Analytical formulations of tunnel-soil-pile interaction under seismic excitations

Tunnel-soil-pile interaction (TSPI) is a vital issue during seismic excitation because of the evaluation of the interactive structural behaviors of the tunnel. This study derives analytical formulae for the proposed TSPI model under transverse horizontal shear, vertical shear, and body waves, considering a series of piles along the tunnel's longitudinal axis. For this reason, the soil medium is considered to be an isotropic, homogeneous, elastic, and infinite. Also, the tunnel is assumed to be a beam element to connect to the series of piles by the linear elastic springs. Parametric studies of proposed formulae show the parabolic and exponential variations of tunnel forces and soil pressures when increases the number of piles. Also, recalculated tunnel moments of previous studies by using proposed formulae vary closely, which may indicate the accuracy of the present formulations. Similar variations are obtained for the previous field study verification by the present formulations. Therefore, the design charts and graphs are addressed in the present research which may be used as a standard to enhance this research in the future.