Elastodynamic model for large-diameter end-bearing shafts

The dynamic response of large-diameter end-bearing cylindrical shafts is studied. First, the popular plane-strain model of Novak is reviewed and its limitations are discussed. An improved model is then developed which, while retaining the simplicity of the original model, accounts for the third dimension by considering the normal and shear stresses acting on the upper and lower faces of a horizontal soil slice. These stresses are incorporated in the analysis by implementing a dynamic Vlasov-Leontiev approximation based on integrating the governing equations over the thickness of the soil layer. It is shown that this operation leads to a set of elastodynamic equations which are similar to those in the plane-strain model, yet properly incorporate the salient 3-D effects. Explicit closed-form solutions are obtained for: (i) the dynamic soil reaction along the shaft; (ii) the dynamic impedance of the shaft; (iii) the displacement field in the soil; and (iv) the dynamic interaction factors between neighboring shafts. Both vertical and lateral oscillations are analyzed for single and grouped shafts. Results are presented in terms of dimensionless graphs which highlight the importance of soil-foundation interaction on the response. It is shown that the proposed model avoids the limitations of the plane strain model.