Mesure de champs cinématiques particulaires

haute définition dans les milieux granulaires bidimensionnels

G. Combe, V. Richefeu

Présenté par O. Jenck

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Schneebeli** rods : a 2D granular material

2D Grains ≡ 6 cm long cylinders of various sections and different diameters

**G. Schneebeli, CRAS, 243(1):125-126 (1956)

ϕ = [1,5 - 2,5 - 3,5 mm] ϕ = [6 - 10 - 16 - 20 mm] PVC rods Wood rods

Mixtures of discs and rectangles

Hexagonal shapes

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2000 wooden rods in 1γ2ε shear device

**H.A. Joer & al, Géotechnique, 48(5):605-619 (1996)1γ2ε** Shear apparatus

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Possible tests

Oedometric compression

Biaxial test: vertical compression,

lateral stress constant

Simple shear test: tilt with

constant vertical stress

Isotropic compression

Test with imposed rotation

of the principal axes of

STRAINS or STRESSES

(more complex)

And

**H.A. Joer & al, Géotechnique, 48(5):605-619 (1996)1γ2ε** Shear apparatus

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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

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1100 pictures - 24.5 MPixelsShear test on 2000 wooden rods

Assessing kinematics using “modern” Digital Camera (2010 ...)➟

movie picture speed x 500

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PIT : Digital Image Correlation technique adapted to track “automatically” full kinematics of rigid bodies

PIT : Particle Image Tracking Combe & Richefeu, Powders and Grains 2013

Rigid-motion relation to track u, v and θ…

… with a subpixel resolution using bilinear, bicubic or biquintic interpolation

Tracker PIT software

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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.

Increased search zoneWell-found bodies

Exclusion zoneBody being « rescued »

Accuracy with synthetic images (from Orteu et al., 2006)

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PIT: Particle Image Tracking Combe & Richefeu, Powders and Grains 2013

➠ Same intrinsic accuracy as the codes used in the GdR CNRS 2519

Courtesy, L. Robert

Accuracy with real images that involve the whole measurement chain.Solid motion = distance and angle conservation

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PIT : Particle Image Tracking Combe & Richefeu, Powders and Grains 2013

Correction of distortion drastically improve the accuracy.

Quasi-Static shear test

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An experimental study inspired from the numerical work of Radjaï & Roux, PRL (2002)

Fluctuations of displacement Richefeu & al., Géotech. Lett., 2, 113-118,(2012)

Quasi-Static shear test

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An experimental study inspired from the numerical work of Radjaï & Roux, PRL (2002)

Fluctuations of displacement Richefeu & al., Géotech. Lett., 2, 113-118,(2012)

Str

eam

lin

es

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Richefeu & al., Géotech. Lett., 2, 113-118,(2012)Fluctuations of displacement

Fluctuations are due to geometrical constraints

➠ Statistical analysis of the fluctuation of displacement

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Richefeu & al., Géotech. Lett., 2, 113-118,(2012)Fluctuations of displacement

**C. Tsallis, Journal of Statistical Physics 52, 479–487 (1988)

**

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Richefeu & al., Géotech. Lett., 2, 113-118,(2012)Fluctuations of displacement

Small shear-strain increment

Large shear-strain increment

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small Δγ long range correlation➠large Δγ short range correlation 10<d>➠ vortice-like structures

Vortex

Richefeu & al., Géotech. Lett., 2, 113-118,(2012)Fluctuations of displacement

ConclusionsAn 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