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

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 coefficient zeta > 0, the ultimate supporting force increases significantly with the increase of horizontal earthquake acceleration coefficient. Conversely, when zeta < 0, the increasing trend of ultimate supporting force decreases with the increase of horizontal earthquake acceleration coefficient. Additionally, when horizontal earthquake acceleration coefficient k(h)=0, that is, in the absence of earthquake action, the normalized ultimate supporting force does not change with the change of proportion coefficient zeta. 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.