Thermal Stress of Fractured Rock Under Solar Radiation Based on a Typical Shape Function Method

Yang Wang () and Wenhua Chen
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Yang Wang: China Academy of Cultural Heritage, Beijing 100029, China
Wenhua Chen: School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China

Mathematics, 2025, vol. 13, issue 17, 1-22

Abstract: Tunnel portal rocks in southern China, which are exposed to intense solar radiation and temperature fluctuations, are susceptible to thermal stress, which directly or indirectly affects the safety, stability, and normal use of a tunnel and its peripheral structures. Fractures act as conduits for solar radiation energy, converting it into thermal energy within the rock, thereby altering the thermal stress field. As formation mechanisms of rock, fractures are complex, and the nonlinear thermal conduction at fracture tips leads to thermal stress concentration. A parabolic shape function for the heat source and thermal stress at tips of rock fractures is herein proposed, and the thermal stress field of fractured rocks under solar radiation is obtained. The applicability of different fracture heat source functions for analyzing the effects of heat on rocks with varying thermodynamic properties is discussed. Compared with a linear heat source function, the thermal stress values of rock fracture tips are larger. The daily maximum σ θ max increases by 8.14% when α c = 0.05 based on the parabolic heat source function, providing more conservative results for the thermal stability analysis of fractured rock under solar radiation. Parabolic heat source functions are more reasonable for soft rocks with high thermal conductivity and low thermal deformation, while linear heat source functions are more appropriate for hard rocks. A parabolic heat source function is a typical function for analyzing the effects of heat on fractured rocks under solar radiation.

Keywords: rock mechanics; solar radiation; fractured rock; thermal stress; shape function method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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