考虑三维波动的饱和土中桩纵向耦合振动理论
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摘要
桩纵向振动理论是动力机器基础设计、桩基抗震设计、基桩动力检测等工作的理论基础。迄今为止，这一理论已经历了近四十年的研究发展，取得了较为丰富的成果，但与工程应用的要求相比，仍存在很多问题，其中一个重要方面是以往关于土中孔隙水对桩振动特性的影响研究甚少。在这一背景下，本文考虑了饱和土的三维波动效应，采用解析方法对三维轴对称成层饱和土中完整桩及各类变阻抗桩的纵向耦合振动理论进行系统研究。主要工作包括：
1、单层饱和土中完整桩纵向振动理论研究。建立饱和土中端承桩和摩擦桩在任意激振力作用下的理论模型，利用位移势函数及微分算子分解方法，得到饱和土层Biot动力固结方程的分离变量解。进而根据桩土动力耦合作用，得到了饱和土中桩纵向振动频域解析解和时域响应半解析解。然后利用上述解析解分析了饱和土层复阻抗，并从饱和土波动理论出发，建立了桩纵向振动引起的饱和土层振动模式，剖析了辐射阻尼产生机理，研究了桩纵向振动引起的饱和土层中剪应力及孔隙水压力分布。对影响桩振动特性的主要因素进行了分析，结果表明，长径比、桩土模量比及桩底支承系数对桩的动力响应影响显著，而渗透系数作为饱和土的一个重要参数，由于荷载作用时间问题，对桩的动力响应影响较小。
2、根据Rayleigh-Love杆理论，计及桩身的径向变形，研究了饱和土中考虑横向惯性效应的大直径嵌岩桩纵向耦合振动理论，分别在考虑与不考虑横向惯性效应下，比较了大直径桩纵向振动的特性。研究表明，长径比越小，两者区别越显著，同样条件下，前者的时域底反峰值小于后者，且对激振频率有依赖性，频率越高，底反峰值越小，而后者不能反映这一现象。
3、建立了饱和土中忽略径向运动影响的简化模型，得到简化模型下桩土纵向耦合振动解析解，并与考虑径向运动影响的模型及胡昌斌的模型加以比较，分析了几种模型的异同及适用性。结果表明，在低频范围内考虑径向运动的解与简化解有较大差别，而在较高频率下两者基本吻合。因此在基础动力设计中应采用较为严格的解，对基桩动测则可以采用简化理论。
4、成层土中变阻抗桩纵向振动理论研究。基于土层层问相互作用，提出了饱和成层土中任意变阻抗桩的纵向振动问题简化层间模型，利用单层土中提出的解析方法，基于这一简化层间模型，求得饱和成层土中任意段变阻抗桩的桩顶频域解析解和时域响应半解析解，并论证了模型的合理性。基于所得解，对饱和成层土中的完整桩及各类变阻抗桩的振动特性进行了分析。研究表明，不仅桩身变阻抗特性会对桩的动力响应产生影响，土层参数的变化也会产生相应的影响。
本文通过建立桩与饱和土层纵向祸合振动模型及其解析解，深入剖析了土中孔隙
水的存在对桩土藕合振动的影响，进一步完善了基桩振动理论，为桩基抗震设计及完
整性检测的反演提供了更加严格的理论支持。
The dynamic soil-pile interaction has been a subject of considerable interest in past four decades. The theory of pile longitudinal vibration investigates dynamic responses of pile under vertical loads. It finds its applications in machinery foundations, pile driving and structures exposed to seismic excitation. And it is also the basis of any kinds of methods in dynamic pile testing. Although many soil-pile interaction models have been developed using a variety of analytical and numerical techniques, how to model soil layer accurately is still a major difficult in pile dynamics. Based on 3D axis-symmetrical soil model and the theory of saturated porous medium originally presented by Biot, an integral pile and pile with variable impedance embedded in layered saturated soil are analytically studied in this dissertation. The principal work includes four items.
Firstly, dynamic interactions between an integral pile and saturated soil are studied. A dynamic interaction schematic of an end bearing or elastic bearing pile with arbitrary force at pile top is founded. By using Helmholtz resolution and the operator decomposition method, Biot's equations governing motions of a porous solid saturated with interstitial fluid are decoupled. Then the rigorous solutions for soil layer vibration are analytically derived by virtue of the separation of variables. By means of the orthogonal expansion technique, the coupling system solutions are finally obtained. Then the dynamic model of saturated soil layer caused by pile longitudinal vibration is founded. Incorporated wave propagations into saturated soil layer, the characteristics of soil resistance factor and the mechanism of the radial damping are analyzed, as well as distributions of shear stress and pore pressure in saturated soil caused by pile vibration. Meanwhile, dynamic responses at pile head are investigated. It is sh
own that the effects of pile slenderness, bearing stiffness of pile toe and the pile-soil modulus ratio on pile impedance are major whereas the ones of the permeability and the soil reaction coefficient are minor.
Secondly, on the basis of the theory of Rayleigh-Love bar, the longitudinal vibration of a large diameter end-bearing pile in saturated soil is investigated considering transverse inertial effect. The vibration of pile considering transverse inertial effect is different from the one not considering this effect significantly at a smaller slenderness. Under the same conditions, the reflective peak of pile toe in time domain in the former is smaller than in
the latter and decreases gradually with the increase of exciting frequencies.
Thirdly, a simplified model neglecting the radial displacement of saturated soil is established and an analytical solution for vertical vibration of the soil-pile system is obtained. By comparison the solution with available viscoelastic solution, the differences are illustrated as well as its applications. The results show that there is significant difference between the solution considering and neglecting the radial displacement at lower frequencies but they are identical at higher ones. So, it is suitable to use the former for aseismic design of pile foundation but the latter for dynamic pile testing.
Finally, dynamic compliances of a pile with variable impedance embedded in layered saturated soil are studied. A simplified layered model is put forward on the basis of the single layer elastic bearing model. By using the same method, analytical solutions in frequency domain hence semi-analytical solutions in time domain representing the dynamic responses at pile head are obtained. By comparison with the single layer solution, the rationality of layered model is verified. Based on these solutions, the dynamic responses of integral pile and pile with various impedances are investigated. The results show that not only variations of pile impedance but also parameters of soil layer can make effects on the dynamic compliances at pile head.
The coupled soil-pile dynamic interaction model and the corresponding
1、单层饱和土中完整桩纵向振动理论研究。建立饱和土中端承桩和摩擦桩在任意激振力作用下的理论模型，利用位移势函数及微分算子分解方法，得到饱和土层Biot动力固结方程的分离变量解。进而根据桩土动力耦合作用，得到了饱和土中桩纵向振动频域解析解和时域响应半解析解。然后利用上述解析解分析了饱和土层复阻抗，并从饱和土波动理论出发，建立了桩纵向振动引起的饱和土层振动模式，剖析了辐射阻尼产生机理，研究了桩纵向振动引起的饱和土层中剪应力及孔隙水压力分布。对影响桩振动特性的主要因素进行了分析，结果表明，长径比、桩土模量比及桩底支承系数对桩的动力响应影响显著，而渗透系数作为饱和土的一个重要参数，由于荷载作用时间问题，对桩的动力响应影响较小。
2、根据Rayleigh-Love杆理论，计及桩身的径向变形，研究了饱和土中考虑横向惯性效应的大直径嵌岩桩纵向耦合振动理论，分别在考虑与不考虑横向惯性效应下，比较了大直径桩纵向振动的特性。研究表明，长径比越小，两者区别越显著，同样条件下，前者的时域底反峰值小于后者，且对激振频率有依赖性，频率越高，底反峰值越小，而后者不能反映这一现象。
3、建立了饱和土中忽略径向运动影响的简化模型，得到简化模型下桩土纵向耦合振动解析解，并与考虑径向运动影响的模型及胡昌斌的模型加以比较，分析了几种模型的异同及适用性。结果表明，在低频范围内考虑径向运动的解与简化解有较大差别，而在较高频率下两者基本吻合。因此在基础动力设计中应采用较为严格的解，对基桩动测则可以采用简化理论。
4、成层土中变阻抗桩纵向振动理论研究。基于土层层问相互作用，提出了饱和成层土中任意变阻抗桩的纵向振动问题简化层间模型，利用单层土中提出的解析方法，基于这一简化层间模型，求得饱和成层土中任意段变阻抗桩的桩顶频域解析解和时域响应半解析解，并论证了模型的合理性。基于所得解，对饱和成层土中的完整桩及各类变阻抗桩的振动特性进行了分析。研究表明，不仅桩身变阻抗特性会对桩的动力响应产生影响，土层参数的变化也会产生相应的影响。
本文通过建立桩与饱和土层纵向祸合振动模型及其解析解，深入剖析了土中孔隙
水的存在对桩土藕合振动的影响，进一步完善了基桩振动理论，为桩基抗震设计及完
整性检测的反演提供了更加严格的理论支持。
The dynamic soil-pile interaction has been a subject of considerable interest in past four decades. The theory of pile longitudinal vibration investigates dynamic responses of pile under vertical loads. It finds its applications in machinery foundations, pile driving and structures exposed to seismic excitation. And it is also the basis of any kinds of methods in dynamic pile testing. Although many soil-pile interaction models have been developed using a variety of analytical and numerical techniques, how to model soil layer accurately is still a major difficult in pile dynamics. Based on 3D axis-symmetrical soil model and the theory of saturated porous medium originally presented by Biot, an integral pile and pile with variable impedance embedded in layered saturated soil are analytically studied in this dissertation. The principal work includes four items.
Firstly, dynamic interactions between an integral pile and saturated soil are studied. A dynamic interaction schematic of an end bearing or elastic bearing pile with arbitrary force at pile top is founded. By using Helmholtz resolution and the operator decomposition method, Biot's equations governing motions of a porous solid saturated with interstitial fluid are decoupled. Then the rigorous solutions for soil layer vibration are analytically derived by virtue of the separation of variables. By means of the orthogonal expansion technique, the coupling system solutions are finally obtained. Then the dynamic model of saturated soil layer caused by pile longitudinal vibration is founded. Incorporated wave propagations into saturated soil layer, the characteristics of soil resistance factor and the mechanism of the radial damping are analyzed, as well as distributions of shear stress and pore pressure in saturated soil caused by pile vibration. Meanwhile, dynamic responses at pile head are investigated. It is sh
own that the effects of pile slenderness, bearing stiffness of pile toe and the pile-soil modulus ratio on pile impedance are major whereas the ones of the permeability and the soil reaction coefficient are minor.
Secondly, on the basis of the theory of Rayleigh-Love bar, the longitudinal vibration of a large diameter end-bearing pile in saturated soil is investigated considering transverse inertial effect. The vibration of pile considering transverse inertial effect is different from the one not considering this effect significantly at a smaller slenderness. Under the same conditions, the reflective peak of pile toe in time domain in the former is smaller than in
the latter and decreases gradually with the increase of exciting frequencies.
Thirdly, a simplified model neglecting the radial displacement of saturated soil is established and an analytical solution for vertical vibration of the soil-pile system is obtained. By comparison the solution with available viscoelastic solution, the differences are illustrated as well as its applications. The results show that there is significant difference between the solution considering and neglecting the radial displacement at lower frequencies but they are identical at higher ones. So, it is suitable to use the former for aseismic design of pile foundation but the latter for dynamic pile testing.
Finally, dynamic compliances of a pile with variable impedance embedded in layered saturated soil are studied. A simplified layered model is put forward on the basis of the single layer elastic bearing model. By using the same method, analytical solutions in frequency domain hence semi-analytical solutions in time domain representing the dynamic responses at pile head are obtained. By comparison with the single layer solution, the rationality of layered model is verified. Based on these solutions, the dynamic responses of integral pile and pile with various impedances are investigated. The results show that not only variations of pile impedance but also parameters of soil layer can make effects on the dynamic compliances at pile head.
The coupled soil-pile dynamic interaction model and the corresponding
引文
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