Vertical vibration of rigid strip footings on saturated soil

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.