Creep of concrete

Vishal Kumar Chaudhary

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Creep deflections arch bridge in Deventer

after the problems at Deventer,At Westervoort bridge extra mid span height has been provided

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Figure 2

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IntroductionCreep is one of the basic property of concrete. It plays significance role in designing of concrete structure, because in concrete the macrostrains of creep varies from 400 to 1000 ×10-

6. When load is applied on concrete , the structure undergoes elastic and inelastic deformation. Just after the application of load elastic deformation occurs, according to Hooke’s Law. Whereas Inelastic deformation is function of time and it increases with time as the concrete experiences a sustained load, it is mostly due to creep. It increases at a decreasing rate during the period of loading. Approximately one-third to one-fourth of ultimate creep occurs during first month of sustained loading and usually one-half to three-fourths of the ultimate creep occurs during the first half year.

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Log TimeStressStrain

constant strain sectionisometric section(relaxation)

constant time sectionisochronous section

constant stress sectioncreep curve

Figure 3. Constant stress-strain-time coordinates

stress and strain induced into the material when it is loaded. These properties are function of time.

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Based upon relative humidity of hydrated

cement paste

Basic creep(100% Relative humidity)

Drying creep(Relative

humidity<100%)

TYPE OF CREEP

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Basic creep(short time-creep)The creep of concrete develops with a high speed right after the load is applied (within a day) and then the process is sharply decelerated.it is caused by stress induced redistribution of capillary water within the structure of hardened cement paste.

Figure 4: Feldman-Sereda model for CSH

Capillary water Void size10-1000nm

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Drying creep (Long term creep)

Due to sustained stress C-S-H lose it’s physically adsorbed water, it leads to drying creep strain. It has been observed that when load is applied on concrete and is simultaneously exposed to low relative humid environment, the total strain is higher than the sum of elastic strain, free shrinkage strain (drying shrinkage strain of unloaded concrete), and basic creep strain (without drying).The additional strain is due to Drying creep.

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Typical behavior of concrete on loading and unloading (In terms of creep strain)

To understand the behavior following experiment has been conducted :-

Plain concrete specimen has been subjected to sustained uniaxial compression for 90 days and thereafter unloaded. It has been observed that instantaneous or elastic recovery is approximately of same order as the initial elastic strain. Elastic strain is followed by a gradual decrease in strain called creep recovery , although rate of creep recovery more than creep ,the recovered creep strain is not equal to total strain.

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Reversibility of creep

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Factors affecting creep :-

Aggregate -Aggregate content in concrete is the most important factor affecting creep. the modulus of elasticity of the aggregate affect most, The grading, maximum size, shape, and texture of aggregate also affect the creep. Also Unhydrated cement in concrete mix does not shrink and therefore may be included in the aggregate.

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-Neville related the creep of concrete (Cc) and cement paste (Cp) with sum of the aggregate(g) and unhydrated cement contents()

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Variation of creep with different type of aggregate :-According Troxell et al.’s study of creep of concrete over a period of 23 years. The corresponding creep values were 600, 800, 1070, and 1500 × 10−6 for the concrete containing limestone, quartz, gravel, and sandstone aggregate, respectively.

According Troxell et al.’s Data the creep of concrete increased 2.5 times when a high elastic modulus aggregate was substituted with a low elastic modulus aggregate.

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Water cement ratio & cement content-For fixed cement content, with increasing water-cement ratio creep are known to increase, Due to increase in the permeability and also decrease in strength(decrease in elastic modulus). If cement content increases it means decrease in aggregate fraction and consequently a corresponding increase in the moisture-dependent deformations in concrete.Although influence of water cement ratio & cement content on creep is indirect.

Type of cement-The rate of gain of strength of cement effects the creep , assuming final strength of cement past is same.

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Time –Creep happens due to diffusion of adsorbed water held by capillary tension in small pores of hydrated cement product ,it is time dependent process.

Humidity-Due to increase in atmospheric humidity, relative rate of moisture flow from inside the concrete to outside atmosphere will decrease.

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From Troxell, G.E. et al., Proc. ASTM, Vol. 58, 1958. From International Recommendations for the Design and Construction of Concrete Structures, CEB/FIP, 1970

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Geometry of the concrete element :-

rate of water loss would be controlled by the length of the path travelled by the water , path resist to water transport from the interior of concrete to the atmosphere. We can relate geometry of concrete to creep by using size and shape parameter (effective or theoretical thickness)

• effective or theoretical thickness = (area of the section)/(semi perimeter in contact with the atmosphere)

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Influence of specimen size and relative humidity on the creep coefficient

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Modified Capillary theory of creep of concrete

First step made by Freyssinet ,according to his theory concrete is assumed capillary porous with linearly elastic framework , internal capillary pressure can be related to external pressure :-

P=qω

p-external pressure q-internal capillary pressure ω -relative wetted cross sectional area(relative volume of capillaries . filled with water)

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Volumetric deformation(by hook’s law)-

Θ=qω/Ko (1)

Ko-volumetric modulus of elasticity (Dry concrete with empty capillaries) also consider as a long term modulus

Equilibrium value of capillary pressure(by Kelvin’s equation)

q= (2)

R – absolute gas constant; T – absolute temperature; – molar volume of water ; ψ – relative humidity of environment

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Direct calculation is done using formulas (1) and (2) in 1974 by L.A. Dulina Result-this theory underestimates the concrete shrinkage value by an order at least

Formula (1) changed to- Θ=κqω (3) κ- subjected to determination

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Volumetric deformation(elastic for solid body)=p/K*

K* -a volumetric modulus of solid body elasticity

-full capillary porosity

(4)

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With account of (4),(2) and (3) formula-

(5)

initial humidity of environment of a sample was before it was transferred to environment with different humidity.

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But when load applied on concrete structure the moisture equilibrium disturbed, capillary forces partially release after which the body tends to restore equilibrium with environment and undergoes forced shrinkage interpreted as a creep. So relative vapor pressure will change in (5)

(7)

Px- introduced for dimensional requirementFurther-

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(8)

The formula (8) Represent Both Natural shrinkage and creep

(9)

According to(9) creep linearly vary with applied load(it is only valid when concrete doesn’t exceed certain load) the formula should (9) corrected under following condition-

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-At zero vapour pressure the wetted area ω(ψ) = 0-at the time of loading the concrete is in equilibrium with the saturated vapour, then ω(ψ) = Ω-according to Kelvin formula the capillary pressure is equal to zero at ψ =1

(10)

The formula(10) describe dependence of creep on temperature and humidity. Dependence on humidity is highly complicated by the multiplier ω(ψ). For simplicity we can put ω(ψ)= ψΩ (11)

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By substituting (10) into (11)-

(13)

For well defined object-

(14)

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Formula (13) can be written as-

(15)

Application-External pressure p is applied on the sample, so vapor pressure will be lowered according to(7) According to (2) at constant temperature To

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Fast application of external pressure leads to isotropic shrinkage,For the practical purpose we can assume Δq ≈ p

volume of creep deformation calculated by (15),as a function temperature and humidity k =1, m = 0 (slot-type capillaries), Ko=E0/2=75.103 MPa According to experimental data order of short term creep=10-6

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According to the above theory it can be concluded that short term creep is related to the capillary forces.

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References :- Applied Mechanics and Materials, ISSN: 1662-7482, Vols.

725-726, pp 493-498. F.H.Wittman Creep and shrinkage Mechanism, chapter6 Creep of concrete: Influencing Factors and Prediction By

Adam M.Neville and Bernard L.Meyers. P. Kumar Metha and P. J. M. Monterio, Concrete-

Microstructures, Properties and Materials,3rd edition. Troxell, G.E. et al., Proc. ASTM, Vol. 58, 1958 https://commons.wikimedia.org/wiki/

File:Creep_deflections_archbridge_in_Deventer,_built_in_the_seventies_of_the_past_century_over_the_IJssel_river,_caused_by_too_high_concrete_compressive_stresses_-_panoramio.jpg

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Thank you