Based on the Biot’s dynamic equations

the vertical vibration of a rigid strip foundation resting on partially saturated soil subgrade which is composed of a dry elastic layer and a saturated substratum is studied. The analysis relied on the use of Fourier integral transform techniques and a pair of dual integral equations governing the vertical vibration of the rigid foundation is listed under the consideration of mixed boundary value condition and the continuity condition. The results are reduced to the case for saturated half-space. The set of dual integral equations are converted to linear equations by means of infinite series of orthogonal functions—the Jacobi polynomials. Consequently

the dynamic compliance Cv for partially saturated soils versus the dimensionless frequency b0 is evaluated. Numerical results indicate that: the thickness has great effect on the dynamic coefficient

and as the thickness of the elastic stratum is less than the tenth half width of the strip foundation

the curve of the dynamic compliance versus the dimensionless frequency basically match together with the saturated half-space; and the saturated half space is the special case of the partially saturated soil subgrade(the thickness of the superimposed elastic soil Hn is equal to 0 ).