Based　on　the　three-variable　Biot　model,　a　numerical　manifold　model　is　presented　to　investigate　dynamic　responses　of　the　fractured　poroelasticity,　especially　the　interaction　between　hydro-mechanical　wave　and　fracture.　The　most　flexible　3-node　triangular　mesh　serves　as　the　mathematical　cover　(MC)　of　the　present　model　regardless　of　the　problem　types,　shunning　difficulties　in　qualified　mesh　generation.　Continuous　nodal　gradients　and　Kroneckerdelta　property　are　achieved　for　the　global　approximations　by　constructing　the　local　approximations　with　a　constrained　and　orthonormalized　least　square　(CO-LS)　scheme,　presenting　more　precise　effective　stress　fields　and　more　convenience　in　implementing　boundary　conditions　for　both　solid　and　fluid　phases.　Incorporating　a　stick-slip　frictional　contact　model　via　the　augmented　Lagrange　multiplier　method,　the　present　model　is　capable　of　accurately　predicting　the　contact　phenomenon　in　fractured　poroelasticity.　In　terms　of　the　energy　balance　condition,　precision　and　stability　of　the　proposed　model　in　time　integration　are　verified.　Fractured　porous　media　involved　multiple　cracks　can　be　addressed　more　naturally　and　conveniently　with　the　present　model　relative　to　extended　finite　element　method　(XFEM)　and　phantom　node　method　(PNM).　By　solving　a　set　of　typical　porous　media　problems,　the　superiority,　accuracy　and　robustness　of　the　present　model　are　verified.　(C)　2020　Elsevier　Inc.　All　rights　reserved.