The shape function method of nonlinear thermal stress of granite fracture tips in a high-temperature environment

Exposed rock masses in tunnel portals are susceptible to thermal deterioration in southern China, where temperatures are relatively high. The thermal stress field of rock masses is affected by fracture shape and distribution as fractures near the surface are channels for solar radiation energy to be converted into rock thermal energy. In this study, a function expression is developed for triangular heat sources of fractured rock masses in a tunnel portal in a high-temperature environment. By the function expression, the temperature field and thermal stress field are calculated, and the influence of fracture shape parameters and multi-fracture interaction is analyzed. The results are as follows: (1) the temperature field and thermal stress field of exposed rocks are redistributed by fractures. The internal temperature of the fractured rocks is higher than that of non-fractured rocks, and thermal stress near the fracture tip increases. (2) For triangular fractures of the same length, thermal stress increases as the apex angle increases. (3) When the spacing between parallel fractures or coplanar fractures is close, the superposition effect of thermal stress becomes significant. (4) In a high-temperature environment, temperature field and thermal stress field of a fractured rock are both nonlinear as temperature and thermal stress around fractures increase significantly. The results provide effective reference for stability evaluation of fractured rock masses in tunnel portals and offer theoretical foundation for thermal diseases analysis and protection measures of tunnel engineering in high-temperature environments of southern China.