Multi-dimensional Dynamic Impedance Analysis Of Pile Foundation Based On Timoshenko Model

Pile foundation,as a column member embedded in soil,is widely used in the field of foundation engineering because of its good mechanical performance,seismic performance and adaptability to various complex geological conditions.According to the existing seismic damage data,there are a lot o f superstructure intact but pile foundation damaged seriously.However,at present,the academia has not been able to better reveal the damage mechanism of pile foundation,so there is no reliable method to calculate the dynamic response value of pile foun dation that is close to the actual value in the current code.Therefore,in order to provide reference for the design specification,it is of great significance to further study the dynamic characteristics of pile foundation.The establishment of a reasonable pile-soil interaction model is the core of the dynamic analysis of pile foundation.However,the Euler beam model which ignores the shear deformation of pile body is often adopted in the existing pile body model,resulting in great errors in the analysis of large-diameter pile.In order to overcome the defects of the algorithm and expand the application scope,this paper,based on Timoshenko pile body model and Winkle foundation beam model,analyzes the horizontal vibration problem of pile foundation in layered soil by using transfer matrix method,and deduces various analytical solutions of dynamic impedance of pile foundation considering the influence of shear deformation of pile body and vertical load of pile top.Using the attenuation function to sol ve the free field displacement of soil,the dynamic balance equation of the passive pile is listed based on the displacement of the active pile tip,and the matrix relation between the displacement of the passive pile tip and that of the active pile tip is derived,and the interaction factor is obtained by using this relation.Based on the dynamic impedance and interaction factor of single pile obtained in the first two steps,the dynamic impedance of pile group under simple harmonic load is obtained by usi ng the superposition principle.The above improvement will make the algorithm more suitable for the analysis and calculation of large diameter piles.In order to compare with the existing Euler model algorithm,the above formula is degraded(ignoring the influence of shear deformation),and the same curve trend proves the rationality of the algorithm.In the aspect of single pile impedance analysis,parameters such as pile body model,pile length to diameter ratio,vertical load and soil elastic modulus have different degrees of influence on the dynamic impedance of single pile.In particular,the results based on Timoshenko model showed a small positive value,and the smaller the pile diameter ratio was,the more obvious the deviation was.In terms of interaction factors,the independent variables in attenuation functions such as distance between piles and Angle between piles also have an influence on them: the calculation results are obviously accelerated with the increase of parameters,and these influences extend to the calculation of pile group.In addition,the analysis of pile group's dynamic impedance also involved: compared with Euler model,Timoshenko model had a small positive value and a large negative value.With the increase of pile group number,the dynamic impedance of all kinds of pile group increases slowly under the premise of keeping consistent fluctuation.At the same time,the dynamic impedance of pile group is not simply superposed by the impedance of each single pile,and its value is related to not only the number of piles,but also the influence factors in the analysis of single pile impedance and interaction factor.