Stability in Concrete

7/31/2019 Stability in Concrete

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Concrete TechnologyDimensiona l Stab i l i t y o f Concre te

Professor Kamran M. Nemati

Spring Quarter 2012 1

Concrete Technology

Dim ensional St ab i l i t y

o f Conc ret e

Concrete Technology

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Conc ret e as a Com posi te Mat er ia l

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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Schemat ic D iagram o f Concre t e 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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Dimensional Stabilit y

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% offc.

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


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Elast ic 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 Cont rol ling Elasti c 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


Transit ion 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 w it hin the elast ic rangeis calledPoissons rat io.

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

StrainAxial

StrainLateralRatiosPoisson'

Poissons Rat io

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Drying Shr inkage and CreepCauses Drying Shrinkage:

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


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Drying Shr inkage 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 Coeffi cient : 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

I I . Curing and testing conditions

Aggregate:

a) Modulus of Elasticity

Factors Affecting Drying Shr inkage and Creep


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I . Material and mix proportions

I I . Curing and testing conditions

Aggregate: b) Aggregate content

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


Concrete Technology

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Factors Affecting Drying Shr inkage 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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Stability in Concrete