基础与复杂层状地基动力相互作用研究

发布时间：2018-06-17 09:23

本文选题：复杂层状地基 + 基础-地基动力相互作用　；参考：《大连理工大学》2014年博士论文

【摘要】：地基动力刚度的求解是结构-地基动力相互作用分析的关键环节,求得地基动力刚度后可以与有限元等数值分析程序相结合进行上部结构和地基系统在地震、爆炸等荷载作用下动力响应的求解。大量的理论研究和分析表明,复杂层状地基对基础以及上部结构的动力特性有十分重要的影响,尤其是当地基具有各向异性特性时,广大的研究者和工程技术人员已经意识到这一点,并开展了很多相关的研究工作,提出了多种针对层状地基动力刚度求解的数值算法。从结构-地基动力相互作用问题的发展现状看,目前的研究算法往往具有局限性,或者对层状地基的层数和厚度有限制,或者对地基的各向同异性特性有限制,或者对基础近场的开挖有限制等。本文基于层状地基动力方程的积分变换,结合精细积分算法和对偶波动方程的应用,提出了一种求解复杂层状地基上明置或埋置基础动力刚度矩阵的混合算法。该算法克服了已有算法的局限性,并具有以下特性：(1)对任意水平层状地基具有广泛适用性,对地基的厚度、弹性地基材料属性没有任何限制；(2)计算中采用精细积分算法,保证了计算结果可以根据要求达到很高的精度,某种意义上可以认为其求解精度由计算所用的计算机精度决定的；(3)该算法中的矩阵维数均较小,因此有较高的求解效率；(4)此算法基于矩阵数值计算,数值求解稳定。本文主要研究内容和取得成果有： 1、针对各向同性层状地基,利用Hankel变换将频率-空间域内的波动方程转换到频率-波数域内,并解耦为平面内运动和出平面运动。引入对偶向量将二阶常微分方程降阶为一阶常微分方程,应用精细积分算法进行求解,最后分别利用Fourier逆变换和Hankel逆变换得到各向同性层状地基表面广义平面波动问题和三维波动问题的格林函数。利用此算法求解得到的格林函数可以求解各向同性层状地基表面条带基础和任意形状基础的动力刚度矩阵。数值算例验证了本文算法的准确性。 2、针对各向异性层状地基,利用Fourier变换将频率-空间域内的波动方程转化到频率-波数域内的二阶常微分方程,引入对偶向量将其转化为一阶常微分方程,应用精细积分算法求解得到频率-波数域内层状地基表面的动力柔度矩阵。最后利用Fourier逆变换得到各向异性层状地基表面广义平面波动问题和三维波动问题的格林函数。利用求解得到的格林函数求解层状地基表面条带基础和任意形状基础的动力刚度／柔度矩阵,进而分析层状地基的各向异性特性对层状地基表面基础动力刚度的影响。结果表明,层状地基的各向异性特性对基础-地基动力相互作用有显著的影响。 3、埋置基础的研究对实际工程有重大的应用价值,对前述求解层状地基表面格林函数的方法进行扩展,求解各向同性和各向异性层状地基内部任意点的格林函数,进而结合容积算法求解开挖条带基础和任意形状埋置基础动力刚度矩阵,数值算例验证了本文算法的精确性。 4、利用本文提出的求解层状地基动力响应的混合算法,分析层状地基相邻基础动力相互作用问题,并对层状地基厚度、地基材料阻尼比、基础间距、层状地基剪切波速比值以及地基的各项异性特性对基础-地基-基础动力相互作用进行广泛的参数分析。结果表明,层状地基的不均匀特性以及各向异性特性对相邻基础动力相互作用均有显著的影响。 5、在求解得到刚性基础的动力阻抗函数基础上,进一步求解层状地基表面刚性基础在集中荷载作用下基础底部地基应力分布,研究应力分布在各种荷载作用下随频率的变化规律以及层状地基的各向异性特性对应力分布的影响,为基础和地基承载力设计提供可靠的数值依据。 6、在得到频域解的前提下,利用Pade级数将频率-空间域离散的基础动刚度拟合成连分式的表达形式,通过混合变量技术构造成层状地基时域内的运动方程,然后利用精细积分时程算法进行求解,最终得到层状地基上任意形状基础时域内动荷载作用下的动力响应。
[Abstract]:The solution of the dynamic stiffness of the foundation is the key link of the structure - foundation dynamic interaction analysis , and the dynamic response of the superstructure and the foundation system under the action of earthquake , explosion and the like can be solved by combining the numerical analysis program such as finite element and the like after the dynamic stiffness of the foundation is obtained .

Based on the integral transformation of the dynamic equation of the layered foundation , combined with the application of the fine integral algorithm and the dual wave equation , a hybrid algorithm is proposed to solve the basic dynamic stiffness matrix on a complex layered foundation . The algorithm overcomes the limitations of the existing algorithm and has the following characteristics : ( 1 ) It has wide applicability to any horizontal layered foundation , and has no restrictions on the thickness of the foundation and the properties of the elastic foundation material ;
( 2 ) A fine integration algorithm is adopted in the calculation to ensure that the calculation results can reach very high accuracy according to the requirements , and the accuracy of the calculation can be considered to be determined by the computer accuracy used in the calculation .
( 3 ) the number of the matrix dimension in the algorithm is smaller , so that the algorithm has higher solving efficiency ;
( 4 ) The algorithm is based on matrix numerical calculation , and the numerical solution is stable .

The main research contents and achievements are as follows :

1 . According to the isotropic layered foundation , the wave equation in the frequency - space domain is transformed into the frequency - wave number domain by Hankel transformation , and the solution is decoupled into plane motion and plane motion . The second order ordinary differential equation is introduced into the first order ordinary differential equation by introducing the dual vector , and the Green function of the generalized planar wave problem and the three - dimensional wave problem of the isotropic layered foundation surface is obtained by using the inverse transformation and Hankel inverse transformation respectively .

2 . According to the anisotropic layered foundation , the wave equation in the frequency - space domain is transformed into the second order ordinary differential equation in the frequency - wave number domain by using the Fourier transform , the dual vector is introduced into the first order ordinary differential equation , and the dynamic flexibility matrix of the surface of the layered foundation in the frequency - wave number domain is obtained by using a fine integration algorithm . Finally , the effect of the anisotropic property of the layered foundation on the dynamic stiffness of the surface foundation of the layered foundation is obtained by using the Green function obtained by the solution . The results show that the anisotropic property of the layered foundation has a significant influence on the foundation - foundation dynamic interaction .

3 . The research on the buried foundation has great application value to the practical engineering , and the method for solving the Green function of the surface of the layered foundation is extended to solve the Green function of any point inside the isotropic and anisotropic layered foundation , and then the excavation strip foundation and the embedded basic dynamic stiffness matrix are solved by the volume algorithm , and the accuracy of the algorithm is verified by numerical examples .

4 . Based on the hybrid algorithm for the dynamic response of the layered foundation , this paper analyzes the interaction of the adjacent basic dynamic of the layered foundation , and analyzes the parameters of the foundation - foundation - foundation dynamic interaction with the thickness of the layered foundation , the damping ratio of the foundation material , the basal spacing , the shear wave velocity ratio of the layered foundation and the anisotropy of the foundation . The results show that the non - uniform characteristics and the anisotropy of the layered foundation have significant influence on the interaction of adjacent basic dynamic forces .

5 . On the basis of solving the dynamic impedance function of the rigid foundation , the stress distribution of the foundation under concentrated load of the rigid foundation of the surface of the layered foundation is further solved . The influence of the stress distribution with the frequency and the anisotropy of the layered foundation on the stress distribution are studied under various loads , which provides a reliable numerical basis for the design of foundation and foundation bearing capacity .

6 . Under the precondition of obtaining the frequency domain solution , the fundamental dynamic stiffness of the frequency - space domain is synthesized by the Pade series . The motion equation in the time domain of the layered foundation is constructed by the mixed variable technique , then the fine integral time history algorithm is used to solve the motion equation , and finally , the dynamic response under the action of any shape base time domain dynamic load on the layered foundation is obtained .
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU435

【参考文献】