In　this　paper,　a　mixed　two-scale　numerical　manifold　computational　homogenization　model　is　presented　for　dynamic　analysis　and　wave　propagation　of　the　discontinuous　heterogeneous　porous　media　based　on　the　first-order　homogenization　theory.　Instead　of　the　conventional　version　which　neglects　microscopic　dynamics,　the　extended　Hill-Mandel　lemma　is　employed　to　incorporate　the　microscale　dynamic　effects.　Microscale　and　macroscale　Initial　Boundary　Value　Problems　(IBVPs)　are　solved　simultaneously　using　the　Numerical　Manifold　Method　(NMM)　with　the　information　conveyed　between　different　scales.　The　microscale　IBVP　is　solved　under　Linear　Boundary　Conditions　(LBCs)　and　Periodic　Boundary　Conditions　(PBCs)　that　are　defined　with　macroscale　solid　displacement,　fluid　pressure　and　their　first-order　gradients.　The　discontinuous　macroscale　IBVP　is　solved　iteratively　using　the　Newton　method　with　the　macroscale　internal　forces　and　Jacobian　determined　by　solving　the　microscale　IBVPs.　A　stick-slip　contact　model　is　implemented　using　an　augmented　Lagrange　multiplier　method　to　impose　frictional　contact　conditions　along　the　macroscale　discontinuities.　Through　various　numerical　simulations,　the　presented　two-scale　NMM　is　shown　to　be　able　to　effectively　and　accurately　capture　the　fully　dynamic　and　wave　propagation　responses　of　the　discontinuous　heterogeneous　porous　media　under　the　fluid　injection　and　impact　loading　condition.　(C)　2021　Elsevier　B.V.　All　rights　reserved.