This paper presents an analytical solution for the quantity of seepage from a rectangular canal underlain by a drainage layer at shallow depth. The solution has been obtained using inverse hodograph and conformal mapping. Using the solution for the rectangular canal and the existing analytical solutions for triangular and trapezoidal canals, simplified algebraic equations for computation of seepage loss from these canals, when the drainage layer lies at finite depth, have been presented, which replace the cumbersome evaluation of complex integrals. Using these seepage loss equations and a general uniform flow equation, simplified equations for the design variables of minimum seepage loss sections have been obtained for each of the three canal shapes by applying a nonlinear optimization technique. The optimal design equations along with the tabulated section shape coefficients provide a convenient method for design of the minimum seepage loss section. A step-by-step design procedure for rectangular and trapezoidal canal sections has been presented.

Design of Minimum Seepage Loss Canal Sections with Drainage Layer at Shallow Depth

This paper presents design equations for the least-cost canal sections considering earthwork cost which may vary with depth of excavation, cost of lining, and cost of water lost as seepage and evaporation from irrigation canals of triangular, rectangular, and trapezoidal shapes passing through a stratum underlain by a drainage layer at shallow depth. The optimal design equations are in explicit form and result into optimal dimensions of a canal in single-step computations. Using these least-cost section equations and applying the Fibonacci search method, equations for computation of the optimal subsection length and corresponding cost of a transmission canal have been presented. The optimal design equations along with the tabulated section shape coefficients provide a convenient method for the optimal design of a transmission canal. A step-by-step design procedure for rectangular and trapezoidal canal sections has been presented to demonstrate the simplicity of the method.

https://web.iitd.ac.in/%7Echahar/Reprints/RP11_TRANSCANAL_ASCE.PDF

Optimal Design of Transmission Canal

An exact analytical solution for the quantity of seepage from a trapezoidal channel underlain by a drainage layer at a shallow depth has been obtained using an inverse hodograph and a Schwarz-Christoffel transformation. The symmetry about the vertical axis has been utilized in obtaining the solution for half of the seepage domain only. The solution also includes relations for variation in seepage velocity along the channel perimeter and a set of parametric equations for the location of phreatic line. From this generalized case, particular solutions have also been deduced for rectangular and triangular channels with a drainage layer at finite depth and trapezoidal, rectangular, and triangular channels with a drainage layer and water table at infinite depth. Moreover, the analysis includes solutions for a slit, which is also a special case of polygon channels, for both cases of the drainage layer. These solutions are useful in quantifying seepage loss and/or artificial recharge of groundwater through polygon channels.

https://web.iitd.ac.in/%7Echahar/Reprints/RP18_PolygonSeepage_ASCE.pdf

Analysis of Seepage from Polygon Channels

https://web.iitd.ac.in/%7Echahar/Reprints/RP19_Recharge_Rectangular_Hydrology.pdf

Recharge/seepage from an array of rectangular channels

The problem of seepage from unlined surface canals or elongated ponds was investigated. Seepage from single or interacting canals has been computed for a variety of boundary conditions at the bottom of the seepage layer. Both the seepage rate and the free surface profile of the resulting seepage plume have been determined using the boundary element method. The boundary element method is appropriate for the solution of the types of problems investigated herein, due to the relative ease with which the location of the plume free surface can be determined. The results of this study were compared with those obtained via other solution techniques and available in the literature. The agreement was generally very good. A novel iteration technique was used for determination of the free surface of the plume that results from seepage through a layer with free drainage at its bottom. The results for all cases that were investigated are given in graphical form for a series of typical configurations.

Seepage from Surface Canals by Boundary Element Method

An exact solution is presented for the seepage flow from a system of parallel trapezoidal channels through a layer of homogeneous, isotropic soil. Under this layer there is a drain that might be represented physically by a bed of gravel or coarse sand. The flow is assumed to obey Darcy’s law and hence there is velocity potential which satisfies the Laplace equation. By constructing the complex potential and the complex velocity planes, the solution is obtained through conformal mapping. General expressions are given for the discharge and shape of the free streamline. A numerical example is presented for which the free surface and the velocity distribution on the channel’s profile were drawn. The quantity of seepage from the bottom and sides were also computed.

Ahmed El Nimr

Papers

Seepage from Parallel Trapezoidal Channels