饱和地基上刚性条形基础的竖向振动分析  

Vertical vibration of rigid strip footings on saturated soil

作　　者：李庆金[1] 王戌平[1] 徐长节[1] 蔡袁强[1] 

机构地区：[1]浙江大学土木工程学系,浙江杭州310027

出　　处：《岩土工程学报》2006年第1期19-23,共5页Chinese Journal of Geotechnical Engineering

摘　　要：基于Biot动力方程,研究了饱和均质弹性半空间上刚性条形基础的竖向振动问题。通过Fourier积分变换求解了饱和土的动力控制方程,并结合上边界为混合边界的条件得到了刚性条形基础的竖向振动对偶积分方程,利用正交多项式对偶积分方程转化为求解一组线性代数方程组,得到了动力柔度系数随无量纲频率的关系曲线;同时,将其退化到单相弹性半空间,得到了单相弹性半空间上刚性条形基础竖向振动的动力柔度系数,并进行了对比。数值分析结果表明:对于饱和半空间上刚性条形基础的竖向振动,动力渗透系数较大时,动力渗透系数对动力柔度系数的影响较大,而当动力渗透系数较小时,则可以忽略动力渗透系数对动力柔度系数的影响。此外,动力柔度系数基本上不受土体参数泊松比的影响,且实部和虚部的绝对值均小于退化到单相弹性半空间上的值。Based on the Biot＇s dynamic equations, the vertical vibration of a rigid strip footing rested on saturated soils was studied. By employing the method of Fourier transform, the dynamic governing differential equations for saturated poroelastic medium were solved. Considering the mixed boundary-value conditions at upper surface, a pair of dual integral equations governing the vertical vibration of the rigid strip footing were then derived, which were further converted to linear equations by means of infinite series of orthogonal functions the Jacobi polynomials. Consequently, the dynamic compliance for saturated soils versus the dimensionless frequency b0 was evaluated. Also, the dynamic compliance for elastic half space versus the dimensionless frequency b0 was studied. Numerical results indicated that, when the dynamic coefficient of permeability was great, its effect on the dynamic compliance must be considered whereas the dynamic coefficient of permeability was small, its effect could be neglected. Moreover the influence of the Poisson＇s ratio of soil on the dynamic compliance was little, and the real part and the absolute value of the imaginary part of the dynamic compliance were less than those for elastic half space.

关 键 词：竖向振动 动力柔度系数 对偶积分方程 

分 类 号：TU435[建筑科学—岩土工程]