盾构隧道拱顶塑性区及地表沉降分析与计算

按平面应变问题分析隧道地表沉降，不考虑重力场的影响作用，而仅认为其是由洞周土体应力释放引起的。在假定隧道周边土体应力释放荷载为均布的前提下，由实际的地表应力为0与圣维南原理可知无穷远处的侧边与底边应力也为0。从而可利用平面弹性力学关于无限大板的理论求出其应力，并将其应力与未开挖前仅受重力场作用下的应力叠加。由此分析拱顶土体的塑性区半径，如果其塑性区半径不大且在工程允许的误差范围内．可以认为隧道开挖后整个土体仍处于弹性状态，从而利用洞周受均布荷栽作用下弹性无限大板的位移解直接推求出地表的沉降方程。

Calculation and Analysis of Plastic Area and Ground Settlement for Shield Tunnel

Without the consideration of the effect of gravity field, the ground settlement rises from the stress according to the analysis of plane strain problems. Under the premise of the load released by the assumption stress be even, not only the actual surrounding stress of the ground is zero but also the infinite side and bottom stress is zero by Saint-venant principles. So the stress of infinite elastic plate can be calculated by using elastic theory of plane strain ,which the stress and the different stress of it only caused before metro tunnel excavation are piled up. Therefore, in order to analyze the radius of plastic area, if the plastic radius of vault is small in some value of release ration of stress, within the range of the allowance repeatability error, ground settlement curve equation is derived from the solution of infinite elastic plate.