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   Journal     of    Water    Resource    and     Protection , 2013, 5, 624-632 http://dx.doi.org/10.4236/jwarp.2013.56063 Published Online June 2013 (http://www.scirp.org/journal/jwarp) Prediction of Water Logging Using Analytical Solutions—A Case Study of Kalisindh Chambal River Linking Canal Dipak N. Kongre, Rohit Goyal Civil Engineering Department, Malaviya National Institute of Technology, Jaipur, India Email: dnkongre@gmail.com, rgoyal_jp@yahoo.com Received April 9, 2013; revised May 9, 2013; accepted May 31, 2013 Copyright © 2013 Dipak N. Kongre, Rohit Goyal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the srcinal work is properly cited. ABSTRACT The canals are designed to transport water to meet irrigation and other water demands or to divert water from surplus  basins to deficient basins to meet the ever increasing water demands. Though the positives of canal network are increase in agricultural output and improvement in quality of life, the negatives of canal introduction and irrigation, along its route, are inherent problems of water logging and salinity due to seepage from canals and the irrigation, when not man-aged properly. To plan strategies to prevent waterlogging and salinity, it is necessary to predict, in advance, the prob-able area which would be affected due to seepage. This paper presents a methodology to predict the area prone to water logging due to seepage from canal by using 2D seepage solutions to 3D field problem. The available analytical solu-tions for seepage from canals founded on pervious medium and asymmetrically placed drains, have been utilized. The area, prone to waterlogging, has been mapped using GIS. Keywords:  Waterlogging; Seepage; Analytical Solutions; GIS; 3D Analyst 1. Introduction Growing need of food and fibre for increasing population needs more agricultural land to be irrigated, necessitating the transportation of water through canals from the res- ervoirs, wherever possible. In India there is a large varia- tion in the rainfall in both time and space leading to sce- nario of droughts and floods simultaneously. To over- come this challenge of droughts and floods and to pro- vide water to the water deficient regions, the Government of India has muted river interlinking project. The Parbati Kalisindh Chambal river interlinking is a part of penin- sular river interlinking project. The surplus water of Par-  bati and Kalisindh basins is to be diverted to meet the demand in upper Chambal basin [1-4]. The construction of this link would surely benefit the recipients of addi- tional water but the problems of water logging and salin- ity due to seepage from canals and irrigation need con- sideration for planning preventive measures. In the north- west part of Rajasthan state, canal irrigation was intro- duced after commissioning Indira Gandhi NaharPariyo-  jna (IGNP) to irrigate nearly 2.2 million ha of arid land. It has increased the food production but it also introduced waterlogging and secondary salinization problems [5,6]. The size of the waterlogged area in the year 1998 was 17,220 ha in stage I of the project and 800 ha in stage II of the IGNP project [7]. The major reasons for water logging and salinization in this area are indiscriminate use of irrigation water, canal seepage, sandy texture and absence of natural surface drainage [8]. The same factors have led to rise in water table in the north-west region of Haryana, India and water logging problems. About 500,000 ha area is waterlogged and unproductive [9,10]. It is es- timated that in India nearly 8.4 million ha is affected by soil salinity and alkalinity, of which about 5.5 million ha is also waterlogged [11]. In the states of Bihar, Gujarat, Madhya Pradesh, Jammu & Kashmir, Karnataka, Kerala, Maharashtra, Odisha and Uttar Pradesh 117.808 thou- sand hectare waterlogged area has been approved for re- clamation under command area development program by Ministry of Water Resources [12]. The total waterlog- ged area in canal command in India, in the year 1996, was around 2.189 million ha [13]. More than 33% of the world’s irrigated land is affected by secondary saliniza- tion and/or waterlogging [14]. These statistics clearly show the need to manage canal seepage and irrigation to re- duce water logging and secondary salinization. Canal linings are used to reduce seepage. Yao et al . [15] studied the effect of canal lining and multilayered soil system on canal seepage and found that the combi- nation of canal lining and a low-permeability layer below Copyright © 2013 SciRes.  JWARP    D. N. KONGRE, R. GOYAL   625 the canal is effective in reducing seepage. Though perfect canal lining can prevent seepage loss, but cracks can de- velop in the lining, and the performance of the canal lin- ing deteriorates with time [16]. Wachyan and Ruston [17] studied several canals and concluded that significant see-  page losses occur even in a well maintained canal with good lining. Seepage from canals can be calculated by physical, empirical and mathematical (analytical and numerical) techniques [18-21]. Empirical formulae and graphical so- lutions are generally used to estimate seepage losses from  proposed canals whereas the direct measurements such as inflow-outflow method, ponding method, seepage meter method are used to evaluate seepage from existing canals [22,23]. Various empirical formulae for estimating seep- age are discussed by Bakri and Awad [24]. The seepage losses from irrigation canals with different lining materi- als, subsurface flow and subsurface storage along the ca- nal, channel longitudinal slope, have been estimated by different researchers using direct measurements or elec- trical resistivity [25-28]. Analytical and electrical anal- ogy solutions of seepage problems related to irrigation canals have been presented by many authors. Zhukovsky was the first to introduce the method for solution of pro-  blems involving unconfined seepage using a function which is now well known as Zhukovsky’s function. Ve- dernikov gave an exact mathematical solution to uncon- fined, steady-state seepage from a triangular and a trape- zoidal canal in a homogeneous, isotropic, porous medium of large depth [29]. Vedernikov [30] solved the problem of seepage from a canal to the symmetrically placed col- lector drainages, neglecting the effect of the canal water depth and side slopes. Many Russian investigators ana- lysed solutions for rectangular, triangular channel of zero depth for different boundary conditions [31,32]. The so- lution for seepage problem for a rectangular canal was  provided by Morel-Seytoux [33]. Sharma and Chawla [34] presented solution of the problem of seepage from a canal to vertical and horizontal drainages, symmetrically located at finite distances from the canal, in a homoge- nous medium extending up to a finite depth. The water depth in the canal was assumed negligible in comparison to the width. Exact solution of the problem of seepage from a canal in a homogeneous medium to asymmetric drains located at finite distance from the canal was pro- vided by Wolde-Kirkos and Chawla [35]. Goyal [36] pro- vided solutions for seepage from canals founded on per- vious soil with asymmetric drainages. Algorithm to solve the nonlinear integral equations to obtain the value of seepage discharges and profile of the free surface was de- veloped. The computer program developed for solutions generates the coordinates of seepage profile and esti- mates the seepage quantities. Ilyinsky et al . [37] have carried out a comprehensive review of analytical solu- tions for seepage problems and observed that though numerical techniques have become more significant in solving practical problems of seepage theory but analyti- cal methods are necessary not only to develop and test the numerical algorithms but also to gain a deeper under- standing of the underlying physics, as well as for the pa- rametric analysis of complex flow patterns and the opti- mization and estimation of the properties of seepage fields. Swamee et al . [38] obtained an analytical solution for seepage from a rectangular canal in a soil layer of fi- nite depth overlying a drainage layer using inversion of hodograph and conformal mapping technique. Bardet and Tobita [39] presented finite difference approach for cal- culating unconfined seepage using spread-sheets. They derived the finite difference equations using flux conser- vation in the general case of non-uniform and anisotropic  permeability and boundary conditions. The flow lines and free surfaces can be obtained using their method but the method cannot be adopted when systems of equations  become large. Sharma and Shakya [40] applied the Bousinessq equa- tion using the Laplace transform and Fourier cosine tran- sform in determining the phreatic surface elevation in horizontal unconfined aquifers along the canal sides. An exact analytical solution for the quantity of seepage from a trapezoidal channel underlain by a drainage layer at a shallow depth obtained by using an inverse hodograph and a Schwarz-Christoffel transformation was presented  by Chahar [41]. It provides a set of parametric equations for the location of phreatic line. To reduce the convey- ance losses due to seepage, many researchers have pro- vided methods to design the canals for minimum seepage [20,38,42,43]. Ayvaz and Karahan [44] provided spread- sheet application of three-dimensional (3D) seepage mo- deling with an unknown free surface. They derived gov- erning equation using finite differences method in the ge- neral case of anisotropic and non-uniform material prop- erties and variable grid spacing and also modified it by the extended pressure method. Only one finite difference equation was applied to the solution domain instead of derivation of additional finite difference equation to im-  pervious boundary conditions, inclined interfaces, etc. So- lution to seepage under the dam has been provided using this method. Ahmed and Bazaraa [45] investigated the  problem of seepage under the floor of hydraulic struc- tures considering the compartment of flow that seeps through the surrounding banks of the canal. A computer  program, utilizing a finite-element method and capable of handling (3D) saturated-unsaturated flow problems, was used. The results produced from the two-dimensio- nal (2D) analysis were observed to deviate largely from that obtained from 3D analysis of the same problem, de- spite the fact that the porous medium was isotropic and homogeneous. These solutions may be suitable for a dam Copyright © 2013 SciRes.  JWARP    D. N. KONGRE, R. GOYAL 626  with finite length but may not prove suitable when it is applied to canals which are longer in length. Though, lot of literature about solution to the seepage  problem and to estimate seepage is available, no case study about the application of these solutions to map the area, susceptible to waterlogging, has been reported. The main objectives of this paper are to use available analytical solution to estimate the probable waterlogged area and to develop methodology for adopting 2D solu- tions to 3D field problem. 2. Analytical Solution The analytical solution for the seepage problem has been  provided by Goyal [36] for the seepage from canals with negligible water depth, founded on finite pervious media and asymmetrically placed drains on the either sides. It has been done using conformal mapping and defining free surface using Zhukovsky’s function. Integral equa- tions were obtained by using Zhukovsky’s function and Schwarz-Christoffel transformation. It is assumed that the soil medium below the canal is homogeneous and isotropic. The seepage flow is assumed to be steady and furthermore the water depth in the canal and drainages and the level of surface does not fluctuate with time. The soil within the seepage domain is saturated. It is also as- sumed that there is no infiltration/evaporation in the see-  page domain under consideration. Problem of seepage  profile has been defined in Figure 1 . Where, B is the base width of the canal, h 1  and h 2  are the difference of levels between free surface level in the canal and the drains on the right and left hand sides re- spectively. L 1  and L 2  are the horizontal distances of the drains from the edge of the canal and T is the depth of impervious layer/bed rock below the canal bed. To solve the equations for seepage profiles and the seepage losses at a cross section, using this analytical so- lution, the dimensionless parameters L 1 /h 1 , L 2 /h 1 , B/h 1 , h 2 /h 1  and T/h 1  at that section are required. These are de- termined from the known values of L 1 , L 2 , B, T, h 1  and h 2 . The user interactive computer program written in C++, on providing the input parameters, calculates profiles of Figure 1. Definition sketch of the seepage problem.  the phreatic surfaces on the left and right sides of the canal and the seepage discharge for that cross section. The solution obtained is only for a 2D section under consideration. The field problem being a 3-D problem, it is required that the 2D solutions are obtained at different sections along the alignment. Therefore the third dimen- sion of the canal, i.e . the length, is discretized by taking sections at regular intervals along its length. The solu- tions obtained for each section can then be combined to get the solution for a problem in 3D space. Geographical Information System (GIS) is a very effi- cient tool for spatial data management and analysis. Map-  ping the canal, the drains and the sections and then ex- tracting the required data of L 1 , L 2 , B, T, h 1 and h 2 , for each section, for calculations of input parameters can be efficiently done using GIS. Its versatility in spatial inter-  polation can be utilized to interpolate the 2-D solutions at each section to get a 3-D solution and then to map the waterlogged area. 3. Study Area The Parbati-Kalisindh-Chambal (PKC) river interlinking  project is one of the projects proposed by National Water Development Agency (NWDA), India [1,2]. The study area, surrounding the Kalisindh-Chambal link canal, lies  between 23 ˚ 29'N and 25 ˚ 0'N latitudes, and 75 ˚ 20'E and 76 ˚ 17'E longitudes. It is bounded by the river Chambal and its tributaries on the west and south west, River Ka- lisindh and its tributaries forms eastern and south eastern  boundary. In its feasibility report, NWDA has prepared feasibility for two of the proposed alternative routes. The alignment of canal between Parbati and Kalisindh rivers is same in both routes. The remaining alignment differs only while joining rivers Kalisindh and Chambal. The two proposed alternative routes are Joining storage dam at Kundaliya on the river Kalisindh with full reservoir level (FRL) of 370 m to: 1) Rana Pratap Sagar dam on river Chambal with FRL of 352.81 m by a 108 Km long gravity canal and 5.25 Km long tunnel, or 2) Gandhi Sagar, with FRL of 399.89 m, on river Chambal involving gravity canal of 76 Km and 20 Km  pipelines and intermediate reservoirs with lift of about 50 m. This requires a net power of about 20 MW/annum [1]. Out of the above two, the first alternative requiring no  power and maximum length of open channel has been considered for the seepage analysis. The part of the PKC  project between Parbati river and Kalisindh river as well as the second route between Kalisindh and Chambal ri- vers which to a large part coincides with first route and thereafter consists of small reservoirs and tunnels is not  being considered for analysis. The alignment has been detailed by NWDA in Technical report in 2004. The Copyright © 2013 SciRes.  JWARP    D. N. KONGRE, R. GOYAL   627 alignment passes through the area covered in the Survey of India Toposheets numbered 45P, 46M, 54D and 55A. It mainly passes through Shajapur district of Madhya Pradesh, Jhalawar, Kota and Chittaurgarh districts of Ra-  jasthan. Kalisindh-Chambal link and various districts are shown in Figure 2 . The hydrogeological fault line on northern side between river Chambal downstream of Ra- na pratap Sagar and river Kalisindh closes the study area. The study area is drained by rivers Kalisindh and its tri-  butaries, rivers Ahu and Kanthili, Amajar and Takli. These rivers are also shown in Figure 2 .   The study area is characterized by high hills on south west side and is sloping towards north east. The digital elevation map of the area and the alignment of proposed link are as shown in Figure 3 . The highest and the lowest elevation in the area are 561 m and 187 m above mean sea level. 4. Methodology The analytical solution of the seepage problem, as de- fined in Figure 1  and presented by Goyal (1994), needs the distances of the drains from the edge of the canal, the thickness of porous media up to the impervious layer and the elevation differences between the canal bed and the drains to define the boundary conditions. To extract this information the canal alignment was mapped using the drawings in the Technical Study under feasibility report of PKC link project. The rivers, viz., Kalisindh, Chambal and their tributaries forming the boundary and the rivers, viz., Ahu and Kanthili, Amajar and Takli draining the area have been mapped using existing maps of the area. Figure 2. Study area.   Figure 3. DEM of study area. The cross sections have been marked at every half kilo- meter along the alignment. The cross sections start from the drain/reservoir on the left side of alignment cross the alignment and end at the drain on its right side. The Ka- lisindh-Chambal link alignment can be taken as made of two straight segments neglecting minor deviations. The cross sections have been marked in two sets. In each set, the cross sections have been kept parallel so that solution of one cross section doesn’t interfere with the solution of other adjacent section. The sample cross sections are also shown in Figure 3 . It is assumed that at the change of direction in alignment the sections which intersect with other sections don’t have impact on the final solutions. The area has complex geology and has alluvium, wea- thered to compact sandstone, limestone, shale and basalt at different depths. The hydrogeological units were ide-alized by combining similar nature of layers as single layer and conceptual hydrogeologic model was devel- oped. The compact shale has hydraulic conductivity less than 1/10 th  of other formations and therefore shale layer has been taken as impermeable layer. The borehole re- cords of Jhalawar, Kota and Chittaurgarh districts of Ra-  jasthan [46], the details of various hydrogeological for- mations at piezometer locations in Madhya Pradesh and Copyright © 2013 SciRes.  JWARP  
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