Dynamic behaviour of pile foundations in homogeneous and non-homogeneous media

A three-dimensional formulation based on Green's functions of cylindrical loads in layered semi-infinite media is employed to investigate the dynamic behaviour of piles in homogeneous and non-homogeneous half spaces. The pile-soil-pile interaction taking place in pile groups is incorporated in the model. The results presented in this paper include the dynamic stiffnesses and dampings of single piles as well as those of representative 2 × 2 and 4 × 4 square pile groups in the soil media considered in this study. In addition, the distribution of forces applied on the pile cap among the individual piles in a group is investigated.     

Nonlinear lateral interaction in pile dynamics

A model for pile lateral response to transient dynamic loading and to harmonic loading is presented allowing for nonlinear soil behaviour, discontinuity conditions at the pile-soil interface and energy dissipation through different types of damping. The approach is used to establish equivalent linear stiffness and damping parameters of single piles as well as dynamic interaction factors for approximate nonlinear analysis of pile groups. The applicability of these parameters to the pile-group analysis was examined, and a reasonable agreement with the direct analysis was found. The superposition technique may be used to analyze the response of small pile groups. Also, the dynamic stiffness of pile groups is greatly affected by both the nonlinear behavior of the soil and the slippage and gapping between the pile and soil. For a basic range of soil and pile parameters, equivalent linear stiffness and damping parameters of single piles and interaction factors for approximate nonlinear analysis are provided.     

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.     

Assessing the effect of bi-directional loading on nonlinear static and dynamic behaviour of masonry-infilled frames with openings

In assessing the structural performance of infilled frames, in particular those with irregular and discontinuous infill panels, under bi-directional seismic excitation, the interaction effect of in-plane and out-of-plane lateral loads should be properly considered. This paper presents an investigation into the effect of bi-directional horizontal loading on the nonlinear static and dynamic behaviour of masonry-infilled reinforced concrete frames with openings in association with discrete-finite element modelling techniques. Out-of-plane loading and openings can significantly soften the bracing action provided by infill walls to the bounding frame. Under static load, the lateral strength of the infilled frames can reduce by 20–50 % when the applied out-of-plane load increase from 0.5 times to 2.0 times the unit weight of infills. The out-of-plane effects are intensified in dynamic loading cases. It is found that the peak base shears of the fully infilled frame under the bi-directional excitations are lower by 24.7 % under the Superstition Hill earthquake (PGA = 0.45 g) and 54.1 % under the Chi–Chi earthquake (PGA = 0.82 g) as compared with the uni-directional load cases. The displacement demands are also greater under bi-directional dynamic loading. For 2/3 height infilled frame, the displacement demands are significantly increased by 99.7 % under Kobe (PGA = 0.65 g) and 111.0 % under Chi–Chi earthquake (PGA = 0.82 g) respectively. For the fully infilled frame, the displacement demands are 84.1 % higher under Kobe and 53.1 % higher under Chi–Chi. Due to the incapability of developing continuous arching action, the infill panels with openings are particularly vulnerable to out-of-plane action and that often leads to progressive collapse of infill components. The worst scenario is that total collapse of infill panels takes place at the first storey, creating a soft-storey that jeopardise the overall structural stability.     

Nonlinear analysis for dynamic lateral pile response

An analysis of pile lateral response to transient dynamic loading and to harmonic loading is presented allowing for nonlinear soil behavior, discontinuity conditions at the pile-soil interface and energy dissipation through different types of damping. Furthermore, the effect of neighbouring piles is taken into account for piles in a group. The validity of the approach was examined and a reasonable agreement with field tests and more rigorous solutions was found. Equivalent linear stiffness and damping parameters of single piles and interaction factors for approximate nonlinear analysis are presented.     

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.     

Experimental study of near-shore pile-to-pile interaction

This paper presents the results of lateral impact load field tests carried out on a system of three steel pipe piles vibro-driven into soft clay in a near-shore marine environment, with the aim of evaluating the pile–soil–pile dynamic interaction. Piles are arranged in an “L” shaped horizontal layout and are instrumented with accelerometers at their free heads. The obtained results show the complex dynamic behaviour at very small strain of the vibrating soil–water–piles system. The role of different type of waves in the pile to pile interaction is investigated by analyzing the results in the time and frequency domains and by means of a time–frequency analysis. The effects of the pile spacing and input direction on these interaction mechanisms are also presented. Finally, important dynamic parameters of the soil, such as the velocities of the shear waves and surface waves (Scholte waves) of the upper soil are directly estimated from the time delays between signals recorded at the pile heads.     

Centrifuge modelling of raked piles

Inclined piles are prohibited by many codes in seismic areas. Nevertheless the battered effect has not yet been clarified because very few data are available. The present work is a comparison, at reduced scale in the centrifuge, of the response of two simplified pile groups: a 1 × 2 vertical piles and 1 × 2 pile group with one inclined pile. Two configurations are considered: end-bearing and floating pile group, both with pile heads rigidly fixed with a massive cap. First, repeatability tests under horizontal cyclic loading were performed on both floating pile groups. Secondly, repeated horizontal impact tests were performed on both end-bearing pile groups. These impact tests, which highlight the influence of inclined piles on the inertial response of a group, are a first step for the more complex analysis of the performance of such groups under seismic loads where inertial and kinematic interactions are combined. The first part of this work revealed the influence of sand structure around the inclined pile tip on the repeatability of the tests performed on floating pile groups. The second part highlighted differences in the dynamic response between the two end-bearing pile groups through measurements of the pile cap acceleration, the bending moment profile and the axial load in the piles.     

Model tests on horizontal pile-to-pile interaction incorporating local non-linearity and resonance effects

Dynamic experimental studies on horizontal interaction factors for laterally loaded model soil–pile systems subjected to low-to-high amplitude pile head loading are reported, focusing on the effect of dynamics and local non-linearity. Results obtained from dynamic experiments with different amplitudes of harmonic lateral loading on instrumented model soil–pile systems conducted on a shaking table indicate that the resonance of soil–pile system shows a profound impact on the horizontal interaction factors. Furthermore, behavior of the soil–pile system becomes highly non-linear with increasing amplitude of loading, as the extent of local non-linearity around the pile increases. Consequently, group effects cannot be predicted by using established approximate equations based on the assumption of linear viscoelastic behavior. To this end, new semi-empirical equations are proposed for obtaining the horizontal interaction factors, as an extension of available approximate equations to incorporate the local non-linear behavior of soil–pile system for both small and large pile spacings.     

Influence of pile spacing on seismic response of piled raft in soft clay: centrifuge modeling

In order to study the influence of pile spacing on the seismic response of piled raft in soft clay, a series of shaking table tests were conducted by using a geotechnical centrifuge. The dynamic behavior of acceleration, displacement and internal forces was examined. The test results indicate that the seismic acceleration responses of models are generally greater than the surrounding soil surface in the period ranges of 2–10 seconds. Foundation instant settlements for 4×4 and 3×3 piled raft (with pile spacing equal to 4 and 6 times pile diameter) are somewhat close to each other at the end of the earthquake, but reconsolidation settlements are greater for 3×3 piled raft. The seismic acceleration of superstructure, the uneven settlement of the foundation and the maximum bending moment of pile are relatively lower for 3×3 piled raft. Successive earthquakes lead to the softening behavior of soft clay, which causes a reduction of the pile bearing capacity and thus loads are transferred from the pile group to the raft. For the case of a 3×3 piled raft, there is relatively smaller change of the load sharing ratio of the pile group and raft after the earthquake and the distribution of maximum bending moments at the pile head is more uniform.

     

A Study of Piles during Earthquakes: Issues of Design and Analysis

The seismic response of pile foundations is a very complex process involving inertial interaction between structure and pile foundation, kinematic interaction between piles and soils, seismically induced pore-water pressures (PWP) and the non-linear response of soils to strong earthquake motions. In contrast, very simple pseudo-static methods are used in engineering practice to determine response parameters for design. These methods neglect several of the factors cited above that can strongly affect pile response. Also soil–pile interaction is modelled using either linear or non-linear springs in a Winkler computational model for pile response. The reliability of this constitutive model has been questioned. In the case of pile groups, the Winkler model for analysis of a single pile is adjusted in various ways by empirical factors to yield a computational model for group response. Can the results of such a simplified analysis be adequate for design in all situations?The lecture will present a critical evaluation of general engineering practice for estimating the response of pile foundations in liquefiable and non-liquefiable soils during earthquakes. The evaluation is part of a major research study on the seismic design of pile foundations sponsored by a Japanese construction company with interests in performance based design and the seismic response of piles in reclaimed land. The evaluation of practice is based on results from field tests, centrifuge tests on model piles and comprehensive non-linear dynamic analyses of pile foundations consisting of both single piles and pile groups. Studies of particular aspects of pile–soil interaction were made. Piles in layered liquefiable soils were analysed in detail as case histories show that these conditions increase the seismic demand on pile foundations. These studies demonstrate the importance of kinematic interaction, usually neglected in simple pseudo-static methods. Recent developments in designing piles to resist lateral spreading of the ground after liquefaction are presented. A comprehensive study of the evaluation of pile cap stiffness coefficients was undertaken and a reliable method of selecting the single value stiffnesses demanded by mainstream commercial structural software was developed. Some other important findings from the study are: the relative effects of inertial and kinematic interactions between foundation and soil on acceleration and displacement spectra of the super-structure; a method for estimating whether inertial interaction is likely to be important or not in a given situation and so when a structure may be treated as a fixed based structure for estimating inertial loads; the occurrence of large kinematic moments when a liquefied layer or naturally occurring soft layer is sandwiched between two hard layers; and the role of rotational stiffness in controlling pile head displacements, especially in liquefiable soils. The lecture concludes with some recommendations for practice that recognize that design, especially preliminary design, will always be based on simplified procedures.     

Response of fixed offshore platforms to wave and current loading including soil–structure interaction

Fixed offshore platforms supported by pile foundations are required to resist dynamic lateral loading due to wave forces. The response of a jacket offshore tower is affected by the flexibility and nonlinear behaviour of the supporting piles. For offshore towers supported by clusters of piles, the response to environmental loads is strongly affected by the pile–soil–pile interaction. In the present study, the response of fixed offshore platforms supported by clusters of piles is investigated. The soil resistance to the pile movement is modelled using dynamic p–y curves and t–z curves to account for soil nonlinearity and energy dissipation through radiation damping. The load transfer curves for a single pile have been modified to account for the group effect. The wave forces on the tower members and the tower response are calculated in the time domain using a finite element package (ASAS). Several parameters affecting the dynamic characteristics of the platform and the platform response have been investigated.     

远场地震作用下桩间横向动力相互作用的研究

在远场地震作用下单桩横向地震响应研究的基础上,引入相互作用因子,研究了远场地震作用下成层地基中桩与桩的横向动力相互作用,得到了桩间距、桩土刚度比、桩顶约束条件、瑞利波入射角度、震动频率是影响群桩横向动力相互作用主要因素的结论,为进一步研究远场地震作用下群桩的横向地震响应打下了基础。     

Dynamic pile-soil-pile interaction. Part I: Analysis of axial vibration

Simple methods of analysis are developed for computing the dynamic steady-state axial response of floating pile groups embedded in homogeneous and non-homogeneous soil deposits. Physically-motivated approximations are introduced to account for the interaction between two individual piles. It is found that such an interaction arises chiefly from the ‘interference’ of wave fields originating along each pile shaft and spreading outward. For homogeneous deposits the wave fronts originating at an individual pile are cylindrical and the interaction is essentially independent of pile flexibility and slenderness. For non-homogeneous deposits the wave fronts are non-cylindrical and ray-theory approximations are invoked to derive pile flexibility-dependent interaction functions. Results are presented for the dynamic stiffness and damping of several pile groups, as well as for distribution of the applied load among individual piles. For deposits with modulus proportional to depth, the agreement with the few rigorous solutions available is encouraging. A comprehensive parameter study focuses on the effects of soil inhomogeneity and pile-group configuration. It is demonstrated that the ‘dynamic group efficiency’ may far exceed unity at certain frequencies. Increasing soil inhomogeneity tends to reduce the respective resonant peaks and lead to smoother interaction functions, in qualitative agreement with field evidence.     

Kinematic internal forces in deep foundations with inclined piles

This paper presents a parametric study that looks into the influence of pile rake angle on the kinematic internal forces of deep foundations with inclined piles. Envelopes of maximum kinematic bending moments, shear forces and axial loads are presented along single inclined piles and 2 × 2 symmetrical square pile groups with inclined elements subjected to an earthquake generated by vertically incident shear waves. Inclination angles from 0° to 30° are considered, and three different pile–soil stiffness ratios are studied. These results are obtained through a frequency–domain analysis using a boundary element–finite element code in which the soil is modelled by the boundary element method as a homogeneous, viscoelastic, unbounded region, and the piles are modelled by finite elements as Euler–Bernoulli beams. The rotational kinematic response of the pile foundations is shown to be a key factor on the evolution of the kinematic internal forces along the foundations. Copyright © 2015 John Wiley & Sons, Ltd.     

A model for the 3D kinematic interaction analysis of pile groups in layered soils

The paper presents a numerical model for the analysis of the soil–structure kinematic interaction of single piles and pile groups embedded in layered soil deposits during seismic actions. A finite element model is considered for the pile group and the soil is assumed to be a Winkler‐type medium. The pile–soil–pile interaction and the radiation problem are accounted for by means of elastodynamic Green's functions. Condensation of the problem permits a consistent and straightforward derivation of both the impedance functions and the foundation input motion, which are necessary to perform the inertial soil–structure interaction analyses. The model proposed allows calculating the internal forces induced by soil–pile and pile‐to‐pile interactions. Comparisons with data available in literature are made to study the convergence and validate the model. An application to a realistic pile foundation is given to demonstrate the potential of the model to catch the dynamic behaviour of the soil–foundation system and the stress resultants in each pile. Copyright © 2009 John Wiley & Sons, Ltd.     

Cyclic behavior of laterally loaded concrete piles embedded into cohesive soil

Modern seismic design codes stipulate that the response analysis should be conducted by considering the complete structural system including superstructure, foundation, and ground. However, for the development of seismic response analysis method for a complete structural system, it is first imperative to clarify the behavior of the soil and piles during earthquakes. In this study, full‐scale monotonic and reversed cyclic lateral loading tests were carried out on concrete piles embedded into the ground. The test piles were hollow, precast, prestressed concrete piles with an outer diameter of 300 mm and a thickness of 60 mm. The test piles were 26 m long. Three‐dimensional (3D) finite element analysis was then performed to study the behavior of the experimental specimens analytically. The study revealed that the lateral load‐carrying capacity of the piles degrades when subjected to cyclic loading compared with monotonic loading. The effect of the use of an interface element between the soil and pile surface in the analysis was also investigated. With proper consideration of the constitutive models of soil and pile, an interface element between the pile surface and the soil, and the degradation of soil stiffness under cyclic loading, a 3D analysis was found to simulate well the actual behavior of pile and soil. Copyright © 2007 John Wiley & Sons, Ltd.     

地震荷载下边坡抗滑桩桩土机理的三维模拟分析

地震是诱发边坡破坏的重要因素之一,而抗滑桩是一种重要的边坡防治工程措施,因此开展地震作用下抗滑桩机理对于边坡防护具有重要的工程意义。本文以广东省梅州市茶阳车站为工程实例,运用ABAQUS软件建立三维模型,对地震作用下的桩土作用机理进行数值模拟分析。研究表明:(1)在地震作用下,边坡中上部水平位移较大,最大值为87.05mm,凹陷处水平位移远小于凸起处;(2)地震作用下抗滑桩会由于地震荷载产生远大于地震前的应力:静力作用下桩身最大值是147.24kPa,地震波输入14s时桩身最大值达到了326.36kPa;(3)地震作用下抗滑桩的应变亦远大于静力作用下的应变:静力作用下抗滑桩应变最大值是4.63×10~(-5),在地震波输入的第14s时桩身应变最大值是34.10×10~(-5)。因此在工程实践中对于地震作用下的抗滑桩边坡加固需要考虑桩的强度与刚度。研究结论对于边坡防治以及工程实践具有一定的指导意义。     

Dynamic characteristics of lateral load-deflection relationships of flexible piles

Most offshore platforms are supported on long and large-diameter piles with variable wall-thickness along the length, and soil properties varying with depth. The design and analyses of these piles are made by modelling the soil-pile system with a beam-on-Winkler foundation. Therefore, evaluation of appropriate soil-pile springs for use in such analyses is a matter of concern. Fundamental characteristics of dynamic lateral load-deflection relationships for piles were studied analytically considering the soil-pile-structure interaction under seismic loading conditions. The soil layer was assumed homogeneous, linearly elastic with hysteretic type material damping, and overlying a rigid base. A superstructure with multi-degrees of freedom was supported by a single vertical pile hinged at the rigid base. Parametric studies were carried out to identify the influence of the system parameters on the behaviour of the dynamic lateral load-deflection relationships of piles. The lateral load-deflection relationships vary considerably with depth and are influenced not only by the dynamic properties of soil but also by the structural properties of a pile and loading conditions. These lateral load-deflection relationships can be used to define the soil-pile springs for the seismic response analysis of a soil-pile-structure system, and the results can be extended to problems with soil profiles with layering and non-linearity.