A numerical study is made on the dynamic through-soil interaction between underground station and nearby pile supported surface structure on viscous-elastic soil layer, under vertically incident S wave. This paper focuses on the dynamic interaction and the interactive influence on seismic response of adjacent surface structure and underground structure. To this end, ANSYS has been further developed for calculation in frequency domain, in which hysteretic damping can be considered, so that structure-soil-structure interaction (SSSI) can be investigated via direct methodology. Discussion is made on the influence of arrangement of structures, distances between structures, shaking direction of seismic wave, shear wave velocity and damping of soil, scale and burial depth of underground structure, storey number, stiffness, style and pile length of surface structure on SSSI, in terms of horizontal acceleration of surface structure and horizontal relative displacement of underground structure. Maximum acceleration and displacement is also presented for 12 seismic inputs. Arrangement and shaking direction are two of the most important factors. The response can be either amplified or attenuated according to the distance, related to dynamic properties of the overall system. The underground structure, surrounded by building with the fundamental frequency approximate to that of free field, is heavily affected.

The structure-soil-structure interaction (SSSI) between high-rise buildings is numerically investigated. ANSYS has been further developed for calculation in the frequency domain, in which hysteretic damping can be considered for both the soil and structure. This study is presented in two subsequent papers. In the first part, i.e., this paper, the variations in the story shear force, interstory drift angle, displacement, velocity and acceleration of the superstructure, the sway of the foundation, and the axial and shearing forces of the pile are presented. The major influencing factors are the excitation frequency of a harmonic wave or the frequency components of a seismic wave, shaking direction of an exciting wave and direction of the structure arrangement. Under harmonic waves, the interaction mainly occurs when the excitation frequency is 1-5 Hz. Under seismic waves, when the shaking direction of an exciting wave is perpendicular to the direction of the structure arrangement and the direction of the structure arrangement is parallel to the lateral axis of the structure, the influence on the superstructure is greatest.

A numerical study is performed on the structure-soil-structure interaction (SSSI) between high-rise buildings. ANSYS has been further developed for calculation in the frequency domain, in which hysteretic damping can be considered for both soil and structures. This study is presented in two subsequent papers. The first part[1] focuses on the influence of the SSSI on each kind of dynamic response, while the second part, i.e., this paper, is a parameter study that focuses on the influence of each key parameter, including the separation distance between structures; the damping ratio, thickness and shear wave velocity of the soil; the length of the pile; the damping ratio, style, material stiffness, mass and story number of the superstructure; and the position and number of the structure, on the SSSI. The interaction decreases with the increase in the separation distance between structures, the increase in the damping ratio and shear wave velocity of the soil, the increase in the damping ratio and mass of the superstructure, or the decrease in the material stiffness of the superstructure in a fluctuating manner.

Rayleigh damping model, which is still adopted by many general finite element programsand widely used in analysis of engineering, leads to the inconformity of the calculating modaldamping ratio with the actual modal damping ratios. The appropriate Rayleigh damping matrix issignificant for accurate dynamic response analysis of complicated field. This paper establishes adual parameter optimization theory for calculation of Rayleigh damping coefficients. The functionalrelation between the relative error of dynamic response and Rayleigh damping coefficients isestablished based on CQC method. By taking the square sum of the errors of peak value ofdisplacement and the error of peak value of acceleration at the multiple points (DOF) of the surfaceof the complex site as the control objective, the equations for solving Rayleigh damping coefficientsare obtained based on the principle of minimizing the control objective. Then, as an example, theseismic response of a valley under the excitation of 28 representative seismic waves which arerandomly selected is calculated and the error due to Rayleigh damping model is analysed. Thenumerical result verifies the accuracy and applicability of the proposed method.