Dynamic Response Of Single Piles To Vertical Excitations By Using Two-parameter Foundation Model

Piles are widely used as foundations for the bridges,rapid transit railway and super buildings due to their excellent load-bearing performance and better applicability.Piles are gradually applied to the design of dynamic machinery foundations and seismic foundations.During vibrations,because of the pile-soil interaction the reponse of piles are basically different with static load.Statical analysis cannot accurately describes the real working state of the piles.Currently,the existing models for the pile-soil dynamic interaction problem are mostly based on Beam on Dynamic Winkler Foundationm(BDWF)model and the continuum model which is difficult to solve in mathematics.Moreover,the dynamic design and testing of pile foundations and piling are dependent on the research of vertical vibration theory of piles.Therefore,the research of pile-soil dynamic interaction not only possess great theoretical meaning but also have significient applicable value.Based on two-parameter foundation model,the dynamic respons of circulal piles subjected to axial loading and rectangular piles under vertically incident P-waves are investigated,respectively.With regard to circulal single piles subjected to axially harmonic loading,the shaft resistance of pile is obtained from a thin soil layer element model at depth in the light of Hamilton's principle.And the shaft resistance consists of three parts.The unknown characteristic parameters in the shaft resistance are determined with the boundary conditions of the soil layer in terms of the wave propagation theory.Considering two-parameter foundation model,a physical model is improved to illustrate the nature soil-pile interation under dynamic loadings.Parametric study is performed to investigate the characteristic of the shaft resistance.It indicates that the incident frequence,slenderness ratio of pile and wave velocity ratio of pile and soil have significant influences on the the shaft resistance.For rectangular single piles under vertically incident P-waves,a displacement model for the soil-pile system is presented.Based on the modified Vlasov model,the governing equations and boundary conditions for the four functions in the displacement model can be obtained by using Hamilton's principle.The unknown displacement and attenuation functions are obtained to be decoupled.An iterative algorithm is recommended to solve the unknown coupled function numerically.A parametric study is performed to evaluate dynamic response of the rectangular pile and the surrounding soil.Comparing to the circular-section pile,totally different response is observed to that of the rectangular pile.The major contribution of this study is:(1)the shaft resistance consists of three parts,which can be discribed as the contributions by the elastic compression of soil,the soil continuity and the inertial force of participating mass of the surrounding soil,besides,the latter two can be idealized as the effect of an membrane;(2)a displacement model for the soil-retangular pile system is presented with the axial displacement function and two attenuation functions along the respective horizontal directions.