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Outline
• Introduction
• Basics on Rheology
• Overview on simple concrete rheology tests
• Flows regime in cementitious materials• Interactions • Consequences and admixtures
• Mix Design of Concrete
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Filling a mold
Casting Visquous fluid
Fluid concreteOrdinary concrete
From N.Roussel
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Back to basics
• Definition about rheology:• science of flow and deformation of matter.• Linked between the strain speed and the applied stress
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑆𝑆𝑆𝑆𝑟𝑟𝑆𝑆 =𝑉𝑉𝑆𝑆
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑠𝑠𝑟𝑟𝑆𝑆𝑆𝑆𝑠𝑠𝑠𝑠 = 𝜑𝜑.𝑔𝑔. 𝑆𝑆. sin(𝜃𝜃)
Flow speed V
Density
Inclination
Depth
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Behaviour’s laws
• To link stress and shear rate, we introduce some behaviour’s equation. The simplest is Newtonian fluid.
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Yield stress fluid
• Yield stress for ordinary concrete : thousands of Pa• Yield stress for ordinary mortar : hundreds of Pa• Yield stress for cement paste : Pa
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Interactions
• Differents interactions:• Brownian motion• Collloidal interactions• Hydrodynamic interactions• Direct contacts
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Parameters
• d particles diameter around 10 microns• 𝜌𝜌𝑝𝑝 density of cement around 3.1• µ0 suspending fluid ex. Water 1mPas at 25°C• Φ volume fraction of solid• W/B
Φ = (1 + 𝜌𝜌𝑝𝑝W/𝜌𝜌𝐸𝐸B)-1
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Thermal agitation
• The random movement of microscopic particles suspended in a liquid or gas,caused by collisions with molecules of the surrounding medium.
𝑘𝑘 𝑇𝑇 𝑤𝑤𝑤𝑤𝑟𝑟𝑆 𝑘𝑘 𝐵𝐵𝐵𝐵𝐵𝐵𝑟𝑟𝐵𝐵𝐵𝐵𝑆𝑆𝐵𝐵𝐵𝐵 𝑐𝑐𝐵𝐵𝐵𝐵𝑠𝑠𝑟𝑟𝑆𝑆𝐵𝐵𝑟𝑟4.10-21 J at 20°C
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Thermal agitation
• d-3 = number of particles in 1 cubic meter
• In Pa.s𝑘𝑘𝑘𝑘�̇�𝛾𝑑𝑑3
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Colloïdal interactions
In physical chemistry, the van der Waals force (or van der Waals' interaction), named after Dutch scientist Johannes Diderik van der Waals, is the sum of the attractive or repulsive forces between molecules (or between parts of the same molecule) other than those due to covalent bonds, or the electrostatic interaction of ions with one another, with neutral molecules, or with charged molecules. The resulting van der Waals forces can be attractive or repulsive. (Wikipedia)
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Colloïdal interactions
• Electrostatic forces The surface of particles are positively charged repulsion
• Steric effectIf you change particles charges by adding polymers or the interstitial liquid , you can modify the suspension
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Colloïdal interactions
At short distance the attractive Van der Waals forces dominate the electrostatic repulsion.
Moreover, Van der Waals forces dominate the Brownian motion.
𝜃𝜃 ≅ 𝐴𝐴0𝑎𝑎∗𝑑𝑑𝐻𝐻2 ≅ 10-16 J
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Defloculation
As attractives forces dominate the system flocculation
To deflocculate , we use plasticizers.
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HPCHigh Performance
Concretes
UHPRC/UHPFCUltra High Performance
Reinforced / Fiber Concrete
Shotcrete SCCSelf Compacting
Concretes
Recent development linked to the SP addition
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Historical development
Vinyl Copolymer* CH CH CH2 CH *
COONaCH2 CO
n
CO
NR1 R2
N
R3 R4
19401950
19601970
19801990
20001930
2010
Poly-Carboxylate-Ether(PCE)
* CH2 C CH2 C *
R
m
R
n
COOH CO-X-(CH2CHRO-)y R
Melaminsulphonate
Naphthalinsulphonate
CH2
*
SO3Na
n
N N
NN N
NH
* CH2
CH2SO3Na
CH2X CH2Y
n
Carbohydrates
Ligninsulphonates O C
MeO
C CNa2S2O5 O C
SO3NaMeO
C C
C
C
C
C
CH2OH
COOM
OHH
HOH
OHH
OHH
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How ?
• Bingham fluid
• By adding SP , we decrease the yield stress
•+= γµττ p0
SP
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Forces interpaticulaires
•Van der Waals Forces (attractives)
Superplasticizers:
• Electrostatic effect to create repulsion
• Electrosteric effect depending on size and conformation of polymers
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Hydrodynamic forces
• When you increase the shear rate the viscous dissipation increases.
• And the energy of the viscous dissipation :
𝜇𝜇0�̇�𝛾𝑓𝑓 Φ
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Hydrodynamic forces
• In dilute system (W/B >6):• Einstein equation:𝑓𝑓 Φ = 1 + 2.5 Φ
• In concentrated suspensions• Krieger Dougherty relation: 𝑓𝑓 Φ = (1 − �Φ Φ 𝑚𝑚)-q
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Inertia
• In high concentrated suspension
• Kinetic energy : 𝜌𝜌𝑝𝑝𝑑𝑑3𝑉𝑉2
• With 𝑉𝑉 = ̇𝑑𝑑𝛾𝛾𝑓𝑓 Φ
• So energy from inertia : 𝜌𝜌𝑝𝑝𝑑𝑑5�̇�𝛾2𝑓𝑓2 Φ
• In Pa.s 𝜌𝜌𝑝𝑝𝑑𝑑2�̇�𝛾𝑓𝑓2 Φ
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Volume fraction
• The numbers of particles plays an important role : inertia but also direct contacts.
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Viscosity agents
• Issue:• To avoid the sedimentation• To increase water retention
•Solutions:• Addition of viscosity agents such as cellulosic ethers, glucose, natural gums
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Air entrainers
• Issue:• Increase of gel resistance
•Solutions: • Addition of air entrainers such as sulfonates or organic fatty acids, they are
anionic
http://www.explorations-architecturales.com/
Lemoniteur.fr
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Effect on rheology
• For ordinary concrete , yield stress is around 2000Pa, air entrainer can help the rheo thinning.
• For self compacting concrete with yield stress close to 50 Pa, air entrainerhelps the shear thickening of the system
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References
• Roussel lectures ENPC• Flatt lectures ETH
• Favier (2013) PhD dissertation• Brumaud (2011) PhD dissertation
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Bolomey method
• Take in consideration the cement content
• 𝑃𝑃(𝑝𝑝𝑆𝑆𝑆𝑆𝑐𝑐𝑆𝑆𝐵𝐵𝑟𝑟𝑆𝑆𝑔𝑔𝑆𝑆 𝐵𝐵𝑓𝑓 𝑟𝑟𝐵𝐵𝑟𝑟𝑆𝑆𝐵𝐵 𝑑𝑑𝑆𝑆𝑑𝑑 𝐵𝐵𝑆𝑆𝑟𝑟𝑟𝑟𝑆𝑆𝑆𝑆) = 𝐴𝐴 + (100 − 𝐴𝐴) 𝑑𝑑𝐷𝐷
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Software
• BetonLab pro ( also available for free but with restrained conditions)
• Based on compaction index
• EMMA
• Optimisation of packing
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Bolomey and SIA
• Swiss standard :
• SIA norm : curve of Fuller B ⇒ 𝑃𝑃 = 100 𝑑𝑑𝐷𝐷
• But cement is not included : SIA gives a minimum cement content 350kg/m3
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Loi de Feret, 1896
Résistance à lacompression
Constante,:Fonction de l‘âge, mode de conservation et liant
Volumes de:c – cimente – eauv – vides
R = K cc + e + v
2
R = K c /(e + v)c / e + v( )+1
2