Nonlinear three-dimensional analysis of pile group supported columns considering pile cap flexibility

A numerical method that takes into account the coupling between the rigidities of the piles, the cap, and the column has been developed for analyzing the response of pile group supported columns. Special attention is given to consideration of pile cap flexibility. A load transfer approach using t–z/q–z and p–y curves is used for the analysis of single piles. The finite element technique is used to combine the pile stiffness with the stiffness of the cap and column. The numerical method developed has been verified by comparing the results with other numerical methods for pile groups. Through comparative studies, it has been found that the maximum load on the individual piles in a group is highly influenced by pile cap flexibility. The prediction of the lateral loads and bending moments in the pile cap is much more conservative in the present analysis than in FBPier 3.0 and shows a definitely larger lateral load and bending moment for various cap thicknesses.     

水平受荷长桩弹塑性计算解析解

当考虑桩侧土体非线性本构关系时对水平受荷桩的计算一般需采用数值方法,解析结果相对较少。基于Winkler地基模型和桩侧土体简化的弹塑性本构关系,对均质地基中水平荷载作用下桩头嵌固的长桩进行了解析推导,得到了桩身最大挠度及最大弯矩与荷载关系的统一解析表达式,并采用相同的方法求得高桩情形下桩头挠度的计算式。计算表明,联合荷载作用下桩身泥面处的挠度和转角不等于单个荷载作用时的线性叠加,采用常规的线性叠加法计算将偏于不安全。所求解析式借助计算器即可进行最大挠度和最大弯矩的计算,大大方便了工程的计算应用。     

A modulus‐multiplier approach for non‐linear analysis of laterally loaded pile groups

A modulus‐multiplier approach, which applies a reduction factor to the modulus of single pile p–y curves to account for the group effect, is presented for analysing the response of each individual pile in a laterally loaded pile group with any geometric arrangement based on non‐linear pile–soil–pile interaction. The pile–soil–pile interaction is conducted using a 3D non‐linear finite element approach. The interaction effect between piles under various loading directions is investigated in this paper. Group effects can be neglected at a pile spacing of 9 times the pile diameter for piles along the direction of the lateral load and at a pile spacing of 6 times the pile diameter for piles normal to the direction of loading. The modulus multipliers for a pair of piles are developed as a function of pile spacing for departure angle of 0, 90, and 180sup>/sup> with respect to the loading direction. The procedure proposed for computing the response of any individual pile within a pile group is verified using two well‐documented full‐scale pile load tests. Copyright © 2006 John Wiley & Sons, Ltd.     

Horizontal soil stress changes around displacement piles

A simplified analysis of the problem of horizontal soil stress changes around circular displacement piles, caused by pile placement, is presented. Pile installation is assumed to cause soil displacements in the horizontal direction only, thus yielding an axisymmetric problem. The soil surrounding the pile is modelled as a weightless non-linear elastic material. Material non-linearity is handled in a simplified manner by adopting secant shear moduli defined in terms of a proportionality coefficient and a softening factor. The resulting equilibrium equation is solved analytically and an expression is obtained which is also conveniently presented in graphical form. The derived expression can be used to estimate horizontal soil stress changes and is incorporated into a simple procedure to estimate the ultimate load or the efficiency of pile groups. Comparisons are made between efficiencies calculated according to this procedure and efficiencies measured in full-scale group load tests in sand.     

Selection of p–y curves for the design of single laterally loaded piles

Two-dimensional finite element analysis has been used to find load–transfer relationships for translation of an infinitely long pile through undrained soil for a variety of soil-constitutive models. It has been shown that these load–transfer curves can be used as p–y curves in the analysis of single piles undergoing lateral pile head loading in undrained soils with non-linear stress–strain laws. Lateral pile response deduced from 2-D analysis input to the subgrade reaction method has been compared to the behaviour of a single pile analysed using three-dimensional finite element analysis. Good agreement between the two methods for non-linear soils suggests that the 2-D analysis may form a useful design method for calculation of p–y curves. Copyright © 1999 John Wiley & Sons, Ltd.     

Visco‐elastic load transfer models for axially loaded piles

Viscoelastic or creep behaviour can have a significant influence on the load transfer (t–z) response at the pile–soil interface, and thus on the pile load settlement relationship. Many experimental and theoretical models for pile load transfer behaviour have been presented. However, none of these has led to a closed‐form expression which captures both non‐linearity and viscoelastic behaviour of the soil. In this paper, non‐linear viscoelastic shaft and base load transfer (t–z) models are presented, based on integration of a generalized viscoelastic stress–strain model for the soil. The resulting shaft model is verified through published field and laboratory test data. With these models, the previous closed‐form solutions evolved for a pile in a non‐homogeneous media have been readily extended to account for visco‐elastic response. For 1‐step loading case, the closed‐form predictions have been verified extensively with previous more rigorous numerical analysis, and with the new GASPILE program analysis. Parametric studies on two kinds of commonly encountered loading: step loading, ramp (linear increase followed by sustained) loading have been performed. Two examples of the prediction of the effects of creep on the load settlement relationship by the solutions and the program GASPILE, have been presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Analysis of axial pile-soil interaction in clay

A method for predicting the maximum mobilized side resistance and unit shaft resistance-displacement curves (load transfer functions) on piles in clay is described. The method was derived using a numerical solution to model pile installation effects and a finite element scheme to model pile loading. Results of three well-documented pile load tests on steel piles were used to develop intermediate steps and final solutions, and the method was verified by comparing predicted results to two other load tests. An expression is proposed to represent load transfer functins for use by practitioners for the design of bridge and other foundations in clay.     

Development of p–y curves for undrained response of piles near slopes

The response of laterally loaded piles placed near the crest of clay slopes is analysed. Three-dimensional finite element analyses are presented for piles of different geometries, installed at several distances from slopes of various inclinations. The results of these analyses are used to establish the pattern of lateral load distribution along the pile length in relation to slope inclination and pile to slope distance. Subsequently, p–y curves are developed for the case of undrained lateral loading of piles near the crest of clay slopes, a case for which no such curves exist so far. The proposed p–y curves are implemented into a commercial subgrade reaction computer code and used to perform a series of parametric numerical analyses. The results of these analyses show that the predicted response of piles near slopes with the proposed p–y curves is in good agreement with the response observed in some pile tests reported in the literature.     

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.     

A simplified design method for energy piles

This paper introduces a simplified method to investigate the influence of thermal loads on the shaft friction and tip resistance of energy piles. The method is based on the influence factors (λ and η) which are back-calculated drawing on a large number of field and model tests. Values for λ and η during heating and cooling are suggested. Moreover, a new equation is proposed to calculate total shaft friction. The equations concerning the relationship between η and temperature difference are recommended to investigate the impacts of the thermal load on the pile tip resistance. The slope of the linear equation of an end-bearing pile is 2.14 times that of a floating pile indicating that the pile tip resistance of an end-bearing pile is much more affected by the same thermal load.

     

Surface displacements due to batter piles driven in cross‐anisotropic media

This article derives the closed‐form solutions for estimating the vertical surface displacements of cross‐anisotropic media due to various loading types of batter piles. The loading types include an embedded point load for an end‐bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The planes of cross‐anisotropy are assumed to be parallel to the horizontal ground surface. The proposed solutions are never mentioned in literature and can be developed from Wang and Liao's solutions for a horizontal and vertical point load embedded in the cross‐anisotropic half‐space. The present solutions are identical with Wang's solutions when batter angle equals to 0^°. In addition, the solutions indicate that the surface displacements in cross‐anisotropic media are influenced by the type and degree of material anisotropy, angle of inclination, and loading types. An illustrative example is given at the end of this article to investigate the effect of the type and degree of soil anisotropy (E/E′, G′/E′, and ν/ν′), pile inclination (α), and different loading types (a point load, a uniform skin friction, and a linear variation of skin friction) on vertical surface displacements. Results show that the displacements accounted for pile batter are quite different from those estimated from plumb piles, both driven in cross‐anisotropic media. Copyright © 2007 John Wiley & Sons, Ltd.     

A method for the analysis of large vertically loaded pile groups

An iterative method is described for the analysis of vertically loaded pile groups with a large number of vertical piles. The individual pile response is modelled using load-transfer (t–z) curves while pile–soil–pile interaction is determined using Mindlin's solution. The present method not only keeps all the advantages of the so-called ‘hybrid method’, but also makes it possible for practising engineers to solve problems of large non-uniformly arranged pile groups in a time-saving way using a personal computer. Good agreement between the present method of analysis and the direct method is observed. A case history is analysed and the computed response of a large pile group compares favourably with the field measurement. Copyright © 1999 John Wiley & Sons, Ltd.     

Static load tests of driven concrete piles under CFRP confinement

ABSTRACT

This paper describes compressive static load tests of concrete driven piles confined by Carbon Fibre Reinforced Polymer (CFRP). The tested piles include one concrete pipe pile and one concrete rectangular pile which are all partially confined by CFRP, and other two piles with the same dimensions without CFRP application. Tests program was performed to obtain the behaviours of these composite piles. Four Static Loading Tests (SLTs) were conducted and the results shown that those two types of composite pile demonstrate less vertical displacement with the same loading of traditional concrete piles. Furthermore, the traditional methods of Load-settlement (Q-s) curves, Settlement-lg (Load) (s-lgQ) curves and Settlement-lg (Time) curves are analysed. Due to un-plunging condition, the interpretation methods of Davisson’s, DeBeers, Double-Tangent as well as Chin’s methods are demonstrated for the ultimate bearing capacity of these four piles. It is concluded that the CFRP confinement increased the ultimate bearing capacity and this composite material can be perfectly applied in geotechnical condition.     

Uncoupled analysis of stabilizing piles in weathered slopes

This paper describes a simplified numerical approach for analyzing the slope/pile system subjected to lateral soil movements. The lateral one-row pile response above and below the critical surface is computed by using load transfer approach. The response of groups was analyzed by developing interaction factors obtained from a three-dimensional nonlinear finite element study. An uncoupled analysis was performed for stabilizing piles in slope in which the pile response and slope stability are considered separately. The non-linear characteristics of the soil–pile interaction in the stabilizing piles are modeled by hyperbolic load transfer curves. The Bishop's simplified method of slope stability analysis is extended to incorporate the soil-pile interaction and evaluate the safety factor of the reinforced slope. Numerical study is performed to illustrate the major influencing parameters on the pile-slope stability problem. Through comparative studies, it has been found that the factor of safety in slope is much more conservative for an uncoupled analysis than for a coupled analysis based on three-dimensional finite element analysis.     

A simplified analysis method for piled raft foundations subjected to ground movements induced by tunnelling

A simplified method of numerical analysis has been developed to estimate the deformation and load distribution of piled raft foundations subjected to ground movements induced by tunnelling and incorporated into a computer program ‘PRAB’. In this method, a hybrid model is employed in which the flexible raft is modelled as thin plates, the piles as elastic beams, and the soil is treated as interactive springs. The interactions between structural members, pile–soil–pile, pile–soil–raft and raft–soil–raft interactions, are modelled based on Mindlin's solutions for both vertical and lateral forces. The validity of the proposed method is verified through comparisons with some published solutions for single piles and pile groups subjected to ground movements induced by tunnelling. Thereafter, the solutions from this approach for the analysis of a pile group and a piled raft subjected to ground movements induced by tunnelling are compared with those from three‐dimensional finite difference program. Good agreements between these solutions are demonstrated. The method is then used for a parametric study of single piles, pile groups and piled rafts subjected to ground movements induced by tunnelling. Copyright © 2005 John Wiley & Sons, Ltd.     

秦巴山区软岩地基桥桩承载性状试验研究

为了研究软岩地基桥桩的荷载传递性状、破坏机理,并获取在该地质条件下更为可靠的桩基计算参数,对秦巴山区软岩地基3根钻孔灌注试桩进行竖向静载试验。结果表明：秦巴山区软岩地基桥桩试桩荷载沉降曲线呈陡降型,实测竖向极限承载力为20 500kN,桩的破坏方式为桩身材料强度破坏;淤泥质亚黏土地层中的碎石起到一定的骨架作用,增强了此地层桩极限侧阻力,发挥极限侧阻力所需的桩土（岩）相对位移为4～8mm;强风化砾岩表现为加工软化型,发挥极限侧阻力所需的桩土（岩）相对位移为3～8mm;中风化砂砾岩表现为明显的加工硬化型,所需的桩岩相对位移大,且桩极限侧阻力的特征点不明显;淤泥质亚黏土地层桩侧阻力占总荷载的60%～70%,随着桩顶荷载的逐步加大,该地层桩侧阻力所占比例不断下降,而嵌岩段桩侧阻力所占比例逐渐上升,达到55%～65%,嵌岩段桩侧阻力沿桩深的分布曲线表现出非线性的特征;试桩为端承摩擦桩,桩端阻力约占桩顶荷载的20%左右,且未充分发挥,在上部结构允许的沉降范围内,适当增加桩端的沉降有利于端阻力的发挥;桩侧阻力先于端阻力发挥,建议单桩承载力设计时分别采用不同的端阻力和侧阻力安全系数。     

Single piles under horizontal loads in sand: determination of <Emphasis Type="Italic">P</Emphasis>–<Emphasis Type="Italic">Y</Emphasis> curves from the prebored pressuremeter test

Lateral load-deflection behaviour of single piles is often analysed in practice on the basis of methods of load-transfer P–Y curves. The paper is aimed at presenting the results of the interpretation of five full-scale horizontal loading tests of single instrumented piles in two sandy soils, in order to define the parameters of P–Y curves, namely the initial lateral reaction modulus and the lateral soil resistance, in correlation with the pressuremeter test parameters. P–Y curve parameters were found varying as a power of lateral pile/soil stiffness, on the basis of which hyperbolic P–Y curves in sand were proposed. The predictive capabilities of the proposed P–Y curves were assessed by predicting the soil/pile response in full-scale tests as well as in centrifuge tests and a very good agreement was found between the computed deflections and bending moments, and the measured ones. Small-sized database of full-scale pile loading tests in sand was built and a comparative study of some commonly used P–Y curve methods was undertaken. Moreover, it was shown that the load-deflection curves of these test piles may be normalised in a practical form for an approximate evaluation of pile deflection in a preliminary stage of pile design. At last, a parametric study undertaken on the basis of the proposed P–Y curves showed the significant influence of the lateral pile/soil stiffness on the non-linear load-deflection response.     

An Empirical Method for Analysis of Load Transfer and Settlement of Single Piles

An empirical method is developed for estimating the load transfer and deformation of drilled, in situ formed piles subjected to axial loading. Firstly, governing equations for soil–pile interaction are developed theoretically, taking into account spatial variations in: (a) shaft resistance distribution and (b) ratio of load sharing between the shaft and base. Then generic load transfer models are formulated based on examination of data from 10 instrumented test piles found in the literature. The governing equations and load transfer models are then combined and appropriate boundary conditions defined. Using an incremental-iterative algorithm whereby all the boundary conditions are satisfied simultaneously, a numerical scheme for solving the combined set of equations is developed. The algorithm is then developed into an interactive computer program, which can be used to predict the load-settlement and axial force distribution in piles. To demonstrate its validity, the program is used to analyse four published case records of test piles, which other researchers had analysed using the following three computationally demanding tools: (a) load transfer (t–z), (b) finite difference and (c) finite element methods. It is shown that the proposed method which is much less resource-intensive, predicts both the load-settlement variation and axial force distribution more accurately than methods: (a–c) above.     

大直径深长钻孔灌注桩竖向承载力特性试验研究

在唐山LNG罐区对9根大直径钢筋混凝土灌注桩进行了竖向荷载现场试验,其中桩端后注浆工艺试桩3根,三岔双向挤扩工艺试桩3根,挤扩支盘工艺试桩3根。基于现场静荷载和桩身应力测试结果,分析了3种不同施工工艺钻孔灌注桩竖向荷载传递规律。试验结果表明：3种不同施工工艺的大直径深长钻孔灌注桩试桩荷载-沉降曲线没有明显拐点,后注浆工艺试桩荷载传递过程表现为摩擦桩的特性,桩侧阻力几乎承担全部荷载,而三岔双向挤扩支盘工艺和挤扩支盘工艺试桩荷载传递过程表现为端承摩擦桩的特性,桩端阻力占总荷载的20%～30%;3种不同施工工艺试桩的轴力及桩-土相对位移变化规律基本相似,桩侧桩端阻力非同步发挥且相互影响,桩侧摩阻力均表现出强化现象。对整个罐区要求单桩承载力特征值不小于8 100 kN。3种施工工艺的钻孔灌注桩承载力均能满足要求。     

Two‐dimensional lower bound analysis of offshore pile foundation systems

The objective of this paper is to present a simplified method to determine the pile foundation system capacity based on the lower bound theorem of plasticity. The motivations for determining the lower bound capacity are the following: (1) to evaluate the accuracy of solutions based on the upper bound method; (2) to provide a conservative and efficient solution to the system capacity; and (3) to provide information about load distribution among individual piles at the verge of failure for the pile system. The failure mechanisms for a single pile and for the pile system are assumed to be two‐dimensional. For a typical long offshore pile, the upper and lower bound analyses produce identical lateral capacities. A simplified failure surface for loads at the single pile head is proposed and verified through analysis of 16 case study piles. With this proposed failure surface for a single pile, the lower bound failure load of the pile foundation system is obtained using the elastic compensation method enhanced with the linear matching method. Comparing with the existing upper bound and finite element solutions, the proposed lower bound method is capable of accurately and efficiently predicting the ultimate capacity of a pile foundation system. Copyright © 2015 John Wiley & Sons, Ltd.