# Thixotropic Behavior of Reconstituted Debris-Flow Mixture

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Experimental Procedures

^{2}) is located in the western part of Switzerland and extends from the summit of the Illhorn mountain (2716 m above sea level (asl)) to the fan apex (850 m asl) and to the outlet of the Illgraben into the River Rhone (610 m asl). A wide variety of flow types have been observed in Illgraben, ranging from granular to muddy debris flows, to hyperconcentrated flows and flood events [21,22]. Debris flows typically occur during intense summer thunderstorms from April to October. The tested material, which has been collected from the deposit areas along the channel, has a specific gravity of 2.633 and it is characterized by the presence of a coarse sediment fraction (80% sand-gravel and 20% silt-clay), as it is shown in Figure 1.

_{s}, conveniently cooled, have been mixed with an appropriate volume of distilled water V

_{w}in order to obtain a mixture having the desired sediment concentration C by volume:

^{−7}–0.2 Nm with a max accuracy of 2 × 10

^{−7}Nm, and a rotational speed ranging from 10

^{−6}1/min to 3 × 10

^{3}1/min.

## 3. Results

^{−1}–10

^{0}s (Figure 4), and it is associated with a low shear rate, which results in two order of magnitude lower than the shear rate corresponding to the flowing steady state regime (Figure 3).

^{1}–10

^{2}Pa⋅s, than after a short-period time (typically 10

^{1}s), the slurry suddenly halts and the viscosity tends to an infinite value. For stress higher than the critical value, the viscosity reduces over a short period of time of about 10

^{1}s, then shows a constant value corresponding to the ultimate flowing steady state (Figure 3).

^{−1}and keeping the mixture at rest 5 s before shearing. Then, the test starts following an increasing and decreasing shear rate ramp. At the end of the decreasing ramp the mixture rested for longer time (35 and 150 min between run F9–F10 and F10–F11, respectively) before it was stirred 5 s at $\dot{\gamma}$ = 600 s

^{−1}, and the next run started. Despite the resting period between the different runs, the mixture exhibits the same steady state apparent viscosity (Figure 9). The resting period affects the shear stress during the increasing shearing ramp. In effect, the longer the resting time, the higher the stress (Figure 8). The flow curves suggest a nonlinear behavior of the static yield stress with respect to resting time, along with an asymptotic trend for longer resting time. Corresponding to the decreasing shear ramp applied, the stress seems much less sensitive to the resting time, showing an almost complete overlapping. As a consequence, the dynamic yield stress and the viscosity rate are the same, no matter the resting period. The complete overlapping of the flux curves corresponding to the lower shear rate is remarkable (i.e., rate $\dot{\gamma}$ < 1–2 s

^{−1}).

^{−1}) applying different resting times (0, 3, and 10 min, respectively, for runs F24, F25 and F26) after pre-stirring, just before running the test for 60 s. In any case, the mixture was pre-stirred at a constant shear rate $\dot{\gamma}$ = 600 s

^{−1}for 30 s. The measured shear stress depends on the resting time: for instance, corresponding to a shear rate of 10

^{−4}s

^{−1}, the shear stress varies over one order of magnitude increasing the resting time. Even in these cases referring to the increasing ramp, the longer the resting time, the higher the shear stress, whereas the flow curve completely overlapped during the decreasing shear ramp (Figure 10a), and the shear stress level remains almost the same (about 10–20 Pa, see Figure 10a), correspondingly the viscosity increase at the same rate by almost three orders of magnitude (Figure 10b).

^{−4}, 10

^{−1}] s

^{−1}(runs F24, F25, and F26) with the reference flow curve at higher shear rate run F22 $\dot{\gamma}$ = [10

^{−2}; 10

^{3}] s

^{−1}and run F23 $\dot{\gamma}$ = [10

^{−4}; 10

^{0}] s

^{−1}. Runs F22 and F23 were carried out pre-stirring the mixture 30 s at a constant shear rate $\dot{\gamma}$ = 600 s

^{−1}followed by a resting period of 5 s. Both tests lasted 60 s, with a semilogarithmic shear rate for the increasing ramp over time. The shear banding (run F22) occurs between about ${\dot{\gamma}}_{c1}$= 4 × 10

^{0}s

^{−1}and ${\dot{\gamma}}_{c2}$ = 10

^{1}s

^{−1}. Once the critical shear rate ${\dot{\gamma}}_{c2}$ has been reached during run F22 (see Figure 11), the mixture starts flowing and the viscosity tends progressively to its steady state value. The static and dynamic shear stress values are the same (i.e., about 45 Pa). When the critical shear rate is not attained during the increasing ramp (i.e., $\dot{\gamma}$ < 4 × 10

^{0}s

^{−1}; run F23, F24, F25 and F26), the stress level remains lower than its critical value (i.e., about 45 Pa, run F22 in Figure 11), and during the following decreasing shear rate ramp the flow curve shows a plateau regime, thus the apparent viscosity reduces at the same rate, no matter the resting period between the subsequence tests (Figure 12). Interestingly, during the run F22, F23 and F24 the mixtures experienced the same initial viscosity of about 10

^{2}Pa⋅s, corresponding to the identical initial condition of the mixture (i.e., pre stirring of 30 s at $\dot{\gamma}$ = 600 s

^{−1}, 5 s resting time before flowing). When longer resting time is applied before flowing (i.e. runs F25 resting time of 3 min, and F26 resting time of 10 min) the initial viscosity increases over orders of magnitudes and no pseudo plateau regime appears. As far as the shear rate approaching its critical value ${\dot{\gamma}}_{c1}$, the viscosity tends to the same value, no matter the initial condition of the mixture (Figure 12).

## 4. Discussion

^{−1}s

^{−1}) the different aged mixtures experience the same apparent viscosity η ≈ 1.5 × 10

^{2}Pa⋅s, which is much larger than the steady state viscosity η ≈ 3 × 10

^{−1}Pa⋅s (test F22 in Figure 12). The descending shear rate curve gives the same stress–strain response no matter the former aging level (Figure 11). Interestingly, the stress level remains almost constant during the reducing shear rate ramp, and it is lower than the dynamic yield.

^{1}s

^{−1}corresponding to yield stress of about 45 Pa) and the shear stress necessary to completely halt the flowing slurry is lower than the threshold yield stress. In this way, it is possible to indicate three different regimes; a lower shear rate regime, corresponding to a shear rate lower than the critical value $\dot{\gamma}{\dot{\gamma}}_{c1}$, in which the increasing shear rate promotes the motion of the slurry, showing viscosity values larger than steady state value by order of magnitude; an intermediate unstable shear rate regime, corresponding to a shear rate ${\dot{\gamma}}_{c1}<\dot{\gamma}<{\dot{\gamma}}_{c2}$, in which the mixtures show a shear banding behavior characterized by yield stress level; and a higher shear rate regime for $\dot{\gamma}{\dot{\gamma}}_{c2}$, where the flowing debris behave as a non-Newtonian fluid characterized by a constant steady state viscosity. The rheological behavior of these three regimes is affected by the initial condition of the mixture, and whereas the ultimate steady state viscosity is not affected by the initial condition. In particular, the long-term period of rest leads to hysteresis on the flow curve, with a distinct dynamic and static yield stress. Eventually the experiments provide evidence of the role of grain concentration on the rheology of the reconstituted debris-flow mixtures.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Barnes, H.A. Thixotropy a review. Non-Newton. Fluid Mech.
**1997**, 70, 1–33. [Google Scholar] [CrossRef] - Barnes, H.A. The yield stress a review or ‘panta rei’ everything flows? Non-Newton. Fluid Mech.
**1999**, 81, 1–33. [Google Scholar] [CrossRef] - Mueth, D.M.; Debregeas, G.F.; Karczmar, G.S.; Eng, P.J.; Nagel, S.R.; Jaeger, H.M. Signatures of granular microstructure in dense shear flows. Nature
**2000**, 406, 385–389. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Huang, N.; Ovarlez, G.; Bertrand, F.; Rodts, S.; Coussot, P.; Bonn, D. Flow of wet granular materials. Phys. Rev. Lett.
**2005**, 94, 028301. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Pellegrino, A.M.; Schippa, L. Macro viscous regime of natural dense granular mixtures. Int. J. Geomate
**2013**, 4, 482–489. [Google Scholar] [CrossRef] - Ovarlez, G.; Bertrand, F.; Rodts, S. Local determination of the constitutive law of a dense suspension of noncolloidal particles through MRI. J. Rheol.
**2006**, 50, 259–292. [Google Scholar] [CrossRef] [Green Version] - Barnes, H.A.; Hutton, J.F.; Walters, K. An Introduction to Rheology; Elsevier: Amsterdam, The Netherland, 1989. [Google Scholar]
- Contreras, S.M.; Davies, T.R.H. Coarse-grained debris flows, hysteresis and time-dependent rheology. J. Hydraul. Eng.
**2000**, 126, 938–941. [Google Scholar] [CrossRef] - Fall, A.; Bertrand, F.; Ovarlez, G.; Bonn, D. Yield stress and shear-banding in granular suspensions. Phys. Rev. Lett.
**2009**, 103, 178301. [Google Scholar] [CrossRef] [Green Version] - Ovarlez, G.; Rodts, S.; Chateau, X.; Coussot, P. Phenomenology and physical origin of shear localization of the shear banding in complex fluids. Rheol. Acta
**2009**, 48, 831–844. [Google Scholar] [CrossRef] [Green Version] - Chen, H.; Lee, C.F. Runout analysis of slurry flows with Bingham model. J. Geotech. Geoenviron. Eng.
**2002**, 128, 1032–1042. [Google Scholar] [CrossRef] - Jeon, S.W.; Leroueil, S.; Locat, J. Applicability of power law for describing the rheology of soils of different origins and characteristics. Can. Geotech. J.
**2009**, 46, 1011–1023. [Google Scholar] [CrossRef] - Schippa, L.; Pavan, S. Numerical modelling of catastrophic events produced by mud or debris flows. Int. J. Saf. Secur. Eng.
**2011**, 1, 403–423. [Google Scholar] [CrossRef] - Schippa, L. Modeling the effect of sediment concentration on the flow-like behavior of natural debris flow. Int. J. Sediment Res.
**2020**, 35, 315–327. [Google Scholar] [CrossRef] - Pellegrino, A.M.; Scotto Di Santolo, A.; Schippa, L. The sphere drag rheometer: A new instrument for analysing mud and debris flow materials. Int. J. Geomate
**2016**, 11, 2512–2519. [Google Scholar] [CrossRef] - Pellegrino, A.M.; Scotto Di Santolo, A.; Schippa, L. An integrated procedure to evaluate rheological parameters to model debris flows. Eng. Geol.
**2015**, 196, 88–98. [Google Scholar] [CrossRef] - Coussot, P.; Nguyen, Q.D.; Huynh, H.T.; Bonn, D. Viscosity bifurcation in thixotropic, yielding fluids. J. Rheol.
**2002**, 46, 573–589. [Google Scholar] [CrossRef] [Green Version] - Coussot, P.; Nguyen, Q.D.; Huynh, H.T.; Bonn, D. Avalanche Behavior in Yield Stress Fluids. Phys. Rev. Lett.
**2002**, 88, 175501. [Google Scholar] [CrossRef] [Green Version] - Pellegrino, A.M.; Schippa, L. Rheological modeling of macro viscous Flows of granular suspension of regular and irregular particles. Water
**2018**, 10, 21. [Google Scholar] [CrossRef] [Green Version] - Pellegrino, A.M.; Schippa, L. A laboratory experience on the effect of grains concentration and coarse sediment on the rheology of natural debris-flows. Environ. Earth Sci.
**2018**, 77, 749. [Google Scholar] [CrossRef] - Badoux, A.; Graf, C.; Rhyner, J.; Kuntner, R.; McArdell, B.W. A debris-flow alarm system for the Alpine Illgraben catchment: Design and performance. Nat. Hazards
**2009**, 49, 517–539. [Google Scholar] [CrossRef] [Green Version] - Bennet, G.L.; Molnar, P.; McArdell, B.W.; Schlunegger, F.; Burlando, P. patterns and control of sediment production, transfer and yield in Illgraben. Geomorphology
**2013**, 188, 68–82. [Google Scholar] [CrossRef] - Nguyen, Q.D.; Boger, D.V. Direct yield stress measurement with the vane method. J. Rheol.
**1985**, 29, 335–347. [Google Scholar] - Scotto Di Santolo, A.; Pellegrino, A.M.; Evangelista, A.; Coussot, P. Rheological behaviour of reconstituted pyroclastic debris flow. Géotechnique
**2012**, 62, 19–27. [Google Scholar] [CrossRef] - Jeong, S.W. Shear Rate-Dependent Rheological Properties of Mine Tailings: Determination of Dynamic and Static Yield Stresses. Appl. Sci.
**2019**, 9, 4744. [Google Scholar] [CrossRef] [Green Version] - Qian, Y.; Kawashima, S. Distinguishing dynamic and static yield stress of fresh cement mortars through thixotropy. Cem. Concr. Comp.
**2018**, 86, 288–296. [Google Scholar] [CrossRef] - Barnes, H.A.; Walters, K. The yield stress myths? Rheol. Acta
**1985**, 24, 323–326. [Google Scholar] [CrossRef] - Schatzmann, M.; Fischer, P.; Bezzolla, G.R. Rheological behaviour of fine and large particle suspensions. J. Hydraul. Eng.
**2003**, 129, 796–803. [Google Scholar] [CrossRef] - Kaitna, R.; Palucis, M.C.; Yohannes, B.; Hill, K.M.; Dietrich, W.E. Effects of coarse grain size distribution and fine particle content on pore fluid pressure and shear behavior in experimental debris flows. J. Geophys. Res. Earth Surf.
**2016**, 121, 415–441. [Google Scholar] [CrossRef] [Green Version] - Jeong, S.W. Grain size dependent rheology on the mobility of debris flows. Geosci. J.
**2010**, 14, 359–369. [Google Scholar] [CrossRef]

**Figure 1.**Grain size distribution. (

**—**) original collected samples. (

**- -**) tested samples obtained from the original samples after separating the grain fraction larger than 0.5 mm.

**Figure 2.**Creep tests. The time–strain trend during the test. (

**a**) Sediment concentration C = 50%. Runs C87–C95 (see Table 2) corresponding to the increasing applied shear as it is reported in the legend. (

**b**) Sediment concentration C = 52%. Runs C36–C42 (see Table 2) corresponding to the increasing applied shear as it is reported in the legend. (

**c**) Sediment concentration C = 56%. Runs C59–C65 (see Table 2) corresponding to the increasing applied shear as it is reported in the legend. (

**d**) Sediment concentration C = 58%. Runs C96–C104 and Run C108 (see Table 2) corresponding to the increasing applied shear as it is reported in the legend.

**Figure 3.**Creep test. The shear-time trend during the test. (

**a**) Sediment concentration C = 50%. Runs C87–C95 (see Table 2) corresponding to the increasing applied shear as it is reported in the legend. (

**b**) Sediment concentration C = 52%. Runs C36–C42 (see Table 2) corresponding to the increasing applied shear as it is reported in the legend. (

**c**) Sediment concentration C = 56%. Runs C59–C65 (see Table 2) corresponding to the increasing applied shear as it is reported in the legend. (

**d**) Sediment concentration C = 58%. Runs C96–C104 and Run C108 (see Table 2) corresponding to the increasing applied shear as it is reported in the legend.

**Figure 4.**Creep test. The apparent viscosity-time trend during the test. (

**a**) Sediment concentration C = 50%. Runs C87–C95 (see Table 2) corresponding to the increasing applied shear as it is reported in the legend. (

**b**) Sediment concentration C = 52%. Runs C36–C42 (see Table 2) corresponding to the increasing applied shear as it is reported in the legend. (

**c**) Sediment concentration C = 56%. Runs C59–C65 corresponding to the increasing applied shear as it is reported in the legend. (

**d**) sediment concentration C = 58%. Runs C96–C104 and Run C108 (see Table 2) corresponding to the increasing applied shear as it is reported in the legend.

**Figure 5.**C = 52%. (

**a**) Flow curves after different premixing period (runs F8, F7, F9—see Table 1—in the legend from the top to the bottom). (

**b**) Viscosity over time for the same runs. Black line: increasing shear ramp (time = 0–60 s); red line: decreasing shear ramp (time = 60–0 s).

**Figure 6.**Flow curves before and after creep test, for different value of grain concentration C (runs F21, F22, F5, F6, F14, F15, F18, F19—see Table 1—in the legend from the top to the bottom).

**Figure 7.**Apparent viscosity derived from the flow curves. Tests carried out before and after creep test, for different value of grain concentration C (runs F21 and F22, F5 and F6, F14 and F15, F18 and F19—see Table 1—in the legend from the top to the bottom). — increasing shear ramp (time 0–60 s); - - decreasing shear ramp (time 60–0 s).

**Figure 8.**Flow curves (C = 52%) after different resting times (runs F9, F10, F11 in the legend from the top to the bottom).

**Figure 9.**Apparent viscosity derived from the flow curves (C = 52%) after different resting times (runs F9, F10, F11 in the legend from the top to the bottom). — increasing shear ramp (time 0–60 s); - - decreasing shear ramp (time 60–0 s).

**Figure 10.**Sediment concentration C = 50%. Low shear rate tests after different resting times. Runs F24 (t = 0 min, reference test), F25 (after resting time of t = 3 min) and F26 (after resting time of t = 10 min). (

**a**) Flow curves. (

**b**) Apparent viscosity. — increasing shear ramp (time 0–60 s); - - decreasing shear ramp (time 60–0 s).

**Figure 11.**Sediment concentration C = 50%. Flow curves at low shear rate after different resting times (F23, F24, F25 and F26) compared to the reference flow curve test (F22). Runs F22, F23, F24, F25 and F26 (from the top to the bottom of the legend). sr

_{max}indicates the maximum shear rate during the test; each test lasts 60 s). — increasing shear ramp; - - decreasing shear ramp.

**Figure 12.**Apparent viscosity derived from the flow curve. Sediment concentration C = 50%. Flow curves at low shear rate after different resting times (F23, F24, F25 and F26) compared to the reference flow curve test (F22). Runs F22, F23, F24, F25 and F26 (from the top to the bottom of the legend). sr

_{max}indicates the maximum shear rate during the test. — increasing shear ramp (time 0–60 s); - - decreasing shear ramp (time 60–0 s).

Runs | Sediment Concentration % | Premixing Period (s) | Resting Time (s) | Shear Rate (1/s) |
---|---|---|---|---|

F5 | 52 | 30 | 5 | 10^{−2}–10^{3} |

F6 | 52 | 30 | 5 | 10^{−2}–10^{3} |

F7 | 52 | 30 | 5 | 10^{−2}–10^{3} |

F8 | 52 | 5 | 5 | 10^{−2}–10^{3} |

F9 | 52 | 60 | 5 | 10^{−2}–10^{3} |

F10 | 52 | 5 | 2.1 × 10^{3} (*) | 10^{−2}–10^{3} |

F11 | 52 | 5 | 9.0 × 10^{3} (**) | 10^{−2}–10^{3} |

F14 | 54 | 30 | 5 | 10^{−2}–10^{3} |

F15 | 54 | 30 | 5 | 10^{−2}–10^{3} |

F18 | 56 | 30 | 5 | 10^{−2}–10^{3} |

F19 | 56 | 30 | 5 | 10^{−2}–10^{3} |

F21 | 50 | 30 | 5 | 10^{−2}–10^{3} |

F22 | 50 | 30 | 5 | 10^{−2}–10^{3} |

F23 | 50 | 30 | 5 | 10^{−4}–10^{0} |

F24 | 50 | 30 | 5 | 10^{−4}–10^{−1} |

F25 | 50 | 30 | 180 | 10^{−4}–10^{−1} |

F26 | 50 | 30 | 600 | 10^{−4}–10^{−1} |

Runs | Sediment Concentration % | Premixing Period (s) | Resting Time (s) | Shear Stress (Pa) |
---|---|---|---|---|

C36 | 52 | 30 | 10 | 50 |

C37 | 52 | 30 | 10 | 70 |

C38 | 52 | 30 | 10 | 100 |

C39 | 52 | 30 | 10 | 105 |

C40 | 52 | 30 | 10 | 110 |

C41 | 52 | 30 | 10 | 130 |

C42 | 52 | 30 | 10 | 115 |

C59 | 56 | 30 | 10 | 280 |

C60 | 56 | 30 | 10 | 350 |

C61 | 56 | 30 | 10 | 380 |

C62 | 56 | 30 | 10 | 390 |

C63 | 56 | 30 | 10 | 400 |

C64 | 56 | 30 | 10 | 450 |

C65 | 56 | 30 | 10 | 550 |

C87 | 50 | 30 | 10 | 40 |

C88 | 50 | 30 | 10 | 50 |

C89 | 50 | 30 | 10 | 55 |

C90 | 50 | 30 | 10 | 58 |

C91 | 50 | 30 | 10 | 60 |

C92 | 50 | 30 | 10 | 62 |

C93 | 50 | 30 | 10 | 65 |

C94 | 50 | 30 | 10 | 68 |

C95 | 50 | 30 | 10 | 75 |

C96 | 58 | 30 | 10 | 200 |

C97 | 58 | 30 | 10 | 500 |

C98 | 58 | 30 | 10 | 550 |

C99 | 58 | 30 | 10 | 700 |

C100 | 58 | 30 | 10 | 750 |

C101 | 58 | 30 | 10 | 800 |

C102 | 58 | 30 | 10 | 850 |

C103 | 58 | 30 | 10 | 900 |

C104 | 58 | 30 | 10 | 1100 |

C108 | 58 | 30 | 10 | 1500 |

Runs | Sediment Concentration % | Premixing Period (s) | Resting Time (s) | Yield Stress (Pa) |
---|---|---|---|---|

C87–C95 | 50 | 30 | 5 | 62–65 |

C36–C42 | 52 | 30 | 5 | 110–115 |

C59–C65 | 56 | 30 | 5 | 380–390 |

C96–C104 | 58 | 30 | 5 | 900–1100 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Schippa, L.; Doghieri, F.; Pellegrino, A.M.; Pavesi, E.
Thixotropic Behavior of Reconstituted Debris-Flow Mixture. *Water* **2021**, *13*, 153.
https://doi.org/10.3390/w13020153

**AMA Style**

Schippa L, Doghieri F, Pellegrino AM, Pavesi E.
Thixotropic Behavior of Reconstituted Debris-Flow Mixture. *Water*. 2021; 13(2):153.
https://doi.org/10.3390/w13020153

**Chicago/Turabian Style**

Schippa, Leonardo, Ferruccio Doghieri, Anna Maria Pellegrino, and Elisa Pavesi.
2021. "Thixotropic Behavior of Reconstituted Debris-Flow Mixture" *Water* 13, no. 2: 153.
https://doi.org/10.3390/w13020153