Analytical Approach for Modeling Axisymmetric Levee Underseepage

Abstract

A variety of real-world levee underseepage problems can best be modeled using an axisymmetric analysis approach. In current practice, axisymmetric levee underseepage analyses are performed using numerical modeling approaches, such as the FEM. In contrast, levee underseepage analyses of planar cross sections are often analyzed using a blanket theory analytical approach, which is quicker and more convenient than numerical modeling. To address this problem, this paper provides a derivation of a series of closed-form blanket theory analytical equations that can be used to perform an axisymmetric levee underseepage analysis. This derivation begins from the governing equation of semiconfined fluid flow beneath a levee in a shallow semiconfined aquifer. The equations that result from this derivation can be used to calculate the total head in the pervious foundation layer and the seepage quantity that passes through the levee foundation over time. Different equations are presented for different seepage directions relative to the axis of rotation and different model boundary conditions. A typical example problem is used to compare results from the axisymmetric analytical equations that are derived with those from axisymmetric finite-element analyses. For this example problem, the analytical equations yield results that are equal to or more conservative than those from the finite-element analysis, where conservative results correspond to greater seepage under the levee and higher heads at the levee toe.