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As is pointed out by the authors, although the logarithmic expression can be a good approximation within a range of shear rates, modification is needed to address the issue that shear stress is expected to approach a constant (rather than infinity) as the shear rate approaches zero.
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As is pointed out by the authors, although the logarithmic expression can be a good approximation within a range of shear rates, modification is needed to address the issue that shear stress is expected to approach a constant (rather than infinity) as the shear rate approaches zero.
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Note that their 2D simulations are performed in a context for which the gravity-induced gradient of normal stress is significant and the upper layers are sufficiently agitated: the imposed normal force is less than the weight of 24 layers of grains with the typical driving speed ranging from 22 to 53(gd)0. 5; the packing thickness is about 102d. In our experiments, the imposed normal stress is more than the weight of 102 layers of grains while the highest driving speed is less than 10-2(gd)0.5; the typical packing is 24 layers thick. The low speed and high normal load in our experiments renders the entire packing quasistatic. The shear banding and the "phase boundary" that occurs in our thick-layer experiments are induced mainly by sidewalls rather than by gravity.
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Note that their 2D simulations are performed in a context for which the gravity-induced gradient of normal stress is significant and the upper layers are sufficiently agitated: the imposed normal force is less than the weight of 24 layers of grains with the typical driving speed ranging from 22 to 53(gd)0. 5; the packing thickness is about 102d. In our experiments, the imposed normal stress is more than the weight of 102 layers of grains while the highest driving speed is less than 10-2(gd)0.5; the typical packing is 24 layers thick. The low speed and high normal load in our experiments renders the entire packing quasistatic. The shear banding and the "phase boundary" that occurs in our thick-layer experiments are induced mainly by sidewalls rather than by gravity.
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