Investigation on One-Dimensional Nonlinear Thermal Consolidation of Saturated Clay under the Impeded Drainage Boundary
Publication: International Journal of Geomechanics
Volume 24, Issue 1
Abstract
Temperature changes affect the nonlinear consolidation process in soils, and there is limited associated theoretical research. In this study, the governing equations for nonlinear consolidation and thermal conduction are developed, and a mathematical model for one-dimensional nonlinear thermal consolidation in saturated clay under the impeded drainage boundary is established, where the temperature-dependent compressibility and permeability are considered. Meanwhile, the finite-difference solutions for nonlinear consolidation and the analytical solutions for thermal conduction are obtained, respectively. Furthermore, the proposed model’s reasonableness is verified by comparison with other theoretical models. Based on this, the impact of several factors on nonlinear thermal consolidation behaviors is investigated. With a rise in temperature increment (ΔT), the dissipation rate of excess pore water pressure (EPWP) accelerates in the later consolidation stage, and the final settlement becomes larger. In addition, the EPWP dissipation rate grows remarkably with an increasing impeded drainage boundary parameter (μ). In particular, the impeded drainage boundary can be degraded into a drainage boundary when the value of μ becomes large (e.g., μ = 100 m−1). Increasing preconsolidation pressure (pcR) results in a reduction in settlement, and the maximum values of EPWP decline with a rising linear loading time (tc). Overall, this study contributes to the accurate prediction of the nonlinear consolidation process taking the thermal effect into account.
Practical Applications
This study might provide a basis for the analysis of soil consolidation features in geotechnical projects that involve thermal effects, which have been growing in number in recent decades. For instance, an approach that combines thermal treatment with surcharge preloading has started to be employed for soft soil reinforcement. When this method is used in practical engineering projects, the changes in EPWP and settlement can be predicted based on the model developed in this study. In addition, this study reveals that increasing the temperature by 60°C can lead to an increase in the final settlement of saturated clay by approximately 25%, compared with ambient temperature treatment. Besides, compacted clay, which typically serves as a bottom engineering barrier, might be subject to consolidation deformation due to varied temperatures and external loading. The model presented could contribute to properly predicting the porosity change in compacted clay under this scenario.
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Data Availability Statement
All data, models, or codes generated or used during this study are available from the corresponding author by request.
Acknowledgments
This work is financially supported by the National Key Research and Development Program of China (Grant No. 2019YFC1804003), the Funds for International Cooperation and Exchange of the National Natural Science Foundation of China (Grant No. 51861165104), and the National Natural Science Foundation of China (Grant No. 42107185). Their support is gratefully acknowledged.
Notation
The following symbols are used in this paper:
- Ce, Cc
- swelling and compressibility indices;
- Ck
- permeability index;
- Cs, Cw
- specific heat capacities of soil particles and pore water;
- CT0, λT0
- initial volumetric specific heat and thermal conductivity;
- e, e0
- void and initial void ratios;
- I, J
- space step and time step numbers;
- Jh
- thermal flux of unit volume in saturated clay;
- kv, Kv
- permeability and intrinsic permeability coefficients;
- kv0, kv0,R
- initial permeability coefficient at temperatures T and R;
- L
- saturated clay thickness;
- mv
- volume compressibility coefficient;
- n
- porosity of saturated clay;
- pcR
- preconsolidation pressure at temperature R;
- q, q0, qu
- surcharge, initial surcharge, and final surcharge loading;
- R, T
- reference temperature and temperature;
- T0
- temperature at the initial time;
- t, t0, tc
- time, given time, and linear loading time;
- Up
- consolidation degree defined by EPWP;
- u, S
- EPWP and settlement;
- V, W
- two variables in Eq. (28);
- vd, g
- Darcy velocity of pore water and acceleration of gravity;
- z
- vertical downward coordinate;
- ΔpcR
- change in preconsolidation pressure;
- ΔT
- temperature increment;
- Δz, Δt
- space and time steps;
- Φ, Φ0
- heat and initial heat contents of unit volume in saturated clay;
- αw, αs, αv
- thermal expansion coefficients of pore water, soil particles, and saturated clay;
- αu
- thermal expansion coefficient of soil skeleton.;
- volume strain;
- θ
- semithermal insulation boundary parameter;
- γ
- empirical parameter of temperature;
- λT
- thermal conductivity of saturated clay;
- λs, λw
- thermal conductivities of soil particles and pore water;
- μ
- impeded drainage boundary parameter;
- ρs,R, ρs
- densities of soil particles at temperatures R and T;
- ρw, η
- density and dynamic viscosity coefficient of pore water;
- σ′,
- effective and initial effective stress; and
- φ, ,
- functions linked with temperature T.
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International Journal of Geomechanics
Volume 24 • Issue 1 • January 2024
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© 2023 American Society of Civil Engineers.
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Received: Jun 23, 2022
Accepted: Jul 11, 2023
Published online: Nov 7, 2023
Published in print: Jan 1, 2024
Discussion open until: Apr 7, 2024
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