Shallow Water SPH Framework for Regional-Scale Debris Flows with Erosion and Entrainment

  • Dolojan, Nilo Lemuel (Tohoku University)
  • Tsuji, Kumpei (Tohoku University)
  • Nomura, Reika (Tohoku University)
  • Terada, Kenjiro (Tohoku University)
  • Moriguchi, Shuji (Tohoku University)

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The consideration of mass growth resulting from bed-sediment erosion and entrainment is essential for accurately capturing changes in debris flow mobility, energy, and runout distance. The application of depth-integrated shallow water equations (SWE) in debris flow modelling discretized using smoothed particle hydrodynamics (SPH) offers a practical and computationally efficient approach for regional-scale hazard assessments [1]. In this approach, only the debris-flow mass is discretized into moving particles, bypassing the need to solve extensive but predominantly inactive domains. However, conventional shallow water SPH (SWSPH) formulations typically employ constant-mass particles, rendering them fundamentally incompatible with the physics of entrainment and mass growth. To overcome this limitation, this study extends the SWSPH framework to explicitly account for mass growth and evolution. It proposes a variable-mass particle formulation in which the entrained material is added from the bed into each particle. To ensure numerical stability and physical consistency, the formulation is supported by three additional developments: (1) a two-way particle-grid coupling algorithm that ensures mass conservation between the moving flow and the erodible bed; (2) an extended variable smoothing length formulation that maintains a stable neighbor count as particle mass and volume evolve; and (3) an adaptive particle refinement strategy to mitigate the loss of spatial resolution. The framework is validated against large-scale U.S. Geological Survey debris-flow flume experiments under both erodible and non-erodible bed conditions [2], demonstrating accurate reproduction of flow-front propagation, erosion depth, volume growth, and depositional geometry. The method is further applied to a real debris-flow event triggered by Typhoon Hagibis in Marumori, Japan, where simulated runout paths, erosion patterns, and deposition agree well with post-event field observations. By overcoming the inherent limitations of constant-mass SWSPH, the proposed variable-mass SWSPH framework successfully captures the entrainment and mass growth observed in debris flows.