Kinematic Response Of Single Piles In Layered Soils To Seismic Excitations By Using The Two-parameter Foundation Model

The pile foundation is widely used in practical engineering.The piles have the advantages such as large bearing capacity,small settlement and excellent seismic performance.The in-situ investigations showed piles were usually damaged during earthquakes,which may induce the collapse of the supperstructures.The current solutions for the kinematic response of piles can not illustrate thoroughly the seismic mechanism of piles durig earthquakes.As a result,applicable methods are unavailable in the design code in China.Therefore,kinematic response of piles is very important for both engineering practice and theory.The key for the kinematic response of piles is the soil-pile interaction.The available methods are divided into the analytical methods and the numerical methods.Most of the analytical methods are based on the assumption of the theory of beams on dynamic Winkler foundation model,in which the reaction of the soil to the pile is assumed to be simulated as a series of springs.This kind of assumption ignores the continuity of the soil because the force on the spring is only dependent on the displacement at this point.Compared to the analytical methods,the numerical methods may solve much more complicated problems such as kinematic response of piles with complex geometry and in layered soil.However,the treatment of the boundary conditions is very difficult to satisfy the radiation at the far field of the domain.In addition,huge resource is required for the computation effort.Thus,the seismic mechanism of piles during earthquakes has not been revealed by the numerical methods.The aim of this study is to investigate the kinematic response of piles in layered soil.First,a novel displacement model for the soil-pile system is proposed in the light of the kinematic soil-pile interaction during earthquakes.Then,the governing equations and corresponding boundaries for the soil-pile system are obtained by using the modified Vlasov foundation model and Hamilton's principle.Moreover,the coupling of the governing equations for the pile shaft and soil coloumn is solved by introducing an iterative procedure.The present methods are verified by comparing the proposed solution results with those available solutions.In addition,the Pasternak foundation model is adopted to simulate the transverse response of soils to the pile shaft.Then,simplified formulae are proposed to evaluate the bending of the shaft in the layered interface.The novelity and new findings are fourfold:(1)A new displacement model for vertically kinematic response of single circular pile in the layered soil to vertical P incidence is proposed based on the modified Vlasov foundation model.The corresponding analytical solution is obtained by using Hamilton's principle.(2)A new displacement model for the transversely kinematic response of single circular pile in the layered soil to vertically incident S waves is proposed based on the modified Vlasov foundation model.Analytical solution for the bending of the shaft at the layered interface is presented.(3)A novel solution for kinematic response of single circular pile in the layered soil is presented by using the Pasternak foundation model.The simplified procedure is provided for the shaft bending at the layered interface.(4)For the rectangular piles,a new displacement model is presented based on the attenuation of the displacement of the soil-pile system.Corresponding analytical solution is derived by using the modified Vlasov model.The vertically and transversely kinematic responses of single piles in the layered soil are investigated,respectively.Parametric study is performed to evaluate the effects of the properties of the soil-pile system and the incident excitations.The parameter study shows the characters of layered soil may significantly influence the kinematic response of single pile which is subjected to the vertical incident P waves.For the two-layer soil,the soft upper layer may intensify the soil-pile interaction and enlarge the scope of soil-pile intercation area.For the three-layer soil,the soft middle layer may aggravate the soil-pile interaction and increasing the scope of the soil-pile intercation area.The characters of layered soil have an obvious impact on the kinematic response of sinlge pile subjecting the vertical incident S waves.For the two-layer soil,the soft upper layer may intensify the soil-pile interaction and increases the kinematic bending of the piles.For the three-layer soil,the soft middle layer may aggravate the soil-pile interaction and increases the kinematic pile bending.The Pasternak model which incorporates the shear force transmission in the soil is more accurate than the Winkler model in most circumstances.In the particular case,the difference between the results of the Pasternak model and that of the Winkler model may up to 25%.In this case,the effects of shear force transmission in the soil should not be ignored.Different shape of pile section may influence the kinematic response of piles obviously.The effects of pile group to the kinematic response of piles can be ignored.The characters of layered soil may significantly influence the kinematic response of rectangular pile.