On Lateral Seismic Response Of Pile Foundation Induced By Far-Field Earthquake

Investigations after earthquakes showed that the failure of pile foundations occurred for its insufficient design moment or its excessive lateral displacement,which made the superstructure out of service. During far-field earthquakes,Rayleigh waves,dominant in energy,have the dispersion characteristics in layered soils. Therefore,at certain earthquake intensity and site eigenperiod,study on the dispersion characteristics in layered soils and the displacement distribution of free field,and calculations of the lateral seismic response of pile foundation are of great importance to the anti-seismic design of pile foundations .In this paper,first of all,several methods to solve the characteristic equation of Rayleigh waves in layered soils were introduced. Dispersion characteristics of Rayleigh waves and the lateral displacement distribution of free field in several commonly-encountered layered soils were analyzed. Afterwards,considering the inertial force from superstructures,analytical solution to lateral seismic response of single pile in layered soils induced by Rayleigh waves was developed based on Winkler beam model. Combining the solution with specific earthquake intensity and site-eigenperiod,lateral seismic responses of free-head and fixed-head single pile were calculated and analyzed. Some conclusions are drawn:1) effect of inertial force from superstructures on the lateral seismic response of single pile can not be ignored;2) The lateral seismic response of single pile induced by far-field earthquake are mainly affected by acceleration mass of superstructure > site eigenperiod . It increases with the increment of acceleration and mass of superstructure. As the site characteristic frequency approaches the self-oscillation frequency of the pile,sympathetic vibration occurs and the value of lateral seismic response reaches maximum;3) As the stiffness ratio of pile to soil increase,the relative displacement of pile to soil increases;4) The lateral seismic response of fixed-head pile is much smaller than that of free-head pile.Based on the analytical method of the lateral seismic response of single pile,the formulas for calculating the seismic response of pile groups in layered soils werederived by introducing the pile-to-pile interaction factor. Combining these formulas with some earthquake intensity and site-eigenperiod,the lateral seismic responses of free-head and fixed-head pile groups were calculated. Effects of pile-to-pile interaction factors on the lateral seismic response of pile groups were analyzed. The following conclusions are drawn:1) The pile-to-pile interaction factors varies periodically with frequency.. The lower the frequency,the lower the interaction factor. When the frequency approaches zero,the factor approaches zero correspondingly;2) The amplitude of interaction factors changes with the incident angle of Rayleigh waves and reaches maximum when is zero. Moreover,with the increase of ,the wave period shortens apparently;(3) The amplitude of interaction factors decreases as the pile spacing increases and approaches to zero when the pile spacing is 15;4) The amplitudes of interaction factors increase clearly with the increasing stiffness ratio of pile to soil;5) The lateral seismic response of fixed-head pile groups is much smaller than that of free-head pile groups. Moreover,the pile-group effects induced by Rayleigh waves can be neglected;6) The lateral seismic response of piles at different location differs from each other. The location of pile has great effect on its lateral seismic response. (7) Increase of pile number will not reduce the seismic response of pile groups. The lateral seismic response of pile groups may be increase clearly to the fixed-head pile groups.Finally,an engineering example was analyzed with the method proposed in this paper,which will be a great direction for the anti-seismic design of piles in far-field earthquakes quantitatively.