Analytical solutions and application of circular cofferdams considering backseal effects

The seepage fields around a circular cofferdam are divided into four regions, and the fractional variable method is used to obtain the sequence solutions of the water head distribution in the four regions under the cylindrical coordinate system, combined with the continuous conditions between the regions, and the analytical solutions of the steady seepage fields of the circular cofferdam are obtained by using the bessel function orthogonality. The correctness and effectiveness of the analytical solutions are proved by comparison with the numerical results and those by other approximate methods. The analytical solutions can be used to solve the water inflow of the cofferdam and the water pressure of the concrete at the bottom of the cofferdam in the case of double-layer soil, and can be degraded to the case of the cofferdam without the bottom of the isotropic soil. Based on the analytical solutions, the distribution laws of the seepage water pressure of subsealing concrete are analyzed, and the instability failure laws of subsealing concrete considering seepage influences are discussed through an engineering example. The results show that the water pressure on the concrete under seepage is not uniformly distributed, but in the form of being small in the center and large in the periphery. The permeability coefficient and thickness of the concrete at the bottom of the seal significantly affect the magnitude and distribution of the seepage water pressure.