Unsaturated flows in soils with self-similar hydraulic conductivity distribution

In this article, we are concerned with the statistics of steady unsaturated flow in soils with a fractal hydraulic conductivity distribution. It is assumed that the spatial distribution of log hydraulic conductivity can be described as an isotropic stochastic fractal process. The impact of the fractal dimension of this process, the soil pore-size distribution parameter, and the characteristic length scale on the variances of tension head and the effective conductivity is investigated. Results are obtained for one-dimensional and three-dimensional flows. Our results indicate that the tension head variance is scale-dependent for fractal distribution of hydraulic conductivity. Both tension head variance and effective hydraulic conductivity depend strongly on the fractal dimension. The soil pore-size distribution parameter is important in reducing the variability of the unsaturated hydraulic conductivity and of the fluxes.     

Influence of pore size and geometry on peat unsaturated hydraulic conductivity computed from 3D computed tomography image analysis

In organic soils, hydraulic conductivity is related to the degree of decomposition and soil compression, which reduce the effective pore diameter and consequently restrict water flow. This study investigates how the size distribution and geometry of air‐filled pores control the unsaturated hydraulic conductivity of peat soils using high‐resolution (45 µm) three‐dimensional (3D) X‐ray computed tomography (CT) and digital image processing of four peat sub‐samples from varying depths under a constant soil water pressure head. Pore structure and configuration in peat were found to be irregular, with volume and cross‐sectional area showing fractal behaviour that suggests pores having smaller values of the fractal dimension in deeper, more decomposed peat, have higher tortuosity and lower connectivity, which influences hydraulic conductivity. The image analysis showed that the large reduction of unsaturated hydraulic conductivity with depth is essentially controlled by air‐filled pore hydraulic radius, tortuosity, air‐filled pore density and the fractal dimension due to degree of decomposition and compression of the organic matter. The comparisons between unsaturated hydraulic conductivity computed from the air‐filled pore size and geometric distribution showed satisfactory agreement with direct measurements using the permeameter method. This understanding is important in characterizing peat properties and its heterogeneity for monitoring the progress of complex flow processes at the field scale in peatlands. Copyright © 2010 John Wiley & Sons, Ltd.     

Remarks upon numerical solutions of infiltration into a soil profile

Abstract

A methodology of time-step estimation for numerically solving the Richards equation is discussed. Its importance in simulating water movement in unsaturated—saturated soils is shown for infiltration into a soil profile by applying various time-step estimations and boundary conditions for different soils. In order to test the results of the computations, infiltration theory was applied. According to infiltration theory, the pressure head in the initially unsaturated part will not take positive values as long as the moisture front has not reached the phreatic level, or, in the case of a profile with a free-draining lower boundary, it is not saturated at the base. In other cases, the appearance of positive values of the pressure head produces incorrect values for the inflow rate q.     

Evaporative losses from soils covered by physical and different types of biological soil crusts

Evaporation of soil moisture is one of the most important processes affecting water availability in semiarid ecosystems. Biological soil crusts, which are widely distributed ground cover in these ecosystems, play a recognized role on water processes. Where they roughen surfaces, water residence time and thus infiltration can be greatly enhanced, whereas their ability to clog soil pores or cap the soil surface when wetted can greatly decrease infiltration rate, thus affecting evaporative losses. In this work, we compared evaporation in soils covered by physical crusts, biological crusts in different developmental stages and in the soils underlying the different biological crust types. Our results show that during the time of the highest evaporation (Day 1), there was no difference among any of the crust types or the soils underlying them. On Day 2, when soil moisture was moderately low (11%), evaporation was slightly higher in well‐developed biological soil crusts than in physical or poorly developed biological soil crusts. However, crust removal did not cause significant changes in evaporation compared with the respective soil crust type. These results suggest that the small differences we observed in evaporation among crust types could be caused by differences in the properties of the soil underneath the biological crusts. At low soil moisture (<6%), there was no difference in evaporation among crust types or the underlying soils. Water loss for the complete evaporative cycle (from saturation to dry soil) was similar in both crusted and scraped soils. Therefore, we conclude that for the specific crust and soil types tested, the presence or the type of biological soil crust did not greatly modify evaporation with respect to physical crusts or scraped soils. Copyright © 2011 John Wiley & Sons, Ltd.     

Stochastic analysis of bounded unsaturated flow in heterogeneous aquifers: Spectral/perturbation approach

This paper describes a stochastic analysis of steady state flow in a bounded, partially saturated heterogeneous porous medium subject to distributed infiltration. The presence of boundary conditions leads to non-uniformity in the mean unsaturated flow, which in turn causes non-stationarity in the statistics of velocity fields. Motivated by this, our aim is to investigate the impact of boundary conditions on the behavior of field-scale unsaturated flow. Within the framework of spectral theory based on Fourier–Stieltjes representations for the perturbed quantities, the general expressions for the pressure head variance, variance of log unsaturated hydraulic conductivity and variance of the specific discharge are presented in the wave number domain. Closed-form expressions are developed for the simplified case of statistical isotropy of the log hydraulic conductivity field with a constant soil pore-size distribution parameter. These expressions allow us to investigate the impact of the boundary conditions, namely the vertical infiltration from the soil surface and a prescribed pressure head at a certain depth below the soil surface. It is found that the boundary conditions are critical in predicting uncertainty in bounded unsaturated flow. Our analytical expression for the pressure head variance in a one-dimensional, heterogeneous flow domain, developed using a nonstationary spectral representation approach [Li S-G, McLaughlin D. A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis. Water Resour Res 1991;27(7):1589–605; Li S-G, McLaughlin D. Using the nonstationary spectral method to analyze flow through heterogeneous trending media. Water Resour Res 1995; 31(3):541–51], is precisely equivalent to the published result of Lu et al. [Lu Z, Zhang D. Analytical solutions to steady state unsaturated flow in layered, randomly heterogeneous soils via Kirchhoff transformation. Adv Water Resour 2004;27:775–84].     

Stochastic analysis of unsaturated transport in soils with fractal log-conductivity distribution

Within the framework of stochastic theory and the spectral perturbation techniques, three-dimensional dispersion in partially saturated soils with fractal log hydraulic conductivity distribution is analyzed. Our analysis is focused on the impact of fractal dimension of log hydraulic conductivity distribution, local dispersivity, and unsaturated flow parameters, such as the soil poresize distribution parameter and the moisture distribution parameter, on the spreading behavior of solute plume and the concentration variance. Approximate analytical solutions to the stochastic partial differential equations are derived for the variance of asymptotic solute concentration and asymptotic macrodispersivities.     

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.     

Particle size characteristics of suspended sediment in hillslope runoff and stream flow

This study examines the particle size characteristics of hillslope soils and fluvial suspended sediments in an agricultural catchment. Samples of surface runoff and stream flow were collected periodically and analysed for the size distributions of the effective (undispersed) sediment. This sediment was subsequently dispersed and the ultimate size distributions determined. The median effective particle size of stream suspended sediment was considerably coarser than the median ultimate particle size, indicating that most of the load included a substantial proportion of aggregates. Moreover, the proportion of fine material (i.e. silt and clay) increased, and the proportion of sand-sized material decreased, with increasing discharge. This decrease in sediment size with increased flow, which is contrary to the traditional assumption of a positive discharge/particle size relationship, is thought to reflect: (i) the influx of silt and clay, predominantly the former, originating on the catchment slopes and brought to the stream by overland flow along vehicle wheelings, roads and tracks; and (ii) erosion of fine material from the channel bed and banks. During large storms, however, the proportion of sand-sized sediment increased during the rising limb of the hydrograph, as a result of the entrainment of coarser source material from the valley floor during overbank flooding. The stream suspended sediment was finer than the catchment soils and considerably finer than material eroding from the catchment slopes during storms. The degree of clay and silt enrichment in the suspended sediments was largely the result of preferential deposition of the coarser fraction during the transport and delivery of sediment from its source to basin outlet. The data from this study confirm that a significant mode of sediment transport in fluvial systems is in the form of aggregates, and that the dispersed sediment size distribution is inappropriate for determining the transportability of sediment by flow. © 1997 by John Wiley & Sons, Ltd.     

PRINCIPES NOUVEAUX POUR DISTINGUER CE QUI EST Dû A L'ÉCOULEMENT SOUTERRAIN SUR L'HYDROGRAPHE DES FLEUVES

Abstract

Throughflow has been measured from three soil horizons on a 12 slope with impermeable, bedrock. Storm flow comes from the 10–45 cm horizon and is controlled by the upslope extent of saturated conditions. Base flow comes from the 45–75 cm horizon and is supplied by slow unsaturated flow from the whole soil mass to a small constant zone of saturation.

Differences between input and output stream hydrographs over 270 metres of channel are attributed to throughflow and correlate well with measured values providing a basis for separating throughflow components from the stream hydrograph. Observed stream flows contain no overland flow or ground water flow components. The main basin flood peak is not generated within this control section of channel but is produced in the headwater zone (0.1 km²) by the faster runoff characteristics of the soils in that area and by topographic factors which lead to rapid channel extension.     

Lateral water flux in the unsaturated zone: A mechanism for the formation of spatial soil heterogeneity in a headwater catchment

Measurements of soil water potential and water table fluctuations suggest that morphologically distinct soils in a headwater catchment at the Hubbard Brook Experimental Forest in New Hampshire formed as a result of variations in saturated and unsaturated hydrologic fluxes in the mineral soil. Previous work showed that each group of these soils had distinct water table fluctuations in response to precipitation; however, observed variations in soil morphology also occurred above the maximum height of observed saturation. Variations in unsaturated fluxes have been hypothesized to explain differences in soil horizon thickness and presence/absence of specific horizons but have not been explicitly investigated. We examined tensiometer and shallow groundwater well records to identify differences in unsaturated water fluxes among podzols that show distinct morphological and chemical differences. The lack of vertical hydraulic gradients at the study sites suggests that lateral unsaturated flow occurs in several of the soil units. We propose that the variations in soil horizon thickness and presence/absence observed at the site are due in part to slope‐parallel water flux in the unsaturated portion of the solum. In addition, unsaturated flow may be involved in the translocation of spodic material that primes those areas to contribute water with distinct chemistry to the stream network and represents a potential source/sink of organometallic compounds in the landscape.     

考虑非饱和特性的黄土湿陷性与微观结构分析

利用扫描电子显微镜测试技术对3个场地16个土样的微观结构进行观测,并使用图像处理软件对微观图像进行处理、对土样孔隙的几何特征参数和分维数进行了提取,土样孔隙分布分维数为1.816~1.936。利用分形几何学原理建立非饱和土的孔隙分布函数,对天然湿度下黄土中水分分布进行分析,运用回归分析的方法对孔隙的分维数、非饱和孔隙孔隙率和湿陷性的关系进行了分析。结果表明：孔隙分维数越大,孔隙结构越复杂;天然湿度下处于非饱和状态的黄土孔隙孔径均大于40μm,黄土的湿陷系数随着孔隙分维数、非饱和孔隙孔隙率的增大而增大,非饱和孔隙是造成黄土湿陷的主要原因。     

Steady flow patterns in saturated and unsaturated,isotropic soils

A comprehensive analysis of steady flow patterns in saturated and unsaturated, possibly heterogeneous, isotropic soils is presented. It is shown that, at any point, the divergence of the unit tangent vector field to the streamlines is equal to the directional derivative along the streamlines of the orthogonal cross-sectional area of an infinitesimal stream tube divided by that area and also equal to the mean curvature of the surface of constant total head. Expressions are derived for the distribution of the flux, the water content, the velocity, the hydraulic conductivity, the total head, and the pressure head along a stream line or an infinitesimal, stream tube. Among the results is a simpler derivation, further interpretation, and extension of earlier work on calculating the hydraulic conductivity distribution from detailed measurements of the total head distribution in combination with measurements of the hydraulic conductivity at a few locations. In the last section, the jumps of various quantities at an interface are discussed.     

Determination of soil hydrophysical characteristics in the Ivankovo Reservoir watershed

The capillary-sorption potential and the unsaturated hydraulic conductivity of soils as functions of soil water content are derived for forest, meadow, and agricultural ecosystems of the Ivankovo Reservoir watershed. The parameters of van Genuchten-Mualem equations were determined for the same soils based on data on soil particle size distribution and density. Computer code HYDRUS-1D and the obtained data were used to calculate the values of field capacity of soils in forest, meadow, and agricultural ecosystems in the drainage basin of the Ivankovo Reservoir.     

Modeling the Impact of Stream Discharge Events on Riparian Solute Dynamics

The biogeochemical composition of stream water and the surrounding riparian water is mainly defined by the exchange of water and solutes between the stream and the riparian zone. Short-term fluctuations in near stream hydraulic head gradients (e.g., during stream flow events) can significantly influence the extent and rate of exchange processes. In this study, we simulate exchanges between streams and their riparian zone driven by stream stage fluctuations during single stream discharge events of varying peak height and duration. Simulated results show that strong stream flow events can trigger solute mobilization in riparian soils and subsequent export to the stream. The timing and amount of solute export is linked to the shape of the discharge event. Higher peaks and increased durations significantly enhance solute export, however, peak height is found to be the dominant control for overall mass export. Mobilized solutes are transported to the stream in two stages (1) by return flow of stream water that was stored in the riparian zone during the event and (2) by vertical movement to the groundwater under gravity drainage from the unsaturated parts of the riparian zone, which lasts for significantly longer time (> 400 days) resulting in long tailing of bank outflows and solute mass outfluxes. We conclude that strong stream discharge events can mobilize and transport solutes from near stream riparian soils into the stream. The impact of short-term stream discharge variations on solute exchange may last for long times after the flow event.     

Experimental study and mathematical modelling of soluble chemical transfer from unsaturated/saturated soil to surface runoff

A one‐dimensional, two‐layer solute transport model is developed to simulate chemical transport process in an initially unsaturated soil with ponding water on the soil surface before surface runoff starts. The developed mathematical model is tested against a laboratory experiment. The infiltration and diffusion processes are mathematically lumped together and described by incomplete mixing parameters. Based on mass conservation and water balance equations, the model is developed to describe solute transport in a two‐zone layer, a ponding runoff zone and a soil mixing zone. The two‐zone layer is treated as one system to avoid describing the complicated chemical transport processes near the soil surface in the mixing zone. The proposed model was analytically solved, and the solutions agreed well with the experimental data. The developed experimental method and mathematical model were used to study the effect of the soil initial moisture saturation on chemical concentration in surface runoff. The study results indicated that, when the soil was initially saturated, chemical concentration in surface runoff was significantly (two orders of magnitude) higher than that with initially unsaturated soil, while the initial chemical concentrations at the two cases were of the same magnitude. The soil mixing depth for the initially unsaturated soil was much larger than that for the initially saturated soil, and the incomplete runoff mixing parameter was larger for the initially unsaturated soil. The higher the infiltration rate of the soil, the greater the infiltration‐related incomplete mixing parameter. According to the quantitative analysis, the soil mixing depth was found to be sensitive for both initially unsaturated and saturated soils, and the incomplete runoff mixing parameter was sensitive for initially saturated soil but not for the initially unsaturated soil; the incomplete infiltration mixing parameter behaved just the opposite. Some suggestions are made for reducing chemical loss from runoff. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of macropores on soil freezing and thawing with infiltration

An understanding of heat transport and water flow in unsaturated soils experiencing freezing and thawing is important when considering hydrological and thermal processes in cold regions. Macropores, such as cracks, roots, and animal holes, provide efficient conduits for enhanced infiltration, resulting in a unique distribution of water content. However, the effects of macropores on soil freezing and thawing with infiltration have not been well studied. A one‐directional soil‐column freezing and thawing experiment was conducted using unsaturated sandy and silt loams with different sizes and numbers of macropores. During freezing, macropores were found to retard the formation of the frozen layer, depending on their size and number. During thawing, water flowed through macropores in the frozen layer and reached the underlying unfrozen soil. However, infiltrated water sometimes refroze in a macropore. The ice started to form at near inner wall of the macropore, grew to the centre, and blocked flow through the macropore. The blockage ice in the macropore could not melt until the frozen layer disappeared. Improving a soil freezing model to consider these macropore effects is required. Copyright © 2016 John Wiley & Sons, Ltd.     

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 Stony Vadose Zonesa

Hydraulic properties of saturated and unsaturated stony soils were studied on a 3.35 m long column, 1.24 m in diameter, filled with alternating sand and boulder layers. The boulders averaged 6.2 × 15 × 20 cm in size and were laid down on their flat side. Tensiometers and a neutron probe access tube were placed in the column for measuring pressure heads and water contents, respectively. Saturated conditions were obtained by ponding the column. The resulting hydraulic conductivity K was 5.1 m/day. This value could also be calculated from the measured K for the sand alone on separate samples, using a simple equation that takes into account the void ratio of the sand alone and that of the boulder-sand mixture. Unsaturated K was determined by applying water at less than ponded infiltration rates. Resulting relations between the unsaturated K and water content or negative pressure head could also be estimated from the relation between unsaturated K and pressure head for the sand alone and the calculated saturated K of the boulder-sand mixture. The method of Millington and Quirk for calculating the relation between unsaturated K and water content also gave reasonable results. The dispersivity of the boulder-sand column was 18 times that of the sand alone. Pore velocity was accurately estimated as the Darcy velocity divided by the volumetric water content. Hydraulic properties of stony vadose zones are difficult to determine. This work shows that they can be estimated from K relations measured in the laboratory on samples of the soil between the rocks. Knowledge of hydraulic properties of vadose zones is important in predicting movement of water and pollutants to the underlying ground water.