A semi-analytical solution for one-dimensional elasto-viscoplastic consolidation of layered soft clay

The last several decades have seen a surge of papers dealing with analytical and semi‐analytical solutions to the problem of one‐dimensional consolidation of soils. But rarely has any of these contributions focused on the time scales arising from combined primary and secondary compression. Primary compression has always been attributed to the dissipation of excess pore pressure as fluid is expelled from the soil skeleton to the drainage boundaries. However, there have been several schools of thought when it comes to the process governing the secondary compression. In this paper, we attribute the secondary compression to any of the following processes occurring either individually or in combination: (a) rate‐dependent (viscoplastic) constitutive response of the soil skeleton; (b) existence of a secondary pore scale system that expels fluid from the smaller‐scale pores to the larger‐scale pores; and (c) delayed compression due to creep following Bjerrum's concept of secondary consolidation. Contributions of the present work include closed‐form analytical solutions to the problem of combined primary and secondary compression of soils in one dimension, as well as a quantitative analysis of the time scales involved in such coupled hydromechanical processes.

Section: Introductionmentioning

confidence: 99%

Time scales in the primary and secondary compression of soils

Liu

Borja

2022

“…The initial excess pore pressures generated after the instantaneous loading

p_{0}

is applied to the two‐layered soils. If the total stress in soil layers is uniform with depth, the initial conditions 29,36,37 are given in the form:

u_{normalw}^{(1)} (z, 0) = u_{normalw}^{0}

u_{normala}^{(1)} (z, 0) = u_{normala}^{0}

u_{normalw}^{(2)} (z, 0) = p_{0}

where

u_{w}^{0}

denote the initial excess pore‐water pressure in unsaturated soils;

u_{a}^{0}

and

u_{w}^{0}

are determined generally with the help of the method proposed by Fredlund and Rahardjo 38 on pages 191–192.…”

Section: Mathematical Modelmentioning

confidence: 99%

Semi‐analytical solution for one‐dimensional consolidation of a two‐layered soil system with unsaturated and saturated conditions

Qin

Jiang

2021

Semi‐analytical solutions to one‐dimensional (1D) consolidation of the two‐layered soils are developed in this paper that can consider a two‐layered soil system with unsaturated upper soils and saturated lower soils. In this case, the upper soil layer remains the water‐air two‐phase flows, while the lower soil layer only involves the flow of the water phase. Based on the assumptions made in the 1D consolidation framework for saturated and unsaturated soils, the analytical solutions in the transformation space for the consolidation model are derived using a decoupling technique and the Laplace transformation. Subsequently, following the Crump algorithm, the numerical inverse Laplace transformation is carried for the related semi‐analytical results that can analyze the consolidation characteristics of the two‐layered soils in the time domain. Furthermore, two typical cases for saturated soils in the literature are shown to examine the methodology and final solutions. Finally, results of a case study in this paper indicate that the excess pore pressures within the unsaturated soil layer near the interface are significantly affected by the water flow in the saturated soil layer, and that the final primary consolidation settlement of soils would be overestimated if the unsaturated condition of upper soils is ignored.

“…Because of the change in soil behavior before and after the effective pressure exceeds the plastic yielding limit, to solve the governing equations, a hybrid combination of analytical and numerical methods, known as the semi‐analytical method, is adopted. In this methodology, the clay layer should first be discretized into a set of sub layers to linearize the governing equations and to determine the analytical solutions; simultaneously, the time period would be divided into couples of short intervals; then, the solutions for the sub layers must be summed in order to obtain the solution for the entire two‐layered soil.…”

Section: Semi‐analytical Solutionsmentioning

confidence: 99%

Study of the 1‐D consolidation behavior of two‐layered soft soils: Parametric studies using a rheological model with viscoplastic body

Zou

Xie

et al. 2018

Summary The governing equations for the coupled processes of consolidation and creep of two‐layered soft soils are established. The Nishihara rheological model is adopted to simulate the elasto‐viscoplastic characteristics of soft soils, disregarding the effects of the soil self‐gravity. A semi‐analytical theory combined with numerical and analytical methods is introduced to solve the governing equations of the one‐dimensional rheological model. The computational procedure and the approximate solutions for two‐layered soft soils subjected to surface loading are obtained for two drainage conditions. The solutions and the computational procedure are used to study the effects of the two layers and constitutive parameters on rheological consolidation behavior of soft soils. It can be concluded that two layers affect the rate of excess pore water pressure dissipation and settlement development. The parametric studies show that when the parameters of the upper layer remain constant, increases in the permeability and elastic modulus in the lower layer accelerate the dissipation of the excess pore water pressure, and meanwhile increases in the viscosity coefficient and viscoplastic limit slows down the dissipation of the excess water pressure.