Observations of rapidly flowing granular-fluid materials

Abstract

The rapid shearing of a mixture of cohesionless glass spheres and air or water was studied in an annular, parallel-plate shear cell designed after Savage (1978). Two types of flow were observed. In the first type of flow the entire mass of the granular material was mobilized. At high shear rates the shear and normal stresses were found to be quadratically dependent upon the mean shear rate (at constant volume concentration), in general agreement with the observations of Bagnold (1954) and Savage & Sayed (1984), and the ‘kinetic’ theory of Jenkins & Savage (1983). The stresses were found to be weakly dependent on the volume concentration up to approximately 0.5, and strongly dependent above this concentration. For flows in which water was the interstitial fluid, the ratio of the shear stress to the normal stress was slightly higher (than in air), and the stresses at lower shear rates were found to be more nearly linearly related to the shear rate. It is suggested that these effects are contributed to by the viscous dampening of grain motions by the water. The second type of flow was distinguished by the existence of an internal boundary above which the granular material deformed rapidly, but below which the granular material remained rigidly locked in place. The thickness of the shearing layer was measured to be between 5 and 15 grain diameters. The stress ratio at the bottom of the shearing layer was found to be nearly constant, suggesting the internal boundary is a consequence of the immersed weight of the shearing grains, and may be described by a Coulomb yield criterion. A scaled concentration is proposed to compare similar data obtained using different-sized materials or different apparatus. An intercomparison of the two types of flow studied, along with a comparison between the present experiments and those of Bagnold (1954) and Savage & Sayed (1984), suggests that the nature of the boundaries can have a significant effect upon the dynamics of the entire flow.

A hypoplastic constitutive model for debris materials

“…By checking the measured normal stress for 1:0 mm beads, we assume that the initial confining pressure of an element at the upper surface of the specimen has a value around 500 N/m 2 . The exact value of C 1 was not reported in the literature [33] and here is assumed equal to 0.64 which is a typical value for monosized spheres [2,16]. Thus, the corresponding minimum void ratio is determined equal to 0.563.…”

“…For the case of a granular-fluid mixture, we take Hanes and Inman's experiments [16] about spherical particles sheared in water as an example. The data for particles with diameter 1:85 mm which were stated as good quality ones are chosen to verify the new model.…”

“…where s is the mean free distance between two particles; C 1 is the asymptotic limit of the maximum measured solid volume fraction as the container dimensions approach infinity, which is also related to the size of the particles [16]. The shear stress for the 'grain-inertia' regime, T i , is formulated as…”

“…Taking the four material constants c 1 $ c 4 as unknowns, a system of four linear equations can be obtained by substituting the corresponded stress and strain rate of the two stress states into the model (16). Therefore, the material constants are determined as functions of the wellestablished parameters in soil mechanics, the initial tangent modulus E i , the initial Poisson ratio t i , the friction angle / 0 and the dilatancy angle w. It should be pointed out that these parameters are related to a specific confining pressure, all the sets of material constants used in this paper are obtained with a confining pressure T h ð3; 3Þ ¼ 100 kPa.…”

“…It means, for same material, same constants c 1 $ c 4 will be obtained for the original and extended models in the case of e ¼ e ecrt . Thus, the material constants emerging in the model (21) can be determined by the same way as done for (16). The dilatancy angle w is equal to zero since there is no volume deformation in this case [44].…”