复变函数法分析盾构隧道开挖引起的土体位移和衬砌变形

盾构隧道开挖引起的地层变形历来是人们所关注的重要课题。目前,既有成果较少考虑隧道衬砌与土体相互作用所带来的影响,尤其是较少针对衬砌变形进行分析,就此基于隧道椭圆化变形边界条件,提出了考虑衬砌与土体两种不同介质相互作用下的地层位移和衬砌变形复变函数解答。在该方法中,隧道埋深只影响共形映射后圆环域的环壁厚度,而解析区域依然保持圆形,具有不会对函数解析产生影响的优势;此外,该法经共形映射后保证了边界连续性,避免了既有应力函数法为保证隧道扰动土体无穷远处位移为零,而对解析解进行修正所导致物理意义不明确的缺陷。通过实例分析,得到了隧道开挖引起的地表沉降,并与实测数据进行了对比验证;通过参数分析,获取了扰动地层和隧道衬砌变形的影响规律。结果表明:复变函数解答得到的土体位移曲线与实测值吻合较好,且地表最大沉降值更接近于实测值;隧道的埋深和半径对土体位移和衬砌变形均有较大影响,衬砌厚度对其影响虽然较小,但仍不可忽略;衬砌径向位移曲线呈仰卧的鸭蛋形,关于90°/270°轴对称,拱顶和拱底被压扁,拱顶压缩量明显大于拱底,左、右两侧压缩量小于上、下两侧,表现为收缩之后又被压扁向左、右两侧突出,且随着埋深的增大,衬砌整体上浮;衬砌环向位移曲线呈侧立的苹果形,关于0°/180°轴对称,且在90°和270°处取值为零,随着隧道埋深的增大,环向位移绝对值增大。

Complex variable analysis of soil displacement and liner deformation induced by shield excavation

The ground deformation caused by shield excavation is always a key issue. The current studies give little attention on the impacts of interaction between tunnel liner and soils. Particularly the deformation analysis of the liner is not conducted. A complex variable solution for ground displacement and liner deformation is proposed considering the interaction of liner-soil and the boundary condition for the oval deformation. In this method, the depth of tunnel affects only the thickness of ring walls after conformal mapping and the analytical region remains round. It will not affect the function analysis. Besides, after the conformal mapping this method guarantees the continuity of boundary. It can make the soil displacements zero at infinity and avoid the analytical defects. That occurs via correcting analytical solution by which the existing stress function methods keep infinity soil displacement zero. Through the case analysis, the ground settlements induced by tunnel excavation are obtained and compared with the measured data. The deformation influence law of ground and tunnel liner is acquired through parameter analyses. The results indicate that the vertical displacement curves of soils are in good agreement with the measured values. The surface maximum settlement is closer to the actual one. The depth and radius of tunnel have a great influence on the soil displacement and liner deformation. Although the influence of thickness of liner is less, it cannot be ignored. The radial displacement of liner presents a shape of supine duck egg, which is symmetrical to the axis 90^°/270^°. Its value is negative, which means that the liner shrinks as a whole. The vault and arch bottom get squashed. The shrinkage in vault is greater than that in arch bottom. The shrinkage at the left and right sides is less than that at the upper and lower sides, which shows that the liner is crushed to the left and right sides after being compressed. With the increase of the tunnel depth, the liner comes up overall. The tangential displacement of the liner presents a shape of a toppled apple which is symmetrical to the axis 0^°/180^°. The values in 90^° and 270^° are zero. The absolute values of tangential displacement increase with the increase of depth.