An analytical approach for levee underseepage analysis

Abstract

Keywords:Analytical approach Groundwater flow Levees Underseepage Pressure head Seepage quantity s u m m a r y Levee underseepage analyses are commonly performed to assess the risk of erosion and piping of levee foundation soils. They are also commonly used to estimate the quantity of seepage that is expected to pass beneath a levee over time, and to assess the risk of excessively high pore pressures at various points in the foundation. A variety of approaches have historically been utilized to perform steady-state underseepage analyses in levees, including flow-nets, closed-form analytical solutions, and numerical techniques such as finite difference or finite element analyses. This paper provides a derivation of a series of closed-form ''blanket theory'' analytical equations that can be used to perform a levee underseepage analysis. This derivation starts from a generic confined flow analytical solution, of the type that is common in groundwater flow analyses. The solution is then extended to simulate semiconfined flow beneath a levee in a shallow aquifer. Equations are presented for calculating total head and seepage quantity values for different model boundary conditions. A typical example problem is used to compare the analytical equations that are derived with the analytical equations that are presented in the US Army Corps of Engineers (USACE) levee design manual. The results provide validation for both the equations that are presented and the conventional USACE analytical design approach. Using the results from the example problem, general guidance and suggestions are provided for designers that use closed-form analytical approaches for modeling levee underseepage.

Analytical Approach for Modeling Axisymmetric Levee Underseepage

“…2 Semiconfined Groundwater Flow: Cartesian Coordinate System (Planar Seepage) Meehan and Benjasupattananan (2012) provide a detailed discussion for the rationale behind using a closed-form blanket theory analytical approach to model planar seepage behavior in the foundation soil beneath levees. This type of analytical approach for modeling levee underseepage has a long history of use by the USACE (USACE 1956a(USACE , b, 2000Turnbull and Mansur 1961) accepted as a reasonable levee underseepage analysis tool, given the many uncertainties that are typically present when characterizing seepage model input parameters for levee analysis.…”

“…When modeling seepage in a semiconfined aquifer using a Cartesian coordinate system characterized by x, y, z-coordinates [ Fig. 1(b)], existing analytical models typically assume (1) that the permeable foundation layer is of constant thickness, d, and (2) that vertical velocities in the permeable foundation layer (v z ) are small compared with the horizontal velocities (v x , v y ) (Meehan and Benjasupattananan 2012). The second assumption is important in the derivation because it indicates that the change in head along the thickness of the permeable layer (∂h/∂z) will be relatively small compared with the change in head that occurs in the other spatial directions throughout the aquifer (∂h/∂x, ∂h/∂y).…”

“…The second assumption is important in the derivation because it indicates that the change in head along the thickness of the permeable layer (∂h/∂z) will be relatively small compared with the change in head that occurs in the other spatial directions throughout the aquifer (∂h/∂x, ∂h/∂y). Following this assumption and utilizing Darcy's law and Laplace's equation, the governing differential equation of fluid flow throughout a shallow semiconfined aquifer in a Cartesian coordinate system can be derived to be (Meehan and Benjasupattananan 2012;Benjasupattananan 2013)…”

“…For modeling planar seepage beneath a uniform levee cross section that has an impermeable base layer, i.e., the type of seepage modeling that is typically performed using the USACE (2000) approach, Eq. (1) can be simplified to (Meehan and Benjasupattananan 2012)…”

“…As noted in the introduction, the current paper is focused on the development of closed-form analytical solutions that can be used for axisymmetric modeling of levee underseepage. The general assumptions that are made during the derivation that is summarized in this paper are the same as those that are made by Meehan and Benjasupattananan (2012) during the derivation of a similar set of planar flow equations, in particular, that the seepage in the levee foundation can be reasonably characterized as shallow semiconfined flow. These assumptions are also the same as those that are made in the derivation of the USACE (2000) levee underseepage analysis approach (Bennett 1946).…”