Chapter 4 Verification of Cracking Due to Heat of ...concrack5/PPT-PDF/Guidelines Chapter 4 (design...JCI Guidelines for Control of Cracking of Mass Concrete 2016 1 ... Chapter 4 Verification

JCI-RILEM International Workshop, CONCRACK5, April 24-26, 2017, Japan

JCI Guidelines for Control of Cracking of Mass Concrete 2016

1

Chapter 4

Shingo Miyazawa

Ashikaga Institute of Technology

Verification of Cracking Due to Heat of Hydration of Cement

- Part 1 -



2

4.1 General

4.2 Design Values of Material Properties

4.3 Verification of Thermal Cracking Based on Three-Dimensional FEM

4.4 Verification of Thermal Cracking Based on Simple Evaluation Method

4.5 Verification for Preventing DEF Cracks

Chapter 4 Verification of Cracking Due to Heat of Hydration of Cement



3

4.1 General(1)Thermal cracking shall be verified by predicting the thermal cracking

probability or thermal crack widths using an analysis method withproven reliability, and by applying limit values prescribed in Section3.2 “Limit values for control target”.

CommentaryChapter 4 presents the verification methods.

3D-FEM, which is used to predict thermal cracking index, must be based on the method prescribed in the Guidelines.

Methods with accuracies equivalent to 3D-FEM can also be used.

For practical convenience, the simple method to estimate thermal cracking index is specified in the Guidelines.



4

4.1 General

(2) If the goal of the control target is to prevent thermal cracking, theverification shall be carried out by confirming that the calculatedvalue of thermal cracking probability is equal to or less than the limitvalue of thermal cracking probability.

(3) If the goal of the control target is to control thermal crack widths,the verification shall be carried out by confirming that the calculatedvalue of thermal crack width is equal to or less than the limit value ofthermal crack width.



5

4.1 General

(4) DEF cracking shall be verified by predicting the maximumtemperature of the concrete member based on actual conditionsusing an analysis method with proven reliability, and by applying thelimit values prescribed in Section “3.2 Limit values for controltarget”.

(5) In order to prevent DEF cracking, the verification shall be carried outby confirming that the calculated value of the maximum temperatureof the concrete member is equal to or less than the limit value.

Commentary (4)

New

New

Since the temperature of the member is taken to be the verification index, the conditions of thermal analysis, thermal properties, adiabatic temperature rise, heat transfer coefficient, ambient temperature should be determined based on actual conditions.



6

4.1 General

(6) The thermal crack control and DEF crack prevention targets may bejudged to be achievable based on sufficient past experience ofdesign and execution in which the targets were attained for existingstructures whose types and conditions approximated those of thestructure to be verified.

(7) The specifications provided in the control planning and preventionplanning can be determined if the verification results are acceptable.

New

Commentary （6）

In order to reduce the burden for verification, it is specified that

experience-based verification may be introduced.



7

4.2 Design values of material properties

4.2.1 General(1) The design values of the material properties of concrete, steel,

ground/bedrock and other materials to be used for temperature and thermal stress analyses shall be empirically determined.

In order to enhance accuracy, the design values shall be based on experiments.

It is also allowable that the design values are based on existing reliable data.

The standard analysis method for verification of thermal cracking shall be three-dimensional FEM.

Commentary



8

4.2.1 General(2) The tensile strength of concrete to be used for calculating the

thermal cracking index shall be the splitting tensile strength.

Thermal cracking index Icr

This test method is widely used in Japan.Cracking probability diagram is provided on the basis of splitting tensile strength.

splitting tensile strength tested in accordance with JIS A 1113, t

( )( )

t ecr

t e

f tI

tσ=



9

4.2.2 Concrete

(1) The design values of concrete properties shall be determined takinginto consideration the materials used, the mixture proportions ofconcrete, the concrete temperature at placement, and thetemperature history.

Thermal propertiesSpecific heat Heat conductivityThermal expansion coefficient

Adiabatic temperature rise

Heat transfer coefficient

Mechanical propertiesCompressive strength Tensile strength Modulus of elasticity Influence of creep

Autogenous shrinkage

Expansion of expansive concrete

The design values of concrete



1010

Notations of Cements

N : Ordinary portland cement

M : Moderate-heat portland cement (C3S ≤ 50%, C3A≤6%))

L : Low-heat portland cement (C2S ≥40%, C3A≤6%)

H : High-early-strength portland cement

BB : Portland blast-furnace slag cement (class B), (BFS=30-60%)

FB : Portland fly-ash cement (class B), (FA=10-20%)



11

4.2.2 Concrete(2) The thermal properties of concrete shall be determined taking into

consideration the materials used and the mixture proportions ofconcrete.

Specific heatin case of no experiment data : 1.15J/gºC may be used

Heat conductivityin case of no experiment data : 2.7W/mºC may be used

Commentary

Thermal expansion coefficientfor portland cement (OPC, M, L, H, FB) :10×10-6/ºC may be usedfor blast-furnace slag cement class B (BB) : 12×10-6/ºC may be used



12

Range of applicabilityC=250～400kg/m3 (2008)

C=250～550kg/m3 (2016)

4.2.2 Concrete(3)The properties of adiabatic temperature rise in concrete may be

determined by Eq. (4.2.1) in which the type of cement, the unit cementcontent, and the concrete temperature at placement are taken intoaccount.

Rate of temperature rise

Age at starting of temperature riseUltimate temperature rise

( ) ( ){ }[ ]ATSQ,AT ttrexpQtQ 01 −−−= ∞ Eq. (4.2.1)

The constants in Eq.(4.2.1) depend on✔ type of cement✔ cement content✔ temperature at placement



13

Type of cement

Constants in Eq. (4.2.1) 400kg/m3＜Ｗｃ≦550kg/m3

N

Q∞=aAT+bAT×Ta aAT =40.0+0.057Ｗｃ bAT =-0.146+0.000308Ｗｃ

rAT= aAT+bAT×Ta aAT =-0.426+0.00207Ｗｃ bAT =0.0471+0.0000188Ｗｃ

sAT= 1t0,Q=aATexp(-bAT×Ta) aAT =0.832-0.000531Ｗｃ bAT =0.0482+0.000068Ｗｃ

M

Q∞=aAT+bAT×Ta aAT =34.8+0.052Ｗｃ bAT =0.0709-0.00016Ｗｃ

rAT= aAT+bAT×Ta aAT =-0.101+0.000811Ｗｃ bAT =0.00679+0.0000631Ｗｃ

sAT= 1t0,Q=aATexp(-bAT×Ta) aAT =1.02-0.000867Ｗｃ bAT =0.0493-0.0000295Ｗｃ

L

Q∞=aAT+bAT×Ta aAT =30.0+0.047Ｗｃ bAT =0.0946-0.000159Ｗｃ

rAT= aAT+bAT×Ta aAT =0.218+0.0003Ｗｃ bAT =-0.00179+0.0000598Ｗｃ

sAT = aAT+bAT×Ta aAT =0.302+0.00104Ｗｃ bAT =0.00293-0.0000216Ｗｃ

t0,Q=aATexp(-bAT×Ta) aAT =1.178-0.00115Ｗｃ bAT =0.0503-0.00000289Ｗｃ

Constants in the equation for adiabatic temperature rise

Extend the range of applicability



14

Relation between predicted and observe adiabatic temperature rise（400kg/m3＜Ｗｃ≦550kg/m3）

L

[Reference material 7]

Cement : N Cement : M



15

Relation between predicted and observe adiabatic temperature rise （400kg/m3＜Ｗｃ≦550kg/m3）


Cement : L Cement : BB



16

(WC=530kg/m3)(WC=472kg/m3)

Relation between predicted and observe adiabatic temperature rise （High-early strength Portland cement）


Cement : H Cement : M



17

4.2.2 Concrete(4) The heat transfer coefficient of concrete shall be determined taking

into consideration the form material, the curing material, the curingmethod, and the meteorological conditions.

Type of form and curing methodHeat transfer coefficient (W/m2 oC)

Steel form, spray curing (depth of ponding < 10 mm) 14Ponding (10 mm ≤ depth of ponding < 50 mm) including straw mat curing 8Ponding (50 mm ≤ depth of ponding < 100 mm) including straw mat curing 8Plywood 8Sheets 6Curing mat, ponding + curing mat, including ponding sheet 6Foam polystyrene (thickness: 50 mm) + sheets 2Airbag (with sheet attached): 2 sheets, 3 sheets, 4 sheets 6, 4, 2Exposed surface on concrete, ground, bedrock 14

Table C4.2.4 Values of heat transfer coefficient



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(4.2.2)

4.2.2 Concrete(5) The compressive strength of concrete may be determined by

Eq. (4.2.2) in which age of concrete, temperature dependence, type of

cement and water cement ratio are taken into account.

( ) ( ) ( )ncfe

feec tf

StbaSttf ′−+

−=′

1 0

400013 65273

n

e ii i

t Δt ×exp .T( Δt ) / T=

⎡ ⎤= −⎢ ⎥+⎣ ⎦∑

Commentary

The parameters a, b, Sf should obtained based on experiments.

Temperature adjusted age:

When the parameters are not obtained by experiments, they may be taken to be the recommended values in the Guidelines.



19

Table C4.2.5 Constants in Eq.4.2.2

Cement Strength control age tn (day)

a = α1+β1(C/W) * b = α2+β2(C/W) * Sfα1 β1 α2 β2

N28 6.31 -1.36 0.771 0.0494

0.3756 6.94 -1.54 0.875 0.027891 7.37 -1.67 0.946 0.0138

M28 12.6 -2.58 0.480 0.1140

0.4256 15.2 -3.21 0.656 0.084091 18.1 -3.96 0.891 0.0350

L28 16.1 -2.55 0.272 0.1430

0.5056 24.0 -4.48 0.584 0.083091 28.7 -5.60 0.788 0.0460

H7 3.27 -0.82 0.512 0.1220

0.3014 3.96 -1.04 0.711 0.075928 4.39 -1.19 0.841 0.042891 4.79 -1.32 0.966 0.0096

BB28 14.4 -3.86 0.477 0.1400

0.4256 17.4 -4.88 0.687 0.087791 19.2 -5.44 0.787 0.0757

FB28 13.4 -3.20 0.514 0.1160

0.4756 16.2 -4.12 0.708 0.073991 18.4 -4.80 0.850 0.0456

improved applicability to high-strength concrete



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Type of cementStrength control age tn

(day)f ’c(tn)=p1+p2(C/W)*

p1 p2

N28 -14.5 28.156 -12.8 28.791 -11.6 29.1

M28 -33.5 36.256 -26.3 36.391 -18.4 35.4

L28 -37.3 36.456 -23.7 35.691 -19.0 36.6

H7 -22.6 30.5

14 -18.2 31.028 -14.9 30.991 -11.5 30.5

BB28 -10.2 24.356 -3.38 23.691 -1.43 24.5

FB28 -27.2 31.856 -24.2 32.991 -22.4 34.0


Table C4.2.6 Constants in Eq.4.2.2



21

Compressive strength predicted by the GuidelinesCement Ｍ（strength control age(tn): 28 days）

W/C=30%W/C=45%W/C=55%

[Reference Materials 8]



22

Cement L （strength control age(tn): 91 days）Compressive strength predicted by the Guidelines

W/C=30%W/C=45%W/C=55%




23

4.2.2 Concrete

(6) The splitting tensile strength of concrete may be determined byEq. (4.2.3).

(4.2.3)

When it is not determined by experiment, it may be obtained by Eq. (4.2.3).

The constants of C1 and C2 in Eq. (4.2.3) are recommended to be 0.13 and 0.85, respectively. .

( ) ( ) 21

Cecet tfCtf ′×=

Commentary



24

4.2.2 Concrete(7) The modulus of elasticity of concrete may be determined by

Eq. (4.2.4) on the basis of compressive strength.

(4.2.4)

CommentaryThe constants C3 and C4 are recommended to be 6300 and 0.45, respectively.

( ) ( ) 43

Cecec tfCtE ′×=



25

4.2.2 Concrete

(8) The influence of creep of concrete may be evaluated by multiplying

modulus of elasticity by a reduction coefficient.

( ) ( ) ( )eceee tEttE ×= ϕ

Effective modulus of elasticity

Reduction constant

φ(te ) is introduced to take into consideration the fact that creep is large in hardening process.



26

4.2.2 Concrete(9) The autogenous shrinkage strain in concrete may be determined

by Eq. (4.2.5) in which age, temperature dependence, type ofcement and water to cement ratio are taken into account.

(4.2.5)( ) ( ),as e c as as et r tε η ε ∞= ･･

( ){ } ( ){ }463070 7 2 50 1 1 2 10 20as , maxε ×exp . W/C exp . T−∞

⎡ ⎤= − + × − − × × −⎢ ⎥⎣ ⎦

( ) ( ){ },1 asas e as e e set

br t exp a t t= − − −

Commentary

Constant that represents influence of type of cement : ηc

The ultimate value of autogenous shrinkage strain (×10-6)

Function that represents development of autogenous shrinkage

N, M, L, H, FB:

( ){ } ( ){ }462350 5 8 80 1 1 2 10 20as, maxexp . W/C exp . Tε −∞

⎡ ⎤= × − + × − − × × −⎢ ⎥⎣ ⎦BB:



27

Autogenous shrinkage of concrete with cement M

Type of cement ηc

N 1.0M 0.5L 0.4H 1.2

BB 1.0FB 1.0

( ) ( ),as e c as as et r tε η ε ∞= ･･





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4.2.2 Concrete

（10）The expansion strain in concrete with expansive additive shall be determined taking into consideration the type of cement, the type and dosage of expansive additive, the temperature dependence, the curing method and so on.

Expansive strain of concrete with standard expansive additive at the standard dosage may be determined by Eq.(C4.2.10)

( ) ( ){ }, ,01 exp exbex e ex ex e ext a t tε ε ∞

⎡ ⎤= − − −⎢ ⎥⎣ ⎦(C4.2.10)

Commentary



29

Commentary

Con

tract

ion

←

0

→

Exp

ansi

on ① Expansion strain calculated by the Guidelines

② Autogenous shrinkage strain calculated by the Guidelines

Age (days)

①＋②

Stra

in

Image of expansion strain and autogenous shrinkage strain



30

Expansive strain of concrete with expansive additive

Type of cement εex,∞ aex bex tex,0

N 150 0.69 1.11 0.30

M 175 0.64 1.13 0.30

L 190 0.30 2.36 0.35

H 160 0.62 1.79 0.20

BB 145 0.27 1.53 0.30

( ) ( ){ }, ,01 exp exbex e ex ex e ext a t tε ε ∞

⎡ ⎤= − − −⎢ ⎥⎣ ⎦



31

Restraint stress of concrete under high temperature was measured and compared with predicted value using the design values in the Guidelines.

Concrete specimen for restraint stress tests

80019

(mm)

10019

100 4

・インバー鋼材（熱膨張係数：0.5×10-6/℃，ヤング係数：140000N/mm2）

ねじ加工ひずみゲージ

熱電対

Strain gauge

Invar rod (steal ratio: 0.7, 1.7, 5.7%)

Thermocouple

screwed



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Restraint stress in expansive concrete

Restraint stress can be estimated on safe side by analysis using design values of concrete properties.

-2.0

-1.5

-1.0

-0.5

0.0

0.5

0 2 4 6 8 10 12 14

Con

cret

e str

ess（

N/m

m2 ）

Age （days）

experiment-0.7%experiment-1.7%experiment-5.7%analysis-0.7%analysis-1.7%analysis-5.7%

M

-1.5

-1.0

-0.5

0.0

0.5

0 2 4 6 8 10 12 14

Con

cret

e str

ess （

N/m

m2 ）

Age （days）

L

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

0 2 4 6 8 10 12 14

Con

cret

e str

ess（

N/m

m2 ）

Age （days）

H



33

4.2.2 Concrete

（11）The drying shrinkage of concrete may be neglected.

Commentary in Chapter 1In the Guidelines, the period for verification is from the time of concrete placement to the time when concrete temperature equilibrates with the ambient temperature.

During this period, the effect of drying shrinkage is negligible and consequently is neglected in the verification procedure.



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Thank you for your kind attention.

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Chapter 4 Verification of Cracking Due to Heat of ...concrack5/PPT-PDF/Guidelines Chapter 4 (design...JCI Guidelines for Control of Cracking of Mass Concrete 2016 1 ... Chapter 4 Verification