基于极限分析上限法的地震作用下分层地基盾构隧道开挖面稳定性研究

Stability of shield tunnel excavation face under seismic action based on upper bound theorem of limit analysis

目前针对盾构隧道开挖面稳定性的研究还较少考虑土体分层特性和地震作用的耦合影响,因此构建了一种在分层土体中考虑地震作用的开挖面三维对数螺旋破坏模型进行研究。首先,将地震引起的动态响应通过拟静力法简化为水平和竖直两个方向上的惯性力作用;其次,在均质土体中的三维对数螺旋破坏机制的基础上,将其改进为适用于分层土体的三维对数螺旋破坏机制;再次,根据上限定理,在虚功率方程中引入地震惯性力所做功率,得到考虑土体分层特性和地震作用条件下的盾构隧道开挖面支护力的上限解;最后,将上限理论解与三维数值模拟结果和既有模型试验结果进行对比,得到了较好的一致性。此外,针对水平地震加速度系数和地层厚度对关键物理特征进行了影响因素分析。结果表明,当比例系数ζ>0时,极限支护力随水平地震加速度系数的增大显著增大;当ζ<0时,极限支护力随水平地震加速度系数增大而增大的趋势减弱。当水平地震加速度系数kh=0时,即在无地震作用情况下,归一化极限支护力不随ζ的变化而变化;在上硬下软土层中,下部土层厚度比的增大会引起极限支护力的增大,在上软下硬土层中,下部土层厚度比的增大会引起极限支护力的减小。

The coupling effect of layered soil characteristics and seismic action is rarely considered in the studies on the stability of shield tunnel excavation face.In this study,a three-dimensional logarithmic spiral failure model of shield tunnel excavation face considering seismic action in layered soil is constructed for study.Firstly,the dynamic response caused by earthquake is reduced to the inertia force in horizontal and vertical directions using pseudo-static method.Secondly,the three-dimensional logarithmic spiral failure mechanism,initially designed for homogeneous soil,is improved to be suitable for layered soil.Then,according to the upper bound theorem,the power of seismic inertia force is introduced into the virtual power equation to derive the upper bound solution of the support force of shield tunnel excavation surface considering the soil stratification characteristics and seismic action conditions.Finally,the theoretical upper bound solution is compared with the 3D numerical simulation results,engineering measured results and existing experimental results,showing good agreement.Furthermore,the key physical characteristics are analyzed according to the horizontal seismic acceleration coefficient and formation thickness.The results show that when the proportional coefficientζ>0,the ultimate supporting force increases significantly with the increase of horizontal earthquake acceleration coefficient.Conversely,whenζ<0,the increasing trend of ultimate supporting force decreases with the increase of horizontal earthquake acceleration coefficient.Additionally,when horizontal earthquake acceleration coefficient kh=0,that is,in the absence of earthquake action,the normalized ultimate supporting force does not change with the change of proportion coefficientζ.Moreover,in the hard above and soft below layered soil,an increase in the thickness ratio of the lower soil layer leads to an increase of the ultimate supporting force.In contrast,in the soft above and hard below layered soil,an increase of the thickness ratio of the lower soil layer results in a decrease of the ultimate supporting force.