Seepage calculation for levees on foundation with double strata

At the both sides of rivers in alluvial plain, the double strata with of upper clay stratum over sand stratum are ubiquitous. For their seepage calculation, there are many systematic theoretical solutions with different boundary conditions. However, the corresponding seepage calculations of levees themselves are widely different from the conditions of homogeneous subgrade and impervious subgrade, whereas there are no theoretical solution. The confined water level in sand stratum under the levees is first calculated, the water level of the middle cross section of levee is almost equal to the confined water level. According to the above discussion, and for the convenience to solve the problem, the integral levee is divided from the middle cross section into two parts, i. e., upstream part and downstream part. For each part, the upstream and downstream boundaries are regarded as stretching to infinite, then by using the conformal translation method, the theoretical solutions of each part of the levee are derived. For the usual slope ratios of levees in China, upstream of 1∶3 and downstream below the release point of 1∶5, numeral results and illustrative example are given. For the downstream part of levees, which is the key place of safty analysis, a series of fitting formulae according to the detailed numerial results are given for convenient application. Compared with the results of electric analog tests, the simplified theoretical solutions possess higher precision. All the results can be extended fully to the levees on the multi-strata foundation with surface clay stratum, and to other slope ratios.