Theoretical solutions for the vertical compressive stress of shallow neighbourhood loess tunnel foundation

Vertical compressive stress of the foundation is a vital parameter for determining the coefficient of self-weight collapsibility of loess tunnels. This paper aims to provide a theoretical solution for the vertical compressive stress of shallow neighbourhood loess tunnel foundation. Firstly, the formula of boundary depth for deep- and shallow-buried neighbourhood loess tunnels with the consideration of the construction order of two holes is derived. In addition, solutions for surrounding rock pressure of the first and rear holes are established. Then, calculation of foundation vertical compressive stress of shallow neighbourhood loess tunnel is deduced by basing on the Flamant's elasticity solution. Finally, the Xi'an metro line NO. 2 is taken as a case study to examine and verify the applicability of the proposed theoretical method. The case study results show that the variation between the proposed formula and numerical simulation is less than 15%, which proves the reliability of our proposed formula and its potential application in the construction of shallow neighbourhood loess tunnels.