An　analytical　model　has　been　developed　to　investigate　the　vertical　dynamic　response　of　single　end-bearing　SDCM　piles　with　partially　treated　DCM　socket.　The　interaction　between　the　cored　pile,　the　surrounding　socket　and　untreated　soil　is　described　using　elastodynamics.　To　evaluate　the　response　of　the　cored　pile,　the　model　is　divided　into　two　regions　within　the　DCM　and　outside　the　DCM　region.　The　eigenfunctions　and　eigenvalues　for　the　pile　displacement　in　these　two　regions　are　derived.　The　displacement　of　the　cored　pile　is　obtained　in　matrix　form　by　finite　truncation　of　the　Fourier　series.　Parametric　studies　show　that　the　axial　strain　of　the　cored　pile　increases　along　the　shaft　depth　due　to　the　occurrence　of　negative　skin　friction.　Pile　stiffness　increases　significantly　with　the　increase　of　the　radius　of　the　DCM　socket.　The　feasible　radius　r1/d　for　effectively　increasing　pile　stiffness　is　5∼10.　The　depth　of　the　DCM　socket　also　has　a　significant　impact　on　the　response　of　the　cored　pile.　©　2025　Elsevier　Ltd