《Table 2 Summary of the determined rheological parameters and associated errors (in italic)》

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《"Flow Behavior of Clay-Silt to Sand-Silt Water-Rich Suspensions at Low to High Shear Rates: Implications for Slurries, Transitional Flows, and Submarine Debris-Flows"》

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The rheological characterization of the suspensions listed in Table 2 was achieved running experiments using a rheometer Anton Paar MCR301 equipped with vane rotor geometry（http://www.anton-paar.com/uk-en/products/details/mcr-rheometer-series/）.The vane geometry was adopted with fine results and was preferred to the ball measuring system suggested by Schatzmann et al.（2003）.Each test was performed both at controlled shear stress（τSS）steps and at controlled shear rateγ·（CSR）steps（Macosko，1994）.Each step duration was long enough to reach a steady state value of viscosity and shear rate.Following Toorman（1997），Kaitna et al.（2007），Maciel et al.（2009），Jeong（2010），Brown and Jaeger（2014），and Seyssiecq et al.（2015），the reached shear rates are up to 900 s-1.Although the shear rates of debris-flows are less than few tens of s-1，our wide range of shear rate values accounts for the analysis of both natural and artificial water-rich clay and silt suspensions，as well as of slurries and sludge（Seyssiecq et al.，2015）.Experiments were performed twice using different samples with the same proportions of water and A and B fractions in order to verify the reproducibility of experiments.For the duration of experiment runs，water evaporation and particle sinking processes can be dismissed.CSS steps allow us to delineate shear rate and viscosity values at a fixed shear stress.Once collected these values at each shear stress allow the flow curves（shear stress vs shear rate and suspension viscosity vs shear rate）can be delineated.Once CSS runs were performed and，the time needed to reach the steady state of viscosity was known，a CSR test was run using the same composition.The flow curves obtained from CSS and CSR tests show good agreement for the results between the two tests（Fig.2）.This means that both tests are useful in delineating flow curves of suspensions.