**3. Results**

## *3.1. Solid Phase Stress Model Sensitivity*

Two simulations were conducted to evaluate the sensitivity of the model results to the choice of the granular stress model: the kinetic theory for granular flows and the *μ*(*I*) rheology. For both simulations, the *k* − *ε* turbulence model was used. The time evolution of the maximum scour depth and the shape of the sediment bed are compared with the experimental data from Mao (1986) [2] and numerical simulation results from Lee et al. (2016) [12] in Figures 2 and 3, respectively.

**Figure 2.** Time evolution of the maximum scour depth for simulations with the *k* − *ε* turbulence model using *μ*(*I*) rheology (orange line) and kinetic theory (green dotted line) compared with the experimental data from Mao (1986) [2] (red dots) and numerical data from Lee et al. (2016) [12] (purple dashed line).

**Figure 3.** Bed profiles from simulations with the *k* − *ε* turbulence model using *μ*(*I*) rheology (orange line) and kinetic theory (green dotted line) at 11 s (top), 18 s (middle), and 25 s (bottom) compared with experimental data from Mao (1986) [2] (red dots) and numerical data from Lee et al. (2016) [12] (purple dashed line).

It clearly appears that the shape of the sediment bed and its time evolution were not very sensitive to the granular stress model. For both models, the temporal evolution of the maximum scour depth (Figure 2) and the upstream part of the sediment bed (Figure 3) agreed reasonably well

with the experimental data from Mao (1986) [2] and the numerical results from Lee et al. (2016) [12]. At 25 s, the *BSS* calculated from the simulations using the *μ*(*I*) rheology (*BSS* = 0.731) and the KT (*BSS* = 0.721) were very close. The quality of the results was therefore equivalent for both granular stress models.

In both simulations, the sediments tended to accumulate at the downstream side of the pipeline, generating a sand dune. According to Lee et al. (2016) [12], this accretion phenomenon can be explained by the inability of the *k* − *ε* model to reproduce the oscillatory wake behind the cylinder (responsible for the lee-wake erosion stage).

The present results demonstrated that the sediment accumulation observed at the lee side of the cylinder was not due to the solid stress model. Since the granular stress models provided similar results, in the following, only the *μ*(*I*) rheology will be used, as it was more computationally efficient.
