初始变形条件下桩—土动力增量理论
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摘要
本文运用增量弹性变形理论,在现有的桩土动力分析理论的基础上,研究了初始应力-应变状态对桩土动力相互作用特征的影响,并在以下几个方面做了较为深入的研究：
运用增量弹性变形理论研究了初始轴向变形状态对各向均质饱和孔隙土体中的端承桩的动力响应问题。桩坐标下的土体运动控制方程参考Biot的增量孔隙弹性理论,而桩体的动力方程是由基桩—维弹性理论推导得到。通过分离变量法得到了桩顶阻抗、桩顶扭转速度的时域和频域响应解析表达式。代入特定的参数分析了初始变形对扭转阻抗、桩顶扭转角速度的影响。
基于初始变形体的增量动力理论,研究由了桩-土相互作用引起的径向非均匀初始应变场作用下的桩基础动力响应问题。推导了初始应变场引起的桩周土体的剪切模量和物理参数沿径向的变化规律。通过将桩周土体划分为若干同心圆土环,并考虑桩土和土环间完全接触条件,得到土体在分界面处的纵向阻抗解析式,并与前人所得结果进行了对比。进而推导出桩顶的纵向阻抗和速度响应的频域解析式和时域半解析表达式。选取合适的参数在低频范围内对界面压力的影响效应进行了探讨。
对分层土体中的纵向变截面桩的径向动力响应问题进行了研究。得到桩顶轴向振动特征的解析解答。分析了初始变形状态的成层性的影响规律以及桩径变化对桩顶速度响应时间信号的影响。
采用分层离散法,研究了径向非均匀初始应变场作用下的扭转波在桩-土结构中的传播弥散特征,建立了相应的特征方程,并采用“二分法”对方程进行了数值解答,通过所得结果对分层数和初始界面压力这两个因素的影响效应进行了探讨。
By coupling incremental elastic deformation theory with available pile-soil dynamic theory, the influences of initial stress-strain state on dynamic characteristics are studied in depth within the following fields:
(1) By utilizing the incremental elastic deformation theory, the influence of initial longitudinal strain state on the dynamic response of an end bearing pile embedded in isotropic saturated soil is investigated. The governing equations for soil, based on the Biot's poroelasticity theory, are derived in cylindrical coordinates and the pile is modeled using one-dimensional elastic theory. The analytical solutions of pile impedance, frequency response of twist angle and time history of velocity response are obtained by using the separation of variables technique. Finally, a parametric study of the influence of initial strains on the torsional impedance, twist angle and velocity response at the top of the pile is undertaken and discussed.
(2) The influence of radially inhomogeneous initial strain field caused by the interfacial pressure at the interface of pile-soil medium on the dynamic response of pile and initially homogeneous soil is discussed based on the theory related to the dynamics of initially stressed bodies. The radially variation rule of shear modulus and physical parameters of soil caused by the initial strain field is deduced. The analytical solution of longitudinal dynamic impedance of soil is obtained by subdividing the soil domain into a number of annular vertical zones and introducing the plane strain and complete P-S (pile-soil) contact assumptions. A comparison between previous solutions and the present one is also carried out.. The longitudinal impedance of pile top and velocity response in frequency and time domains, are then obtained. The parametrical study of interfacial pressure on the dynamic response of P-S system is undertaken within relative lower frequency domain.
(3) The longitudinal dynamic response of pile with variable section in layered soil medium is studied. The analytical solutions of longitudinal dynamic characteristics at the top of pile are obtained. The effect of layered property of initial deformation state, together with the effect of section change on the characteristics of reflected signal at the top of pile is discussed.
(4) By employing "layer discrete method", the dispersion relation of torsional wave propagation in radially inhomogeneously strained pile-soil structure is investigated. The corresponding eigen-value problem is formulated and numerically solved by employing the "bisection method". The effects of influence parameters such as the number of layer and initial interface pressure is discussed according to the numerical results.
运用增量弹性变形理论研究了初始轴向变形状态对各向均质饱和孔隙土体中的端承桩的动力响应问题。桩坐标下的土体运动控制方程参考Biot的增量孔隙弹性理论,而桩体的动力方程是由基桩—维弹性理论推导得到。通过分离变量法得到了桩顶阻抗、桩顶扭转速度的时域和频域响应解析表达式。代入特定的参数分析了初始变形对扭转阻抗、桩顶扭转角速度的影响。
基于初始变形体的增量动力理论,研究由了桩-土相互作用引起的径向非均匀初始应变场作用下的桩基础动力响应问题。推导了初始应变场引起的桩周土体的剪切模量和物理参数沿径向的变化规律。通过将桩周土体划分为若干同心圆土环,并考虑桩土和土环间完全接触条件,得到土体在分界面处的纵向阻抗解析式,并与前人所得结果进行了对比。进而推导出桩顶的纵向阻抗和速度响应的频域解析式和时域半解析表达式。选取合适的参数在低频范围内对界面压力的影响效应进行了探讨。
对分层土体中的纵向变截面桩的径向动力响应问题进行了研究。得到桩顶轴向振动特征的解析解答。分析了初始变形状态的成层性的影响规律以及桩径变化对桩顶速度响应时间信号的影响。
采用分层离散法,研究了径向非均匀初始应变场作用下的扭转波在桩-土结构中的传播弥散特征,建立了相应的特征方程,并采用“二分法”对方程进行了数值解答,通过所得结果对分层数和初始界面压力这两个因素的影响效应进行了探讨。
By coupling incremental elastic deformation theory with available pile-soil dynamic theory, the influences of initial stress-strain state on dynamic characteristics are studied in depth within the following fields:
(1) By utilizing the incremental elastic deformation theory, the influence of initial longitudinal strain state on the dynamic response of an end bearing pile embedded in isotropic saturated soil is investigated. The governing equations for soil, based on the Biot's poroelasticity theory, are derived in cylindrical coordinates and the pile is modeled using one-dimensional elastic theory. The analytical solutions of pile impedance, frequency response of twist angle and time history of velocity response are obtained by using the separation of variables technique. Finally, a parametric study of the influence of initial strains on the torsional impedance, twist angle and velocity response at the top of the pile is undertaken and discussed.
(2) The influence of radially inhomogeneous initial strain field caused by the interfacial pressure at the interface of pile-soil medium on the dynamic response of pile and initially homogeneous soil is discussed based on the theory related to the dynamics of initially stressed bodies. The radially variation rule of shear modulus and physical parameters of soil caused by the initial strain field is deduced. The analytical solution of longitudinal dynamic impedance of soil is obtained by subdividing the soil domain into a number of annular vertical zones and introducing the plane strain and complete P-S (pile-soil) contact assumptions. A comparison between previous solutions and the present one is also carried out.. The longitudinal impedance of pile top and velocity response in frequency and time domains, are then obtained. The parametrical study of interfacial pressure on the dynamic response of P-S system is undertaken within relative lower frequency domain.
(3) The longitudinal dynamic response of pile with variable section in layered soil medium is studied. The analytical solutions of longitudinal dynamic characteristics at the top of pile are obtained. The effect of layered property of initial deformation state, together with the effect of section change on the characteristics of reflected signal at the top of pile is discussed.
(4) By employing "layer discrete method", the dispersion relation of torsional wave propagation in radially inhomogeneously strained pile-soil structure is investigated. The corresponding eigen-value problem is formulated and numerically solved by employing the "bisection method". The effects of influence parameters such as the number of layer and initial interface pressure is discussed according to the numerical results.
引文
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[3]Akbarov S. D. and Guliev M. S., Axisymmetric longitudinal wave propagation in a finite pre-strained compound circular cylinder made from compressible materials. Cmes-Computer Modeling in Engineering & Sciences,2009,39 (2),155-177.
[4]Akbarov S. D. and Guliev M. S., The influence of the finite initial strains on the axisymmetric wave dispersion in a circular cylinder embedded in a compressible elastic medium. International Journal of Mechanical Sciences,2010a,52 (1),89-95.
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