Semi-analytical method for vertical vibration response of end-bearing pile in layered unsaturated soils
MA Wenjie1，2，WANG Changdan1，2，WANG Binglong1，2，ZHOU Shunhua1，2
(1. Key Laboratory of Road and Traffic Engineering of the Ministry of Education，Tongii University，Shanghai 201804，China；
2. Shanghai Key Laboratory of Rail Infrastructure Durability and System Safety，Tongii University，Shanghai 201804，China)
Abstract：Based on the dynamic governing equations of unsaturated soils，and considered the effects of matrix suction，three-phase(solid phase，liquid phase and gas phase) compression characteristics，as well as the effect of the degree of saturation on dynamic shear modulus，the vertical vibration response of end-bearing pile in layered unsaturated soils was investigated. Combined with Euler-Bernoulli bar theory，the vertical vibration response model of an end-bearing pile in layered unsaturated soils under three-dimensional axisymmetric harmonic load was proposed. The governing equation of unsaturated soils was derived by utilizing the Laplace transform，potential function and operator decomposition methods. In the frequency domain，the analytical solution of the dynamic impedance of the pile top was solved through the pile-soil coupling condition and impedance function transfer method. The semi-analytical solution of the pile top was obtained by using the inverse Fourier transform and convolution theorem in the time domain. After the correctness of the solution was verified，the effect of modulus ratio and thickness ratio of layered soil on the dynamic response of pile was investigated. The results shown that when pile in upper-hard-and-lower-soft two-layered soil，the fluctuation of dynamic stiffness and damping of the pile decreased，and the admittance had the phenomenon of“small peak sandwiching large peak”，the peak became larger. Conversely，the admittance presented“large peak sandwiching small peak”. Compared with the upper and lower homogeneous soil，the reflected signal at the pile bottom was obviously weakened. The thicker the soft soil layer was，the greater the oscillation amplitude of the pile. When the thickness of the soil layer was different，there was a reflection signal at the interface of the soil layer in the velocity time history curve，and the reflection position was closely related to the boundary position of the soil layer.
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2023, Vol. 42 
