Lecture5 DryingShrinkage Slides

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Lecture 5Drying shrinkage

Pietro Lura

Concrete & Construction Chemistry

Shrinkage and Cracking of Concrete: Mechanisms and Impact on Durability, ETHZ, 19.10.11

2

Contents

� Drying conditions

� Drying of cement pastes at equilibrium

� Drying gradients

� Self-induced stresses and degree of restraint

2

3

Drying shrinkage cracking

Photo: Loser 2008

4

Stimulus -response

Weiss 2008

Ivan Pavlov (1849 –1936)Nobel prize 1904

3

5

Volume change due to mechanical loading

Weiss 2008

� Stimulus – application of a force

� Response – length change and compensation in the transverse direction

F = K ∆

Ten

sio

n

Co

mp

ress

ionFo

rce

Deformation

K

6

Volume change due to temperature change

δTEMP

Temperature Deformations

• Stimulus is change in temperature

• Response is the change in length (volume)

• This happens in nearly all materials

δTEMP=α · L · ∆TεTEMP=α · ∆T -1

000

-800

-600

-400

-200 0

200

400

600

800

1000

Longitudinal Strain (µε)

-20

0

20

40

60

80

100

Tem

per

atu

re C

han

ge

(C)

1α

Weiss 2008

4

7

Shrinkage due to moisture loss

-70 -60 -50 -40 -30 -20 -10 0Change in Relative Humidity (%)

-5000

-4000

-3000

-2000

-1000

0

1000

Sh

rin

kag

e S

trai

n (

µεµε µεµε)

30 40 50 60 70 80 90 100Relative Humidity (%)

0% SRA

-70 -60 -50 -40 -30 -20 -10 0Change in Relative Humidity (%)

-5000

-4000

-3000

-2000

-1000

0

1000

Sh

rin

kag

e S

trai

n (

µεµε µεµε)

30 40 50 60 70 80 90 100Relative Humidity (%)

0% SRA

( )31 RHNSH −=∞− βε

• Stimulus is change in moisture (drying external or internal) and chemical reaction

• Response is the change in length (volume)

Weiss 2008

8

Drying conditions (1)

Moisture

RH T v

RH

5

9

Drying conditions (2)

Pore Volume

after Bentz and Jensen CCC 2004

r1r2

( )W

cap V

RTp

⋅= RHln

( ) RT

Vcosr W

⋅⋅⋅−=

RHln

2 ϑγPore Radius

r3

r3 r2 r1

10

Drying shrinkage of old cement pastes (1)

Loser and Lura 2009-2011

w/c 0.3 cement pastes, water cured for 6 months prior to dryingSmall samples, 10x10x80 mm3

5-6 weeks before equilibrium at each RH step

-1000

-800

-600

-400

-200

0

200

70 75 80 85 90 95 100

Relative humidity [%]

Stra

in [

m/m

]

CEM III/B w/c 0.3

6

11


Drying to 94⇒86⇒75%

0.1

1

10

100

1000

10000

405060708090100

Relative humidity (%)

Cap

illar

y p

ress

ure

(M

Pa)

-140

-120

-100

-80

-60

-40

-20

0

Kel

vin

rad

ius

(nm

)

p cap

Kelvin radius

rK=17 nm

rK=7 nm

94% 86%

pcap= -20.4 MPa

pcap= -8.4 MPa

−⋅

⋅=ε

S

capcap K

1

K

1

3

pS

� Capillary tension calculated directly from RH

� Degree of saturation S from water loss at given RH, if water loss at complete drying is knownRough estimate: S=0.9 at 94%, 0.8 at 86%, 0.7 at 75%

rK=4 nm

pcap= -38.9 MPa

Bentz et al. 1998

75%


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−⋅

⋅=ε

S

capcap K

1

K

1

3

pS

)21(3

EK

ν−⋅=

� Bulk modulus of paste K calculated from measured E modulus and ν=0.15 (assumed)Measured E modulus at 182 d E=24.6 GPaCalculated K=11.7 GPa

� Bulk modulus of solids Ks=45 GPaKs influences results less than K

Bentz et al. 1998


7

13


Relatively good agreement up to 86% RH, difference at 75%Input could be more refined (e.g. calculation of S)Other models could be used (Lecture 4A)

-1000

-800

-600

-400

-200

0

200

70 75 80 85 90 95 100

Relative humidity [%]

Stra

in [

m/m

]

CEM III/B w/c 0.3

Simulation (Bentz et al.


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Drying shrinkage of young concrete

Note: this is an approximation, drying affects also hydration Age of Specimen (Days)

Drying = Sealed - Unsealed

Unsealed

Sealed

Mea

sure

d S

hri

nka

ge

( µεµε µεµε)

0 28 56 84

0

400

800

1200

1600

Sealed Specimen

Unsealed Specimen

Drying

0 28 56 84

0

400

800

1200

1600

Sealed Specimen

Unsealed Specimen

Drying

Weiss 2008

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15

Samples with different exposure (1)

Khelidj et al. MS 1998

Sealed, drying from 2 sides, drying from all sides

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Samples with different exposure (2)

Khelidj et al. MS 1998

Gradient in RH in samples sealed from 2 sides

Different shrinkage depending on exposure and drying rate

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17

Moisture diffusion in a sample

Weiss 2008

40 60 80 100

Relative Humidity (%)

1.0

0.8

0.6

0.4

0.2

0.0

No

rmal

ized

Sp

ecim

en

Th

ickn

ess

(X/D

)

HAMBIENT HINTERNAL

Surface

As the Specimen

Dries

( )CgradHdivdt

dH =

18

Linear diffusion

Weiss 2008

erfc

IRH),( txRH

x

tD

: relative humidity

: distance from the surface (m)

: time (sec)

: complementary error function

: diffusion coefficient (m2/s)

⋅−−=Dt2

xerfc)H(RHHt)RH(x, SII RR

: Internal RH

SRH : drying surface RH

(100%)

(50%)

Dt2=γ

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Humidity profile

Weiss 2008

50 60 70 80 90 100

Relative Humidity (RH%)

60

40

20

0

Dep

th f

rom

th

e su

rfac

e (m

m)

=0.001 =0.004 =0.008 =0.02 =0.05

=0.1 =0.2 =1.0 =100

RHIRHS

γ (m)

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Humidity profile

Weiss 2008

40 60 80 100


1.0

0.8

0.6

0.4

0.2

0.0

No

rmal

ized

Sp

ecim

en

Th

ickn

ess

(X/D

)

HAMBIENT HINTERNALSurface

As the Specimen

Dries

40 60 80 100


1.0

0.8

0.6

0.4

0.2

0.0

No

rmal

ized

Sp

ecim

en

Th

ickn

ess

(X/D

)

HAMBIENT HINTERNALSurface

Drying

Self-Desc

Higher W/C Lower W/C( )dt

dHCgradHdiv

dt

dH SelfDesc+=Weiss 2008

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21

Moisture gradients and curling

MOISTURE GRADIENT

INITIAL

INCREASING

AGE

CONCRETE SLAB

SHRINKAGE STRAIN GRADIENT

DRYING

INITIAL SLAB CURLING IN A SLABWeiss 2008

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Drying shrinkage cracking

Loser and Leemann MS 2009

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Cracking frame (1)

Cracking frame at EmpaConcrete / Construction Chemistry Laboratory

� Concrete is poured into the mould and sealed with plastic sheets

� Demoulding after 1 day or less, concrete normally exposed to drying

� Can be used for sealed specimens made of high performance concrete (autogenous shrinkage only)

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Cracking frame (2)

Tension

Compression

� Passive system, shrinkage of concrete is restrained by steel columns

� There is always some deformation of the steel columns, shrinkage of concrete is never totally restrained

� Stress in concrete is calculated from strain measured on steel columns

150 mm

100 mm

sc FF =

csssc A/AE ⋅⋅ε=σsscc AA ⋅σ=⋅σ0.5xFs0.5xFs Fc

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25

Cracking frame (3)

0

0.5

1

1.5

2

0 7 14 21 28Time (days)

Str

ess

(MP

a)

CEM ICEM III/B

� Stress increases due to shrinkage (both due to drying and to hydration)

� The higher the stiffness, the higher the stress

� Stress is reduced by creep/relaxation in the cement paste

� Stress is proportional to the degree of restraint

� Stress can lead to cracking of the concrete (not in this specific case)

csred,cc Ek ε⋅⋅=σDegree of restraint

Reduced elastic modulus

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Cracking frame (4)

� Creep/relaxation reduces the elastic stresses

� The more concrete creeps, the more the stresses are reduced, the lower the probability of cracking

� Here, concrete made with blast furnace slag cement (CEM III/B) shows less stress relaxation

0

2

4

6

8

0 7 14 21 28Time (d)

Str

ess

(MP

a)

Elastic stress CEM I

Measured stress CEM I

Elastic stress CEM III/B

Measured stress CEM III/B

csred,cc Ek ε⋅⋅=σcsel,cel,c Ek ε⋅⋅=σ

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27

Calculation of degree of restraint (1)

� If restrained specimen has no strain, k=1 or 100%

� Degree of restraint of cracking frame depends only on geometry and modulus of elasticity)AE/()AE(/ sscccs ⋅⋅=εε

FreestrainedReFree /)(k εε−ε=

)/1/(1)/()(k csscssc εε+=ε+εε−ε+ε=0.5xFsFc

sc FF =

sssccc AEAE ⋅⋅ε=⋅⋅ε

)]AE/()AE(1/[1)/1/(1k sscccs ⋅⋅+=εε+=

0.5xFs

scFree ε+ε=εsstrainedRe ε=ε

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Calculation of degree of restraint (2)

Degree of restraint decreases with concrete stiffness

0

10

20

30

40

50

0 7 14 21 28

Time (days)

Co

ncr

ete

elas

tic m

od

ulu

s (G

Pa)

0.5

0.6

0.7

0.8

0.9

1

Deg

ree

of r

estr

ain

t k (-

)

15

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Summary

� Drying shrinkage is the response to a relative humidity change in the concrete

� Development in time of drying shrinkage depends on specimen size, final value similar

� In HPC, self-desiccation combines with drying

� Moisture gradients and shrinkage gradients

� Cracking frames and degree of restraint

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Acknowledgements

� J. Weiss

� R. Loser

Lecture5 DryingShrinkage Slides

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