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.

Simulation Research on Local Settlement of Kiln Foundation Based on Winkler Theory

“…In 1867, Winkler, a Czech engineer, proposed an elastic foundation model that divides the soil into several vertical soil columns, each of which can be replaced by an independent spring whose pressure on each spring is proportional to the deformation of that spring, and the shape of the vertical displacement at the base of the foundation is similar to that of the base reaction graph, as shown in Equation (1).…”

“…Due to the diversity of foundation models, the linear elastic model is more frequently used for its study, among which the Winkler elastic foundation model is the simplest and most convenient foundation model. Zhang B et al [1] based on Winkler's elastic foundation beam theory and arranged horizontal and rotational springs around the shaft to model; Zhang C R et al [2][3] linked the Winkler foundation modulus to the earth pressure free field by selecting a suitable pipe -soil interaction; Kurian N P et al [4] obtained the actual nonlinear response of the characterized soil to the applied load by fitting the load-settlement data nonlinearly through the Winkler model. Okeagu B J et al [5] found that the soil reaction coefficients around the pipe varied widely and the magnitude was related to the span of the pipe, the depth of the soil and the direction of action.…”