This paper proposes a rational framework for levee underseepage analysis that can be used for either deterministic or probabilistic assessment of a levee system. An analytical methodology is presented for modeling levee underseepage along straight and curved levee alignments. Taken together, the equations that are presented herein can be used to model a variety of different two-dimensional and three-dimensional levee configurations. These analytical solutions are developed using a coordinate transformation process in conjunction with convergent series expansions that utilize Bessel functions. The resulting equations that are presented illustrate the effect of boundary condition assumptions on calculated values of total head. Results from the analytical equations are compared with those from finite element analyses for certain example cases. Minor differences observed between the analytical solution and finite element calculation approaches are attributed to one of the major assumptions that is made during the derivation of the analytical model solutions: that the flow through the blanket layer is vertical, and that the flow through the foundation layer is horizontal. The remainder of the paper focuses on utilizing probabilistic analysis tools for levee underseepage analyses, in conjunction with the two-dimensional and three-dimensional equations that have been developed. An advanced-first order second moment (AFOSM) probabilistic approach is utilized to quantify the reliability index for a simple example problem, for different types of levee alignments (e.g., convex, straight, and concave levee sections).
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