Stress distribution inside a powder bed: does Janssen’s model applicable locally in a granular medium

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Submitted on 3 Jun 2020

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Stress distribution inside a powder bed: does Janssen’s model applicable locally in a granular medium

Agnès Duri-Bechemilh, Sandra Mandato, Bernard Cuq, Thierry Ruiz

To cite this version:

Agnès Duri-Bechemilh, Sandra Mandato, Bernard Cuq, Thierry Ruiz. Stress distribution inside a powder bed: does Janssen’s model applicable locally in a granular medium. 7. World Congress on Particle Technology (WCPT7), May 2014, Pekin, China. �hal-01606814�

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Stress distribution inside a powder bed:

does Janssen’s model applicable locally

in a granular medium?

Sandra Mandato, Agnès Duri*_{, Bernard Cuq and Thierry Ruiz}

2 Place Pierre Viala - 34000 Montpellier – FRANCE

UMR IATE

http://umr-iate.cirad.fr/

WCPT 7

(3)

Motivation

What is the local stress distribution

in an ensiled granular media ?

(4)

Applications:

• Stability of silos

• Initial state before powder flowing

(mixing processing…)

Motivation

What is the local stress distribution

in an ensiled granular media ?

(5)

Weight measurement at the bottom of a cylindrical grain column

(6)

Weight measurement at the bottom of a cylindrical grain column

The well-known Janssen’s experiment (1895)

From a certain height of bed, any powder addition does not make

any variation of mass weighed at the bottom

Hydrostatic pressure rgh

Weight measured

at the bottom of the column

Weight

poured

in the

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Janssen’s model

Pressure at the bottom of a cylindrical grain column

3 hypotheses: • Lateral uniformity of the vertical stress (layer model)

• The horizontal stress is proportional to the vertical stress • Slipping at the wall (Coulomb criterion)

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l

= D/4µK

Janssen’s model

Weight deflection into lateral sides of the column

Pressure at the bottom of a cylindrical grain column

3 hypotheses: • Lateral uniformity of the vertical stress (layer model)

• The horizontal stress is proportional to the vertical stress • Slipping at the wall (Coulomb criterion)

Hydrostatic pressure rgh

P =

r

g

l

(1-e

-h/l

₎

Pressure: P Height of grain in the colum : h

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BOTTOM

Stakes Janssen’s model? z Height of grain in the colum : h Vertical stress: s_zz ( z) at the bottom

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BULK

BOTTOM

Stakes Janssen’s model?

Profile of the local vertical stress in an ensiled granular media?

Effect of the particle size?

?

z z

?

r Vertical stress: s_zz (r, z) in the bed Height of grain in the colum : h Depth in the bed of grains : z Vertical stress: s_zz ( z) at the bottom

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Method ETUDE STATIQUEStakes

Janssen’s model?

Side view

of the texture analyser

Probe Force sensor Front view Large probe Rheological device Rheological device

Janssen’s experiment: large probe

Measurement of the vertical stress

at the bottom of the cell

0 < z ≤ 14 cm (height of the bed)

z

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Side view

of the texture analyser

Method ETUDE STATIQUEStakes

2D rheological device 2D rheological device

Measurement of the vertical stress

in the granular bed

0 < x ≤ 4 cm & 0 < z ≤ 14 cm (position in the bed)

2D-cartography of the local vertical stress

Local experiment: small probe

0

14 cm

x

Front view

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• A range of 5 wheat-based powders : native and agglomerated particles

Material ETUDE STATIQUEStakes

Janssen’s model? Sample Name d₅₀ (µm) dsp Fine semolina 210 1.53 Medium semolina 300 1.46 Fine couscous 680 0.95 Medium couscous 950 0.54 Wheat-based powders Wheat-based powders

• Native powder : durum wheat semolina (pasta, noodle, couscous…) Characterisation of the local vertical stress profiles

Effect of the size and the structure on the local vertical stress profiles

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Janssen’s profile:

• Deviation from the hydrostatic profile •

l

= 23 cm 14 12 10 8 6 4 2 00.0 0.2 0.4 0.6 0.8 1.0 1.2

Vertical stress (kPa)

Janssen's model Hydrostatic profile

Semolina height (cm)

Results

Janssen’s approach

Screening of the weight

by the lateral sides of the cell

d

Material and method Stakes

Janssen’s profile Janssen’s profile

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Local profile ¹ Janssen’s profile

Results Material and method

Janssen & local vertical stress profiles in the center of the cell Janssen & local vertical stress profiles in the center of the cell

12 10 8 6 4 2 00.0 0.2 0.4 0.6 0.8 1.0 1.2

Semolina height/Depth of the probe (cm)

Local approach - x=0

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14 12 10 8 6 4 2 00.0 0.2 0.4 0.6 0.8 1.0 1.2

l

_b» 2 cm

l

_h» 4 cm

II

• 3 zones

• 2 characteristic lengths:

l

_h » 4 cm and

l

_b » 2 cm

• Jannsen value at the bottom of the cell !

I

III

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12 10 8 6 4 2 00.0 0.2 0.4 0.6 0.8 1.0 1.2

l

» 2 cm

l

_h» 4 cm

II

• 3 zones

l

_h » 4 cm and

l

_b » 2 cm

I

III

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14 12 10 8 6 4 2 00.0 0.2 0.4 0.6 0.8 1.0 1.2

l

_b» 2 cm

l

_h» 4 cm

II

• 3 zones

l

_h » 4 cm and

l

_b » 2 cm

I

III

Janssen !

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14 cm de profondeur 11 cm de profondeur

l _s

3 cm de profondeur

l_s

Lateral side effect over l_s» 2 cm Constant vertical stress

Local vertical stress profiles in horizontal planes Local vertical stress profiles in horizontal planes

x (cm)

Vertical Stress (kPa

)

x (cm)

)

"Camel’s hump" shape Local vertical stress profiles in horizontal plane Local vertical stress profiles in horizontal plane

4 cm 14 cm z 0 cm 3 cm 0 cm x

• Zone I: Lateral uniformity of the vertical stress

• Zone II & III: Lateral inohomogeneity of the vertical stress

12 cm I I II II III III

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Vertical Stress (kPa)

x

Stakes Janssen’s model? 2D iso-stress cartography 2D iso-stress cartography Surface Bottom z

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l_h

Stakes Janssen’s model? 2D iso-stress cartography 2D iso-stress cartography Surface Hydrostatic II I III l_b Network percolation Stress screening x z Surface Janssen - Bottom

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Stakes Janssen’s model? III II I 2D iso-stress cartography 2D iso-stress cartography l_h Hydrostatic l_b Network percolation Stress screening Janssen -l_s l_s Stress screening x z Surface Janssen - Bottom

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Stakes Janssen’s model? III II I 2D iso-stress cartography 2D iso-stress cartography l_h Hydrostatic l_b Network percolation Stress screening l_s l_s Stress screening x z Surface Janssen - Bottom

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Stakes Janssen’s model? II I 2D iso-stress cartography 2D iso-stress cartography l_h Hydrostatic l_b Network percolation Stress screening l_s l_s Stress screening III

effect

The bottom is a side as an other…

x

z

Surface

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Particle size effect ? Particle size effect ?

Particle size

does not affect:

• Shape of the profile • Characteristic lengths 0.0 0.4 0.8 1.2 16 12 8 4 0 d₅₀=210 µm

Depth of the probe (cm)

0.0 0.4 0.8 1.216 12 8 4 0 d₅₀=680 µm 0.0 0.4 0.8 1.2 16 12 8 4 0 d₅₀=950 µm 0.0 0.4 0.8 1.216 12 8 4 0 Vertical Stress (kPa)

d₅₀=1100 µm

l

_b» 2 cm

l

_h» 4 cm

l

_b» 2 cm

l

_h» 4 cm II I III II I III

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14 12 10 8 6 4 2 00.0 0.2 0.4 0.6 0.8 1.0 1.2

d₅₀=210 µm

d₅₀=300 µm

d₅₀=680 µm

d₅₀=950 µm

d₅₀=1110 µm

Depth of the probe (cm)

Particle size effect ? Particle size effect ?

II I

III

Particle size affects :

Intensity of the local vertical stress

l

_b» 2 cm

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Conclusions

• Generic device

implementation for

measuring

2D-cartography

of the

vertical stress

in

ensiled granular powders.

• Non-equivalence

between

global

and

local

vertical stress

measurements

except

at the

bottom

of the cell (

semolina

).

• Particle size affects

the

intensity

of the

local vertical stress

but

not

the

shape

of the vertical stress profile and the

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Stress distribution inside powder bed: does Janssen’s model applicable locally

in a granular medium?

Sandra Mandato, Agnès Duri*_{, Bernard Cuq and Thierry Ruiz}

2 Place Pierre Viala - 34000 Montpellier – FRANCE

UMR IATE

http://umr-iate.cirad.fr/

WCPT 7

T1.2 Particle property and inter-particle force characterization