A critical review of methods for pile design in seismically liquefiable soils

Collapse and/or severe damage to pile-supported structures are still observed in liquefiable soils after most major earthquakes. Poor performance of pile foundations remains a great concern to the earthquake engineering community. This review paper compares and contrasts the two plausible theories on pile failure in liquefiable soils. The well established theory of pile failure is based on a flexural mechanism; where the lateral loads on the pile (due to inertia and/or lateral spreading) induce bending failure. This theory is well researched in the recent past and assumes that piles are laterally loaded beams. A more recent theory based on buckling instability treats the piles as laterally unsupported slender columns in liquefiable soils and investigates the buckling instability (bifurcation). The objective of this paper is to investigate the implications to practical pile foundation design that flow from both these theories. Provisions for design made by major international codes of practice for pile design including the Japanese Highway Code (JRA) will be considered. The necessity for such codes to consider alternative forms of failure mechanisms such as the buckling instability of piles in liquefied ground will be discussed. S. Bhattacharya–Previously Departmental Lecturer in Engineering Science, University of Oxford, UK and Fellow of Somerville College, Oxford. S. P. G. Madabhushi–Fellow of Girton College, Cambridge.     

Bending–buckling interaction as a failure mechanism of piles in liquefiable soils

This paper investigates the importance of bending–buckling interaction in seismic design of piles in liquefiable soils using numerical techniques. A pseudo-static analysis has been performed using a well documented case history, where the pile–soil interaction is modelled as a beam on nonlinear winkler foundation (BNWF). Six possible analytical methods, three force based and three displacement based, are performed in which the pile is subjected to both lateral and axial load. Three out of six analysis cases did not predict the failure of the piles when analysed only for bending (i.e., lateral loads only). The buckling analysis showed that the pile was also safe against pure buckling during full liquefaction. Further, two out of those three cases which did not predict failure in bending were reanalysed for bending–buckling interaction (i.e., lateral and axial loads acting simultaneously). These combined analyses showed a more realistic behaviour of pile response and did predict the pile failure. Hence, it can be concluded that if a pile is designed for bending and buckling criteria separately and safe for these individual design criteria, it may fail due to their combined effect.     

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.     

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.     

均质介质中排桩对瑞利波的阻隔试验分析

本文通过室外试验的方法并绘制二维等值线图以及将波长和双桩变量进行归一化处理来分析瑞利波通过双桩时周边土体振动的变化,结果表明：在桩间、桩前存在振动加强的现象,其中桩间以及桩角处振动强度最大;桩长与波长的比值的增加会使得桩前、桩间土体振动加强,同时也会使得双桩的隔振效果提升。当比值为0.691~0.781的范围内时,各点处变化幅度趋于平缓;桩间距的增加会使得双桩失去相互影响作用,当桩间距与波长的比值在0.34~0.42时,桩前、桩间以及桩后的A_r值趋近于1,即不存在振动加强以及衰减现象;桩径的增加可提升双桩的隔振效果,同时随着桩径与波长的比值增加,桩前、桩间的A_r值均有较小幅度的增加;振源距的增加会使得双桩的隔振效果增强,随着振源距与波长的比值的增加,桩前的A_r值降低了0.13左右,桩间仅仅降低了0.068左右,而桩后的A_r值降低了0.108左右,隔振效果增强,但增强的幅度较小。     

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。     

Experimental investigation of plastic demands in piles embedded in multi-layered liquefiable soils

Multi-layered soil profiles, where one or more layers consist of loose liquefiable material, most commonly require pile foundations extending beyond the liquefiable layer to competent material. Under seismic loads, if the loose layer liquefies, then large localized plastic demands may be generated in the piles. To study this behavior and provide detailed data to validate numerical models, a 1-g shaking table experiment was conducted considering a single reinforced concrete pile embedded in a three-layer soil system. The model pile of 25 cm diameter was tested under increasing amplitude earthquake excitation in a sloped laminar soil box. The test specimen was designed at the lower bound of typical design to promote yielding, per ATC-32 (Applied Technology Council, 1996) [1]. The pile penetrated 7D (D=pile diameter) into a multi-layered soil configuration composed of a stiff uppermost crust overlying a saturated loose sand layer and a lower dense layer of sand. Plastic demands in the pile were characterized using curvature profiles coupled with back-calculation of the plastic hinge length and post-test physical observations. Results from this test quantify the post-yield behavior of the pile and serve as a complement to previously conducted centrifuge tests.     

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。     

Generalized cyclic p–y curve modeling for analysis of laterally loaded piles

Owing to their simplicity and reasonable accuracy, Beam on Nonlinear Winkler Foundation (BNWF) models are widely used for the analysis of laterally loaded piles. Their main drawback is idealizing the soil continuum with discrete uncoupled springs representing the soil reactions to pile movement. Static p–y curves, obtained from limited full-scaled field tests, are generally used as a backbone curve of the model. However, these empirically derived p–y curves could not incorporate the effects of various pile properties and soil continuity. The strain wedge method (SWM) has been improved to assess the nonlinear p–y curve response of laterally loaded piles based on a three-dimensional soil–pile interaction through a passive wedge developed in front of the pile. In this paper, the SWM based p–y curve is implemented as the backbone curves of developed BNWF model to study the nonlinear response of single pile under cyclic lateral loading. The developed nonlinear model is capable of accounting for various important soil–pile interaction response features such as soil and pile yielding, cyclic degradation of soil stiffness and strength under generalized loading, soil–pile gap formation with soil cave-in and recompression, and energy dissipation. Some experimental tests are studied to verify the BNWF model and examine the effect of each factor on the response of laterally loaded pile embedded in sand and clay. The experimental data and computed results agree well, confirming the model ability to predict the response of piles under one-way and two-way cyclic loading. The results show that the developed model can satisfactorily simulate the pile stiffness hardening due to soil cave in and sand densification as observed in the experiment. It is also concluded from the results that the gap formation and soil degradation have significant effects on the increase of lateral pile-head deflection and maximum bending moment of the pile in cohesive soils.     

Newmark sliding block model for pile-reinforced slopes under earthquake loading

Recent studies have demonstrated that the use of a discretely-spaced row of piles can be effective in reducing the deformations of slopes in earthquakes. In this paper, an approximate strain-dependant Newmark sliding-block procedure for pile-reinforced slopes has been developed, for use in analysis and design of the piling scheme, and the model is validated against centrifuge test data. The interaction of the pile within the slipping soil was idealised using a non-linear elasto-plastic (P–y) model, while the interaction within the underlying stable soil was modelled using an elastic response model in which (degraded) soil stiffness is selected for an appropriate amount of shear strain. This combined soil–pile interaction model was incorporated into the improved Newmark methodology for unreinforced slopes presented by Al-defae et al. [1], so that the final method additionally incorporates strain-dependent geometric hardening (slope re-grading). When combined with the strain-dependent pile resistance, the method is therefore applicable to analysis of both the mainshock and subsequent aftershocks acting on the deformed slope. It was observed that the single pile resistance is mobilised rapidly at the start of a strong earthquake and that this and the permanent slope deformation are therefore strongly influenced by pile stiffness properties, pile spacing and the depth of the slip surface. The model shows good agreement with the centrifuge test data in terms of the prediction of permanent deformation at the crest of the slope (important in design for selecting an appropriate pile layout/spacing i.e. S/B) and in terms of the maximum permanent bending moments induced in the piles (important for appropriate structural detailing of the piles), so long as the slip surface depth can be accurately predicted. A method for doing this, based on limit analysis, is also presented and validated.     

大直径钢管桩土塞效应的拟静力判断方法

钢管桩在贯入过程中土塞效应的正确判断对打桩阻力及承载力的预测有重要影响,常用的静力平衡土塞效应判断方法主要适用于小直径钢管桩。随着海洋平台工作水深的不断增加及海上风电工程的建设,直径大于2m的大直径钢管桩被广泛采用,管桩直径的增加改变了桩管内土体的受力与变形特征。通过数值模拟方法获得砂土中不同径长比的钢管桩在打桩过程中桩周土体的破坏模式,确定采用梅耶霍夫公式计算打桩过程中桩端土体阻力,同时分析锤击惯性力对桩管内土塞的影响,提出采用拟静力平衡法判断大直径钢管桩的土塞闭塞效应。开展不同径长比管桩的室内小比尺打桩模型试验,并对实际工程中的土塞闭塞效应进行判断,验证拟静力平衡法对判断大直径钢管桩土塞效应的适用性。     

大直径扩底灌注桩的抗震性能研究

深入分析土-大直径扩底灌注桩体系动力相互作用机理是地震工程的重要研究内容。本文采用快速拉格朗日FLAC~(3D)有限差分程序建立地震荷载作用下扩底桩-土和等直径桩-土动力相互作用体的三维数值模型,分析大直径扩底桩与普通等直径桩地震反应的差异。桩周土采用Mohr-Coulomb弹性模型以考虑土体的非线性,桩体采用线弹性模型,桩与桩周土之间采用"切割模型"法设置桩土间接触面。输入5·12汶川地震波,对两种桩基的地震反应进行了数值计算与分析。结果表明:扩底桩的抗震性能优于等直径桩;与具有显著差异的加速度时程曲线相比,扩底桩对位移动力响应并不敏感。     

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。     

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。     

A case study of damages of the Kandla Port and Customs Office tower supported on a mat–pile foundation in liquefied soils under the 2001 Bhuj earthquake

A case study is presented of the interaction between the bending due to laterally spreading forces and axial-load induced settlement on the piled foundations of the Kandla Port and Customs Tower located in Kandla Port, India, during the 2001 Bhuj earthquake. The 22 m tall tower had an eccentric mass at the roof and was supported on a piled-raft foundation that considerably tilted away as was observed in the aftermath of the earthquake. The soil at the site consists of 10 m of clay overlaid by a 12 m deep sandy soil layer. Post-earthquake investigation revealed the following: (a) liquefaction of the deep sandy soil strata below the clay layer; (b) settlement of the ground in the vicinity of the building; (c) lateral spreading of the nearby ground towards the sea front. The foundation of the tower consists of 0.5 m thick concrete mat and 32 piles. The piles are 18 m long and therefore passes through 10 m of clayey soil and rested on liquefiable soils. Conventional analysis of a single pile or a pile group, without considering the raft foundation would predict a severe tilting and/or settlement of the tower eventually leading to a complete collapse. It has been concluded that the foundation mat over the non-liquefied crust shared a considerable amount of load of the superstructure and resisted the complete collapse of the building.     

高速铁路桥梁-桥墩-桩基础-地基耦合系统的地震反应

高速铁路中的桥梁常采用灌注桩基础以控制沉降,地震作用是桩基础的设计工况之一。建立桥梁-桥墩-桩基础-地基为一体的耦合系统非线性三维数值分析模型,以典型地震波为输入,考虑上部结构和基础的共同工作、土-结构动力相互作用、材料非线性和土层对桩的侧阻及端阻作用,开展三向地震作用下的动力有限元计算,并对地基主要土层压缩模量、桩体材料弹性模量、桩径和桩长进行参数敏感性分析。计算结果表明:现行的桩基础设计方案能有效控制地震荷载作用下桥梁的变形;地震过程中的不同时刻,桩侧阻发挥程度不同且不可忽略,以单纯的梁单元模拟桩的动力学行为的适用性值得商榷;桩长和地基主要土层压缩模量对桥梁地震反应影响最大,桩体材料弹性模量的影响次之,桩径的影响最小。     

Characteristics of non-uniform cross-section piles in drivability

A numerical analysis of pile driving for tapered piles is presented in this paper. A three-dimensional finite difference analysis for tapered angle and geometry effects has been used on pile driving response of tapered piles. The simulation considers an idealization for pile–soil system in drivability. The vertical pile is assumed to have linear and elastic behavior. It is also assumed that the soil is elasto-plastic material and its failure stage is controlled using the Mohr–Coulomb failure criterion. At the soil–pile contact surfaces along the pile shaft and pile toe, slip is allowed to occur during the driving procedure using interface elements. Quiet boundaries are used to prevent waves traveling in the lateral and vertical directions for the soil. Cylindrical, fully tapered, and semi-tapered piles were analyzed. The results obtained from numerical analyses were compared with those obtained from available laboratory tests and also other available numerical data, resulting in a satisfactory agreement. The results have shown that among piles of the same length and material volume, with increasing the taper angle from zero (representing a cylindrical pile), the driving stresses decrease and the permanent pile toe settlement (set) increases. These are interesting in pile driving and are on the safe side for driven piles and increasing the driving efficiency. It has also been found that the geometry of the pile can generally influence the pile drivability. Generally speaking, tapered and partially tapered piles offer better drivability performance than cylindrical piles of the same volume and length.     

基于Pasternak地基模型和Adomian分解方法的扩底桩水平动力响应分析

工程上广泛采用基于Winkler模型的层状地基反力系数法对桩土水平动力响应进行分析,该方法忽略了地基土剪切作用的影响,与工程实际有一定偏差。另外,对桩土的非线性相互作用和如扩底桩、楔形桩等变截面桩问题常用的传递矩阵法或中心差分法,计算过程较为繁琐。基于Pasternak地基模型和Adomian分解方法,提出一种考虑地基土剪切作用的桩土水平动力相互作用近似计算方法,该方法计算简便且结果精度较高,对变截面桩问题有很好的适用性;并基于该方法,对扩底桩水平动力响应问题和影响因素进行分析。结果指出,扩底半径和上部桩周土弹性模量对扩底桩水平动力响应影响较大,随着扩底半径的增加和桩周土弹性模量的增大,扩底桩水平振动位移幅值逐渐减小。另外,在较低频率的荷载激励下,应考虑土层对桩的剪切作用。     

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。     

Interpretation from large-scale shake table tests on piles undergoing lateral spreading in liquefied soils

Results from a benchmark test on full-scale piles are used to investigate the response of piles to lateral spreading. In the experiment, two single piles, a relatively flexible pile that moves together with the surrounding soil and a relatively stiff pile that does not follow the ground movement have been subjected to large post-liquefaction ground displacement simulating piles in laterally spreading soils. The observed response of the piles is first presented and then the results are used to examine the lateral loads on the pile from a non-liquefied soil at the ground surface and to evaluate the stiffness characteristics of the spreading soils. The measured ultimate lateral pressure from the crust soil on the stiff pile was about 4.5 times the Rankine passive pressure. The back-calculated stiffness of the liquefied soil was found to be in the range between 1/30 and 1/80 of the initial stiffness of the soil showing gradual decrease in the course of lateral spreading.