Vibration amplification zone phenomenon on the ground surface under various types of buried dynamic loads within metro tunnel

Abstract

Accurately predicting ground-borne vibrations transmitted from tunnels is essential for assessing the vibration level in buildings and designing effective vibration mitigation measures. In the empirical prediction models, ground vibration is assumed to decrease monotonically with distance from the tunnel alignment. In reality, the measurements and simulations suggest the existence of a vibration amplification zone (AZ) on the ground surface away from the tunnel centreline. This paper aims to investigate the AZ phenomenon on the ground surface under various buried loads within the metro tunnel using analytical models. First, the analytical models for the moving loads are extended to cover the cases of fixed harmonic loads based on the generalized wavenumber technique. The AZ phenomena under the fixed harmonic load, moving harmonic and periodic loads, and moving train load are then thoroughly investigated using the proposed analytical model, and their causes are explored according to the theory of elastic waves. The results show that under the fixed harmonic load, the AZ phenomenon occurs above a certain frequency which is determined by the upper limit frequency within which the Rayleigh wave is generated by an underground vibration source. The AZ phenomenon results from the superposition of the body waves. Its distance with the tunnel alignment depends largely on the force depth and their ratio is usually around 1.0. Similar observations are exhibited in the case of the moving harmonic and periodic loads. However, under the moving-point load, the AZ phenomenon is induced only when the tunnel structure is considered. The AZ phenomenon is determined by the response frequency rather than the load frequency. Considering the moving train load, the AZ phenomenon is attributed to the combination of body waves within the frequency range of 31.5–63 Hz. The amplification zone phenomenon should be incorporated into the empirical model to improve the accuracy of environmental vibration predictions.