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基于平面弹性复变函数中的保角变换方法,推导出带有衬砌的非圆形隧洞在原始地应力作用下的应力解析解。根据衬砌内边界的应力边界条件及围岩衬砌接触面上的应力和位移连续条件,获得求解围岩和衬砌解析函数的基本方程,计算了围岩和衬砌中的应力和位移。在求解过程中,考虑了支护滞后于开挖的力学过程,并认为围岩和衬砌之间紧密接触,不会相互分开和相对滑动。以马蹄形隧洞为例,获得了围岩开挖边界和衬砌内外边界的切向应力及围岩与衬砌接触面上的接触应力分布规律,并与ANSYS数值方法结果对比,算例表明两种方法的计算结果吻合很好。
Based on the conformal mapping method in planar elastic complex function, the stress analytical solution of the non-circular tunnel with lining under the original in-situ stress is deduced. According to the stress boundary conditions of lining inner boundary and the continuous stress and displacement conditions on the contact surface of surrounding rock lining, the basic equations for solving the analytic function of surrounding rock and lining are obtained. The stress and displacement in surrounding rock and lining are calculated. In the process of solving, the mechanical process lagging behind the excavation was taken into consideration, and the close contact between the surrounding rock and the lining was considered and would not separate and slide relative to each other. Taking the horseshoe-shaped tunnel as an example, the tangential stress of the surrounding rock excavation boundary and lining internal and external boundaries and the contact stress distribution law of the contact surface between the surrounding rock and the lining were obtained. Comparing with the ANSYS numerical results, the results show that the two methods The calculated results are in good agreement.