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.     

Simple formulas for the dynamic stiffness of pile groups

Simple formulas are derived for the dynamic stiffness of pile group foundations subjected to horizontal and rocking dynamic loads. The formulations are based on the construction of a general model of impedance matrices as the condensation of matrices of mass, damping, and stiffness, and on the identification of the values of these matrices on an extensive database of numerical experiments computed using coupled finite element–boundary element models. The formulations obtained can be readily used for the design of both floating piles on homogeneous half‐space and end‐bearing piles and are applicable for a wide range of mechanical and geometrical parameters of the soil and piles, in particular for large pile groups. For the seismic design of a building, the use of the simple formulas rather than a full computational model is shown to induce little error on the evaluation of the response spectra and time histories. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

A numerical model for the dynamic analysis of inclined pile groups

The paper presents a numerical model for the dynamic analysis of pile groups with inclined piles in horizontally layered soil deposits. Piles are modelled with Euler–Bernoulli beams, while the soil is supposed to be constituted by independent infinite viscoelastic horizontal layers. The pile–soil–pile interaction as well as the hysteretic and geometric damping is taken into account by means of two‐dimensional elastodynamic Green's functions. Piles cap is considered by introducing a rigid constraint; the condensation of the problem permits a consistent derivation of both the dynamic impedance matrix of the soil–foundation system and the foundation input motion. These quantities are those used to perform inertial soil–structure interaction analyses in the framework of the substructure approach. Furthermore, the model allows evaluating the kinematic stress resultants in piles resulting from waves propagating in the soil deposit, taking into account the pile–soil–pile interactions. The model validation is carried out by performing accuracy analyses and comparing results in terms of dynamic impedance functions, kinematic response parameters and pile stress resultants, with those furnished by 3D refined finite element models. To this purpose, classical elastodynamic solutions are adopted to define the soil–pile interaction problem. The model results in low computational demands without significant loss of precision, compared with more rigorous approaches or refined finite element models. Copyright © 2015 John Wiley & Sons, Ltd.     

A numerical and experimental study of hollow steel pile in layered soil subjected to lateral dynamic loading

The present study aims at investigating the nonlinear behavior of single hollow pile in layered soil subjected to varying levels of horizontal dynamic load. A finite element model has been developed using commercially available FEM based software. Mohr–Coulomb plasticity model is used to simulate the soil plasticity whereas the pile-material is idealized as elastic. Numerical results are validated comparing with the experimental results. The experimental investigations were carried out in the field located at IIT Kharagpur. Two types of motion: horizontal and rocking are studied. The effects of various influencing parameters, namely, exciting moment, length and diameter of the pile etc. on the nonlinear dynamic response of piles are investigated. It is found that separation of pile from the surrounding soil considerably affects the resonance frequency and amplitude of the pile foundations.     

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.     

Experimental study of the effect of inclined pile on the seismic behavior of pile group

Seismic behavior of inclined piles has been considered detrimental for years. However, recent researches show that battered piles can have a beneficial effect. In this framework, a series of centrifuge tests on an inclined pile group is performed. The analysis is based on the comparative response of two 2×1 simplified pile groups: one with vertical piles and the other with one vertical and one inclined pile. The response of these pile groups to repeated earthquakes or sinusoidal inputs is analyzed through the response frequencies, the envelop curves of bending moment profiles, the axial loads measured in both piles and the kinematic response of the cap. Results highlight that the effect of inclined pile is highly influenced by the frequency content of the input. In addition, the inclined pile induces non-negligible residual bending moments, higher horizontal stiffness at the pile cap and larger rotation.     

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.     

Influences of type of wave and angle of incidence on seismic bending moments in pile foundations

When analysing the seismic response of pile groups, a vertically‐incident wavefield is usually employed even though it does not necessarily correspond to the worst case scenario. This work aims to study the influences of both the type of seismic body wave and its angle of incidence on the dynamic response of pile foundations. To this end, the formulation of SV, SH and P obliquely‐incident waves is presented and implemented in a frequency‐domain boundary element‐finite element code for the dynamic analysis of pile foundations and piled structures. Results are presented in terms of bending moments at cap level of single piles and 3 × 3 pile groups, both in frequency and in time domains. It is found that, in general, the vertical incidence is not the most unfavourable situation. In particular, obliquely‐incident SV waves with angles of incidence smaller than the critical one, a situation in which the mechanism of propagation of the waves in the soil changes and surface waves appear, yield bending moments much larger than those obtained for vertically‐incident wavefields. It is also shown that the influence of pile‐to‐pile interaction on the kinematic bending moments becomes significant for non‐vertical incidence, especially for P and SV waves. Copyright © 2013 John Wiley & Sons, Ltd.     

Load distribution in large pile groups under static and dynamic loading

Research on the action of pile groups in resisting lateral loading is usually based on analysis, field and centrifuge tests of small pile groups. The interaction between piles in these groups is modelled by modifying the lateral resistance p–y curves developed for a single pile using row dependent reduction factors or a group factor for the entire group to simulate the effect of soil–pile–soil interaction. The modifying factors for the p–y curves and the appropriate group factors for pile groups are based entirely on static tests and there is no direct verification that these factors are appropriate to handle the dynamic loading of earthquake induced ground motions. In this paper we investigate the interaction effects between piles under static and seismic loading using the computer program VERSAT-P3D, which uses an equivalent linear constitutive model for the soil. The analytical procedure is calibrated using data from a static field load test on a single pile. Several pile groups, 2 × 2, 3 × 3, 4 × 4, 5 × 5, 8 × 8, 10 × 10, 10 × 2 and 15 × 2 were analysed for the study. Each group was subjected to static pushover and earthquake loading and the distribution of static and dynamic shear forces at various lateral displacements were evaluated. The study shows that the distribution of load within a pile group under dynamic loading varies significantly from the distribution under static loading and is strongly load intensity dependent. Current practice assumes that the distributions are similar.     

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.     

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.     

Modelling of raked pile foundations in liquefiable ground

Raked piles are believed to behave better than vertical piles in a laterally flowing liquefied ground. This paper aims at numerically simulating the response of raked pile foundations in liquefying ground through nonlinear finite element analysis. For this purpose, the OpenSees computer package was used. A range of sources have been adopted in the definition of model components whose validity is assessed against case studies presented in literature. Experimental and analytical data confirmed that the backbone force density–displacement (p–y) curve simulating lateral pile response is of acceptable credibility for both vertical and raked piles. A parametric investigation on fixed-head piles subject to lateral spreading concluded that piles exhibiting positive inclination impart lower moment demands at the head while those inclined negatively perform better at liquefaction boundaries (relative to vertical piles). Further studies reveal substantial axial demand imposed upon negatively inclined members due to the transfer of gravity and ground-induced lateral forces axially down the pile. Extra care must be taken in the design of such members in soils susceptible to lateral spreading such that compressive failure (i.e. pile buckling) is avoided.     

Dynamic response of pile groups with different configurations

A general methodology is outlined for a complete seismic soil—pile-foundation—structure interaction analysis. A Beam-on-Dynamic-Winkler-Foundation (BDWF) simplified model and a Green's-function-based rigorous method are utilized in determining the dynamic response of single piles and pile groups. The simplified model is validated through comparisons with the rigorous method. A comprehensive parameter study is then performed on the effect of pile group configuration on the dynamic impedances of pile foundations. Insight is gained into the nature of dynamic pile—soil—pile interaction. The results presented herein may be used in practice as a guide in obtaining the dynamic stiffness and damping of foundations with a large number of piles.     

不同厚度饱和砂土中群桩P-Y滞回曲线规律研究

根据Buckingham π定理设计制作直群桩和斜群桩相似模型,通过电磁式振动台试验方法,分别考虑非液化砂土、300 mm和380 mm两种不同厚度饱和砂土,开展在规则正弦波输入下桩土相互作用P-Y滞回曲线规律研究.结果 表明:在非液化砂土中,P-Y滞回曲线的主斜率变化较小,说明在振动输入过程中,桩周土体刚度并未发生显...     

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.     

多桩型复合地基作用机理与动力特性研究

对由碎石桩和CFG桩构成的多桩型复合地基的作用机理进行分析,通过数值模拟,对多桩型复合地基的动力特性进行研究,探讨桩型配比、桩径、桩长、CFG桩桩体刚度和碎石桩桩体渗透性等设计参数对多桩型复合地基动力特性的影响。研究结果表明:相同条件下地震期多桩型复合地基的动变形小于碎石桩复合地基而大于CFG桩复合地基,震后沉降量相对较小,在工程设计时碎石桩与CFG桩的桩型配比宜为4∶5;随桩体长度、桩体直径和CFG桩刚度的增加,多桩型复合地基地震期的竖向动变形逐渐减小;随碎石桩桩体渗透性的增加,多桩型复合地基中的超动孔隙水压力减小,震后沉降量降低。     

液化场地桥梁群桩-土耦合体系强震反应分析

针对振动台试验,采用u-p形式控制方程表述饱和砂土的动力属性,选用土的多屈服面塑性本构模型刻画饱和砂土和黏土的力学特性,引入非线性梁-柱单元模拟桩,建立试验受控条件下液化场地群桩-土强震相互作用分析的三维有限元模型,并通过试验结果验证数值建模途径与模拟方法的正确性。以实际工程中常用的2×2群桩为例,建立桩-土-桥梁结构强震反应分析三维有限元模型。基于此,针对不同群桩基础配置对液化场地群桩-土强震相互作用影响展开具体分析。对比发现,桩的数量相同时,桩排列方向与地震波输入方向平行时比垂直时桩基受力减小5%~10%,而对场地液化情况无明显影响;相同排列形式下,三桩模型中土体出现液化的时间约比双桩模型延缓5s,桩上弯矩和剪力减小33%~38%。由此可见,桩基数量增加,桩-土体系整体刚度更大,场地抗液化性能显著,桩基对上部桥梁结构的承载性能明显增强,其安全性与可靠性更高。这对实际桥梁工程抗震设计具有一定的借鉴意义。     

Efficient analysis of pile-group effect on seismic stiffness and strength design of buildings

A new efficient method is developed for the analysis of pile-group effects on the seismic stiffness and strength design of buildings with pile foundations. An efficient continuum model consisting of a dynamic Winkler-type soil element and a pile is used to express the dynamic behavior of the structure-pile-soil system with only a small numerical error. The pile-group effect is taken into account through the influence coefficients among piles which are defined for interstory drifts and pile-head bending moments. It is shown that, while the pile-group effect reduces the interstory drift of buildings in general, it may increase the bending moment of piles at the head. This means that the treatment without the pile-group effect results in the conservative design for super-structures and requires a revised member design for piles.