Fluid-solid coupling is a common phenomenon in the studies of granular materials, geotechnical engineering and so on. Based on a multiphase fluid model in the framework of lattice Boltzmann method (LBM) and the discrete element method (DEM), a multiphase fluid-solid coupling algorithm of LBM-DEM is proposed, where the coupling module is developed on the basis of two open-source codes, Palabos and Yade. The feasibility and accuracy of the algorithm are validated through three classical fluid-solid coupling examples: a single sphere settling in a fluid, a sphere falling into a fluid from the air and two spheres colliding with each other in fluid. Then two complex phenomena in geotechnical engineering, transient-state flow and debris flow, are simulated. The results indicate that the LBM-DEM coupled method has strong advantages in the numerical simulation of complex fluid-solid coupling problems. It can accurately reveal the fluid-solid interaction mechanisms, physical & mechanical behaviors and failure process at both macroscopic and mesoscopic scales. Furthermore, from the numerical simulation results, the process of debris flow can be divided into three stages: steady seepage stage, startup stage and flow stage of the fluid-solid mixture. Display omitted •A multiphase fluid-solid coupling algorithm of LBM-DEM is proposed.•The feasibility and accuracy of the algorithm are validated through two classical fluid-solid coupling examples.•As complex applications, two complex phenomena in geotechnical engineering are simulated.•The analysis results provide evidences and insights into the mechanism of fluid-solid coupling.•Based on the numerical results, the process of debris flow can be divided into three stages.