Drainage of Sloping Lands with Variable Recharge: Analytical Formulas and Model Development

Semianalytical transient equations for shallow subsurface transverse drainage systems installed in sloping lands are developed. They provide a general relationship between drain flow rates, water table elevations, and recharge rates. This relationship demonstrates that, depending on the recharge intensity, several drain flow rates can be observed at a given water table elevation. The recharge contribution is shown to depend on a water table shape factor and to decrease when the water table is low or the slope is steep. For very steep slopes, the recharge intensity no longer influences the drain flow rate. These equations can be used to confirm previous results obtained in steady-state conditions and to determine precisely under which conditions slope needs to be considered in drainage design. They have been incorporated into the field drainage model SIDRA, which simulates hourly values of water table elevations and drain flow rates. The model predictions are compared with the predictions of a steady-state equation and a numerical model, which solves the Boussinesq equation (SLOP model).     

Comparison of Models for Computing Drainage Discharge

The WAVE model describes the transport and transformations of matter and energy in the soil, crop, and vadose environment. A lateral field drainage subprogram was added to the WAVE model to simulate lateral subsurface drainage flow. The subsurface drainage is considered as the drainage provided by evenly spaced parallel drains with a free outlet: drain tubing or ditch. The rate of subsurface water movement into drain tubes or ditches depends on the hydraulic conductivity of the soil, drain or ditch spacing, hydraulic head in the drains, profile depth, and water table elevation. Hooghoudt's steady-state equation was selected for incorporation in the WAVE model. The subsurface drainage subprogram was calibrated and validated by comparison with the SWAP model (The Netherlands) and DRAINMOD (the United States) and partially by using 7 years of drain outflow data from an experimental field under fallow and cropped conditions. The comparative study revealed that the three models performed equally well and that the models were reliable and accurate tools for predicting the drainage flux as a function of rainfall-evapotranspiration and local conditions. The WAVE model, in comparison to the SWAP and DRAINMOD model, provided as good a prediction of the lateral subsurface drainage flow to drains. The statistical analysis between each model and observed data revealed that the three models were able to predict with sufficient accuracy the observed drainage discharge. The DRAINMOD model, however, has the advantage of giving a more accurate estimate of the discharge, resulting in a more precise modeling. The models were consistent in predicting water table levels, but they could not be verified against field data because of a lack of suitable measurements.     

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.     

Potential Impact of Climate Change on Subsurface Drainage in Iowa’s Subsurface Drained Landscapes

The study presents hydrologic simulations assessing the potential impact of climate change on subsurface drainage and its pattern in Iowa’s subsurface drained landscapes. The contemporary (representing the decade of 1990s) and future (representing the decade of 2040s) climatic scenarios were generated by downscaling the projections of global climatic model HadCM through two regional climatic models RegCM2 and HIRHAM to a regional grid box of 52–55?km2, which contains Perry, IA. These climatic scenarios were used to drive the field scale deterministic hydrologic model DRAINMOD to simulate subsurface drainage from one of Iowa’s predominant hydric soils, WEBSter, cultivated with Continuous Corn (WEBS_CC), and equipped with a conventional drainage system (30-m drain spacing at 1.2-m drain depth). The simulation results consistently indicate an increase in subsurface drainage from WEBS_CC under future climatic scenario as compared to contemporary climatic scenario. This increase in subsurface drainage would be more in the winter months (from December to March) and early spring months (from April to May) than summer and fall months. Since subsurface drainage is a primary carrier of nitrate-nitrogen (NO3–N) from the agricultural lands, the extrapolation of this study simulations suggest that there would be a potential for increased NO3–N loss from Iowa’s subsurface drained landscapes under future (in the decade of 2040s) climatic conditions.     

Process Modeling of Storm-Water Flow in a Bioretention Cell

A two-dimensional variable saturated flow model was developed to simulate subsurface flow in bioretention facilities employing the Richards’ equation. Variable hydrologic performances of bioretention are evaluated using the underdrain outflow hydrographs, outflow volumes for 10 storms with various duration and depth, and flow duration curves for 25 different storms. The effects of some important design parameters and elements are tested, including media type, surrounding soils, initial water content, ratio of drainage area to bioretention surface area, and ratio of cell length to width. Model results indicate that the outflow volume via underdrain is less than the inflow; the flow peak is significantly reduced and delayed. Underdrain outflow volume from loamy sand media (with larger Ks) is larger than that from sandy clay loam media. The saturated hydraulic conductivity, storage capacity, and exfiltration into surrounding soils contribute to the hydrologic performance of a bioretention cell. Initial media storage capacity is affected by the hydraulic properties of media soils, initial water content, and bioretention surface area. The exfiltration volume is determined by the surrounding soil type and exfiltration area, dominated by flow through the bottom of the media.     

Economics of Nitrate Losses from Drained Agricultural Land

Some of the highest losses of nitrate to surface waters come from drained agricultural land. This research studied, for Belgian farming conditions, (i) the effect of subsurface drainage density on nitrate losses and (ii) the economics of nitrate losses, using the nitrogen version of the program DRAINMOD-N. DRAINMOD was used to simulate the performance of the drainage system of the Hooibeekhoeve experiment, situated in the sandy region of the Kempen (Belgium) for a 14-year (1985–1998) period. A continuous cropping with maize was assumed. Daily NO3-N losses were predicted for a range of drain spacings and depths, two drainage strategies (conventional and controlled), and three fertilizer application rates (225, 275, and 325 kg?N?ha?1). Losses of N in subsurface drainage were assumed to occur almost entirely in the NO3-N form. Losses of organic and inorganic N in the form of NO3-N in surface runoff are small and were neglected. Hydrologic results indicated that increasing drain spacing or decreasing drain depth reduces drainage discharge while it increases runoff. The use of controlled drainage reduces subsurface drainage and increases runoff. Results also revealed that increasing the drain spacing or decreasing the drain depth reduces nitrate-nitrogen (NO3-N) drainage losses and net mineralization, while increasing denitrification and runoff losses. Controlled drainage caused a predicted reduction in drainage losses and an increase in denitrification and runoff losses. The optimal combination of drain density and management is one that maximizes profits and minimizes environmental impacts. Simulated results indicated that NO3-N losses to the environment could be substantially reduced by reducing the drainage density below the level required for maximum profits based on grain sales. The study concluded that, if the environmental objective is of importance equal to or greater than profits, drainage systems can be designed and managed to reduce NO3-N losses while still providing an acceptable profit.     

Influence of Stress State on Soil-Water Characteristics and Slope Stability

A soil-water characteristic curve defines the relationship between the soil (matric) suction and either the water content or the degree of saturation. Physically, this soil-water characteristic is a measure of the water storage capacity of the soil for a given soil suction. Conventionally, the soil-water characteristic curves (SWCCs) are determined in the laboratory using a pressure plate apparatus in which vertical or confining stress cannot be applied. For investigating the influence on the stress state on the soil-water characteristics, a new stress controllable pressure plate apparatus has been developed. Effects of K0 stress conditions on the SWCCs of an “undisturbed” volcanic soil in Hong Kong are determined and illustrated. The net normal stresses considered in the apparatus are 40 and 80 kPa, which are appropriate for many slope failures in Hong Kong. Experimental results show that the soil-water characteristic of the soil specimens is strongly dependent on the confining stress. Numerical analyses of transient seepage in unsaturated soil slopes using the measured stress-dependent soil-water characteristic curves predict that the distributions of pore-water pressure can be significantly different from those predicted by the analyses using the conventional drying SWCC. For the cut slope and the rainfall considered, the former analyses predicted a considerably lower factor of safety than that by the latter analyses. These results suggest that wetting stress-dependent soil-water characteristic curves should be considered for better and safer assessment of slope instability.     

不同应力状态下孔隙结构特征对土-水特征曲线的影响

针对传统土-水特征曲线测试仪无法实现荷载作用的不足,研制吸力控制式三轴试验装置,开展不同应力状态作用下土-水特征曲线试验,讨论应力状态对孔隙特征的作用.结果表明,固结压力和基质吸力均能使土体产生不可逆的收缩变形.固结压力越大,土颗粒就越紧密,孔隙比越小,孔隙尺寸和数量越小,渗透性越差,表现出较好的持水能力,空气难以进入土体,土体排水困难,导致进气值增大和减湿率减小.土-水特征曲线与孔隙结构特征的关系紧密,与应力状态无直接关系.固结压力对土-水特征曲线的影响是通过改变孔隙结构特征来体现的.孔隙结构特征相近时,应力状态对其土-水特征曲线不会产生影响.      

Pilot-Scale Evaluation of Denitrification Drainage Bioreactors: Reactor Geometry and Performance

Denitrification drainage bioreactors are emerging as an innovative practice to address water quality concerns stemming from nitrate leaching from drained agricultural lands. Although installation of these systems has begun in farms in the midwestern United States, the understanding of their design and in-field performance remains deficient. This study utilized a set of pilot-scale drainage bioreactors to evaluate the impact of bioreactor geometry on reactor hydraulic properties and to determine nitrate removal under steady-state conditions and during a simulated storm event. Bioreactors with different cross-sectional geometries but similar depths and total volumes were evaluated. The percent reduction of the influent nitrate mass was linearly correlated to the theoretical hydraulic retention time (HRT) with 30 to 70% NO3--N removals observed within the 4 to 8?h of retention time suggested for field installations. Tracer tests revealed that in situ HRTs were at least 1.5 times larger than theoretical HRTs.     

Generalized Analytical Solutions for Groundwater Head in Inclined Aquifers in the Presence of Subsurface Drains

Analytical solutions for groundwater head in the presence of subsurface drains are important in assessing the effectiveness of an existing drainage system under a probable extreme variation in the rate of recharge and designing a new drainage system. Generalized analytical solutions for groundwater head in inclined aquifers in the presence of parallel subsurface drains are obtained considering the transient rate of recharge as a power series (polynomial) function and depth-dependent rate of evapotranspiration. An appropriate function, new to analytical drainage studies, is used for correctly representing the depth-dependent rate of evapotranspiration. The solutions are obtained considering the practical situation of drains placed at shallow depth in a considerable depth of aquifer. Two conditions of large and small saturated thicknesses in comparison to the increase in groundwater head are considered. A mathematical criterion is proposed to distinguish between large and small saturated thicknesses. The analytical equations for discharge to drains for different cases considered are also obtained. The discharge equations used by prior investigators are found inappropriate.     

Numerical Solution of Boussinesq Equations to Simulate Dam-Break Flows

To investigate the effect of nonhydrostatic pressure distribution, dam-break flows are simulated by numerically solving the one-dimensional Boussinesq equations by using a fourth-order explicit finite-difference scheme. The computed water surface profiles for different depth ratios have undulations near the bore front for depth ratios greater than 0.4. The results obtained by using the Saint Venant equations and the Boussinesq equations are compared to determine the contribution of individual Boussinesq terms in the simulation of dam-break flow. It is found that, for typical engineering applications, the Saint Venant equations give sufficiently accurate results for the maximum flow depth and the time to reach this value at a location downstream of the dam.     

Rational Coefficients for Steeply Sloped Watersheds

When computing peak discharges for the design of drainage systems using the rational method, it is important to have an accurate value for the rational coefficient (C). For steeply sloped watersheds the origin of values of the rational coefficient are unknown and lack even modeling verification. A model that shows the relationship between the rational coefficient and watershed slope was developed for steeply sloped watersheds. Using Horton’s infiltration equation, Manning’s equation, the velocity method for computing times of concentration, and generalized intensity-duration-frequency curves, a model was developed to test the effect of variation of several watershed characteristics on the relationship between slope and the rational coefficient. Analyses with the model showed that both Manning’s coefficient and land use had the greatest effect on the relationship between C and slope. A mathematical function was then developed from data generated from the Horton–Manning model. This model allows C to be estimated for a given slope and a value of Manning’s coefficient for the land cover. A rational coefficient at a 6% slope is also required input. The model was tested using several watersheds with moderate to steep slopes. This relationship should be used to better estimate values of C on steep slopes, and thereby, lead to more accurately hydrologic designs.     

Simultaneous Prediction of Saturated Hydraulic Conductivity and Drainable Porosity Using the Inverse Problem Technique

The saturated hydraulic conductivity K and the effective porosity f are two important input parameters needed for lateral drain spacing design, as well as some other applications. The technical and economic justification, of most drainage projects, is mainly connected to these two parameters. The current design procedure is based upon calculation of the lateral spacing, using some average values of K and f within the drainage area. The objectives of this study were to introduce a new method for simultaneous estimation of K and f parameters using the inverse problem technique, and to evaluate five different unsteady drainage analytical models of the Boussinesq equation, suggested by different researchers for simultaneous prediction of the parameters. Consequently, five different analytical models for predicting water table profiles were solved, using the inverse problem technique. Each model was then evaluated. A physical drainage model of 2.2?m length, 0.3?m width, and 0.5?m height was established in the laboratory and carefully packed with a sandy loam soil. A perforated drainage pipe of 4.5?cm in diameter was installed at the bottom end of the model. Many piezometers were inserted in the soil for spatial and temporal water table monitoring. Different data sets from the experiments and literature were used for model calibration. The newly proposed approach that is based upon measuring water table profiles, at different times, was then evaluated with both constant and variable f. The predicted values of the proposed approach indicated reasonable agreement with the measured data. With variable effective porosity, the method was even more accurate to predict the water table profiles. Using the inverse problem technique, all the analytical models provided good agreement with the measured data. Among these, however, the Topp and Moody model predicted more accurate results than other models.     

Field Data and Water-Balance Predictions for a Monolithic Cover in a Semiarid Climate

Water-balance predictions made using four codes (UNSAT-H, VADOSE/W, HYDRUS, and LEACHM) are compared with water-balance data from a test section located in a semiarid climate simulating a monolithic water-balance cover. The accuracy of the runoff prediction (underprediction or overprediction) was found to affect the accuracy of all other water-balance quantities. Runoff was predicted more accurately when precipitation was applied uniformly throughout the day, the surface layer was assigned higher saturated hydraulic conductivity, or when Brooks-Corey functions were used to describe the hydraulic properties of the cover soils. However, no definitive or universal recommendation could be identified that would provide reasonable assurance that runoff mechanisms are properly simulated and runoff predictions are accurate. Evapotranspiration and soil-water storage were predicted reasonably well (within ≈ 25?mm/yr) when runoff was predicted accurately, general mean hydraulic properties were used as input, and the vegetation followed a consistent seasonal transpiration cycle. However, percolation was consistently underpredicted (>3?mm total) even when evapotranspiration and soil-water storage were predicted reliably. Better agreement between measured and predicted percolation (or a more conservative prediction) was obtained using mean properties for the soil-water characteristic curve and increasing the saturated hydraulic conductivity of the cover soils by a factor between 5 and 10. Evapotranspiration and soil-water storage were predicted poorly at the end of the monitoring period by all of the codes due to a change in the evapotranspiration pattern that was not captured by the models. The inability to capture such changes is a weakness in current modeling approaches that needs further study.     

Method of Solution of Nonuniform Flow with the Presence of Rectangular Side Weir

An iterative step method for solving the nonlinear ordinary differential equation, governing spatially varied flows with decreasing discharge, like the flow over side weirs, is developed. In the procedure, starting at a known flow depth and discharge in the control section, the analytical integration of the dynamic equation with bed and friction slope is carried out. The specific energy, the weir coefficient and the velocity distribution coefficient are considered as local variables, then for the explicit integration, the respective average values along the short side weir elements are assumed. The water surface profiles and the discharges for flow over side weirs, obtained with the proposed relation and valid for rectangular channels, are compared with experimental data for subcritical and supercritical flow conditions. The validation of the method is accomplished by the comparison with the solution obtained by De Marchi’s classical hypothesis, about the specific energy, which is constant along a side weir. In addition, the influence of the coefficient velocity distribution is considered.     

Overfall in U-Shaped Channels

Free overfall in U-shaped channels is theoretically analyzed, applying a momentum equation based on the Boussinesq approximation, to obtain the equation of end depth. The end-depth ratio is 0.75 up to normalized critical depth 0.50; and then it decreases gradually with an increase in normalized critical depth. A method to estimate discharge from the end depth is presented. The upstream flow profile of a free overfall is computed using the streamline curvature at the free surface. Experiments were conducted in two U-shaped channels to verify the model. The results obtained using the model agree satisfactorily with the experimental data.     

Analytical Ground-Water Flow Solutions for Channel-Aquifer Interaction

A general solution scheme for determining ground-water levels for channel∕group-water systems with recharge is developed and verified. The analytical solution uses the Laplace transform method to solve a linearized form of the Boussinesq equation. Unlike other solutions, this scheme allows for both boundaries and sources∕sinks to vary as a function of time and space. To verify the analytical scheme, three one-dimensional case studies of flow between two line sources in an unconfined aquifer were explored through a base run and a set of sensitivity analyses. These runs involved comparisons to MODFLOW and changes in the boundary conditions and dimensions. As noted, the flow equations were linearized about a point called the representative flow depth. A value of havg, defined as the average water depth between the initial and steady flow conditions, was used as the representative flow depth. Results of the proposed method matched very well with MODFLOW solutions for all times and locations using an optimal linearization point. In addition, using havg improved the solutions compared to those obtained previously.     

静水压与溶解氧耦合作用对低合金高强钢腐蚀电化学行为的影响

采用动电位极化测试和扫描电子显微镜/能谱仪表征, 通过理想动电位极化曲线分析方法和微观腐蚀形貌观察研究了静水压与溶解氧耦合作用对低合金高强钢在质量分数为3.5% NaCl溶液中腐蚀电化学行为的影响. 结果表明: 随着静水压和溶解氧溶度的同时增大, 腐蚀电位先增高而后逐渐降低, 腐蚀电流呈非线性增长; 静水压与溶解氧在腐蚀过程中存在相互竞争抑制关系, 在静水压与溶解氧同时增长过程中, 溶解氧首先促进阴极反应过程并抑制阳极反应过程, 而后静水压逐渐加速阳极过程并对阴极反应过程有一定的抑制作用; 静水压与溶解氧耦合作用加速了腐蚀产物膜的生长, 增加了低合金高强钢表面点蚀坑的数量和生长尺寸.      

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.     

Combination Subsurface Irrigation and Drainage Systems in North-Central South Dakota

The 340,000 ha Lake Dakota Plain area in north-central South Dakota has the topographical and soil characteristics required for the use of combination subsurface drainage and irrigation systems. Corn yield data from a research site and a county-wide reporting service were used to determine that DRAINMOD, a water balance and corn yield estimation computer model, could be employed to assess the feasibility of using a combination system for the area. Three soils ranging in texture from a sandy loam to a silt loam and 19 years of climatic data were used in the feasibility analysis. Drain line spacings were determined for average yield goals of 90, 95, and 100% of estimated maximum corn yields for each soil. There are possibilities for the economical use of combination subsurface irrigation and drainage systems in the Lake Dakota Plain area.