Wenbing Wu

Vertical dynamic response of pile embedded in layered transversely isotropic soil

The dynamic response of pile embedded in layered transversely isotropic soil and subjected to arbitrary vertical harmonic force is investigated. Based on the viscoelastic constitutive relations for a transversely isotropic medium, the dynamic governing equation of the transversely isotropic soil is obtained in cylindrical coordinates. By introducing the fictitious soil pile model and the distributed Voigt model, the governing equations of soil-pile system are also derived. Firstly, the vertical response of the soil layer is solved by using the Laplace transform technique and the separation of variables technique. Secondly, the analytical solution of velocity response in the frequency domain and its corresponding semianalytical solution of velocity response in the time domain are derived by means of inverse Fourier transform and convolution theorem. Finally, based on the obtained solutions, a parametric study has been conducted to investigate the influence of the soil anisotropy on the vertical dynamic response of pile. It can be seen that the influence of the shear modulus of soil in the vertical plane on the dynamic response of pile is more notable than the influence of the shear modulus of soil in the horizontal plane on the dynamic response of pile.

Vertical dynamic impedance of tapered pile considering compacting effect

Based on complex stiffness transfer model, the vertical vibration of tapered pile embedded in layered soil is theoretically investigated by considering the compacting effect of the soil layer surrounding the tapered pile in the piling process. Allowing for the stratification of the surrounding soil and variable crosssection of the tapered pile, the pile-soil system is discretized into finite segments. By virtue of the complex stiffness transfer model to simulate the compacting effect, the complex stiffness of different soil segments surrounding the tapered pile is obtained. Then, substituting the complex stiffness into the vertical dynamic governing equation of tapered pile, the analytical solution of vertical dynamic impedance of tapered pile under vertical exciting force is derived by means of the Laplace technique and impedance function transfer method. Based on the presented solutions, the influence of compacting effect of surrounding soil on vertical dynamic impedance at the pile head is investigated within the low frequency range concerned in the design of dynamic foundation.

Torsional Dynamic Impedance of a Tapered Pile Considering its Construction Disturbance Effect

The dynamic response of a tapered pile (considering its construction disturbance effect) is investigated when the tapered pile is subjected to a time-harmonic torsional loading. For most engineering conditions, the surrounding soil may be weakened or strengthened owing to the construction disturbance effect of the tapered pile, resulting in the soil becoming radially inhomogeneous. In order to consider this problem, the circumferential shear complex stiffness transfer model is proposed to simulate the radial inhomogeneity of soil. Then, the governing equations of a tapered pile-soil system subjected to torsional dynamic loading are established. By virtue of the circumferential shear complex stiffness transfer method and the impedance function transfer method, the analytical solution of torsional dynamic impedance at the head of the tapered pile is derived. Based on the presented solution, the influence of the construction disturbance effect of the surrounding soil on the torsional dynamic impedance at the pile head is investigated within the low-frequency range concerned in the design of a dynamic foundation. The results show that, even if the hardening range and softening range of the surrounding soil vary within a smaller scale, the hardening effect and softening effect also have a notable influence on the torsional dynamic impedance at the pile head.

Dynamic Behavior of Beam–Pile Structure Under Vertical Transient Excitation

The dynamic response of beam–pile–soil system under vertical transient excitation is investigated. Both piles and beam are assumed to be one-dimensional rods and subjected to vertical exciting forces. The uniformly distributed Voigt models are introduced to simulate the pile tip resistances, and the dynamic interactions between piles and beam are simplified as a set of concentrated point loads. Then, the plane strain model, the theory of longitudinal vibration of one-dimensional rod, and the Timoshenko beam theory are used to establish the mathematical models for the motion of soil, piles, and beam, respectively. On this basis, the matrix equation for solving the governing equations is constructed in the Laplace domain and the time-domain response is then obtained by the discrete inverse Fourier transform. Comparisons with numerical simulations and model tests are conducted to evaluate the rationality of the present solution. The results show that the dynamic responses calculated by the proposed solution are generally consistent with simulated curves and experimental data.

Analytical solution for one-dimensional consolidation of double-layered soil with exponentially time-growing drainage boundary

In this article, the exponentially time-growing drainage boundary is introduced to study the one-dimensional consolidation problem of double-layered soil. First, the one-dimensional consolidation equations of soil underlying a time-dependent loading are established. Then, the analytical solution of excess pore water pressure and average consolidation degree is obtained by utilizing the method of separation of variables when the soil layer is separately undergone instantaneous load and single-stage load. The validity of the present solution is proven by the comparison with other existing analytical solution. Finally, the influence of soil properties and loading scheme on the consolidation behavior of soil is investigated in detail. The results indicate that, the present solution can be degraded to Xie’s solution utilizing Terzaghi’s drainage boundary by adjusting the interface parameter, that is to say, Xie’s solution can be regarded as a special case of the present solution. The interface parameter has a significant influence on the excess pore water pressure of soil, and the larger interface parameter means the better drainage capacity of the soil layer.

Vertical Vibration Characteristics of a Variable Impedance Pile Embedded in Layered Soil

In engineering applications, various defects such as bulging, necking, slurry crappy, and weak concrete are always observed during pile integrity testing. To provide more reasonable basis for assessing the above defects, this paper proposed simple and computationally efficient solutions to investigate the vertical vibration characteristics of a variable impedance pile embedded in layered soil. The governing equations of pile-soil system undergoing a vertical dynamic loading are built based on the plane strain model and fictitious soil pile model. By employing the Laplace transform method and impedance function transfer method, the analytical solution of the velocity response at the pile head is derived in the frequency domain. Then, the corresponding semianalytical solution in the time domain for the velocity response of a pile subjected to a semisinusoidal force applied at the pile head is obtained by adopting inverse Fourier transform and convolution theorem. Based on the presented solutions, a parametric study is conducted to study the vertical vibration characteristics of variable cross-section pile and variable modulus pile. The study gives an important insight into the evaluation of the construction quality of pile.

Vertical dynamic impedance of pile considering the dynamic stress diffusion effect of pile end soil

ABSTRACT A new analytical model is presented to analyze the dynamic stress diffusion effect of pile end soil on the vertical dynamic impedance of the pile. The surrounding soil of the pile is modeled by using the plane strain model and the pile is simulated by using one-dimensional elastic theory. Finite soil layers below the pile end are modeled as conical fictitious soil pile with stress diffusion angle which reflects the dynamic stress diffusion effect of pile end soil. By means of the Laplace transform and impedance function transfer method, the analytical solution of the vertical dynamic impedance at the pile head in frequency domain is yielded. Then, a comparison with other models is performed to verify the conical fictitious soil pile model. Finally, based on the proposed solution, the selected numerical results are compared to analyze the influence of dynamic stress diffusion effect for different design parameters of the soil-pile system on the vertical dynamic impedance at the pile head.

Consolidation Theory for a Stone Column Composite Foundation under Multistage Loading

The consolidation theories considering instant load cannot fully reveal the consolidation mechanism of a stone column composite foundation used in the expressway embankments due to the time effect of loading; that is, the expressway embankments are often constructed in several stages for a long time. Meanwhile, owing to the special property that the pile-soil stress ratio is larger than 1, the consolidation theory for sand drain well foundation cannot be used directly in the consolidation analysis of stone column composite foundation. Based on the principle that the vertical load applied on the composite foundation is shared by the stone column and the surrounding soil, the governing solutions for the stone column composite foundation under a multistage load are established. By virtue of the separation of variables, the corresponding solutions of degree of consolidation for loading stage and maintaining load stage are derived separately. According to the Carrillo theorem, the solution for the average total degree of consolidation of entire composite foundation is also obtained. Finally, the reasonableness of the present solution has been verified by comparing the consolidation curve calculated by the present solution with that measured by site test.

Longitudinal Dynamic Impedance of a Static Drill Rooted Nodular Pile Embedded in Layered Soil

ABSTRACT The static drill rooted nodular (SDRN) pile is a new type of precast pipe pile with equally spaced nodes distributed along the shaft and wrapped by the surrounding cemented soil. In this paper, the longitudinal dynamic response of the SDRN pile embedded in layered soil is investigated with respect to the complexity of the pile body structure and the pile–soil contact condition. First, the shear complex stiffness transfer model is used to simulate the radial inhomogeneity of the surrounding soil. Then, the governing Equations of the pile–soil system subjected to longitudinal dynamic loading are established. The analytical solution for the dynamic response at the pile head is obtained by the shear complex stiffness transfer method and the impedance function transfer method. The degenerate case of the present solution is compared with the published solution to verify its reliability, and the complex impedance of the SDRN pile is compared with that of the precast pipe pile and the bored pile. Finally, a parametric study is conducted to investigate the influence of pile–soil parameters on the complex impedance at the pile head within the low frequency range concerned in the design of the dynamic foundation.

A New Model for the Dynamic Interaction of a Pile and Pile End Soil

Allowing for the shortcomings of the existing dynamic interaction models of pile and pile end soil, this paper presents a new model to simulate the dynamic interaction of pile and pile end soil - namely, fictitious soil pile model. At first, finite soil layers below pile end are modeled as fictitious soil pile whose cross-section area is the same as that of the pile. Meanwhile, the surrounding soil layers of pile are modeled by using a plane strain model. Then, the semi-analytical solution of longitudinal dynamic response at the pile head in time domain is derived by means of the Laplace transform and impedance function transfer method. Based on this solution, a parametric study is conducted to study the influence of parameters of soil below pile end on the longitudinal dynamic response at the pile head.