A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II: Numerical predictions and experimental tests.

*(English)*Zbl 1371.86007
Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 470, No. 2170, Article ID 20130820, 31 p. (2014).

Summary: We evaluate a new depth-averaged mathematical model that is designed to simulate all stages of debris-flow motion, from initiation to deposition. A companion paper shows how the model’s five governing equations describe simultaneous evolution of flow thickness, solid volume fraction, basal pore-fluid pressure and two components of flow momentum. Each equation contains a source term that represents the influence of state-dependent granular dilatancy. Here, we recapitulate the equations and analyse their eigenstructure to show that they form a hyperbolic system with desirable stability properties. To solve the equations, we use a shock-capturing numerical scheme with adaptive mesh refinement, implemented in an open-source software package we call D-Claw. As tests of D-Claw, we compare model output with results from two sets of large-scale debris-flow experiments. One set focuses on flow initiation from landslides triggered by rising pore-water pressures, and the other focuses on downstream flow dynamics, runout and deposition. D-Claw performs well in predicting evolution of flow speeds, thicknesses and basal pore-fluid pressures measured in each type of experiment. Computational results illustrate the critical role of dilatancy in linking coevolution of the solid volume fraction and pore-fluid pressure, which mediates basal Coulomb friction and thereby regulates debris-flow dynamics.

For Part I, see [the authors, ibid. 470, No. 2170, Article ID 20130819, 31 p. (2014; Zbl 1371.86008)].

For Part I, see [the authors, ibid. 470, No. 2170, Article ID 20130819, 31 p. (2014; Zbl 1371.86008)].

##### MSC:

86A05 | Hydrology, hydrography, oceanography |

86-08 | Computational methods for problems pertaining to geophysics |

76M12 | Finite volume methods applied to problems in fluid mechanics |

65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |

76T20 | Suspensions |

76T25 | Granular flows |