One‐dimensional self‐weight consolidation with continuous drainage boundary conditions: Solution and application to clay‐drain reclamation

Abstract

Summary Traditional consolidation theories cannot provide good predictions of consolidation settlement in land reclamation because of their assumptions that the influence of soil's self‐weight is often neglected, and the drainage boundary is considered as fully pervious/impervious. In view of these limitations, an analytical solution is derived for one‐dimensional self‐weight consolidation problems with a continuous drainage boundary using the finite Fourier sine transform method. Following the classical Terzaghi's small strain theory, the soil's self‐weight is considered to produce consolidation settlement in dredged materials with a constant coefficient of consolidation. The continuous drainage boundary can essentially describe the time‐dependent variation of drainage capacity at the interface between two adjacent soil layers. By reducing the interface parameters, the effectiveness of the calculation is demonstrated against the Terzaghi's solution. The influence of interface parameters and soil's self‐weight stress coefficient on self‐weight consolidation is discussed. As expected, the rate of consolidation considering the self‐weight stress is faster, although the dependency of consolidation rate on the material property of void ratio is neglected. Moreover, the plane of maximum excess pore‐water pressure is estimated as a function of time factor, based on which a design chart is developed to optimize the layout of horizontal drains in land reclamation.

One‐dimensional consolidation of soil under multistage load based on continuous drainage boundary

“…In the Terzaghi consolidation theory, the boundary surface is just assumed to be pervious or impervious, which results in the boundary condition ( u (0, t ) = 0) being inconsistent with the initial condition ( u ( z ,0) = p ). Therefore, as demonstrated in Figure , this article introduces the continuous drainage boundaries as follows: where b , c , B , and C represent the interface parameters related to the properties of adjacent soil layers and reflect the drainage properties of the drainage boundaries, and they can be obtained through experimental simulation or engineering measurement inversion. Note that B and C are the normalized expressions of b and c , respectively, and the normalized time factor T v = C v t / h 2 .…”

“…In this comparison, a one‐stage ramp load with T c = 0.2 as shown in Figure is exerted onto the surface of the soil. It was explained from previous studies that the interface parameters B and C reflect the drainage capacities of the top and bottom surfaces of the soil, respectively, and the larger the values of these interface parameters, the stronger the drainage capacity of the corresponding boundary. It is also found from Figure that with the gradual increase of interface parameters B and C , the top and bottom surfaces of the soil are increasingly able to drain water, and when the interface parameters B and C become large enough (ie, B = C = 800 in this case), the distribution of the excess pore‐water pressure obtained by the present solution is consistent with that calculated by Conte and Troncone's solution .…”

“…According to the conventional Terzaghi consolidation theory, the plane of the maximum excess pore‐water pressure is at the mid‐height of the soil layer for double‐side drainage condition (ie, the top and bottom boundaries are pervious) and is at the bottom of the soil layer for single‐side drainage condition (ie, the top boundary is pervious, but the bottom boundary is impervious). However, as indicated by Feng et al, the position of the plane of the maximum excess pore‐water pressure is often not at the mid‐height or bottom of the soil layer and is dependent on the time factor, the coefficient of permeability, and the interface parameters of the top and bottom boundaries and other factors. In what follows, the influence of interface parameters and time factor on the plane of the maximum excess pore‐water pressure will mainly be investigated.…”

“…Recently, Mei et al have proposed a continuous drainage boundary and obtained an analytical solution for the one‐dimensional consolidation of soil under instantaneous load. The continuous drainage boundary was later extended to investigate more general engineering cases by Liu and Lei, Wu et al, Sun et al, Feng et al, and Zhang et al However, the original continuous drainage boundary from Mei et al is only made available for the cases of instantaneous load; it may be irrational to apply it directly into the cases of time‐dependent load, because there is a phenomenon of pore‐water pressure superposition in the latter cases (see detailed explanation in below sections). Therefore, a general continuous drainage boundary suitable for arbitrary time‐dependent load will be developed in this study.…”

Improved Double-Layer Soil Consolidation Theory and Its Application in Marine Soft Soil Engineering

“…Wang et al [39] showed that the continuous boundary has good applicability and extends to the semi-analytical solution of one-dimensional consolidation of unsaturated soil. Feng et al [40] established the one-dimensional consolidation equation for the continuous drainage boundary and studied the contribution of a soil's self-weight stress. Sun et al [41] established a general analytical solution for the one-dimensional consolidation of soil for the continuous drainage boundary under a ramp load.…”