地表超载作用下隧道失稳破坏的上限有限元分析

针对地表超载作用下隧道稳定性和破坏模式问题，基于刚体平动运动单元上限有限元理论编程并计算分析，获得了浅埋隧道失稳临界超载系数上限解和刚性运动块体体系破坏模式。通过与现有的刚性块体极限分析上限法以及极限分析上、下限有限元法计算结果的对比分析，验证了上限解的可靠性。研究结果表明，（1）临界超载系数 黏聚力c之比 随土体内摩擦角 和隧道埋深C与直径D之比( )的增大而相应增大，随土体重度与黏聚力参数 的增大而减小；（2） 和 对隧道破坏模式的影响较明显； 增大，则隧道破坏范围增加；内摩擦角 增大，刚性运动块体破坏模式相互错动更加显著，相比而言， 对破坏模式的影响并不显著；（3）刚体平动运动单元上限有限元上限解精度高，所得刚性运动块体破坏模式具有滑移线形态，能精细地反映隧道失稳破坏特征。

Finite element upper bound analysis of tunnel instability under surcharge loading

Stability and failure mechanism of shallow tunnel under surcharge loading is studied. The program is compiled based on finite element upper bound theory with rigid blocks translatory moving elements to obtain upper bound solution of critical surcharge coefficients and rigid block movements failure mechanism. Comparing with current results of rigid blocks upper bound solution and finite element upper and lower bound solutions of limit analysis, it is proved that the proposed upper bound solution is reliable. The results show that: critical surcharge coefficients increases with increment of soil internal frictional angle and ratio of depth to diameter of tunnel C/D; and decreases with increment of soil weight and cohesion factor ; C/D and have great influence on tunnel failure mechanism. Failure area expanded when C/D increases; as internal frictional angle increases, failure mechanism composed by rigid moving blocks mutually split up significantly. In contrast, influence of on failure mechanism is comparatively less potent. The proposed solution obtained for finite element upper bound method with rigid blocks translatory moving elements is accurate. Obtained failure mechanism composed by rigid moving blocks is presented as slip-lined shape, which precisely indicates characteristics of failure mechanism for unstable tunnel.