Centrifuge modeling of batter pile foundations under sinusoidal dynamic excitation

Batter pile (or inclined pile) foundations are widely used in civil engineering structures. However, their behavior under dynamic loadings is not yet thoroughly understood. This paper presents an experimental work on the behavior of batter and vertical piles considering dynamic soil-pile-superstructure interactions. A series of dynamic centrifuge tests were performed using sinusoidal excitations. The influence of the base shaking (frequency content and amplitude) and of the height of the center of gravity of the superstructure is investigated. Seismic responses are analyzed considering the pile cap displacements and forces (total base shear, overturning and residual moments, axial forces). It is found that in certain cases batter piles play a beneficial role on the dynamic behavior of the pile foundation system. This novel experimental work provides an important database on the behavior of batter pile foundations under dynamic loadings.     

Response of a RC pile group in liquefiable soil: A shake-table investigation

Soil liquefaction induced by earthquakes frequently cause costly damage to pile foundations. However, various aspects of the dynamic behavior and failure mechanisms of piles in liquefiable soils still remain unclear. This paper presents a shake-table experiment conducted to investigate the dynamic behavior of a reinforced-concrete (RC) elevated cap pile foundation during (and prior to) soil liquefaction. Particular attention was paid to the failure mechanism of the piles during a strong shaking event. The experimental results indicate that decreasing the frequency and increasing the amplitude of earthquake excitation increased the pile bending moment as well as the speed of the excess pore pressure buildup in the free-field. The critical pile failure mode in the conducted testing configuration was found to be of the bending type, which was also confirmed by a representative nonlinear numerical model of the RC pile. The experimental results of this study can be used to calibrate numerical models and provide insights on seismic pile analysis and design.     

Prediction of pile response to lateral spreading by 3-D soil–water coupled dynamic analysis: Shaking in the direction perpendicular to ground flow

The 1995 Kobe earthquake seriously damaged numerous buildings with pile foundations adjacent to quay walls. The seismic behavior of a pile group is affected by movement of quay walls, pile foundations, and liquefied backfill soil. For such cases, a three-dimensional (3-D) soil–water coupled dynamic analysis is a promising tool to predict overall behavior. We report predictions of large shake table test results to validate 3-D soil–water coupled dynamic analyses, and we discuss liquefaction-induced earth pressure on a pile group during the shaking in the direction perpendicular to ground flow. Numerical analyses predicted the peak displacement of footing and peak bending moment of the group pile. The earth pressure on the pile in the crustal layer is most important for the evaluation of the peak bending moment along the piles. In addition, the larger curvatures in the bending moment distribution along the piles at the water side in the liquefied ground were measured and predicted.     

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.     

Analytical and centrifuge studies of pile groups in liquefiable soil before and after site remediation

The objectives of this paper are to show practically: (1) the validation of a proposed three-dimensional effective stress analysis for the pile foundations, and (2) the effectiveness of remedial deposits on pile stresses under liquefaction by making comparisons between the results of centrifuge tests and those of the proposed analysis. Two foundation models supported by end-bending piles were studied with improved and unimproved deposits. There exists a good consistency between the numerical and experimental results for excess pore water-pressure ratios ranging from 0 to about 0·9. From the numerical results, the bending moment at the pile top with the improved deposit is about 50 per cent lower than that with the unimproved deposit. However, it was found that the smaller the bending moment develops in the pile with the improved deposit, the larger the compressive and/or tensional axial stresses in the pile. This is due to the predominant excitation of rocking vibration of the foundation. From the analytical and experimental results, it has been found that the remedial method can be a variable means to protect piles from soil liquefaction hazards. However, both axial stress and bending moment produced in piles should be considered in assessing the liquefied seismic capacity of group pile-foundation–structural systems with improved soil deposits. © 1998 John Wiley & Sons, Ltd.     

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.     

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.     

桩基础抗震性能的简易评价方法

桩基础的抗震性能可从承载力和变形两方面来评价.承载力可考虑地震时作用于结构上的荷载组合,多采用拟静力法进行分析,不同因素变异的影响可用概率分析或可靠度方法予以考虑.变形分析多为按承载力设计之后的校核,其中地震力和土体参数以及地质条件等因素影响可分别加以评估.本文着重阐明基于一维波动方程和概率分析的桩基抗震性能实用分析方法,并以桥梁桩基础为例进行讨论,其中考虑的关键因素为设计地震加速度、测站记录、基桩尺寸及其配筋率.研究表明,当土层液化可忽略时最大弯矩会发生在桩顶,故增加桩顶延性可有效提升桩基础的抗震性能.     

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.     

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.     

地震作用下液化场地变截面桩与等截面桩的动力响应对比分析

为研究液化场地变截面桩的动力响应,依托翔安大桥实体工程,采用有限元软件,建立变截面桩－土和等截面桩－土相互作用模型,模拟液化场地变截面桩及等截面桩在地震作用下的振动反应,分析在地震作用下变截面位置不同的变截面桩及等截面桩的动力响应特征。结果表明:地震作用下,液化土层不同深度处的孔压比变化规律基本相同,均从0逐渐增大最后趋于稳定;变截面桩的桩身加速度和桩身位移均大于等截面桩,且桩顶加速度峰值出现的时刻均滞后于桩底;在饱和砂土层处,桩身位移变化趋势均较陡;变截面桩的桩身弯矩峰值和桩身剪力峰值均大于等截面桩,且其峰值出现的位置较等截面桩深;地震作用下,变截面桩及等截面桩的弯矩与剪力均在安全范围之内;液化场地变截面梁桥桩基础抗震设计时,应着重分析液化土层与非液化土层分界面以下的抗弯能力设计及液化土层中抗剪能力设计。     

地震作用下预应力混凝土管桩运动响应三维数值分析

基于黏弹性人工边界,建立上部结构-桩-土的共同作用三维有限元模型,分析地震作用下预应力混凝土管桩的运动响应特性。分别针对预应力混凝土管桩的桩径、双层软硬土剪切波速比值、上覆土层厚度、上部结构荷载等影响因素进行数值计算。参数分析表明:在地震作用下,桩径的增大会导致桩身整体弯矩相应增加,特别是桩身土层分界面处增大明显;软硬土层剪切波速比及上覆土层厚度的增加,引起土层分界面处桩身峰值弯矩增加;固定桩头条件下,桩头与桩身软硬土层分界面处均会产生较大的运动弯矩;上部结构的惯性荷载对固定桩头的内力有着较大影响,对桩身深处段弯矩影响较小。本文研究结论可为预应力混凝土管桩抗震设计提供有益的理论参考。     

Strain effects on kinematic pile bending in layered soil

The kinematic bending of single piles in two-layer soil is explored to account for soil stiffness degradation and associated damping increase with increasing levels of shear strain, a fundamental aspect of soil behaviour which is not incorporated in current simplified seismic design methodologies for pile foundations.A parametric study of a vertical cylindrical pile embedded in a two-layer soil profile to vertically-propagating S waves, carried out in the time domain by a pertinent beam-on-dynamic-Winkler-foundation (BDWF) model, is reported. Strain effects are treated by means of the equivalent-linear procedure which provides soil stiffness and damping ratio as function of shear strain level. Whereas the approach still represents a crude representation of the actual soil behaviour to dynamic loading, it is more realistic than elementary solutions based on linear visco-elasticity adopted in earlier studies.The paper highlights that soil nonlinearity may have either a detrimental or a beneficial effect on kinematic pile bending depending on the circumstances. The predictive equations for kinematic pile bending in visco-elastic soil recently developed by the Authors are extended to encompass strain effects. Numerical examples and comparisons against experimental data from case histories and shaking table tests are presented.     

Flexible support of a pile embedded in unsaturated soil under Rayleigh waves

Under the action of Rayleigh waves, pile head is easy to rotate with a concrete pile cap, and pure fixed-head condition is rarely achieved, which is a common phenomenon for it usually occurs on the precast piles with insufficient anchorage. In addition, the propagation characteristics of Rayleigh wave have been changed significantly due to the existence of capillary pressure and the coupling between phases in unsaturated soil, which significantly affects the pile-soil interaction. In order to study the above problems, a coupled vibration model of unsaturated soil–pile system subjected to Rayleigh waves is established on the basis that the pile cap is equivalent to a rigid mass block. Meanwhile, the soil constitution is simplified to linear-elastic and small deformations are assumed to occur during the vibration phase of soil–pile system. Then, the horizontal dynamic response of a homogeneous free-field unsaturated soil caused by propagating Rayleigh waves is obtained by using operator decomposition theory and variable separation method. The dynamic equilibrium equation of a pile is established by using the dynamic Winkler model and the Timoshenko beam theory, and the analytical solutions of the horizontal displacement, rotation angle, bending moment and shear force of pile body are derived according to the boundary conditions of flexible constraint of pile top. Based on the present solutions, the rationality of the proposed model is verified by comparing with the previous research results. Through parametric study, the influence of rotational stiffness and yield bending moment of pile top on the horizontal dynamic characteristics of Rayleigh waves induced pile is investigated in detailed. The analysis results can be utilized for the seismic design of pile foundation under Rayleigh waves.     

3-D Simulation Study on Seismic Response of Bridge Piles in Landslide

The anti-slide support structure is widely used in the anti-seismic reinforcement of bridge foundations, but related experimental research was processing slowly. Based on the prototype of the Jiuzhaigou bridge at the Chengdu-Lanzhou Railway, a 3-D simulation model was established on the basis of the shaking table model test, and the rationality of the dynamic analysis model was verified by indicators such as the bending moment of the bridge piles, peak soil pressure, and PGA amplification factors. The results show that the inertia force of the bridge pier has an important influence on the deformation of the pile foundation. The bending moment and shearing force are larger in lateral bridge piles, and the maximum value is near the pile top. The PGA amplification factor is stronger in the back of the rear anti-slide piles and so is it in front of the bridge pier, and the soil is prone to slip and damage. The bedrock is rigid and the dynamic response is maintained at a low level. The anti-slide piles in the rear row play a major role in the anti-seismic reinforcement design, and the anti-slide piles in the front row can be used as an auxiliary support structure.     

Soil–pile-bridge structure interaction in liquefying ground using shake table testing

The evaluation of seismic pile response is particularly useful for geotechnical engineers involved in the design of foundations in liquefying site. Shake table testing was performed to study the dynamic interactive behavior of soil–pile foundations in liquefying ground under different shaking frequency and amplitude. The soil profile consisted of a clayey layer over liquefiable sand over clay. The model was tested with a series of El Centro earthquake motions with peak accelerations ranging from 0.15g to 0.50g, and time step from 0.006 to 0.02 s. Representative data, including time histories of accelerations and excess pore pressure ratios that characterize the important aspects of soil–pile interaction in liquefying ground are presented. The shaking frequency has no significant effect on the magnitudes of excess pore pressure ratio, ground and pile accelerations and pile bending moments. Excess pore pressure ratio, ground acceleration and pile acceleration, and pile bending moment largely depend on the shaking amplitude.     

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.     

液化侧扩流场地桥梁群桩效应分析

基于u-p有限元公式模拟饱和砂土中水和土颗粒完全耦合效应,建立液化侧向流场地群桩动力反应分析的三维数值模型。模型中,砂土采用多屈服面弹塑性本构模型模拟、黏土采用多屈服面运动塑性模型模拟,群桩在计算过程中保持线弹性状态;采用20节点的六面体单元和考虑孔压效应的20-8节点分别划分黏土层和饱和砂层;选用剪切梁边界处理计算域的人工边界,模拟地震过程中土层的剪切效应;应用瑞利阻尼考虑体系的阻尼效应。随后对比分析2×2群桩中各单桩的地震反应规律,结果表明,各单桩的弯矩、位移时程规律基本一致,峰值弯矩及峰值位移出现时刻滞后于输入加速度峰值时刻,上坡向桩的弯矩和位移峰值大于下坡向的桩的反应值。接着通过改变桩间距研究群桩效应,随着桩间距增加,群桩中各单桩的弯矩最大值均出现在土层分界处,且各单桩的弯矩、桩顶位移逐渐增大。最后给出液化侧向流场地群桩效应的基本原因,得出该类场地群桩抗震设计的基本认识。     

Pile–soil–pile interaction in pile groups with batter piles under dynamic loads

A simple analytical solution is developed for computing the dynamic interaction tensor for floating pile groups with batter piles. For this purpose, the governing differential equations are derived for an unloaded batter floating pile closely spaced to another loaded pile with the same properties. The reaction of soil against pile deformation is modeled by the springs and dashpots along the length of the pile. The soil is assumed linear viscous elastic and the pile behavior is linear elastic. The closed form solutions of governing equations are obtained using appropriate boundary conditions. The results are verified and compared with rigorous and approximate analytical solutions for vertical piles. The proposed method can be readily applied by engineers in the design of pile groups with batter piles.     

地震区跨活动断层桥梁桩基动力时程响应分析

为了研究强震区桥梁跨活动断层时,桩基在地震中的动力响应,以海文大桥为工程背景,利用Midas GTS有限元软件建立其强震区桩-海床岩土体-断层耦合作用的数值模型,研究不同强度(0.20g～0.60g)的50年超越概率为10%的地震波(后文简称5010地震波)作用下,桥梁桩基加速度、位移、弯矩及剪力的动力时程响应特性。结果表明：上部大厚度松散土体对桩身加速度有放大及滤波作用,而基岩对桩身加速度几乎不产生作用;断层上、下盘桩基础的桩顶水平位移随输入地震动强度的增大而增大,但达到振幅的时刻一致;上、下盘桩基础桩顶竖向位移时程响应都在50 s以后产生永久沉降;桩身最大弯矩截面处时程响应均在40 s以后产生永久弯矩;应重点考虑上部覆盖层软硬土体界面和基岩界面的抗弯承载力设计,及桩顶和基岩面附近的抗剪承载力设计;上盘桩基础按桩身加速度、弯矩、桩顶水平位移等动参数控制设计,下盘桩基础按动剪应力控制设计。