成层地基中倾斜偏心荷载下单桩计算分析

针对工程中地基土性质变化的具体情况,假定地基系数满足(mz+C)的线性增长规律,考虑P-Δ效应并计入桩身自重和桩侧摩阻力的影响,采用矩阵计算方法,分别得到单层土中倾斜偏心荷载作用、桩段顶端倾斜偏心荷载作用以及桩身水平分布荷载共同作用下的竖向单桩计算分析的幂级数解答。并在此基础上,利用上述两幂级数解答对成层地基中倾斜偏心荷载下单桩的受力进行了分析计算,列出了具体的计算步骤;最后,结合某具体实例,对上述方法进行了验证,结果表明,该解答与实际吻合较好,具有一定的应用价值。     

双层地基水平受荷桩受力变形分析

基于双层地基中的水平受荷桩的特性,对其受力变形进行了分析。将水平受荷桩视为竖直放置的弹性地基梁,基于Winkler弹性地基梁理论,考虑桩土共同工作得到水平受荷桩位移控制微分方程及其幂级数解答,进而根据内力与位移的连续条件得到了由桩顶受力及变形条件表示任一深度处桩身的水平位移、转角、弯矩及剪力的计算矩阵表达式。通过一具体算例将幂级数解计算结果与《公路桥涵地基与基础设计规范》推荐的简化计算公式计算结果进行了比较。结果表明：当第1层地基土的厚度在某一定值时,《规范》简化计算方法所得结果与幂级数解接近;但当层厚不在该值附近时,两个方法计算结果存在差异。     

桩基承台梁受力分析的幂级数解答

将桩基承台梁视为置于弹性地基上的有限长梁,将竖向桩体及承台梁下桩间土体视为刚度不同的弹簧系列,基于Winkler弹性地基梁理论,推导出考虑桩土共同工作的承台梁竖向位移控制微分方程,并给出其幂级数半解析解,进而导得了在集中荷载、外加弯矩及分布荷载共同作用下桩基承台梁的竖向位移、转角、弯矩及剪力的计算公式。最后通过与链杆法、Newmark法的比较,验证了本文幂级数解答的正确性。在此基础上,探讨分析了基桩差异性、承台梁下土体作用、桩径及荷载形式等因素对桩基承台梁受力变形的影响。研究表明：当考虑上述因素影响时,桩基承台梁的竖向变形、弯矩及桩顶反力均发生不同程度的变化,因此,在实际的设计计算中应予以考虑。     

传递矩阵法分析层状地基中桩的扭转变形

研究了扭矩作用下单桩的扭转变形.采用积分变换和传递矩阵方法,求解了成层土在内部环形荷载作用下的基本解;利用此基本解并考虑桩土位移协调条件,提出了层状地基中单桩扭转变形分析的解析方法;并按此理论方法对匀质地基模型进行了数值计算,其结果与已有经典解答相当吻合.     

成层土中轴横受荷桩水平响应的非线性解

对于承受轴向荷载的水平受荷桩,以往研究大多基于线弹性或弹塑性水平荷载传递模型。为提升轴横受荷桩的计算设计水平,采用轴向荷载传递法计算桩身轴力,考虑桩身轴力引起的P-Δ效应,基于双曲线型水平荷载传递模型考虑桩-土体系变形的非线性特征,对成层土中轴横受荷桩的水平响应进行分析求解,得到了轴横荷载作用下桩身变形和内力的非线性有限差分解,并采用MATLAB语言编制了计算程序。使用模型试验算例与基于现场试验的有限元算例对非线性解的准确性进行对比验证,结果表明:计算结果与算例数据吻合良好,可靠性较高;采用不同荷载传递模型的计算结果在不同荷载水平下有所差异,在较大荷载水平下桩-土变形的非线性特点不容忽视。     

水平谐振荷载作用下桥梁基桩的动力反应

针对桥梁基桩在施工和运营过程中不可避免承受动力作用的问题,在考虑桩顶承受轴向和横向静力荷载共同作用的基础上,将激振荷载简化为水平谐振荷载作用,并基于动力Winkler地基梁模型,将桩周土由一系列分布的彼此独立的弹簧和阻尼器所代替,建立桥梁基桩在瞬态荷载激励下的横向振动方程,求解基桩横向非线性动力学响应。在考虑桩-土接触和透射边界的基础上,引入有限单元方法建立基桩的二维非线性动力有限元模型,分析了基桩各项设计参数。计算结果表明：基桩桩顶位移大致随荷载频率的变化呈驼峰形,其位移量随着荷载振幅的增大而增加;基桩的自振频率随着长径比的增加而增大,且随着桩-土模量比的增加,自振频率有减小的趋势;增大桩径会增大基桩的受力,其对应的变形也将有所减小,且基桩的稳定性增加。     

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。     

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。     

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。     

竖向力与水平向力同时作用下管桩的性状研究

用解析方法研究了管桩在轴向力和水平向力（倾斜力）联合作用下的受力及变形性状。在高层建筑、桥梁工程、海洋工程、新型海堤护岸等工程中桩基自由长度上作用土压力、风荷载、波浪荷载等荷载型式,基桩经常在竖向、水平向荷载同时作用下工作。国内外学者通过大量试验和理论研究得出了计算竖向、水平向荷载下基桩内力和挠度的半经验公式以及张氏法公式。为了分析竖向、水平向荷载同时作用下自由荷载的作用,在现行m法假设的基础上,从弹性桩的挠曲微分方程出发,导出了任意自由荷载作用下桩任意截面的水平变位、倾角、弯矩、剪力和地基反力计算表达式。桩的挠曲微分方程是分段函数,包括地上部分和地下部分桩,相应的内力和变位求解也分为两段。最后通过一个算例分析了桩顶竖向荷载、桩顶水平力和自由荷载对桩身的受力性状各参数的影响。计算结果表明, 桩顶水平力对桩身最大弯矩和桩顶水平变位的影响最大,而桩周内外摩阻力及桩身自重对桩身受力性状影响较小。     

Influences of axial load on the lateral response of single pile with integral equation method

This article revisits the influences of axial load on the lateral response of single pile with integral equation method. The problem is formulated by decomposing the pile soil system into an extended elastic soil and a fictitious pile, the former of which is analyzed by making use of the fundamental Mindlin's solution for a concentrated horizontal load whereas the latter is modeled by the conventional beam bending theory. According to the rotation compatibility condition between the fictitious pile and the extended soil, a Fredholm integral equation of the second kind is established with the shear strain and rotation angle of the fictitious pile being the basic unknowns. The bending moment and displacement distribution along the pile are subsequently obtained. Comparison with existing solutions validates the accuracy and applicability of the present formulation. The results of parametric analysis indicate that the influences of axial load on the lateral response of single piles could be significant, and in general, the bending moment and horizontal displacement distributions along the pile increase considerably with the increase of axial load. 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.     

水平荷载作用下风电机桩基础的离心模型试验研究

桩基础是近海风机经常采用的基础形式。由于风电机组对基础的承载力和变形有着严格的要求,而水平荷载常常是控制荷载,因此,研究水平荷载作用下风机桩基础的应力、变形特性具有重要意义。针对风机单桩基础,选取典型的黏土地基,进行了水平加载条件下的离心模型试验,重点分析了桩身的响应及桩周围土体的变形特点。试验结果表明,在水平荷载作用下,桩顶的水平位移随着水平力的增加而增加,位移的增加速率在临界荷载之后增长较快;桩身弯矩分别在埋深1/5和3/5处附近分别出现极大值和极小值,且桩底具有一定弯矩值;桩周围土体的变形随着离桩距离的增加而减小,可分为主动区和被动区。桩对土体变形的影响区域随着水平力的增加而不断扩展,最后基本稳定在2倍桩径范围内。     

Seismic analysis of laterally loaded pile under influence of vertical loading using finite element method

An efficient analytical approach using the finite element (FE) method, is proposed to calculate the bending moment and deflection response of a single pile under the combined influence of lateral and axial compressive loading during an earthquake, in both saturated and dry homogenous soil, and in a typical layered soil. Applying a pseudo-static method, seismic loads are calculated using the maximum horizontal acceleration (MHA) obtained from a seismic ground response analysis and a lateral load coefficient (a) for both liquefying and non-liquefying soils. It is observed that for a pile having l/d ratio 40 and embedded in dry dense sand, the normalized moment and displacement increase when the input motion becomes more severe, as expected. Further increasing of a from 0.1 to 0.3 leads to increase in the normalized moment and displacement from 0.033 to 0.042, and 0.009 to 0.035, respectively. The validity of the proposed FE based solution for estimating seismic response of pile is also assessed through dynamic centrifuge test results.     

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.”     

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.     

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.