Abstract: Aiming at the contradiction between the initial condition and the boundary condition in the existing consolidation problem, a continuous drainage boundary is introduced, and a continuous drainage boundary condition considering the arbitrary loadings is deduced on the basis of it, a one-dimensional consolidation model of the foundation under arbitrary loadings is established, and its dimensionless general answer was obtained. Then the Fourier series expansion of the trapezoidal cyclic loadings is substituted into the consolidation analysis. Finally, the superposition principle is used to superimpose the obtained consolidation solution, which is the one-dimensional consolidation analytical solution of trapezoidal cyclic loading under a continuous drainage boundary. The trapezoidal loading is reduced to a sudden load and compared with the existing literature to verify the rationality of the solution. The influence of interface parameters and trapezoidal cyclic loadings on the consolidation behavior was studied by parametric analysis.