液化场地桩—土动力相互作用p-y曲线模型研究
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摘要
场地液化是导致桩基桥梁震害的重要原因之一。液化场地桩一土动力相互作用研究是解决液化场地桩基桥梁抗震问题的有效途径。动力p-y曲线分忻方法作为研究桩一土动力相互作用的一个重要方法，为发展基于变形的液化场地桥梁桩基抗震设计方法提供了一般性的技术思路。但是，该法用于液化场地桩土动力相互作用分析的关键在于合理确定砂土动力p—y曲线。然而，已有研究工作更多集中于如何基于砂土的标准静力p-y曲线构建考虑液化效直的p-y曲线，用于实际设计尚缺乏充分的试验与理论依据。事实上，尽管地震中场地未完全液化，但是砂土的力学性能因孔压上升而发生很大变化。如今，对两个重要问题尚缺乏系统研究：其一为如何定量确定液化场地桩一土动力相互作用p-y属性，其二为液化场地桩一土动力相互作用分析中如何合理考虑不同孔压比下砂土p-y曲线属性。
鉴于上述，本文针对液化场地桩一土动力相互作用p-y曲线的构建方法问题，通过振动台试验且理论分忻相结合，研究可靠的建立液化场地桩一土动力相互作用p-y曲线的技术方法和引入p-y曲线简化模型的液化场地桩一土动力相互作用三维有限元分析方法。同时，考察液化场地桩一土动力相互作用p-y曲线的主要影响因素，提出了基于动力p-y曲线构建其骨干线的修正方法，给出了场地液化前、后砂土p-y曲线简化模型，发展了液化场地桩一土动力相互作用简化分析方法。本文主要研究工作与取得的若干认识如下：
(1)采用钢筋混凝土单桩一柱墩基础型式，针对表层覆盖粘土层的液化场地，选用输入正弦波的加载方式，成功完成了考虑幅值、频率变化的正弦波输入下液化场地桩一土动力相互作用振动台试验。对同一试验体进行间隔24小时的两次试验，获得了试验开始时地基砂层两种不同相对密度的试验结果(第一次试验的地基砂土为中密砂层，第一次试验结束静置24小时进行第二次试验，第二次试验的地基砂土为密砂层)，据此研究了地基中密砂层和密砂层孔压累积过程中液化场地桩一土动力相互作用的机理与规律，归纳了中密砂层和密砂层两种不同场地条件下土层液化的动力特性与桩基桥梁结构动力反应规律，特别剖析了不同相对密度的砂土层对地基、桩基桥梁结构动力的显著影响效应，并为建立考虑砂土中孔压累计过程的液化场地桩一土动力相互作用p-y曲线提供了必要的试验数据。
(2)直接针对振动台试验，基于梁的基本理论，提出了液化场地桩一土动力相互作用p-y曲线建立方法且给出了相应的验证，据此获得一系列不同振幅、频率的正弦波输入下中密砂和密砂动力p-y曲线，全面归纳了场地液化前、后中密砂和密砂动力p-y曲线的基本特征，初步分忻了孔压、动载频率、砂层相对密度等因素对动力p-y曲线的影响，研究发现了场地液化后中密砂动力p-y曲线出现上“凹”形式的典型特征且相应给出了其砂土液化物理意义的详细解释，并浅析了液化砂土p-y曲线形状对桩一土动力相互作用的影响。
(3)归纳了饱和砂土两相介质动力耦合作用的三种有限元分析模式，重新推导了u-p形式的控制方程矩阵形式与时间离散、空间离散的数值方法，并获得了三维有效直力动力分析的体系基本方程组。基于Opensees有限元数值模拟平台，直接针对振动台试验，采用推导的u-p形式控制方程的有限元实现形式，引入模拟循环荷载作用下饱和砂土液化动力特性、液化剪胀特性与粘土动力属性的多屈服面弹塑性本构模型，桩采用基于欧拉一伯努利梁理论建立的梁一柱单元模拟，桩一土动力相互作用采用考虑体积效应的刚性连接单元处理，建立试验受控条件下液化场地桩一土动力相互作用三维有限元分析模型与相应的计算方法。通过桩基桥梁结构动力反直、场地液化动力特性(特别是孔压)、液化对桩基和自由场地动力响直的影响、中密砂土的剪胀效应等数值模拟与振动台试验结果比较分忻，验证了建立的有限元分析模型与相应的计算方法的正确性，可以很好模拟砂土相对密度不同的液化场地桩一土动力相互作用。
(4)采用建立三维有限元分析模型与相应的计算方法，针对液化场地桩一土桥梁结构动力相互作用，输入正弦波进行反复的数值模拟，据此获得了不同幅值1Hz正弦波输入下液化场地桩一土动力相互作用p-y曲线，研究了孔压比、桩径、砂土相对密度等主要因素对砂土动力p-y曲线的影响情况。以0.2m桩径建立的三维有限元分析模型为基准，分段建立了不同孔压比下土反力的桩径影响因子与桩径之间经验公式。通过分时段考虑孔压比的途径，建立了对应各时段不同孔压比下砂土的动力p-y曲线簇，引入土的应力一应变关系曲线骨干线的构建思路，提出了以孔压比为基本控制参量的中密砂动力p-y曲线骨干线的修正方法。
(5)建立了不同孔压比下砂土动力p-y曲线骨干曲线簇初始刚度的经验公式。鉴于此，根据构建不同孔压比下砂土动力p-y曲线骨干曲线簇，分段建立了以孔压比为基本控制变量且能够体现场地液化前、后曲线形式转变的砂土p-y曲线简化模型，给出了具体的模型表达式与参数取值方法。考虑到工程设计的需要，选取API规范推荐的循环荷载作用下饱和砂土极限土反力作为简化模型的极限土反力。(6)根据对桩一土动力相互作用宏单元基本理论和构建宏单元力学元件的分析，得出液化场地桩一土动力相互作用宏单元中宜采用串联辐射阻尼形式且不宜采用裂缝单元组合形式的一般认识。鉴于此，通过弹簧单元、阻尼单元、塑性单元的合理组合，构建了液化场地桩一土动力相互作用分析的宏单元模型，给出了模型计算参数的合理确定方法与具体表达式，特别融入了新建砂土p-y曲线简化模型，很好考虑了砂土液化对桩一土动力相互作用土弹簧的影响。直接针对振动台试验，基于非线性文克尔地基梁模型，采用构建的宏单元模型，考虑桩周参振土的质量惯性力、上部结构的惯性力、土的辐射阻尼等效应，研究并建立了液化场地桩一土一桥梁结构动力相互作用简化分忻方法，通过振动台试验与有限元分忻方法验证了简化分忻方法的正确性，给出了简化分析方法的实施步骤。选用土的多屈服面塑性模型，饱和砂土采用u-p形式模拟的一维非线性有限元计算程序，实施自由液化场地动力分析，得到土层位移和孔压比时程作为数值分析模型外部输入。最后，采用简化分析方法，进行了桩径、桩土初始刚度比、上部结构配重等参数对液化场地桩一土动力相互作用影响的分忻，获得了若干重要认识，为实际桥梁桩基抗震设计提供一定参考。
Liquefaction is one of the main reasons of earthquake-induced damage to the pile-supported bridge. The study on dynamic pile-soil-structure interaction is the key to solve this problem in liquefying ground. Dynamic p-y curve method provides an effective way to investigate dynamic pile-soil interaction, and a technical approach to develop a base-displacement seismic design method for bridge pile foundation in liquefying ground. The most important step before application in analyzing dynamic pile-soil interaction is to determine the reasonable p-y curves of liquefying sand. However, the previous studies concern more about how to develop dynamic p-y curves for liquefying sand based on static p-y curve, which seems lack of experimental support and theoretical basis for seismic design. In fact, notwithstanding that the sand isn’t fully liquefied, the properties of sand have changed a lot as a result of the increase of pore pressure. At present, the following two questions need to be systematically researched: one is how to determine dynamic p-y properties of liquefying ground quantificationally, the other is how to consider the effect of pore pressure ratio on p-y curve for analyzing of pile-soil interaction in liquefying ground.
In view of the above-mentioned factors, the establishing procedure of p-y curves is proposed and three-dimensional finite element method (3D FEM) to investigate dynamic pile-soil interaction in liquefying ground based on shaking table tests. On the other side, the main factors affecting p-y curves are also studied and a modified method is proposed for the backbone curve of dynamic p-y curves, based on which it provided the modified model for pre-liquefaction and post-liquefaction and developed the modified dynamic pile-soil interaction model in liquefying ground. The main content and understandings obtained are as follows:
Firstly, a series of large-scale shaking table tests for dynamic pile-soil-bridge structure interaction in liquefying ground were conducted successfully corresponding to liquefying ground covered with clay layer at surface and adopting reinforced concrete single pile-pier under sine waves with different amplitudes and frequencies. The same test had been conducted twice at the interval of 24 hours to obtain different conditions of relative density of sand. The sand was of medium-dense sand in the first test while it was dense sand in the second test. Based on the tests, the mechanism and the law of dynamic pile-soil interaction in liquefying ground are studied in the accumulation process of pore pressure in medium-dense sand and dense sand, this paper concluded the dynamic behavior of sand and pile foundation-supported bridge structure under two different ground conditions of medium-dense and dense sand, and specially analyzed the remarkable effect of different relative density sand on the dynamic behavior of pile foundation and bridge structure. Meanwhile, the tests provided the necessary test data for developing p-y curves of dynamic pile-soil interaction in liquefying ground in view of the accumulation process of pore pressure.
Secondly, the method of developing p-y curves of dynamic pile-soil interaction in liquefying ground was proposed and verified according to beam theory from the results of shaking table tests. A series of dynamic p-y curves of medium-dense and dense sand were obtained under sine waves with different amplitudes and frequencies. Based on the above results, this study comprehensively concluded the basic features of p-y curves in pre-liquefied and post-liquefied state and preliminarily analyzed the effects of pore pressure, dynamic load frequency and sand relative density on dynamic p-y curves, a concave-up form of p-y curve for the medium-dense sand in post-liquefied state was discovered, the detailed physical meanings of liquefaction were explained, subsequently, the effects of p-y curves form of liquefying sand on dynamic pile-soil interaction were discussed.
Thirdly, three finite element analysis models about dynamic coupling effect of saturated sand were summarized. Some governing equations of u-p formulation, and numerical method of time and spatial discrete were anew derived, and the basic equations group of 3D effective stress dynamic system were obtained. Based on OpenSees finite element numerical simulation platform, aiming at the finished shaking table tests, and adopting finite element manifestation of u-p formulation governing equation, a 3D finite element model and its solution approach was developed to investigate dynamic pile-soil interaction by introducing plastic multi-yield surface constitutive model which can take dynamic properties and shear dilatation of saturated sand and clay under cyclic loading into consideration. The pile linked with soil by rigid connector element, which could consider volume effect in the model, was simulated by beam-column element according to the theory of Euler-Bernoulli beam. The correctness of finite element model and calculation method was verified, according to the comparative analysis between numerical simulation and shaking table tests, including dynamic response of pile and bridge structure, dynamic characteristics especially pore pressure of liquefying ground, the effects of liquefaction on dynamic response of pile and free ground and the dilatation effect of medium-dense sand, which can effectively simulate pile-soil interaction in liquefying ground with different relative density.
Fourthly, a series of numerical simulation from 3D finite element analysis method were conducted under a series of sine waves to investigate dynamic pile-soils-bridge structure interaction and the effects of pore pressure ratio, pile diameter, relative density of sand on dynamic p-y curves in liquefying ground, obtaining some dynamic p-y curves under sine waves with different amplitudes and frequency of 1Hz. An impact factor formulation of pile diameter was established based on different pore pressure ratios relative to the response of 0.2m pile diameter from three-dimensional finite element method. A series of p-y curves corresponding to different pore pressure ratios were obtained by dividing pore pressure ratio time histories into several segments, and a modified method of backbone curves of dynamic p-y curves taking pore pressure ratio as a control factor was proposed by adopting the establishing approach for backbone curves of stress-strain curve.
Fifthly, an empirical formulation of initial stiffness of backbone curves cluster for dynamic p-y curves was provided under different pore pressure ratios. In light of the above-mentioned research, according to the backbone curve cluster of dynamic p-ycurves taking pore pressure ratio as the controlling variable, a simplified p-y curve model reflecting the form transformation of p-y curves between pre-liquefaction and post-liquefaction state was established piece-wisely, then the concrete expression of model and the evaluation technique of the parameters were presented. Besides, by considering the need of engineering design, the ultimate resistance of saturated sand under cyclic loading from API was selected as the ultimate resistance of simplified model.
Finally, it’s concluded that employing radiation damping in series rather than gap element in the macroelement will be better for dynamic pile-soil interaction via analyzing theory and mechanical components of macroelement. As for the above-mentioned conclusions, the macroelement of dynamic pile-soil interaction in liquefying ground was established by combining spring element, damping element and plasticity element reasonably, and by providing the calculation parameters and formulations. Herein, one thing to be noted was that the macroelement combines the new p-y model of medium-dense sand which well considered of the effects of liquefaction on soil springs in dynamic pile-soil interaction analysis. Through adopting the new-built macroelement, a simplified analysis method was investigated and established based on nonlinear Winkler foundation beam theory aiming at shaking table test, which considered the effect of lumped soil mass, inertial force from superstructure and radiation damping on dynamic response of the system. Finite element method was adopted to carry out numerical analysis and the reliability of the simplified model was verified by comparison between results from shaking table tests and calculations. Subsequently, the procedure of analyzing dynamic pile-soil interaction in liquefying ground was provided. A dynamic analysis of free liquefying ground was implemented based on the nonlinear finite element program which coupled fluid and solid for saturated sand in u-p formulation adopting multi-yield surface plastic constitutive model, the displacement and pore pressure ratio time histories obtained from numerical calculation were taken as the boundaries of the model. Finally, the effects of pile diameter, initial stiffness ratio between pile and soil and superstructure mass on dynamic pile-soil interaction was conducted by employing the proposed modified model, and some important understandings were obtained which aimed at providing significant reference for seismic design of bridge pile foundation.
鉴于上述，本文针对液化场地桩一土动力相互作用p-y曲线的构建方法问题，通过振动台试验且理论分忻相结合，研究可靠的建立液化场地桩一土动力相互作用p-y曲线的技术方法和引入p-y曲线简化模型的液化场地桩一土动力相互作用三维有限元分析方法。同时，考察液化场地桩一土动力相互作用p-y曲线的主要影响因素，提出了基于动力p-y曲线构建其骨干线的修正方法，给出了场地液化前、后砂土p-y曲线简化模型，发展了液化场地桩一土动力相互作用简化分析方法。本文主要研究工作与取得的若干认识如下：
(1)采用钢筋混凝土单桩一柱墩基础型式，针对表层覆盖粘土层的液化场地，选用输入正弦波的加载方式，成功完成了考虑幅值、频率变化的正弦波输入下液化场地桩一土动力相互作用振动台试验。对同一试验体进行间隔24小时的两次试验，获得了试验开始时地基砂层两种不同相对密度的试验结果(第一次试验的地基砂土为中密砂层，第一次试验结束静置24小时进行第二次试验，第二次试验的地基砂土为密砂层)，据此研究了地基中密砂层和密砂层孔压累积过程中液化场地桩一土动力相互作用的机理与规律，归纳了中密砂层和密砂层两种不同场地条件下土层液化的动力特性与桩基桥梁结构动力反应规律，特别剖析了不同相对密度的砂土层对地基、桩基桥梁结构动力的显著影响效应，并为建立考虑砂土中孔压累计过程的液化场地桩一土动力相互作用p-y曲线提供了必要的试验数据。
(2)直接针对振动台试验，基于梁的基本理论，提出了液化场地桩一土动力相互作用p-y曲线建立方法且给出了相应的验证，据此获得一系列不同振幅、频率的正弦波输入下中密砂和密砂动力p-y曲线，全面归纳了场地液化前、后中密砂和密砂动力p-y曲线的基本特征，初步分忻了孔压、动载频率、砂层相对密度等因素对动力p-y曲线的影响，研究发现了场地液化后中密砂动力p-y曲线出现上“凹”形式的典型特征且相应给出了其砂土液化物理意义的详细解释，并浅析了液化砂土p-y曲线形状对桩一土动力相互作用的影响。
(3)归纳了饱和砂土两相介质动力耦合作用的三种有限元分析模式，重新推导了u-p形式的控制方程矩阵形式与时间离散、空间离散的数值方法，并获得了三维有效直力动力分析的体系基本方程组。基于Opensees有限元数值模拟平台，直接针对振动台试验，采用推导的u-p形式控制方程的有限元实现形式，引入模拟循环荷载作用下饱和砂土液化动力特性、液化剪胀特性与粘土动力属性的多屈服面弹塑性本构模型，桩采用基于欧拉一伯努利梁理论建立的梁一柱单元模拟，桩一土动力相互作用采用考虑体积效应的刚性连接单元处理，建立试验受控条件下液化场地桩一土动力相互作用三维有限元分析模型与相应的计算方法。通过桩基桥梁结构动力反直、场地液化动力特性(特别是孔压)、液化对桩基和自由场地动力响直的影响、中密砂土的剪胀效应等数值模拟与振动台试验结果比较分忻，验证了建立的有限元分析模型与相应的计算方法的正确性，可以很好模拟砂土相对密度不同的液化场地桩一土动力相互作用。
(4)采用建立三维有限元分析模型与相应的计算方法，针对液化场地桩一土桥梁结构动力相互作用，输入正弦波进行反复的数值模拟，据此获得了不同幅值1Hz正弦波输入下液化场地桩一土动力相互作用p-y曲线，研究了孔压比、桩径、砂土相对密度等主要因素对砂土动力p-y曲线的影响情况。以0.2m桩径建立的三维有限元分析模型为基准，分段建立了不同孔压比下土反力的桩径影响因子与桩径之间经验公式。通过分时段考虑孔压比的途径，建立了对应各时段不同孔压比下砂土的动力p-y曲线簇，引入土的应力一应变关系曲线骨干线的构建思路，提出了以孔压比为基本控制参量的中密砂动力p-y曲线骨干线的修正方法。
(5)建立了不同孔压比下砂土动力p-y曲线骨干曲线簇初始刚度的经验公式。鉴于此，根据构建不同孔压比下砂土动力p-y曲线骨干曲线簇，分段建立了以孔压比为基本控制变量且能够体现场地液化前、后曲线形式转变的砂土p-y曲线简化模型，给出了具体的模型表达式与参数取值方法。考虑到工程设计的需要，选取API规范推荐的循环荷载作用下饱和砂土极限土反力作为简化模型的极限土反力。(6)根据对桩一土动力相互作用宏单元基本理论和构建宏单元力学元件的分析，得出液化场地桩一土动力相互作用宏单元中宜采用串联辐射阻尼形式且不宜采用裂缝单元组合形式的一般认识。鉴于此，通过弹簧单元、阻尼单元、塑性单元的合理组合，构建了液化场地桩一土动力相互作用分析的宏单元模型，给出了模型计算参数的合理确定方法与具体表达式，特别融入了新建砂土p-y曲线简化模型，很好考虑了砂土液化对桩一土动力相互作用土弹簧的影响。直接针对振动台试验，基于非线性文克尔地基梁模型，采用构建的宏单元模型，考虑桩周参振土的质量惯性力、上部结构的惯性力、土的辐射阻尼等效应，研究并建立了液化场地桩一土一桥梁结构动力相互作用简化分忻方法，通过振动台试验与有限元分忻方法验证了简化分忻方法的正确性，给出了简化分析方法的实施步骤。选用土的多屈服面塑性模型，饱和砂土采用u-p形式模拟的一维非线性有限元计算程序，实施自由液化场地动力分析，得到土层位移和孔压比时程作为数值分析模型外部输入。最后，采用简化分析方法，进行了桩径、桩土初始刚度比、上部结构配重等参数对液化场地桩一土动力相互作用影响的分忻，获得了若干重要认识，为实际桥梁桩基抗震设计提供一定参考。
Liquefaction is one of the main reasons of earthquake-induced damage to the pile-supported bridge. The study on dynamic pile-soil-structure interaction is the key to solve this problem in liquefying ground. Dynamic p-y curve method provides an effective way to investigate dynamic pile-soil interaction, and a technical approach to develop a base-displacement seismic design method for bridge pile foundation in liquefying ground. The most important step before application in analyzing dynamic pile-soil interaction is to determine the reasonable p-y curves of liquefying sand. However, the previous studies concern more about how to develop dynamic p-y curves for liquefying sand based on static p-y curve, which seems lack of experimental support and theoretical basis for seismic design. In fact, notwithstanding that the sand isn’t fully liquefied, the properties of sand have changed a lot as a result of the increase of pore pressure. At present, the following two questions need to be systematically researched: one is how to determine dynamic p-y properties of liquefying ground quantificationally, the other is how to consider the effect of pore pressure ratio on p-y curve for analyzing of pile-soil interaction in liquefying ground.
In view of the above-mentioned factors, the establishing procedure of p-y curves is proposed and three-dimensional finite element method (3D FEM) to investigate dynamic pile-soil interaction in liquefying ground based on shaking table tests. On the other side, the main factors affecting p-y curves are also studied and a modified method is proposed for the backbone curve of dynamic p-y curves, based on which it provided the modified model for pre-liquefaction and post-liquefaction and developed the modified dynamic pile-soil interaction model in liquefying ground. The main content and understandings obtained are as follows:
Firstly, a series of large-scale shaking table tests for dynamic pile-soil-bridge structure interaction in liquefying ground were conducted successfully corresponding to liquefying ground covered with clay layer at surface and adopting reinforced concrete single pile-pier under sine waves with different amplitudes and frequencies. The same test had been conducted twice at the interval of 24 hours to obtain different conditions of relative density of sand. The sand was of medium-dense sand in the first test while it was dense sand in the second test. Based on the tests, the mechanism and the law of dynamic pile-soil interaction in liquefying ground are studied in the accumulation process of pore pressure in medium-dense sand and dense sand, this paper concluded the dynamic behavior of sand and pile foundation-supported bridge structure under two different ground conditions of medium-dense and dense sand, and specially analyzed the remarkable effect of different relative density sand on the dynamic behavior of pile foundation and bridge structure. Meanwhile, the tests provided the necessary test data for developing p-y curves of dynamic pile-soil interaction in liquefying ground in view of the accumulation process of pore pressure.
Secondly, the method of developing p-y curves of dynamic pile-soil interaction in liquefying ground was proposed and verified according to beam theory from the results of shaking table tests. A series of dynamic p-y curves of medium-dense and dense sand were obtained under sine waves with different amplitudes and frequencies. Based on the above results, this study comprehensively concluded the basic features of p-y curves in pre-liquefied and post-liquefied state and preliminarily analyzed the effects of pore pressure, dynamic load frequency and sand relative density on dynamic p-y curves, a concave-up form of p-y curve for the medium-dense sand in post-liquefied state was discovered, the detailed physical meanings of liquefaction were explained, subsequently, the effects of p-y curves form of liquefying sand on dynamic pile-soil interaction were discussed.
Thirdly, three finite element analysis models about dynamic coupling effect of saturated sand were summarized. Some governing equations of u-p formulation, and numerical method of time and spatial discrete were anew derived, and the basic equations group of 3D effective stress dynamic system were obtained. Based on OpenSees finite element numerical simulation platform, aiming at the finished shaking table tests, and adopting finite element manifestation of u-p formulation governing equation, a 3D finite element model and its solution approach was developed to investigate dynamic pile-soil interaction by introducing plastic multi-yield surface constitutive model which can take dynamic properties and shear dilatation of saturated sand and clay under cyclic loading into consideration. The pile linked with soil by rigid connector element, which could consider volume effect in the model, was simulated by beam-column element according to the theory of Euler-Bernoulli beam. The correctness of finite element model and calculation method was verified, according to the comparative analysis between numerical simulation and shaking table tests, including dynamic response of pile and bridge structure, dynamic characteristics especially pore pressure of liquefying ground, the effects of liquefaction on dynamic response of pile and free ground and the dilatation effect of medium-dense sand, which can effectively simulate pile-soil interaction in liquefying ground with different relative density.
Fourthly, a series of numerical simulation from 3D finite element analysis method were conducted under a series of sine waves to investigate dynamic pile-soils-bridge structure interaction and the effects of pore pressure ratio, pile diameter, relative density of sand on dynamic p-y curves in liquefying ground, obtaining some dynamic p-y curves under sine waves with different amplitudes and frequency of 1Hz. An impact factor formulation of pile diameter was established based on different pore pressure ratios relative to the response of 0.2m pile diameter from three-dimensional finite element method. A series of p-y curves corresponding to different pore pressure ratios were obtained by dividing pore pressure ratio time histories into several segments, and a modified method of backbone curves of dynamic p-y curves taking pore pressure ratio as a control factor was proposed by adopting the establishing approach for backbone curves of stress-strain curve.
Fifthly, an empirical formulation of initial stiffness of backbone curves cluster for dynamic p-y curves was provided under different pore pressure ratios. In light of the above-mentioned research, according to the backbone curve cluster of dynamic p-ycurves taking pore pressure ratio as the controlling variable, a simplified p-y curve model reflecting the form transformation of p-y curves between pre-liquefaction and post-liquefaction state was established piece-wisely, then the concrete expression of model and the evaluation technique of the parameters were presented. Besides, by considering the need of engineering design, the ultimate resistance of saturated sand under cyclic loading from API was selected as the ultimate resistance of simplified model.
Finally, it’s concluded that employing radiation damping in series rather than gap element in the macroelement will be better for dynamic pile-soil interaction via analyzing theory and mechanical components of macroelement. As for the above-mentioned conclusions, the macroelement of dynamic pile-soil interaction in liquefying ground was established by combining spring element, damping element and plasticity element reasonably, and by providing the calculation parameters and formulations. Herein, one thing to be noted was that the macroelement combines the new p-y model of medium-dense sand which well considered of the effects of liquefaction on soil springs in dynamic pile-soil interaction analysis. Through adopting the new-built macroelement, a simplified analysis method was investigated and established based on nonlinear Winkler foundation beam theory aiming at shaking table test, which considered the effect of lumped soil mass, inertial force from superstructure and radiation damping on dynamic response of the system. Finite element method was adopted to carry out numerical analysis and the reliability of the simplified model was verified by comparison between results from shaking table tests and calculations. Subsequently, the procedure of analyzing dynamic pile-soil interaction in liquefying ground was provided. A dynamic analysis of free liquefying ground was implemented based on the nonlinear finite element program which coupled fluid and solid for saturated sand in u-p formulation adopting multi-yield surface plastic constitutive model, the displacement and pore pressure ratio time histories obtained from numerical calculation were taken as the boundaries of the model. Finally, the effects of pile diameter, initial stiffness ratio between pile and soil and superstructure mass on dynamic pile-soil interaction was conducted by employing the proposed modified model, and some important understandings were obtained which aimed at providing significant reference for seismic design of bridge pile foundation.
引文
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