Comparing thixotropic and Herschel–Bulkley parameterizations for continuum models of avalanches and subaqueous debris flows

Abstract

Abstract. Avalanches and subaqueous debris flows are two cases of a wide range of natural hazards that have been previously modeled with non-Newtonian fluid mechanics approximating the interplay of forces associated with gravity flows of granular and solid-liquid mixtures. The complex behaviors of such flows at unsteady flow initiation (i.e., destruction of structural jamming) and flow stalling (restructuralization) imply that the representative viscositystress relationships should include hysteresis: there is no reason to expect the timescale of microstructure destruction is the same as the timescale of restructuralization. The nonNewtonian Herschel-Bulkley relationship that has been previously used in such models implies complete reversibility of the stress-strain relationship and thus cannot correctly represent unsteady phases. In contrast, a thixotropic nonNewtonian model allows representation of initial structural jamming and aging effects that provide hysteresis in the stress-strain relationship. In this study, a thixotropic model and a Herschel-Bulkley model are compared to each other and to prior laboratory experiments that are representative of an avalanche and a subaqueous debris flow. A numerical solver using a multi-material level-set method is applied to track multiple interfaces simultaneously in the simulations. The numerical results are validated with analytical solutions and available experimental data using parameters selected based on the experimental setup and without post hoc calibration. The thixotropic (time-dependent) fluid model shows reasonable agreement with all the experimental data. For most of the experimental conditions, the HerschelBulkley (time-independent) model results were similar to the thixotropic model, a critical exception being conditions with a high yield stress where the Herschel-Bulkley model did not initiate flow. These results indicate that the thixotropic relationship is promising for modeling unsteady phases of debris flows and avalanches, but there is a need for better understanding of the correct material parameters and parameters for the initial structural jamming and characteristic time of aging, which requires more detailed experimental data than presently available.

The Tribological and Rheological Properties of Vegetable Lubricating Grease Modified of TiO2 Nanoparticles

“…The Herschel-Bulkley model it's the easiest model to describe the flow curves of non-linear plastic-viscous fluids [60][61][62]:…”

The influence of base oil type on the rheological properties of ecological lubricating greases

“…The Herschel-Bulkley model is the simplest model for describing the flow curves of nonlinear viscoelastic fluids (Gavrilov et al, 2017;Chauhan et al, 2018;Jeon and Hodges, 2018):…”

The Effects of Sediment Size and Concentration on the Rheological Behavior of Debris Flows

“…It is worth noting thixotropic behavior, as it is evident from the flow curves (Figures 2, 3), which exhibit a stress level independent on the shear rate (for shear rate less than 10 0 -10 1 s À1 depending on sediment concentration) having different values between increasing and decreasing shear stress ramp. The behavior of these granular-fluid mixtures at flow initiation and flow stalling put in evidence that the timescale of microstructure destruction is not the same as that of restructuralization, and it reflects on the yield stress [30]. Notwithstanding the existence of a yield stress, which marks the transition between solid and fluid state, it is still a controversial issue [31], it may be defined a static yield stress τ c1 , that is, the critical stress allowing steady state flow (run-up test), and the dynamic yield stress τ c2 corresponding to the complete stoppage of the flowing material.…”

“…A thixotropic flow model may represent both initial structure jamming and aging effects, whereas the non-Newtonian time-independent yield stress model implies the complete reversibility of stress-strain relationship. In many cases, the Herschel-Bulkley model results very similar to the time-dependent thixotropic model [30], and it has widely implemented in viscous-flow simulations [39,40], even though it still remains challenging the treatment of the non-smoothness constitutive equation [41].…”