Analysis of rectangular piles subjected to lateral loads in nonhomogeneous soil using a Winkler model approach

An analytical approach using a Winkler model based on two lateral soil displacement components in a three‐dimensional soil is investigated to provide analytical solutions of horizontal response of a rectangular pile subjected to lateral loads in nonhomogeneous soil. The two lateral displacement components of a soil surrounding the rectangular pile are represented by the Fourier series of displacement potential functions in the elastic three‐dimensional analysis. The lateral stiffness coefficient of the rectangular pile shaft in nonhomogeneous soil is derived from the rocking stiffness coefficient taking into account rocking rotation of a rigid pile shaft. The relationship between horizontal displacement, rotation, moment, and shear force for the rectangular pile subjected to horizontal loads in nonhomogeneous soil is obtainable in the form of the recurrence equation. The formulation of lateral displacement and rotation for a rectangular pile subjected to lateral loads on the pile base in nonhomogeneous soil is proposed by taking into account Mindlin's equation and the equivalent thickness for soil layers in the equivalent elastic method. The difference of lateral behavior between square and circular piles subjected to lateral loads is insignificant. The effect of aspect ratio of the rectangular pile on the lateral behavior is great for the lower stiffness ratio between pile and soil and the larger length–equivalent diameter ratio. The effect of the value of Poisson's ratio of soil on lateral stiffness coefficient is relatively small except Poisson's ratio close to 0.5. The comparison of the results calculated by the current method for a rectangular pile subjected to lateral loads in nonhomogeneous soil has shown good agreement with those obtained from the analytical methods and the finite element method. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

超高层建筑桩筏基础的桩顶反力计算研究

根据上海高88层、筏板厚度为4 m的金茂大厦和高101层、筏板厚度为4.5 m的上海环球金融中心桩筏基础的实测沉降资料,论证超高层建筑的桩筏基础为弹性体。对以上两幢超高层建筑和正在建造中的高121层、筏板厚度为6 m的上海中心大厦的桩筏基础,采用偏心受压公式和高层建筑与地基基础共同作用理论方法(混合法)进行详细对比计算,论证按弹性体计算桩顶反力的合理性,阐明《建筑桩基技术规范》(JGJ 94–2008)的3.1.8条的正确性和合理性。期望能够改变过去按偏心受压公式计算桩顶反力的传统观念,提高设计水平。     

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。     

竖向荷载作用下桩筏基础可视化模型试验研究

进行了群桩基础可视化模型试验。在试验过程中对各级竖向荷载作用下群桩基础桩、土的变形采用高清晰数码相机拍摄了照片。通过对照片进行后处理分析,得到了桩、土的位移场,也对桩身轴力也进行了量测,在该基础上研究了群桩基础的变形性状和破坏模式,重点分析对比了桩间距和桩长对桩端土体沉降以及桩身侧摩阻力的影响。试验发现,桩距是影响桩土相对滑移量的主要因素,桩距越大,桩身与土的相对滑移量就越大,桩端刺入量也越大。在柔性筏基下,随桩距增加中桩的桩土相对滑移量可能会大于边桩。桩端刺入量是大桩距桩基础主要的沉降构成,以桩端刺入量为研究对象建立一套大桩距基础新的沉降计算理论,似乎值得进一步研究。桩顶向上刺入（可通过设置褥垫层、桩顶预留净空或设置可压缩垫块来实现）有利于桩间土的压密,减小桩端刺入量,甚至改变破坏模式。     

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.     

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.     

竖向荷载下刚性板桩筏基础分析方法

根据群桩中桩侧摩阻力分布规律,在桩筏基础中基于弹性理论中的变形协调关系、桩体物理方程和力的平衡关系,推导了竖向荷载作用下桩筏基础的荷载和位移之间的刚度矩阵,从而提出了一种刚性板下桩筏基础的分析方法。刚性板桩筏基础分析中考虑了4种相互作用,分别为桩-土-桩、桩-土-板、板-土-桩和板-土-板相互作用。基础中各桩可具有不同的桩长、桩半径和刚度等特性。应用该方法不需要划分桩-土体单元,分析中的计算矩阵仅与基础中桩数和筏板下土节点数量相关而与其他变量无关,分析过程简洁通用。通过与各种分析方法的比较验证,证明该方法是合理可行的。     

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.     

基于Winkler模型的有效桩长研究

有效桩长的定义有基于承载力角度和沉降角度两种方法,由于影响因素的多样性,有效桩长的研究比较复杂。运用桩顶刚度控制法确定有效桩长。基于Winkler地基模型,以荷载传递法为工具,推导出双层土的桩顶刚度计算公式,并对有效桩长影响因素进行了分析。结果表明,桩径的增大有效桩长增加;土层刚度比(第二层土刚度与第一层土刚度之比)增大有效桩长减小;桩端刚度的增大对有效桩长的影响都不明显,第一土层厚度的增加在一定范围内对提高有效桩长是有用的     

移动荷载作用下Winkler地基板的等参元分析

采用基于Mindlin板理论的8节点等参单元和Newmark逐步积分法,对Winkler地基上的弹性薄板和厚板在移动荷载作用下的动力响应进行了分析,并与已有的薄板有限条法分析结果进行了对比。考察了荷载移动速度、地基基床系数、系统阻尼比对地基板动力响应的影响。分析结果表明,系统存在固有的共振速度,地基基床系数是确定共振速度的最重要因素,薄板与厚板的挠度响应模态有很大差异。结果证明了该方法的有效性和准确性,对实际工程有重要的应用价值。     

Elastoplastic multiphase model for simulating the response of piled raft foundations subject to combined loadings

A multiphase model and corresponding computational time‐saving finite element code is proposed in this paper for predicting the settlements experienced by a piled raft foundation when subject to the combined action of vertical and lateral loadings. This model, which is formulated in the framework of an elastoplastic behaviour for the soil and the reinforcing piles as well, explicitly accounts for the shear and flexural behaviour of the latter. Starting from a simple analytical example where all the concepts attached to this model are clearly illustrated, the main stages leading to its finite element implementation are then presented. The numerical tool thus elaborated, is applied to the simulation of a pile‐reinforced strip foundation submitted to a horizontally applied seismic load in addition to a permanent vertical load. One of the key results of such a simulation in terms of design recommendation, lies in the conclusion that, while the shear and flexural contributions of the reinforcement play quite a negligible role in the case of a vertical load (as compared with their axial resistance), they remain absolutely essential for withstanding the seismic lateral loading. Copyright © 2006 John Wiley & Sons, Ltd.     

Vertical response of pile raft foundations subjected to tunneling‐induced ground movements in layered soil

A simplified analysis method has been developed to estimate the vertical movement and load distribution of pile raft foundations subjected to ground movements induced by tunneling based on a two‐stage method. In this method, the Loganathan–Polous analytical solution is used to estimate the free soil movement induced by tunneling in the first stage. In the second stage, composing the soil movement to the pile, the governing equilibrium equations of piles are solved by the finite difference method. The interactions between structural members (such as pile–soil, pile–raft, raft–soil, and pile–pile) are modeled based on the elastic theory method of a layered half‐space. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups, and pile rafts subjected to ground movements induced by tunneling. Good agreements between these solutions are demonstrated. The method is also used for a parametric study to develop a better understanding of the behavior of pile rafts influenced by tunneling operation in layered soil foundations. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of piles subjected to lateral soil movements using a three‐dimensional displacement approach

An analytical approach using the three‐dimensional displacement of a soil is investigated to provide analytical solutions of the horizontal response of a circular pile subjected to lateral soil movements in nonhomogeneous soil. The lateral stiffness coefficient of the pile shaft in nonhomogeneous soil is derived from the rocking stiffness coefficient that is obtained from the analytical solution, taking into account the three‐dimensional displacement represented in terms of scalar potentials in the elastic three‐dimensional analysis. The relationship between horizontal displacement, rotation, moment, and shear force of a pile subjected to lateral soil movements in nonhomogeneous soil is obtainable in the form of the recurrence equation. For the relationship between the lateral pressure and the horizontal displacement, it is assumed that the behavior is linear elastic up to lateral soil yield, and the lateral pressure is constant under the lateral soil yield. The interaction factors between piles subjected to both lateral load and moment are calculated, taking into account the lateral soil movement. The formulation of the lateral displacement and rotation of the pile base subjected to lateral loads in nonhomogeneous soils is presented by taking into account the Mindlin equation and the equivalent thickness for soil layers in the equivalent elastic method. For lateral movement, lateral pressure, bending moment, and interaction factors, there are small differences between results obtained from the 1‐D and the 3‐D displacement methods except a very flexible pile. Copyright © 2015 John Wiley & Sons, Ltd.     

饱和黏弹性地基土中管桩纵向振动研究

用解析方法在频率域内研究考虑质量耦合效应的饱和黏弹性地基土中管桩的纵向振动特性。基于Biot理论,采用薄层法,推导得到饱和黏弹性地基土的位移、应力等的表达式。将管桩等效为一维弹性杆件处理。根据界面连续性条件,给出饱和黏弹性地基土中管桩的纵向振动一般分析方法和桩顶动力复刚度的表达式。在该基础上,对比分析饱和地基土中实心桩和管桩纵向振动特性。通过算例分析,考察桩周土和桩芯土的力学参数对桩顶刚度因子和等效阻尼的影响。研究表明,饱和黏弹性地基土中实心桩和管桩的纵向振动有明显的差异。     

新型螺旋成孔根植注浆竹节管桩抗压性状数值模拟研究

新型螺旋成孔根植注浆竹节管桩是一种新的组合桩型,具有承载力高、技术含量高和安全性能好等特点。为了更好地了解新型组合桩的抗压承载机制,应用ABAQUS软件进行抗压数值模拟。通过将模拟结果与现场试验结果对比,验证了数值模型的可靠性。分析模拟结果,发现桩身竹节处存在2～3倍桩径的应力影响范围,并且存在1.6～1.8倍桩径的空壳区,竹节极限承载力从上到下排列线性增长（除第1节和最后一节）。结果还表明,竹节间距、水泥土厚度、桩侧土弹性模量以及桩端土弹性模量都对组合桩极限承载力有影响,而水泥土弹性模量的影响则可忽略。以往相似工法的极限承载力公式都不能很好地诠释本桩型的受力特性,因此,结合理论分析与抗压受力机制,提出考虑侧阻竹节影响系数的单桩极限承载力公式,与现场试验结果对比,较为接近。     

基于土体三维波动模型的饱和土中管桩竖向振动

基于土体的三维波动模型研究了饱和土中单个管桩的竖向振动。将桩周土和桩芯土视为两相多孔介质,管桩视为等截面的圆管杆单元。在考虑桩周饱和土和桩芯饱和土径向位移和竖向位移的情况下,建立了基于土体三维波动模型的饱和土-管桩竖向耦合振动模型。借助势函数和分离变量法并考虑土体边界条件,求解了考虑土体三维波动的桩周饱和土和桩芯饱和土的竖向振动。在此基础上,考虑管桩桩端边界条件,利用三角函数正交性求解了饱和土中单个管桩的竖向振动,得到了管桩桩顶的竖向复刚度。通过数值算例,对比分析了土体三维波动模型解和不考虑土体径向位移的简化模型解的计算结果,分析了主要桩、土参数对饱和土中管桩竖向振动的影响。研究表明：当管桩壁较薄时且低频时不应忽略土体径向位移的影响,在动态刚度因子和等效阻尼随频率变化曲线峰值峰谷处不宜忽略土体液相的影响,管桩壁不宜过薄。管桩壁厚、长径比、桩芯饱和土与桩周饱和土密度比、剪切模量比以及桩-土模量比对饱和土中管桩竖向振动有较大影响,在进行管桩设计时需要综合考虑相关参数。     

Multiphase model for inclusion‐reinforced geostructures: Application to rock‐bolted tunnels and piled raft foundations

A multiphase model is proposed to describe the mechanical behaviour of geomaterials reinforced by linear inclusions. This macroscopic approach considers the reinforced soil or rock mass as the superposition of continuous media. Equations of motion and constitutive laws of the model are first derived. Its implementation in a finite element computer code is then detailed. A modified implicit algorithm for elastoplastic problems is proposed. The model and its implementation are fully validated for rock‐bolted tunnels (comparison with scale model experiments) and piled raft foundations (comparison with the classical ‘hybrid method’). The Messeturm case history is finally presented to assess the handiness of the approach for real structures. Copyright © 2001 John Wiley & Sons, Ltd.     

基于双曲线模型的带帽刚性桩复合地基荷载传递机制研究

假定带帽刚性桩复合地基桩土荷载传递函数为双曲线模型,对其荷载传递机制进行了非线性分析。根据文献[1]的方法,建立了桩体、桩帽下土体及桩帽间土体的竖向位移、竖向应力、界面侧摩阻力与深度之间的控制微分方程。利用微分方程近似解法,得到了相应的解析表达式。直接把桩顶沉降作为已知条件进行求解,计算结果能反映带帽刚性桩复合地基工作性状规律,可为工程设计提供理论基础。     

路基填土对桥台桩基影响的试验与数值仿真分析

台后路基荷载会使地基软弱下卧层发生压缩和水平移动,致使桥台桩基的受力性状非常复杂。在现场测试结果的基础上,建立了三维有限元模型,模拟了台后路基荷载作用下桥台桩基的受力性状,并与实测结果进行了对比分析。结果表明,有限元计算结果与实测结果较为一致。中间桩排和后排桩桩身最大弯矩与台后路基荷载的关系呈双折线型,与Stewart等提出的一致,但双折线转折点所对应的路基填土荷载并不一致。中间桩排的填土荷载为软土层固结不排水黏聚力强度ccu与土层厚度的加权平均值的3.34倍,后排桩约为2.22倍;前排桩的最大弯矩与路基填土荷载呈线性变化。桩顶变形与台后路基荷载呈非线性关系,可以分为两部分。前排桩桩身最大弯矩位置一直在软土层中,不随台后路基荷载变化;而后排桩桩身最大弯矩位置在台后路基荷载较小时位于软土层中,随着台后路基荷载的增大,最终出现在桩顶。