Mesure de champs
cinématiques particulaires
haute définition dans les milieux
granulaires bidimensionnels
G. Combe, V. Richefeu
Présenté par O. Jenck
Schneebeli** rods : a 2D granular material
**G. Schneebeli, CRAS, 243(1):125-126 (1956)
2D Grains ≡ 6 cm long cylinders of various sections and different diameters
PVC rods ϕ = [1,5 - 2,5 - 3,5 mm]
Mixtures of discs
and rectangles
Wood rods ϕ = [6 - 10 - 16 - 20 mm]
Hexagonal
shapes
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2000 wooden rods in 1γ2ε shear device
3
**
1γ2ε
Shear apparatus
**H.A. Joer & al, Géotechnique, 48(5):605-619 (1996)
Possible tests
Oedometric compression
Isotropic compression
And
Simple shear test: tilt with
constant vertical stress
Biaxial test: vertical compression,
lateral stress constant
Test with imposed
rotation of the
principal axes of
STRAINS or
STRESSES
(more complex)
4
**
1γ2ε
Shear apparatus
**H.A. Joer & al, Géotechnique, 48(5):605-619 (1996)
What do we measure ?
- Macroscopic level (sample scale):
• Lengths and tilt of the boundaries ➟ Strain macroscopic tensor
• Forces at the corners of the frame ➟ Stress macroscopic tensor
- Microscopic level (grain scale):
• Position and orientation of grains ➟ full grain kinematics
➟ Contacts list
5
Assessing kinematics using “modern” Digital Camera (2010 ➟ ...)
Shear test on 2000 wooden rods
1100 pictures - 24.5 MPixels
movie picture
speed x 500
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PIT : Particle Image Tracking
Combe & Richefeu, Powders and Grains 2013
PIT : Digital Image Correlation technique adapted to track “automatically”
full kinematics of rigid bodies
Tracker PIT software
Rigid-motion relation to track u, v
and θ…
… with a subpixel resolution using
bilinear, bicubic or biquintic
interpolation
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PIT: Particle Image Tracking
Combe & Richefeu, Powders and Grains 2013
Correlation works between the first and the current images
(thanks to rigid motion and ZNCC)
➡ digital truncation errors are NOT cumulated.
A rescue procedure that basically increase the search zone and
avoid exclusion zones of well-found bodies.
Body being « rescued »
Exclusion zone
Well-found bodies
Increased search zone
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PIT: Particle Image Tracking
Combe & Richefeu, Powders and Grains 2013
Accuracy with synthetic images (from Orteu et al., 2006)
Courtesy, L. Robert
➠ Same intrinsic accuracy as the
codes used in the GdR CNRS 2519
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PIT : Particle Image Tracking
Combe & Richefeu, Powders and Grains 2013
Accuracy with real images that involve the whole measurement chain.
Solid motion = distance and angle conservation
Correction of distortion drastically improve the accuracy.
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Fluctuations of displacement
Richefeu & al., Géotech. Lett., 2, 113-118,(2012)
An experimental study inspired from the numerical work of Radjaï & Roux, PRL (2002)
Quasi-Static shear test
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Fluctuations of displacement
Richefeu & al., Géotech. Lett., 2, 113-118,(2012)
An experimental study inspired from the numerical work of Radjaï & Roux, PRL (2002)
Quasi-Static shear test
12
Fluctuations of displacement
Richefeu & al., Géotech. Lett., 2, 113-118,(2012)
Fluctuations
are due to
geometrical
constraints
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Fluctuations of displacement
Richefeu & al., Géotech. Lett., 2, 113-118,(2012)
➠ Statistical analysis of the fluctuation of displacement
**
**C. Tsallis, Journal of Statistical Physics 52, 479–487 (1988)
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Fluctuations of displacement
Small shear-strain
increment
Richefeu & al., Géotech. Lett., 2, 113-118,(2012)
Large shear-strain
increment
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Fluctuations of displacement
Richefeu & al., Géotech. Lett., 2, 113-118,(2012)
Vortex
small Δγ ➠ long range correlation
large Δγ ➠ short range correlation 10<d>
vortice-like structures
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Conclusions
An digital image correlation tool has been developed with a special
concern with “particle tracking”.
It has been shown to be as accurate as other tools used in the field of
continuous materials.
On a direct 2D shear test, the displacement fluctuations was defined
as the measured displacements subtracted by the displacements
interpolated from the boundary movements (affine field).
Some specific features of the fluctuations, that play a role analogue to
the dislocations in steel plasticity, have been characterized.
And now… we work on how to derive a plastic model of granular material
from the fluctuations of grain displacements.
Thank you for your attention