In　the　analysis　of　geological　disasters,　various　coupling　problems　can　be　involved.　The　coupling　problems　may　concern　a　variety　of　interactions　between　different　components,　such　as　rock-water　interaction,　rocky　or　flexible　structure-water　interaction,　rock-soil　interaction,　and　rocky　or　flexible　structure-soil　interaction.　It　is　thus　significant　to　analyze　these　coupling　problems.　The　coupling　of　different　numerical　methods　is　a　potential　approach　to　addressing　the　complex　interaction　problems,　which　is　usually　difficult　for　a　single　numerical　method.　Because　a　coupled　method　can　fully　utilize　both　methods　involved.　The　coupling　of　smoothed　particle　hydrodynamics　(SPH)　with　discontinuous　deformation　analysis　(DDA)　is　a　potential　tool　for　various　coupling　problems,　which　is　developed　in　our　previous　studies.　In　the　developed　DDA-SPH　method,　DDA　and　SPH　are　suitable　for　simulating　rocks　and　rocky　or　flexible　structures,　and　modelling　water　and　soil,　respectively.　To　bridge　the　two　methods,　a　coupling　scheme　based　on　a　penalty　method　is　used.　Several　numerical　examples　of　classical　coupling　problems　involved　in　geological　disasters　are　presented　here.　The　simulated　results　suggest　that　the　coupled　method　can　be　successfully　applied　to　handle　various　complex　interaction　problems.　©　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.　2024.