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.
Highlights
The consolidation problem of soil has always been one of the key problems of soil mechanics, for it has close relation with the deformation, strength, stability, and seepage of soil mechanics
By introducing the exponentially time-growing drainage boundary, this paper investigated the one-dimensional consolidation problem of soil under a ramp load
The results show that the solution obtained by Terzaghi’s drainage boundary can not be reduced to the solution degenerated from the presented solution, and the curves obtained by the solution based on Terzaghi’s drainage boundary are not smooth and have mutations at the top and bottom drainage surfaces
Summary
The consolidation problem of soil has always been one of the key problems of soil mechanics, for it has close relation with the deformation, strength, stability, and seepage of soil mechanics. Considering the significant influence of initial condition on the consolidation process of soil, a large number of investigators have proposed various solutions for onedimensional consolidation problem of soil under different loads, such as linear load [8], rectangular load [9], random load [10], cyclic loading [11,12,13], and ramp loading [13,14,15]. The drainage at the boundaries of consolidating soil is impeded for most engineering applications [16] With regard to this aspect, Gray [16] first proposed an impeded drainage boundary which was later pursued by Schiffman and Stein [17] to investigate the consolidation problem of soil with variable permeability and compressibility. The objective of this article is to develop a general analytical solution for the one-dimensional consolidation of soil with exponentially time-growing drainage boundary (abbreviated as ETGD boundary for convenience) under a ramp load. The influence of the interface parameters of the ETGD boundary on the consolidation behavior of soil is discussed in detail based on the present solution
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