Source: www.almohand www.almohandiss.com iss.com
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F OIS OISO ONNEM ENT DU SABL E
Définition : Foisonnement : Augmentation du volume en vrac (ou apparent) d'un matériau pulvérulent suite a un remaniement ou une augmentation de la teneur en eau (foisonnement d'un sable par ex.). La masse volumique apparente : La masse volumique apparente d'un matériau est la masse volumique d'un mètre cube du matériau pris en tas, comprenant à la fois des vides perméables et imperméables de la particule .
But de l’essai :
Le But de l’essai est de déterminer la variation de la masse volumique apparente d’un sable en fonction de sa teneur en eau. Pour cela il faut déterminer la masse volumique apparente à différentes valeurs de la teneur en eau du sable et tracer la courbe masse volumique apparente en ordonnée et la teneur en eau en abscisse.
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Le cœfficient de foisonnement du sable f est :
f = M vapp vapp/M /M vapp vappw(1+Wm) w(1+Wm) - 1
Où Mvappo : Masse volumique du granulat sec Mvappw : Masse volumique minimale du sable remanié (Valeur lu sur le graphique) Wm : Teneur en eau correspondante (%)
Matériel utilisés : Un
bac à sable Une éprouvette graduée pour évaluer le volume du sable Une règle pour araser le sable Une
éprouvette graduée pour ajouter l’eau
Une
balance
Tableau de mesure
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eau(%) 500± 1 Volume 320 (V) ±2,5 Mvapp 1,56± (M/V) 0,017 Masse (M)
493± 1 320 ±2,5 1,54± 0,015
471± 1 320 ±2,5 1,47± 0,014
463± 1 320 ±2,5 1,45± 0,014
444± 1 320 ±2,5 1,39± 0,014
415± 1 320 ±2,5 1,29± 0,013
426± 1 320 ±2,5 1,33± 0,013
437±1 320 ±2,5 1,37 ± 0,014
Unités utiliser : Pour la masse : g Pour le volume : ml(=cm3)
Justification des incertitudes : Pour la masse on masse on a : ΔM = 1g i.e la plus petite masse que
peut détecter l’instrument de mesure(la balance). Pour le volume : volume : on a VΔ = 2,5 cm 3 i.e la plus petite valeur bien estimer à l’œil nu.
Pour la masse volumique : volumique :
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d’où
ΔMvapp = Mvapp*[ ΔM/M + ΔV/V ]
Graphe obtenu :
Mvapp en fct de W 2 1,5 p p a v M
1
Série2
0,5 0 1
2
3
4
5
6
7
8
W(%)
On trouve alors : f = 1,75/1,29(1+5) - 1 A.N
f = 7,14
Calcul de l’incertitude :
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Δf = (f+1)*[ ΔMvappo/ Mvappo + ΔWm/(1+Wm) + ΔMvappw/Mvappw ] Avec :
ΔMvappo = Mvappo*[ ΔM/Mo + ΔV/V ] et
ΔMvappw= Mvappw*[ ΔM/Mw + ΔV/V ] A.N : Mvappo = 1,56 ; Mvappw = 1,29 ; ΔWm = 1
ΔM = 1g ; ΔV = 2,5 cm3 V = 320 cm3 ; Mo = 500g ; Mw = 415g
D’où
Δf = 1,52 Et finalement on peut écrire
f = 7,14 ± 1,52 On remarque que le coefficient de foisonnement de se sable est important, ce qui peut causer de grave conséquences
économiques dans le transport en cas de présence d’antécédent cas d’humidités…
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corps pour 1 m3 de volume,mais uniquement la masse des grains constituant le granulat,sans granulat,s ans prendre compte des vides inter granulaires
Principe de l’essai :
On prolonge dans un volume d’eau une masse d’agrégat ,on obtiendra la masse volumique absolue par la devisions de cette masse par la déférences des volumes.
Mabs=M/(V2-V1)
Avec Mabs=masse volumique absolue en t /m 3 M=masse du matériau étudié
V1=volume dans l’éprouvette avant introduction de la masse d’agrégat V2= volume dans l’éprouvette après introduction de la masse d’agrégat Conduite de l’essai :
On procède comme suit : 1) remplir une éprouvette graduée avec un volume V1 et
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Tableau des mesures :
1) le sable :
1 2 3 4 5
V 1 (en (en M (e (en n g) V 2 (e (en n M vab vabss (e (en n cm3) cm3) g /cm3) 200 ± 2,5 300 ±1 316 ± 2,5 2 ,50 ± 0 ,12 300 ± 2,5 300 ±1 420 ± 2,5 2,50 ± 0 ,12 350 ± 2,5 300 ±1 465 ± 2,5 2,60 ± 0 ,12 400 ± 2,5 300 ±1 515 ± 2,5 2,60 ± 0 ,12 250 ± 2,5 300 ±1 365 ± 2,5 2 ,60 ± 0 ,12 Moyenne Mvabs=2,57 ± 0 ,12 g/cm3
OÛ ∆V=2,5 i .e incertitude de l’écriture sur l’éprouvette l’éprouvette utilisée
∆M=1 g : la plus petites masse que peut évaluer la balance Calcul de ∆Mvabs : On a Mvabs =M /(V2-V1) log on trouve
et en introduisant le
∆Mvabs=Mvabs(∆M /M+(∆V2+∆V1)/│V2 /M+(∆V2+∆V1)/│V2- V1│min) V1│min)
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2
300 ± 2 ,5 300 ± 1
416 ± 2 ,5
3
250 ± 2 ,5 300 ± 1
365 ± 2 ,5
4
350 ± 2 ,5 300 ± 1
465 ± 2 ,5
5
400 ± 2 ,5 300 ± 1
513 ± 2 ,5
2,58 ± 0 12 2,60 ± 0 12 2,60 ± 0 12 2,65 ± 0 12
Moyen Mvabs=2,60±0 12 g/cm3
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Cet essai permet de déterminer la masse volumique apparente
d’un corps (sable, gravier…) C'est-à-dire C'est-à-di re la masse en t(tonne) de ce corps,pour 1 m3 m3 de
volume .cette masse volumique intègre les grains de l’agrégat ainsi que les vides compris entre les grains Principe de l’essai :
On remplie un récipient dont on connaît le volume, en prenant de grandes précautions pour éviter les phénomènes parasites
provoqués par le tassement. on pèse ensuite l’échantillon en prenant soin de de déduire la masse masse du récipient .la masse de l’échantillon est devisée par le vol ume du récipient pour donner la masse volumique apparente du matériau Mvapp=M/V
Mvapp=masse volumique apparente en g/cm3 M=masse du matériau étudié en g
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5) Tableau de mesures : 1) le sable
pes es 1 2 3 4 5
M0 (en g)
M1 ( en g)
M2 ( en g)
V ( en cm3) Mvapp ( en g/cm3)
98±1 98±1 98±1 98±1 98±1
561,64±1 565±1 565,24±1 568,70±1 567,94±1
463,64±1 467± 467,24±1 470,7±1 469,94±1
385±2 ,5 385±2,5 385±2,5 385±2,5 385±2,5
1,20±0,15 1,21±0,15 1,21±0,15 1,22±0,15 1,22±0,15
Moyenne Mvapp=1,21±0 ,15 2) le gravier
pes es 1 2
M0 (en g)
M1 ( en g)
M2 ( en g)
V ( en cm3)
Mvapp ( en g/ cm3)
98±1 98±1
521±1 507±1
423±1 409±1
385±2,5 385±2,5
1,09±0,15 1,06±0,15
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Principe de l’essai:
Le coefficient volumétrique d’un gravier est le rapport du volume V du grain sur le volume Vi de la plus petite sphère circonscrite . Si d est la plus grande dimension diamétrale du grain c'est-àdire la plus grande distance séparent deux plans parallèles tangents a celui ci alors le volume Vi de la sphère circonscrite est : 3
V i = (∏*d )/6
Le coefficient volumétrique d’un gravier constitué d’un ensemble de n grains de volume total V est :
C= ∑ V/ (∑ ∏*d3/6) Où
C=V total/ (∑ ∏*d3/6) Conduite de l’essai
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échantillon 1
échantillon 2
échantillon 3
échantillon 4
grai Di n max
grai Di n max
grai Di n max
grai Di n max
Vi
Vi
Vi
Vi
1
2,8
11,5
1
2,4
7,23
1
2,5
8,18
1
2,5
8,18
2
2,2
5,57
2
1,9
3,59
2
2,2
5,57
2
2,4
7,23
3
2,4
7,23
3
2,6
9,20
3
2,3
6,37
3
1,9
3 ,6
4
1,9
3,59
4
2
4,18
4
2,2
5,57
4
1,8
3,05
5
2,3
6 ,4
5
1,8
3,05
5
2,8
11,5
5
2,9
12,8
6
2,1
4,84
6
2,2
5,57
6
2,4
7,23
6
3
14,1
7
2,4
7,23
7
1,8
3,05
7
2
4,18
7
2,8
11,5
8
2,1
4 ,9
8
1,9
3,59
8
2,4
7,23
8
2,8
11,5