Analytical Solution for the Steady Seepage Field of a Circular Cofferdam in Nonhomogeneous Layered Soil

Abstract

The analytical solution of the steady-state seepage field of a circular cofferdam in nonhomogeneous layered soil of finite depth is derived, including the head function, exit hydraulic gradient formula, and seepage flow formula. The head function is obtained by dividing the circular cofferdam seepage field into regions and then using the separated variable method combined with the Sturm–Liouville theory, and the unknown coefficients in the head function are determined by constructing a system of equations through the integral transformation of the Bessel function. Based on the head function, an analytical equation is also given for the exit hydraulic gradient and seepage flow. The accuracy of the proposed analytical solution is verified by a comparison with numerical results as well as with the results of other methods. The proposed analytical solution is a display analytical solution without singularities and can be used as an effective tool for the analysis of circular cofferdam seepage problems.