Steady‐state subsurface drainage of ponded fields by rectangular ditch drains

A comprehensive analytical solution is presented for the steady‐state two‐dimensional drainage problem of the water flow from a horizontal ponded surface into rectangular cross‐section array ditches. The ditches partially penetrate into a homogeneous and isotropic porous medium of finite depth over an impervious layer. The solution includes the equations for drainage discharge into ditches, the drainage discharge through the seepage face and the water depth portion of a ditch, and seepage velocities along the ponded surface. The equations are obtained using the Schwarz–Christoffel transformation in the conformal mappings of the physical and hodograph planes on to an auxiliary plane. The proposed analytical solution is validated by comparing the results with the known experimental data and the other analytical works. The results of the analyses show that seepage velocity along the ponded surface water decreases with distance from the ditch and accordingly leaching of salts is non‐uniform. Closer spacing between two adjacent ditches, shallower water depth in the ditches, and deeper depth of the ditches are advantageous in removing salts from fields.