The released load then causes a stress redistribution and deformation surrounding the tunnel.
First, most studies focused on the vertical load released from the bottom of pits and no horizontal released load from the sidewalls of the pits is considered.
A deep pit excavation above a tunnel breaks the mechanical balance and generates a released load from the pit.
The tunnel deflection is caused by the released load in vertical direction as being discussed in Sect.
Similarly, the equivalent released load on the tunnel axis induced by the horizontal released load and horizontal support force on the sidewalls ②, ③, and ④ can be derived as (sigma_{{z}}^{(2)} (x_{0},y,z_{0} )), (sigma_{{z}}^{(3)} (x_{0},y,z_{0} )), and (sigma_{{z}}^{(4)} (x_{0},y,z_{0} ),) respectively.
The horizontal released load of soil mass on the sidewall of the pit, Q s, can be calculated as varvec{Q}_{{text{s}} } = sumlimits_{n = 1}^{{N_{text{s}} }} {Delta varvec{q}^{(n)} }. (8).
Based on the above, the horizontal released load and horizontal support force of retaining wall, Q rs, can be expressed as Q_{text{rs}} = Q_{text{s}} + Q_{text{r}}.
In order to estimate the response of the existing tunnel to the equivalent released load, the tunnel is assumed to be a continuous and slender beam on an elastic foundation.
As mentioned previously, the release load comes not only from the vertical unloading at the pit bottom, but also from the horizontal unloading and contribution of support structures on the pit sidewalls.
Therefore, the equivalent released load on the tunnel axis induced by the horizontal released load and horizontal support force (including retaining walls and lateral braces) on the sidewall ①, (sigma_{{z}}^{(1)} (x_{0},y,z_{0} )), can be superimposed as sigma_{{z}}^{(1)} (x_{0},y,z_{0} ) = sigma_{{z{text sr}}}^{(1)} (x_{0},y,z_{0} ) + sigma_{{z{text b}}}^{(1)} (x_{0},y,z_{0} ).
