Deterministic and probabilistic approaches for modeling levee underseepage

Levees are earthen structures that are used to provide flood protection, especially in lowland areas. They are typically built along rivers to protect surrounding areas against seasonal or flash flooding, or along coastal areas to prevent intrusion of the sea. Currently in the United States, there are more than 100,000 miles of levees that protect a wide range of urban and rural property. However, this levee system is extremely susceptible to disaster, as failure of even a single levee in a given flood protection system can lead to failure of the entire system. In many areas, failure of a single levee could lead to significant loss of life and economic damages ranging in the billions of dollars; recent levee failures in New Orleans during Hurricane Katrina have illustrated the widespread damage that can occur when a levee system fails. From historical observation, a number of earthen levee failures have been caused by concentration of seepage flow through levee foundations, a phenomenon which is commonly referred to as levee underseepage. This concentration of seepage in the levee foundation can generate excessively high pore pressures in the soil matrix, and can subsequently lead to particle erosion of the foundation soil. Significant soil erosion leads to formation of seepage pipes, which can progressively lead to collapse of the levee itself. In order to prevent levee failures via this underseepage piping failure mechanism, analytical or numerical modeling techniques are typically used to perform a levee underseepage analysis using a set of deterministic design tools. The most commonly utilized approach for performing a levee underseepage analysis in the United States is to use the simplified analytical solutions that are presented in the United States Army Corps of Engineers (USACE) levee design manual that employ a blanket theory approach. This design tool offers a quick assessment tool for levee underseepage that minimizes the use of computer software and numerical models. In general, the solutions that are developed for the different levee cases in the USACE levee design manual are two-dimensional in nature; they are designed to be applied to a representative planar levee cross section, which corresponds to the seepage behavior that occurs beneath a long, straight levee. This type of simplified analysis approach implies that there are no three-dimensional effects on levee underseepage, resulting from a non-linear levee system alignment. However, there are many field situations where it may be necessary to curve the alignment of a levee to follow the path of a waterway that it bounds. The first goal of this research is to extend current analytical design tools for earthen levee underseepage that can be utilized for both straight and curved levee configurations. Three different sets of analytical solutions that cover three different types of underseepage flow (i.e. planar flow, convex axisymmetric flow, and concave axisymmetric flow) were derived for four practical boundary condition combinations. Two-dimensional finite element underseepage analyses are conducted to verify the series of the analytical solutions that were developed in this study. A comprehensive study is also performed using three-dimensional finite element underseepage analyses to provide a better understanding of the differences in behavior between a real curved levee model and the analytical ones. It should be noted that the series of proposed analytical solutions is deterministic in nature, and does not provide a means for assessing the risk of failure of a given levee system, or of its individual components. In order to convert conventional levee underseepage analysis tools into a reliability-based framework, it was necessary to incorporate probabilistic tools. The second goal of this research is to investigate the underlying uncertainty in predictions of levee underseepage by incorporating the developed deterministic analytical solutions into a probabilistic analysis framework. Three probabilistic analysis models, including the mean-value first order second moment (MVFOSM), advanced first order second moment (AFOSM), and Monte Carlo simulation (MCS) approaches, are utilized to assess the probability of failure for a given underseepage case. A comparison among the three probabilistic models provides an insight into their suitability of use for levee underseepage. Parametric study analyses are also conducted to investigate the sensitivity of design input parameters to the probability of failure. Taken together, general guidelines and useful recommendations for underseepage probabilistic analysis are also provided for practicing engineers.