Study On Pile Torsional Vibration In Heterogeneous Saturated Soils

Based on wave equation of fluid-saturated porous medium and one-dimensional equation of motion of an elastic pile, the torsional dynamic interactions between elastic pile and heterogeneous soils are systematically investigated by the analytical methods. The principal contents and original work are as follows:1. For an end bearing pile embedded in saturated soil and subjected to harmonic torsional loading, the equations of equilibrium of saturated soil undergoing axisymmetric torsional deformations in cylindrical coordinates are solved by using the separation of variables technique. Then, the vibration displacement solution with an undetermined constant of the soil is obtained. Based on perfect contact between the pile and soil, the solution is coupled into an one-dimensional governing equation of a pile, and the dynamic response of the pile top is obtained in a closed form in the frequency domain. By virtue of inverse Fourier transform and convolution theorem, a semi-analytical solution for the velocity response of a pile subjected to a semi-sine wave exciting torque is obtained in the time domain. In addition, the dynamic response of an elastic bearing pile embedded in saturated soil and subjected to harmonic torsional loading is investigated.2. On the basis of the dynamic equations of saturated soil and the stress-strain relationships of transversely isotropic medium, the dynamic governing equations of the transversely isotropic saturated soil are derived in cylindrical coordinates. In combination with boundary and continuous conditions of the pile-soil system, the analytical solutions for the dynamic response of an end bearing pile are gained in the frequency domain by utilizing the separation of variables technique. Furthermore, by virtue of inverse Fourier transform and convolution theorem, a semi-analytical solution for the velocity response of an end bearing pile subjected to a semi-sine wave exciting torque is obtained in the time domain.3. To study the dynamic response of a pile with variable impedance embedded in a multi-layered saturated soil and subjected to harmonic torsional loading, a simplified and practical mathematical model for simulating dynamic interaction of the adjacent soil layers is developed. By using the same solving methods employed in single layer saturated soil and through the recursion of the impedance function, the analytical and semi-analytical solutions for the dynamic response of the pile top are derived in the frequency and time domain, respectively. Moreover, the accuracy and feasibility of the simplified model is verified by comparing with the single layer rigorous solution.4. The dynamic response of an elastic bearing pile embedded in radially inhomogeneous saturated soil and subjected to harmonic torsional loading is investigated by using the radially inhomogeneous soil model theory. The radially inhomogeneous soil is divided into two regions, the inner annular disturbed region and outer semi-infinite undisturbed region. Furthermore, a more feasible function that describes the variation of the complex-valued shear modulus is developed. Then, the inner disturbed region is subdivided into many thin concentric annular zones. Combined with the boundary and continuous conditions of the soil layers, the torsional impedance of the radially inhomogeneous soil is derived through the recursion of the shearing rigidity of soil layer. Then, the analytical and semi-analytical solutions for the dynamic response of the pile top are obtained in the frequency and time domain, respectively.5. Based on these solutions, the corresponding computer programs are developed and parameter study is made to investigate the torsional vibration characteristics of pile, and valuable conclusions are obtained for pile foundation.The torsional pile-soil dynamic interaction models and corresponding solutions developed in this dissertation are more rigorous and feasible than the previous theories. Therefore, the present dissertation provides more reasonable and rigorous theoretical support for seismic design of pile foundation and pile dynamic testing.