考虑土体屈服的纵横荷载单桩变形内力分析

为提高桩身变形较大时纵横荷载单桩的设计计算水平,假定地基反力系数沿深度线性增加,考虑土体屈服及纵向荷载的P-?效应并计入桩身自重和桩侧摩阻力的影响,得到了地面以下桩身变形和内力的幂级数解。结合已有的地面以上桩身响应的幂级数解,采用Fortran语言编制了计算程序。计算结果表明：桩顶位移、地面处桩身位移及桩身最大弯矩均随纵横向荷载和自由段桩长的增加而增大,并随土体屈服位移的增加而减小;纵向荷载足够大时桩基失稳;桩顶约束条件对桩的响应影响很大。计算值与模型试验的实测值吻合较好,所得解和程序是可靠的。     

A Winkler model approach for vertically and laterally loaded piles in nonhomogeneous soil

An investigation is made to present analytical solutions provided by a Winkler model approach for the analysis of single piles and pile groups subjected to vertical and lateral loads in nonhomogeneous soils. The load transfer parameter of a single pile in nonhomogeneous soils is derived from the displacement influence factor obtained from Mindlin's solution for an elastic continuum analysis, without using the conventional form of the load transfer parameter adopting the maximum radius of the influence of the pile proposed by Randolph and Wroth. The modulus of the subgrade reaction along the pile in nonhomogeneous soils is expressed by using the displacement influence factor related to Mindlin's equation for an elastic continuum analysis to combine the elastic continuum approach with the subgrade reaction approach. The relationship between settlement and vertical load for a single pile in nonhomogeneous soils is obtained by using the recurrence equation for each layer. Using the modulus of the subgrade reaction represented by the displacement influence factor related to Mindlin's solution for the lateral load, the relationship between horizontal displacement, rotation, moment, and shear force for a single pile subjected to lateral loads in nonhomogeneous soils is available in the form of the recurrence equation. The comparison of the results calculated by the present method for single piles and pile groups in nonhomogeneous soils has shown good agreement with those obtained from the more rigorous finite element and boundary element methods. It is found that the present procedure gives a good prediction on the behavior of piles in nonhomogeneous soils. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Nonlinear analysis of laterally loaded rigid piles in cohesionless soil

In this paper, a method is developed for nonlinear analysis of laterally loaded rigid piles in cohesionless soil. The method assumes that both the ultimate soil resistance and the modulus of horizontal subgrade reaction increase linearly with depth. By considering the force and moment equilibrium, the system equations are derived for a rigid pile under a lateral eccentric load. An iteration scheme containing three main steps is then proposed to solve the system equations to obtain the response of the pile. To determine the ultimate soil resistance and the modulus of horizontal subgrade reaction required in the analysis, related expressions are selected by reviewing and assessing the existing methods. The degradation of the modulus of horizontal subgrade reaction with pile displacement at ground surface is also considered. The developed method is validated by comparing its results with those of centrifugal tests and three-dimensional finite element analysis. Applications of the developed method to laboratory model and field test piles also show good agreement between the predictions and the experimental results.     

海洋工程中大直径管桩垂直水平荷载试验研究

通过海洋环境条件下大直径管桩的垂直和水平荷载试验,分析了管桩在垂直和水平荷载作用下的受力特点,得到了管桩的垂直极限承载力、侧摩阻力及端承力、轴向反力系数等结果,以及水平荷载作用下桩顶位移和转角关系、弯矩分布、土抗力、水平地基反力系数的比例系数和最大弯矩点等参数。试验结果表明：垂直荷载作用下,极限承载力可达12000kN,在沉桩过程中部分桩有一定程度的闭塞;大直径管桩能够抵抗水平荷载的作用,弹性长桩的受力性质主要受上部土层的影响。根据试验结果计算的水平地基抗力比例系数m值,对本工程及同类地质条件的桩基设计具有参考价值。     

成层土中倾斜荷载作用下桩承载力有限元分析

利用有限元方法对现场单桩水平载荷试验进行模拟,在此基础上,分析了成层土中桩在倾斜荷载作用下其竖向分量的有利作用和横向土抗力分布特点。计算结果表明,在地面下一定范围内,倾斜荷载作用下的桩侧摩阻力比水平荷载作用下的桩侧摩阻力大。在土层分界处土抗力分布有明显的跳跃。达到一定深度后,横向土抗力主要是静止土压力,而由荷载引起的横向土抗力很小。承台能有效减小土体及桩的水平位移。模拟的灌注桩和钢管桩桩顶在地面以上的自由长度较小,竖向分量由于桩身挠曲变形而产生的P-Δ效应较小,所以就算例中的灌注桩和钢管桩而言,荷载倾斜度不大时,荷载竖向分量提高了桩的侧阻并由此增大桩侧土竖向应力,对桩水平承载力总体上起到了有利的作用。     

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.     

桩网结构路基承载特性的现场试验研究

为了考察路堤荷载作用下桩网结构路基桩土间的荷载分担与传递、垫层筋带拉力的组成与分布,选择某新建铁路桩网结构路基试验工点进行了现场试验,测试了地基变形、路堤基底压力、孔隙水压力、桩身轴力和格栅拉力等数据。测试数据表明：①地基沉降以压密下沉为主,路基结构稳定,软土较厚一侧地基变形较大;②当桩、土间沉降差与桩间净距的比值为5.93%时,土拱效应完全发挥,之后增加的路堤荷载完全由桩承担;③桩间土竖向附加应力在加固区内沿深度呈K型分布;④筋带拉力沿路基横向呈M型分布,软土较厚一侧拉力较大;⑤筋带拉力由路堤荷载作用下的桩间筋带张力与路堤横向滑移引起的筋带拉力两部分组成,设计筋带时二者均需考虑。     

On the influence of vertical loads on the lateral response of pile foundation

The influence of vertical loads on the lateral response of group piles installed in sandy soil and connected together by a concrete cap is studied through finite elements analyses. The analyses focus on the five piles in the middle row of 3 × 5 pile groups. The vertical load is applied by enforcing a vertical displacement equivalent to 2% of the pile diameter through the pile cap prior to the application of the lateral loads. The results have shown that the lateral resistance of the leading pile (pile 1) does not appear to vary considerably with the vertical load. However, the vertical load leads to 23%, 36%, 64%, and 82% increase in the lateral resistance of piles 2–5, respectively. The increase in the lateral pressures in the sand deposit is the major driving factor to contribute the change in the lateral resistance of piles, depending on the position of the pile in the group. The distribution of lateral loads among piles in the group tends to be more uniform when vertical loads were considered leading to a more economical pile foundation design.     

Scour effects on the response of laterally loaded piles considering stress history of sand

Scour is the removal of soils around pile foundations of bridges or offshore platforms, resulting in reduced capacity of the foundations in either lateral or vertical direction. A common way to analyze the scour-affected pile foundations is to remove the scoured soil layers while keeping the properties of the remaining soil unchanged. However, this approach ignores the fact that the remaining soil experiences different stress histories before and after scour, which can be expected to change the properties of the remaining soil. As a result, the resistance of the remaining soil provided to the pile foundation may be different. The present study focused on the response of laterally loaded pile foundations in sand under scour considering the stress history of the remaining sand. Relative density and coefficient of lateral earth pressure of the sand were evaluated when it changed from a normally consolidated (NC) soil to an over-consolidated (OC) soil due to scour. The relative density was then used to estimate other properties of sand, e.g., unit weight, friction angle, and modulus of subgrade reaction of the sand based on their correlation. The lateral load–deflection (p–y) curve for a pile in sand was modified and input into the computer software, LPILE Plus V 5.0, to account for the effect of the stress history induced by scour. A field test was referenced as an example to compare the calculated results from the modified p–y curves with those from the initially developed p–y curves for the tested sand. The results showed that the change in the over-consolidation ratio (OCR) resulted in the most significant effect on the lateral soil resistance among all the effects due to the changes in the properties of the remaining sand. The sand changing from an NC to OC state increased the lateral soil resistance to the pile foundation. Ignoring the stress history would result in a conservative design of laterally loaded piles under scour.     

Nonlinear analysis of laterally loaded single piles in sand using modified strain wedge model

This paper proposes a modified strain wedge model for the nonlinear analysis of laterally loaded single piles in sandy soils by using the Duncan–Chang model as well as the Mohr–Coulomb model to describe the stress–strain behavior of soils in the strain wedge. The input soil property for sandy soils only needs a relative density which can be easily estimated from in situ tests. The strain wedge depth is calculated by an iterative process and the subgrade reaction modulus below the strain wedge is assumed to increase linearly with depth, though it does not change with the lateral load applied to the pile. Seven case histories are used to verify the applicability of the proposed method. The results show the following: (1) good agreements are found between the predicted and the measured results of full scale tested piles; (2) the predicted deflections and moments using the Duncan–Chang model are almost the same as those using the Mohr–Coulomb model; and (3) the size effect of the pile diameter or width on the subgrade reaction modulus should be considered.     

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.     

路堤荷载下地基的侧向变形计算分析

目前关于路基侧向变形研究,大都是基于现场测试或数值模拟,却鲜有理论上的计算与分析。为深入研究路堤荷载下地基的侧向变形,基于布辛奈斯克等弹性理论解及平面应变问题,推导出无限长线荷载、均布条形荷载、三角形分布条形荷载及梯形分布条形荷载下地基侧向变形解析表达式,并与有限元数值计算结果对比验证了解析解的正确性。在此基础上,重点分析了土体的泊松比、路堤宽度以及路堤边坡宽度等参数对地基侧向位移场的影响。计算结果表明,路堤荷载下地基同一垂直线上土体的侧向变形沿深度呈弓形状,变形最大值在地表下某深度处。泊松比对地基侧向位移有较显著的影响：在坡脚附近地表浅层处,随着泊松比的增加,土体侧向变形的方向由向路堤内逐渐转为向路堤外;另泊松比越大,土体的水平位移也相对越大,且最大位移发生位置逐渐上移。研究结果可为类似路堤工程地基变形分析及稳定性控制监测提供一定理论支撑。     

Modulus of subgrade reaction that varies with magnitude of displacement of cohesionless soil

Modulus of subgrade reaction is one of the required design parameters in any structural analyses of shallow foundations. However, the constant values of modulus of subgrade reaction that are determined from either from literature studies or the results of plate load tests, regardless of magnitude of soil’s displacement under design loads, have been used in structural designs of foundations. In this study, the results of 43 published full-scale field plate load tests in cohesionles soils were gathered to expose any variation in the values of modulus of subgrade reaction as soil’s displacement increases. Extensive finite element (FE) analyses were carried out while the results of FE analyses were compared with actual measured results of field load tests. The results of analyses indicated that both the modulus of subgrade reaction decrease with increase in magnitude of displacement of soils and internal forces of a design of structural frame is higher with the values of modulus of subgrade reaction that are sensitive to soil’s displacement are implemented into analyses. Therefore, structural dimensions of any structure with the constant values of modulus of subgrade reaction would not be a precise engineering solution.     

Settlement analysis of rectangular piles in nonhomogeneous soil using a Winkler model approach

An analytical approach using a Winkler model is investigated to provide analytical solutions of settlement of a rectangular pile subjected to vertical loads in nonhomogeneous soils. For a vertically loaded pile with a rectangular cross section, the settlement influence factor of a normal pile in nonhomogeneous soils is derived from Mindlin's solution for elastic continuum analysis. For short piles with rectangular and circular cross sections, the modified forms of settlement influence factors of normal piles are produced taking into account the load transfer parameter proposed by Randolph for short circular piles. The modulus of subgrade reaction along a rectangular pile in nonhomogeneous soils is expressed by using the settlement influence factor related to Mindlin's solution to combine the elastic continuum approach with the subgrade‐reaction approach. The relationship between settlement and vertical load for a rectangular pile in nonhomogeneous soils is available in the form of the recurrence equation. The formulation of settlement of soils surrounding a rectangular pile subjected to vertical loads in nonhomogeneous soils is proposed by taking into account Mindlin's solution and both the equivalent thickness and the equivalent elastic modulus for layers in the equivalent elastic method. The difference of settlement between square and circular piles is insignificant, and the settlement of a rectangular pile decreases as the aspect ratio of the rectangular pile cross section increases. The comparison of results calculated by the present method for a rectangular pile in nonhomogeneous soils has shown good agreement with those obtained from the analytical methods and the finite element method. Copyright © 2014 John Wiley & Sons, Ltd.     

Load transfer approach for laterally loaded piles

A two‐parameter model has been proposed previously for predicting the response of laterally loaded single piles in homogenous soil. A disadvantage of the model is that at high Poisson's ratio, unreliable results may be obtained. In this paper, a new load transfer approach is developed to simulate the response of laterally loaded single piles embedded in a homogeneous medium, by introducing a rational stress field. The approach can overcome the inherent disadvantage of the two‐parameter model, although developed in a similar way. Generalized solutions for a single pile and the surrounding soil under various pile‐head and base conditions were established and presented in compact forms. With the solutions, a load transfer factor, correlating the displacements of the pile and the soil, was estimated and expressed as a simple equation. Expressions were developed for the modulus of subgrade reaction for a Winkler model as a unique function of the load transfer factor. Simple expressions were developed for estimating critical pile length, maximum bending moment, and the depth at which the maximum moment occurs. All the newly established solutions and/or expressions, using the load transfer factor, offer satisfactory predictions in comparison with the available, more rigorous numerical approaches. The current solutions are applicable to various boundary conditions, and any pile–soil relative stiffness. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

多向荷载作用下层状地基刚性桩筏基础分析

提出一种多向荷载作用下层状地基中刚性桩筏基础的计算方法。基于剪切位移法,采用传递矩阵形式分析了竖向荷载下桩顶面-桩顶面相互作用;引入修正桩侧地基模量,采用有限差分法分析了水平荷载下桩顶面-桩顶面相互作用;基于层状弹性半空间理论,分析了多向荷载下桩顶面-土表面、土表面-桩顶面、土表面-土表面的相互作用关系。建立了桩土体系柔度矩阵,得到了多向荷载下层状地基中刚性桩筏基础的受力和变形的关系以及桩的内力和变形沿桩身分布规律。通过与有限元对比,验证了该方法的合理性和修正地基模量的优越性,并对多向荷载作用下的桩筏基础进行了计算分析,计算结果表明,水平力将会引起桩筏基础的倾斜。     

高铁荷载下桩承式路基动力响应及土拱效应研究

土拱效应的作用机制是桩承式路堤荷载传递的关键性技术问题,然而高铁荷载作用下桩承式路堤中土拱效应的研究尚不充分。基于高铁设计规范的相关内容,建立了高铁荷载作用下桩承式路堤三维有限元分析模型,并采用已有研究结论验证了数值模型的正确性。根据该数值分析模型,首先分析了高铁荷载作用下路基的动力响应,研究了高铁荷载作用下道床和路堤不同位置处的竖向位移随时间的变化规律,以及路基中速度与加速度沿深度的分布规律。研究发现：道床和路堤表面处的竖向位移随时间变化呈倒“M”型周期变化,而路堤底部处呈“V”型周期变化;速度与加速度在路基深度范围内衰减了80%。通过变化桩间距、路堤高度以及路堤材料参数,分析其对高铁荷载作用下路堤应力和沉降发展规律的影响,进而分析其对土拱效应的影响。研究结果表明：动载作用下土拱效应依然存在,但有所减弱,动载峰值作用下减弱程度最大,谷值情况下有所恢复;桩间距和路堤高度对高铁荷载作用下桩承式路堤中土拱效应的影响较为明显,而路堤填料内摩擦角和剪胀角的影响则相对较小。     

高速铁路超长桥桩承载特性试验研究

超长桩广泛已应用于土木工程各个领域,但黄土地区超长桩的承载性状和变形特性尚不十分清楚,需要进一步研究。通过对郑西铁路客运专线某特大桥的4根超长桩现场测试项目的资料分析,得出了超长桩桩身轴力及侧阻力的变化规律,对超长桩的承载特性有了更为清晰的了解。试验结果表明,在桩顶竖向荷载作用下,桩身轴力随荷载的增加发生了局部调整,砂性土层的桩侧摩阻力具有增强效应,黏性土层的桩侧摩阻力具有退化效应;单桩竖向刚度随桩顶荷载的增加而减小,单桩竖向刚度降低40 %～70 %。