3D Numerical Manifold Method for Modeling Heat Conduction and Thermo-Mechanical in Quasi-Brittle Materials

Abstract

ABSTRACT Thermal fractures are common in natural rock masses, and numerous works are concentrated on this topic at present. Comprehending the failure mechanism of thermo-mechanical problems is crucial for enhancing the effectiveness and safety of engineering applications. Despite considerable endeavors to experimental results, precisely simulation 3D thermo-mechanical coupling remains a formidable challenge. This paper proposes a novel thermo-mechanical coupling model (3DNMM-TM) that integrates a heat conduction algorithm with the numerical manifold method (NMM) to effectively simulate problems related to heat conduction and thermo-mechanical coupling. The discrete equations for the system equation are derived using a variational method, and the penalty method is utilized to solve the crucial boundary conditions. The accuracy of the proposed 3DNMM-TM model is verified through numerical tests which compares with analytical solution. The results show that the proposed heat conduction model can effectively capture the effect of cracks on heat conduction as well as the sudden temperature change across the cracks. The model can be used as a robust tool to study the whole process and basic mechanism of thermodynamic behavior in quasi-brittle materials. INTRODUCTION The field of engineering frequently utilizes quasi-brittle materials, including but not limited to concrete, ceramics, and rock. The thermal conductivity within these solids is a crucial factor to consider (Ezekoye, 2016). Any temperature variation could potentially modify the thermal and mechanical characteristics of quasi-brittle materials (Gautam et al., 2018; Tan et al., 2022), leading to material degradation and engineering mishaps. For example, when a fire breaks out in a tunnel, its temperature can swiftly escalate to 700 °C or beyond within a brief period (Shen et al., 2023). A significant temperature gradient within concrete can result in thermal cracking (Committee, 2007). During CO2 geological sequestration, the injection of CO2 into the brine stratum at a depth ranging from 1000 to 2500 m may give rise to shrinkage or even fracturing of the adjacent saline rocks owing to the frigidity of the CO2 (Taylor & Bryant, 2014). In the subterranean repository of nuclear waste, the thermal energy generated by nuclear decay may elevate the temperature of the surrounding rock, leading to thermal cracking, and incidents involving nuclide leakage may transpire (Kim et al., 2011). Consequently, it is imperative to investigate the interdependent thermal-mechanical impact.