Abstract:Seismic response analysis of soil plays a major role in the seismic safety assessment of engineering sites；it reflects the influence of the characteristics of engineering sites on the input ground motion parameters of a structure.Seismic analysis can either be performed in the time or frequency domains.The dynamic analysis of soil is based on the principle of soil dynamics and the viscous damping model，and the Rayleigh proportional damping matrix is built on the assumption that the vibration modes are orthogonal about the damping matrix；therefore，two structural vibration modes can be chosen to obtain the proportion coefficient of the damping matrix.The selection of viable damping models is important for seismic response analysis of deep soil layers in the time domain，and in this paper，the influence is discussed using six different damping matrices formed by the hysteretic damping ratio and modal damping ratio. The paper first introduces two damping matrices based on the hysteretic damping ratio and Rayleigh damping，which is based on the viscous damping ratio.Then，six different damping matrices are constructed for the seismic response analysis of a deep soil site: the first and second frequencies，the first frequency and the frequency closest to the predominant frequency of the seismic wave，the first frequency and third frequencies，a common model based on the first frequency used in soil dynamics，and other forms，such as equivalent damping matrices based on the first frequency and the translation frequency.The damping frequency can be considered as independent in the frequency domain and an accurate solution can be obtained.The time domain solution is obtained using ANSYS，which uses a one dimensional soil column for the simulation.Using a deep soil site as an example，the influence of the different damping matrices on the seismic response is analyzed under an input of synthetic bedrock seismic waves and a natural seismic wave，the Shanghai Sheshan bedrock seismic wave，recorded in the Wenchuan earthquake.The seismic response results at different depths of the soil are compared with the frequency domain solution. The results show that the influence of the damping matrix is greater on the accelerations than on the displacements. The peak ground acceleration is most overvalued by 47.28%，and most undervalued by 32.53% compared to the frequency domain solution.The cause for the different influences of these damping matrices is investigated.The chosen wave spectrum characteristics are different，and the degree of influence of a damping matrix also varies depending on the input wave spectrum characteristics.The spectrum characteristics of a seismic wave should be considered during the selection of a damping matrix.The frequency information of actual bedrock seismic records are generally abundant and due to the frequency correlation of the selected damping in the time domain，using only one frequency is often not sufficient to reasonably reflect the characteristics of a seismic wave.Therefore，both the spectrum of a seismic wave and the actual soil condition at the site should be considered to determine an appropriate damping matrix to obtain more accurate and reasonable results.