NY Times, 4 oct. 2005

Transcription

1 NY Times, 4 oct. 2005

2 Fluid avalanches, quicksand and quickclay landslides ( geo-rheology ) Daniel Bonn (LPS de l ENS-Paris and WZI-Amsterdam) with: P. Moller (ENS) P. Coussot, S. Rodts (LCPC) Julie DRAPPIER E. Khaldoun, G. Wegdam (WZI-Amsterdam) J.O. Fossum, Y. Méheust (NTNU, Trondheim)

3 Yield stress fluids -in your refrigerator: mayonnaise, ketchup, yoghurt, whipped cream -in your bathroom: beauty creams, hairgel, shaving foam -in civil engineering: (wet) sand, concrete, cement. -in geophysisics: sand, quicksand, quick clay Liquid and Julie solid DRAPPIER at the same time!

4 ! Yield stress fluids Simple yield stress fluids: Herschel-Bulkley model " = " y + k σ! # n No flow " y «Flow curve» " y "!&

5 Yield stress, thixotropy and aging Two HUGE problems: 1. Yield stress is difficult, if not impossible to measure experimentally ( παντα ρει ) 2. Herschel-Bulkley model does NOT account for shear localization (shear banding)

6 1. Measurement of the yield stress Bentonite suspension: a typical colloidal clay gel Mayonnaise: a stable emulsion Stress loop: increase then decrease (time on the order of 2 min.) for different pasty or granular materials Shear stress (Pa) 10 2 Stress increase Bentonite suspension Stress decrease 10 1 Shear stress (Pa) 10 2 Emulsion (Mayonnaise) Shear rate (1/s) Shear rate (1/s) Stress increase Stress decrease

7 2. Shear localization (banding)

8 A first important clue: aging Aging: increase of the viscosity at rest, and at zero (or very low) shear complex viscosity (Pas) Bentonite 5% clay gel house of cards structure 0,1 0, aging time (s)

9 Second important clue: «shear rejuvenation» (thixotropy or the «French yoghurt effect» ) viscosity (Pas) stress 4Pa stress 6Pa stress 10Pa 1 0, time (s) Abou et al. J. Rheol. 2003

10 Yield stress, aging and shear rejuvenation Competition between aging and shear rejuvenation is general for soft materials, and leads to AVALANCHES Bentonite avalanche on an inclined plane " y = #ghsin($)

11 Sand avalanches McDonald and Anderson, 1988

12 RHEOLOGY: VISCOSITY BIFURCATION viscosity (Pas) stress (Pa) Aging Shear rejuvenation time (s) Bentonite (colloidal gel), 5% Coussot et al., PRL 2002

13 The phenomenon The is general! is general! viscosity (Pas) stress (Pa) viscosity (Pas) stress (Pa) viscosity (Pas) , time (s) Colloidal gel (Bentonite) time (s) Polymer gel (hairgel) 0, time (s) Colloidal glass (Laponite) Shear rate (1/s) 10 1 Stress (Pa): Foam Time (s) Foam (shaving foam) Rotation velocity (rad/s) 10 1 Polystyrene beads Torque (mnm): Time (s) Granular matter (polystyrene beads) QUESTION: WHAT HAPPENS IF A SHEAR RATE IS IMPOSED THAT IS NOT ACCESSIBLE WHEN FIXING THE STRESS? Coussot et al., PRL 2002 Da Cruz et al PRE 2003

14 Vertical MRI, 40cm borehole, T Inserted rheometer Controlled rotation velocity r1 2 cm gap r2 v! ω Material 12 cm Tangential velocity measured in a central fluid portion

15 MRI velocity profile measurement in a Couette cell Bentonite again Deformation of fictive lines within the material in a Couette geometry

16 Velocity profiles: shear localization velocity (m/s) 0,09 0,08 0,07 0,06 Increasing speed 0,05 0,04 0,03 0,02 0,01 0-0,01 4 4,2 4,4 4,6 4,8 5 5,2 R (cm)

17 MRI on cone-plate: homogeneous stress ω ω R angle Cone-plate cell NO NEED FOR STRESS HETEROGENIETY TO GET SHEAR BANDING!

18 Instantaneous state of structure (degree of jamming) E " # Simplest possible model 10 3 Stress: e.g. n! "(!) = " 0(1 +! ) d" dt = 1 # $% & "! 10 2 Viscosity Time Coussot et al., PRL 2002 J. Rheol. 2002

19 Yield stress, shear rejuvenation & aging! «Unstable flow curve» σ! No flow Herschel-Bulkley real fluid σ! c real fluid Herschel-Bulkley σ! c! σ " c Coussot et al., PRL 2002, J. Rheol. 2002!&

20 The overall picture: Wet granular material: Huang et al., PRL 2005

21 Rheology conclusion Interplay between yield stress and thixotropy is GENERAL for structured complex fluids (we, in any case, haven t found an exception) and lead naturally to -a viscosity bifurcation -shear localization and -a critical shear rate All this implies that the yield stress in NOT a property of the material, since the critical stress for the bifurcation depends on the (shear) history of the material. This provides a natural explanation for the irreproducibility of the experimentally determined yield stress. Experimentally: preshear is needed for reproducible results Coussot et al., Phys.Rev.Lett 2002, Huang et al., Phys.Rev.Lett 2005, Moller et al. Soft Matter 2006 (minireview, free download)

22 Geo-rheology This provides a common framework (the rheological properties) To describe glasses, gels, granular matter, emulsions, clayey soils.. Applications in geophysics? Landslides, quicksand?

23 Earthquake quicksand ( geophysicists quicksand ) Water flow

24 Eartquake quicksand (Japan, 1964)

25 Desert quicksand Lawrence: Well, I, it's, uh, let me see, I killed two people. One was a boy. That was yesterday. I led him into a quicksand. The other was a man. That was before Aqaba anyway. I had to execute him with my pistol...and Daud slowly sinks away into the quicksand and dies.

26 Dry laboratory quicksand D. Lohse et al. Nature 2005

27 «Real quicksand» (Crusoe, Tarzan, Flash Gordon, Jungle Book, King Solomons Mines..)

28 Quicksand Three Quicksand Myths: 1) once in, don't move 2) once in, hard to get out 3) once in, one drowns Julie DRAPPIER

29 Salt lake between Teheran and Qom

30 What is quicksand? Natural quicksand From Qom-Iran (salt lake) And Tarfaya-Maroc (close to the sea) Sand+water + CLAY +SALT Gypsum Quartz Cristobali te Hematite Swelling Clays 50% 25% 15% 3% 7 % Results of X-ray analysis Size of the sand particles 20-50µm other forms of quicksand: -fluidized sand -loose sand

31 Rheology of quicksand (a) (b) viscosity [Pas] W%Quick sand 1Pa 1.3Pa 1.35Pa 1.4Pa 1.5Pa viscosity [Pas] Pa 4Pa 5.8Pa 50W%Laboratory Quick sand 7Pa time [s] 10 5 salinity 10-1 (c) mole/l stic modulus [Pa] 1.6Pa Pa 8Pa time [s] Don t move: difference 10 4 between sinking:1mm/15 min and 1m/s By mixing sand 10 and clay (bentonite) 3 Quicksand in salt water, laboratory quicksand can be created. salinity > mole/l

32 Fig.1.and phase separation (a) (b) 10 with 4 10 a very high 4 1Pa viscosity [Pas] W%Quick sand 1Pa 1.3Pa 1.35Pa 1.4Pa 1.5Pa 1.6Pa time [s] 10 5 From salt lake: salinity (c) 10-1 mole/l modulus [Pa] Pa 7Pa 6Pa To 10-1 get your foot out you have to 8Pa Salt is essential 10 4 for the collapse: salinity needs to be > mole/l for the laboratory quicksand Quicksand Phase separation: sedimented sand viscosity: 10 3 You re stuck!! viscosity [Pas] 4Pa 50W%Laboratory Quick sand " # 0.8 ω introduce water in the sand packing: at 1 cm/s : time F=10 [s] 4 N! water sand

33 Elastic modulus 10-2 from rheology time [s] 10 5 Elastic modulus [Pa] (c) 1.6Pa 6Pa Quicksand Laboratory quicksand time [s] 8Pa 10 1 F A Volume % of quicksand Quicksand can support the weight of an adult person at φ=0.4! = 50kg *10m /s2 10 "2 m 2 = 5#10 4 Pa $ E (supposing normal and shear forces to be similar)

34 Piling up oranges More than 2/3 of space occupied by the oranges

35

36 Sinking test.

37 Quicksand Three Quicksand Myths: 1) once in, don't move: TRUE 2) once in, hard to get out: TRUE (there is a way to get out, however..) 1) once in, one drowns: FALSE (but beware.the high tide may come in) A. Khaldoun Julie DRAPPIER et al., Nature 2005 But what is quick clay????

38 Quick clay landslides With: Jon Otto Fossum and Yves Méheust Department of Physics NTNU, Trondheim University (Norway)

39 Quick clay landslides (the Rissa raset)

40 St Jean-Vianney, 1971, Canada

41 WHAT IS QUICKCLAY? Natural quickclay from Trondheim, Norway (Bulk sample) 60-80% non swelling clays: illite chlorite some kaolinite 20-40% primary minerals: Quartz amphibol felspar pyrite

42 WHAT IS QUICKCLAY? Natural quickclay from Trondheim, Norway <2µm fraction of the sample Name: quickclay Norway, <2um, Mg 2+ saturated 14Å 10Å 7Å untreated C 4% swelling clays: Vermiculate montmorillonite counts % non swelling clays: illite kaolinite Norway2um June 5, :33:46 AM 2! CuK" IBED; Fac. N.W.I.; Universiteit van Amsterdam.

43 WHAT IS QUICKCLAY? Natural quickclay from Trondheim (Norway) SEM microscopy The quartz particles are small and also plate like!! Texture analysis %!m Quickclay (Norway) < Total The particles are in the fine silt size

44 RHEOLOGY of QUICKCLAY Catastrophic liquefaction above a certain stress (=slope) 50 wt% natural quickclay Fixed cylinder Vane geometry (inner cylinder) 10 4 Viscosity, Pa Pa 3Pa 4Pa 4.4Pa 4.5Pa 5Pa Time, s aging Factor of 10 6 Thixotropy Yield stress

45 RHEOLOGY of QUICKCLAY Catastrophic liquefaction (After rain)!! At fixed Shear stress, 5Pa (=fixed slope) Varying water content % difference In water content Viscosity, Pas wt% 58wt% 55wt% 52wt% 51wt% 48wt% Time, s Factor of 10 6!!

46 LABORATORY QUICKCLAY Elastic modulus, G', Pa 10 3 illite Quickclay Salt effect Factor of 10 3!! At 0 gram salt ω ω added salt ω ω conductivity, Scm -1 Increasing added salt (steps of 0.005g)

47 LABORATORY QUICKCLAY Laboratory quickclay is: 3% washed bentonite +97% illite Elastic modulus, G', Pa Natural quickclay Laboratory quickclay 1E-4 1.2E -4 5E -4 1E conductivity, Scm -1 Increasing added salt

48 Laboratory landslides

49 LANDSLIDE EXPERIMENT Depending on the WATER CONTENT, Quickclay has FOUR!!! different flow regimes: θ=50 Quickclay sample yield surface H Flow θ liquid regime 55Wt% Yield stress regime 59Wt% 61Wt% 63Wt% Solid regime Landslide regime " = #g(h $ y)sin% = " y

50 Landslide experiment " = " y + # $ n 55wt% 59wt% 61w% 63wt%

51 CONCLUSION -Yield stress problem solved to a great extent, leading to new physical phenomena: fluid avalanches.. Geo-rheology allows for a quantitative insight into geophysical phenomena: -quicksand: one cannot drown.. -landslides of clayey soils travel much farther than predicted by models but now that we understand the rheology, we can do much better.