A three-dimensional lattice Boltzmann method for simulating the run-out of debris flows

Debris flows pose significant geological hazards distinguished by their high velocities and extensive run-out distances. Their inherent unpredictability and destructive power make direct field monitoring exceptionally difficult. Numerical simulation provides a valuable alternative, allowing for the reconstruction of debris flows. In this paper, we present a three-dimensional numerical method directly based on the lattice Boltzmann method (LBM) with a Herschel–Bulkley–Papanastasiou (HBP) rheological model for simulating the run-out of debris flows. The proposed approach employs a single-phase free-surface LBM to track the evolution of the granular–air interface. The constitutive behavior is captured by incorporating a Mohr–Coulomb criterion with a pore pressure ratio into the HBP model to calculate the yield stress. This HBP model can effectively describe frictional dissipation and the saturation influence. Furthermore, a cross-platform OpenCL-based graphics processing unit parallelization technique is implemented to accelerate the three-dimensional simulations. The established method is first validated through the simulation of a small-scale laboratory experiment. Subsequently, the validated method is applied to simulate the catastrophic landslide at the Shenzhen landfill. The simulation results show good agreement with field observations, demonstrating that the proposed LBM-based method can effectively simulate the initiation, propagation, and deposition of debris flows over complex three-dimensional terrain, enabling the accurate prediction of its run-out distance.