Interaction Between Pile And Soil With Nonlinearly Changing Shear Modulus With Depth Under Horizontal Vibration

With the fast development of city in our country, pile foundation has been used widely for its merit(high bearing capacity, well antiseismic performance). So the research of pile-soil system dynamic performance attracts universal attention. The interaction between the pile and the soil whose shear modulus changes with depth under horizontal harmonic vibration is investigated. The influence of dimensionless parameters to the pile-soil system is discussed, such as pile slenderness ratio, excitation frequency, Poisson's ratio, damping, wave velocity ratio, nonlinear coefficientβof the soil layer shear modulus and so on.The soil layer is simulated as a viscoelasticity whose shear modulus is increasing exponentially with depth. By the application of the theoretics of Novak plane strain, the model of the pile-soil dynamic interaction is built. Firstly, a complex closed form solution of the soil resistance to a horizontal harmonic vibration can be obtained by solving the wave equation of the soil. The soil layer impedance function is expressed as a dimensionless form. The analysis of influence of parameters on the soil layer impedance factor indicates that the soil stiffness depends mostly on the mode number below the resonant frequency. With frequency increasing, the resistance factor converges to a constant independent of the mode of vibration. Pile's slenderness ratio has effect upon the damping character. The changing rate of soil resistance factor (real part) increases with Poisson's ratio and decreases with pile slenderness ratio,material damping. Nonlinear coefficientβof the soil layer shear modulus has obvious scale-up effect on the soil layer stiffness. But this kind of phenomenon is only restricted in small mode number, low frequency situation. With the mode number and the frequency increasing, the influence ofβdoes not become so conspicuous.Secondly, the dynamic stiffness of the pile is obtained through substituting the soil layer impedance function into pile vibration differential equation. Following meaningful laws can be obtained through the discussion of the parameters involved: the variation of real part of the dynamic stiffness with frequency can be very dramatic for stiff piles, very weak soil and small material damping; while it is remarkably modest for slender piles, stiff soil and large material damping. The effect of material damping is significant in the region below the natural frequency of the soil layer. Above this region, small material damping has little significance but large material damping reduces the stiffness with increasing frequency. Nonlinear coefficientβof the soil layer shear modulus has an obvious scale-up effect on the resonance region on the dynamic stiffness. But in the region of above resonance frequency, differentβhas no influence on the dynamic stiffness. Howeverβhas little effect on the dynamic damping.