为量化隧洞开挖引起的围岩压力、输水运行中的内外水压在围岩-衬砌结构中的传递和分配，采用复变函数方法建立一种地层-结构计算模型。将作用于圆环衬砌上的内外水压简化为径向均布荷载，并基于围岩-衬砌完全接触边界条件，即应力连续和位移协调，求解反映两者相互作用关系的解析函数，由此得到围岩-衬砌结构内任意位置处的应力和位移分量。分析结果表明： 1)围岩-衬砌之间的接触径向应力呈余弦分布，剪力呈正弦分布； 2)外水压的存在导致围岩-衬砌之间的有效应力减小； 3)考虑外水压作用时可在一定程度上减小高内水压运行引起的衬砌拉应力区。

To analyze the transfer and distribution of surrounding rock pressure caused by tunnel excavation, as well as internal and external hydraulic pressures acting on the rock-lining structure, a formation-structure calculation model is established using the complex function theory. The hydraulic pressure on the ring lining is simplified to a radial uniform load. An analytical function describing the interaction between the surrounding rock and lining is derived using complete contact boundary conditions, specifically, stress continuity and displacement coordination. Finally, the stress and displacement components at any position in the surrounding rock and lining structure are derived. The analysis yields the following results: (1) The radial contact stress between the surrounding rock and lining exhibits a cosine distribution, whereas the shear force exhibits a sine distribution. (2) The external hydraulic pressure reduces the effective stress between the surrounding rock and lining. (3) The action of the external hydraulic pressure partially reduces the lining tension stress zones caused by high internal hydraulic water pressure.