Vertical Vibration Theory Of Pile-Soil System Based On Fictitious Soil Pile Method And Its Application

The pile-soil dynamic interaction is a complicated contact problem. The pile vibration theory can provide a valuable guide for both earthquake-resistance design and various dynamic testing methods of pile. Over the past decades, many dynamic interaction models have been presented to investigate the behavior of surrounding soil-pile dynamic interaction. It can be noted that extensive and in-depth research work has been done in the field of surrounding soil-pile dynamic interaction. By contrast, less attention is attracted by the topic on underlying soil-pile dynamic interaction. Therefore, by means of fictitious soil pile method, this paper systematically investigates the dynamic response of elastic and viscoelastic pile and large diameter pipe pile, which are embedded in homogeneous foundation, layered foundation and radial inhomogeneous foundation. The principal contents and original work are as follows:1.Considering vertical wave effect and viscoelastic property of soil, the dynamic interaction model of pile-surrounding soil, pile-underlying soil is established by using fictitious soil pile method when the pile is embedded in homogeneous foundation. The dynamic equilibrium equations of soil undergoing arbitrary vertical exciting force are solved by virtue of the separation of variables technique. Then, according to the boundary conditions at the interface of soil and pile, the theoretical solutions for the dynamic response of pile in the frequency domain are derived by using integral transform technique to solve the dynamic governing equation of pile. By means of inverse Fourier transform technique and convolution theorem, the semi-analytical solution for the velocity response of a pile undergoing half-cycle sine pulse at the pile head is obtained in the time domain. Based on these solutions, a parametric study is conducted to study emphatically the effects of parameters of underlying soil on dynamic response at the pile head. It is shown that the finite underlying soil layer adjacent to the pile toe has a significant influence on the pile dynamic response and there is a critical influence depth for underlying soil.2.To investigate the dynamic response of a viscoelastic pile embedded in layered foundation and subjected to arbitrary vertical exciting force, a simplified and practical mathematical model is developed for simulating dynamic interaction of the adjacent soil layers. By means of the same solving methods presented in homogeneous foundation and through the recursion of the impedance function, the complex stiffness at the fictitious soil pile head is derived and used as boundary condition at the pile toe to obtain the theoretical solutions of pile dynamic response. Furthermore, the accuracy and feasibility of the simplified model is verified by comparing with the homogeneous foundation rigorous solution. Based on these solutions, the influence of the properties of layered underlying soil and pile end sediment on pile dynamic response is thoroughly analyzed.3. The complex stiffness transform model is developed to simulate the radially inhomogeneous property of surrounding soil and underlying soil of pile which caused by pile construction effect. Then, combining the boundary conditions between radially adjacent soil zones, the dynamic equilibrium equations of all soil zones are solved one by one from undisturbed region to disturbance region and the complex stiffness of the interface of pile and its surrounding soil is derived. By means of the same solving methods presented in layered foundation, the theoretical solutions of pile dynamic response are obtained both in frequency domain and time domain. Based on these solutions, the influence of construction effect of pile surrounding soil and compaction effect of pile end soil on pile dynamic response are analyzed in detail. The dynamic response of a pile with arbitrary variable impedance are systematically investigated.4. Based on the stress-strain relationships of transversely isotropic medium and dynamic equations of single phase elastic soil, the dynamic governing equations of the layered transversely isotropic soils are obtained in cylindrical coordinates considering their vertical wave effect and viscoelastic property. By virtue of the same solving methods developed in layered foundation, the theoretical solutions of pile dynamic response are derived both in frequency domain and time domain. The parametric studies show that the influence of vertical shear modulus on the vertical dynamic response of pile is more significant than the influence of horizontal shear modulus. So, it can be noted that the vertical shear modulus plays a dominant role in the vibration characteristics of the pile-soil system when the vertical wave effect of layered soils is taken into consideration.5. By using plane strain model and additional mass method to simulate the dynamic interaction of soil plug and pipe pile, the definite problem of large diameter pipe pile embedded in layered foundation is established by considering the soil plugging effect. The analytical solutions of dynamic response at the pipe pile head are derived in the frequency domain and its corresponding semi-analytical solution for the velocity response of a pile undergoing half-cycle sine pulse at the pipe pile head is obtained in the time domain. The parametric studies show that the effective test length of pipe pile decreases as the thickness of pipe pile decreases for both large diameter concrete pipe pile and large diameter steel pipe pile. It also can be noted that there is reverse reflection signal at the position of soil plug top in the velocity response curves of pipe pile in the time domain. Due to the presence of soil plug, the integrated velocity of the pile section filling soil plug is less than the elastic longitudinal wave velocity of pipe pile, and the higher the height of soil plug is, the smaller the integrated velocity of the pile section filling soil plug is. Moreover, the conception of Apparent Wave Velocity of Pipe Pile (AWVPP) is defined in this paper, which is of great importance in foundation pile integrity testing. And, it is stated that the AWVPP should be choosed as the testing velocity in the engineering test.The fictitious soil pile method is an useful supplement to the research of dynamic interaction of pile and its underlying soil. The new results and new phenomenons presented in this paper can be used in earthquake-resistance design of pile foundation, anti-vibration design of dynamic foundation and dynamic testing of pile.