层状土场中冲刷作用下部分埋置单桩动力响应分析

桩周土场受冲刷作用的变化是部分埋置单桩结构失效的主要原因之一。工程中土场多呈层状,此类场地中桩基的力学特性研究日益受到关注。为精确揭示冲刷作用对层状土场中部分埋置单桩动力响应的影响,基于改进Vlasov地基模型,利用Hamilton原理建立层状土场中横向受荷单桩的动力学模型。利用有限差分法求解受冲刷作用单桩的固有频率,实现对冲刷作用下土−结构相互作用系统的准确建模,进而用Green函数法求得单桩受迫振动的解析解。通过数值计算和参数分析,研究了层状土场的物理特性对受冲刷作用部分埋置单桩动力响应的影响。结果表明：基于改进Vlaosv地基模型建立的层状土场中部分埋置单桩动力学模型可精确预测冲刷作用对桩基动力学特性的影响。随冲刷程度加剧,层状土场中单桩的第一阶固有频率显著降低,改进Vlasov地基模型中各层土体的地基反力系数均减小,剪切系数则增大。当冲刷至非埋置段桩长 （ 为桩长）时,部分埋置单桩在动荷载作用下出现横向失稳现象。随底层土体厚度增加,各冲刷等级下单桩的第一阶固有频率均增大。如果第1层土的弹性模量增大了约0.43倍、1.14倍、1.86倍,则冲刷等级为0时单桩第一阶固有频率分别增大了约8.9%、19.5%、27.1%。     

饱和土中单桩复合地基上块体的速度导纳特性分析

根据饱和土弹性波动方程,建立了饱和地基轴对称竖向振动问题的一种有限元-无限元耦合解法并编制了计算程序,其精度应用Lamb问题的理论解来进行检验。参数分析结果表明,地基土的渗透性对单桩复合地基上块体竖向振动速度导纳的低频特性及共振频率影响甚微,但会使高频下的速度导纳幅值有所增大。该方法对饱和土中单桩复合地基动测技术的研究与应用具有一定的理论指导作用。     

基于薄层法和移动坐标系法的地铁竖向振动在成层土层中传播

针对地铁竖向振动在成层地基中的传播,提出了移动荷载作用下层状地基的分析模型。基于该模型,利用狄拉克函数及三重傅里叶变换将时空域内单个移动简谐荷载转换为频率-波数域内的荷载,结合薄层法和移动坐标系法推导了单个移动简谐荷载和移动简谐线荷载作用下三维层状地基动力响应的解析解,并给出了移动简谐线荷载动力响应解析解中参数n的经验取值范围;分析了荷载的移动速度对层状地基动力响应的影响以及弹性模量、泊松比、阻尼比和荷载频率对土体临界速度的影响。结果表明：荷载的移动速度对不同频带的动力响应的影响范围不同;移动速度对低频响应的影响程度大于对高频响应的影响程度;相比于泊松比和阻尼比,弹性模量对土体临界速度的影响最大;频率越接近荷载振动频率的振动响应,其幅值越大,临界速度越小。     

横观各向同性饱和地基竖向振动的衰减特性

基于提出的横观各向同性饱和多孔介质Biot波动方程的一般解,研究了饱和半空间地基在竖向点源简谐激振荷载作用下地表振动的衰减特征,分析了激振频率以及横观各向同性饱和土介质的各向异性参数和孔隙渗透系数对地表振动特征的影响。计算结果表明,低频和高频激振时,地表位移衰减特性存在明显差异;在饱和土的各向异性参数中,纵向和水平方向动态渗透系数比值和刚度系数比值对地表位移衰减影响最大,这也说明采用各向同性饱和介质的动力学模型不能准确地描述具有明显各向异性特性的饱和土地基的动力特性。     

竖向简谐荷载下二维层状饱和地基的解析层元解

基于Biot固结理论,运用解析层元方法求解竖向简谐荷载作用下二维层状饱和地基的动力响应问题。从直角坐标平面应变问题控制方程出发,通过Fourier-Laplace变换将偏微分方程组转化为常微分方程组,求解得到单层饱和地基的解析层元。结合层间连续条件和边界条件,组装得到多层饱和地基的总刚度矩阵方程,进而求得变换域内的解。借助Fourier-Laplace逆变换的数值积分方法,获得平面应变动力问题在物理域内的解,编制了相应的计算程序,其计算结果与已有文献结果吻合较好。通过算例分析了荷载圆频率、荷载作用深度及地基成层性对地基竖向位移的影响。计算结果表明：随荷载圆频率的增大,地基竖向位移先增加后减小;地基竖向位移在荷载作用点处呈现波峰,且受表层土性的影响较大。     

成层地基中单桩竖向承载力鲁棒性设计

城市建设中桩基应用广泛,单桩竖向承载力的计算方法及可靠性越来越受到设计人员重视。针对桩基设计中岩土参数的不确定性及桩基穿越成层地基对桩身承载力的影响问题,提出基于可靠度理论的鲁棒性设计方法。利用岩土参数变异性的平均值及标准差充分考虑岩土参数的不确定性,并通过扩大考虑地基土的不确定因素将单桩竖向承载力鲁棒性设计由砂土推广到黏土等一般性土壤;提出采用分层计算桩侧摩阻力作为不确定因素考虑地基土成层分布问题,按照承载力极限状态与正常使用极限状态作为目标函数进行桩基竖向承载力设计。单桩承载力鲁棒性设计将鲁棒性作为安全性评价标准,来评估桩基设计方案的可行性,以鲁棒性与经济性为优化目标对桩基设计进行多目标优化,设计方案在满足桩基承载力要求的同时,保证了桩基设计方案的鲁棒性与经济性。     

层状地基中基于Laplace变换的桩基横向振动阻抗计算

基于Laplace变换,对层状地基中桩土横向振动阻抗计算问题进行了研究。考虑土层天然分层的特性及桩顶轴向力的参与作用,结合频域内桩-土动力文克尔理论,采用传递矩阵法并通过拉普拉斯变换,将振动微分方程变成代数方程以求解桩的横向振动响应参数,并导出了单桩横向振动阻抗。基于所得解,进一步计算出桩-土-桩水平动力相互作用因子。通过实例分析对比,验证其有效性和可行性。该方法计算工作量小,易于理解,计算结果与已有结果具有良好的一致性,并能保证解的连续性,对桩-土动力相互作用的研究具有一定的实用意义。     

竖向入射S波作用下单桩水平地震响应简化解析方法

基于连续介质模型并考虑桩-土运动相互作用,将单桩视为一维线弹性梁,研究了竖向入射S波作用下的单桩水平地震响应问题。将竖向入射S波模拟为基岩水平位移,基于平面应变模型建立的土体控制方程,推导出地震作用下土体水平动力阻抗函数表达式。将土体阻抗代入单桩控制方程并联立桩-土接触条件及桩顶和桩底的边界条件,得出了竖向入射S波作用下单桩的地震响应解析解。通过将所得解与已有文献理论解和有限元结果进行对比,验证了该方法的合理性。基于所得理论解进行参数分析得出：桩-土模量比的增加可以明显降低桩-土运动相互作用因子的最小值,而较大桩身长径比以及土体滞回阻尼对桩-土运动相互作用因子的影响较小;对于桩顶水平地震放大因子来说,桩-土模量比的增加仅在高共振频率处抑制其幅值,较大桩身长径比对其影响较小,而滞回阻尼比的增加会显著抑制共振频率处的幅值;桩身地震响应仅在较小桩径比时受桩-土模量比的影响明显,并随桩-土模量比的增加而降低。     

边载作用下桥梁基桩-立柱的位移特征与受力分析

为了揭示单侧边载对既有工程桩的不利影响,结合张家港某高速公路枢纽高架桥基桩-立柱偏移事故的工程实例,分析了路基边载作用下软土地基桥梁桩柱的位移特征和受力机制;根据桥梁桩柱沿竖向受力模式的不同,将边载作用下桥梁桩柱划分为自由段、被动受荷段和主动作用段;在此基础上,考虑到地基塑性屈服和上部结构约束边界的影响,基于三参数地基模型,建立了桥梁基桩-立柱受力响应的微分控制方程,并通过矩阵传递法给出了半解析解答。通过对工程实例中2排桩柱水平位移和受力弯矩的验算,验证了计算方法的适用性,并通过算例分析了桩身离散单元长度、被动段深度对计算结果的影响规律,结果可为单侧边载作用下被动桩受力响应的计算分析提供参考。     

考虑成层土路堤荷载下复合地基加固区沉降计算

考虑土的成层性,假定桩周成层土弹性模量的不同不影响桩中性点位置,应用弹性理论和桩土位移协调条件及边界条件,推导了路堤荷载下复合地基加固区桩及桩周土压缩量计算的解析式,同时得到了各层土范围内桩、桩周土竖向应力及桩侧剪应力的表达式,并利用有限元分析了桩周土弹性模量的变化对桩中性点位置的影响规律,验证了假定。结果表明:使用该计算方法分析路堤荷载下复合地基加固区内桩和桩周土的变形,计算结果与有限元及实测结果比较接近,满足工程计算精度要求,能为类似地基土成层分布工程沉降分析提供有益参考。     

Axial and lateral response of pile groups embedded in nonhomogeneous soils

A numerical method of analysis based on elasticity theory is presented for the analysis of axially and laterally loaded pile groups embedded in nonhomogeneous soils. The problem is decomposed into two systems, namely the group piles acted upon by external applied loads and pile–soil interaction forces, and a layered soil continuum acted upon by a system of pile–soil interaction forces at the imaginary positions of the piles. The group piles are discretized into discrete elements while the nonhomogeneous soil behaviour is determined from an economically viable finite element procedure. The load–deformation relationship of the pile group system is then determined by considering the equilibrium of the pile–soil interaction forces, and the compatibility of the pile and soil displacements. The influence of soil nonlinearity can be studied by limiting the soil forces at the pile–soil interface, and redistributing the ‘excess forces’ by an ‘initial stress’ process popular in elasto-plastic finite element analysis. The solutions from this approach are compared with some available published solutions for single piles and pile groups in homogeneous and nonhomogeneous soils. A limited number of field tests on pile groups are studied, and show that, in general, the computed response compares favourably with the field measurements.     

Torsional dynamic response of a pile embedded in layered soil based on the fictitious soil pile model

The torsional dynamic response of a pile embedded in layered soil is investigated while considering the influence of the pile end soil. The finite soil layers under the end of the pile are modeled as a fictitious soil pile that has the same cross-sectional area as the pile and is in perfect contact with the pile end. To allow for variations of the modulus or cross-sectional area of the pile and soil, the soil surrounding and below the pile is vertically decomposed into finite layers. Using the Laplace transform and impedance function transfer method, the analytical solution for the dynamic response of the pile head in the frequency domain is then obtained, and the relevant semi-analytical solution in the time domain is derived using the inverse Fourier transform and convolution theorem. The rationality and accuracy of the solution is verified by comparing the torsional dynamic behavior of the pile calculated with the fictitious soil pile with those based on a rigid support model and a viscoelastic support model. Finally, a parametric study is conducted to investigate the influence of the properties and thickness of the pile end soil on the torsional dynamic response of the pile.     

Longitudinal vibration of a pile embedded in layered soil considering the transverse inertia effect of pile

The dynamic response of a viscoelastic bearing pile embedded in multilayered soil is theoretically investigated considering the transverse inertia effect of the pile. The soil layers surrounding the pile are modeled as a set of viscoelastic continuous media in three-dimensional axisymmetric space, and a simplified model, i.e., the distributed Voigt model, is proposed to simulate the dynamic interactions of the adjacent soil layers. Meanwhile, the pile is assumed to be a Rayleigh–Love rod with material damping and can be divided into several pile segments allowing for soil layers and pile defects. Both the vertical and radial displacement continuity conditions at the soil–pile interface are taken into account. The potential function decomposition method and the variable separation method are introduced to solve the governing equations of soil vibration in which the vertical and radial displacement components are coupled. On this basis, the impedance function at the top of the pile segment is derived by invoking the force and displacement continuity conditions at the soil–pile interface as well as the bottom of pile segment. The impedance function at the pile head is then obtained by means of the impedance function transfer method. By means of the inverse Fourier transform and convolution theorem, the velocity response in the time domain can also be obtained. The reasonableness of the assumptions of the soil-layer interactions have been verified by comparing the present solutions with two published solutions and a set of well-documented measured pile test data. A parametric analysis is then conducted using the present solutions to investigate the influence of the transverse inertia effect on the dynamic response of an intact pile and a defective pile for different design parameters of the soil–pile system.     

A three‐dimensional displacement approach for analysis of laterally loaded piles in nonhomogeneous soil

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 loads in nonhomogeneous soil. The rocking stiffness coefficient of the pile shaft in homogeneous soil is derived from the analytical solution taking into account the three‐dimensional displacement represented in terms of scalar potentials in the elastic three‐dimensional analysis. The lateral stiffness coefficient of the pile shaft in nonhomogeneous soil is derived from the rocking stiffness coefficient taking into account the rocking rotation of a rigid pile shaft. The relationship between horizontal displacement, rotation, moment, and shear force of a pile subjected to horizontal loads in nonhomogeneous soil is obtainable in the form of the recurrence equation. 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 Mindlin's equation and the equivalent thickness for soil layers in the equivalent elastic method. There is little difference between lateral, rocking, and couple stiffness coefficients each obtained from both the two‐dimensional and three‐dimensional methods except for the case of Poisson's ratio near 0.5. The comparison of results calculated by the current method for a pile subjected to lateral loads in homogeneous and nonhomogeneous soils has shown good agreement with those obtained from analytical and numerical methods. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

A “T-Z” approach for cyclic axial loading analysis of single piles

A simple and efficient numerical approach is presented for the cyclic axial loading analysis of vertical single piles embedded in a layered soil profile. The soil medium along the embedded pile is represented by simple “t–z” curves which define the shear stres-vertical displacement response of the soil at each particular depth. A hyperbolic “t-z” representation of the soil medium presented by Chin and Poulos, which caters for the case of a two-layered and “Gibson” soil profiles, is utilised. Under cyclic loading conditions, the well-known Masing's criteria governing the unloading and reloading responses are incorporated into the “t-z” curves. The cyclic loading effects of pile capacity degradation and accumulation of pile displacement are catered for in an approximate manner. Some numerical results are presented to show the important parameters affecting the cyclic response of single piles embedded in a layered soil. Finally, a comparison with field measurements of a cyclic pile load test shows general agreement between numerical and field results.     

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.     

A simplified analysis method for piled raft foundations in non‐homogeneous soils

A simplified method of numerical analysis based on elasticity theory has been developed for the analysis of axially and laterally loaded piled raft foundations embedded in non‐homogeneous soils 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 and the piles as elastic beams and the soil is treated as springs. The interactions between structural members, pile–soil–pile, pile–soil–raft and raft–soil–raft interactions, are approximated based on Mindlin's solutions for both vertical and lateral forces with consideration of non‐homogeneous soils. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups and capped pile groups in non‐homogeneous soils. Thereafter, the solutions from this approach for the analysis of axially and laterally loaded 4‐pile pile groups and 4‐pile piled rafts embedded in finite homogeneous and non‐homogeneous soil layers are compared with those from three‐dimensional finite element analysis. Good agreement between the present approach and the more rigorous finite element approach is demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.     

Effect of compressible parameters on vertical vibration of an elastic pile in multilayered poroelastic media

This paper mainly investigates the influences of compressible parameters on the vertical vibration of a pile embedded in layered poroelastic soil media. The pile is treated as a 1D elastic bar by the finite element method, and fundamental solutions for the layered poroelastic soils due to a vertical dynamic load are obtained by the analytical layer element method. Based on the compatibility conditions, the pile-soil dynamic interaction problem is solved. The numerical scheme has been compiled into a Fortran program for numerical calculation. Influences of the pile-soil stiffness ratio, compressible parameters, vibration frequency and the soil stratification are discussed.