Abstract
A μ(I) rheology–based avalanche flow model whose governing equations are established in a rectangular Cartesian coordinate system is proposed in this paper. The motivation is updating the term related to gradients of the depth-averaged pressure and extending the application of μ(I) rheology to natural avalanche simulation. The main advantage of the proposed method is that it captures the constitutive properties of the avalanche by introducing the μ(I) rheology. The main novelty of the present model that distinguishes other μ(I) rheology–based approaches is that the in-plane shear is not considered in our model (consistent with the traditional Savage–Hutter theory); thus, the μ(I) rheology only plays a part in describing the normal transverse stresses. Experimental example shows that the proposed model can predict the moving process of granular flow satisfactorily. Simulation of a natural case (the Ermanshan avalanche in China) demonstrates that the simulation can approximately reproduce real avalanches tolerably well.
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