【作者】 王小岗；

【导师】 黄义；

【作者基本信息】 西安建筑科技大学 ， 结构工程， 2004， 博士

【摘要】 土—结构动力相互作用的本质就是波动在结构．地基系统内传播时引起的结构和地基的动力反应问题。研究土—基础结构的动力相互作用是分析土—结构动力相互作用的关键。本文基于Biot两相介质波动理论，采用横观各向同性饱和半空间及横观各向同性饱和有限层地基模型，对饱和地基的三维动力响应及横观各向同性饱和地基—基础(板)的动力相互作用进行了系统研究。 本文首先对横观各向同性饱和土的Biot波动方程及参数作了系统的比较研究，阐述了波动方程及各项参数的物理力学意义。其次，基于Biot波动理论，在圆柱坐标系下求解了横观各向同性饱和土的Biot波动方程：通过引入位移函数，在圆柱坐标系下将横观各向同性饱和土的Biot波动方程转化为两个解耦的6阶和2阶控制方程，然后根据方位角的Fourier展开和径向Hankd变换，求解波动方程，得到以土骨架位移和孔隙水压力为基本未知量的积分形式一般解，并用一般解给出了饱和土总应力分量的表达式；再以基本解为基础，系统地研究了横观各向同性饱和半空间体的Lamb问题，考虑表面排水或不排水两种情况后，首次得到横观各向同性饱和半空间体在表面竖向和水平谐振力作用的下径向、竖向和周向位移的解析解。研究表明采用各向同性饱和介质的动力学模型不能准确描述横观各向同性饱和土地基的动力特性。 借助位移函数及双重Fourier变换，研究了直角坐标系下横观各向同性饱和土的动力响应问题，得到了饱和半空间体在任意分布的表面谐振荷载作用下稳态响应的一般解。 在圆柱坐标系下研究了层状横观各向同性饱和地基的对任意地震力的动力响应问题。基于饱和土的Biot波动理论，通过Fouricr变换，将横观各向同性饱和土三维非轴对称波动方程转化为一组一阶常微分方程组，再经Har止el变换，建立问题的状态方程，求解状态方程得到传递矩阵;利用传递矩阵，结合饱和层状地基的边界条件、排水条件及层间接触和连续条件，首次给出层状横观各向同性饱和地基在任意地展力作用下的三维非轴对称动力响应的解析解。 研究了直角坐标系下横观各向同性饱和层状地基的稳态动力响应问题。首先建立直角坐标系下波动问题的状态方程，经双重Fo吐er变换求解状态方程后得到传递矩阵:利用递矩阵给出直角坐标系下层状横观各向同性饱和地基在任意分布简谐荷载作用下稳态动力响应的一般解。 系统研究了简谐激励下饱和半空间/有限层地基与弹性圆薄板和中厚板的动力相互作用问题。基于横观各向同性饱和半空间/有限层地基非轴对称波动方程的通解，按混合边值问题建立饱和地基与弹性圆板非轴对称动力相互作用的积分方程，求解积分方程后得到横观各向同性饱和地基上圆板非轴对称动力响应的一般解，并分析了饱和地基上圆薄板和中厚板振动的若干特征。 基于直角坐标系下横观各向同性饱和地基稳态响应的一般解，结合矩形薄板的幻rchboff弯曲理论，采用半解析半数值的求解方法，系统研究了横观各向同性饱和地基一矩形板的动力相互作用问题。更多还原

【Abstract】 Soil-structure dynamic interaction is the dynamic responding of soils, foundation and superstructures excited by wave propagation in soils and structure virtually and, dynamic analysis of soil-foundation interaction is the key problem in studying soil-structure interaction. In the dissertation, a systematic study on the 3-D dynamic responding of transversely isotropic saturated half-space/layered saturated strata produced by harmonic loading and seismic loading and dynamic interaction of saturated soils- foundation (circular plate) based on Biot’s theory for fluid-saturated porous media and the model of elastic half-space.The dissertation starts with the analysis for Biot’s theory for transversely isotropic fluid-saturated porous media. A group of governing equations and parameters is presented. Thereafter, the 3-D Biot’s wave equations in cylindrical coordinate for transversely isotropic saturated poroelastic media are transformed into the two uncoupling governing different equations of 6-order and 2-order respectively by means of the displacement functions. Then, the differential equations are solved by the Fourier expanding and Hankel integral transform method. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media are obtained. Furthermore, a systematic study on Lamb’s problems in transversely isotropic saturated half-space is performed. Integral solutions for surface radial, vertical and tangentical displacements are obtained both in the case of drained surface and in the case of undrained surface excited by vertical and tangentical harmonic resources respectively. Numerical results show the obvious difference between the model of isotropic saturated poroelastic media and that of transversely isotropic saturated poroelastic media.Secondly, the work is extended to the case of a general harmonic source distributing on arbitrary surface zone of the half-space with transversely isotropic saturated poroelastic half-space. Using the displacement functions and the technique of double Fourier transform, the governing differential equations for transverselyisotropic saturated poroelastic media are easily solved and , the Fourier transformed stress and displacement solutions coorespondingly are obtained. Then, under the boundary conditions, the analytical solutions for half-space are presented.Thirdly, the method to calculate the 3-D dynamic responding of layered transversely isotropic saturated soils to an arbitrary buried source in cylindrical coordinate as well as to an arbitrary harmonious source in rectangular coordinate is presented respectively. Based on Biot’s wave theory, the 3-D wave equations in cylindrical coordinate for transversely isotropic saturated poroelastic media are transformed into a group of governing different equations with 1-order by the Fourier expanding with respect to azimuth and Hankel integral transform method or by the double Fourier transform method with respect to horizontal coordinates in rectangular coordinate. Then, transfer matrixes within layered media are derived under the continuous conditions, drainage conditions and the boundary conditions. By the transfer matrixes, the solutions of 3-d dynamic response of layered transversely isotropic saturated soils are presented.Fourthly, the solutions for non-axisymmetical dynamic responding of elastic circular plate (thin and thick plate)rested on transversely isotropic saturated half-space/layered ground subjected to arbitrary harmonic loading are presented. Under the contact conditions, the problem leads to a pair of dual integral equations which describs the mixed boundary-value problem. Furthermore, the dual integral equations can be reduced to the Fredholm integral equations of the second kind and solved by numerical procedure. At the end of this chapter, the numerical analysis for dynamic interaction characters of saturated half-space/layered ground and circular plate is evaluated.Finally, the solutions for 3-D dynamic responding of elastic rect更多还原