Analytical Solution for One-Dimensional Consolidation of Soil with Exponentially Time-Growing Drainage Boundary under a Ramp Load

Abstract

By introducing the exponentially time-growing drainage boundary, this paper investigated the one-dimensional consolidation problem of soil under a ramp load. Firstly, the one-dimensional consolidation equations of soil are established when there is a ramp load acting on the soil surface. Then, the analytical solution of excess pore water pressure and consolidation degree is derived by means of the method of separation of variables and the integral transform technique. The rationality of this solution is also verified by comparing it with other existing analytical solutions. Finally, the consolidation behavior of soil is studied in detail for different interface parameters or loading scheme. The results show that the exponentially time-growing drainage boundary can reflect the phenomenon that the excess pore water pressure at the drainage boundaries dissipates smoothly rather than abruptly from its initial value to the value of zero. By adjusting the values of interface parametersbandc, the presented solution can be degraded to Schiffman’s solution, which can compensate for the shortcoming that Terzaghi’s drainage boundary can only consider the two extreme cases of fully pervious and impervious boundaries. The significant advantage of the exponentially time-growing drainage boundary is that it can be applied to describe the asymmetric drainage characteristics of the top and bottom drainage surfaces of the actual soil layer by choosing the appropriate interface parametersbandc.