Kinematic interaction factors of deep foundations with inclined piles

The beneficial or detrimental role of battered piles on the dynamic response of piled foundations has not been yet fully elucidated. In order to shed more light on this aspect, kinematic interaction factors of deep foundations with inclined piles, are provided for single‐battered piles, as well as for 2 × 2 and 3 × 3 groups of piles subjected to vertically incident plane shear S waves. Piles are modelled as linear‐elastic Bernoulli beams, whereas soil is assumed to be a linear, isotropic, homogeneous viscoelastic half‐space. Different pile group configurations, pile‐soil stiffness ratios, and rake angles are considered. The relevance and main trends observed in the influence of the rake angle on the kinematic interaction factors of the analysed foundations are inferred from the presented results. An important dependence of the kinematic interaction factors on the rake angle is observed together with the existence of an inclination angle at which cap rotation and excitation become out of phase in the low‐to‐mid frequency range. The existence of a small batter angle that provides minimum cap rotation is also shown. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

带深桩基础高层建筑结构的地震动输入问题

带深桩基础高层建筑结构的地震反应分析通常按刚性地基假定选择地震动输入,其合理性一直受到工程界关注。本文探讨了此类结构考虑桩-土-结构相互作用的整体有限元分析的地震激励施加、单元网格划分、积分步长确定、边界处理等问题,通过整体有限元分析模型和常规分析模型的算例分析对比,探讨了常规地震动输入方法的合理程度。结果表明,常规输入法总体偏于安全,是基本可行的,但可能低估结构底部几层的地震反应,应引起注意。     

Mechanism and bounding of earthquake energy input to building structure on surface ground subjected to engineering bedrock motion

The mechanism of earthquake energy input to building structures is clarified by considering the surface ground amplification and soil–structure interaction. The earthquake input energies to superstructures, soil–foundation systems and total swaying–rocking system are obtained by taking the corresponding appropriate free bodies into account and defining the energy transfer functions. It has been made clear that, when the ground surface motion is white, the input energy to the swaying–rocking model is constant regardless of the soil property (input energy constant property). The upper bound of earthquake input energy to the swaying–rocking model is derived for the model including the surface ground amplification by taking full advantage of the above-mentioned input energy constant property and introducing the envelope function for the transfer function of the surface ground amplification. Extension of the theory to a general earthquake ground motion model at the engineering bedrock is also made by taking full advantage of the above-mentioned input energy constant property.     

Simplified discrete systems for dynamic analysis of structures on footings and piles

A simplified discrete system in the form of a simple oscillator is developed to simulate the dynamic behavior of a structure founded through footings or piles on compliant ground, under harmonic excitation. Exact analytical expressions for the fundamental natural period and the corresponding damping coefficients of the above system are derived, as function of geometry and the frequency-dependent foundation impedances. In an effort to quantify the coupling between swaying and rocking oscillations in embedded foundations such as piles, the reference system is translated from the footing–soil interface to the depth where the resultant soil reaction is applied, to ensure a diagonal impedance matrix. The resulting eccentricity is a measure of the coupling effect between the two oscillation modes. The amounts of radiation damping generated from a single pile and a surface footing are evaluated. In order to compare the damping of a structure on a surface footing and a pile, the notion of static and geometric equivalence is introduced. It is shown that a pile may generate significantly higher radiation damping than an equivalent footing, thus acting as an elementary protective system against seismic action.     

Simplified approximate method for analysis of rocking systems accounting for soil inelasticity and foundation uplifting

A simplified approximate method to analyze the rocking response of SDOF systems lying on compliant soil is introduced, accounting for soil inelasticity and foundation uplifting. The soil–foundation system is replaced by a nonlinear rotational spring, accompanied by a linear rotational dashpot, and linear horizontal and vertical springs and dashpots. Considering a square footing on clay under undrained conditions, the necessary moment–rotation (M–θ) relations are computed through monotonic pushover finite element (FE) analyses, employing a thoroughly-validated constitutive model. Cyclic pushover analyses are performed to compute the damping–rotation (C_R–θ) relations, necessary to calibrate the rotational dashpot, and the settlement–rotation (Δw–θ) relations, required to estimate the dynamic settlement. The effectiveness of the simplified method is verified through dynamic time history analyses, comparing its predictions with the results of 3D FE analyses. The simplified method is shown to capture the entire rotation time history θ(t) with adequate accuracy. The latter is used to compute the time history of dynamic settlement w(t), employing a simplified approximate procedure. The proposed simplified method should, by no means, be considered a substitute for more sophisticated analysis methods. However, despite its limitations, it may be utilized for (at least preliminary) design purposes.     

Dimensional analysis of structures with translating and rocking foundations under near-fault ground motions

This paper evaluates the inertial soil–structure interaction (SSI) effects on linear and bilinear structures supported on foundation that is able to translate and rock when subject to near-fault ground motions. Through rigorous dimensional analysis, the peak structural responses (e.g. structural drift and total acceleration) of the soil–foundation–structure interacting (SFSI) systems are characterized by a set of dimensionless Π-parameters, which can decisively describe the interactive behavior of SFSI systems. By comparing the normalized structural responses of various structure–foundation systems with their fixed-base counterparts, the study reveals that SSI effects highly depend on the structure-to-pulse frequency ratio, Π_ω, the foundation-to-structure stiffness ratio, Π_k, damping coefficient of foundation impedance, Π_c, the foundation rocking, and the development of nonlinearity in structures. For linear structures, the SSI effects are insignificant when the structure-to-pulse frequency ratio (Π_ω) is smaller than 1.5 and can amplify the structural responses when Π_ω is higher than 1.5. Foundation rocking can shift and enlarge the response amplification zone of SSI. For nonlinear structures, SSI tends to reduce the structural responses for Π_ω<3 while can increase the ductility demands for Π_ω≥3. The bilinear structures may experience more significant SSI effects than linear structures in certain frequency ranges. The numerical simulations on ten real building cases exhibiting significant rocking and a detailed case study on a nine-story frame structure demonstrate the applicability of dimensional analysis results to predict the SSI effects on realistic building structures. The study demonstrates that the dimensional analysis provides a concise and systematic way of evaluating SSI effects.     

Effects of wave passage on the relevant dynamic properties of structures with flexible foundation

An evaluation of the wave passage effects on the relevant dynamic properties of structures with flexible foundation is presented. A simple soil–structure system similar to that used in practice to take into account the inertial interaction effects by the soil flexibility is studied. The kinematic interaction effects due to non‐vertically incident P, SV and Rayleigh waves are accounted for in this model. The effective period and damping of the system are obtained by establishing an equivalence between the interacting system excited by the foundation input motion and a replacement oscillator excited by the free‐field ground motion. In this way, the maximum structural response could be estimated from standard free‐field response spectra using the period and damping of the building modified by both the soil flexibility and the travelling wave effects. Also, an approximate solution for the travelling wave problem is examined over wide ranges of the main parameters involved. Numerical results are computed for a number of soil–structure systems to identify under which conditions the effects of wave passage are important. It comes out that these effects are generally negligible for the system period, but they may significantly change the system damping since the energy dissipation within the soil depends on both the wave radiation and the diffraction and scattering of the incident waves by the foundation. Copyright © 2001 John Wiley & Sons, Ltd.     

On the performance of lumped parameter models with gyro‐mass elements for the impedance function of a pile‐group supporting a single‐degree‐of‐freedom system

Lumped parameter models with a so called “gyro‐mass” element (GLPMs) have been proposed recently in response to a strong demand for efficiently and accurately representing frequency‐dependent impedance functions of soil–foundation systems. Although GLPMs are considered to be powerful tools for practical applications in earthquake engineering, some problems remain. For instance, although GLPMs show fairly close agreement with the target impedance functions, the accuracy of the transfer functions and the time‐histories of dynamic responses in structural systems comprising GLPMs have never been verified. Furthermore, no assessment has been performed on how much difference appears in the accuracy of dynamic responses obtained from GLPMs and those from conventional Kelvin–Voigt models comprising a spring and a dashpot arranged in parallel with various frequency‐independent constants. Therefore, in this paper, these problems are examined using an example of 2×4 pile groups embedded in a layered soil medium, supporting a single‐degree‐of‐freedom system subjected to ground motions. The results suggest that GLPMs are a new option for highly accurate computations in evaluating the dynamic response of structural systems comprising typical pile groups, rather than conventional Kelvin–Voigt models. Copyright © 2011 John Wiley & Sons, Ltd.