Ditch Drainage System Research Articles

Analytical solutions for predicting seepage in a layered ditch drainage system under Dirichlet and lagging Robin boundary conditions

ABSTRACT The present study proposes two analytical solutions for a layered ponded ditch drainage system with Dirichlet and lagging Robin boundary conditions. The flow domain is assumed to be saturated, layered, and anisotropic. The first analytical model considers flow to a ditch drainage network from a ponded field through a two-layered soil considering the Dirichlet boundary condition, whereas the second model is developed considering a lagging Robin condition at the ditch face and surface of the soil. The study highlights that the lagging Robin condition can better mimic the actual flow scenario as compared to the standard Robin boundary condition. A comparison study has been carried out to assess the top layer’s permissible depth under which a homogeneous drainage system with Robin boundary condition can approximate a layered drainage system. Further, the residence time distributions are observed to follow power-law-like distributions with heavier tails for both single and two-layered ditch drainage systems.

Experimental and Analytical Investigation of Ponded Ditch Drainage System with Temporal Boundaries

AbstractAn analytical solution is proposed for a two-dimensional, fully-penetrating ditch drainage system by considering the boundaries at the ditch face and at the soil surface to change with time...

Analytical Steady-State Solution for a Three-Dimensional Partially Penetrating Ditch Drainage System Receiving Water from an Uneven Ponding Field

AbstractA steady-state analytical solution is proposed for computing three-dimensional seepage into a partially penetrating ditch drainage system receiving water from an uneven ponding field of fin...

A two-dimensional transient analytical solution for a ponded ditch drainage system under the influence of source/sink

An analytical solution is developed for predicting two-dimensional transient seepage into ditch drainage network receiving water from a non-uniform steady ponding field from the surface of the soil under the influence of source/sink in the flow domain. The flow domain is assumed to be saturated, homogeneous and anisotropic in nature and have finite extends in horizontal and vertical directions. The drains are assumed to be standing vertical and penetrating up to impervious layer. The water levels in the drains are unequal and invariant with time. The flow field is also assumed to be under the continuous influence of time–space dependent arbitrary source/sink term. The correctness of the proposed model is checked by developing a numerical code and also with the existing analytical solution for the simplified case. The study highlights the significance of source/sink influence in the subsurface flow. With the imposition of the source and sink term in the flow domain, the pathline and travel time of water particles started deviating from their original position and above that the side and top discharge to the drains were also observed to have a strong influence of the source/sink terms. The travel time and pathline of water particles are also observed to have a dependency on the height of water in the ditches and on the location of source/sink activation area.

Analysis of three-dimensional transient seepage into ditch drains from a ponded field

An analytical solution in the form of infinite series is developed for predicting time-dependent three-dimensional seepage into ditch drains from a flat, homogeneous and anisotropic ponded field of finite size, the field being assumed to be surrounded on all its vertical faces by ditch drains with unequal water level heights in them. It is also assumed that the field is being underlain by a horizontal impervious barrier at a finite distance from the surface of the soil and that all the ditches are being dug all the way up to this barrier. The solution can account for a variable ponding distribution at the surface of the field. The correctness of the proposed solution for a few simplified situations is tested by comparing predictions obtained from it with the corresponding values attained from the analytical and experimental works of others. Further, a numerical check on it is also performed using the Processing MODFLOW environment. It is noticed that considerable improvement on the uniformity of the distribution of the flow lines in a three-dimensional ponded drainage space can be achieved by suitably altering the ponding distribution at the surface of the soil. As the developed three-dimensional ditch drainage model is pretty general in nature and includes most of the common variables of a ditch drainage system, it is hoped that the drainage designs based on it for reclaiming salt-affected and water-logged soils would prove to be more efficient and cost-effective as compared with designs based on solutions developed by making use of more restrictive assumptions. Also, as the developed model can handle three-dimensional flow situations, it is expected to provide reliable and realistic drainage solutions to real field situations than models being developed utilizing the two-dimensional flow assumption. This is because the existing two-dimensional solutions to the problem are actually valid not for a field of finite size but for an infinite one only.

Influences of specific ions in groundwater on concrete degradation in subsurface engineered barrier system.

Many disposal concepts currently show that concrete is an effective confinement material used in engineered barrier systems (EBS) at a number of low-level radioactive waste (LLW) disposal sites. Cement-based materials have properties for the encapsulation, isolation, or retardation of a variety of hazardous contaminants. The reactive chemical transport model of HYDROGEOCHEM 5.0 was applied to simulate the effect of hydrogeochemical processes on concrete barrier degradation in an EBS which has been proposed to use in the LLW disposal site in Taiwan. The simulated results indicated that the main processes that are responsible for concrete degradation are the species induced from hydrogen ion, sulfate, and chloride. The EBS with the side ditch drainage system effectively discharges the infiltrated water and lowers the solute concentrations that may induce concrete degradation. The redox processes markedly influence the formations of the degradation materials. The reductive environment in the EBS reduces the formation of ettringite in concrete degradation processes. Moreover, the chemical conditions in the concrete barriers maintain an alkaline condition after 300 years in the proposed LLW repository. This study provides a detailed picture of the long-term evolution of the hydrogeochemical environment in the proposed LLW disposal site in Taiwan.

Analysis of transient seepage into equally spaced ditch drains from a ponded field

An analytical solution is proposed for simulating transient seepage into a system of ditch drains placed in parallel in a homogeneous and anisotropic soil confined by an impermeable layer and receiving water from an infinitely extended ponded field. The solution assumes the ponding depth over the surface of the soil to be uniform and the soil fluid to be of constant density. The model can be applied for both equal and unequal water levels in adjacent drains. The accuracy of the developed solution is checked by comparing for a flow situation the hydraulic heads and streamlines as obtained from the proposed model with the corresponding results obtained from an available steady state solution of the problem as provided by Kirkham [14]. A numerical check on the proposed solution is also performed for a particular flow configuration of the problem in the transient zone. The study shows that flow in a ponded ditch drainage system is greatly influenced by anisotropy and directional conductivities of soils. The uniformity of surface flux distribution is found to be quite sensitive to the anisotropy ratio (the ratio of horizontal and vertical saturated hydraulic conductivities of soil) of a soil column – a higher anisotropy ratio favors and a low anisotropy ratio weakens this distribution. Furthermore, the time to attain steady state by a ditch drainage system can be considerable, particularly for situations where the drains are dug relatively deeper into a soil having a high anisotropy ratio. The analytical model presented here is significant as it can be used to design ditch drainage networks for reclaiming a salt-affected and/or waterlogged soil within a specified time.

Hydraulics of a Partially Penetrating Ditch Drainage System in a Layered Soil Receiving Water from a Ponded Field

AbstractThis study deals with the development of an analytical solution for predicting seepage into an array of ditch drains dug in a three-layered soil underlain by an impervious barrier and receiving water from a ponded field of infinite extent. The solution is of a general nature and can account for partial penetration, finite width and spacing of drains, finite depth of the impervious stratum, anisotropy of individual layers, and a uniform ponding distribution at the surface of the soil. The validity of the developed solution for the single-layered situation is checked by first reducing the proposed multilayered solution to that of a single-layered one by treating the conductivity of the layers as the same and then comparing for a few flow situations the hydraulic heads as predicted by the reduced model with corresponding values obtained from the analytical and experimental works of others. A numerical check on the developed analytical model for a multilayered soil is also carried out. The study shows...

Evaluation of drainage and tillage effect on watertable depth and maize yield in wet inland valleys in southwestern Nigeria

A study was conducted in three wet inland valley bottoms, namely, high (MHW), medium (MMW) and low (MLW) watertable sites to evaluate the effect of drained (D) and control (Do), and mound-tillage (MT), ridge-tillage (RT) and no-tillage (NT) treatments on watertable depth and yield of maize in 1990 wet and 1990/1991 dry season in southwestern Nigeria. The watertable depth averaged 30.0 cm in the drained plot and <15.0 cm in the control plot in 1990. The watertable tended toward its lowest depth averaging 44.8 cm in the drained and 26.2 cm in the control plot in 1990/1991. Soil moisture content was lower ( P<0.01) and air-filled porosity greater ( P<0.01) in the mound-tilled compared with the ridge tilled and no-till soils in both drained and control plots in 1990 and 1990/1991. Equally, green maize yield from the mound-tillage and ditch drainage system was greater ( P<0.01) than the ridge-tillage and no-tillage systems in both seasons. Maize may be grown successfully with a ditch drainage and mound-tillage system in the wet soils in inland valley bottoms regardless of their watertable regimes in southwestern Nigeria.

Modeling water-table fluctuations in a sloping aquifer with random hydraulic conductivity

To prevent environmental problems like water logging and increase in soil salinity which are responsible for the degradation of the top productive soils, an optimum ditch drainage design is required. For this purpose a knowledge of the spatio-temporal variation of the water table is essential. In this study the spatio-temporal variation of the water table in a sloping ditch drainage system has been modeled from a stochastic point of view, incorporating randomness in hydraulic conductivity to get the expression for the mean and the standard deviation of the water-table height. The hydraulic conductivity has been considered to be a realization of a log-normal distribution. Application of these expressions in the prediction of mean water-table variation with the associated error bounds has been demonstrated with the help of a ditch drainage problem of a sloping aquifer. The sensitivity analysis has also been carried out to see the effect of variability in the hydraulic conductivity on the water-table fluctuations. The error bounds quantified on the water-table height will thus help in the decision-making process for proper drainage design.

PHOSPHORUS AVAILABILITY AND SORPTION IN AN ATLANTIC COASTAL PLAIN WATERSHED DOMINATED BY ANIMAL-BASED AGRICULTURE

The Inland Bays watershed in southern Delaware is dominated by a large and growing poultry industry that uses land application as the primary means for disposal of manure. Runoff and drainage waters from an extensive ditch drainage system in the area eventually enter the Inland Bays. Phosphorus in these waters has been suggested as a contributing factor to eutrophication of the Inland Bays. Soil test P (STP, Mehlich 1, 0.05N HCI + 0.025N H2SO4) levels in cultivated and field border areas and P sorption maxima (PSM) were determined for selected profiles of agricultural fields and non-cultivated field borders. Relationships between PSM and soil properties and a rapidly determined p sorption index (PSI) were also investigated. STP in cultivated topsoils from 48 sites ranged from 43 to 632 mg/kg and from 42 to 568 mg/kg at 0–5 and 5–20 cm, respectively, relative to a high value for STP for agronomic crops of 35 mg/kg. STP levels were consistently greater in cultivated profiles than in field borders. Downward movement of P in some cultivated profiles occurred to a depth of 40 cm. PSM ranged from 95 to 2564 mg/kg in cultivated soils and from 200 to 2000 mg/kg in field borders. PSM was highly correlated (r = 90) with clay content and was consistently higher in subsoil horizons. When clay contents were similar, P sorption was usually greater in field borders than in cultivated fields. PSI was highly correlated with PSM (r† = 0.94) except when PSI exceeded 1400 mg/kg. This study suggests that past and current P management practices in the Inland Bays have increased soil P levels in this watershed to levels that may require much more intensive management of manure and fertilizer P in the future. Although subsoil horizons may prevent direct P leaching into groundwater, the high P values noted at the 0 to 5-cm depth and in some subsoils point to the need to assess the potential for soluble P losses in runoff and drainage waters.

Water table fluctuation in a sloping aquifer with transient recharge

An analytical solution of the linearized Boussinesq equation with a complex transient recharge function is presented to describe the water table fluctuation in a sloping aquifer of finite width. The solution is obtained by using an eigenvalue-eigenfunction expansion method. Some previously known solutions for different recharge functions have been shown to be special cases of the present general solution. Applications of the solutions in prediction of the spatio-temporal distribution of the water table in a ditch drainage system are illustrated with the help of synthetic examples.

On the predictability of the water-table variation in a ditch-drainage system

The irrigation in regions of brackish groundwater in many parts of the world results in the rise of the water-table very close to the groundsurface. The salinity of the productive soils is therefore increased. A proper layout of the ditch-drainage system and the prediction of the spatio-temporal variation of the water table under such conditions are of crucial importance in order to control the undesirable growth of the water-table. In this paper, an approximate solution of the nonlinear Boussinesq equation has been derived to describe the water-table variations in a ditch-drainage system with a random initial condition and transient recharge. The applications of the solution is discussed with the help of a synthetic example.

Water table fluctuation with a random initial condition

The nonlinear Boussinesq equation is used to understand water table fluctuations in various ditch drainage problems. An approximate solution of this equation with a random initial condition and deterministic boundary conditions, recharge rate and aquifer parameters has been developed to predict a transient water table in a ditch-drainage system. The effects of uncertainty in the initial condition on the water table are illustrated with the help of a synthetic example. These results would find applications in ditch-drainage design.

Non-Darcy Flow and its Implications to Seepage Problems

Analytical solutions for the problems of drainage spacing in a ditch drainage system and steady-state seepagee through confined aquifer of variable thickness incorporating Izbash's nonlinear velocity-gradient response v=Min are presented. The effect of nonlinearity in the flow response on the drainage spacing, discharge characteristics, and piezometric pressure distribution in relation to the corresponding Darcian linear case is brought out. The solutions derived show that nonrecognition of even a weakly non-Darcy flow would lead either to an uneconomical or unsafe (depending on the value of non-Darcy parameter n) drainage spacing for ditch drainage problems and would lead to considerable over or under prediction of discharge for confined aquifer problem. Apart from the previously mentioned analytical solutions, a perspective view of non-Darcy flow through porous media is incorporated and its importance in various drainage projects is examined.

A treatment of the gappy drain problem in drainage theory

An expression is derived for the relationship between the maximum water-table height and steady-state rainfall rate for the particular gappy drainage system provided by parallel vertically sided ditches which are dug to a horizontal impermeable floor and whose banks are shored up by means of impermeable shutters. This indicates that the effect of the gaps on the water-table height is not only dependent on the width and spacing of the gaps along the drainage channel, but also on the drain spacing. For drain tubes laid on the impermeable floor of a hydraulic model sand tank experimental results are in agreement with those predicted for a similar ditch-drainage system, but for drain tubes laid at an effectively infinite height above the impermeable floor, water-tables are higher than predicted.