Dynamic response of single piles embedded in transversely isotropic layered media

Dynamic response of single piles embedded in transversely isotropic layered media is investigated using the finite element method combined with dynamic stiffness matrices of the soil derived from Green's functions for ring loads. The influence of soil anisotropy on the dynamic behaviour of piles is examined through a series of parametric studies.     

Dynamic stiffness of deep foundations with inclined piles

The influence of inclined piles on the dynamic response of deep foundations and superstructures is still not well understood and needs further research. For this reason, impedance functions of deep foundations with inclined piles, obtained numerically from a boundary element–finite element coupling model, are provided in this paper. More precisely, vertical, horizontal, rocking and horizontal–rocking crossed dynamic stiffness and damping functions of single inclined piles and 2 × 2 and 3 × 3 pile groups with battered elements are presented in a set of plots. The soil is assumed to be a homogeneous viscoelastic isotropic half‐space and the piles are modeled as elastic compressible Euler–Bernoulli beams. The results for different pile group configurations, pile–soil stiffness ratios and rake angles are presented. Copyright © 2010 John Wiley & Sons, Ltd.     

Static equivalent method for the kinematic interaction analysis of single piles

This paper presents a static equivalent approach to estimate the maximum kinematic interaction effects on piles subjected to lateral seismic excitation. Closed-form expressions are reported for the evaluation of the maximum free-field soil movements and for the computation of maximum pile shear force and bending moments. Firstly, modal analysis, combined with a suitable damped response spectrum, is used to evaluate the maximum free-field response. Secondly, the pile is schematised as a Winkler's beam subjected to equivalent static forces defined according to soil vibration modal shapes and amplitude. The method may be applied by using response spectra suggested by National Standards or those obtained with accelerograms. The procedure proposed may be conveniently implemented in simple spreadsheets or in commercial finite element programs and easily used by practicing engineers. Method accuracy is demonstrated by comparing the results with those obtained with a more rigorous model. Good results may be achieved by considering only the first soil vibration mode making the procedure straightforward for practical design purposes.     

Transient response of single piles under horizontal excitations

The general time-domain boundary element in cylindrical co-ordinates developed for the study of wave propagation in a layered half-space is extended to the response analysis of single piles under horizontal transient excitations. The pile is treated as a beam, and therefore, only the bending stiffness has to be considered in the analysis. As required by the non-axisymmetric nature of the problem, the soil is modelled by boundary (cylindrical) elements with the vertical, radial and tangential displacements as well as their corresponding tractions as independent variables. The characteristic matrices for the two different types of element can be formed in the usual manner, and they are combined to form the equation of motion for the whole system by virtue of compatibility and equilibrium conditions along the pile-soil interface. The transient responses of a pile under Heaviside loads are found to converge to the static values. Parametric studies are carried out to reveal the influences of pile-soil stiffness ratio (E_p/E_s) and soil layering.     

Dynamic response of rigid tanks with inhomogeneous liquids

A study of the response to horizontal ground shaking of a rigid cylindrical tank containing an inviscid liquid with a continuous vertical variation in density is presented. In addition to the free vibrational sloshing characteristics of the liquid, the responses examined include the vertical displacements at the free surface, and the impulsive and convective components of the hydrodynamic wall pressures and associated tank forces. The equations of motion for the system are formulated for an arbitrary variation in liquid density but the solutions presented are for a density that increases exponentially from top to bottom. Comprehensive numerical data are included which elucidate the underlying response mechanisms and the effects and relative importance of the various parameters involved. The solution for the continuous density variation considered herein is also compared with a previously reported solution in which the liquid was modelled as a multi-layered, discrete system.     

Experimental investigation on seismic behavior of single piles in sandy soil

This paper describes a quasi-static test program featuring lateral cyclic loading on single piles in sandy soil. The tests were conducted on 18 aluminum model piles with different cross sections and lateral load eccentricity ratios, e/d, (e is the lateral load eccentricity and d is the diameter of pile) of 0, 4 and 8, embedded in sand with a relative density of 30% and 70%. The experimental results include lateral load-displacement hysteresis loops, skeleton curves and energy dissipation curves. Lateral cap...     

Experimental investigation on seismic behavior of single piles in sandy soil

This paper describes a quasi-static test program featuring lateral cyclic loading on single piles in sandy soil. The tests were conducted on 18 aluminum model piles with different cross sections and lateral load eccentricity ratios, e/d, (e is the lateral load eccentricity and d is the diameter of pile) of 0, 4 and 8, embedded in sand with a relative density of 30% and 70%. The experimental results include lateral load-displacement hysteresis loops, skeleton curves and energy dissipation curves. Lateral capacity, ductility and energy dissipation capacity of single piles under seismic load were evaluated in detail. The lateral capacities and the energy dissipation capacity of piles in dense sand were much higher than in loose sand. When embedded in loose sand, the maximum lateral load and the maximum lateral displacement of piles increased as e/d increased. On the contrary, when embedded in dense sand, the maximum lateral load of piles decreased as e/d increased. Piles with a higher load eccentricity ratio experienced higher energy dissipation capacity than piles with e/d of 0 in both dense and loose sand. At a given level of displacement, piles with circular cross sections provided the best energy dissipation capacity in both loose and dense sand.     

Nonlinear response of single piles under lateral inertial and seismic loads

A macroscopic model that consists of distributed hysteretic springs and frequency dependent -pots is utilized to model the lateral soil reaction and a practical method based on one-dimensional finite element formulation is developed to compute the nonlinear response of single piles under dynamic lateral loads. The model is physically motivated, adequate for cohesive and cohesionless soils, and involves standard geotechnical parameters. Only two parameters have to be calibrated by fitting experimental data. Hysteretic and radiation damping are modeled realistically within the practical range of amplitudes and frequencies. The model is calibrated and validated against five well instrumented full-scale experiments and typical values for the range of the model-parameters are provided. Subsequently, the developed model is utilized to study the nonlinear seismic response of single piles. Finally, the developed method and the calibrated model are used to predict the inertial and seismic response of one of the piles used in the foundation of the Ohba bridge near Tokyo, Japan.     

1-g Experimental investigation of bi-layer soil response and kinematic pile bending

The effect of soil inhomogeneity and material nonlinearity on kinematic soil–pile interaction and ensuing bending under the passage of vertically propagating seismic shear waves in layered soil, is investigated by means of 1-g shaking table tests and nonlinear numerical simulations. To this end, a suite of scale model tests on a group of five piles embedded in two-layers of sand in a laminar container at the shaking table facility in BLADE Laboratory at University of Bristol, are reported. Results from white noise and sine dwell tests were obtained and interpreted by means of one-dimensional lumped parameter models, suitable for inhomogeneous soil, encompassing material nonlinearity. A frequency range from 0.1 Hz to 100 Hz and 5 Hz to 35 Hz for white noise and sine dwell tests, respectively, and an input acceleration range from 0.015 g to 0.1 g, were employed. The paper elucidates that soil nonlinearity and inhomogeneity strongly affect both site response and kinematic pile bending, so that accurate nonlinear analyses are often necessary to predict the dynamic response of pile foundations.     

Vertical response of single piles: transient analysis by time-domain BEM

The transient dynamic response of single piles in a layered half-space under a time-dependent vertical force is analyzed by an FEM-BEM coupling approach. The pile is modeled by FEM and the layered half-space is modeled by a general cylindrical coordinates time-domain BEM. Only one-dimensional discretization is necessary on the boundaries of the three-dimensional layered half-space by virtue of the Fourier theory, while the pile shaft can be discretized as a one-dimensional elastic beam. The compatibility and equilibrium conditions between pile shaft and soil layers are employed to assemble respective equations into one. Fairly good agreement between two unknown solutions and the current approach is found. Parametric studies reveal the influences of several dimensionless factors, such as E_p/E_s, l/r₀, _p/_s and ν_s. The effect of soil layering and the support condition of the pile tip is also reported by numerical examples.     

基岩弹性刚度对土层地震反应的影响

将基岩上均匀、各向同性土层的地震反应,简化为置于弹性支座上的一维剪切梁模型进行分析。将地震激励假定为白噪声谱,在随机边界激励下,主要探讨了土层与基岩2种介质间的波阻抗比、波速比、土层厚度和阻尼特性对土层地震反应的影响。计算结果表明,对于一定的土层厚度,在一定阻尼比条件下,土层和基岩的阻抗比小到一定程度时,可以将基岩假定为刚性约束,而误差可以控制在一定的范围内。     

1D harmonic response of layered inhomogeneous soil: Analytical investigation

The seismic response of inhomogeneous soil deposits is explored analytically by means of one-dimensional viscoelastic wave propagation theory. The problem under investigation comprises of a continuously inhomogeneous stratum over a homogeneous layer of higher stiffness, with the excitation defined in terms of vertically propagating harmonic S waves imposed at the base of the system. A generalized parabolic function is employed to describe the variable shear wave propagation velocity in the inhomogeneous layer. The problem is treated analytically leading to an exact solution of the Bessel type for the natural frequencies, mode shapes and base-to-surface response transfer function. The model is validated using available theoretical solutions and finite-element analyses. Results are presented in the form of normalized graphs demonstrating the effect of salient model parameters such as layer thickness, impedance contrast between surface and base layer, rate of inhomogeneity and hysteretic damping ratio. Equivalent homogeneous soil approximations are examined. The effect of vanishing shear wave propagation velocity near soil surface on shear strains and displacements is explored by asymptotic analyses.     

Dynamic response of single span highway bridges

The dynamic response of single span simply supported bridge decks subjected to the passage of vehicles is examined. A modal analysis approach is adopted that is based upon a finite strip idealization of the deck. The vehicle is modelled as a rigid body supported at two points by a suspension idealization that accounts for the effect of tyre stiffness and the frictional nature of real suspension systems. Results are presented for an orthotropic slab deck and a box girder deck that illustrate the effects of (i) the initial precompression of the suspension system as the vehicle enters the span, (ii) the ratio of the vehicle's natural frequency to that of the bridge deck and (iii) a bridge deck surface profile that is not perfectly horizontal.     

Dynamic stiffness of foundation on layered soil half-space using cone frustums

Approximate dynamic-stiffness coefficients of a disk on the surface of a single layer on a half-space may be calculated using cone models. This concept is generalized to the case of a horizontally stratified site consisting of many layers on a homogeneous half-space. After constructing the so-called ‘backbone cone’ determining the radii of the disks at all interfaces, the dynamic-stiffness matrices of the layers (modelled as cone frustums) and the dynamic-stiffness coefficient of the underlying half-space (modelled as a cone) are assembled to that of the site. The dynamic-stiffness matrix of a layer is a complex-valued function of frequency because radiation of energy in the horizontal direction is considered. In this model of the layered half-space the properties of the cone reproduce themselves (cloning). The advantages of using cone models are also present for the layered half-space; in particular, no transformation to the wave-number domain is performed.     

浅埋地下结构和土层在动荷载作用下的反应分析

在日本阪神大地震中,地下结构遭到了严重破坏。正确分析地下结构的地震反应,提出合理的抗震设计和安全性评价方法十分必要。用FLAC v4．0对某地的一个地铁车站进行了动力分析,发现随着埋深变浅,土体的加速度时程曲线表现出以某一确定的频率振动,该振动频率与模型的基频相近;位移在正方向和负方向的振幅都随埋深的增加而变小：在地表处达到最大值。一些认识和结论对于正确的进行抗震设计有指导意义。     

Kinematic response of single piles to vertically incident P‐waves

Dynamic response of single piles to seismic waves is fundamentally different from the free‐field motion because of the interaction between the pile and the surrounding soil. Considering soil–pile interaction, this paper presents a new displacement model for the steady‐state kinematic response of single piles to vertically incident P‐waves on the basis of a continuum model. The governing equations and boundary conditions of the two undetermined functions in the model are obtained to be coupled by using Hamilton's principle. Then, the two unknown functions are decoupled and solved by an iterative algorithm numerically. A parametric study is performed to investigate the effects of the properties of the soil–pile system on the kinematic response of single piles. It is shown that the effects of the pile–soil modulus ratio, the slenderness ratio of the pile, and the frequency of the incident excitations are very significant. By contrast, the influence of soil damping on the kinematics of the system is slight and can be neglected. Copyright © 2013 John Wiley & Sons, Ltd.     

Artificial neural network application to estimate kinematic soil pile interaction response parameters

Six artificial neural network (ANN) models are developed to predict various response parameters of kinematic soil pile interaction. These responses include (1) kinematic response factors for free and fixed head piles in homogenous soil layer to derive foundation input motion (2) normalized bending moment at fixed head of pile in homogenous soil layer (3) normalized kinematic pile moment at the interface of two soil layers of sharply different soil stiffnesses. These ANN models represent simple solutions that can be implemented in a simple calculator capable of matrix operation and bypass the site response analysis and the complex wave diffraction analysis. The data required for ANN training is generated using beam on dynamic Winkler formulation (BDWF). Fifty percent of the data is used to train the ANN models while remaining 50% is used to test the ANN models. The trained ANN models show good agreement with BDWF results.     

Model tests and numerical analyses on horizontal impedance functions of inclined single piles embedded in cohesionless soil

Horizontal impedance functions of inclined single piles are measured experimentally for model soil-pile systems with both the effects of local soil nonlinearity and resonant characteristics.Two practical pile inclinations of 5° and 10° in addition to a vertical pile embedded in cohesionless soil and subjected to lateral harmonic pile head loadings for a wide range of frequencies are considered.Results obtained with low-to-high amplitude of lateral loadings on model soil-pile systems encased in a laminar shear box show that the local nonlinearities have a profound impact on the horizontal impedance functions of piles.Horizontal impedance functions of inclined piles are found to be smaller than the vertical pile and the values decrease as the angle of pile inclination increases.Distinct values of horizontal impedance functions are obtained for the ’positive’ and ’negative’ cycles of harmonic loadings,leading to asymmetric force-displacement relationships for the inclined piles.Validation of these experimental results is carried out through three-dimensional nonlinear finite element analyses,and the results from the numerical models are in good agreement with the experimental data.Sensitivity analyses conducted on the numerical models suggest that the consideration of local nonlinearity at the vicinity of the soil-pile interface influence the response of the soil-pile systems.     

Kinematic response of single piles for different boundary conditions: Analytical solutions and normalization schemes

Kinematic pile–soil interaction is investigated analytically through a Beam-on-Dynamic-Winkler-Foundation model. A cylindrical vertical pile in a homogeneous stratum, excited by vertically-propagating harmonic shear waves, is examined in the realm of linear viscoelastic material behaviour. New closed-form solutions for bending, displacements and rotations atop the pile, are derived for different boundary conditions at the head (free, fixed) and tip (free, hinged, fixed). Contrary to classical elastodynamic theory where pile response is governed by six dimensionless ratios, in the realm of the proposed Winkler analysis three dimensionless parameters suffice for describing pile–soil interaction: (1) a mechanical slenderness accounting for geometry and pile–soil stiffness contrast, (2) a dimensionless frequency (which is different from the classical elastodynamic parameter a₀=ω d/V_s), and (3) soil material damping. With reference to kinematic pile bending, insight into the physics of the problem is gained through a rigorous superposition scheme involving an infinitely-long pile excited kinematically, and a pile of finite length excited by a concentrated force and a moment at the tip. It is shown that for long piles kinematic response is governed by a single dimensionless frequency parameter, leading to a unique master curve pertaining to all pile lengths and pile–soil stiffness ratios.