Discussion on modeling issues of Rayleigh damping matrix in soil layers with deep deposit

The seismic response of soil layers is calculated by using the methods of time domain and frequency domain separately. Through the comparison of the calculated results between the time domain and the frequency domain, the importance of reasonable modeling by Rayleigh damping matrix in time domain analysis of earthquake response of soil layers with deep deposit is discussed. The numerical results show that in the time domain analysis of earthquake response of soil layers with deep deposit, different modeling methods of Rayleigh proportional damping matrix have great influence on the accuracy of the results of the acceleration response of soils but a very limited impact on that of the displacement response of soils. It is suggested that when the fundamental frequency of soil layers is higher than the excitation frequency of the main component of the bedrock seismic waves, the low-order natural frequency such as the second or third should be selected as the second natural frequency to determine the Rayleigh damping matrix proportion coefficient. When the fundamental frequency of the soil layer is close to and especially much lower than the excitation frequency of the main component of the bedrock seismic waves, the contribution of high-order modes resonance effect on the seismic response of soil layers should be highlighted and ω_n should be selected as the response spectrum peak frequency ω_R of the input bedrock seismic waves.