Abstract: Based on the instantaneous loading with continuous drainage boundary conditions, a continuous drainage boundary condition under arbitrary loading is derived. The one-dimensional consolidation equation of linear loading is established under the continuous drainage boundary conditions under arbitrary loading. Using the finite Fourier sine transformation method, the analytical solution is presented. The effectiveness of the solution is demonstrated by formula degradation and a comparison with finite element analysis results. The influence of the loading rate and interface parameters on the excess pore-water pressure and consolidation degree is discussed. The results show that the loading rate has a significant effect on consolidation, and that the greater is the loading rate, the faster the excess pore-water pressure dissipates. When the loading rate approaches to infinity, linear loading degradation is instantaneous loading. With the increase of the interface parameters, the excess pore-water pressure dissipates and the consolidation increases rapidly. When the interface parameter approaches to infinity, the drainage boundary degenerates into a complete permeable boundary. In engineering practice, when the interface parameters (or surcharge time) are determined, it is of certain significance to select suitable loading time (or interface parameters) to ensure the stability of foundation and to increase engineering benefits.