Study of Drawdown–Drain Discharge Relationship and its Application in Design of Cost Effective Subsurface Drainage System in Mugogo Swamp, Busogo, Rwanda

Mostly the swamps in Rwanda are surrounded by volcanic hills with small streams flowing to discharge runoff and seepage water. Mugogo swamp is located in Busogo sector, Musanze district, North province. Total area of the swamp is approximately 50 ha. The swamp is surrounded by hills and elevated volcanic rocky terrains. Potato is the main crop cultivated in the swamp. The average production rate of potato is 7 MT/ha which is very low compared to 12 MT/ha in well drained areas. During rainy season seepage water and runoff water from the surrounding hills cause the waterlogged condition of the swamp and affecting the potato cultivation and land productivity. The remedial measure for this swamp is to divert separately the runoff and seepage water from surrounding catchment area and then remove the recharge water by pumping through a system of subsurface drains. Hydraulic head–drain discharge relationship can be fitted with quadratic equation. Equivalent drainable porosity and equivalent hydraulic conductivity are determined as 0.105 m/day and 0.34% respectively for drain depth of 40 cm from soil surface. Effective hydraulic conductivity in the soil profile shows that its average value in the top 15 cm of soil layer is 0.17 m/day and that in the remaining depth up to impermeable layer is 0.015 m/day. Third degree polynomial expressions are made for Head–hydraulic conductivity and head–drainable porosity relationships. The nonlinear relation of hydraulic conductivity and drainable porosity with drawdown shows that the proximity of Kinoni stream does not affect drainage parameters of the area because of less seepage from the stream. The study also reveals that adoption of 7 m drain spacing is very less if crop parameter is not considered and will result higher drain cost. Drainage coefficient of 5 mm/day is arrived considering the rainfall distribution, infiltration rate of soil, allowable water logging tolerance of potato crop. Required drain spacings are calculated for different drainage coefficients of 1, 2, 3, 4 and 5 mm/day under different drawdown conditions to plot subsurface drainage characteristic curves of the swamp. These curves are useful to directly read the drain spacing and drain depth for the required drainage coefficient without going for tedious calculations. Cost analysis shows that the ratio of drain spacing to drain depth can be a decisive factor to select best combination of drain depth and drain spacing. For drainage coefficient of 5 mm/day, optimum drain spacing-depth ratio is found as 7.2 with a cost of 0.689 million Frw/ha. For different drainage coefficients in the swamp, the drain depth of 1.5 m is crucial and optimum cost occurs at this depth. It is also found that any increase in drawdown beyond the drawdown at critical drain depth will not reduce the cost significantly.     

TRANSIENT FLOW DRAINAGE EQUATIONS CONSIDERING BOTH DELAYED GRAVITY RESPONSE AND EVAPORATION FROM WATER TABLE

The drainable porosity is one of the important parameters in the unsteady drainage formulas. Due to delayed gravity response the drainable porosity is a function of the rate of drawdown and the depth of water table. The evaporation from groundwater plays an important role in lowering water table, in drainage design formulas it should be taken into account. Drainage equations considering evaporation from groundwater varying with water table depth and evaporation from water surface and involving constant drain-able porosity have been proposed by many authors. In this paper new formulas considering both delayed gravity yield and evaporation as a function of water table depth are developed and verified by experimental data.     

Numerical Solution of 2D Free Surface to Ditch Drains in Presence of Transient Recharge and Depth-Dependent ET in Sloping Aquifer

Water table variations between drains have been investigated by various researchers in response to transient recharge. Recent studies have shown the importance of incorporating the effect of evapotranspiration (ET) in the design of subsurface drainage systems. In arid and semi-arid regions, ET plays a crucial role in lowering the water table resulting in increased drain spacing. In this paper, a numerical solution of two-dimensional free surface flow to ditch drains is presented in presence of transient recharge and depth-dependent ET from land surface for an aquifer with sloping impermeable base. The midpoint water table variations obtained from the proposed solution compare well with experimental results as well as already existing mathematical solution. When ET from the land surface is taken into account in combination with recharge, the model results can provide accurate and reliable estimates of water table fluctuation under complex situations, which are highly related to the hydrology of waterlogged and saline soils.     

盐渍兼治的动态控制排水新理念与排水沟（管）间距计算方法探讨

根据灌区地下水位降落过程的不同阶段有不同控制要求这一特点,为充分发挥各级排水工程的综合控制能力,本文从北方易受盐渍危害的渠灌区实际出发,针对现有农田排水设计方法的局限性,提出以盐渍兼治为目标的地下水位分期动态控制指标的排水标准新理念,并用"模糊档次"分级方法近似处理隔水层深度,推导出计算组合排水沟(管)间距的非稳定流简化通式,对原有设计方法予以改进。通过实例验证表明,地下水位动态过程指标与实测结果吻合一致,计算间距的简化通式使用方便,其结果能满足设计精度要求。     

The Pros and Cons of Encouraging Shallow Groundwater Use through Controlled Drainage in a Salt-Impacted Irrigation Area

Encouraging shallow groundwater use through water table management or controlled drainage in irrigated areas can relief crop water stress under water shortage condition. But substituting fresh irrigation water with saline groundwater may speed up salinity buildup in the crop root zone, and consequently increase water use for salt leaching. With a proposed analytical model, this paper presents a case study demonstrating the effect of encouraging shallow groundwater use through controlled drainage on salt and water management in a semi-arid irrigation area in northwestern China. Based on the average rainfall condition, the model assumes that salt accumulates in the crop root zone due to irrigation and shallow groundwater use; till the average soil salinity reaches the crop tolerance level, leaching irrigation is performed and the drainage outlet is lowered to discharge the salt-laden leaching water. For the relatively salt tolerant crop–cotton in the study area, the predicted leaching cycle was as long as 751 days using the fresh water (with salinity of 0.5 g/L) irrigation only; it was shortened to 268 days when the water table depth was controlled at 2 m and 23% of the crop water requirement was contributed from the saline groundwater (with salinity of 4.43 g/L). The predicted leaching cycle was 140 days when the water table depth was controlled at 1.5 m and groundwater contribution was 41% of the crop water requirement; it was shortened to 119 days when the water table depth was controlled at 1.2 m and the groundwater contribution was 67% of the crop water requirements. So the benefit from encouraged shallow groundwater use through controlled drainage is obtained at the expense of shortened leaching cycle; but the shallow groundwater use by crops consists of a significant portion of crop water requirements, and the leaching cycle remains long enough to provide a time window for scheduled leaching in the off season of irrigation. Weighing the pros and cons of the encouraged shallow groundwater use may help plan irrigation and drainage practices to achieve higher water use efficiency in saline agricultural areas.     

半干旱灌溉地区采用地下排水控制土地盐化的效果评价

一项大规模地下排水研究项目RAJAD（拉贾斯坦邦农业排水研究项目），在印度的拉贾斯坦邦实施，旨在控制因灌溉引起的土壤盐碱化问题。在12个野外试验地点获得了大量的地下排水数据。田间结果表明，地下排水系统对控制土壤盐碱化具有积极意义。广泛的监测结果显示，地下排水系统是控制土壤盐碱化的有效途径。试验数据表明，有地下排水系统的所有地区，其土壤盐化度都呈现出逐渐下降的趋势。土壤的脱盐速度在排水间距较小（〈40m）时比排水间距较大时（〉40m）要快。雨季通过地下排水系统淋洗排出的盐分数量大于灌溉季节引入的盐分数量。     

多层建筑物排水（污）系统非恒定流数学模型

建筑物污水排放系统中的水流为非恒定流，研究其系统中的非恒定流波的传播现象不但对预估管道中的各种水流现象，进行最优设计有着紧密的联系，同时对进一步研究管道中固体物的运动机理及水气两相流问题也有着重要的意义。本文通过应用特征差分方法，数值求解圣维南方程组，对管道中非恒定流进行了分析并建立了相应的计算机程序；对建筑物排污系统常见的边界情况进行了研究，并建立了无量纲的经验公式，这些公式作为边界条件与计算机程序相结合，可直接用于多层建筑物排水系统的模拟及预估     

Analytical solutions of unsteady drainage problems for soils subjected to variable recharge from a semi-confined aquifer

In drainage of agricultural lands, the upward vertical recharge from a semi-confined aquifer depends on the difference of the piezometric heads on the two sides of the semi-impermeable layer through which this recharge takes place. This means that the recharge through the semi-impermeable base depends on the unknown height of the unsteady water table. In the nonhomogeneous Boussinesq equation, which describes the drainage problems, the downward uniform rate of the recharge from rain or irrigation and the recharge from the semiconfined aquifer are expressed by two terms. By solving the Boussinesq equation expressions for the nondimensional height of the water table and the nondimensional discharge of the drains per unit drained area are obtained for three different initial conditions. Some known solutions are shown as special cases of the present solutions. Variation of nondimensional water table heights at half distance of the drain spacing and the nondimensional discharge of the drains with nondimensional time have been graphically illustrated with the help of synthetic examples.Notation B _s thickness of the semi-impervious layer [L] - c hydraulic resistance of the semi-impervious layer [T] - D depth of the drains from the base [L] - d _e equivalent depth [L] - h=h(x, t) height of the water table [L] - h ₀ initial height of the water table [L] - h _t water table height at mid-distance of drains att [L] - h _j ,h _k water table height at mid-distance of drains at timej andfk, respectively [L] - H ₀ piezometric head in the semi-confined aquifer [L] - K hydraulic conductivity of the soil [LT^–1] - K _s hydraulic conductivity of the semi-impervious layer [LT^–1] - k ₀,k ₁,k ₂ nondimensional constants - L distance between the drains [L] - q ₀ upward recharge per unit surface area through the semi-impervious layer [LT^–1] - q _t discharge per unit drainable area of drains at timet [LT^–1] - R,R ₀ recharge per unit surface area from rain or irrigation during the unsteady and steady-state, respectively, [LT^–1] - S specific yield of the soil - t time of observation [T] - x distance measured from the drain [L] - leakage factor [L] - nondimensional distance - nondimensional time     

Sensitivity Analysis of a Physically Based Distributed Model

The objective of this study is to perform a sensitivity analysis of the SHETRAN model on the example of the torrential Lukovska River catchment in Serbia. The sensitivity analysis of the model was performed for the following parameters: the vertical saturated hydraulic conductivity of the subsurface soil, the horizontal saturated hydraulic conductivity in the saturated zone, the Strickler roughness coefficients for overland flow and for streams, the available water content in the soil and the erodibility coefficients due to rain and due to overland flow. It can be concluded that the water and sediment discharge are very sensitive to the values of the vertical saturated hydraulic conductivity of the subsurface soil in the range of 0.001 to 0.1 m/day; to the values of the horizontal saturated hydraulic conductivity in the saturated zone in the range of 0.01 to 5 m/day and to the values of the Strickler’s coefficients for overland flow and for rivers in the range of 0.1 to 100 m1/3s-1 and 15 to 40 m1/3s, respectively. The sediment concentrations in a flow and sediment discharge are very sensitive to the values of erodibility coefficient due to overland flow in the range of 0.5 to 1.5 mg/m2s and to the values of erodibility coefficient due to rain in the range between 0.1 and 40 J-1. The obtained results could be used to simplify the parameter calibration procedure and to facilitate estimation of parameters in ungauged mountainous basins of similar characteristics.     

表征干燥失水诱发膨胀土收缩-开裂-沉陷机理的数学模型

膨胀土因干燥失水引起的收缩、开裂和沉陷会使其水力与力学特性发生显著变化,从而对膨胀土地区水工建筑物的稳定性产生负面影响,因此有必要研究这三个物理过程的细观机理和宏观响应。为此,先建立团粒、裂隙和沉陷这三个区域分布的数学模型;再通过分析收缩-开裂-沉陷过程中理想土块与裂隙之间的几何关系,推得裂隙相对宽度的理论计算公式;最后,对安康膨胀土开展收缩-开裂-沉陷的室内试验,并结合已有文献所述室内和现场试验结果,验证了这三种区域的数学模型在采用同一组参数描述团粒孔隙率、裂隙率及其相对宽度、沉陷率变化规律时的有效性,并建立了膨胀土团粒孔隙率-含水率-基质吸力的关系。该组数学模型为定量描述膨胀土的体变特征和渗透特性提供了一种新方法。     

Estimation of Peak Flow Rates for Small Drainage Areas

Runoff plots are important for soil loss measurements, and increasing numbers of plots use automatic equipment. To choose equipment with appropriate capacities, the peak flow rate must be known. The peak flow rate is also an important parameter in the modified universal soil loss equation (MUSLE) which calculate the soil loss from upland slope. The available peak flow rate equations are primarily for the watershed scale, not for small drainage areas like runoff plot. This study’s purpose was to derive an equation suitable for the small drainage areas. A total of 149 runoff events on 5 runoff plots were used to develop a peak flow rate equation for the hillslope scale. All plots are located in the Tuanshangou catchment, Zizhou county, Shaanxi province, China. Dimensionless analyses were used to determine the equation form of linear regression analyses. The results revealed that the peak flow rate was significantly correlated with plot area, slope steepness, runoff depth, rainfall depth and the maximum 30-min rainfall intensity. Two equations were developed to estimate peak flow. The model efficiencies of both equations exceeded 0.9. The equations developed in this study represent an important complement to existing peak flow rate equations. These new equations will facilitate the design of soil conservation practices and/or the selection of flow-observation equipment for small drainage areas.     

COMPUTER-AIDED ANALYSIS OF UNSTEADY PARTIALLY FILLED FLOWS IN DRAINAGE SYSTEMS

The partially filled pipeflows encountered in drainage systems belong to a family of unsteady flow problems capable of numerical solution via the method of characteristics.The defining equations in terms of flow depth,velocity and surface wave speed are developed and numerically solved by characteristic-difference method with time-lineinterpolation scheme.Boundary conditions for inflow,outflow,moving hydraulic jump and junctions are developed both experimentally and numerically.Full scale model experiments were carried out and it was consequently clarified that numerical model is capable of predicting flow characteristics in realistic drainage networks.     

Transformation Technique for Water Table Estimation in a 2-D Aquifer with Inclined Base Subjected to Variable ET

An analytical solution for two-dimensional water table variation in an aquifer basin with inclined impermeable base has been proposed incorporating the effect of depth-dependent evapotranspiration (ET) from land surface. The proposed analytical solution has been obtained by devising a sound mathematical transformation, which transforms a complex partial differential equation into the simplest form. The results obtained from the proposed solution are in good agreement with the already existing mathematical solutions. The results of the proposed solution have been illustrated to study the variation of water table in the 2-D aquifer. Since the water table profiles are obtained lower by consideration of ET, the solution will result in wider drain spacing and, thus, economy in the drainage design. The proposed analytical solution can be used as an important tool for reliable prediction of water table variation in the salinity affected croplands of arid and semi-arid regions where the ET rate is very high.     

Urbanisation and Shallow Groundwater: Predicting Changes in Catchment Hydrological Responses

The impact of urbanisation on catchment hydrological response was investigated by using a process-based coupled surface water–groundwater model (MODHMS). The modelling estimated likely changes in river discharge as a result of land-use change in the Southern River catchment in Western Australia, underlined by a highly transmissive aquifer, has permeable soils and a shallow watertable. A significant increase in total annual discharge was predicted as a result of urbanisation area with the runoff coefficient rising from 0.01 to more than 0.40. In contrast with urban areas elsewhere, these changes were mainly due to a shift in the subsurface water balance, leading to significant reduction in evaporative losses from the soil profile and shallow watertable after urbanisation (from nearly 80 % of infiltration to less than 20 %). The infiltration of roof and road runoff and establishment of subsurface drainage adopted in local construction practice leads to higher groundwater recharge rates and subsequently groundwater discharge to the urban drainage network. Urban density and groundwater abstraction for urban irrigation most strongly influence the urbanisation impact on catchment fluxes. The results shows that urban development leads to a production of ‘harvestable’ water; and depending on local needs, this water could be used for public and private water supply or to improve environmental flows.     

Water Drainage in Layered Soils. Laboratory Experiments and Numerical Simulation

Experimental results during first and second drainage in a vertical column of saturated layered soil were compared to those predicted from simulation. The sample was composed of a sandyloam soil overlying a fine sand. The soil water content was measured by using -ray absorption method (²⁴¹Am) and the water pressure through tensiometers, arranged vertically along the column and connected to pressure transducers. From the evaluation of moisture and pressure versus time, the characteristic curves () of the layers were obtained and approximated by van Genuchten's analytical equation. The relationship K() between hydraulic conductivity and moisture was estimated by van Genuchten's prediction model. () and K() equations were used as inputs in the numerical model. The drainage of water was simulated by Richard's partial differential equation, which was solved with the finite differences computational scheme type Laasonen. The upper and lower boundary conditions were zero flux and a periodically changing head respectively. Numerical results show a good agreement with experimental data, with small deviations for certain hours.     

Modeling Rainwater Storage in Distributed Reservoir Systems in Humid Subtropical and Tropical Savannah Regions

Using a hydrologic model this study estimated rainwater storages in field-scale on-farm reservoir (OFR) systems at two locations: (1) Fort Worth, Texas, US; (2) Kharagpur, West Bengal, India. The water storages were estimated for variable OFR sizes: 1%, 5%, 10%, 15%, and 25% of the farm area. Water losses through seepage and evaporation were estimated using variable saturated hydraulic conductivity conditions: 0.33, 0.64, 1.3, 5 cm/h, which corresponded to the ranges of hydraulic conductivity of loam, sandy loam, loamy sand, and sandy soils, respectively. Results indicated that the water loss through evaporation was dominant at the first location, while seepage was at the second location. Changing the OFR sizes captured 5 to 28% of the total rainfall received in the farm area of the first location and 20–40% at the second location. Finally, a comparative economic analysis was made between a distributed OFR system and a centralized large reservoir that indicated that the distributed OFR system benefits exceeded the benefits of a large reservoir.     

Delineation of Groundwater Potential Zones of Coastal Groundwater Basin Using Multi-Criteria Decision Making Technique

Delineation of groundwater potential zones (GWPZ) has been performed for a coastal groundwater basin of eastern India. The groundwater potential zone index (GWPZI) map is generated by using Analytic Hierarchy Process (AHP) from different influencing features, e.g., Land Use/Land Cover (LU/LC), soil (S), geomorphology (GM), hydrogeology (HG), surface geology (SG), recharge rate (RR), drainage density (DD), rainfall (RF), slope (Sl), surface water bodies (SW), lineament density (LD), and Normalized Difference Vegetative Index (NDVI). Recharge rate values are estimated from hydrological water balance model. Overlay weighted sum method is used to integrate all thematic feature maps to generate GWPZ map of the study area. Four zones have been identified for the coastal groundwater basin [very good: 36.39 % (273.53 km², good: 43.57 % (327.47 km²), moderate: 18.27 % (137.30 km²), and poor: 1.77 % (13.27 km²)]. Areas in north to south-west and south-east direction show very good GWPZ due to the presence of low drainage density. GWPZ map and well yield values show good agreement. Sensitivity analysis reveals that exclusion/absence of rainfall and lineament density increases the poor groundwater potential zones. Omission of hydrogeology, soils, surface geology, and NDVI show maximum increase in good GWPZ. Obtained GWPZ map can be utilized effectively for planning of sustainable agriculture. This analysis demonstrates the potential applicability of the methodology for a general coastal groundwater basin.     

Optimization and Simulation Modelling for Managing the Problems of Water Resources

Waterlogging and secondary salinization have become a serious problem in the canal irrigated areas of arid and semi–arid regions worldwide. In this study, a unique and simple technique was evolved in which a linear programming (LP) optimization model was first developed that allocates available land and water resources in order to maximize net annual returns by mitigating the waterlogging problems. A finite–difference two–dimensional simulation model was then used to evaluate the long–term impacts of various water management strategies on the groundwater table with the optimal land and water use parameters which were obtained through the optimization model. The model was used to combat the waterlogging and salinity problem of an area located in Haryana State of India. The calibration, validation, sensitivity analysis, and error analysis of the model was performed before it was used to study the impact of various water management scenarios on the long-term groundwater level. Based on the model results a change in cropping pattern with reduced rice area is suggested. Groundwater withdrawal should be increased by 1–7 % in the various nodes. It is concluded from the analysis of various scenarios that implementing multiple approaches simultaneously are more effective in controlling waterlogging problems as compared to individual interventions.     

Unsteady Flow Simulation and Erosion Assessment in a Ditch Network of a Drained Peatland Forest Catchment in Eastern Finland

We developed and applied a computational model for simulating unsteady flow in a drainage network of a boreal forested peatland site. The input to the model was the hourly runoff produced by a hydrological model. The simulations of the flow in the ditch network were performed using an iterative procedure for solving the Saint-Venant equations that govern the flow in each of the network channels. These equations were solved separately for each ditch branch, and the flow depths at the junctions were corrected using the method of characteristics. The model was applied to the drainage network of a peatland catchment in Eastern Finland over a period of 15 months. Because flow resistance in the ditches depended strongly on flow conditions, flow resistance (Manning’s n) was introduced as a function of discharge. The model was calibrated and validated against field data and the simulation results were further applied to assess erosion risk. The highest risk of erosion occurred during long lasting flows induced by snowmelt at ditch sections with a steep slope and a large upstream area. These model results can aid in the design and siting of water protection measures within the drained area.     

Numerical Models for the Simulation of Overland Flow in Fields Within Surface Irrigation Systems

Discharges in a network of drainage ditches generated by intense rainfall are influenced by overland flow dynamically interacting with infiltration. Therefore a detailed estimation of the overland flow, especially in agricultural fields prepared for surface irrigation, is essential to the design of drainage ditches. In order to simulate overland flow, which in that case may be considered unsteady and one dimensional, numerical models were developed based on the numerical solution of the Saint-Venant equations, externally coupled with the Green-Ampt equation to account for the dynamic interaction between surface flow and infiltration. The numerical solution of the Saint Venant equations in their complete form (dynamic model) and in the simplified forms of the diffusion (diffusion model) and the kinematic wave equations (kinematic model) was obtained by applying the MacCormack explicit computational scheme. Overland flow models’ simulations were conducted in order to study the effect of the soil surface parameters on the hydrographs at the downstream end of the fields, as well as the accuracy of the diffusion and kinematic equations. It was found that the kinematic wave equations were unable to describe overland flow, while the diffusion model results were close to the results of the dynamic model.