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 引用本文: 李岩松, 陈寿根. 寒区非圆形隧道冻胀力的解析解[J]. 力学学报, 2020, 52(1): 196-207.
Li Yansong, Chen Shougen. ANALYTICAL SOLUTION OF FROST HEAVING FORCE IN NON-CIRCULAR COLD REGION TUNNELS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 196-207.
 Citation: Li Yansong, Chen Shougen. ANALYTICAL SOLUTION OF FROST HEAVING FORCE IN NON-CIRCULAR COLD REGION TUNNELS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 196-207.

## ANALYTICAL SOLUTION OF FROST HEAVING FORCE IN NON-CIRCULAR COLD REGION TUNNELS

• 摘要: 利用复变函数相应理论引入一种求解考虑衬砌结构的季节性冻土地区非圆形隧道冻胀力和冻胀变形的方法. 方法克服了隧道断面形状为非圆形状并且同时考虑非圆形隧道支护、冻胀圈、未冻围岩时, 经典的复变函数理论不能直接应用求解非圆形隧道应力和位移的问题. 方法通过将经典复变函数理论与连续性条件结合, 导出了非圆形隧道衬砌-冻胀圈-未冻围岩系统在正交曲线坐标系\zeta 平面内的解析式, 然后通过保角变换求得直角坐标系Z平面上考虑衬砌支护的寒区非圆形隧道冻胀力和冻胀变形. 将推导的解析式应用于鹧鸪山隧道洞口段研究中, 得到鹧鸪山隧道洞口段冻胀应力和冻胀位移解析解, 并将解析解与数值解进行对比,验证解析解的正确性. 由结果可知: 围岩冻胀力对衬砌影响明显, 在拱顶、拱脚、拱底处因冻胀造成的环向附加应力显著增大; 在拱脚及两侧拱肩处会受到较大的法向附加应力; 由于衬砌几何形状的原因, 造成了衬砌冻胀变形的不均匀, 进而造成冻胀力分布不均.应用复变函数理论将冻胀圈考虑为马蹄形、直墙拱形等非圆形状较以往将冻胀圈考虑为单一圆环的冻胀力研究更符合实际, 较以往研究更能反映实际工况. 研究结果为季节性冻土地区非圆形隧道冻胀力的弹塑性分析奠定了基础.

Abstract: A complex variable method is presented of stress and displacement problems for non-circular cold region tunnels. The complex variable method considers the non-circle tunnel support, the frost heaving circle and the unfrozen surrounding rock at the same time, making the problem from the single connected domain to multi connected domain problem, and can not directly apply the classical complex function theory to solve the problem of the stress and displacement of the non-circular tunnel. The analytical formula in Zeta plane orthogonal curvilinear coordinate system of non-circular tunnel lining to frozen surrounding rock to unfrozen surrounding rock system is derived by using classical complex variable method and continuity condition with power series and conformal transformation. Then, the frost heaving force and frost heaving deformation of the non-circular cold region tunnel are obtained by conformal transformation. This complex variable method is applied to Zhegushan tunnel research, and the analytical solution of Zhegushan tunnel openning frost heave stress and frost heave displacement is obtained. Comparing the analytical solution with the numerical solution to verify the correctness of the analytical solution. It can be seen from the results that frost heaving force has an obvious influence on the lining, and the additional circumferential stresses caused by frost heaving at the vault, arch foot and arch bottom are significantly increased. The additional normal stresses caused by frost heaving at the vault and both sides of arch shoulder are significantly increased. Because of the geometric configurations of lining, the frost heaving deformation is uneven, which leads to uneven distribution of frost heaving forces. Compared with previous studies, which consider the frost heaving ring as a single ring, the complex variable method is more practical. And the research results were expected to provide a referenced basis for elasto-plastic analysis of cold-region tunnel.

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