Eulerian-Lagrangian formulation for flow in soils: Theory

An Eulerian scheme is used to reformulate the equations of groundwater with pressure dependent density flowing through saturated zones, and moisture transport in unsaturated zones. The governing equation is decomposed into advection along characteristic path lines and propagation of the residue at a fixed frame of reference. This formal decomposition enables the handling of physical phenomena that incorporate discontinuities and/or steep gradient without the need for means of artificial smoothing.     

Unstable flow in layered soils: A review

Release of water from the soil in the process of internal drainage, and its continued downward movement through the vadose zone, constitute the main mechanism of groundwater recharge. Water released from the soil generally contains solutes, and these are conveyed to the groundwater via the same pathways as the drained water. Knowledge of those pathways is essential in any attempt to minimize the likelihood of groundwater pollution. Solutes generally interact with the medium in which they reside or travel, and the spatial and temporal pattern of their movement influences the nature and extent of their interactions. For many years, the assumption had prevailed that flow in the vadose zone is a steady-state, uniform process. Hence the vadose zone can serve to filter, attenuate, as well as degrade, potential pollutants. Recently, however, the existence of preferred pathways has come to light. Such pathways might connect the soil's upper zone directly to the water-table, thus bypassing the greater volume of the vadose zone and evading its filtering mechanisms. Groundwater recharge models that ignore the possibility of such spurts of contamination may be highly misleading. Preferred flow path may be cracks, animal burrows, or decayed root channels. Less easily discernible are transient and random paths associated with the phenomenon of ‘unstable flow’, which is most likely to occur in layered soils during infiltration. The wetting front, instead of remaining horizontal and advancing continuously from one layer to the next, may begin (particularly in transition from a fine-textured to a coarse-textured layer) to form bulges, called ‘fingers’, which propagate downwards and may become, in effect, vertical pipes. At present we are aware only of the occasional occurrence and potential importance of such phenomena, but as yet have neither the systematic empirical data, nor a proven comprehensive theoretical framework, by which to assess where, when, and according to what pattern, they are likely to occur.     

Numerical analysis of one-dimensional unsaturated flow in layered soils

The paper deals with numerical solutions to the Richards equation to simulate one-dimensional flow processes in the unsaturated zone of layered soil profiles. The equation is expressed in the pressure-based form and a finite-difference algorithm is developed for accurately estimating the values of the hydraulic conductivity between two neighboring nodes positioned in different soil layers, often referred to as the interlayer hydraulic conductivity. The algorithm is based upon flux conservation and continuity of pressure potential at the interface between two consecutive layers, and does not add significantly to simulation run time. The validity of the model is established for a number of test problems by comparing numerical results with the analytical solutions developed by Srivastava and Yeh²⁹ which hold for vertical infiltration towards the water table in a two-layer soil profile. The results show a significant reduction in relative mass balance errors when using the proposed model. Some specific insights into its numerical performance are also gained by comparisons with a numerical model in which the more common geometric averaging operator acts on the interlayer conductivities.     

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.     

Quantifying preferential flow in soils: A review of different techniques

Preferential flow (PF) in soil has both environmental and human health implications since it favours contaminant transport to groundwater without interaction with the chemically and biologically reactive upper layer of soil. PF is, however, difficult to measure and quantify. This paper reviews laboratory and field techniques, such as breakthrough curves, dye tracing, and scanning techniques, for evaluating PF in soil at different scales. Advanced technologies, such as scanning techniques, have increased our capability to quantify transport processes within the soil with minimal soil disturbance. Important issues with respect to quantifying PF concern large-scale studies, frozen soil conditions, tracing techniques for particles and gases, a lack of simple mathematical tools for interpreting field data, and the lack of a systematic approach for comparing PF data resulting from different measurement techniques. Also, more research is required to quantify the relative importance of the various PF processes that occur in soil rather than the integrated result of all PF processes in soils.     

Viscous fluid characteristics of liquefied soils and behavior of piles subjected to flow of liquefied soils

Lateral movement of sloping ground due to flow liquefaction has caused many pile foundations to fail, especially those in ports and harbor structures. Several researchers have found and verified that the behavior of liquefied soils can be simulated appropriately by modeling the liquefied soils as viscous fluid. In this study, the influence of the lateral movement of liquefied sloping ground on the behavior of piles was analyzed on the assumption that the flow of liquefied soils can be treated as viscous fluid flow. Sinking ball tests and pulling bar tests were performed to measure the viscosity of liquefied Jumoonjin sand. Then, the behavior of a single pile installed in liquefiable infinite slopes consisting of sand was investigated by numerical analyses. The liquefied sand behaved as non-Newtonian fluid, whose viscosity decreased with increasing shear strain rate. Furthermore, the flow of liquefied soils had a crucial effect on the stability of piles installed in the sloping ground.     

Free vibration of soils during large earthquakes

Free vibration of soils happens frequently during some large earthquakes, perhaps seeming like a paradox. This happens because the energy released from seismic sources in some cases is not stationary in time, allowing relaxation intervals in between without important seismic wave arrivals in which free soil vibration happens. Two techniques to estimate the natural period of the free vibration from accelerograms are presented: autocorrelograms and Fourier spectra. Both techniques sometimes allow measuring higher mode frequencies of the soil for the three first modes as well as modal damping. Free vibration modal periods satisfy the classic 1D equation S-wave theory. The presence of free vibrations corresponds to shear wave soil energy radiation episodes rather than to energy amplification of incoming stationary seismic shear waves suggested by the dynamic soil amplification. These results explain the discrepancies observed between the theoretical soil dynamic amplification and the accelerographic measurement. Observation of free vibration of soils is not always possible, it depends on the duration of the time windows without important seismic waves arrivals compared to the natural period and damping of the soil.     

Unified macroscopic model for unsaturated water flow in soils of bimodal porosity

Abstract

Natural soils very often contain micro- and macropores, having different hydraulic properties. At the macroscopic scale, the unsaturated flow in such soils can be described with various models, depending on the hydraulic diffusivity ratio of the components and the connectivity of the most conductive component. Three macroscopic models recently derived by the homogenization method are discussed. The limit passages between the models are studied. A unified model suitable for the entire range of the hydraulic diffusivity ratio is proposed. A numerical example shows the application of the model to macroscopically one-dimensional infiltration in a porous medium containing inclusions. A parametric study for varying conductivity (diffusivity) ratio is performed.     

Role of water flow in modeling methane emissions from flooded paddy soils

Methane (CH₄) is a potent greenhouse gas that is emitted from paddy fields, and the large CH₄ fluxes represent a worldwide issue for the rice production eco-compatibility. In this work a model is proposed to investigate the role of water flows on CH₄ emissions from flooded paddy soils. The model is based on a system of partial differential mass balance equations of the chemical species affecting CH₄ fate, and water flows are modeled by the Darcy equation. Moreover, in order to properly model the dynamics of CH₄, a number of physico-chemical processes and features not included in currently available CH₄ emission models are considered: paddy soil stratigraphy; nutrient adsorption and root water uptake; gas transport and respiration within root aerenchyma compartment. The proposed model allows to simulate the spatio-temporal dynamics of chemical compounds within paddy soil as well as to quantify the influence of different processes on nutrient input/output budgets. Simulations without water flow have shown a considerable overestimation of CH₄ emissions due to a different spatio-temporal dynamics of dissolved organic matter (DOC – source of energy for CH₄ production). In particular, when water fluxes have not been modeled the overestimation can reach 54%, 41% and 67% of daily minimum, daily maximum, and total over the whole growing season CH₄ emission, respectively. Moreover, the model results suggest that roots influence CH₄ dynamics principally due to their nutrient uptake, while root effect on advective flow plays a minor role. Finally, the analysis of CH₄ transport fluxes has shown the limiting effect of upward dispersive transport fluxes on the downward CH₄ percolation.     

Comparison of conductivity averaging methods for one-dimensional unsaturated flow in layered soils

One of the important factors influencing the accuracy of the numerical solution of 1D unsaturated flow equation (Richards’ equation) is the averaging method applied to compute hydraulic conductivity between two adjacent nodes of the computational grid. A number of averaging schemes have been proposed in the literature for homogeneous soil, including arithmetic, geometric, upstream and integrated means, as well as more sophisticated approaches, based on the local solution of steady state flow between the neighboring nodes (Darcian means). Another group of methods have been developed for the case when a material interface is present between the nodes. They range from simple arithmetic averaging to more complex schemes using the pressure- and flux-continuity conditions at the interface. In this paper we compare several averaging schemes for a number of steady and unsteady flow problems in layered soils. The first group of methods is applied in the framework of the vertex-centered approach to spatial discretization, where the nodes are placed at the material interfaces, while the second group is used with the cell-centered approach, where the material interfaces are located between computational nodes. The resulting numerical schemes are evaluated in terms of accuracy and computational time. It is shown that the averaging schemes based on Darcian mean principle [19] used in the framework of either vertex-centered or cell-centered approach compare favorably to other methods for a range of test cases.     

Nonlinearity in the response of soils in the 1995 Kobe earthquake in vertical components of records

Strong motion records provided by seismic vertical arrays allow estimation of stress–strain relations in soils at depths from the surface to the location of the deepest device. As an example, time-dependent nonlinear soil behavior was estimated in vertical components of records obtained in the epicentral area of the 1995 Kobe earthquake. Degradation of the rigidity of soils in the strong motion was observed. The constructed nonlinear models of the soil behavior were used for estimating the nonlinear parts in the ground response by the nonlinear system identification technique. Nonlinear parts in the ground response were found to be as high as 50% at 2 km from the fault and 10% at 6–15 km from the fault plane. Odd types of nonlinearity, such as cubic, the fifth, seventh, etc. order, were found to be typical for soils, whereas, nonlinearities of even types are usually weak, but increase in liquefied soils.     

The use of gypsum spheres for identifying water flow routes in soils

Gypsum (plaster of paris) has been cast into spheres and placed in soils; weight loss has been used to identify relative water flow routes. Theoretical considerations and laboratory experimentation show that solutional weight loss of the material used increases with increasing water flow, but is independent of pH above pH 4. Results for gypsum sphere weight loss are presented for soils where moisture conditions have been measured independently using tensiometers. The data suggest that the weight loss method provides a viable time-integrated demonstration of relative water flow routes.     

Contrasting flow pathways within tropical forest slopes of Ultisol soils

There are very few experimental studies identifying hydrological pathways within rain forest slopes. Such knowledge is, however, necessary to understand why forest disturbance affects rainfall–riverflow response and nutrient migration. This study examines flow pathways within lowland rain forest slopes comprising Udults of the Ultisol soil order. Experimentation was conducted on four SE Asian hillslope units (each 5 × 5 m in plan) in the Bukit Timah catchment (Singapore Island), and in the W8S5 catchment (Sabah, Borneo Island). The flow pathways were identified by artificial tracer experiments. We evaluated how well hydrometric calculations based on tensiometry and permeametry measurements predicted the tracer patterns. The tracer work indicated much faster subsurface flows at Bukit Timah than W8S5 for the storms studied. Some explanation of the greater subsurface waterflows at Bukit Timah in comparison to W8S5 is afforded by the less steep moisture release curves which maintain hydraulic conductivity as the soil dries. Vertical flow of the tracer through the upper 1 m of soil predominated (>90 per cent of percolation) in the Bukit Timah slopes. In some contrast, a major component (approximately 60 per cent) of the tracer percolation was directed laterally within the W8S5 slopes. The flow vectors calculated using the hydrometric methods did, however, grossly under‐estimate the degree of lateral deflection of waterflow generated at W8S5 and to a lesser extent over‐estimated it at Bukit Timah. In part, these errors may relate to the inability of traditional hydrometric techniques to fully characterize the effect of the large and small ‘natural soil pipes’ present within both catchments. In conclusion, the study indicates that marked variations in flow vectors exist within the Udult great group of SE Asian soils and hydrometric calculations may be poor predictors of these dominant pathways. Copyright © 2005 John Wiley & Sons, Ltd.     

Nonlinear determinism in river flow: prediction as a possible indicator

Whether or not river flow exhibits nonlinear determinism remains an unresolved question. While studies on the use of nonlinear deterministic methods for modeling and prediction of river flow series are on the rise and the outcomes are encouraging, suspicions and criticisms of such studies continue to exist as well. An important reason for this situation is that the correlation dimension method, used as a nonlinear determinism identification tool in most of those studies, may possess certain limitations when applied to real river flow series, which are always finite and often short and also contaminated with noise (e.g. measurement error). In view of this, the present study addresses the issue of nonlinear determinism in river flow series using prediction as a possible indicator. This is done by (1) reviewing studies that have employed nonlinear deterministic methods (coupling phase‐space reconstruction and local approximation techniques) for river flow predictions and (2) identifying nonlinear determinism (or linear stochasticity) based on the level of prediction accuracy in general, and on the prediction accuracy against the phase‐space reconstruction parameters in particular (termed as the ‘inverse approach’). The results not only provide possible indications to the presence of nonlinear determinism in the river flow series studied, but also support, both qualitatively and quantitatively, the low correlation dimensions reported for such. Therefore, nonlinear deterministic methods are a viable complement to linear stochastic ones for studying river flow dynamics, if sufficient caution is exercised in their applications and in interpreting the outcomes. Copyright © 2006 John Wiley & Sons, Ltd.     

Plant root traits affecting the resistance of soils to concentrated flow erosion

The effect of plant species on erosion processes may be decisive for long‐term soil protection in degraded ecosystems. The identification of functional effect traits that predict species ability for erosion control would be of great interest for ecological restoration purposes. Flume experiments were carried out to investigate the effect of the root systems of three species having contrasted ecological requirements from eroded marly lands of the French Southern Alps [i.e. Robinia pseudo acacia (tree), Pinus nigra austriaca (tree) and Achnatherum calamagrostis (grass)], on concentrated flow erosion rates. Ten functional traits, describing plant morphological and biomechanical features, were measured on each tested sample. Analyses were performed to identify traits that determine plant root effects on erosion control. Erosion rates were lowest for samples of Robinia pseudo acacia, intermediate in Achnatherum calamagrostis and highest in Pinus nigra austriaca. The three species also differed strongly in their traits. Principal components analysis showed that the erosion‐reducing potential of plant species was negatively correlated to root diameter and positively correlated to the percentage of fine roots. The results highlighted the role of small flexible roots in root reinforcement processes, and suggested the importance of high root surface and higher tensile strength for soil stabilization. By combining flume experiment to plant functional traits measurements, we identified root system features influencing plant species performance for soil protection against concentrated flow erosion. Plant functional traits related to species efficiency for erosion control represent useful tools to improve the diagnosis of land vulnerability to erosion, plant community resistance and the prediction of ecosystem functioning after ecological restoration. Copyright © 2012 John Wiley & Sons, Ltd.     

Nonlinear model reduction of unconfined groundwater flow using POD and DEIM

Nonlinear groundwater flow models have the propensity to be overly complex leading to burdensome computational demands. Reduced modeling techniques are used to develop an approximation of the original model that has smaller dimensionality and faster run times. The reduced model proposed is a combination of proper orthogonal decomposition (POD) and the discrete empirical interpolation method (DEIM). Solutions of the full model (snapshots) are collected to represent the physical dynamics of the system and Galerkin projection allows the formulation of a reduced model that lies in a subspace of the full model. Interpolation points are added through DEIM to eliminate the reduced model's dependence on the dimension of the full model. POD is shown to effectively reduce the dimension of the full model and DEIM is shown to speed up the solution by further reducing the dimension of the nonlinear calculations. To show the concept can work for unconfined groundwater flow model, with added nonlinear forcings, one-dimensional and two-dimensional test cases are constructed in MODFLOW-OWHM. POD and DEIM are added to MODFLOW as a modular package. Comparing the POD and the POD-DEIM reduced models, the experimental results indicate similar reduction in dimension size with additional computation speed up for the added interpolation. The hyper-reduction method presented is effective for models that have fine discretization in space and/or time as well as nonlinearities with respect to the state variable. The dual reduction approach ensures that, once constructed, the reduced model can be solved in an equation system that depends only on reduced dimensions.     

Experimental study of consolidation properties of unsaturated soils during draining

Changes in groundwater elevation may cause a change in the net normal stress and matric potential within the soil mass, which results in volume changes of unsaturated soil. This research investigated the relationship between the drawdown of groundwater and the characteristics of volumetric compressibility of unsaturated soil. Sand column experiments were designed and conducted to measure the volume changes of coarse and fine sands under different types of drainage conditions at fast and slow drainage rates. The finite element program FEMWATER was calibrated and used to simulate the distributions of stress, tension and moisture content within the sands. Finally, based on the changes of net normal stress and matric potential and the observed volume change of the sands, a least‐square method was applied to determine the volumetric consolidation parameters of the unsaturated soils. Copyright © 2004 John Wiley & Sons, Ltd.     

On the controls of preferential flow in soils of different hillslope position and lithological origin

Soils derived from different lithologies and their controls on preferential flow remain underexplored in forested landscapes. In the same lithology, the propensity for preferential flow occurrence at different hillslope positions also remains largely elusive. By utilizing a soil moisture response time method, we compared preferential flow occurrence between a shale site (Shale Hills, silt loam soils) and a sandstone site (Garner Run, sandy loam soils) at four hillslope positions: ridge-top, North- and South-facing mid-slopes and toe slope, for over 2 years. The catchments are neighbouring and covered by temperate forest. For the four hillslope positions, Shale Hills had higher preferential flow frequencies compared to Garner Run. Between these two catchments, the South-facing mid-slope sites showed the highest contrasts in preferential flow frequency (33.5% of events at Shale Hills vs. 8.8% at Garner Run) while the ridge-top sites showed the lowest contrasts (18.7 vs. 13.2%). Additionally, over the unfrozen period, for seven out of eight monitoring sites, drier antecedent conditions tended to be more favourable for preferential flows to occur, with significant (p < .01) relationships at two sites. Except for the South-facing mid-slope sites, both Shale Hills and Garner Run had two preferential flow pathways. The characteristic preferential flow pathways at Shale Hills were the B_w and C horizons, and for Garner Run, preferential flow moved from the E/AE horizon to the B_w horizon. This study shows that shale-derived soils tended to have higher preferential flow occurrence than sandstone soils, but hillslope positions exhibit different levels of contrasts. More effort should be paid to study the impact of lithology on preferential flows in the context of land surface modelling and biogeochemical reactions to improve ecosystem services of headwater catchments.