Debris Flows - Environmental Geomechanics - page 14

in the design of specific rheometers compatible with the relatively large size of
particles involved in geophysical flows. Coaxial-cylinder (Couette) rheometers and
inclined flumes are the most popular geometries. Another source of trouble stems from
disturbing effects such as particle migration and segregation, flow heterogeneities,
fracturation, and layering. These effects are often very pronounced with natural
materials, which may explain the poor reproducibility of rheometrical investigations
[CON 00, IVE 03b, MAJ 92]. Poor reproducibility, complexity in the material
response, and data scattering have at times been interpreted as the failure of the one-
phase approximation for describing rheological properties [IVE 03b]. In fact, these
experimental problems demonstrate above all that the bulk behavior of natural material
is characterized by wide fluctuations, which can be as wide as the mean values. As for
turbulence and Brownian motion, we should describe not only the mean behavior, but
also the fluctuating behavior to properly characterize the rheological properties. For
concentrated colloidal or granular materials [LOO 03, TSA 01], experiments on well-
controlled materials have provided evidence that to some extent, these fluctuations
originate from jamming in the particle network (creation of force vaults sustaining
normal stress and resisting against shear stress, both of which suddenly relax). Other
processes such as ordering, aging, and chemical alteration occur in natural slurries,
which may explain their time-dependent properties [MAR 06]. Finally, there are
disturbing effects (e.g. slipping along the smooth surfaces of a rheometer), which may
bias measurement. Table 1.1 reports a number of experimental investigations run on
natural samples collected in the field or materials mimicking natural materials. The
list is far from exhaustive. For Coulomb plastic materials, Major et al . [MAJ 97];
Major [MAJ 97, MAJ 00] carried out geotechnical tests on natural samples while
Denlinger and Iverson [DEN 01], Iverson [IVE 97], and Major [MAJ 96] investigated
unsteady avalanches mobilizing natural mixtures down a long steep flume. Apart from
these authors, most authors have tried to document that shear stress depends on the
solid concentration or the shear rate, as expected from kinetic theory or Bagnold-
like phenomenological laws [ARA 95, ARM 05, EGA 01, NIS 93, NIS 98, POU 02,
TAK 91, TUB 93]. These authors are not cited in Table 1.1.
When the bulk is made up of fine colloidal particles, phenomenological laws
are used to describe rheological behavior. One of the most popular is the Herschel-
Bulkley model, which generalizes the Bingham law
τ = τ c + K γ n ,
where τ c is the yield stress and K and n are the two constitutive parameters. In
practice, this phenomenological expression successfully describes the rheological
behavior of many materials over a sufficiently wide range of shear rates [BIR 83],
except at very low shear rates [COU 02]. For numerical purposes, a viscoplastic model
may be regularized using a biviscous model [WIL 02], Papanastasiou's exponential
model [PAP 87], or the extended forms of Zhu et al. [ZHU 05]. Indeed, the existence