An Analytical Solution for Predicting Transient Seepage into Partially Penetrating Ditch Drains Receiving Water from a Ponded Field

A transient analytical model is worked out for predicting seepage from a ponded field of infinite extent to a network of equally spaced ditch drains in a homogeneous and anisotropic soil underlain by an impervious barrier at a finite distance from the surface of the soil. The solution can account for finite width and finite level of water in the ditches, finite penetration of the drains in the soil, and also a variable ponding field at the surface of the soil. The study highlights the fact that the transient state duration of a partially penetrating ponded drainage scenario may be considerable should the drains be dug in a lowly conductive soil with a high storage coefficient, particularly if the underlying impervious layer lies at a large distance from the bottom of the ditches and the separation between the adjacent ditches is also large at the same time.     

Exact solution for horizontal displacement at center of the surface of an elastic half space under horizontal impulsive punch loading

The exact analytical solution for the horizontal displacement at the center of the surface of an elastic half space under an impulsive loading having the same spatial distribution as the contact stresses that arise underneath a rigid disk when subjected to a static, horizontal load, is obtained using the Cagniard–De Hoop method. The solution can be used to study the dynamical interaction between soil and structures, and can also be used to assess numerical computations with a finite element or a boundary element program.     

Local‐ and field‐scale infiltration into vertically non‐uniform soils with spatially‐variable surface hydraulic conductivities

We studied the problem of local‐ and field‐scale infiltration over a particular class of heterogeneous soils. At the local scale, the soils are described as being vertically non‐uniform, with the saturated hydraulic conductivity continuously decreasing with depth according to a power law function. Analogous to the Green–Ampt model, analytical expressions are first developed for local‐scale infiltration using a sharp front approximation, and model results are compared with numerical solutions of the Richards equation. These results show that saturation does not occur from below in soils with such vertical non‐uniformity, thereby allowing for the use of a sharp front approximation. Because of vertical non‐uniformity, ponding conditions are achieved locally even for rainfall rates less than the surface saturated hydraulic conductivity. Furthermore, infiltration rates asymptotically approach zero at long times. To determine field‐scale infiltration properties, the spatial variability in the surface saturated hydraulic conductivity is represented by a log‐normal random field. Using cumulative infiltration as the independent variable, expressions are developed for the ensemble mean of field‐scale infiltration and the expected time for a given depth of water to infiltrate over the field. Surface horizontal heterogeneity is found to control field‐scale infiltration at small times, whereas local vertical non‐uniformity exerts a strong control at long times. Copyright © 2011 John Wiley & Sons, Ltd.     

Torsional and coupled vibrations of embedded footings

An approximate analytical solution is presented for torsional vibrations of footings partially embedded into a semi-infinite medium or a stratum. Simple formulas derived for pure torsional motion make it possible to apply a correction for the effect of embedment to the known solutions of surface footings. The solution completes an approach to the analysis of all modes of footing vibrations, including the coupled modes. The approach to coupled modes is illustrated by the solution of coupled response involving horizontal translation, rocking and torsion. Formulas are presented for stiffness and damping coefficients that can be used in the analysis of embedded footings or structures supported by such footings Field experiments were conducted with concrete footings featuring circular, square and rectangular bases and variable embedment depths. The experimental results were compared with theoretical predictions of pure torsional vibrations.     

Improvement of TOPLATS‐based discharge predictions through assimilation of ERS‐based remotely sensed soil moisture values

In this paper, we investigate the possibility to improve discharge predictions from a lumped hydrological model through assimilation of remotely sensed soil moisture values. Therefore, an algorithm to estimate surface soil moisture values through active microwave remote sensing is developed, bypassing the need to collect in situ ground parameters. The algorithm to estimate soil moisture by use of radar data combines a physically based and an empirical back‐scatter model. This method estimates effective soil roughness parameters, and good estimates of surface soil moisture are provided for bare soils. These remotely sensed soil moisture values over bare soils are then assimilated into a hydrological model using the statistical correction method. The results suggest that it is possible to determine soil moisture values over bare soils from remote sensing observations without the need to collect ground truth data, and that there is potential to improve model‐based discharge predictions through assimilation of these remotely sensed soil moisture values. Copyright © 2002 John Wiley & Sons, Ltd.     

Investigation of sloshing damping in baffled rectangular tanks subjected to the dynamic excitation

In this research, an analytical model is developed to estimate the hydrodynamic damping ratio of liquid sloshing for wall bounded baffles using the velocity potential formulation and linear wave theory. Here, an analytical solution approach and experimental investigations are conducted for describing the hydrodynamic damping which is provided by vertical and horizontal baffles in partially filled rectangular liquid tanks. In order to evaluate the accuracy of the analytical solution which is developed in present work, a series of experiments are carried out with a rectangular liquid tank excited by harmonic oscillation. The parametric study is conducted on the damping efficiencies of both vertical and horizontal baffles with various dimensions and locations. According to the results of the present investigations, the hydrodynamic damping is significantly affected by the size and location of baffles. Furthermore, the validity of the developed analytical approach as well as the effectiveness of various baffle configurations are discussed. Finally, a simple approach is proposed for estimating the damping ratios of the baffles during earthquake motions.     

Soil reaction to lateral harmonic pile motion

The analytical representation of dynamic soil reaction to a laterally-loaded pile using 3D continuum modeling is revisited. The governing elastodynamic Navier equations are simplified by setting the dynamic vertical normal stresses in the soil equal to zero, which uncouples the equilibrium in vertical and horizontal directions and allows a closed-form solution to be obtained. This physically motivated approximation, correctly conforming to the existence of a free surface, was not exploited in earlier studies by Tajimi, Nogami and Novak and leads to a weaker dependence of soil response to Poisson's ratio which is in agreement with numerical solutions found in literature. The stress and displacement fields in the soil and the associated reaction to an arbitrary harmonic pile displacement are derived analytically using pertinent displacement potentials and eigenvalue expansions over the vertical coordinate. Both infinitely long piles and piles of finite length are considered. Results are presented in terms of dimensionless parameters and graphs that highlight salient aspects of the problem. A detailed discussion on wave propagation and cutoff frequencies based on the analytical findings is provided. A new dimensionless frequency parameter is introduced to demonstrate that the popular plane-strain model yields realistic values for soil reaction only at high frequencies and low Poisson's ratios.     

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.     

Analytical solutions of one‐dimensional infiltration before and after ponding

This paper is a continuation of previous research, which obtained a convenient solution for arbitrary surface fluxes before ponding. By means of Fourier Transformation this has been extended to derive analytical solutions of a linearized Richards' equation for arbitrary input fluxes after surface saturation. Copyright © 2003 John Wiley & Sons, Ltd.     

An analytical solution for ground water transit time through unconfined aquifers

An exact, closed-form analytical solution is developed for calculating ground water transit times within Dupuit-type flow systems. The solution applies to steady-state, saturated flow through an unconfined, horizontal aquifer recharged by surface infiltration and discharging to a downgradient fixed-head boundary. The upgradient boundary can represent, using the same equation, a no-flow boundary or a fixed head. The approach is unique for calculating travel times because it makes no a priori assumptions regarding the limit of the water table rise with respect to the minimum saturated aquifer thickness. The computed travel times are verified against a numerical model, and examples are provided, which show that the predicted travel times can be on the order of nine times longer relative to existing analytical solutions.     

Dynamics of rigid strip foundations embedded in orthotropic elastic soils

This study is concerned with the dynamic response of an arbitrary shaped rigid strip foundation embedded in an orthotropic elastic soil. The foundation is subjected to time-harmonic vertical, horizontal and moment loadings. The boundary-value problem related to an embedded foundation is analysed by using the indirect boundary integral equation method. The kernel functions of the integral equations are displacement and traction Green's functions of an anisotropic elastic half plane. Exact analytical solutions are used for the Green's functions. The boundary integral equation is solved by using numerical techniques. Selected numerical results are presented for the impedances of rectangular and semi-circular rigid strip foundations embedded in four types of anisotropic soils. A discussion on the influence of soil anisotropy and frequency of excitation on the impedances is presented. The versatility of the analysis is demonstrated by considering the through soil interaction between two semi-circular strip foundations.     

Linear and angular momentum conservation in hydraulic jump in diverging channels

This paper addresses the integral conservation of linear and angular momentum in the steady hydraulic jump in a linearly diverging channel.The flow is considered to be divided into a mainstream that conveys the total liquid discharge, and a roller where no average mass transport occurs. It is assumed that no macroscopic rheological relationship holds, so mass, momentum and angular momentum integral balances are independent relationships. Normal stresses are assumed to be hydrostatic on vertical, cylindrical surfaces. Viscous stresses are assumed to be negligible with respect to turbulent stresses. Assuming that the horizontal velocity distribution in the mainstream is uniform and that the horizontal momentum and angular momentum in the roller are negligible with respect to their mainstream counterparts, an analytical solution is obtained for the free surface profile of the flow. This solution is fundamental for finding the sequent depths and their positions. Consequently, it permits solving for the length of the jump, which is assumed to be equal to the length of the roller. Mainstream and roller thicknesses can also be derived from the present solution. This model may also be theoretically used to derive the average shear stresses exerted by the roller on the mainstream and the power losses per unit weight. This second relationship, which returns the well-known classical expression for total power loss in the jump, demonstrates that the strongly idealized mechanical model proposed here is internally consistent.     

Simplified subgrade model for three-dimensional soil-foundation interaction analysis

A simple mechanical model is presented for the three-dimensional dynamic soil-structure interaction analysis of surface foundations. The model is made of one-dimensional vertical beams with distributed mass and horizontal springs which interconnect the two adjacent beams. Its parameters are rather uniquely related with the soil properties alone and thus are minimally dependent on the loading condition and the foundation conditions like geometry, flexibility and size. Formulations are provided to determine the model parameters from the soil properties. Solving the governing equations of this model, expressions for the subgrade behavior in response to the applied load and soil-foundation interaction are developed in analytical forms for various cases. The dynamic and static response of three-dimensional surface foundations are computed by these expressions. It is verified that the model is well capable of reproducing the three-dimensional soil-structure interaction behavior.     

Occurrence of water ponding on soil surfaces depending on infiltration rates on Mongolian rangeland

The occurrence of water ponding on soil surfaces during and after heavy rainfall produces surface run‐off or surface water accumulation in low‐lying areas, which might reduce the water supply to soils and result in a reduction of the soil water that plants can use, especially in arid climates. On Mongolian rangeland, we observed ponded water on the surface of a specific soil condition subjected to a heavy rainfall of 30 mm/hr. By contrast, ponded water was not observed for the same type of soil where livestock grazing had been removed for 6–8 years via a fence or for nearby soil containing less clay. We measured the infiltration rate (the saturated hydraulic conductivity of the surface soil, K_s) of the three sites by applying ponded water on the soil surface (an intake rate test). The results showed that K_s in the rangeland was lower than the rainfall intensity in the site where water ponded on the soil surface; however, K_s of the soil inside of the fence has recovered to 3 times that of the soil outside of the fence to exceed the rainfall intensity. Heavy rainfall that exceeds the infiltration rate occurs several times a year at the livestock grazing site where we observed ponded water. Slight water repellency of the soil reduces rain infiltration to increase the possibility of surface ponding for the soil.     

A numerical model for simulating Hortonian overland flow on tropical hillslopes with vegetation elements

This paper describes a two‐dimensional hydrodynamic model that characterizes surface runoff process resulting from a varying rainfall intensity event, on an infiltrating soil surface. The soil surface has spatially varied soil physical, hydraulic and microtopographic characteristics. Infiltration process is modelled with the Philip two‐term equation and the time before ponding approximated with the time compression algorithm. Vegetation is modelled as a dynamic component with the modified Gash model. The equation is solved with a modified second order Leapfrog explicit finite difference scheme with centred time and space derivatives. The model was validated with standard analytical solutions. Evaluation with results from field campaigns in the Volta Basin of West Africa during the 2002 rainfall season indicates good agreement, with r² values ranging from 0·89 to 0·96. The developed method will be useful in studying the dynamics of surface runoff generation under complex microtopographic conditions, spatially varying soil hydraulic characteristics and temporally dynamic rainfall intensity, as found in many tropical catchments. Copyright © 2007 John Wiley & Sons, Ltd.     

Seasonal and event‐based drivers of runoff and phosphorus export through agricultural tile drains under sandy loam soil in a cool temperate region

Frequent algal blooms in surface water bodies caused by nutrient loading from agricultural lands are an ongoing problem in many regions globally. Tile drains beneath poorly and imperfectly drained agricultural soils have been identified as key pathways for phosphorus (P) transport. Two tile drains in an agricultural field with sandy loam soil in southern Ontario, Canada were monitored over a 28‐month period to quantify discharge and the concentrations and loads of dissolved reactive P (DRP) and total P (TP) in their effluent. This paper characterizes seasonal differences in runoff generation and P export in tile drain effluent and relates hydrologic and biogeochemical responses to precipitation inputs and antecedent soil moisture conditions. The generation of runoff in tile drains was only observed above a clear threshold soil moisture content (~0.49 m³·m^?3 in the top 10 cm of the soil; above field capacity and close to saturation), indicating that tile discharge responses to precipitation inputs were governed by the available soil‐water storage capacity of the soil. Soil moisture content approached this threshold throughout the non‐growing season (October – April), leading to runoff responses to most events. Concentrations of P in effluent were variable throughout the study but were not correlated with discharge (p > 0.05). However, there were significant relationships between discharge volume (mm) and DRP and TP loads (kg ha^?1) for events occurring over the study period (R² ≥ 0.49, p ≤ 0.001). This research has shown that the hydrologic and biogeochemical responses of tile drains in a sandy loam soil can be predicted to within an order of magnitude from simple hydrometric data such as precipitation and soil moisture once baseline conditions at a site have been determined. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Field Evaluation of Arid Soils Wetting Pattern in Subsurface Drip Irrigation Scheme

A field study evaluating wetted radius (Wr), downward depth (Dd), and upward movement (Um) under different emitter discharges and lateral depths was conducted. Four emitter discharges (2, 4, 8, and 16 L/h) and four lateral depths (0, 10, 20, and 30 cm) were tested in a clay loam soil. Relationships were found between the emitter discharge and lateral depth versus Wr, Dd, and Um. Wetting area at the surface occurs under different emitter discharges and lateral depths except at 30 cm lateral depth. At lateral depth of 0 and 10 cm, Wr and emitter discharge were positively correlated. The Dd was not affected by emitter discharge except for laterals installed at 20 cm depth. At 30 cm lateral depth, the correlations between each of Wr, Um, and Dd with emitter discharge were poor. The ratios of Wr/Dd and Um/Dd, with respect to emitter position, were less than unity over different emitter discharges and lateral depths. These results shed some light on the design of subsurface drip irrigation scheme so that the spacing between emitters should be determined based on the lateral depths and discharge of emitters. Evaporation losses were negligible for the 30‐cm‐lateral depth since the upward moisture movement has not reached the soil surface area at all discharge rates tested in the study.     

Analytical solutions of infiltration process under ponding irrigation

The objective of this paper is to simulate the progress of the soil water content distribution in the soil profile with a water table at the bottom of the soil profile during ponding irrigation. This simulation can be done by solving the two‐dimensional Richards's equation for the assimilation of the advancing water jet, which uses the conditions of the two exponential functional forms k = k_s e^αψ and θ = θ_r + (θ_s − θ_r) e^αψ to represent the hydraulic conductivity and volumetric water content, with ψ the pressure as the third variable. We assume that the ground surface becomes ponded and saturated as soon as the water flux passes the dry ground surface. By the technique of transformation, the analytical solution of these two‐dimensional Richards' equations has enabled figures of volumetric water content distribution to be obtained in successive time periods after irrigation. For the example of loam soil, it can simulate the variation of volumetric water content during and after irrigation in the soil profile. The analytical solutions of this paper reflect the real situation simulated, and can be applied to verify those complicated solutions from other analytical models. Copyright © 2005 John Wiley & Sons, Ltd.     

Heat as a tracer to estimate dissolved organic carbon flux from a restored wetland

Heat was used as a natural tracer to characterize shallow ground water flow beneath a complex wetland system. Hydrogeologic data were combined with measured vertical temperature profiles to constrain a series of two-dimensional, transient simulations of ground water flow and heat transport using the model code SUTRA (Voss 1990). The measured seasonal temperature signal reached depths of 2.7 m beneath the pond. Hydraulic conductivity was varied in each of the layers in the model in a systematic manual calibration of the two-dimensional model to obtain the best fit to the measured temperature and hydraulic head. Results of a series of representative best-fit simulations represent a range in hydraulic conductivity values that had the best agreement between simulated and observed temperatures and that resulted in simulated pond seepage values within 1 order of magnitude of pond seepage estimated from the water budget. Resulting estimates of ground water discharge to an adjacent agricultural drainage ditch were used to estimate potential dissolved organic carbon (DOC) loads resulting from the restored wetland. Estimated DOC loads ranged from 45 to 1340 g C/(m2 year), which is higher than estimated DOC loads from surface water. In spite of the complexity in characterizing ground water flow in peat soils, using heat as a tracer provided a constrained estimate of subsurface flow from the pond to the agricultural drainage ditch.