Analytical solution of tunnel-sand-structure interaction model under seismic loading considering retrofit strategy of piles

• Analytical formulations are derived for the tunnel-sand-structure interaction model. • Proposed formulations are verified with previously published works. • Proposed idealized retrofit technique of pile is verified by analytical solutions. The interaction is a vital issue for the aboveground and underground structures during seismic excitation. For this reason, this research proposes an innovative analytical solution technique to evaluate responses (i.e. displacement and strain) of the tunnel-sand-structure interaction model under seismic loading. The whole tunnel-sand-structure interaction model is considered to be an equivalent single-degree-of-freedom (SDOF) system. Another new insight of this research is an idealized retrofit strategy of the pile with its verification by implementing the proposed analytical solution. The proposed analytical solution is verified with the previously published works to obtain a minimum range of difference in results of (3 to 7) %, which may represent a proper verification of this novel approach. The range of the displacement and strain variations between two consecutive seismic zone factors is found to be (8.2 to 9.9) % for all variable parameters. Also, these variations in the case of the retrofitted pile are (5.1 to 6.8) % lower than the green-conditioned pile. However, there is a scope to enhance this research in the future by considering multi-layered soil, multi-degree-of-freedom (MDOF) systems, variable peak ground acceleration (PGA) inputs, etc.