盾构隧道开挖面稳定极限理论研究

Limit theoretical study on face stability of shield tunnels

基于村山氏极限平衡法和极限分析上限法研究了盾构隧道开挖面稳定性,推导了维持开挖面稳定的最小极限支护压力计算公式。类似于Terzaghi地基承载力的叠加原理,将极限支护压力表示为土体黏聚力、地表超载和土体重度三项贡献的叠加,并对各自影响系数进行了分析。分析结果表明,极限平衡法得到的黏聚力影响系数随土体内摩擦角增大而增大,随隧道埋深比增加而减小,地表超载和土体重度影响系数均随土体内摩擦角增大而减小,地表超载影响系数随隧道埋深比增加而减小,土体重度影响系数随隧道埋深比增大而增大。当内摩擦角较小时,极限分析法得到的三项系数与土体内摩擦角和隧道埋深比的关系表现出与极限平衡相同的规律,但当土体摩擦角达到一定值时,土体黏聚力和土体重度的影响系数则不再随隧道埋深比而变化,地表超载影响消失。极限分析法得到的极限支护压力及三项系数均低于极限平衡法,但更接近现有文献中的有限元数值模拟结果。

Based on the limit equilibrium of Murayama and the upper bound limit analysis method,the face stability of shield tunnels is studied.Formulas for calculating the least support pressure at collapse are deduced.Analogous to Terzaghi＇s superposition method commonly used in bearing capacity analysis,the least support pressure is expressed by the summation of the cohesion c,surcharge load q and gravity γ multiplied by the corresponding influence numbers Nc,Nq,Nγ.In the limit equilibrium,Nc increases with the increase of the friction angle and the decrease of the ratio of tunnel depth C to diameter D,Nq and Nγ decrease with the increase of the friction angle Nq decreases and Nγ increases with the increasing value of C/D.In the upper bound limit analysis,the three stability numbers show the same trends only when the friction angle is less than an appropriate value which depends on C/D;otherwise Nc and Nγ keep constant,and Nq turns to be zero for any value of C/D.The three stability numbers obtained from the upper bound limit analysis are less than the results of the limit equilibrium and fit to the results obtained by the FE numerical simulation in the literatures.