coefficients are obtained in simpler closed form. All but the sorptivity depend on the form of the conductivity function.

A MULTIPHASE ANALYSIS FOR ENVIRONMENTAL IMPACT ASSESSMENT WITH θ-STOCK FINITE ELEMENT PROGRAM

In the THM modeling of multiphase medium, the coupling effects of skeleton, suction, and temperature have been integrated via the concept of state surfaces of void ratio and degree of saturation. Based on proposed formulation, a fully coupled numerical model for the behavior of soil deformation, water flow, air flow, heat flow in unsaturated soil has been developed and integrated in a finite element code θ-Stock by the first author. This program is conceived with this idea that it will be able to analyze the response of a soil in different states of humidity to mechanical, thermal loading, and also damage phenomena. Damage model is dedicated to unsaturated brittle rocks. It mixes phenomenological and micromechanical concepts and is formulated based on the use of independent state variables. The expression of the liquid permeability is modified in order to represent the influence of fracturing on interstitial fluid flows. The final matrix form of established field equations of the proposed model for unsaturated case has been encoded for this particular purpose, in a finite element program which had been developed for dry and saturated soils previously.

Infiltration from supply at constant water content: an integrable model

An integrable version of Richards’ equation for time-dependent unidimensional flow in unsaturated soil is subjected to boundary conditions of constant water content. The nonlinear boundary problem is transformed to a linear diffusion problem with modified Stefan boundary conditions. A formal series is developed, leading to successive approximations to the solution at early times. Each additional term of the series for the location of the free boundary in the transformed problem leads directly to another coefficient in the Philip infiltration series in the original problem.

Environmental isotope (δ 18O) and hydrological data to assess water flow in unsaturated soils planted with different crops: Case study lysimeter station “Wagna” (Austria)

Summary Modelling variable soil water fluxes and transport processes under natural conditions in the unsaturated zone is often restricted and difficult to perform. Highly sophisticated numerical models are required and numerous parameters are needed. However, these parameters are difficult to estimate especially for heterogeneous systems. Therefore, the aim of this study was to investigate whether a simple lumped parameter approach is applicable in the unsaturated zone of cropped soils. The environmental isotope contents of δ18O and δ2H were used as tracers to study the flow processes in two lysimeters containing the same soil and planted with different crops (maize monoculture and crop rotation). The results from lumped parameter modelling were compared with those obtained with a numerical model approach. It was shown that the lumped parameter approach is, to some extent, applicable in the unsaturated zone. The simulations of the isotope contents in the discharge gave a general trend of mean transit times when the estimation of the tracer concentration in the inflow (input function) was weighted according to the amount of precipitation as well as when the observation period was separated into single vegetation periods. The resulting flow and transport parameters were similar to those from numerical modelling. The lumped model yielded adequate results particularly during the winter periods with grass cover. Although filled with the same soil material, different hydraulic flow systems were established in both lysimeters due to the differences in crop growth. In general, smaller fluxes were observed during crop rotation compared to maize monoculture whereas the smallest fluxes were found for canola.

Application of the environmental isotope δ 18O to study water flow in unsaturated soils planted with different crops: Case study of a weighable lysimeter from the research field in Neuherberg, Germany

Summary An attempt was made to improve the application of a lumped parameter model in the unsaturated soils planted with different crops. A first step of such an improvement was shown in Stumpp et al. [Stumpp, C., Maloszewski, P., Stichler, W., Fank, J., 2009. Application of the environmental isotope δ18O to study the water flow in unsaturated soils planted with different crops: 1. Case study – Lysimeter station “Wagna”, Austria. Journal of Hydrology] where the tracer concentrations in the recharging water were weighted according to the precipitation rate and by separating the observation period to different vegetation sub periods. However, during strongly variable flow conditions this improvement was still not sufficient enough to yield adequate modelling results. Therefore, in the present paper we investigated the flow processes in a high sophisticated lysimeter setup. The lysimeter had a length of 2 m and a surface area of 1 m2 and was weighable which yielded water content as a function of time. This data enabled a further development of the lumped parameter approach to variable flow conditions. A new method was found to estimate the tracer concentration in the recharging water (input function) that takes the actual evapotranspiration rates into account which was indirectly determined from weighing the lysimeters’ mass. Thus, it was possible to use a lumped dispersion model with such a new estimated input function to investigate the δ18O transport in soils planted with crop rotation with relatively high accuracy. The results obtained with the lumped dispersion model were compared with more exact numerical transient flow modelling, which however requires more detailed soil hydraulic data. The results of both modelling approaches yielded similar system parameters. The lumped parameter approach resulted in water contents of 0.14–0.30 cm3 cm−3 during the different vegetation periods and a mean value of 0.22 cm3 cm−3 for the whole observation period. The transient flow modelling yielded a mean water content of 0.21 cm3 cm−3. The dispersion parameter found in both models was in the same range. This study shows that a lumped dispersion model is applicable in the unsaturated zone even under strongly variable flow conditions having additional information about the water balance.

Free‐Form estimation of soil hydraulic properties using Wind’s method

SummaryTransient evaporation experiments offer the potential to determine simultaneously the soil hydraulic properties necessary to simulate water flow in unsaturated soils. We present a new algorithm for determining the retention and conductivity curve from evaporation experiments which uses Wind’s method with a free‐form soil water retention function. Our algorithm estimates nodal values of volumetric water content and derives a smooth and monotone retention curve by cubic Hermite interpolation. A multilevel routine increases the number of nodes and their adequate number is identified by a performance criterion which balances goodness of fit, the cross correlation between the estimated water contents and the number of degrees of freedom. We calculate point values of unsaturated hydraulic conductivity by the instantaneous profile method and discard unreliable conductivity estimates by a statistical filter criterion. Results for three synthetic data sets including an uncertainty analysis of the estimated retention curves show that the algorithm is suitable to identify, both correctly and precisely, the soil hydraulic properties. An application to a real data set confirms these results. In order to enable the free‐form functions to be used in numerical flow simulations, we extrapolate the retention function to the dry range and compute a coupled conductivity function based on the Mualem model. Major advantages of the proposed method are the enormous flexibility provided by the free‐form functions, the low level of parameter cross‐correlation in comparison with classic parametric functions, and the possibility of assessing the uncertainty of the retention curve individually in different ranges of pressure head.

Coiled Time Domain Reflectometry Matric Potential Sensor

Matric potential is a measure of the combined capillary and adsorptive forces of soil particles and is imperative for determining both the direction and magnitude of water flow in unsaturated soils. Measuring soil matric potential in semiarid and arid environments is a challenge. Current methods cannot measure the entire range of values, from 0 to −1.5 MPa. The objective of this research was to develop a new sensor capable of measuring the relationship between the dielectric constant of a ceramic core and the range of field soil matric potential values. This instrument uses two Cu TDR rods wrapped around a dual‐threaded Plexiglas core, which is inserted into a porous ceramic block salvaged from damaged Campbell Scientific 229 heat dissipation sensors. The relationship of the ceramic's measured dielectric constant to soil matric potential is determined through a laboratory calibration curve. Calibration of the probe involved the use of a tension table and pressure plate apparatus. The dielectric constant of the probe was measured at a range of points between 0 and −1.5 MPa, and a modified van Genuchten water retention model was used to fit the data (R2 = 0.84). The proposed instrument provided an effective method of measuring soil matric potentials from 0 to −1.5 MPa.

Historical development of soil-water physics and solute transport in porous media

The science of soil-water physics and contaminant transport in porous media began a little more than a century ago. The first equation to quantify the flow of water is attributed to Darcy. The next major development for unsaturated media was made by Buckingham in 1907. Buckingham quantified the energy state of soil water based on the thermodynamic potential energy. Buckingham then introduced the concept of unsaturated hydraulic conductivity, a function of water content. The water flux as the product of the unsaturated hydraulic conductivity and the total potential gradient has become the accepted Buckingham-Darcy law. Two decades later, Richards applied the continuity equation to Buckingham's equation and obtained a general partial differential equation describing water flow in unsaturated soils. For combined water and solute transport, it had been recognized since the latter half of the 19th century that salts and water do not move uniformly. It wasn't until the middle of the 20th century that scientists began to understand the complex processes of diffusion, dispersion, and convection and to develop mathematical formulations for solute transport. Knowledge on water flow and solute transport processes has expanded greatly since the early part of the 20th century to the present.