盾构施工引起地表固结沉降问题的研究

将隧道周围土体视为均质连续各向同性的饱和弹性介质，采用保角变换的方法将含有隧道的半无限平面映射为同心圆环计算域。根据Terzaghi-Rendulic二维固结理论，建立隧道在不透水的情况下周围土体超孔隙水压力分布的控制方程。然后，采用分离变量法计算得到土体超孔隙水压力分布的解析解，最后，根据弹性理论计算得出隧道中线上方地表固结沉降的计算公式。结合算例，分析盾构施工扰动程度、土体渗透系数、土体弹性模量及隧道埋深等因素对隧道中心上方地表处固结沉降的影响。研究结果表明，地表固结沉降的增加值与隧道外侧初始超孔隙水压力值C0的变化量成正比例关系，施工扰动程度越大所引起的固结沉降越大；土体的渗透系数越大固结沉降速度越快，但土体的渗透系数与最终的地表固结沉降量无关；土体的弹性模量越大，最终的地表固结沉降量越小；隧道埋深越深，地表固结沉降所需时间越长，最终的地表固结沉降量也越大。

Research on consolidation settlement of ground surface caused by shield tunnelling

Regarding the soil around the tunnel as homogeneous, continuous, isotropic, saturated and elastic medium, the conformal mapping method is applied to transform the considered region in the physical plane into concentric ring region in the image. The control equation for dissipation of excess pore water pressure is established based on Terzaghi-Rendulic theory of two-dimensional consolidation when the lining is impermeable. The analytical solution for dissipation of excess pore water pressure is obtained using separation variables method; and the formula for consolidation settlement is got according to the theory of elasticity. Combined with an example, consolidation settlement of ground surface is discussed considering disturbance degree of soil, soil’s coefficient of permeability, soil’s modulus of elasticity and the depth of tunnel. The results show that there is a proportional relationship between the added value of consolidation settlement and the variation of initial excess pore water pressure in the outside of tunnel. And the greater the disturbance degree is, the larger the consolidation settlement is. The greater the coefficient of permeability is, the faster the consolidation settlement is. There is no relationship between the coefficient of permeability and the final value of consolidation settlement. The larger the modulus of elasticity is, the larger the final value of consolidation settlement is. The deeper the tunnel is, the longer the time of consolidation settlement is, and the larger the final value of consolidation settlement is.