Fictitious Soil Pile Model Research Articles

Novel analytical approach for vertical dynamic response of floating pile groups based on a fictitious soil pile model

A novel analytical model for the vertical dynamic response of floating pile groups is established based on a fictitious group soil pile model (FGSP). Analytical solutions of the pile-to-pile interaction factor and dynamic impedance for the FGSP are obtained by combining the superposition and matrix transform methods. The obtained solutions are then validated by comparison with model test results and published analytical solutions. A numerical analysis is further performed to examine the effects of pile and soil parameters on the dynamic response of the FGSP. Results indicate that the effects of pile end soil on the pile-to-pile interaction factor and dynamic impedance of the FGSP are significant. Consequently, the established novel analytical model has better applicability to the dynamic problems of floating pile groups due to its consideration of the effects of pile end soil.

Fictitious soil pile model for dynamic analysis of pipe piles under high-strain conditions

Fictitious soil pile model for dynamic analysis of pipe piles under high-strain conditions

A simplified non-axisymmetric pile-soil interaction model for pile integrity testing analysis

A simplified model of non-axisymmetric pile-soil interaction (NPSI) that considers both vertical and radial motions of the pile body is developed and applied to the investigation of pile integrity test (PIT) with eccentric hammer impact. The pile is treated as a simplified three-dimensional (3D) continuum and the soil along the pile shaft is simulated as a series of independent thin soil layers, while the soil under the pile base is defined by the fictitious soil-pile model. Theoretical solution of the velocity-time history of each point on the pile top section is deduced by integral transformation technique. Based on the NPSI model, characteristics of test signals of PIT for large-diameter piles under non-axisymmetric condition are analyzed. The optimal testing position for acquiring signals, which minimizes the influence of high frequency (HF) interference resulting from the pile body 3D effect, is identified. Findings from this study provide the basis for accurate interpretation of the PIT of large-diameter piles with eccentric hammer impact.

Influence of pile end soil on torsional vibration of pile considering the stress diffusion

This study focuses on the influence of the pile end soil on the torsional vibration of a pile based on a fictitious soil pile model considering stress diffusion. The pile end soil is simulated as a cone-shaped fictitious soil pile whose parameters remain the same as the soil. The dynamic equilibrium equations for the pile–soil system subjected to torsional dynamic loadings are developed and solved to obtain the corresponding analytical solution. Then, comparisons with other solutions are conducted to verify the reliability of the proposed solution. Finally, parametric analysis results are presented based on the proposed solution to portray the influence of the stress diffusion angle, thickness and shear wave velocity of the pile end soil.

Nonlinear fictitious-soil pile model for pile high-strain dynamic analysis

Existing numerical models for simulating the pile behaviours in high-strain dynamic load tests (DLTs) cannot account for the wave propagation in base soil. This paper proposes a nonlinear fictitious-soil pile (FSP) model to better simulate the base soil. The proposed model regards the base soil as a FSP with a cone angle extending from pile toe to bedrock, and simulates shaft resistance by improved Randolph model. The pile-soil system is discretized into a series of mass-nonlinear springs, and was solved based on the Newmark’s β method. The proposed model was validated by comparing its predictions with those obtained from Randolph model and Smith model, as well as field measurements of driven and bored piles in different sites. Parametric study demonstrated that the calculated results were significantly affected by the discretization degree, FSP dimensions and soil nonlinearity. The displacement attenuation in base soil is nonlinear, and the impact energy is consumed rapidly near pile toe. Besides, large-diameter piles tend to have a larger affected zone, in which the wave phenomenon in base soil should be considered. Empirical formulas for soil affected zone and required pile displacements in DLTs were proposed to facilitate the practical application of FSP model.

Vertical vibration of a floating pile considering the incomplete bonding effect of the pile-soil interface

Based on the dynamic Winkler model and fictitious soil pile model to consider the relative sliding at the pile-soil interface and the propagation effect of soil beneath the pile toe, respectively, a more rigorous analytical model for the vertical vibration problems of a floating pile is established. The general solution for the displacement of soil is derived by combining the Laplace transform and variable separation methods. Then, the vertical dynamic solution of the floating pile is obtained by introducing the pile-soil interface condition and transfer function recursion method. Furthermore, extensive parametric analyses are performed to investigate the effects of the stiffness coefficient for the dynamic Winkler model, the length of the fictitious soil pile, and the inhomogeneity of the soils and pile on the vertical vibration for the floating pile. This indicates that the proposed analytical model provides a wider range and more rigorous application for the vertical vibration problems of floating piles embedded in layered and limited thickness soils. Moreover, the reduced form of the obtained solution can also be applied to investigate the corresponding vibration problems of end-bearing piles.

Analytical model of large-diameter viscoelastic floating pile and application in pile low-strain integrity testing

Based on a three-dimensional fictitious soil pile model, a rigorous analytical model of a large-diameter viscoelastic floating pile is developed by considering the material damping of the pile and the soil. Subsequently, closed-form solutions of the pile dynamic response of this analytical problem are derived. The rationality and accuracy of the proposed model and its relevant theoretical solutions are verified by comparison with the results of previous studies. Finally, parametric analyses are further conducted to investigate the effects of the radial direction position, length of the fictitious soil pile, material damping coefficient of the pile, and soil-to-pile stiffness ratios on the dynamic response of the pile. Based on the obtained results, an appropriate method to eliminate high-frequency interferences and evaluate the material damping coefficient of a pile in actual pile low-strain integrity testing is established. Furthermore, the proposed methodology affords legible theoretical insights into the wave propagation in large-diameter viscoelastic floating piles.

Vertical Dynamic Impedance of a Viscoelastic Pile in Arbitrarily Layered Soil Based on the Fictitious Soil Pile Model

The vertical vibration of a viscoelastic pile immersed in arbitrarily layered soil is investigated by taking the interaction among pile, pile surrounding soil (PSS) and pile end soil (PES) into account. Firstly, considering both the stratification and stress wave effect of soil, a mathematical model of the pile–soil system is established based on the fictitious soil pile (FSP) model. Then, utilizing the impedance function transfer method and Laplace transform technique, the analytical solutions of the vertical dynamic impedance of pile are derived in the frequency domain. The analytical solutions are validated by comparing them with other existing solutions. Finally, a parametric study is put forward to investigate the properties of PES on the vertical dynamic impedance of pile. The results reveal that the properties of PES have a significant effect on the vertical dynamic impedance of pile, but there is a critical influence thickness for this effect. For the cases of the PES thickness exceeding the critical influence thickness, further increase of PES thickness will not affect the dynamic behavior of the pile–soil system.

Nonlinear analysis of single pile settlement based on stress bubble fictitious soil pile model

AbstractTaking both pile end stress diffusion effect and pile‐soil interface softening effect into account, a new nonlinear method for the vertical settlement of pile is proposed in this paper. In detail, a new model, namely stress bubble fictitious soil pile model, is proposed to simulate the support from the pile bottom soil. The nonlinear soil softening model is introduced to establish the relationship between unit pile shaft friction and pile‐soil relative displacement. Then, a nonlinear calculation method for load‐settlement analysis in multilayered soil is developed with the integration of these two models. The validity and accuracy of the proposed method are verified through the comparisons against experimental and existing simplified methods. At last, a detailed parametric study is conducted to assess the influence of the parameters related to the proposed model and pile‐soil system on the load‐displacement behavior of single pile. The promotion of this method could hugely boost the prediction of the single pile settlement for the preliminary design of pile foundation in layered soil.

A new approach for estimating the vertical elastic settlement of a single pile based on the fictitious soil pile model

The development of settlement at pile heads due to vertical loads is one of the most important factors in pile design. For large-scale pile-supported infrastructure and elevated roads, the cumulative plastic deformation caused by cyclic loads could be so dangerous that only elastic deformation is permitted. However, existing methods rely heavily on measurements from field tests, while only a few analytical approaches have been developed based on the Winkler model or load transfer functions, which are mostly empirical. Moreover, present theories can hardly unify the computation of end-bearing piles and floating piles, since the classification between these two types of piles is often ambiguous. In this study, a new approach based on the fictitious soil pile model is proposed, and a semi-analytical is derived. The efficacy of the solution is demonstrated via comparisons against measured curves in the field and rigorous numerical results. Finally, a parametric study is performed to investigate the influence of pile and soil properties and the existence of a strong or weak soil interlayer on the vertical settlement of a single pile. On this basis, a new pile design factor referred as ‘optimal aspect ratio’ is proposed to acquire suitable pile dimensions.

Simplified model of defective pile-soil interaction considering three-dimensional effect and application to integrity testing

A new simplified model for defective pile-soil interaction (DPSI) is developed to account for the three-dimensional (3D) effect in the pile integrity test (PIT) for large diameter piles. To account for the 3D effect, the defective pile is treated as linear continuum rather than the conventional 1D rod model. The surrounding soil is simulated employing the classical plane strain model and the soil resistance at the pile base is represented by the fictitious soil pile model. Theoretical solutions for the velocity field of the defective pile under vertical half-sine excitation are derived by integral transformation technique. The developed DPSI model and solutions are then used to investigate the 3D effect in the PIT for defective pile considering four common pile defect types. The obtained results provide important insights into the high-frequency (HF) interferences on the velocity-time history of the defective pile top caused by the 3D effect. Recommendations to minimize the HF interferences in the actual PIT are consequently provided. Application of the DPSI model in interpreting PIT measurements can improve accuracy of pile defect diagnosis.

Analytical solution for longitudinal vibration of a floating pile in saturated porous media based on a fictitious saturated soil pile model

Based on Biot’s theory of wave propagation in saturated porous media, a new analytical approach for the vertical vibration of a floating pile in saturated viscoelastic soil is proposed, by combining the differential operator method with a fictitious saturated soil pile (FSSP) model. As an extended fictitious soil pile model, the FSSP model can fully consider the wave propagation in saturated soil with limit thickness beneath pile toe. The analytical solution for the velocity admittance of pile head is derived by introducing the completely coupled conditions at the pile-soil interface. The accuracy of the proposed approach and relevant solutions are degenerated and subsequently verified via comparisons with previous solutions. In addition, comparative analyses are further carried out to examine the effects of the porosity and shear modulus of soil as well as the layer thickness of the saturated soil layer beneath pile toe on the dynamic behavior of the floating pile. It is indicated that the presented approach and relevant solutions provide a more wide-ranging application for vertical vibration problems of a floating pile in saturated soil, which can be degenerated for the vertical vibration problems of a floating pile in single-phase soil or an end-bearing pile in saturated soil.

Torsional dynamic response of tapered pile considering compaction effect and stress diffusion effect

Considering both the compaction effect of pile surrounding soil and the stress diffusion effect of pile end soil, this paper theoretically investigates the torsional vibration characteristics of tapered pile. Utilizing the complex stiffness transfer model to simulate compaction effect and tapered fictitious soil pile model to simulate stress diffusion, the analytical solution for the torsional impedance at tapered pile top is obtained by virtue of Laplace transform technique and impedance transfer method. Based on the present solution, a parametric study is conducted to investigate the rationality of the present solution and the influence of soil and pile properties on the torsional vibration characteristics of tapered pile embedded in layered soil. The results show that, both the compaction effect and stress diffusion effect have significant influence on the torsional vibration characteristics of tapered pile, and these two factors should be considered during the dynamic design of pile foundation.

Vertical dynamic response of a pile embedded in radially inhomogeneous soil based on fictitious soil pile model

The vertical dynamic response of a pile embedded in radially inhomogeneous soil is investigated while allowing for the vertical wave effect of soil. For most engineering applications, the soil adjacent to pile may be hardened or softened due to the construction disturbance effect of pile, leading to the radial inhomogeneity of soil which has a significant influence on the vibration characteristics of pile. To consider this problem, this paper introduced the vertical shear complex stiffness transfer model to simulate the radial inhomogeneity of the surrounding soil and underlying soil of pile. Then, the governing equations of pile-soil system subjected to vertical dynamic loading are established based on the fictitious soil pile model. By means of Laplace transfer method, vertical shear complex stiffness transfer method and impedance function transfer method, the analytical solution of the vertical dynamic impedance of pile head is derived in the frequency domain. The present solution is verified by comparing it with existing solution. Based on the present solution, a parametric study is conducted to study the influence of the construction disturbance effect of pile surrounding soil and underlying soil on the vertical dynamic response of pile head. The results show that, even if the surrounding soil of pile is hardened or softened within a very small range, the construction disturbance effect still has a remarkable influence on the vertical dynamic response of pile head.

Torsional vibration solution of tapered pile considering stress diffusion effect of pile end soil

Based on the torsional plane strain model and tapered fictitious soil pile model, the torsional vibration characteristics of tapered pile considering stress diffusion effect of pile end soil is investigated theoretically. Considering the coupling conditions of pile-soil system, the torsional impedance at the tapered pile head is obtained by means of Laplace transform and impedance transfer method. A parametric study is performed, the rationality of the tapered fictitious soil model is verified and the influence of the cone angle of tapered fictitious soil pile on the torsional vibration characteristics of tapered pile embedded in layered soil is studied. The results show that: the cone angle of tapered fictitious soil pile has obvious effect on the torsional vibration characteristics of tapered pile with the shorter length.

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.

Torsional dynamic response of a pile embedded in layered soil based on the fictitious soil pile model

The torsional dynamic response of a pile embedded in layered soil is investigated while considering the influence of the pile end soil. The finite soil layers under the end of the pile are modeled as a fictitious soil pile that has the same cross-sectional area as the pile and is in perfect contact with the pile end. To allow for variations of the modulus or cross-sectional area of the pile and soil, the soil surrounding and below the pile is vertically decomposed into finite layers. Using the Laplace transform and impedance function transfer method, the analytical solution for the dynamic response of the pile head in the frequency domain is then obtained, and the relevant semi-analytical solution in the time domain is derived using the inverse Fourier transform and convolution theorem. The rationality and accuracy of the solution is verified by comparing the torsional dynamic behavior of the pile calculated with the fictitious soil pile with those based on a rigid support model and a viscoelastic support model. Finally, a parametric study is conducted to investigate the influence of the properties and thickness of the pile end soil on the torsional dynamic response of the pile.

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

ABSTRACTA 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.

Nonlinear analysis of pile load—settlement behavior in layered soil

A simplified approach is presented to analyze the single pile settlement in multilayered soil. First, a fictitious soil—pile model is employed to consider the effect of layered soil beneath pile toe on pile settlement behavior. Two approximation methods are proposed to simplify the nonlinear load transfer function and simulate the nonlinear compression of fictitious soil—pile, respectively. On this basis, an efficient program is developed. The procedures for determining the main parameters of mathematical model are discussed. Comparisons with two well-documented field experimental pile loading tests are conducted to verify the rationality of the present method. Further studies are also made to evaluate the practicability of the proposed approach when a soft substratum exists, and the results suggest that the proposed method can provide a constructive means for assessing the settlement of a single pile for use in engineering design.

Longitudinal vibration of pile in layered soil based on Rayleigh-Love rod theory and fictitious soil-pile model

The dynamic response of pile in layered soil is theoretically investigated when considering the transverse inertia effect. Firstly, the fictitious soil-pile model is employed to simulate the dynamic interaction between the pile and the soil layers beneath pile toe. The dynamic interactions of adjacent soil layers along the vertical direction are simplified as distributed Voigt models. Meanwhile, the pile and fictitious soil-pile are assumed to be viscoelastic Rayleigh-Love rods, and both the radial and vertical displacement continuity conditions at the soil-pile interface are taken into consideration. On this basis, the analytical solution for dynamic response at the pile head is derived in the frequency domain and the corresponding quasi-analytical solution in the time domain is then obtained by means of the convolution theorem. Following this, the accuracy and parameter value of the hypothetical boundaries for soil-layer interfaces are discussed. Comparisons with published solution and measured data are carried out to verify the rationality of the present solution. Parametric analyses are further conducted by using the present solution to investigate the relationships between the transverse inertia effects and soil-pile parameters.