Old tunnels that were constructed using conventional methods in Japan often have voids around the tunnel crown, i.e., there are partial discontinuities between the lining and ground, and almost all tunnels that were severely damaged by the earthquake have those defects. For understanding the effect of a void behind the lining on seismic damage of tunnels and for planning countermeasures against a severe earthquake, three-dimensional elastic solutions for a deep cylindrical tunnel, with a void behind the lining, under the oblique-incidence of shear wave are derived. Numerical results show that a void does not cause the large stress concentration to the lining under oblique-incidence of shear wave. Reinforcements of the lining where large stress concentration has already occurred are necessary as the countermeasure because it is probable that there are high correlations between large stress concentration in the lining caused by voids before an earthquake and seismic damage of tunnels.
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