Analytical solution for dynamic responses of the vertical shaft in a shaft-tunnel junction under transverse loads

This paper proposes an analytical solution for dynamic responses of the vertical shaft in a shaft-tunnel junction under transverse loads. The assumption is that the shaft could be regarded as a rigid body under certain circumstances. Based on that premise, equations originally developed for rigid caissons are incorporated with terms of shaft-tunnel and soil-tunnel interactions. Two specific dynamic scenarios are considered. The first one is when the shaft is subject to transverse dynamic loads above the ground surface. The second one is when the shaft-tunnel junction is under transverse seismic excitations. Validity of the proposed solution is examined in both scenarios by finite element method. Then, the proposed solution is used to evaluate influence of the tunnel. In the first scenario, the tunnel has a major influence on dynamic responses of the shaft. Displacements of the shaft are likely to be reduced because the tunnel adds to the stiffness matrix. Yet, in the second scenario, influence of the tunnel is minor enough to be neglected. Seismic responses of the shaft are approximately the same with or without the tunnel.