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.     

Centrifuge modeling of batter pile foundations under earthquake excitation

Although batter pile foundations are widely used in civil engineering structures, their behavior under seismic loadings is not yet thoroughly understood. This paper provides insights about the differences in the behavior of batter and vertical piles under seismic soil-pile-superstructure interaction. An experimental dynamic centrifuge program is presented, where the influences of the base shaking signal and the height of the gravity center of the superstructure are investigated. Various seismic responses are analyzed (displacement and rotation of the pile cap, total shear force at the pile cap level, overturning moment, residual bending moment, total bending moment and axial forces in piles). It is found that in certain cases batter piles play a beneficial role on the seismic behavior of the pile foundation system. The performance of batter piles depends not only on the characteristics of the earthquakes (frequency content and amplitude) but also on the type of superstructures they support. This novel experimental work provides a new experimental database to better understand the behavior of batter pile foundations in seismic regions.     

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.     

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.     

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。     

Dynamic nonlinear response of pile foundations under vertical vibration—Theory versus experiment

The influence of nonlinearity on the dynamic response of cast-in-situ reinforced concrete piles subjected to strong vertical excitation was studied. Forced vibration test of single piles (L/d=10, 15, 20) and 2×2 pile groups (s/d=2, 3, 4 for each L/d) were conducted in the field for two different embedded conditions of pile cap. From the measured nonlinear response curves, the effective pile–soil system mass, stiffness and damping were determined and the nonlinear response curves were back-calculated using the theory of nonlinear vibration. The test results were compared with the continuum approach of Novak with dynamic interaction factor approach using both linear and linear-equivalent numerical methods. Reasonable match between the measured and predicted response was found for linear-equivalent methods by introducing a weak boundary-zone around the pile to approximately account for the nonlinear behaviour of pile–soil system. The test data were used to establish the empirical relationship in order to estimate the extent of soil separation around the pile with soil under vertical vibration.     

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.     

Numerical and test study on vertical vibration characteristics of pile group in slope soil topography

Topography effects on the vertical vibration responses of pile group are revealed though numerical analysis and model tests.First,a series of model tests with different topography of ground and bedrock are conducted.The results indicate that displacement amplitude of the pile head in sloping ground topography is larger than in horizontal ground.Differential displacement at various positions of the pile cap is observed in non-horizontal topography.Afterwards,a numerical algorithm is employed to further explore the essential response characteristics in group piles of different topography configurations,which has been verified by the test results.The lengths of the exposed and frictional segment,together with the thickness of the subsoil layer,are the dominant factors which cause non-axisymmetric vibration at the pile cap.     

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.     

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.     

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.     

Uplift in seismic response of pile supported buildings

To resist seismic overturning moments piles are often designed for tensile forces which require pile connection to the cap and sometimes, socketing. For typical buildings, this paper theoretically examines the effect of these measures on seismic response, forces and pile loading in dependence on pile numbers, configuration and tip conditions.     

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 method for assessing kinematic bending moments at the pile head

The conventional design methods for seismically loaded piles still concentrate in providing adequate resistance from the pile to withstand only the inertial bending moments generated from the oscillation of the superstructure, thus neglecting the effect of kinematic interaction between pile and soil. By contrast there has been extensive research on kinematic effects induced by earthquakes and a number of simplified methods are available for a preliminary evaluation of kinematic bending moments at the interface between two soil layers. Less attention has been paid to the effects of kinematic interaction at the pile‐head. The paper summarizes recent research work on kinematic response analysis of fixed‐head piles aimed at the performance evaluation of a piled foundation. Results from an extensive parametric study, undertaken by means of three‐dimensional FE analyses, suggest a new criterion to predict kinematic bending effects at the pile head, where the combination of kinematic and inertial effect may be critical. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Evidence of beneficial role of inclined piles: observations and summary of numerical analyses

The behaviour under seismic loading of inclined piles embedded in two idealized soil profiles, a homogeneous and a non-homogenous “Gibson” soil, is analysed with 3D finite elements. Two structures, modeled as single-degree-of-freedom oscillators, are studied: (1) a tall slender superstructure (H _st = 12 m) whose crucial loading is the overturning moment, and (2) a short structure (H _st = 1 m) whose crucial loading is the shear force. Three simple two-pile group are studied: (a) one comprising a vertical pile and a pile inclined at 25°, (b) one consisting of two piles symmetrically inclined at 25°, and (c) a group of two vertical piles. The influence of key parameters is analysed and non-dimensional diagrams are presented to illustrate the role of raked piles on pile and structure response. It is shown that this role can be beneficial or detrimental depending on a number of factors, including the slenderness of the superstructure and the type of pile-to-cap connection.     

土-桩-框架结构非线性相互作用的精细数值模型及其验证

利用有限元软件ABAQUS,建立了土-桩-框架结构非线性相互作用（SSI）的二维精细有限元模型,分别采用记忆型粘塑性嵌套面模型和损伤塑性模型模拟土体和混凝土材料,采用梁单元和rebar单元模拟RC桩基及其内部纵筋,采用接触面对法模拟桩土接触效应,取得了良好的计算效果。将自由场、框架、土-桩-框架结构模型的分析结果和其它成熟的计算软件进行对比,验证了数值模型的有效性。分析发现：桩基外侧靠近承台处的土体的非线性反应很强烈,而桩基内部土体的非线性反应较小,很大程度上只是跟随群桩一起运动。由于桩土动力接触,桩顶的加速度反应可能超出上部结构,并且桩顶的加速度时程曲线上有非常明显的＂针＂状突变。随着地震动强度的增加,上部框架逐渐表现出单自由度体系的动力特征,加速度反应谱有从多个波峰退化为单一波峰的趋势。     

Dynamic response of pile groups embedded in a poroelastic medium

The dynamic response of pile groups embedded in a homogeneous poroelastic medium and subjected to vertical loading is considered. The piles are represented by compressible beam-column elements and the porous medium uses Biot's three-dimensional elastodynamic theory. The dynamic impedance of pile groups can be computed directly by using pile–soil–pile dynamic interaction factors. The axial forces and pore pressures along the length of pile groups are computed by superposition method, which greatly reduces the computational time for the direct analysis of pile groups. Parametric studies are conducted for various conditions of pile groups. The superposition method is proposed for the dynamic response analysis of pile groups that is computationally feasible for practical applications.     

Kinematic bending moments in pile foundations

In this paper the kinematic seismic interaction of single piles embedded in soil deposits is evaluated by focusing the attention on the bending moments induced by the transient motion. The analysis is performed by modeling the pile like an Euler–Bernoulli beam embedded in a layered Winkler-type medium. The excitation motion is obtained by means of a one-D propagation analysis. A comprehensive parametric analysis is carried out by varying the main parameters governing the dynamic response of piles like the soil properties, the bedrock location, the diameter and embedment in the bedrock of piles. On the basis of the parametric analysis, a new design formula for predicting the kinematic bending moments for both the cross-sections at the deposit–bedrock interface and at the pile head is proposed.