单桩横向非线性动力响应简化分析方法研究
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摘要
地震运动过程中，地基土-桩基础的横向动力相互作用，分别称为
桩基础的横向惯性响应和运动地震响应。关于桩基础横向动力响应的简
化分析方法，大多数采用基于线粘弹性假设的动力Winkler地基梁模型
(动力p-y曲线法)。不过，线性分析仅局限于小位移梯度，而在强烈的
地震运动过程中，由于应力集中，桩周土将产生较大的非线性应力场和
位移场，导致土-桩界面分离，桩基础的动力响应，也将呈现强烈的非
线性。因此，在线弹性动力学理论框架下建立的简化分析方法，不能满
意地描述桩基础的动力学响应。本文主要研究单桩横向非线性动力响应
问题。首先，利用有限元分析软件ANSYS，构造了一个能够反映非线性
因素影响的三维有限元模型，利用该模型，较为全面地研究了不同荷载
作用下的单桩横向非线性动力响应，详细讨论了各种几何、物理参数和
非线性因素对单桩横向非线性动力响应的影响。其次，根据数值模拟分
析结果和地震运动过程中地基土-桩基础-上部结构系统动力相互作用
的基本特征，采用描述迟滞非线性系统本构关系的Bouc-Wen模型，在
Winkler-Kelvin地基模型的基础上，建立了一个新的、能够考虑各种非线
性因素影响的、研究单桩横向非线性动力响应的简化分析模型。该模型
采用非线性Winkler-Kelvin地基模型，将复杂的地基土-单桩动力相互
作用的三维问题，简化为一维问题，即，地基土对桩轴的横向非线性作
用力， 由随深度均匀分布的水平非线性弹簧模拟，非线性弹簧恢复力由
退化的Bouc-Wen模型描述；地基土中由于能量耗散和内部摩擦而产生的
幅射阻尼和材料阻尼，由与水平非线性弹簧并联的粘壶表示。该模型能
够反映动力荷载作用下，桩周土的屈服、滞后性、变形积累、强度和刚
度退化等材料非线性，以及土-桩界面分离等状态非线性，对单桩横向
动力响应的影响，可以较好地描述桩周土由弹性变形到塑性变形的整个
非线性变形过程。该模型适用于不同的地质条件，计算参数都为土力学
参数，可以利用现行的设计规范、通过拟合准静态单调加载或循环加载
现场试验数据曲线，加以确定和校准。最后，利用该简化分析模型、相
关的计算方法、以及运动响应因子的概念，分别研究了单桩横向非线性
惯性响应和非线性运动地震响应问题，并进一步讨论了各种系统参数和
非线性因素的影响。计算结果表明，本文建立的简化分析模型，能够有
单桩横向非线性动力响应简化分析方法研究
效地模拟单桩横向非线性动力响应问题。
关键词:工程结构;单桩横向非线性动力响应;有限元;B。uc一Wen模型;
简化分析;惯性响应;运动响应
The lateral dynamic responses of pile-foundation in the earthquake are generally divided into lateral inertial response and kinematic seismic response. Most of the simplified analysis methods for dynamic responses of pile-foundation adopt the dynamic Winkler foundation models (the dynamic p~y curves methods) based on the linear visco-elastic hypothesis. However, the linear analysis is only within the limits of the small displacement gradient, whereas nonlinear stress- and displacement-field in the vicinity of the pile will be generated due to stress concentration and the interface of the soil-pile leaded to separation and the dynamic response of pile-foundation also presented intense non-linearity in the strong seismic motion. Therefore, the simplified analysis methods based on the linear visco-elastic dynamic theories cannot satisfactorily describe the nonlinear dynamic responses of pile-foundation. Responses of the lateral nonlinear dynamics of single piles are studied in this dissertation. First, a 3-D finite element model, which can reflects a lot of influences of the non-linear factors, is constructed using a large finite element analysis software ANSYS. With this model, this dissertation gives a relatively complete analysis the lateral nonlinear dynamic responses of the single piles and has a comparative detailed discussion about the influences resulted from the geometrical and physical parameters and the nonlinear factors over the lateral nonlinear dynamic responses of single piles. Second, Based on the predicted results of the 3-D finite element numerical simulation and the principal characteristics of the dynamic interactions of the soil-pile foundation-superstructure system, using the basic theory of the random vibration for the hysteretic nonlinear systems, e.g. Bouc-Wen model, a newer simplified model which can be truthfully reflect the main characteristics of the lateral nonlinear dynamic responses of the single piles is established. The nonlinear Winkler-Kelvin sub-grade model is adopted in this simplified model and the complicated 3-D problems of the soil-single piles dynamic interaction are simplified to the 1-D, that is to say, the lateral nonlinear acting force of the soil to the pile shift is simulated with the
horizontal nonlinear springs which have the continuous uniform distribution, while the nonlinear spring restoring force is described by the deteriorated Bouc-Wen model; the radiation damping and material damping due to the energy dissipation and inner friction in the soil are displayed with the dashpots which are in parallel with the horizontal nonlinear springs. The influences of the material non-linearity, such as, the yielding, the hysteretic effects, the mechanical property deterioration of the soil surrounding the piles, and state non-linearity, such as no continuous conditions of the soil-pile interface, etc, on the behaviors of the lateral dynamics of the single piles are taken into consideration in this model. The whole process of the nonlinear deformation from elastic to plastic of the soil surrounding the pile can also be described with this simplified model. The simplified model is applicable in various geological conditions. Only two model parameters have to be calibrated by fitting experimental data and using current design codes. Finally, with the developed methods, calibrated model and the concepts of the kinematic response factors, the lateral nonlinear inertial responses and kinematic seismic responses of the single piles are studied respectively. It is also studied that the influences of various kinds of the systematic parameters and nonlinear factors over the lateral dynamic responses of the single piles. The predicted results show that the simplified model developed in this dissertation can simulate the lateral nonlinear dynamic responses of single piles effectively.
桩基础的横向惯性响应和运动地震响应。关于桩基础横向动力响应的简
化分析方法，大多数采用基于线粘弹性假设的动力Winkler地基梁模型
(动力p-y曲线法)。不过，线性分析仅局限于小位移梯度，而在强烈的
地震运动过程中，由于应力集中，桩周土将产生较大的非线性应力场和
位移场，导致土-桩界面分离，桩基础的动力响应，也将呈现强烈的非
线性。因此，在线弹性动力学理论框架下建立的简化分析方法，不能满
意地描述桩基础的动力学响应。本文主要研究单桩横向非线性动力响应
问题。首先，利用有限元分析软件ANSYS，构造了一个能够反映非线性
因素影响的三维有限元模型，利用该模型，较为全面地研究了不同荷载
作用下的单桩横向非线性动力响应，详细讨论了各种几何、物理参数和
非线性因素对单桩横向非线性动力响应的影响。其次，根据数值模拟分
析结果和地震运动过程中地基土-桩基础-上部结构系统动力相互作用
的基本特征，采用描述迟滞非线性系统本构关系的Bouc-Wen模型，在
Winkler-Kelvin地基模型的基础上，建立了一个新的、能够考虑各种非线
性因素影响的、研究单桩横向非线性动力响应的简化分析模型。该模型
采用非线性Winkler-Kelvin地基模型，将复杂的地基土-单桩动力相互
作用的三维问题，简化为一维问题，即，地基土对桩轴的横向非线性作
用力， 由随深度均匀分布的水平非线性弹簧模拟，非线性弹簧恢复力由
退化的Bouc-Wen模型描述；地基土中由于能量耗散和内部摩擦而产生的
幅射阻尼和材料阻尼，由与水平非线性弹簧并联的粘壶表示。该模型能
够反映动力荷载作用下，桩周土的屈服、滞后性、变形积累、强度和刚
度退化等材料非线性，以及土-桩界面分离等状态非线性，对单桩横向
动力响应的影响，可以较好地描述桩周土由弹性变形到塑性变形的整个
非线性变形过程。该模型适用于不同的地质条件，计算参数都为土力学
参数，可以利用现行的设计规范、通过拟合准静态单调加载或循环加载
现场试验数据曲线，加以确定和校准。最后，利用该简化分析模型、相
关的计算方法、以及运动响应因子的概念，分别研究了单桩横向非线性
惯性响应和非线性运动地震响应问题，并进一步讨论了各种系统参数和
非线性因素的影响。计算结果表明，本文建立的简化分析模型，能够有
单桩横向非线性动力响应简化分析方法研究
效地模拟单桩横向非线性动力响应问题。
关键词:工程结构;单桩横向非线性动力响应;有限元;B。uc一Wen模型;
简化分析;惯性响应;运动响应
The lateral dynamic responses of pile-foundation in the earthquake are generally divided into lateral inertial response and kinematic seismic response. Most of the simplified analysis methods for dynamic responses of pile-foundation adopt the dynamic Winkler foundation models (the dynamic p~y curves methods) based on the linear visco-elastic hypothesis. However, the linear analysis is only within the limits of the small displacement gradient, whereas nonlinear stress- and displacement-field in the vicinity of the pile will be generated due to stress concentration and the interface of the soil-pile leaded to separation and the dynamic response of pile-foundation also presented intense non-linearity in the strong seismic motion. Therefore, the simplified analysis methods based on the linear visco-elastic dynamic theories cannot satisfactorily describe the nonlinear dynamic responses of pile-foundation. Responses of the lateral nonlinear dynamics of single piles are studied in this dissertation. First, a 3-D finite element model, which can reflects a lot of influences of the non-linear factors, is constructed using a large finite element analysis software ANSYS. With this model, this dissertation gives a relatively complete analysis the lateral nonlinear dynamic responses of the single piles and has a comparative detailed discussion about the influences resulted from the geometrical and physical parameters and the nonlinear factors over the lateral nonlinear dynamic responses of single piles. Second, Based on the predicted results of the 3-D finite element numerical simulation and the principal characteristics of the dynamic interactions of the soil-pile foundation-superstructure system, using the basic theory of the random vibration for the hysteretic nonlinear systems, e.g. Bouc-Wen model, a newer simplified model which can be truthfully reflect the main characteristics of the lateral nonlinear dynamic responses of the single piles is established. The nonlinear Winkler-Kelvin sub-grade model is adopted in this simplified model and the complicated 3-D problems of the soil-single piles dynamic interaction are simplified to the 1-D, that is to say, the lateral nonlinear acting force of the soil to the pile shift is simulated with the
horizontal nonlinear springs which have the continuous uniform distribution, while the nonlinear spring restoring force is described by the deteriorated Bouc-Wen model; the radiation damping and material damping due to the energy dissipation and inner friction in the soil are displayed with the dashpots which are in parallel with the horizontal nonlinear springs. The influences of the material non-linearity, such as, the yielding, the hysteretic effects, the mechanical property deterioration of the soil surrounding the piles, and state non-linearity, such as no continuous conditions of the soil-pile interface, etc, on the behaviors of the lateral dynamics of the single piles are taken into consideration in this model. The whole process of the nonlinear deformation from elastic to plastic of the soil surrounding the pile can also be described with this simplified model. The simplified model is applicable in various geological conditions. Only two model parameters have to be calibrated by fitting experimental data and using current design codes. Finally, with the developed methods, calibrated model and the concepts of the kinematic response factors, the lateral nonlinear inertial responses and kinematic seismic responses of the single piles are studied respectively. It is also studied that the influences of various kinds of the systematic parameters and nonlinear factors over the lateral dynamic responses of the single piles. The predicted results show that the simplified model developed in this dissertation can simulate the lateral nonlinear dynamic responses of single piles effectively.
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