*2.2. Granular Stress Models*

The particle pressure is the sum of the the pressure induced by collision *p<sup>s</sup>*, calculated differently depending on the solid phase stress closure model and the pressure induced by the permanent contact between the particles *pf f* defined as:

$$p^{ff} = \left\{ \begin{array}{c} 0, \phi < \phi\_{\text{min}}^{Fric} \\ Fr\frac{(\phi - \phi\_{\text{min}}^{Fric})^{\eta\_0}}{(\phi\_{\text{max}} - \phi)^{\eta\_1}}, \phi \ge \phi\_{\text{min}}^{Fric}, \end{array} \right. \tag{9}$$

where *φFric min* = 0.57, *Fr* = 0.05, *η*0 = 3, and *η*1 = 5 are empirical coefficients. In the present work, numerical simulations are conducted using two granular stress models: the dense granular flow rheology (*μ*(*I*) rheology) and the kinetic theory for granular flows (KT).
