饱和地基上条形基础的摇摆振动特性分析
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摘要
土体与结构的相互作用(SSI)是当代力学领域的前沿性研究课题,并涉及到土动力学、结构动力学、非线性振动理论、地震工程学、岩土及结构抗震工程学、计算力学及计算机技术等众多学科。随着科学计算技术的迅猛发展和实验手段的不断改进,重大和复杂体系工程的不断建造,促进了土与结构动力相互作用的深入研究。地基与基础的相互作用问题不仅对于弹性动力学理论的发展有重要的学术价值,而且在地球物理学、地震工程及岩土力学等工程问题中均具有重要的现实意义,有着广泛的应用前景。
本文在平面应变条件下研究了饱和地基上条形刚性基础的摇摆振动问题。基于Biot动力控制方程,作者首先采用Fourier积分变换解析求解了Biot方程,得到了该动力控制方程在Fourier变换域上的一组通解,然后由混合边值条件建立了地基上基础摇摆振动的对偶积分方程,并应用Jacobi正交多项式将其转化为一组线性代数方程组,通过求解得到了不同无量纲频率下基础振动的动力柔度系数C_M,着重分析了动力渗透系数、泊松比对摇摆振动动力柔度系数的影响,并将其退化到单相弹性半空间,与经典弹性半空间解进行了比较。
接下来本文进一步研究了饱和地基上条形弹性基础的摇摆振动问题。用类似分析刚性基础的方法建立了一组描述条形弹性基础摇摆振动的对偶积分方程,并结合弹性基础的混合边值条件分别考虑了基础的弹性特性参数、土体的动力渗透系数等对摇摆振动的影响,并通过若干算例分析总结了弹性基础摇摆振动的一些规律。
此外,实际工程中,由于地下水的存在,地下水位以下的土可视为饱和土,而地下水位以上的土层可视为理想的单相弹性层。基于工程实际本文分别研究了下卧饱和半空间弹性土层上条形刚性基础和弹性基础的摇摆振动问题。对于下卧饱和半空间弹性土层上条形刚性基础,分析了单相弹性层厚度对动力柔度系数的影响;而对于下卧饱和半空间弹性土层上条形弹性基础的摇摆振动,则分析了单相弹性层厚度、弹性基础的弹性特性等参数对摇摆振动的影响。
最后本文根据Biot平面动力固结方程,运用积分变换和矩阵传递的方法,研究了层状饱和地基上条形刚性基础的摇摆振动问题,得到了单层饱和地基上条形刚性基础动力柔度系数随无量纲频率变化曲线。
在论文中,作者侧重于问题的解析解及半解析解,并进行了相应的数值计算处理,得到了饱和地基上条形刚性基础和弹性基础的摇摆振动规律。
The problem of dynamic soil-structure interaction (SSI) is a leading topic in the field of modern mechanics which involves the knowledges of soil dynamics, structure dynamics, nonlinear oscillation theory, earthquake engineering, earthquake resistance engineering, computational mechanics and computer technology. Recently the computation and experiment technology have made significant development, meanwhile, the significant and complex system project are becoming increasingly popular. Above all this promotes the development of the problem of dynamic soil-structure interaction. The study of dynamic interaction of foundations and soils is of great value to the development of the elastodynamics and is helpful to physical geography, seismography, and rock and soil mechanics, owning practical.
The rocking vibration analysis of rigid strip foundation resting on saturated soils is studied under conditions of plane strain. Based on the Biot's dynamic equations, the governing differential equations are solved by Fourier transform, then, under consideration of the mixed boundary value condition, a pair of dual integral equations about the rocking vibration are listed which are converted to linear algebra equations by the Jacobi orthogonal polynomial and solved by numerical procedures. Consequently, the dynamic compliance coefficient C_M versus the dimensionless frequency is derived, and the program is compiled. The parameters of dynamic permeability coefficient and the Poisson's ratio are adopted to evaluate the rocking vibration, and the response of elastic homogeneous half space is further discussed, then the numerical results are compared with classical result.
Then, the rocking vibration analysis of elastic strip foundation resting on saturated grounds is investigated. Using the similar method which is adopted to analyse the problem of the rigid strip foundation, under consideration of the mixed boundary value condition, the corresponding dual integral equations can be derived. The influence of the dynamic permeability coefficient, the Poisson's ratio and the parameter indicated the flexibility of foundation are analyzed by some numerical examples.
Moreover, considering the existing of the ground water, the author treat the soil layer below the water lever as the saturated one and the soil layer above the water level as single-phased elastic one. Utilzing this model, the rocking vibrations of the rigid and flexible foundation resting on saturated ground with an elastic layer are studied. For rigid strip foundation on elastic soils with saturated substratum, the parameter of superimposed elastic soil thickness is studied; For flexible strip foundation on elastic soils with saturated substratum, the parameter indicating the flexibility of foundation is also investigated.
Finally, based on Biot's dynamic consolidation equations, utilizing the method of integral transform and matrix transfer, the rocking vibration of rigid strip foundation on layered saturated soils is studied.
In this dissertation, the analytical and semi-analytical solution are the focus of interest and some numerical methods are employed. Moreover, the numerical result of the rocking vibration of rigid foundation and flexible foundation on soils is presented.
本文在平面应变条件下研究了饱和地基上条形刚性基础的摇摆振动问题。基于Biot动力控制方程,作者首先采用Fourier积分变换解析求解了Biot方程,得到了该动力控制方程在Fourier变换域上的一组通解,然后由混合边值条件建立了地基上基础摇摆振动的对偶积分方程,并应用Jacobi正交多项式将其转化为一组线性代数方程组,通过求解得到了不同无量纲频率下基础振动的动力柔度系数C_M,着重分析了动力渗透系数、泊松比对摇摆振动动力柔度系数的影响,并将其退化到单相弹性半空间,与经典弹性半空间解进行了比较。
接下来本文进一步研究了饱和地基上条形弹性基础的摇摆振动问题。用类似分析刚性基础的方法建立了一组描述条形弹性基础摇摆振动的对偶积分方程,并结合弹性基础的混合边值条件分别考虑了基础的弹性特性参数、土体的动力渗透系数等对摇摆振动的影响,并通过若干算例分析总结了弹性基础摇摆振动的一些规律。
此外,实际工程中,由于地下水的存在,地下水位以下的土可视为饱和土,而地下水位以上的土层可视为理想的单相弹性层。基于工程实际本文分别研究了下卧饱和半空间弹性土层上条形刚性基础和弹性基础的摇摆振动问题。对于下卧饱和半空间弹性土层上条形刚性基础,分析了单相弹性层厚度对动力柔度系数的影响;而对于下卧饱和半空间弹性土层上条形弹性基础的摇摆振动,则分析了单相弹性层厚度、弹性基础的弹性特性等参数对摇摆振动的影响。
最后本文根据Biot平面动力固结方程,运用积分变换和矩阵传递的方法,研究了层状饱和地基上条形刚性基础的摇摆振动问题,得到了单层饱和地基上条形刚性基础动力柔度系数随无量纲频率变化曲线。
在论文中,作者侧重于问题的解析解及半解析解,并进行了相应的数值计算处理,得到了饱和地基上条形刚性基础和弹性基础的摇摆振动规律。
The problem of dynamic soil-structure interaction (SSI) is a leading topic in the field of modern mechanics which involves the knowledges of soil dynamics, structure dynamics, nonlinear oscillation theory, earthquake engineering, earthquake resistance engineering, computational mechanics and computer technology. Recently the computation and experiment technology have made significant development, meanwhile, the significant and complex system project are becoming increasingly popular. Above all this promotes the development of the problem of dynamic soil-structure interaction. The study of dynamic interaction of foundations and soils is of great value to the development of the elastodynamics and is helpful to physical geography, seismography, and rock and soil mechanics, owning practical.
The rocking vibration analysis of rigid strip foundation resting on saturated soils is studied under conditions of plane strain. Based on the Biot's dynamic equations, the governing differential equations are solved by Fourier transform, then, under consideration of the mixed boundary value condition, a pair of dual integral equations about the rocking vibration are listed which are converted to linear algebra equations by the Jacobi orthogonal polynomial and solved by numerical procedures. Consequently, the dynamic compliance coefficient C_M versus the dimensionless frequency is derived, and the program is compiled. The parameters of dynamic permeability coefficient and the Poisson's ratio are adopted to evaluate the rocking vibration, and the response of elastic homogeneous half space is further discussed, then the numerical results are compared with classical result.
Then, the rocking vibration analysis of elastic strip foundation resting on saturated grounds is investigated. Using the similar method which is adopted to analyse the problem of the rigid strip foundation, under consideration of the mixed boundary value condition, the corresponding dual integral equations can be derived. The influence of the dynamic permeability coefficient, the Poisson's ratio and the parameter indicated the flexibility of foundation are analyzed by some numerical examples.
Moreover, considering the existing of the ground water, the author treat the soil layer below the water lever as the saturated one and the soil layer above the water level as single-phased elastic one. Utilzing this model, the rocking vibrations of the rigid and flexible foundation resting on saturated ground with an elastic layer are studied. For rigid strip foundation on elastic soils with saturated substratum, the parameter of superimposed elastic soil thickness is studied; For flexible strip foundation on elastic soils with saturated substratum, the parameter indicating the flexibility of foundation is also investigated.
Finally, based on Biot's dynamic consolidation equations, utilizing the method of integral transform and matrix transfer, the rocking vibration of rigid strip foundation on layered saturated soils is studied.
In this dissertation, the analytical and semi-analytical solution are the focus of interest and some numerical methods are employed. Moreover, the numerical result of the rocking vibration of rigid foundation and flexible foundation on soils is presented.
引文
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