Analytical solution for one-dimensional consolidation of double-layered soil with exponentially time-growing drainage boundary

Wenbing Wu,Rongzhu Liang,Mengfan Zong,M Hesham El Naggar,Guoxiong Mei

doi:10.1177/1550147718806716

Abstract

In this article, the exponentially time-growing drainage boundary is introduced to study the one-dimensional consolidation problem of double-layered soil. First, the one-dimensional consolidation equations of soil underlying a time-dependent loading are established. Then, the analytical solution of excess pore water pressure and average consolidation degree is obtained by utilizing the method of separation of variables when the soil layer is separately undergone instantaneous load and single-stage load. The validity of the present solution is proven by the comparison with other existing analytical solution. Finally, the influence of soil properties and loading scheme on the consolidation behavior of soil is investigated in detail. The results indicate that, the present solution can be degraded to Xie’s solution utilizing Terzaghi’s drainage boundary by adjusting the interface parameter, that is to say, Xie’s solution can be regarded as a special case of the present solution. The interface parameter has a significant influence on the excess pore water pressure of soil, and the larger interface parameter means the better drainage capacity of the soil layer.

Highlights

Natural soils are often composed of several soil layers with different properties.[1]
For the present solution based on the ETGD boundary, the upper and lower soil layers have the same consolidation coefficients, the excess pore water pressure of soil with double-drainage boundaries decreases with the increase in a and b
These results show that, for practical engineering, even though the early consolidation process of the soil with the boundary surfaces designed according to the ETGD boundary is slow, it can make more sufficient dissipation of the excess pore water pressure of the whole soil layer, and it will not lead to the slow drainage of the lower soil layer or even the discharge of water after the consolidation of the upper soil layer

Summary

Introduction

Natural soils are often composed of several soil layers with different properties.[1]. International Journal of Distributed Sensor Networks an analytical solution for the one-dimensional nonlinear consolidation of double-layered soil associated with time-dependent loading on the basis of the work in Davis and Raymond.[3] More recently, Lee et al.,[5] Zhu and Yin,[6] Chen et al.,[7] Liu et al.,[8] and Liang et al.[9] further investigated the consolidation problems of multi-layered soil for different engineering conditions. Following Gray’s work, solutions of one-dimensional consolidation have been presented for one-,11–14 two-,15 and multi-layered soils[16,17,18,19] with various impeded drainage boundaries. The main objective of this article is to derive a general analytical solution for the one-dimensional consolidation of double-layered soil with exponentially time-growing drainage boundaries (abbreviated as ETGD boundary for convenience) underlying a timedependent loading.

H Àz xlm h1

Degeneration of solution for instantaneous load

Degeneration of solution for single-stage load

Conclusion