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.     

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。     

Degradation model for one-way cyclic lateral load on piles in soft clay

The analysis of laterally loaded piles in soft clay is carried out idealising the pile as beam elements and the soil by nonlinear inelastic spring elements modeled with elasto-plastic sub-elements. The nonlinear hyperbolic model for static load condition is developed based on the undrained shear strength and modulus of subgrade reaction. An iterative procedure is adopted to perform a nonlinear finite element analysis and the effect of static lateral load on deflection is studied. Based on the lateral deflection at the end of first cycle (static load), the degradation factor is assumed and the p-y curve is modified. The cyclic load analysis is carried out using the static analysis program idealising the soil by modified p-y curve, which considers the effect of number of cycles and magnitude of cyclic lateral load. The results of the proposed analytical model compare well with the published experimental results, on piles subjected to one-way cyclic loading for different magnitude of cyclic lateral load and number of cycles.     

砂土中桩土侧向相互作用的应变楔模型修正

提出了砂土中水平受荷单桩的修正应变楔方法。从3个方面对应变楔模型进行了修正,首先假设三维被动土楔后桩身的水平位移呈非线性变化,从而使得楔形体内的水平应变不再是一常量,而是沿深度变化。其次引入了两个双曲线型的模型分别用以模拟楔形体中土体的水平应力增量-应变关系和桩-土界面处桩侧剪应力-位移关系。然后通过算例验证了修正方法的有效性,模拟结果与实测结果吻合较好。最后分析了各个修正因素对计算结果影响,结果显示,非线性位移假设的引入对原应变楔模型计算的水平承载力偏高有明显地改善,新的水平应力增量-应变关系和桩侧剪应力-位移关系的引入使得应变楔方法更加简便有效。     

Modification of strain wedge method for lateral soil-pile interaction in sandEI北大核心CSCD

A modified strain wedge (SW) method for analyzing the behavior of laterally loaded single piles in sand is proposed. The modified model assumes that the lateral displacements of a pile behind the three-dimensional passive soil wedge are nonlinear, which makes the horizontal soil strain variable with depths instead of a constant value in the original strain wedge model, and also employs two different hyperbolic models, one for describing horizontal stress increment-strain behavior of soil in the wedge, and the other for describing the shear stress-displacement property at the interface between soil and pile shafts. An example is analyzed to demonstrate the effectiveness of the modified method, and a good agreement is obtained. Finally, the effects of modifications on the lateral bearing capacity of pile shafts are discussed. The results show that the problem of overestimating the lateral bearing capacity of piles with strain wedge method can be ameliorated by introducing the assumption of nonlinear lateral displacements of piles. It makes the SW method more convenient and effective in analyzing the behavior of laterally loaded piles by introducing the new relationships of horizontal stress increment-strain and shear stress-displacement.     

Analysis of laterally loaded rigid monopiles and poles in multilayered linearly varying soil

A new method for calculation of head displacement and rotation of laterally loaded rigid monopiles and poles in multilayered heterogeneous elastic soil is presented. The analysis considers the soil as a layered elastic continuum in which the modulus vary linearly with depth within each layer. Rational pile and soil displacement fields are assumed, and the interaction between the pile and soil is taken into account by using the principle of virtual work. Two sets of equilibrium equations, one describing the pile displacement and rotation and the other describing the displacements in the soil, are obtained and solved analytically and numerically following an iterative algorithm. The new method produces pile responses as accurate as those obtained from three-dimensional finite element analysis but does not require any elaborate input for geometry and mesh.     

General Analytical Solution for Laterally-Loaded Pile-Based Miche Model

Piles subjected to lateral loading can create problems in soil-structure interaction. Several differing methods of analysis have been proposed to solve the problem of laterally loaded piles, resulting in the determination of pile bending and the bending moment as a function of depth below soil surface. These piles are widely used to support laterally loaded piles, such as bridge pillars, offshore platforms, communication towers and others. This study presents an analytical solution to Miche’s problem as a continuous function of depth: deflection and moment, as well as a dimensional plots to be used in projects involving piles subjected to laterally loading only including data concerning laterally loading test and pile geometry. A new formula is presented to calculate the pile head displacement as well as an equation to determine maximum moment for a generalized Miche model and further analysis. In addition, this paper proposes an equation for the determination of constant horizontal subgrade reaction \((n_{h})\) based on the CPT in-situ test and the geometric characteristics of the pile. Calibration of the analytical model showed good fit and conservative results regarding inclinometer data from an bored pile and good agreement with the literature results.

     

Variation of limiting lateral soil pressure with depth for pile rows in clay

Pile group interaction effects on the lateral pile resistance are investigated for the case of a laterally loaded row of piles in clay. Both uniform undrained shear strength and linearly increasing with depth shear strength profiles are considered. Three-dimensional finite element analyses are presented, which are used to identify the predominant failure modes and to calculate the reduction in lateral resistance due to group effects. A limited number of two-dimensional analyses are also presented in order to examine the behaviour of very closely spaced piles. It is shown that, contrary to current practice, group effects vary with depth; they are insignificant close to the ground surface, increase to a maximum value at intermediate depths and finally reduce to a constant value at great depth. The effect of pile spacing and pile–soil adhesion are investigated and equations are developed for the calculation of a depth dependent reduction factor, which when multiplied by the limiting lateral pressure along a single pile, provides the corresponding variation of soil pressure along a pile in a pile row. This reduction factor is used to perform p–y analyses, which show that, due to this variation of group effects on the lateral soil pressures with depth, the overall group interaction effects depend on the pile length. Comparisons are also made with approaches used in practice that assume constant with depth reduction factors.     

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.     

双排桩双梁组合支护刚度计算的改进与位移分析

双排桩支护组合体系作为一种新型悬臂类支护结构,其整体刚度的提升有利于保持基坑边侧的安全稳定。本文依托于张家口万全区某双排桩基坑支护工程案例,以现有双排桩冠梁刚度系数计算方法为基础,引入冠梁与连梁作用效应系数优化改进考虑连梁和冠梁作用的基坑矩形双排桩支护结构横向支撑刚度的计算方法,并对双梁组合支护体系下不同土性对双排桩前后排桩桩身最大横向位移的影响进行探讨。结果显示:（1）在双排桩结构计算中需考虑冠梁与连梁对双排支护桩的共同横向约束作用,并将冠梁与连梁的刚性连接作为一个整体以提高矩形双排桩双梁横向支撑刚度系数。（2）双梁组合支护体系组合刚度对桩顶位移有较大影响,组合刚度为40～50 MN/m下的位移与观测值较为贴近;冠梁计算长度与引入的冠梁与连梁作用效应系数对双梁组合支护体系组合刚度影响较大,计算长度对组合刚度呈负相关,效应系数对组合刚度呈正相关。（3）双梁组合支护体系下双排桩横向支撑刚度受前后排桩竖向与横向位移差影响,前后排桩桩身最大横向位移受土层内摩擦角、黏聚力和土体水平抗力比例系数影响;改变抗拉强度不会影响双排桩桩体位移。在基坑埋深以下及桩底范围内桩身存在位移拐点,拐点处各不同内摩擦角、不同黏聚力条件下位移相等。     

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.     

嵌固段顶部拓宽型抗滑桩计算方法

针对边坡工程中可能出现的普通抗滑桩嵌固段顶端前侧地层抗力不足的问题,提出嵌固段顶部拓宽型抗滑桩结构。基于水平受荷的弹性地基梁模型,推导滑床为多层岩土体的嵌固段顶部拓宽型桩的内力、位移、地层反力计算公式。实例分析表明,当桩体局部拓宽宽度为原桩宽度2倍时,嵌固段顶端地层反力可减小约25%,桩体最大弯矩及剪力减少5%~10%。讨论了拓宽宽度与深度、桩体嵌固深度、桩间距等主要因素对拓宽型桩内力与位移的影响,结果显示:普通桩经嵌固段顶部拓宽后,桩身水平位移与嵌固段顶端前侧地层反力显著降低;拓宽宽度与深度、嵌固段深度的增加均能增强拓宽型抗滑桩的水平承载能力,但当拓宽宽度达到原桩2倍、拓宽深度超过嵌固段深度40%后,继续拓宽对桩体水平承载能力的增加效果不显著。     

Response of rigid piles during passive dragging

This paper develops a three‐layer model and elastic solutions to capture nonlinear response of rigid, passive piles in sliding soil. Elastic solutions are obtained for an equivalent force per unit length p_s of the soil movement. They are repeated for a series of linearly increasing p_s (with depth) to yield the nonlinear response. The parameters underpinning the model are determined against pertinent numerical solutions and model tests on passive free‐head and capped piles. The solutions are presented in non‐dimensional charts and elaborated through three examples. The study reveals the following:

• On‐pile pressure in rotationally restrained, sliding layer reduces by a factor α, which resembles the p‐multiplier for a laterally loaded, capped pile, but for its increase with vertical loading (embankment surcharge), and stiffness of underlying stiff layer: α = 0.25 and 0.6 for a shallow, translating and rotating piles, respectively; α = 0.33–0.5 and 0.8–1.3 for a slide overlying a stiff layer concerning a uniform and a linearly increasing pressure, respectively; and α = 0.5–0.72 for moving clay under embankment loading.
• Ultimate state is well defined using the ratio of passive earth pressure coefficient over that of active earth pressure. The subgrade modulus for a large soil movement may be scaled from model tests.
• The normalised rotational stiffness is equal to 0.1–0.15 for the capped piles, which increases the pile displacement with depth.

The three‐layer model solutions well predict nonlinear response of capped piles subjected to passive loading, which may be used for pertinent design. Copyright © 2016 John Wiley & Sons, Ltd.     

Analysis of laterally loaded piles with rectangular cross sections embedded in layered soil

An analysis is developed to determine the response of laterally loaded rectangular piles in layered elastic media. The differential equations governing the displacements of the pile–soil system are derived using variational principles. Closed‐form solutions of pile deflection, the slope of the deflected curve, the bending moment and the shear force profiles can be obtained by this method for the entire pile length. The input parameters needed for the analysis are the pile geometry and the elastic constants of the soil and pile. The new analysis allows insights into the lateral load response of square, rectangular and circular piles and how they compare. Copyright © 2007 John Wiley & Sons, Ltd.     

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。     

斜坡地基刚性桩水平承载力上限分析

为探讨斜坡地基刚性桩水平极限承载力的计算方法，介绍柔性桩的等效刚性桩有效嵌入深度并引入极限水平地基反力分布形式。根据荷载指向坡外及坡内两种情况，提出适用于斜坡地基桩前土体的两种极限破坏模式。然后，基于极限分析上限定理，推导出两种荷载方向下的刚性桩极限承载力，并引入多组现场试验，验证了理论方法的合理性。探讨了边坡坡角、内摩擦角、黏聚力及荷载方向对极限承载力的影响，得出了一些规律性结论，并基于以上分析结果，提出斜坡地基刚性桩水平极限承载力随坡角变化的拟合公式。这些分析为斜坡地基上基桩设计提供了一定的参考，具有理论及工程应用价值。     

基于传递矩阵法的层状土中管桩水平动力阻抗分析

在考虑土体分层特性的基础上,分别建立了管桩桩周土体和桩芯土体的水平振动控制方程。通过引入势函数并考虑桩周土和桩芯土径向位移和环向位移的边界条件及其奇偶性,求得了管桩-土动力相互作用的刚度系数和阻尼系数。将土体模拟为连续分布的弹簧-阻尼器,并考虑桩芯土和桩周土的作用,建立了层状土中管桩的水平振动方程。借助初参数法和传递矩阵法求解了管桩的水平振动,得到了管桩桩顶的水平动力阻抗。通过数值分析,得到了土层剪切模量、管桩壁厚、桩周土和桩芯土剪切模量比、土层厚度等对管桩桩顶动力阻抗的影响规律。土层剪切模量、管桩壁厚、桩周土和桩芯土剪切模量比对层状土中管桩水平振动的影响主要在低频处,土层厚度在较宽的频率范围内对管桩水平振动有影响;管桩壁越厚,桩周土的剪切模量越大时,管桩水平动力阻抗的绝对值越大。     

砂土中考虑冲刷的水平受荷桩等效应变楔方法

冲刷引起桩周土体的损失,研究冲刷效应对桩基水平承载特性的影响非常必要。基于桩前土体楔形受力的应变楔方法可以推导桩侧p-y曲线,进而分析水平受荷桩的受力变形特性,但只适于地表水平的情况。基于冲刷坑坑底以上土体的自重荷载对楔形体的开展范围进行深度等效,建立了冲刷条件下砂土中水平受荷桩的等效应变楔方法。通过与文献对比,验证了该方法的可行性。研究结果表明：冲刷深度增加,冲刷坑底宽度增大及冲刷坡角减小均会降低桩基水平承载性能。与仅考虑冲刷引起的桩侧极限抗力削弱的简化方法相比,本研究得到的桩基最大弯矩偏小。将冲刷坑底以上土层全部剥蚀的做法,忽略了冲刷深度内的土层作用,计算结果会偏于保守。     

Method of initial parameters for laterally loaded piles embedded in layered soils

The method of initial parameters (MIP) was originally developed to solve the problem of a beam on an elastic foundation with applied concentrated forces along the span, which introduce discontinuities in the mathematical formulation of the problem. MIP is modified in this paper so that it can be used for solving the problem of a laterally loaded pile with discontinuities due to soil layering along the length of the pile. In this paper, the basis of MIP is outlined, and its use to find the deflection, slope, bending moment and shear force of laterally loaded piles is illustrated. Example problems of laterally loaded piles embedded in multi-layered soil media are provided.     

软土地基中PHC管桩水平受荷性状的试验研究

桩在水平荷载作用下的受力性状是一个复杂的桩土相互作用过程。针对软土地集中预应力管桩受水平荷载的问题,结合工程实例,通过水平静载试验,实测得到了水平荷载作用下PHC（超长预应力）桩与土共同作用时的工作性状,分析了PHC桩受水平力作用时的内力、变形和临界承载力以及地基土的水平抗力比例系数。试验结果可为今后同类地区水平受荷桩的设计与研究提供参考。