THE EFFECT OF CREEP AND SHRINKAGE ON TALL BUILDINGS

CIV_ENV 499 - INDEPENDENT STUDY

CONCRETE, CREEP AND SHRINKAGE

Oluwatobi Fiyin BABARINDE MS Structural Engineering and Infrastructure Materials

Northwestern University, Evanston IL.

Supervisors:

Prof Gianluca CUSATIS

Prof. David CORR

March 2015

CONCRETE

Concrete is the most widely-used construction materials for 3 major reasons although there are others. First, concrete is highly durable against the action of water, also because it easy to manufacture it into different shapes desires and lastly because it is relatively the cheapest material available to the engineer.

Concrete is a composite material comprising of aggregates and hydrated cement paste (HCP) with/without admixtures. Generally, based on strength concrete can be classified as low, moderate or high strength based on the compressive strength after 28 days. Also, concrete can be categorized based the weight as light, normal and heavy weight.

PROPERTIES OF CONCRETE

i. Strength: is amount of load till failure. Concrete has excellent compressive strength, while the tensile and compressive strengths are about 10 and 15% of the compressive strength.

ii. Modulus of Elasticity: it is noteworthy that the elastic modulus of concrete is lower than that of its constituents HCP and aggregates. This can be traced back to the micro structure.

iii. Toughness: this is the amount of energy required till fracture. Typically, it is the area under the stress-strain curve. Concrete is mostly brittle since it doesnt experience great elongations or compression before failure.

iv. Creep: is the strain that occur in concrete (and materials) when stress is held constant. The adsorbed water in the HCP is main factor that affect this property.

v. Shrinkage: is the change in strain that concrete experience due to changes in the surrounding temperature or humidity. When restrained, shrinking concrete develops tensile stresses, and since the tensile strength is low, this leads to cracking.

vi. Durability: this a measure of how resistant concrete is to attack from acids or other substances that could cause loss of strength or detrimental changes in properties.

MICROSTRUCTURE OF CONCRETE

Concrete is a heterogeneous material and to understand behavior of this material an understanding of the properties on the microscopic level go a long way shedding light on behaviors like creep and shrinkage that .concrete exhibit. Macroscopic observation of the structure of concrete identifies 2 major phases in concrete namely- the aggregates and the hydrated cement paste HCP. However, on the microscopic scale, an additional and very important region, called the interfacial transition zone, exist between the aggregates and the hydrated cement paste. The microstructure of concrete is not an intrinsic property by can change with temperature or humidity or time. Aggregate Phase: This comprises of both the fine and coarse aggregates in concrete. Generally,

this phase affect properties like Elasticity modulus, unit weight and dimensional stability of concrete. The sizes and texture of aggregates have a role to play in the formation of internal bleeding which leads to micro-cracks in the transition phase. This internal bleeding can be explained to occur when water tends to be pooled at the large flat surfaces of aggregates hence making the water-cement ratio in the region higher, leading to the formation of bigger capillary voids, more ettringites in the region, as well as the hexagonal-prism-shaped calcium hydroxide CaOH (all having the impact of strength reduction).

Hydrated Cement Paste: This phase can be considered to consist of solids, liquids and voids. The solids include the calcium silicate hydrate CSH which is about 50-60% of the HCP, calcium hydroxide, which are about 20-25% by composition, calcium sulphoaluminate hydrates and unhydrated clinker grains. The presence of monosulphates in concrete makes it susceptible to acid attack hence affecting durability. The different properties of these solids affect properties of the concrete, but since CSH is the largest by volume, it dominates. However, in the transition layer, there is more likelihood of CaOH and ettringites been formed which leads to relatively lower strength and higher chances micro-cracking.

Voids and Water: the voids in HCP include interlayer spaces of CSH layers, capillary voids, and air voids from entrained air, while similarly water in HCP include capillary water, adsorbed water, interlayer water and chemically combined water.

CREEP AND SHRINKAGE IN CONCRETE

Terminologies:

Total Strain: This is the total change in length per unit length observed on a specimen Shrinkage: is the strain measured on a load-free concrete sample

o Basic shrinkage: this is a strain cause by water loss due to the hydration of cement. o Drying shrinkage: here, the strain is due to moisture loss to the atmosphere due to

relative humidity less than 100%. o Carbonation shrinkage: this is due to the reaction of Ca(OH)2 in the concrete with CO2 of

the atmosphere o Plastic shrinkage: refers to the shrinkage concrete experiences before setting o Swelling: is the expansion of concrete due to the reduction of capillary forces when

immersed in water. Load induced strain: is the strain measured due to load application. It comprises of the initial

strain and creep strain. Creep strain: This is the strain concrete experiences due to a constant stress level. It consists of:

o Basic creep: Is the creep occurring without water content reduction i.e. a sealed sample. o Drying creep: as the name implies, is the creep strain accompanying moisture loss.

3 specimens are used to determine the drying creep: loaded and exposed, loaded but sealed and unloaded and exposed samples. Drying Creep = Total strain Loaded and Sealed Strain Unloaded and exposed strain Figure 1 shows a plot of how the strains above are related.

Compliance: Defined as the amount of strain at a time t due to a unit sustained uniaxial stress applied since time t

J(t, t) =

Specific Creep: is the creep strain per unit load Creep coefficient: Ratio of creep strain to initial strain (obtained as early as 2 minutes age).

Figure 1: Showing the Relationship between Derived and Measure Strain Values

Mechanisms of Creep and Shrinkage:

Creep and shrinkage in concrete are usually discussed together because the governed by mostly the same factors and can be modelled similarly. Several explanations have been put forward to discuss the process of creep and shrinkage in concrete and the internal changes that occur, however, none of them can be said to be 100% accurate because concrete is a complex material. Hence, a possibility is that a combination of the mechanisms are governing the behavior of concrete with respect to creep and shrinkage. Some mechanisms are:

The adsorbed water acting as a lubrincant that helps sliding and shear of cement paste during creep or shrinkage.

Consolidation due to the seepage of adsorbed water Delayed elasticity due to hcp acting as a restrains to the elastic deformation of the aggregates Microcracking occuring in the transistion zone in concrete Mechanical deformation

Factors Affecting Creep and Shrinkage

The following are some of the factors affecting creep and shrinkage as presented in ACI 209 1R-05:

i. Mix proportion and Concrete Content - The amount of aggregate in concrete is known to affect affect shrinkage. Governed by-

Sc = Sp(1-g)n where Sc is the shrinkage of concrete, Sp is the shrinkage of cement paste, g is the fractional volume of the aggregates and n is a constant (1.2-1.7) There is a similar relation found to govern creep as well.

- Aggregate size also affect shrinkage as large aggregate imply large surface areas and hence more internal bleeding in the transistion zone and hence formation of microcracks which ultimately affects both shrinkage and creep

- Water content has been observed to increase shrinkage when increased. At a constant cement content, basic and drying creep in concrete increases with water content in concrete. However, a comparison between different w/c ratios is inappropriate as different w/c ratios have different strength.

- Elastic Modulus of Aggregate. A stiffer aggregate will make the overall concrete experience lesser shrinkage or creep and vice versa.

- Some properties of cement itself is known to affect shrinkage. For example, finely ground cement has more shrinkage than coarse ones, higher aluminate content makes shrinkage to be more rapid and lower sulphate cement has increased shrinkage.

- Admixtures: these have been found to either increase the shrinkage or otherwise depending on what admixture is been considered

ii. Environmental Factors - Relative humidity is a major factor affecting shrinkage and creep. A relation between

shrinkage is:

S 1 (h/100)b b is from 1-4

- Cyclic hummidity affects shrinkage as well. Concrete specimens stored at a constant relative humidity environment of 65% exhibited greater drying shrinkage than specimens stored in an environment that cycled between 40 and 90% relative humidity, with an average relative humidity of 65%. The reverse is the case however in creep of samples, with only a slight difference in creep strains.

iii. Effects of Design and Construction Practises

- Curing for long period reduced drying shrinkage and creep. Predrying samples can reduce creep as well.

- Heat and steam curing: this practise increases concrete strength from an early age hence reducing shrinkage and creep for as much as 30% in both.

- Size and shape of member. Generally, thinner member experience more shrinkage than this ones and there is an inverse relationship between shrinkage and the square of the ratio of the volume and surface area of a member.

- Load and loading age: there exists a linear relationship between creep strain and concrete strengths 0.3fc to 0.6fc. Also creep depends on time the time since load application.

PREDICTION OF CREEP, SHRINKAGE AND TEMPERATURE EFFECTS IN CONCRETE STRUCTURES

All these factors discussed in the previous section are important and a good model for prediction of creep or shrinkage must be able to account for all these factors to yield good forecasts of expected values. However, accounting for all of these in the model great increases the complexity of an already complex task. Therefore different models sought to simplify the problem to bring varying level of ease of use for practicing engineers or researchers. These simplifications come at the price of accuracy of prediction. Calculating the effects of creep and shrinkage on a structure is far more complex and of

lesser overall impact compared to the ease of calculating effects due to service loads and greater importance this has on the building.

ACI 209.2R-08 put forward some guidelines to help in formulating models for predicting creep and shrinkage while the following assumptions were made:

a. Shrinkage and creep are additive that is, they occur independent of each other b. A linear aging model is assumed for creep with applied stress level less than 40% since creep can

be approximately proportional to the applied stress. Strain response due to stress increment are then added by superimposition. Stress reversals are excluded while temperature and moisture are held constant for superimposition to be applicable.

c. Creep is separated into basic and drying creep and basic creep is considered as a constitutive property of the concrete

d. Experimental strains of creep and shrinkage are measured on the surface of the specimen whereas such measurement are determined along the longitudinal axis by ASTM C157/C157M for prismatic member. Hence it is assumed there is no gradient of strain in the section of the member unless FE is used or gradient is linear.

e. Stresses induced during curing are negligible Criteria for Prediction Models Models are a compromise between accuracy and ease-of-use. However, the committee recommended that at a minimum a model should include properties such as:

- Mix proportion, strength, elastic modulus etc - Ambient relative humidity - Duration of drying - Duration of loading - Specimen size

Since a model has to be calibrated and compared with existing data, models are to ensure adherence to the following evaluation criteria to make predictions a good fit with data from the vast data in the RILEM databank.

Evaluation Criteria for Models - Drying shrinkage and creep do not increase indefinitely with time - Equations should be capable of extrapolation in time and size - Appropriate from databank should be used to compare the model - Model equations should be easy to use and not highly sensitive to input parameters - Shrinkage and creep curves predicted over a broad range of time should agree with test results. - Compliance instead of creep coefficient should be used - Creep equations should allow for the effect of pre-drying before loading - Also equations should be able to account for cement contents such as fly-ash and other pozolans - Should accommodate varying specimen sizes as well as relative humidity changes

1. ACI 209R-92 MODEL

The philosophy behind this model is that creep and shrinkage are predicted for a standard condition and various correction factors are then applied to cater for deviation from the standard condition occurring at the normal condition being considered. Here are some of the models of some material properties:

Strength (fc')t =

+

(fc')28

Modulus of Rupture fr = gr[w(fc')t]1/2 Direct Tensile Strength ft = gt[w(fc')t]1/2

Secant Modulus of Elasticity Ect = gct[w3(fc')t]1/2 where w is unit weight of concrete Creep

t =

+u

Shrinkage

(sh)t =

+(sh)u

Further relations were then given to model structural response due to creep and shrinkage, it should be noted that the models are quite easy to use busy sacrifice accuracy and are more suited to the need of practicing engineers desirous of accounting for these effects in structures.

2. CREEP AND SHRINKAGE CONSTITUTIVE RELATIONS

Baant (1982) presented models based on constitute relations for creep and relaxation that could be implemented in finite element software to predict creep and shrinkage in concrete. Based on the principle of superimposition (applicable because concrete is treated as viscoelastic aging material), model were formulated using 2 approaches: using history integrals and rate type relations.

a. Linear Constitutive Relations with History Integrals

At stress levels lower than 40% of the strength of concrete, the material can be treated as an aging linear viscoelastic material. However, as much as the linearity helps to simplify the structural analysis, the aging rather complicates it. Because of the linearity, we can employ the principle of superposition in modelling the response of concrete. The principle in simple terms allows the discretization of the stress into d(t), and the response of the structure at a time t is the sum of all the individual responses of d(t) acting since time t=t.

So we can write the strain as:

() = (, )() + ()0

Where J(t,t) is the compliance function and 0(t) is the stress independent strain.

The above integral is applicable if stress are below 40% of strength as earlier noted, furthermore, the strain must not increase in magnitude, no significant drying and there should not be a large increase in stress after initial loading. The requirement on drying is of particular importance because it tends to undermine the linearity of concrete due to cracking and microcracking that may occur.

The above integral can be re-written in term of the stress impulse memory function L(t,t) by integration by parts as:

() = ()()

+ (, )() + ()0

At constant strain, the phenomena in which the stress decrease is called stress relaxation and a relation similar to (1) in terms of the relaxation modulus can be written to obtain the stress at a time t.

() = (, )[() + ()]0

In the absence of drying, it is possible to obtain J(t,t) from R(t,t) that will be very accurate when compared to experimental values can be obtained, and the same is true for obtain R(t,t) from J(t,t).

As the above equations have been obtained for a uniaxial stress state, it is possible to write a multiaxial generalization in the form:

3v(t) = (, )() + ()

0

2D (t) = (, )()

0

Where (, ) = 6(. 5 )(, ) and (, ) = 2(1 + )(, )

For computer implementation, the above integrals can be evaluated numerically, by considering the integral as a summation of a finite series of tiny strips taken of time. The function is the summed using the trapezoidal rule. This procedure is similar to that used in the analysis of a structure to ground acceleration data. This type of approach works well for small to medium size structures, how for large structure, the data involve becomes very large and demand rather high computational resources, however, more efficient approaches have been formulated.

b. Linear Constitutive Relations without History Integrals

This approach approximates the compliance function of the previous integrals by the form:

Where: and are both functions of time.

In terms of the retardation time,

This then allows the integral relation previous presented to be written as shown below after substitutions:

More detailed relations could be obtained in the referenced text. The major benefit of this approach is that it eliminates the large computation storage space need as the complete history is no longer needed.

CONCLUSION

Other models such as CEB MC90-99, GL 2000 and BP model among others are also available based on various approximations and yielding varying levels of accuracy. Only few of the models available for predicting creep and shrinkage have been presented here, but the aim was not to get into the details of all possible models but to give an overview of various models that have been developed for the task and more importantly the considerations and factors that impact the prediction of creep and shrinkage since these are processes that occur very slowly and we generally desire to be able to foretell what it will have on concrete structures.

REFERENCES

ACI 209.2R-08 Guide for Modelling and Calculating Shrinkage and Creep in Hardened Concrete

ACI 209R-92 Prediction of Creep and Shrinkage and Temperature Effects in Concrete Structures

ACI 209-1R-05 Report on Factors Affecting Shrinkage and Creep of Hardened Concrete

Mehta P.k. and Monterio P.J.M. (1993), Concrete: Microstructure, Properties and Materials, 2nd ed., McGraw-Hill New York.

Baant Z.P, 1982, Creep and Shrinkage in Concrete Structures, ed Baant Z.P and Wittmann F.H., John Wiley & Sons Chichester.

CONCRETEPROPERTIES OF CONCRETEMICROSTRUCTURE OF CONCRETECREEP AND SHRINKAGE IN CONCRETEMechanisms of Creep and Shrinkage:Factors Affecting Creep and ShrinkagePREDICTION OF CREEP, SHRINKAGE AND TEMPERATURE EFFECTS IN CONCRETE STRUCTURES1. ACI 209R-92 MODEL2. CREEP AND SHRINKAGE CONSTITUTIVE RELATIONSa. Linear Constitutive Relations with History Integralsb. Linear Constitutive Relations without History IntegralsCONCLUSIONREFERENCES