复杂非均质土中桩土竖向振动理论研究
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摘要
本文分析了非均质土中纵向振动荷载作用下桩的动力响应问题。基于土体及桩的本构关系,建立非均质土体平面的或三维轴对称的波动方程及一维粘弹性或弹性桩的波动方程,再引入边界条件以及桩-土接触条件,采用解析的方法求解桩-土动力振动方程,由此建立了非均质土体的复刚度传递平面应变模型以及三维轴对称连续介质模型,较系统和深入地研究了弹性桩或粘弹性桩与非均质土在纵向振动力作用下的动力耦合振动问题。主要工作和创新成果包括:
1.在考虑土体径向非均质性情况下,利用平面应变土体模型,结合边界条件对黏弹性土体从外至内通过复刚度传递,求得土体与桩接触面上的复刚度,进而推导得到单桩桩顶受纵向激振力作用下的桩振动方程的频域表达式,再利用卷积定理和Fourier逆变换得到桩顶的时域响应半解析解。基于所得解对桩-土耦合振动的机理以及土体动力反应特性进行研究,重点研究了土体的非均质性对桩-土动力特性的影响。研究表明,土体的非均质性对桩-土动力特性有着明显的影响,考虑土体非均质性十分必要。
2.在考虑土体径向非均质性情况下再考虑纵向成层性,利用复刚度传递平面应变土体模型求得纵向不同性质桩侧土层的复刚度,进而对各段变截面粘弹性桩身从下往上逐段推导得到单桩桩顶受纵向激振力作用下的桩基振动的频域响应解析解以及时域半解析解。通过对土体参数研究,得出了双向非均质土中桩顶动力响应的特性。
3.在三维轴对称条件下利用连续介质理论研究径向非均质土中桩-土的纵向振动问题。对任意圈层完全连续土体动力平衡方程由外而内逐圈层求解,进而利用桩-土完全耦合条件求解桩动力平衡方程,得到桩顶的频域响应解析解和时域响应半解析解。在此基础上,研究了双向非均质土中粘弹性支承桩受纵向动力荷载作用下的响应问题,得到了桩基振动的频域解析解和时域半解析解。对桩身变阻抗性质和土体非均质的研究,用以揭示非均质土中变截面桩的振动特性。
4.对径向非均质土体中复刚度传递的多圈层平面应变模型、多弹簧串联的多圈层平面应变模型和精确的三维连续介质模型进行对比研究,发现复刚度传递的多圈层平面应变模型和精确的三维连续介质模型在绝大多数情况下计算结果比较接近,而采用多弹簧串联的多圈层平面应变模型的结果误差较大,说明复刚度传递平面应变模型具有足够高精度,可以用相对简单的复刚度传递平面应变模型代替复杂的连续介质模型进行桩-土动力研究。
5.通过对桩底支承的研究,提出了虚土桩模型,把桩底有限层土体对桩基的支承作用模拟为一段土柱,土柱与桩完全接触,从而求得桩顶频域响应解析解和时域响应半解析解。虚土桩法求解桩基动力响应问题,桩底土支承直接与土体性质联系,使桩-土动力耦合作用更严密更精确。
本文是在其他现有理论上的基础上进一步深入的理论,全面分析了桩-非均质土耦合振动问题,揭示了非均质土中桩基振动的机理。
Dynamic response analysis of a pile considering soil inhomogeneity under vertical vibration load is presented. Dynamic wave equations of plane or three-dimensional axisymmetric inhomogeneous soil and one-dimensional viscoelastic or elastic pile are constructed based on constitutive relations of soil and pile. Leading-in boundary conditions and pile-soil contact condition, the dynamic equations are solved by analytical solution method, thereout a complex stiffness transfer plane-strain model or three-dimensional axisymmetric continuum medium model in inhomogeneous soil are constructed. The dynamic interactions of pile and inhomogeneous soil under vertical vibration load are systematically investigated. The principal contents and original work are as follows:
1. A new model for analyzing vertical dynamic response of pile under vibration load is presented. The soil is assumed to be viscoelastic and radially inhomogeneous, by utilizing the plane strain model and combining the boundary condition, complex stiffness at the interface of pile and soil is derived by complex stiffness transfer method from outer zone to inner zone. Then, the pile is modeled as one-dimension elastic theory valid for long straight bar, the expression of the impedance function and frequency response function at pile top are derived by solving the dynamic equation. Subsequently, the relevant responses in time domain are obtained by the convolution theorem and the Inverse Fourier Transform. Finally, pile-soil interactions and dynamic characteristics of soil are obtained by investigating the influences of soil inhomogeneity caused by construction. The researched results prove that soil inhomogeneity is necessary to take into account and complex stiffness transfer plane strain model considering the soil inhomogeneity is fit for the engineering practice.
2. The soil is assumed to be radially inhomogeneous and vertically layered. At first, complex stiffness at the interface of pile sections and soil is derived by complex stiffness transfer plane strain model, and then an analytical solution of dynamic response in frequency domain and a semi-solution of dynamic response in time domain are derived by solving the dynamic equations of pile sections from bottom to top step by step. Finally, rules of dynamic response in vertical layered and radially inhomogeneous soil are obtained by soil parametric analysis.
3. A radially inhomogenous continuum medium model is presented. Based on the three-dimensional axisymmetric soil model, the vertical dynamic response of a pile embedded in radially inhomogeneous soil layers caused by construction effect of pile is investigated, in which the soil surrounding the pile is subdivided into arbitrary numerous annular zones to consider the inhomogeneity of soil. Then combining the boundary conditions and continuum conditions of displacement and stress between adjacent soil zones, the dynamic equilibrium equations of every soil zone are solved one by one from outer zone to inner zone. At last, by means of the coupled condition of pile-soil interface, the dynamic equilibrium equation of pile is also solved and analytical solutions in frequency domain and semi-analytical solutions in time domain are obtained. Based on the new model, dynamic response of pile in radially inhomogeneous layered soil under vertical dynamic loading is investigated. Analytical solutions in frequency domain and a semi-analytical solution in time domain are obtained. Influences of a pile with variable impedance and layered imhomogeneous soil are investigated, the rules of dynamic response of pile with variable impedance in vertical layered and radially inhomogeneous soil.
4. The comparisons of complex stiffness transfer plane-strain model, series connection spring plane-strain model and precise three-dimensional continuous medium model in radially inhomogeneous soil are presented. The comparative results of the three models show that the differences between the 3-D continuum model and the complex stiffness transfer plane-strain model are small as a whole, and the precision of complex stiffness transfer plain-strain model is enough. However, the contrastive results also show that precision of the series connection spring plane-strain model is short. It can be concluded that complex stiffness transfer plane-strain model which has enough precision and relative simpleness can substitute the 3-D continuous medium model to analyze the pile-soil dynamic response in general cases.
5. Based on some researches of support at the pile bottom, "fictitious soil pile" model is present, in which the finite soil layer below the pile bottom is modeled as a fictitious soil pile with soil parameters. The fictitious soil pile and pile is continuous and then the analytical solution and semi-analytical solution of dynamic response at the top of pile in frequency domain or time domain are obtained, respectively. It could be proved that the results are much more rigorous and precise by the "fictitious soil pile" model than other approximate model.
The vertical pile-soil dynamic interaction models in inhomogeneous soil layers developed in this dissertation are the further theories based on existing pile-soil theories. Pile-inhomogeneous soil dynamic interaction is completely investigated to point out the rules of pile vibration.
1.在考虑土体径向非均质性情况下,利用平面应变土体模型,结合边界条件对黏弹性土体从外至内通过复刚度传递,求得土体与桩接触面上的复刚度,进而推导得到单桩桩顶受纵向激振力作用下的桩振动方程的频域表达式,再利用卷积定理和Fourier逆变换得到桩顶的时域响应半解析解。基于所得解对桩-土耦合振动的机理以及土体动力反应特性进行研究,重点研究了土体的非均质性对桩-土动力特性的影响。研究表明,土体的非均质性对桩-土动力特性有着明显的影响,考虑土体非均质性十分必要。
2.在考虑土体径向非均质性情况下再考虑纵向成层性,利用复刚度传递平面应变土体模型求得纵向不同性质桩侧土层的复刚度,进而对各段变截面粘弹性桩身从下往上逐段推导得到单桩桩顶受纵向激振力作用下的桩基振动的频域响应解析解以及时域半解析解。通过对土体参数研究,得出了双向非均质土中桩顶动力响应的特性。
3.在三维轴对称条件下利用连续介质理论研究径向非均质土中桩-土的纵向振动问题。对任意圈层完全连续土体动力平衡方程由外而内逐圈层求解,进而利用桩-土完全耦合条件求解桩动力平衡方程,得到桩顶的频域响应解析解和时域响应半解析解。在此基础上,研究了双向非均质土中粘弹性支承桩受纵向动力荷载作用下的响应问题,得到了桩基振动的频域解析解和时域半解析解。对桩身变阻抗性质和土体非均质的研究,用以揭示非均质土中变截面桩的振动特性。
4.对径向非均质土体中复刚度传递的多圈层平面应变模型、多弹簧串联的多圈层平面应变模型和精确的三维连续介质模型进行对比研究,发现复刚度传递的多圈层平面应变模型和精确的三维连续介质模型在绝大多数情况下计算结果比较接近,而采用多弹簧串联的多圈层平面应变模型的结果误差较大,说明复刚度传递平面应变模型具有足够高精度,可以用相对简单的复刚度传递平面应变模型代替复杂的连续介质模型进行桩-土动力研究。
5.通过对桩底支承的研究,提出了虚土桩模型,把桩底有限层土体对桩基的支承作用模拟为一段土柱,土柱与桩完全接触,从而求得桩顶频域响应解析解和时域响应半解析解。虚土桩法求解桩基动力响应问题,桩底土支承直接与土体性质联系,使桩-土动力耦合作用更严密更精确。
本文是在其他现有理论上的基础上进一步深入的理论,全面分析了桩-非均质土耦合振动问题,揭示了非均质土中桩基振动的机理。
Dynamic response analysis of a pile considering soil inhomogeneity under vertical vibration load is presented. Dynamic wave equations of plane or three-dimensional axisymmetric inhomogeneous soil and one-dimensional viscoelastic or elastic pile are constructed based on constitutive relations of soil and pile. Leading-in boundary conditions and pile-soil contact condition, the dynamic equations are solved by analytical solution method, thereout a complex stiffness transfer plane-strain model or three-dimensional axisymmetric continuum medium model in inhomogeneous soil are constructed. The dynamic interactions of pile and inhomogeneous soil under vertical vibration load are systematically investigated. The principal contents and original work are as follows:
1. A new model for analyzing vertical dynamic response of pile under vibration load is presented. The soil is assumed to be viscoelastic and radially inhomogeneous, by utilizing the plane strain model and combining the boundary condition, complex stiffness at the interface of pile and soil is derived by complex stiffness transfer method from outer zone to inner zone. Then, the pile is modeled as one-dimension elastic theory valid for long straight bar, the expression of the impedance function and frequency response function at pile top are derived by solving the dynamic equation. Subsequently, the relevant responses in time domain are obtained by the convolution theorem and the Inverse Fourier Transform. Finally, pile-soil interactions and dynamic characteristics of soil are obtained by investigating the influences of soil inhomogeneity caused by construction. The researched results prove that soil inhomogeneity is necessary to take into account and complex stiffness transfer plane strain model considering the soil inhomogeneity is fit for the engineering practice.
2. The soil is assumed to be radially inhomogeneous and vertically layered. At first, complex stiffness at the interface of pile sections and soil is derived by complex stiffness transfer plane strain model, and then an analytical solution of dynamic response in frequency domain and a semi-solution of dynamic response in time domain are derived by solving the dynamic equations of pile sections from bottom to top step by step. Finally, rules of dynamic response in vertical layered and radially inhomogeneous soil are obtained by soil parametric analysis.
3. A radially inhomogenous continuum medium model is presented. Based on the three-dimensional axisymmetric soil model, the vertical dynamic response of a pile embedded in radially inhomogeneous soil layers caused by construction effect of pile is investigated, in which the soil surrounding the pile is subdivided into arbitrary numerous annular zones to consider the inhomogeneity of soil. Then combining the boundary conditions and continuum conditions of displacement and stress between adjacent soil zones, the dynamic equilibrium equations of every soil zone are solved one by one from outer zone to inner zone. At last, by means of the coupled condition of pile-soil interface, the dynamic equilibrium equation of pile is also solved and analytical solutions in frequency domain and semi-analytical solutions in time domain are obtained. Based on the new model, dynamic response of pile in radially inhomogeneous layered soil under vertical dynamic loading is investigated. Analytical solutions in frequency domain and a semi-analytical solution in time domain are obtained. Influences of a pile with variable impedance and layered imhomogeneous soil are investigated, the rules of dynamic response of pile with variable impedance in vertical layered and radially inhomogeneous soil.
4. The comparisons of complex stiffness transfer plane-strain model, series connection spring plane-strain model and precise three-dimensional continuous medium model in radially inhomogeneous soil are presented. The comparative results of the three models show that the differences between the 3-D continuum model and the complex stiffness transfer plane-strain model are small as a whole, and the precision of complex stiffness transfer plain-strain model is enough. However, the contrastive results also show that precision of the series connection spring plane-strain model is short. It can be concluded that complex stiffness transfer plane-strain model which has enough precision and relative simpleness can substitute the 3-D continuous medium model to analyze the pile-soil dynamic response in general cases.
5. Based on some researches of support at the pile bottom, "fictitious soil pile" model is present, in which the finite soil layer below the pile bottom is modeled as a fictitious soil pile with soil parameters. The fictitious soil pile and pile is continuous and then the analytical solution and semi-analytical solution of dynamic response at the top of pile in frequency domain or time domain are obtained, respectively. It could be proved that the results are much more rigorous and precise by the "fictitious soil pile" model than other approximate model.
The vertical pile-soil dynamic interaction models in inhomogeneous soil layers developed in this dissertation are the further theories based on existing pile-soil theories. Pile-inhomogeneous soil dynamic interaction is completely investigated to point out the rules of pile vibration.
引文
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