Babylonia,Babylonia,Mesopotamia,Mesopotamia,Approx. 1800 BCApprox. 1800 BC

Powers’ modelPowers’ model

Ole Mejlhede Jensen

Building Materials GroupTechnical University of Denmark

Studies of Water Vapor Adsorption of Hardened Portland Cement Paste

1934-1945

PCA bulletin 22PCA bulletin 22

Experimental contentExperimental contentMeasurements•Adsorption isotherms

•Non-evaporable water•Strength•E-modulus•Heat of hydration•Heat of water adsorption•Freezing dilation•Drying shrikaage•Termal deformation•Permeability

(1st, 2nd, 3rd, ad- & desorption + partial)

Parameters•w/c•Age•Cement type•Curing conditions

Sorption isotherm experimentSorption isotherm experimentRH20°C

23%43%54%66%75%81%85%91%95%98%K2SO4:

KNO3:BaCl2:

(NH4)2SO4:KCl:

NaCl:NaNO3:Mg(NO3)2:K2CO3:CH3COOK:

Salt

LiCl: 12%

Sorption isothermSorption isotherm

0 20 40 60 80 100Relative humidity (%)

Moisture content (g/g)

water uptake bycapillary suction

water uptake fromwater vapour

Experimental resultsExperimental results

Capillarywater

Gel water

Chemicallybound water

0RH (%)

1000

0.2

Tota

l wat

er (g

/g c

emen

t)

0.1

0.3

0.4

50

7

1428

5690180365

w/c= 0.309water cured, 25°C

Days of hardening

Phases of water in cement pastePhases of water in cement paste

Key figures in Powers’ modelKey figures in Powers’ model

Non-evaporable water~ 0.23 g/g cement reacted

Gel water~ 0.19 g/g cement reacted

Chemical shrinkage~ 6.4 ml/100 g cement reacted

33--D packing of identical spheresD packing of identical spheres

Chemical shrinkageChemical shrinkageTime

Formulas in Powers’ ModelFormulas in Powers’ Model

Vc.s = 0.2·(1-p)·α

Vc.w = p - 1.3·(1-p)·α

Vg.w = 0.6·(1-p)·α

Vg.s = 1.5·(1-p)·α

Vc = (1-p)·(1-α)

p = w/c + ρw/ρc

w/c ρw =1000 kg/m3 ρc =3150 kg/m3

= ρc·6.4·10-5·(1-p)·α

= p - (ρc/ρw )·(0.19+0.23)·(1-p)·α

= (ρc/ρw)·0.19·(1-p)·α

= (1-ρc·6.4·10-5+(ρc/ρw)·0.23)·(1-p)·α

Powers’ ModelPowers’ Model

pores

capillary water

gel water

gel solid

cement

w/c > 0.42

Vol

ume

Degree of Hydration0

1

0 1

Sealed system

cement

capillary watergel water

gel solid

pores

w/c < 0.42

0 1Degree of Hydration

Vol

ume

αmax0

1Sealed system

Degree of hydrationDegree of hydrationα=Σiwi·αi

Stability of reaction productsStability of reaction products

C4AH196H

~85% RHC4AH13

2H

~10% RHC4AH11

4H

~0.01% RHC4AH7

C2AH7.5C3AH1.43

CAH10 C2AH5

C4A3H3

C3AH6CAH7

CAH4

C12A7H

C2AH8

Chemical shrinkage of componentsChemical shrinkage of components

25

20

15

10

5

0

Cemen

t

C3S C2S C3AC4A

FSilic

a fum

e

(ml/100 g)

Water bound in cement pasteWater bound in cement paste

Temperature [°C]

0

0.40

0.20

0.10

0.30

0.60

0.50

Held water [g/g cement]

RH [%]20 40 60 80 100100 03005007009001100

Jensen (2005)

The true volumesThe true volumes100

50

Rel

ativ

e vo

lum

e [%

]

C-S-H + gel water

CHC3A

C3S

C2S

Capillary water

w/c=0.50

AFt and AFm

C4AF

00 50 100

Degree of hydration [%]

Entrapped air

CS_

Tennis & Jennings (2002)

Hydration indicatorsHydration indicators

0 0.10 0.20

1

2

3

4

5

6

0

Wn (g/g cement)

∆V (ml/100 g cement)•Non-evaporable water

•Chemical shrinkage

•BET specific surface area

•Heat evolution

•Calcium hydroxide content

•Compressive strength

Key figures in Powers’ modelKey figures in Powers’ model

Non-evaporable water~ 0 g/g silica fume reacted

Gel water~ 0.6 g/g silica fume reacted

Chemical shrinkage~ 24 ml/100 g silica fume reacted