Vertical Vibration Analysis Of Strip Foundation On Saturated Soils

Based on the Biot's dynamic equations, the vertical vibration analysis of strip foundation are studied in this paper. At first, 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 vertical 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 Cv versus the dimensionless frequency is derived, and the program is compiled. Then, the author evaluates the vertical vibration of the rigid foundation, flexible foundation on saturated soils and on elastic soils with saturated substratum respectively, and the influence of various parameters on the vertical vibration is studied too. For rigid strip foundation on saturated soils, the parameters of dynamic permeability coefficient and the Poisson's ratio are adopted to evaluate the vertical vibration, and the response of elastic homogeneous half space is further discussed, then the numerical result is compared with classical result; For flexible strip foundation on saturated soils, the parameters of dynamic permeability coefficient, the Poisson's ratio and the parameter indicated the flexibility of foundation are adopted; For rigid strip foundation on elastic soils with saturated substratum, the parameter of superimposed elastic soil thickness is adopted; And the parameter indicated the flexibility of foundation is also adopted for flexible strip foundation on elastic soils with saturated substratum. The analytical and semi-analytical solution are the focus of interest and some numerical methods are employed in the paper. Moreover, the numerical analytic result of the vertical vibration of rigid foundation and flexible foundation on soils is presented.