ANALYTICAL SOLUTION OF THE VERTICAL DYNAMIC RESPONSE OF ROCK-SOCKED PILE CONSIDERING TRANSVERSE INERTIAL EFFECT IN UNSATURATED SOIL

Based on the dynamic governing equations of unsaturated soil, a continuous medium model regarding vertical dynamic response of rock-socked pile in three-phase unsaturated medium was established in this paper, taking the transverse inertial effect into consideration. The Laplace transformation is then used to solve the dynamic governing equations. In frequency domain, potential function and operator decomposition methods are also used to resolve the governing equations, thus obtained the expressions of soil vertical vibration displacement and shear stress. To solve the soil-pile coupling system, the vertical vibration equation of pile foundation and the continuity conditions are both adopted. Eventually, complex stiffness and admittance of the pile butt, vertical vibration displacement and shear stress of the model are obtained in frequency domain. And the travel curve of vibration velocity under half sine excitation load has also been deducted with the help of Laplace inverse transformation. The model is verified through the comparison with the saturated models. Finally, a case study of dynamic response of a pile in unsaturated soil is presented. The influences of transverse inertial effect, Poisson's ratio, saturation, pile length-diameter ratio and pile-soil modulus ratio on response of pile are investigated. The results show that:(1) Dynamic stiffness, damping and admittance oscillate with the frequency, and the pile resonance occur at the natural frequency of pile. (2) Dynamic response of the pile is sensitive to Poisson's ratio, saturation, pile length-diameter ratio and pile-soil modulus, while the sensitivity with higher frequency. (3) Larger Poisson's ratio causes smaller amplitude of dynamic stiffness, damping and admittance, as well as smaller reflection signal at bottom of the pile in its speed history curve. (4) Larger saturation leads to larger amplitude of pile response and peak value of reflection signal from the pile bottom.