关键词: 非圆形寒区隧道, 应力分布, 解析解, 复变函数法, 幂级数法

Abstract: In previous studies on stress analysis of tunnels in cold regions, the assumption of an equivalent circular cross-section is often adopted. However, this simplification significantly deviates from the noncircular cross-sections commonly encountered in engineering practice, resulting in considerable stress calculation errors. To overcome this limitation, an analytical solution for stress distribution in support-free noncircular tunnels in cold regions is proposed. First, a mapping function is derived using conformal transformation and optimization techniques, enabling the transformation of a noncircular domain in the z plane into a circular domain in the image plane. Then, utilizing complex function theory combined with the power series method, analytical functions that satisfy the stress-displacement boundary conditions are established, and a comprehensive analytical solution for the stress distribution in support-free noncircular tunnels is developed. This solution is subsequently validated through numerical simulations. Finally, a case study on the Dabanshan tunnel located in a cold region is conducted to examine the stress distribution in the surrounding rock mass. The results reveal that: (1) The stress variation amplitude and absolute stress values in both frozen and unfrozen surrounding rock within the 120°－150° segment are the highest, with the radial and tangential stresses at the interface between frozen and unfrozen rock reaching their maximum values at the arch foot of the tunnel. This indicates that stress concentration predominantly occurs at the arch foot of horseshoe-shaped tunnels. (2) In the absence of support, the region near the inner boundary of the frozen surrounding rock experiences tensile stress in the radial direction, while the unfrozen surrounding rock is subjected to compressive stress radially and tensile stress circumferentially. (3) An increase in the lateral pressure coefficient leads to a reduction in circumferential stress in the unfrozen surrounding rock and an increase in circumferential stress at the outer boundary of the frozen surrounding rock. Moreover, as the elastic modulus ratio between frozen and unfrozen surrounding rocks increases, the growth in radial stress at the contact interface is more pronounced than that of tangential stress.

Key words: noncircular tunnel in cold region, stress distribution, analytical solution, complex function method, power series method