基于Terzaghi‐Rendulic二维固结理论，将土体视为饱和弹性介质，采用保角变换的方法将含有圆环（隧道）的半无限空间区域映射为圆环域，建立衬砌在不透水的情况下隧道周围土体超孔隙水压力分布的控制方程。采用分离变量法对该控制方程进行求解，得到处于饱和弹性土体中隧道周围土体超孔隙水压力消散的解析解。结合算例分析不同隧道埋深的情况下隧道顶部及水平向超孔隙水压力随时间变化的情况，以及埋深一定时隧道上方土体超孔隙水压力的变化规律。研究结果表明：隧道埋深越深，周围土体中超孔隙水压力的消散速度越慢；在开始阶段超孔隙水压力消散速度较快，随着时间的推移消散速度逐渐减慢；隧道周围土体水平向超孔隙水压力的消散速度要比竖向的消散速度快；隧道上方土体距离隧道越近，超孔隙水压力的消散速度越快。%Based on Terzaghi‐Rendulic two‐dimensional consolidation theory , soil is regarded as saturated elastic medium . With the semi infinite space area that contains circular ring (tunnel) being mapped to a circular ring region using conformal mapping method , the control equation for dissipation of excess pore water pressure in the soil around the tunnel was established in the case of impermeable lining . The method of separation of varia‐bles was applied to solve the control equation , to obtain the analytical solution for dissipation of excess pore water pressure in the soil around the tunnel that is situated in saturated elastic soil .Combined with the calcula‐tion ,an analysis was performed on the time‐varying excess pore water pressure at the top of tunnel and hori‐zontal level under different depth of tunnel ,as well as on the change law of excess pore water pressure in the soil above the tunnel . The results showed that the deeper the tunnel was , the slower the dissipating speed of excess pore water pressure in the surrounding soil . The dissipating speed of excess pore water pressure was faster at the beginning , while it became slower gradually with the passage of time . The dissipating speed of horizontal excess pore water pressure in the soil around the tunnel was faster than that of verticle excess pore water pressure .The closer the soil above the tunnel is to the tunnel ,the faster the dissipating speed of excess pore water pressure .
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