A New Nonlinear Hysteretic Rule for Winkler Type Soil-Pile Interaction Springs that Considers Loading Pattern Dependency

We propose a new hysteretic rule for p-y curves to be used in the dynamic analysis of deep foundations. We first examine the results of past lateral cyclic pile load experiments to clarify the characteristics that are to be modeled in the load transfer hystereses in p-y curves. We then undertake an analytical study of soil element behavior when subject to cyclic passive (compressive) and active (extensile) deformation. We found that the soil resistance intensity to piles varies with different cyclic loading patterns, as the stress-dilatancy behavior in soil varies with cyclic loading patterns. We developed a new hysteretic rule that satisfies the observed dominant characteristics. Although the proposed hysteretic rule has its background in the peak-oriented rule, it is further extended to be a function of the loading pattern. Numerical tests using the proposed model showed that the model is capable of reproducing observed differences in the behavior of piles subjected to fully-reversed cyclic loading and one-sided cyclic loading, even though the typical peak-oriented rules are unable to predict these outcomes.     

Effect of Slope on P-Y Curves Due to Surcharge Load

An extensive program of laboratory model tests was undertaken to study the effect of slope on p-y curves due to surcharge load in dry sand. The paper concerns the method developed in a series of laboratory model tests to experimentally determine p-y curves. Bending moment curves are differentiated by using curve fitting method of cubic polynomial function. The study includes effect of slope angle and relative density on bending moment, lateral soil resistance, lateral deflection and non-dimensional p-y curves. The non-dimensional p-y curves for piles on sloping ground under surcharge load are developed modifying API RP 2A (2000) method by including a Reduction Factor (R) using the experimental results.     

Deducing Pile Responses and Soil Reactions from Inclinometer Data of a Lateral Load Test

This paper presents a regressive model to deduce the internal forces and soil reactions of a laterally loaded test pile from the data of inclinometer measurements. This model simulates the distribution of bending moments of the pile by using a composite function of which the upper part is modeled by a polynomial and the lower part is modeled by the characteristic function of an analytical solution for a semi-infinite pile supported by uniform Winkler soil springs. Through successive regressive analyses, the optimal composite function obtained can effectively simulate the pile responses including the deflections, bending moments, shear forces, and the associated soil reactions. For verification, both the solution of a finite element analysis and the results of an in-situ load test have been adopted and the results of regressive analyses can satisfactorily obtain the pile responses. In addition, on the basis of curves of pile deflection and soil reaction deduced from the results of the pile test, a set of site-specific p-y curves can thus be established. Finally, a parametric study has shown that accurate estimate of moment-curvature relationship of a pile section is essential to the accuracy of the deduced pile internal forces, soil reactions, and p-y curves.     

海洋高桩基础水平单调及循环加载现场试验

开展了海洋软黏土中 2 根大直径高桩基础的现场水平单调和循环加载试验,实测获得了桩顶荷载 – 位移关系、桩身变形和桩身弯矩及桩侧土压力和孔隙水压力,揭示了水平单调和循环荷载作用下桩土相互作用规律及桩基水平位移和桩身弯矩发展规律。利用实测桩身水平位移推算了桩周土反力,在此基础上提出了相应的双曲线型 p – y 曲线,通过引进 Poulos 循环弱化模型建立了水平循环荷载作用下的桩基双曲线型 p – y 曲线分析模型,水平单调及循环荷载作用下桩顶荷载 – 位移关系、桩身变形和桩身弯矩及桩侧土压力等计算结果与实测值均吻合良好。通过现场试验发现规范 p – y 曲线法计算结果偏保守的主要原因是所采用的 p – y 曲线的刚度偏小;不同时段的循环荷载对桩基循环累积变形有叠加效应。 建议设计中应考虑桩基全寿命服役期内所承受的所有循环荷载的影响, 对于重要工程应开展相应的现场水平加载试验,实测桩身水平位移或桩身弯矩,进而利用所推算的桩周土反力来分析桩基受力变形及承载力。     

Influence mechanism of vertical-horizontal combined loads on the response of a single pile in sand

Pile foundations are used to support both vertical and horizontal loads in many geotechnical projects, such as the coastal and offshore engineering. The responses of piles under vertical-horizontal combined loading are separately analyzed and then superposed in current design practice. This simplified analysis approach does not take the coupling effect of the combined loads into consideration. The research on this topic is limited and the results reported to date are inconclusive with regard to the influence of vertical loads on the horizontal response of piles. In this paper, a series of centrifuge model tests under different vertical-horizontal combined loading conditions was performed to investigate the influence rules and mechanism of the combined loads on the response of piles in sand. The vertical load is shown to densify the soil near the pile and therefore decrease the horizontal displacement and bending moment of the pile: this is termed the “soil densification effect”. The vertical load induces an additional bending moment of the pile due to the lateral deformation of the pile: this is termed the “P-Δ effect”. The soil densification effect plays a dominant role in the early horizontal loading while the P-Δ effect is strengthened as the horizontal loads increases. These compound effect of these two seemingly opposing effects is a decrease in the bending moment of the pile decrease first then increase as the horizontal load increases. Additional settlement of the pile is caused by horizontal loading and isa positively correlated with the pre-vertical loads.     

Numerical investigation of the ultimate lateral resistance of piles in soft clay

The paper presents a numerical study on the undrained lateral response of a single, free-head, reinforced concrete pile in soft clays. Soil conditions simulating normally consolidated clays are examined—undrained shear strength increasing with depth—and the pile-soil interaction under static lateral loading is analyzed. The nonlinear p-y curves proposed in literature for soft clays are imported into a beam-on-nonlinear-Winkler-foundation simulation in order to predict the pile head lateral load—displacement curve and the distribution of the horizontal displacement and bending moment along the pile. The striking differences among these methods require further investigation via 3D finite element analyses. The determination of the ultimate soil resistance p _ult from the results of the finite element analyses aims at providing the estimation of a range of values for the ultimate soil resistance coefficient N _p with depth and the comparison of the derived values to the corresponding ones proposed by existing methodologies.     

砂土中大直径单桩水平受荷离心模型试验

大直径桩基在海洋工程中已越来越广泛应用。针对目前API规范p-y曲线对水平受荷大直径单桩的不适用性,通过离心模型试验研究了砂性土中大直径单桩分别在水平静力和循环荷载作用下的受力和变形特性。验证了通过实测桩身弯矩推算桩身变形和桩周土反力的有效性,分别获得了干砂和饱和砂的大直径单桩水平静力p-y曲线。在修正p-y曲线初始刚度的基础上,采用双曲线型p-y曲线分析了水平受荷大直径单桩的内力和变形。揭示了水平单向循环荷载下大直径单桩的桩身变形及内力变化特性,试验结果显示桩身变形和最大弯矩近似与循环次数的对数线性相关。最后,由各循环次数下的桩身弯矩获得了大直径单桩水平循环p-y曲线,提出了循环应力比相关的p-y曲线循环弱化因子,以及相应的桩基变形累积和内力变化分析方法。     

A multidirectional p–y model for lateral sand–pile interactions

The lateral loads applied to pile foundations, as induced by winds or earthquakes, are usually multidirectional. Experimental studies have indicated that the lateral resistance of the pile under multidirectional paths is generally lower than that under a unidirectional path and the degree of reduction depends on the characteristics of the loading paths. On the other hand, most currently used p–y models can take the soil–pile interaction under unidirectional lateral loading into account, but it cannot be applied directly to analyze the response of piles under multidirectional lateral loading. A multidirectional p–y model is proposed in this study, which is formulated within the framework of the bounding-surface elastoplastic theory and consists of two loading mechanisms: the parallel loading and the orthogonal loading. The model has five parameters, which are readily available or calibrated. To demonstrate its ability to model soil–pile interactions under both unidirectional and multidirectional lateral loadings, the proposed model is incorporated into a finite-element program to analyze laterally loaded piles. The responses of piles with different embedment lengths subject to various loading paths are investigated. The non-coaxial relationship between the force increment and the displacement increment vectors at the pile head under the multidirectional loading, and the impact of the multidirectional loading on the lateral resistance are well captured in the analyses.     

水平荷载作用下斜坡刚性桩非线性分析

在综合分析现有水平荷载作用下桩基分析方法的基础上,建立了考虑桩侧土体受力状态的斜坡刚性桩力学模型;根据极限平衡原理,建立横向荷载作用下斜坡刚性桩弯矩和应力平衡方程;引入考虑斜坡影响的p y曲线方法,提出了综合考虑桩侧土体极限承载力与水平抗力系数沿深度呈线性增加的侧向极限承载力与土体抗力承载力系数计算方法,同时,将该方法应用于计算实例,通过与已有有限元和理论计算方法对比分析,计算结果验证了本文方法的合理性与可行性;并利用该方法,分析了斜坡坡角、桩土接触面系数以及地基水平抗力系数对斜坡刚性桩承载特性的影响因素。分析表明:斜坡的坡角、桩土接触面系数对侧向荷载作用下斜坡刚性桩的荷载位移曲线影响明显,而桩侧土的抗力系数对侧向荷载作用下斜坡刚性桩的荷载位移曲线影响不明显。     

斜坡基桩的斜坡空间效应及其水平承载特性研究

为研究水平荷载作用下斜坡基桩的斜坡空间效应对其承载特性的影响,设计并完成了不同坡度及水平荷载作用角度下斜坡基桩室内模型试验,测得了桩顶荷载位移曲线及桩身弯矩分布。结果分析表明：水平荷载相同时,桩顶水平位移及桩身最大弯矩均随坡度增加呈非线性增大,随水平荷载作用角度增加而呈线性减小;基桩水平极限承载力却随坡度增加而减小,随水平荷载作用角度增加而增大。坡度每增加30°,桩顶水平位移约增大1.3~1.9倍,桩身最大弯矩增大约17%~30%;水平荷载作用角度每增加30°,桩顶水平变形减小约25%~30%,桩身最大弯矩减小约6%~11%。斜坡基桩的桩身最大弯矩位于地面以下3~6倍桩径范围内,坡度越大桩身最大弯矩位置越深。分析得到了基桩水平极限承载力拟合公式,可以为斜坡基桩设计提供参考。     

Construction and verification of a unified <Emphasis Type="Italic">p</Emphasis>–<Emphasis Type="Italic">y</Emphasis> curve for laterally loaded piles

Estimation of the lateral pile load capacity is the key design procedure for structures where lateral loads are predominant, such as bridges, tall buildings and offshore platforms. In the process of laterally loaded pile design, the p–y curve method is the mainstream method and preferred by designers compared to the elastic continuum or finite element analysis. The traditional p–y curves are derived from some specific field tests and limited data, which do not reflect the overall conditions. In this study, a unified p–y curve based on the stress increment perspective was constructed by introducing Vesic cavity expansion theory and considering the actual stress state of the surrounding soils. The proposed p–y curve combines the contributions of the expansion-induced soil radial stress increment, vertical stress increment and lateral soil resistance caused by deep pile rotation. To validate the proposed method, case examples of lateral pile load tests in various soil conditions were prepared and used to compare the p–y curves from the test results and proposed methods. The p–y curves calculated from the proposed method show reasonable agreement with measured results and give a good prediction in large deformation analysis.     

Seepage and Inertia Effect on Rate-Dependent Reaction of a Pile in Liquefied Soil

The seepage and inertia effects on the rate-dependent subgrade reaction of a single pile in liquefied soil are clarified through numerical studies. The quasi-static (for seepage effect) and dynamic (for inertia effect) numerical analyses are performed with a soil-water coupled formulation and a simplified cyclic elasto-plastic constitutive model for liquefied sand. The constitutive model can explicitly deal with the liquefaction intensity by changing the lower bounds of the mean effective stress. The liquefied soil at a certain depth around a pile is modeled with finite elements under a plane stress condition. The results of the quasi-static analyses under monotonic loading conditions show that the apparent rate-dependency of the subgrade reaction is caused by the seepage of pore water around the pile due to soil positive dilatancy under large strain range. The results of the dynamic analyses under cyclic loading conditions show that the positive correlation in a p-v (subgrade reaction-pile relative velocity) relation can be explained with the phase difference in movement between a pile and the neighboring soil around the pile due to inertia under small strain range.     

Nonlinear Analysis of Torsionally Loaded Pile Groups

An empirical approach is developed to analyze the nonlinear torsional behavior of free-standing pile groups with rigid pile caps. In this approach, the lateral and torsional responses of individual piles in a pile group are modeled by p-y and τ-θ curves; the interaction among lateral resistances of the individual piles is predicted through Mindlin's elastic solutions; the interactions between the torsional and lateral resistances of the individual piles are described through Randolph's solution; and the coupling effect of lateral resistance on torsional resistance of the individual piles is quantified using an empirical factor “β”. The proposed approach is capable of capturing the most significant aspects of pile-soil-pile interactions and coupling effect in pile groups subjected to torsion. The proposed approach is verified using results of centrifuge model tests. In general, the applied torque-twist angle response and the transfer of applied torque in pile groups can be reasonably well predicted and are sensitive to the pile group configuration.     

In-situ horizontal cyclic loading tests on composite foundation composed of soilbags and piles

The authors have been developing a new composite foundation composed of piles and soilbags. The foundation is characterized by the laying of soilbags between the pile heads and the footing on which a superstructure stands. The expected effect of the foundation is to cut off the fixed connection between the piles and the footing in order to reduce the bending moment of the piles and the response acceleration of the structure. In this study, in-situ horizontal cyclic loading tests were conducted on the proposed composite foundation with two piles to investigate the seismic response characteristics of the foundation at real scale. It was found from the tests that the horizontal force reached its peak due to the uplift of the footing during horizontal loading, and that larger hysteresis damping was obtained than that of spread foundations due to the hysteresis effect in the shear deformation of the soilbags. As for the sectional force of the piles and the vertical stress inside the soilbags, it was found that the axial force and bending moment of the piles concentrated on the pile on the front side in the loading direction, and that the vertical stresses inside the soilbags concentrated just above the pile head on the front side in the loading direction. Although residual horizontal displacement and settlement occurred due to the cyclic load, little damage to the soilbags was observed.     

On predicting displacement-dependent earth pressure for laterally loaded piles

This paper presents the derivation of a depth-dependent soil displacement model for laterally loaded piles for use in the calculation of displacement-dependent earth pressure. A set of fourth-order differential equations are proposed to compute the pile deflection profile along the pile length. The radial displacement of the soil due to pile movement can be evaluated based on the geometric compatibility requirements. The soil displacement pattern is then used in the earth pressure model to provide the pattern of earth pressure distributed around the pile circumference. The experimental data of the pile response, in terms of the p-y curves reported in the literature, are employed for a comparison with calculations from the proposed approach and other analytical models. The advantages of the developed calculation framework have been demonstrated, namely, that it can accurately reproduce the experimental measurements of soil reactions acting on a pile at different depths and that the influence of the pile installation can be taken into account. An illustrative example of cantilever sheet piles is finally provided to show the ability of the proposed method to analyse complicated problems.     

不平衡土压力对整体式桥台-H型钢桩-土体系力学性能影响试验

为研究不平衡土压力对整体式桥台-H型钢桩-土体系力学性能的影响,在已开展的不平衡土压力下整体式桥台-H型钢桩-土相互作用拟静力试验研究基础上,进一步开展了更大不平衡土压力(台后土表面均布荷载增大了3.81 kPa)下整体式桥台-H型钢桩-土相互作用拟静力试验研究,对比分析了更大不平衡土压力对桩身水平变形、桩侧土压力、应变和弯矩等方面的影响。结果表明:在试验条件下,更大不平衡土压力对桩身水平变形、土抗力、应变和弯矩的分布规律无影响; 正向加载时,更大不平衡土压力使得桩身累积变形的位置更深,桩侧最大土抗力和桩身弯矩增大; 负向加载时,更大不平衡土压力也使得桩身累积变形的位置更深和弯矩增大; 正向加载时,更大不平衡土压力使得累积变形减小,负向加载时则相反; 正向加载时LAHP模型的桩侧土抗力、应变和弯矩显著大于负向加载时的,正向加载时的最大桩侧土抗力和弯矩分别为负向加载时的2.2倍和2.1倍。     

Hysteretic behaviour of tubular joints under cyclic loading

This paper examines the cyclic performance of CHS joints used in steel tubular structures. Quasi-static experimental study into the response of eight T-joint specimens is described. Four of them are subjected to cyclic axial load, and the other four are subjected to cyclic in-plane bending. The general test arrangement, specimen details, and most relevant results (failure modes and load-relative deformation hysteretical curves) are presented. Some indexes to assess the seismic performance of tubular joints, including strength, ductility and energy dissipation, are synthetically analyzed and compared. Test results show that failure modes of axially loaded joints mainly contain weld cracking in tension and chord plastification in compression. But for joints under cyclic in-plane bending, both punching shear and chord plastification become regular failure modes accompanied by ductile fracture of the welds. Hysteretic curves take on a plump form in general. Ultimate strengths of joints are also compared with equation values for monotonic loading from various design codes. Results indicate the strength at a certain deformation limit can be regarded as the ultimate strength of a T-joint under cyclic loading and existing codes can be used to check it. It is also found that there is a significant distinction in the energy dissipation mechanism for tubular joints under different loading conditions. Finite element analyses are performed by taking into account weld geometry to facilitate the interpretation of the test results. It is identified that high tensile stress triaxiality can be one primary cause of weld cracking which happened under low cyclic load level.     

软黏土中导管架基础水平循环加载离心模型试验

为研究海上风机四腿导管架基础在风、浪等水平循环荷载作用下的受力及变形特性,开展了近海饱和软黏土地基四腿导管架基础水平循环加载离心模型试验。实测获得了水平循环荷载下导管架顶部的位移、基桩顶部的水平位移以及桩身弯矩,并利用实测桩身弯矩推导出桩身变形与桩周土反力。试验结果表明:水平循环荷载作用下导管架顶部的荷载–位移曲线表现出明显的非线性;后排桩的水平位移约为前排桩的80%,且均小于导管架顶部的水平位移,导管架发生了一定角度的倾斜;桩身最大弯矩值出现在泥面下约6D深度处。在此基础上,采用双曲正切型p–y曲线方法拟合试验结果并与API规范作对比,发现API规范p–y曲线的初始刚度和极限土反力均偏小。试验进一步揭示了泥面下5D深度范围内需考虑桩周土反力的弱化现象,且前排桩周土反力的弱化程度明显大于后排桩,在工程设计时应分开考虑下基桩桩周土的强度弱化情况。     

Analytical behaviour of concrete-filled double skin steel tubular (CFDST) beam-columns under cyclic loading

Concrete-filled double skin steel tubes (CFDST) have a great potential to be used in the construction of bridges and buildings. Limited information is available on the models for the moment (M) versus curvature (φ) response, and the lateral load (P) versus lateral displacement (Δ) relationship of these columns subjected to axial load and cyclically increasing flexural loading. A mechanics model is developed in this paper for CFDST beam-columns subjected to constant axial load and cyclically increasing flexural loading. The predicted cyclic responses for the composite columns are in good agreement with test results. Based on the theoretical model, parametric analysis was performed on the behaviours of moment (M) versus curvature (φ) response and lateral load (P) versus lateral displacement (Δ) relationship for the composite columns. Finally, simplified models for the moment (M) versus curvature (φ) response, and the lateral load (P) versus lateral displacement (Δ) relationship were suggested.     

考虑台后不平衡土压力下整体桥H型钢桩基-土相互作用内力计算方法

在台后填土作用下整体式桥台-H型钢桩-土相互作用和大不平衡土压力下(台后土表面均布荷载增大了3.81 kPa)整体式桥台-H型钢桩-土相互作用拟静力试验研究的基础上,提出了考虑台后不平衡土压力下整体桥桩基-土相互作用的内力计算方法,计算了整体桥台底弯矩和剪力以及桩身弯矩和剪力,并与现有的台后土压力理论和桥梁规范的计算值进行比较。结果表明:正向加载时,采用现有的台后土压力理论和桥梁规范计算得到的台底弯矩和剪力以及桩身弯矩和剪力均与试验结果存在较大偏差; 采用黄-林法可较准确地计算AHP模型的台底弯矩和剪力以及桩身弯矩和剪力; 对于LAHP模型,试验值均与各理论计算值相差较大; 正向加载时,随着位移荷载的增加,AHP和LAHP模型的台底和桩身弯矩均逐渐增大; 台后堆载(大不平衡土压力)对整体桥台底剪力和弯矩以及桩身的剪力和弯矩产生较大的影响,LAHP模型的台底和桩身弯矩整体上均大于AHP模型的,而LAHP模型的台底剪力小于AHP模型的,桩身剪力大于AHP模型的。