Effects of soil nonlinearity on the active length of piles embedded in cohesionless soil: model studies

Dynamic experimental studies on the active lengths of a fixed-head floating pile under static and dynamic loading conditions are reported, focusing on the effects of local nonlinearity and resonant behavior of soil. Results obtained from the laterally loaded model soil-pile system subjected to low-to-high amplitude pile head loading suggest a strong influence of local nonlinearity on the active lengths of the pile. Such obtained experimental results are further compared with the available approximate equations for estimating the active lengths. The comparisons reveal the closeness in values for very low amplitude of loadings, but for intermediate-to-high amplitude of loadings, the experimental values are smaller than predicted by the approximate equations. Moreover, both the static and dynamic active lengths of the pile converge to an approximately identical value of six times the diameter of the pile for intermediate-to-high amplitude of loadings. This suggests that the active lengths of the pile are, in fact, the same for both the static and dynamic loadings, under nonlinear conditions. Additionally, results also suggest that the passive-type failures of soil induced by the applied lateral loadings in front of the pile govern the active lengths. Furthermore, the dynamic active lengths of the pile do not show any significant dependency on the resonance in the soil.     

Effect of local nonlinearity in cohesionless soil on optimal radius minimizing fixed-head pile bending by inertial and kinematic interactions

This study presents the effects of a local nonlinearity in cohesionless soil upon the optimal radius minimizing the bending strains of a vertical, cylindrical fixed-head pile embedded in a layered soil stratum in a soil–pile–structure system where the kinematic interaction dominates. The seismic deformation method (SDM) with discretized numerical models is applied since the SDM is a static numerical method that can easily consider realistic conditions of layered soil strata and the nonlinearity of the soil. In the numerical models, the local nonlinearity of the soil in the vicinity of the pile is represented by subgrade springs having bi-linear skeleton curves with a simple hysteretic loop. Various amplitudes of the lateral displacements of the soil and the lateral forces at the head of the pile are considered as numerical parameters. The results of parametric analyses reveal the presence of an optimal pile radius that locally minimizes the bending strains of the piles under strong nonlinearity of the soil, and the optimal pile radius tends to increase as the degree of nonlinearity increases. Criteria are presented for predicting the increment in the optimal radius of soil–pile–structure systems under strong nonlinearity in the soil.     

A hypoplastic macroelement formulation for single batter piles in sand

Batter piles are widely used in geotechnical engineering when substantial lateral resistance is needed or to avoid the interference with existing underground constructions. Nevertheless, there is a lack of fast numerical tools for nonlinear soil‐structure interactions problems for this type of foundation. A novel hypoplastic macroelement is proposed, able to reproduce the nonlinear response of a single batter pile in sand under monotonic and cyclic static loadings. The behavior of batter piles (15°, 30°, and 45°) is first numerically investigated using 3D finite element modeling and compared with the behavior of vertical piles. It is shown that their response mainly depends on the pile inclination and the loading direction. Then, starting from the macroelement for single vertical piles in sand by Li et al (Acta Geotechnica, 11(2):373‐390, 2016), an extension is proposed to take into account the pile inclination introducing simple analytical equations in the expression describing the failure surface. 3D finite element numerical models are adopted to validate the macroelement that is proven able to reproduce the nonlinear behavior in terms of global quantities (forces‐displacements) and to significantly reduce the necessary computational time.     

Influence of seismic motions on behavior of piles in liquefied soils

In the present study an analytical procedure based on finite element technique is proposed to investigate the influence of vertical load on deflection and bending moment of a laterally loaded pile embedded in liquefiable soil, subjected to permanent ground displacement. The degradation of subgrade modulus due to soil liquefaction and effect of nonlinearity are also considered. A free headed vertical concrete elastic nonyielding pile with a floating tip subjected to vertical compressive loading, lateral load, and permanent ground displacement due to earthquake motions, in liquefiable soil underlain by nonliquefiable stratum, is considered. The input seismic motions, having varying range of ground motion parameters, considered here include 1989 Loma Gilroy, 1995 Kobe, 2001 Bhuj, and 2011 Sikkim motions. It is calculated that maximum bending moment occurred at the interface of liquefiable and nonliquefiable soil layers and when thickness of liquefiable soil layer is around 60% of total pile length. Maximum bending moment of 1210 kNm and pile head deflection of 110 cm is observed because of 1995 Kobe motion, while 2001 Bhuj and 2011 Sikkim motions amplify the pile head deflection by 14.2 and 14.4 times and bending moment approximately by 4 times, when compared to nonliquefiable soil. Further, the presence of inertial load at the pile head increases bending moment and deflection by approximately 52% when subjected to 1995 Kobe motion. Thus, it is necessary to have a proper assessment of both kinematic and inertial interactions due to free field seismic motions and vertical loads for evaluating pile response in liquefiable soil.     

深厚场地大型桥梁桩基础随机地震反应及可靠性分析

以苏通长江大桥主墩特大型群桩基础为研究背景,考虑地震动的不确定性,将地震激励作为平稳随机过程,采用随机地震反应分析方法,对深厚场地上群桩基础受上部桥墩荷载下的地震反应进行研究。土体动力非线性性能采用等效线性化方法考虑。由于桥墩惯性作用以及软土土层对桩身位移的约束作用,地震激励下桩身位移呈三角形分布。土体位移与土体和基础间距离有关,桥墩-桩-土相互作用对基础两侧1.5倍基础宽度的土体位移有较大影响。桩体内力反应结果表明,桩顶及桩身上部剪力及弯矩均较大,边桩剪力显著大于中间桩剪力。此外,基于强度破坏准则,对以桩身屈服剪力作为控制指标的群桩基础动力可靠性进行了分析。     

Centrifuge shaking table tests on 4 × 4 pile groups in liquefiable ground

A series of centrifuge shaking table model tests are conducted on 4?×?4 pile groups in liquefiable ground in this study, achieving horizontal–vertical bidirectional shaking in centrifuge tests on piles for the first time. The dynamic distribution of forces on piles within the pile groups is analysed, showing the internal piles to be subjected to greater bending moment compared with external piles, the mechanism of which is discussed. The roles of superstructure–pile inertial interaction and soil–pile kinematic interaction in the seismic response of the piles within the pile groups are investigated through cross-correlation analysis between pile bending moment, soil displacement, and structure acceleration time histories and by comparing the test results on pile groups with and without superstructures. Soil–pile kinematic interaction is shown to have a dominant effect on the seismic response of pile groups in liquefiable ground. Comparison of the pile response in two tests with and without vertical input ground motion shows that the vertical ground motion does not significantly influence the pile bending moment in liquefiable ground, as the dynamic vertical total stress increment is mainly carried by the excess pore water pressure. The influence of previous liquefaction history during a sequence of seismic events is also analysed, suggesting that liquefaction history could in certain cases lead to an increase in liquefaction susceptibility of sand and also an increase in dynamic forces on the piles.     

Depth of Fixity of Piles in Clay Under Dynamic Lateral Load

Dynamic experiments were carried out on instrumented model aluminium single piles embedded in clay of different consistencies to study its bending behaviour under lateral loads. Piles with different length to diameter ratios were used. Dynamic lateral load of different magnitudes ranging from 7 to 30 N at wide range of frequencies from 2 to 50 Hz were applied. The load transferred to the pile, pile head displacement and the strain variation along the pile length were measured using a dedicated data acquisition system. Static lateral load tests were also performed to investigate the magnification of dynamic response of piles in clay. It is found that the maximum bending moment due to dynamic load is magnified by about 1.5–4 times in comparison to the static load for short piles but about 9 times for long piles. Depth of fixity and effective pile length is also largely amplified under dynamic loads, thus indicating that a pile which behaves as a flexible pile under static load, may not exhibit flexible behaviour under dynamic load.     

An experimental study on static and dynamic bending behaviour of piles in soft clay

Static and dynamic lateral load tests were carried out on model aluminium single piles embedded in soft clay to study its bending behaviour. Model aluminium piles with length to diameter ratios of 10, 20, 30 and 40 were used. Static lateral load tests were conducted on piles by rope and pulley arrangement upto failure and load–deflection curves were obtained. Dynamic lateral load tests were carried out for different magnitudes of load ranging from 7 to 30 N at wide range of frequencies from 2 to 50 Hz. The load transferred to the pile, pile head displacement and the strain variation along the pile length were measured using a Data Acquisition System. Safe static lateral load capacity for all piles is interpreted from load–deflection curves. Dynamic characteristics of the soil–pile system were arrived from the acquired experimental data. The soil–pile system behaves predominantly in nonlinear fashion even at low frequency under dynamic load. The displacement amplitude under dynamic load is magnified by 4.5–6.5 times the static deflection for all piles embedded in soft clay. But, the peak magnification factor reduces with an increase in the magnitude of lateral load mainly because of increase of hysteretic damping at very soft consistency. The maximum BM occurs at the fundamental frequency of the soil–pile system. Even the lower part of the pile affects the pile head response to the inertial load applied at the pile head. The maximum dynamic BM is magnified by about 1.5 times the maximum static BM for model piles in tested consistency of clay. The maximum dynamic BM occurs at a depth of about 1.5 times the depth of maximum static BM for model piles, which indicates an increase of active pile length under dynamic load.     

Elastic analysis of laterally loaded pile in multi-layered soil

An analysis is developed to determine the response of laterally loaded piles in layered elastic media. The differential equations governing pile deflections in different layers due to a concentrated static force and/or moment acting at the pile head are obtained using the principle of minimum potential energy and calculus of variations. The differential equations are solved analytically using the method of initial parameters. Pile deflection, slope of the deformed axis of the pile, bending moment and shear force can be reliably obtained by this method for the entire pile length. The input parameters needed for the analysis are the pile geometry and the elastic constants of the soil and pile. It is observed that soil layering has a definite impact on pile response and must be taken into account for proper analysis and design. The analysis forms the basis for future formulations that can consider stress–strain nonlinearity.     

水平循环荷载下桩基变形特性的离心模型试验研究

波浪、船舶等长期水平循环荷载作用下,桩基将不可避免地产生附加应力和变形。针对饱和黏土地层,开展离心模型试验研究了船舶系泊水平荷载作用下单桩和群桩的变形特性。发现水平循环加-卸载诱发了桩周土体的塑性变形,进而导致桩身产生了不可恢复的水平位移和弯曲变形。随着循环荷载的增加,单桩和群桩的桩顶最大水平位移和残余水平位移均同时增加,但残余水平位移明显小于最大水平位移。单桩的桩顶残余水平位移与最大位移比值介于0.17～0.22;群桩的桩顶残余水平位移与最大水平位移比值介于0.30～0.84。水平循环加-卸载作用下,桩身残余弯曲应变明显小于最大弯曲应变。单桩的残余弯曲应变与最大弯曲应变比值介于0.13～0.50;群桩的桩身残余弯曲应变与最大弯曲应变比值介于0.23～0.82。群桩前桩的残余和最大弯曲应变明显大于后桩,前桩与后桩的最大弯曲应变、残余应变比值分别高达3.2和3.1。因此,前桩要采取合理的加固和保护措施,以确保桩基长期服役的安全性。     

A Three Dimensional Comparative Study of Seismic Behaviour of Vertical and Batter Pile Groups

To a practicing foundation engineer, the performance of batter pile under seismic conditions still remains a questionable prospect. The contradictory findings reported by various investigators with regard to the performance of batter piles add to this dilemma. This calls for a rigorous three-dimensional investigation to evaluate seismic behavior of batter pile groups. In this study, a comparative assessment of three-dimensional seismic behavior of a 2 × 2 vertical and batter pile groups having batter angle of 15° was carried out using a full three-dimensional finite element code developed in MATLAB (Sarkar 2009). The effects of centre to centre spacing of piles and soil modulus values were investigated. Idealized soil profiles having constant and triangular variation of soil modulus were adopted for the study. Results of analyses for both the vertical and batter pile groups are presented in terms of dynamic stiffness and kinematic interaction factors. Results indicate better seismic performance of batter pile groups in comparison to that of vertical pile groups. To demonstrate the importance of the findings, a five-storied portal frame structure supported separately on vertical and batter pile groups were considered and analyzed for El-Centro Earthquake (1940) time history. The difference in structural response considering vertical and batter pile groups is highlighted.     

桩基础对邻近场地冲击荷载的响应分析

桩基础对邻近场地作用冲击荷载的响应本质上是桩-土组成的体系在冲击荷载下的整体动力相互作用问题。为了研究该问题,采用有限元法模拟冲击荷载引起桩基础的振动。利用通用有限元分析软件ABAQUS建立了有限元-无限元（FE-IFE）耦合分析模型,分析了冲击荷载作用时桩基础动力响应的规律,并对影响桩基础响应的因素进行了探讨。计算结果表明,桩的振动程度取决于冲击荷载作用间距和冲击荷载能量,而冲击荷载作用间距越远,桩的振动波长越长。     

Numerical analysis of the response of battered piles to inclined pullout loads

This paper presents a three‐dimensional finite element analysis of the response of battered piles to the combined lateral and vertical pullout loads. Analyses are carried out using an elastoplastic constitutive law based on the non‐associated Mohr–Coulomb criterion. The influence of the contact condition at the pile–soil interface is also investigated. Analyses show that the load's inclination with regard to the pile's axis affects both the lateral and axial response of the battered piles. Analyses also show that the pullout capacity of battered piles is affected by the pile's inclination regarding the vertical axis as well as the load's inclination regarding the pile's axis. The investigation of the influence of the contact condition at the soil–pile interface shows that the possibility of sliding at the soil–pile interface affects the response of battered piles subjected to loads with low inclination regarding the pile's axis. Copyright © 2008 John Wiley & Sons, Ltd.     

Pseudostatic approach for seismic analysis of pile group

This paper evaluates a simple approximate pseudostatic method for estimating the maximum internal forces and horizontal displacements of pile group subjected to lateral seismic excitation. The method involves two main steps: (1) computation of the free-field soil movements caused by the earthquake, and (2) the analysis of the response of the pile group based on the maximum free-field soil movements (considered as static movements) as well as a static loading at the pile head, which depends on the computed spectral acceleration of the structure being supported. The methodology takes into account the effects of group interaction and soil yielding at pile–soil interface. The applicability of this approach has been validated by a similar approach for single piles and then verified by both experimental centrifuge models of pile-supported structures and field measurements of Ohba-Ohashi Bridge in Japan. It is demonstrated that the proposed method yields reasonable estimates of the pile maximum moment, shear, and horizontal displacement for many practical cases despite of its simplicity. Limitations and reliability of the methodology are discussed and some practical conclusions on the performance of the proposed approach are presented.     

悬臂抗滑桩静、动力学性能试验的全过程

基于悬臂抗滑桩治理堆积型滑坡的静、动力离心模型试验,利用土压力传感器、应变片以及加速度传感器采集到的试验数据,研究了静、动力条件下抗滑桩的受力特性,分析了被治理滑坡的地震响应特征。结果表明：静、动力条件下桩后土压力以及桩身弯矩的分布规律均不同;桩后静土压力大于地震动引起的动土压力,但桩身静弯矩远小于地震动引起的动弯矩;桩后动土压力和动弯矩随峰值地震动的增大而增大;地震作用时土压力和桩身弯矩最大值的作用点低于静力的;滑体加速度响应存在浅表放大效应和高程放大效应,坡肩附近的波型转化现象显著,抗震设计时应予以重视。     

Response of Pile Groups Driven in Sand Subjected to Combined Loads

Although the loads applied on piles are usually a combination of both vertical and lateral loads, very limited experimental research has been done on the response of pile groups subjected to combined loads. Due to pile–soil–pile interaction in pile groups, the response of a pile group may differ substantially from that of a single pile. This difference depends on soil state and pile spacing. This paper presents results of experiments designed to investigate pile interaction effects on the response of pile groups subjected to both axial and lateral loads. The experiments were load tests performed on model pile groups (2 × 2 pile groups) in calibration chamber sand samples. The model piles were driven into the sand samples prepared with different relative densities using a sand pluviator. The combined load tests were performed on the model pile groups subjected to different axial load levels, i.e., 0 (pure lateral loading), 25, 50, and 75% of the ultimate axial load capacity of the pile groups, defined as the load corresponding to a settlement of 10% of the model pile diameter. The combined load test results showed that the bending moment and lateral deflection at the head of the piles increased substantially for tests performed in the presence of axial loads, suggesting that the presence of axial loads on groups of piles driven in sand is detrimental to their lateral capacity.     

A simplified analysis method for piled raft and pile group foundations with batter piles

A simplified method of numerical analysis has been developed to estimate the deformation and load distribution of piled raft foundations subjected to vertical, lateral, and moment loads, using a hybrid model in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. Both the vertical and lateral resistances of the piles as well as the raft base are incorporated into the model. Pile–soil–pile, pile–soil–raft and raft–soil–raft interactions are taken into account based on Mindlin's solutions for both vertical and lateral forces. The validity of the proposed method is verified through comparisons with several existing methods for single piles, pile groups and piled rafts. Workable design charts are given for the estimation of the lateral displacement and the load distribution of piled rafts from the stiffnesses of the raft alone and the pile group alone. Additionally, parametric studies were carried out concerning batter pile foundations. It was found that the use of batter piles can efficiently improve the deformation characteristics of pile foundations subjected to lateral loads. Copyright © 2002 John Wiley & Sons, Ltd.     

动荷载下桩承式路堤的承载特性及机制研究

对于桩承式路堤作用效应的研究目前主要侧重于对静荷载作用下桩土应力比和土拱效应等,较少考虑动荷载的影响,而车辆运行产生的动应力会对路堤中的土拱产生一定的影响,进而影响桩承式路堤的整体性能。为了分析静、动荷载作用下桩承式加筋路堤的性能变化,采用可视化模型试验和颗粒流数值模拟相结合的方法,对桩承式路堤在静载和动载下的应力传递和变形性状进行研究,分析动载作用下填土高度、桩帽、桩距、加筋形式、荷载频率的影响。试验结果表明,在动载下无筋路堤的桩顶的应力减小,而桩间的应力和位移增大,并且变化的幅度均比加筋路堤大,加筋材料的设置有利于减小动载的影响效应,但不同加筋形式下桩承式路堤的工作性状有所不同,受动载影响程度的大小主要与土拱效应的强弱有关。设置双层加筋时,因加筋材料与周围砂土形成半刚性平台,土拱效应减弱,故受动载影响的程度最小,单层加筋时,格栅设于桩顶上方10 cm比格栅置于桩顶受动载影响的程度明显减小,颗粒流的模拟结果验证了以上结果,并且进一步得出随荷载频率的增加、填土高度与桩净距的减小,动载的影响效应增大的结论。     

Semi-analytical solutions for vertically and laterally loaded piles in multilayered soil deposits

In geotechnical practice, it is of considerable importance to assess the behavior of vertical–lateral coupled loading piles in multilayered soil deposits. This study deals with a semi-analytical formulation for the performance of a pile suffering from combined vertical and lateral loads. The emphasis is on quantifying the mobilization of the subgrade reaction provided by the layered soil stratums. In the proposed method, subgrade reactions, correlated with both the accumulative axial load transfer and side resistances depending upon the pile–soil interaction, are abstracted as a series of nonlinear springs in both vertical and lateral directions. On account of this, an alternative transfer matrix method is applied to characterize the pile reaction along the depth under the identified boundary conditions atop the pile; meanwhile, the condition of static equilibrium, between two specific pile segments located at the border of soil layers, is also essential. On this basis, validation of the solution is conducted by comparing with observations from experiments and predictions obtained from other existing methods. In addition, the influence of properties in shallow soil layer and the vertical load on the lateral response of the pile is also discussed. The results indicate a reduction in the lateral displacement and the maximum bending moment within the pile with the increase in the shallow soil stiffness, but a growth with the increase in vertical load due to the “P-Δ effect.”