General Winkler Model for Kinematic Responses of Shafts in Linear Soil

Abstract

A simplified model for calculating the seismic responses of the shaft is proposed in this paper. Based on the theory of Winkler elastic foundation beam, the urban shaft is simplified as a vertical beam. The horizontal soil reaction and vertical shear tractions between the shaft circumference and the surrounding soils are considered through horizontal springs and rotating springs on the sidewall of the shaft. The translation and rocking motion of the shaft are considered through horizontal springs and rotating springs at the bottom of the shaft. Then, the dynamic analysis model of the shafts under seismic motion is established, and the control equation of the dynamic response of the shaft in frequency domain is deduced. The analytical solution of the steady state response of the shaft is obtained. Considering the randomness of the earthquake motion, this method can get the shaft kinematic responses under different ground motions efficiently in conceptual design process.