Torsional Vibration of a Pile in Transversely Isotropic Saturated Soil Considering Its Construction Disturbance Effect

The torsional dynamic response of a pile embedded in transversely isotropic saturated soil is investigated while allowing for the construction of disturbance effect. The dynamic governing equations of soil are established based on Biot’s poroelastic theory. By virtue of the continuous conditions of stress and displacement of adjacent disturbance circle and the boundary conditions of pile-soil coupling system, the circumferential displacement of soil and the shear stress on pile-soil contact surface are derived. Subsequently, a closed-form solution for the torsional dynamic response of a pile is derived in the frequency domain. By using inverse Fourier transform and the convolution theorem, a quasi-analytical solution for the velocity response of the pile head subjected to a semi-sine excitation torque is derived in the time domain. The proposed analytical solution is verified by comparing with the two existing solutions available in literature. Following the present solution, a parameter study is undertaken to portray the influence on the complex impedance, twist angle and torque of pile.

An Integral Equation Model for a Pile in a Layered Transversely Isotropic Saturated Soil

Objective: In this paper, an integral equation model is established to predict the time-dependent response of a vertically loaded pile embedded in a layered Transversely Isotropic Saturated Soil (TISS). Methods: Based on the fictitious pile method, the pile-soil system is decomposed into an extended saturated half-space and a fictitious pile. The extended half-space is treated as a layered TISS, while the fictitious pile is considered as a 1D bar. The pile-soil compatibility is accomplished by requiring that the axial strain of the fictitious pile be equal to the vertical strain of the extended layered TISS along the axis of the pile. The second kind Fredholm integral equation of the pile is then derived by using the aforementioned compatibility condition and the fundamental solution of the layered TISS, which is equivalent to the solution of the layered TISS subjected to a uniformly-distributed load acting vertically over a circular area with the radius equal to that of the pile. The fundamental solution of the layered TISS is obtained via the Reflection-Transmission Matrix (RTM) method for the layered TISS. Applying the Laplace transform to the Fredholm integral equation, and solving the resulting integral equation, the transformed solution is obtained. The time domain solution of the pile-soil system is retrieved via the inverse Laplace transform. Results and Conclusion: Numerical results of this paper agree with existing solutions very well, validating the proposed pile-soil interaction model. A parametric study is carried out to examine the influence of some parameters on the response of the pile-soil system.

Dynamic Response of an Elastic Foundation on Transversely Isotropic Saturated Soil to Harmonic Torsional Loading

An analytical method is presented to investigate the torsional dynamic response of an elastic foundation resting on transversely isotropic saturated soil subjected to harmonic loading. The dual integral equations of an elastic foundation are established according to the mixed boundary-value conditions at the interface and the dynamic torsional characterizes, which are further converted into a Fredholm integral equation of the second kind. The torsional dynamic response problem is solved by solving the Fredholm integral equation. By comparing present numerical solution with that of other’s, the correctness of this paper has been verified.