Hydraulics of Seepage from Trapezoidal Channels

Abstract

A tractable analytical solution for steady-state two-dimensional seepage from a trapezoidal channel in a homogeneous, isotropic porous medium of considerable depth is presented. The analysis is performed by applying the method of inversion and the Schwarz-Christoffel transformation accounting for the capillary action. Because the right half-seepage domain is a mirror image of the left half-seepage domain about the vertical axis (on either side of the channel central plane) owing to the axisymmetric channel, a solution is sought for the right half-seepage domain. The results show that an increase in channel bottom width boosts seepage flux. On the other hand, an increase in channel side slope also amplifies seepage flux. In addition, capillarity plays a subtle role in augmenting the seepage flux from a channel. The analysis suggests that the dynamic capillary rise (i.e., the vertical rise of seepage water along the side slope owing to capillary action) is always less than the static capillary rise. The analysis also presents the relation for the seepage velocity distribution along a channel perimeter. The equations of seepage line coordinates yield the seepage line initially curving downward with a significant lateral shift and eventually becoming vertical at a great depth. Particular solutions for the triangular and rectangular channels and the vertical slit, which is a channel with vertical sides and negligible top width, can be obtained from the generalized solution for the trapezoidal channel. Therefore, this study provides insight into the hydraulics of seepage from a trapezoidal channel, including its particular cases, revealing some new features.