Based　on　the　Biot＇s　theory　of　wave　propagation,　a　saturated　virtual　soil　pile　model　is　proposed.　Considering　the　three-dimensional　wave　effect　and　saturation　characteristics　of　surrounding　soil　and　beneath　the　pile　toe,　a　three-dimensional　system　including　saturated　viscoelastic　soil,　virtual　soil　pile　and　solid　pile　is　established.　The　analytical　solution　for　displacement　of　saturated　soil　is　also　derived　by　potential　function　method.　The　vertical　dynamic　impedance　at　the　pile　head　is　obtained　using　the　pile-soil　compatibility　conditions.　Finally,　the　obtained　solution　is　reduced　to　verify　its　validity　with　existing　solutions.　Furthermore,　extensive　parametric　analysis　is　performed　to　investigate　the　effects　of　saturated　soil　parameters　on　the　vibration　characteristics　at　the　pile　head.　The　computational　results　show　that　the　amplitude　and　resonance　frequency　of　dynamic　impedance　at　the　pile　head　in　saturated　soil　decrease　with　increase　of　saturated　soil　thickness　beneath　the　pile　toe.　When　the　thickness　of　saturated　soil　beneath　the　pile　toe　increases　to　a　certain　extent,　the　pattern　of　staggering　peak　become　evident.　The　porosity　of　saturated　soil　beneath　the　pile　toe　has　significant　effects　on　both　the　resonance　amplitude　and　resonance　frequency　of　the　dynamic　impedance　at　the　pile　head,　while　the　porosity　of　saturated　surrounding　soil　only　influence　the　resonance　amplitude.　With　increasing　shear　modulus　of　surrounding　soil　and　soil　beneath　the　pile　toe,　the　amplitude　of　the　dynamic　impedance　at　the　pile　head　is　significantly　reduced,　and　it　is　more　affected　by　the　shear　modulus　of　surrounding　soil.　©　2019,　Science　Press.　All　right　reserved.