Vertical dynamic impedance of pile groups partially embedded in multilayered, transversely isotropic, saturated soils

In this paper we develop a simplified analytical solution for the impedance function of viscoelastic pile groups partially embedded in a layered, transversely isotropic, liquid-saturated, viscoelastic soil medium under a vertical time-harmonic load. In developing our solution, we use the porous medium model established by de Boer to describe the soil and the Rayleigh-Love rod model to describe the pile groups. To obtain the vertical impedance function of the pile groups, based on a "two pile model" consisting of an active pile and a passive pile, we first get a displacement attenuation function and shearing forces to piles of the soil by using a separation method of variables to solve motion equations for the soil. Second, using this displacement attenuation function and shearing forces, we derive a dynamic interaction factor of pile to pile. Then, by means of the dynamic interaction factor and a superposition principle, we obtain the vertical impedance function of the pile groups. We validate our model by comparing it to the reported results of purely elastic soils. Finally, we conduct numerical examples obtained from our model to show the effects of main parameters, such as the non-embedded length of piles, the transversely isotropic parameter of soils, and the liquid-solid coupled coefficient of soils on the vibration characteristics of a typical pile group. From these analyses, we conclude that the dynamic interaction factors of pile to pile for single-phase soils suggested by Dobry and Gazetas are not suitable for the vibration problems of pile groups in saturated soils. Thus, it is necessary to present corresponding dynamic pile-pile interaction factors for such problems. Moreover, the non-embedded length of piles, the transversely isotropic parameter of soils, and the liquid-solid coupled coefficient of soils have noticeable effects on the dynamic impedance of pile groups, which is valuable for pile foundation designs.