Interfacial thermal contact model for consolidation of multilayered saturated soils subjected to time-dependent heating and loading

Abstract

Heat transfers at the interface of adjacent saturated soil primarily through the soil particles and the water in the voids. The presence of water induces the contraction of heat flow lines at the interface, leading to the emergence of the thermal contact resistance effect. In this paper, four thermal contact models were developed to predict the thermal contact resistance at the interface of multilayered saturated soils. Based on the theory of thermal-hydro-mechanical coupling, semi-analytical solutions of thermal consolidation subjected to time-dependent heating and loading were obtained by employing Laplace transform and its inverse transformation. Thermal consolidation characteristics of multilayered saturated soils under four different thermal contact models were discussed, and the effects of thermal resistance coefficient, partition thermal contact coefficient, and temperature amplitude on the thermal consolidation process were investigated. The outcomes indicate that the general thermal contact model results in the most pronounced thermal gradient at the interface, which can be degenerated to the other three thermal contact models. The perfect thermal contact model overestimates the deformation of the saturated soil during the thermal consolidation. Moreover, the effect of temperature on consolidation properties decreases gradually with increasing interfacial contact thermal resistance.

1. Introduction

Soil consolidation is a critical consideration in analyzing the long-term safety and stability of geotechnical projects, such as land reclamation, embankments, raft foundations, and pile foundations, especially in the case of saturated soft soils with high compressibility and low permeability [1−9]. In recent years, there has been an increasing occurrence of coupled thermal-hydro-mechanical (THM) consolidation in saturated soils under non-isothermal conditions in the fields of energy and civil engineering. Examples of such applications, including geothermal mining [10], nuclear waste storage [11], deep drilling and excavation [12], energy pile [13], heat pipes [14], and thermal drainage consolidation method for soft foundations [15], are attracting the attention of an increasing number of scholars. In naturally saturated soils, the parameters of soil layers at different depths exhibit significant variations, resulting in significant layered characteristics. The interface between two layers of saturated soil with different parameters exhibits a significant roughness and tiny voids, through which heat primarily transfers via the soil grains and the water in the voids. Due to the significant difference in thermal conductivity between the two mediums, the presence of water causes an increase in resistance to heat transfer compared to fully compacted soil grains. This leads to the heat flow lines shrinking at the interface, leading to a difference in temperature increment between the upper and lower surfaces of the interface, known as the thermal resistance effect [16]. The thermal resistance at the interface can decrease the heat transfer rate and significantly impact the effect of thermal consolidation during the thermal consolidation. Therefore, it is essential to establish a thermal contact model that predicts the thermal resistance of the interface in the thermal consolidation analysis of multilayered saturated soils.

BIOT [17] first established the quasi-static governing equations for saturated porous media and subsequently obtained an analytical solution for the consolidation problem. Afterward, Biot’s work was extended from isothermal consolidation to non-isothermal states [18]. Based on Biot’s consolidation theory, numerous scholars have conducted extensive studies on the consolidation behavior of soil under the influence of thermal loads. BOOKER and SAVVIDOU [19, 20] derived exact solutions for thermal consolidation of soils subjected to point and spherical heat sources. ZHOU et al [21, 22] established the THM coupling model for saturated porous media that considered thermo-osmosis and thermal filtration effects, providing analytical solutions for the thermal consolidation of porous media subjected to columnar and spherical heat sources. MCTIGUE [23] proposed a linear theory for fluid-saturated porous media cons