General analytical solutions for one‐dimensional nonlinear consolidation of saturated clay under non‐isothermal distribution condition

Abstract

The fluctuation of temperature leads to the changes of physical‐mechanical properties of clayey soils. In some practical projects such as landfills, the compacted clay liner is usually subjected to a non‐isothermal distribution state. For one‐dimensional nonlinear consolidation process of saturated clay under non‐isothermal distribution condition, the general analytical solutions considering time‐dependent loading are derived for the first time, where the methods of algebraic transformation and separation variable are used. Moreover, two forms of boundary conditions are included according to engineering practice. Referring to the proposed general analytical solutions, the expressions for the analytical solutions under instantaneous loading pattern and single‐stage linear loading pattern are developed. Besides, the correctness of the presented analytical solutions is validated by comparing with the existing analytical solutions and finite difference solutions. Based on the proposed analytical solutions, the influence of temperature gradient, final loading and loading time on the consolidation behaviors is analyzed. It is found that the increase in temperature gradient accelerates the consolidation rate, and the average volume compressibility coefficient decreases by 65.4% when final loading increases from 50 to 500 kPa. In conclusion, the analytical solutions proposed in this study are more comprehensive and can be applied in different engineering cases.

Consolidation calculation of a foundation partially penetrated by concrete‐cored gravel (CCG) columns

“…The proposed analytical solutions will be promoted if the time‐dependent variations of these consolidation‐related parameters are involved 28,29 . In addition, the proposed analytical solutions are expected to spread into more circumstances, such as unsaturated soft soils causing varying negative and positive friction along the pile shaft 30,22 and nonlinear constitutive models of subsoils 31,32 …”

“…28,29 In addition, the proposed analytical solutions are expected to spread into more circumstances, such as unsaturated soft soils causing varying negative and positive friction along the pile shaft 30,22 and nonlinear constitutive models of subsoils. 31,32 Notation: Basic SI units are given in parentheses…”

Coupled model for one‐dimensional nonlinear consolidation and organic contaminant transport in a triple‐layer composite liner considering the nonisothermal distribution condition

“…Using the variation of dynamic viscosity coefficients with temperature at standard atmospheric pressure (see Table 1), 61,68 the following relationship can be adopted approximately: $$$$\begin{equation} \eta \ \left({T}_{c}\right)=\frac{36.42\ensuremath{\times{}}{10}^{-3}}{{T}_{c}+19.2}\ \mathrm{Pa}\cdot \mathrm{s}\ (\ {R}^{2}=\ 0.99) \end{equation}$$$$…”

“…Moreover, the semi‐logarithmic relationship is commonly applied to describe the nonlinear variation of permeability coefficient with void ratio as the CCL consolidation proceeds 7,61,69 : $$$$\begin{equation}e\ = {e_0}\ + {C_k}\lg [{k_v}\left( {{T_c}} \right)/{k_{v0}}\left( {{T_c}} \right)]\end{equation}$$$$where $${C_k}$$ represents the permeability index; $${k_{v0}}( {{T_c}} )$$ denotes the initial permeability coefficient at temperature $${T_c}$$.…”

“…Besides, Li et al. developed a 1D analytical model for nonlinear consolidation of clay under a nonisothermal environment, where the effect of temperature‐dependent permeability was taken into account 61 . These experimental and theoretical studies indicate that the nonisothermal distribution condition in composite liners has an effect on the nonlinear consolidation behaviors of CCL, and thus also impacts the transport characteristics of organic contaminant.…”