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Concrete TechnologyDimensional Stability of Concrete

Professor Kamran M. Nemati

Winter Quarter 2013 1

Concrete Technology

Dimensional Stability

of Concrete

Concrete Technology

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Concrete as a Composite Material

Typical stress-strainbehavior of cementpaste, aggregate, andconcrete.

Both cement paste and aggregates show linearelastic properties.

The non-linear portion of the stress-strain curve forconcrete is due to cracking of the cement paste.

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Schematic Diagram of Concrete Behavior

*Based on J. Glucklich, P roc. Int. Conf. on the Structure of Concrete, Cement and Concrete Association, Wexham Springs,Slough, U.K., 1968, pp. 176-85.

Figure below is the Diagrammatic representation of the stress-

strain behavior of concrete under uniaxial compression*. The progress of internal microcracking in concrete goes through

various stages, which depend on the level of applied stress.

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Even before the application of external loads,microcracks already exist in the transition zonebetween the matrix mortar and coarse aggregate.

The number and width of these cracks depend on:

Bleeding characteristics

Strength of TZ Curing history of concrete

Below 30% of the ultimate load, the transitionzone cracks remain stable.

S

t

a

g

e

1

Figure in the previous slide reflects fourstages of concrete behavior:

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Above 30% offc, as the stress

increases, the TZ microcracks begin toincrease in length, width andnumbers.

Until about 59% of the ultimatestress, a stable system of microcracksmay be assumed in TZ.

At 50 to 60% offc, cracks begin to

form in the matrix.

S

t

a

g

e

2


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Increase the stress up to 75% of fc.

The TZ cracks become unstable.

The cracking in the matrix will increase.

At 75 to 80% offc the rate of strain

energy release reaches the critical levelnecessary for spontaneous crack growth.

S

t

a

g

e

3

St

a

g

e

4

Above 75% offc bridging of cracks in

matrix and TZ.


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Elastic Modulus of Concrete Types of Elastic Modulus (E)

E is given by the shape of curve for concreteunder uniaxial loading (since the curve forconcrete is nonlinear, three methods forcomputing moduli are used).

Tangent Modulus (slope of a line drawntangent to the curve at any point on thecurve)

Secant Modulus (slope of the line drawn fromthe origin to a point on the curve corresponding

to a 40%fc)

Chord Modulus (slope of a line drawnbetween two points on the curve)

Static

Dynamic

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Elastic Modulus of ConcreteDifferent types of elastic moduli and the method bywhich these are determined.

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Elastic Modulus of Concrete

According to ACI Building Code 318, with aconcrete unit weight between 90 and 155lb/ft3, the modulus of elasticity can bedetermined from:

2/15.1 33 ccc fWE Where: Ec = elastic modulus

Wc = unit weight of concrete (lb/ft3)fc = the 28-day compressive strength

of standard cylinders

cc fwE ,f

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Factors Controlling Elastic Modulus

In single phase solids (homogeneousmaterials) a direct relationship existsbetween density and modulus of elasticity.

In heterogeneous, multi-phase materials,i.e., concrete, the volume fraction, density,and modulus of elasticity of each phase,

and the characteristics of TZ determine theelastic behavior of the composite.

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Aggregate: Porosity of aggregate (determines stiffness) is the

most important factor that affects E of concrete.Dense aggregates have a high E.

In general, the larger the amount of coarseaggregate with a high elastic modulus in a concretemixture, the greater would be the modulus ofelasticity of concrete.

Elastic Mismatch:

Granite 20106 psi

Sandstone (porous) 3-7 106 psiLightweight expanded shale 1-3 106 psi

Ea

HCP

Will develop morecracks in the TZdue to elasticmismatch


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Hydrated Cement Paste (HCP):

The elastic modulus of the cement paste matrix (Ep)is determined by its porosity.

The factors controlling the porosity of the cementpaste are: w/c, air content, mineral admixtures, anddegree of cement hydration.

gEgEE pac 1

Volume of

cement paste

Volume fraction

of aggregate


Transition zone (TZ):Void space, microcracks, and orientation of CH

crystals are more common in TZ than in bulk cementpaste; therefore they play a very important role indetermining the stress-strain relationship in concrete.

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For a material subjected to simple axialload, the ratio of the lateral strain to axialstrain within the elastic rangeis calledPoissons ratio.

With concrete the values of Poissons ratiogenerally vary between 0.15 and 0.20.

StrainAxial

StrainLateralRatiosPoisson'

Poissons Ratio

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Drying Shrinkage and CreepCauses Drying Shrinkage:

Loss of surface adsorbed water from C-S-H + loss ofhydrostatic tension in small capillaries (

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Drying Shrinkage and Creep

ds 400 - 120010-6 in/in

(depending on aggregate type and cement)

Factors affecting drying shrinkage:

material and mix proportionsAggregate type and content

Cement type and content

ds

(time under drying)

npc gSS 1

nVSS ppc ,,f

Shrinkage

of concrete

Shrinkage of

cement paste

n Related to

aggregate

n1.2 to 1.7

Volume of

cement paste

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Creep of Concrete Creep: deformation with time under certain load.

Considering the various combination of loading, restraining, andhumidity conditions, the following terms are defined: True orbasic creep, specific creep, drying creep, and creep coefficient.

Creep in concrete is a post-elastic phenomena.

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Creep of Concrete True or Basic Creep: Creep with no loss of water to the

environment (under 100% RH)

When drying shrinkage and creep happen together, it ismore than basic creep.

Specific Creep: is defined as creep strain per unit of stress:

Drying Creep: is the additional creep that occurs when thespecimen under load is also drying.

Creep Coefficient: is defined as the ratio of creep strain toelastic coefficient.

crCreepSpecific

E

cr

tCoefficienCreep

gC

C

c

p

1

1loglog

gCCpc 1

Cc = creep of concreteCp = creep of cement paste

g = aggregate content

= unhydrated cement

0

(In well-cured

concrete) aEE,,,f a

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I. Material and mix proportions

II. Curing and testing conditions

Aggregate:

a) Modulus of Elasticity

Factors Affecting Drying Shrinkage and Creep

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I. Material and mix proportions

II. Curing and testing conditions

Aggregate: b) Aggregate content

Any increment of these two factors reduce thedrying shrinkage & creep.


Concrete Technology

20Creep is inversely proportional to the s trength of concrete

Factors Affecting Drying Shrinkage and CreepCement: a) Water/cement ratio:

For a constant cementcontent an incrementalincrease in W/C ratioincreases both dryingshrinkage and creep.

b) Cement content:

For a constant W/C ratioan incremental increase

in cement contentreduces the creep butincreases the dryingshrinkage. This is theonly case in which existsan opposite effect.

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Humidity:

One of the most important factors for both shrinkage and creepis the relative humidity of the medium surrounding theconcrete. For a given concrete, creep is higher the lower therelative humidity.

An incremental increase on relative humidity of air decreasesboth the drying shrinkage and creep.


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Temperature:

Given the same curing history for twospecimens, the one that is kept in ahigher temperature will have morecreep and drying shrinkage than theother one.


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Age of loading:

There is a direct proportionality between the magnitudeof sustained stress and the creep of concrete.

Because of the effect of strength on creep, at a givenstress level, lower creep values were obtained for thelonger period of curing before the application of theload. Shrinkage is not affected by this factor.

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