Analytical Solution for Transient Water Table Heights and Outflows from Inclined Ditch-Drained Terrains

This paper presents two analytical solutions of the linearized Boussinesq equation for an inclined aquifer, drained by ditches, subjected to a constant recharge rate. These solutions are based on different initial conditions. First, the transient solution is obtained for an initially fully saturated aquifer. Then, an analytical expression is derived for the steady state solution by allowing time to approach infinity. As this solution represents the groundwater table shape more realistically, this water table profile is used as an initial condition in the derivation of the second analytical solution for the groundwater table height, and the in- and outflow into the ditches. The solutions allow the calculation of the transient behavior of the groundwater table, and its ouflow, due to changing percolation rates or water level heights in both ditches.     

Water Table Rise in Sloping Aquifer due to Canal Seepage and Constant Recharge

Analytical solutions of the linearized Boussinesq equation and a fully implicit finite-difference numerical solution of the nonlinear Boussinesq equation were obtained to study transient and steady-state water table rise in a homogeneous, isotropic, and incompressible unconfined sloping aquifer. The rise was due to seepage from two canals located at different elevations above the sloping impermeable barrier and constant recharge from the land surface. Proposed analytical solutions were verified with existing analytical solutions for a horizontal aquifer and were found in close agreement. The effect of recharge and slope of the impermeable barrier on water table rise predicted by both analytical and numerical solutions was studied by considering a numerical example. The effect of the linearization of the Boussinesq equation on water table rise was also studied by comparing the water table heights predicted by the numerical solution with those computed from the analytical solution. The analytical solution overestimates water table elevations compared to those obtained from the numerical solution, and the difference in water table in the middle region decreases with increase in time.     

Water Table Fluctuation in the Presence of a Time-Varying Exponential Recharge and Depth-Dependent ET in a Two-Dimensional Aquifer System with an Inclined Base

An analytical solution is presented for water table fluctuation between ditch drains in presence of exponential recharge and depth-dependent evapotranspiration (ET) from groundwater table in a two-dimensional gently sloping aquifer. The groundwater head above the drain is small compared to the saturated thickness of the aquifer. A sound mathematical transformation is devised to transform the two-dimensional groundwater flow equation into a simple form, which makes possible to obtain an analytical solution. The transient midpoint water table variations from the proposed solution compare well with the already existing solutions for horizontal aquifer. A numerical example is used to illustrate the combined effect of depth-dependent ET coupled with a time-varying exponential recharge on the water table fluctuation. The inclusion of a depth-dependent ET in the solution results in water table decline at a faster rate as compared to the case when ET is not considered. With an increase in slope of the aquifer base, water table profiles become asymmetric and the water table divide shifts towards the lower drain. The height of the water table profiles increases on moving away from the boundary of the aquifer and the highest level of the ground water table is obtained in the central portion of the aquifer basin due to the presence of drainage ditches on the aquifer boundary. When the effect of ET is incorporated in combination with recharge, the analytical solution results in accurate and reliable estimates of water table fluctuations under situations subjected to a number of controlling factors. This study will be useful for alleviation of drainage problems of the aquifers receiving surface recharge and surrounded by streams.     

Unsteady Solution for Well Recharge in a Low Diffusive Aquifer

Finite aquifer solution exists for the constant head in a fully penetrating well. Their use for well recharge is limited, as they do not permit simultaneous computation of unsteady wellhead pressure and variable recharge rate. In the present paper semianalytical solutions are presented for well recharge under variable head boundary condition. These solutions were developed using the method of separation of variables and Duhamel’s convolution theorem. The solution developed in the paper was verified with the Jacob-Lohman solution and subsequently validated using field data pertinent to constant-head boundary conditions. Subsequently for variable head boundary condition such an appropriate background was found missing in the literature.     

Drainage of Sloping Lands with Variable Recharge Model Validation and Applications

Semianalytical transient equations describing the behavior of water tables in subsurface drained soils when drains rest on a sloping impervious barrier have been derived previously and represent the bases of the SIDRA model. To validate (SIDRA), water table elevations and drainflow rates have been monitored for six years in the French Alps on fields with a slope of 8%. The predicted drain flow rates and water table shapes compare reasonably well with data of a drainage experiment site but the improvement provided by taking the slope into consideration was limited. Running the model with different slopes confirmed that high water table elevations and peak flows were not significantly changed with a slope of 8%. As could be predicted from the analysis in steady state, low water table elevations were the most affected by slope. With the soil parameters of the field experiment and from an analysis in tail recession conditions, it was shown that there is a clear threshold of 12% slope below which the slope has no significant influence and can be neglected in drainage design.     

Tide-Induced Water Table Fluctuations in Coastal Aquifers Bounded by Rhythmic Shorelines

Previous studies on tidal water table dynamics in unconfined coastal aquifers have focused on the inland propagation of oceanic tides in the cross-shore direction based on the assumption of a straight coastline. Here, two-dimensional analytical solutions are derived to study the effects of rhythmic coastlines on tidal water table fluctuations. The computational results demonstrate that the alongshore variations of the coastline can affect the water table behavior significantly, especially in areas near the centers of the headland and embayment. With the coastline shape effects ignored, traditional analytical solutions may lead to large errors in predicting coastal water table fluctuations or in estimating the aquifer’s properties based on these signals. The conditions under which the coastline shape needs to be considered are derived from the new analytical solution.     

Potential for 17β-Estradiol and Estrone Degradation in a Recharge Aquifer System

The potential for degradation of two important endocrine disrupting chemicals, 17β-estradiol (E2) and estrone (E1) in a wastewater effluent recharged aquifer system was assessed using lab scale microcosms. Biotransformation by microorganisms present in the aquifer material was found to be the major mode of removal for both organic contaminants in the microcosms. The addition of ultrafiltered secondary effluent, simulating recharge of aquifer, did not significantly alter the behavior of both E2 and E1 in the aquifer microcosms. A significant difference in E2 removal rates in microcosms that received E2 as a concentrated stock in methanol as opposed to direct dissolution of E2 into groundwater shows that the presence of methanol could alter the biodegradation kinetics of the organic pollutant of interest. The rapid utilization of methanol by indigenous methanol degraders, which was present as an alternative carbon substrate, caused rapid depletion of oxygen and, hence, development of anoxic conditions in the microcosms. Increased oxygen supply led to corresponding improved E2 biotransformation rates, indicating that E2 degradation under anoxic conditions was much slower than under aerobic conditions. On the other hand, in the presence of a high initial concentration of methanol, E1 was more persistent in the medium under aerobic conditions than under anoxic conditions. Apparently, the initial high concentration of methanol had an inhibitory effect on aerobic E1 degraders in the microcosms.     

Comparative Study of SVMs and ANNs in Aquifer Water Level Prediction

In this research, a data-driven modeling approach, support vector machines (SVMs), is compared to artificial neural networks (ANNs) for predicting transient groundwater levels in a complex groundwater system under variable pumping and weather conditions. Various prediction horizons were used, including daily, weekly, biweekly, monthly, and bimonthly prediction horizons. It was found that even though modeling performance (in terms of prediction accuracy and generalization) for both approaches was generally comparable, SVM outperformed ANN particularly for longer prediction horizons when fewer data events were available for model development. In other words, SVM has the potential to be a useful and practical tool for cases where less measured data are available for future prediction. The study also showed high consistency between the training and testing phases of modeling when using SVM compared to ANN. While for the proposed SVM model the relative error of mean square error increased by an average of 42% from the training phase to testing the phase, the corresponding testing error of the ANN model raised by approximately seven times the training error.     

Water Table Management to Improve Drainage Water Quality in Semiarid Climatic Conditions of Iran

A lysimeter study was conducted in the field in Karaj, Iran to investigate the effects of water table management on water quality of subsurface drainage effluents. Drain volumes, nitrate-N concentration, phosphorus concentration, and electrical conductivity of drain effluents were monitored during the growing seasons of alfalfa (Medicago scutellata). Totally 12 lysimeters consisted of four treatments were used in this study, of which nine of them were equipped with subirrigation (SI) and the other three with free drainage (FD) systems. Annual alfalfa (Medicago scutellata) was planted in all lysimeters. Water table levels were kept at 30 cm (SI30), 50 cm (SI50), and 70 cm (SI70) below the soil surface in SI-lysimeters and more than 100 cm below the soil surface in FD-lysimeters. The results of this 2-year study showed a significant reduction in nitrate-N concentrations in SI-lysimeters compared to FD-lysimeters. In 2005, the mean nitrate-N concentrations in drainage effluent were reduced by 84% in the SI30 and by 82% in the SI50, relative to FD. Similarly, in 2006, drain water depth and nitrate-N concentrations were significantly reduced relative to FD. The forage dry matter production from SI30 and SI50 were significantly higher than those from FD in both years. In 2006, the average of dry matter production was increased by 69 and 89% by the SI30 and SI50, respectively, relative to FD. The average electrical conductivity of drainage water was reduced in SI lysimeters compared to FD lysimeters that meet Iranian standard level (3 dS/m). There are no statistically significant differences in phosphorous concentration in drainage water of different treatments. Finally, the results of this 2-year study indicate that the water table management practices are economically and environmentally feasible in Iran in order to have a sustainable agriculture.     

Sustainable Root Zone Salinity and Shallow Water Table in the Context of Land Retirement

This study uses five years of field data from the Land Retirement Demonstration Project located in western Fresno County of California to develop a comprehensive theoretical and numerical modeling framework to evaluate the specific site conditions required for a sustainable land retirement outcome based on natural drainage. Using field data, principles of mass balance in a control volume, the HYDRUS-1D software package for simulating one-dimensional movement of water, heat, and multiple solutes in variably-saturated media, and a model-independent parameter optimizer, the processes of soil water and solute movement in root zone and deep vadose zone were investigated. The optimization of unsaturated soil hydraulic parameters and downward flux (natural drainage) from the control volume against observed vadose zone salinity levels and shallow groundwater levels yield difficult to obtain natural drainage rate as a function of water table height within the control volume. The results show that the unsaturated soil hydraulic properties and the downward flux from the soil profile are the critical parameters. A “natural drainage approach” to sustainable land management for drainage-impaired land is proposed. With this approach it is feasible to design a sustainable land use regimen for drainage-impaired lands in general and retired lands in particular.     

Water Table Fluctuation between Drains in the Presence of Exponential Recharge and Depth-Dependent Evapotranspiration

A linearized form of the Boussinesq equation was solved analytically to predict the water table fluctuation in subsurface drained farmland in the presence of recharge and evapotranspiration (ET). The recharge was assumed to be variable with time and the ET considered decreasing linearly with a decrease in the water table height above the drains. The proposed analytical solution was verified for special cases with the existing solutions. There was a close match between the solutions. Applications of the solution in prediction of the water table height in a drainage system are illustrated with the help of physical examples.     

Effects of Long-Term Dynamic Loading and Fluctuating Water Table on Helical Anchor Performance for Small Wind Tower Foundations

The application of this study is to use helical anchors as a foundation system for small wind tower (1–10?kW) guyed cables. Helical anchors are currently used to anchor guyed cables of cell or transmission towers. However, the increased dynamic vibrations a wind turbine adds to the tower and foundation system under working loads, as well as extreme environmental conditions (e.g., straight line winds, ice load, or sudden furling shocks), require additional knowledge about the behavior of helical anchors. These field conditions were simulated in this study from tower-instrumented field data on wind speed and tower response. These tower responses were then transmitted to the helical anchors through an extensive, large-scale testing program that included monitoring the performance of the helical anchor foundation under dynamic loads, subject to natural variations in both wind regimes, precipitation (water level) and variations in helical anchor geometry. This paper compares the uplift prediction methods used in helical anchor design as well as discusses the effects of long-term dynamic loading and fluctuating water table on helical anchor performance.     

Fully Nonlinear Boussinesq-Type Equations for Waves and Currents over Porous Beds

The paper introduces a complete set of Boussinesq-type equations suitable for water waves and wave-induced nearshore circulation over an inhomogeneous, permeable bottom. The derivation starts with the conventional expansion of the fluid particle velocity as a polynomial of the vertical coordinate z followed by the depth integration of the vertical components of the Euler equations for the fluid layer and the volume-averaged equations for the porous layer to obtain the pressure field. Inserting the kinematics and pressure field into the Euler and volume-averaged equations on the horizontal plane results in a set of Boussinesq-type momentum equations with vertical vorticity and z-dependent terms. A new approach to eliminating the z dependency in the Boussinesq-type equations is introduced. It allows for the existence and advection of the vertical vorticity in the flow field with the accuracy consistent with the level of approximation in the Boussinesq-type equations for the pure wave motion. Examination of the scaling of the resistance force reveals the significance of the vertical velocity to the pressure field in the porous layer and leads to the retention of higher-order terms associated with the resistance force. The equations are truncated at O(μ4), where μ = measure of frequency dispersion. An analysis of the vortical property of the resultant equations indicates that the energy dissipation in the porous layer can serve as a source of vertical vorticity up to the leading order. In comparison with the existing Boussinesq-type equations for both permeable and impermeable bottoms, the complete set of equations improve the accuracy of potential vorticity as well as the damping rate. The new equations retain the conservation of potential vorticity up to O(μ2). Such a property is desirable for modeling wave-induced nearshore circulation but is absent in existing Boussinesq-type equations.     

Water Quality Aspects of Irrigation and Drainage: Past History and Future Challenges for Civil Engineers

This paper presents a brief history of irrigation and drainage related to ASCE activities on its Jubilee. This paper discusses legislation and policies that affect irrigation and drainage practices, water quality constituents of increasing concern in irrigation and drainage practices, and presents a prognosis on the future of declining freshwater resources available for irrigated agriculture and growing water quality problems in irrigation and drainage. Civil engineers in ASCE’s Irrigation and Drainage Division have compiled an 80-year history of highly meritorious service and accomplishments. In the next millennium, civil engineers will face a formidable challenge in managing and protecting the precious freshwater resources in the U.S.     

Mathematical Formulation and Validation of a Mixed Finite Element–Finite Difference Model for Simulating Phreatic Surfaces

The phreatic surface in an unconfined aquifer exists as a movable interface between the saturated and unsaturated zones. The movement of the phreatic surface depends on recharge, hydraulic conductivity, porosity, and horizontal and vertical flows. The location of the phreatic surface helps define the variably saturated flow domain in the subsurface. The variably saturated flow process in the subsurface is described by a parabolic partial differential equation. In this equation, the hydraulic conductivity and soil moisture capacity are used as the subsurface characteristics. The location of the phreatic surface is governed by a first-order partial differential equation. The governing parabolic partial differential equation is solved using a variational finite element formulation. The first order phreatic surface equation is then solved by loosely coupling with the governing parabolic partial differential equation describing the variably saturated flow. In the present study, a two-dimensional space is used to investigate the movement of the phreatic surface in a variably saturated unconfined flow domain. Based on the time-varying solutions of hydraulic heads, the location of the phreatic surface is simulated in a finite two-dimensional space.     

Effect of Covers for Soil and Water Conservation Using Tilting Flume

The effect of stone and vegetative covers was evaluated for soil and water conservation in a waterway on alfisols. Experiments were conducted on a hydraulic tilting flume under simulated flow (93 and 40 cm2?s?1) and slope (0.1, 1.0, 3.0, and 5.0%) conditions. The depth of soil was maintained at 0.35 m over a perforated bed to facilitate deep drainage. A comparative study of bare soil, stone cover (50%), and vegetative cover (50%) is made to evaluate soil loss, deep drainage, Manning’s roughness coefficient, and the Froude number. The study has revealed that stone cover is more effective than vegetative cover at lower discharge in reducing the flow velocity, and thereby soil erosion. Deep drainage has been reduced from lower to higher discharge for all the slopes with cover measures, including bare soil. It is found that cover measures are necessary beyond 3% slope in order to prevent rill erosion in alfisols.     

Graphical Solutions for Hillslopes: Discharge, Head, and Velocity Diagrams

Graphical solutions for discharge (Q), head (h), and velocity are presented for general recharge conditions on hillslopes underlain by a horizontal impermeable layer and with a constant-head boundary at the toe and a no-flow boundary upslope. Recharge (R) may be defined for different sections of the hillslope having constant, but not necessarily equal, hydraulic conductivities. Q diagrams are determined using conservation of mass, which requires that the change in Q between two points on a hillslope be equal to the area of the R diagram between them. h diagrams have “exact” (with Dupuit’s assumptions) values for head. Darcy velocity, q, diagrams may be made by dividing the value of the Q diagram at any point by the value of the h diagram at that point. Pore velocity diagrams may be made by dividing values from the q diagrams by the effective porosity. Three examples illustrate the graphical solutions for various scenarios.     

Development and Evaluation of Soil Moisture-Based Seepage Irrigation Management for Water Use and Quality

A 2-year study was conducted at a seepage-irrigated vegetable farm in south Florida to develop and evaluate an improved, soil moisture-based irrigation management practice that could potentially reduce irrigation water use, prevent water quality impairment, and maintain or improve crop yield. The improved practice reduced irrigation water use by 36% compared to the conventional irrigation management. Moreover, the improved practice also increased rainfall retention and decreased runoff events by lowering the water table 13?cm compared to the conventional practice. Total dissolved phosphorus (P) concentrations in groundwater were higher (p<0.01) for the improved practice compared with the conventional practice in two of the three fields where ground water quality was monitored. Higher P concentrations for the improved practice were likely due to the dilution effect. Statistically, no differences (p>0.05) were observed in groundwater nitrogen (N) (NOx–N, NH4–N, and total dissolved N) concentrations between the improved and the conventional practices. Similarly, no statistical difference was observed in crop yield between the improved and the conventional practices, although the average total yield was higher for the improved practice. The improved practice also reduced the incidence of plant disease compared to the conventional practice which resulted in crop failure in some fields. Thus, use of the improved practice reduced irrigation water use without impacting crop yield.     

180 t转炉底吹气体与熔池相互作用的水模型实验

通过10:1水模型研究了转炉底吹流量0.55～0.75 m3/h和底吹喷嘴4孔对称、2孔对称、2孔不对称分布以及喷嘴位置d/D=0.1～0.9(d-喷嘴所在同心圆直径,D-转炉熔池直径)对熔池均混时间的影响.结果表明,d/D=0.3,底吹流量0.70 m3/h,4孔对称底吹时熔池搅拌效果最佳;2孔不对称喷吹时,最佳流量为0.60～0.70m3/h,最佳喷嘴位置d/D=0.3～0.5;2孔对称喷吹时最佳流量与喷嘴位置分别为0.65 m3/h和d/D=0.7.