Spectral Correlation Between the Non-uniform Input Ground Motion and the Dynamic Response of the Surrounding Rocks of a Long Tunnel

Abstract

To generate several different time-history curves of ground motion, which have the ability to reflect local site effects, such as the traveling-wave effect and attenuation effect, for long circular tunnels, a random method for the synthesis of ground motion is employed. The dynamic response of the surrounding rocks of a long tunnel under the uniform and non-uniform input ground motions is analyzed using the vertical input method. Based on this, the spectral correlation between the input ground motion and the dynamic response of the surrounding rocks is investigated through the coherence function. Unlike the results under the uniform input ground motion, the transmission coefficient of the surrounding rock monitoring points of each section along the axial direction of the tunnel under the non-uniform input ground motion varies in the main frequency band. In addition, at the same frequency, the transmission coefficient of the monitoring points gradually increases along the tunnel’s axial direction, but the increasing magnitude is variable. The correlation function of each monitoring point along the tunnel axis under the non-uniform input ground motion generally decreases with frequency. Moreover, the further the distance from the tunnel entrance, the faster the attenuation of correlation. The maximum coherence coefficient and the axial distance of the tunnel are basically in conformity with the quadratic polynomial relationship. However, the maximum coherence coefficient of the non-uniform input ground motion is considerably greater than that of the uniform input ground motion. The gap increases with the distance, and the maximum gap is about 0.15.