Chapter 2: LITERATURE REVIEW
2.3 Concrete Shrinkage and Creep Mechanism
2.3.2 Factors affect drying shrinkage
The factors affecting drying shrinkage in concrete are grouped into two main categories. On one hand, the environmental factors will set up the external conditions, such as humidity level, ambient temperature or wind velocity. The second group involves the characteristic (intrinsic) properties of the concrete material, as may be the aggregate content and their properties, the w/c ratio, the water content and the cement content. The curing and storage conditions are somewhere in the middle of the previous classification, since they consist of the often controlled external conditions which will to a great extent define the quality of the material, i.e. its characteristic properties.
The environmental conditions will define the severity of the drying process, being more detrimental when there is a combination of dry conditions (low RH), elevated temperatures and a high wind velocity. A low ambient RH will produce strong gradients near the drying surface, thus increasing the drying rate. The effects of wind velocity and temperature are
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smaller than that of RH and their consideration is more important for determining the early age shrinkage strains (e.g. plastic shrinkage).
The presence of aggregates in concrete restricts the overall deformations, as regular aggregates do not generally show appreciable creep when subjected to stress, nor they are subjected to dry due to the low permeability in contrast to the cement paste. Neville had reported that influence of aggregate content on drying shrinkage. It can be clearly noticed that the higher the aggregate/cement ratio, the lower the shrinkage strains, due to the mentioned restraining effect, but most of all because the shrinking volume fraction of the composite material (concrete) decreases.
The w/c ratio and the contents of water and cement are three interrelated factors, since by fixing any pair of them the third one can be immediately determined. Starting with the effect of the concentration of these two components (water and cement), it can be shown that the greater the concentration, the greater the shrinkage deformations. In the case of water, increasing its content will lead to increasing the amount of evaporable water, and thus the potentiality to suffer shrinkage strains. On the other hand, the cement content determines the fraction of cement paste in concrete. Obviously, shrinkage will be greater the higher the cement paste content, which represents the shrinking phase of the material (since aggregates are generally inert).
The effect of mineral admixtures (e.g. slag, fly ash...) on the shrinkage strains and mechanisms is diverse. Their addition produces changes in the microstructure of the cement paste, as well as modifications of the pore structure.[5]
23 2.3.3 Factors Influencing Creep
Concrete that exhibits high shrinkage generally also shows a high creep, but how the two phenomena are connected is still not understood. The evidence suggests that they are closely related. When hydrated cement is completely dried, little or no creep occurs; for a given concrete, the lower the relative humidity and the higher the creep.
The strength of concrete has a considerable influence on creep, and within a wide range creep is inversely proportional to the strength of concrete at the time of application of load.
From this it follows that creep is closely related to the water-cement ratio. There is no doubt also that the modulus of elasticity of aggregate controls the amount of creeps that can be realized and concretes made with different aggregates exhibit creep of varying magnitudes.[21]
2.3.4 Effect of Creep
Creep affects strains, and deflections, also often stress distribution, but the effects of creep vary with the type of structure. Creep of plain concrete does not affect the strength, although under very high stresses creep hastens the approach of the limiting strain at which failure takes place; this applies only when the sustained load is above 85 or 90 percent of the rapidly applied static ultimate load.[22]
The influence of creep on the ultimate strength of a simply supported reinforced concrete beam subjected to a sustained load is not significant, but the deflection increases considerably and may in many cases be a critical consideration in design. According to Glanville and Thomas,[23] there are two distinct neutral surfaces in a beam subjected to
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sustained loading; one of the zero stresses, the other of zero strains. [24] This arises from the fact that an increase in the strain in concrete leads to an increased stress in the steel and a consequent lowering of the neutral axis when an increasing depth of concrete is brought into compression. As a result, the elastic strain distribution changes, but the creep strain is not canceled out, so that at the level of the new stress-neutral-axis a residual tensile strain will remain. At some level above this axis, there is a fiber of zero strains at any time although there is a stressed acting.[25]
With respect to reinforced concrete columns, creep results in a gradual transfer of load from the concrete to the reinforcement. Once the steel yields, any increases in load is taken by the concrete, so that the full strength of both the steel and the concrete is developed before failure takes place, a fact recognized by the design formula. However, in eccentrically loaded columns, creep increases the deflection and can lead to buckling.[26] In statically indeterminate structures, creep reduced internal stresses due to non-uniform shrinkage so that there is a reduction in cracking. In calculation creep effects in structures it is important to realize that the actual time-dependent deformation is not the free creep of concrete but a value modified by the quantity and position of reinforcement.
On the other hand, with regarding to mass concrete, creep in itself may be a cause of cracking when restrained concrete mass undergoes a cycle of temperature change due to the development of the heat of hydration and subsequent cooling. Creep relieves the compressive stress induced by the rapid rise in temperature so that the remaining compression disappears as soon as some cooling take place. On further cooling of concrete, tensile stresses develop and, since the rate of creep is reduced with age, cracking may occur
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even before the temperature has dropped to the initial value. For this reason, the rise in temperature in the interior of a large concrete mass must be controlled by the use of low heat cement, low cement content, pre-cooling of mix ingredients, limiting the height of concrete lifts, and cooling of concrete by circulating refrigerated water through a network of pipes embedded in the concrete mass.
The loss of prestress due to creep is well known and, accounts for the failure of all early attempts at prestressing. It was only the introduction of high tensile steel, whose elongation is several times the contraction of concrete due to creep and shrinkage that made prestressing a successful proposition.[27]
The effects of creep may thus be harmful but, on the whole, creep, unlike shrinkage, is beneficial in relieving stresses concentrations and has contributed very considerably to the success of concrete as a structural material.
2.3.5 Autogenous Volume Changes and Expansion Cements
Before volume changes resulting from drying or wetting of hardened concrete are discussed, autogenous volume changes should be mentioned because they occur where little or no change in total moisture content is possible and are of particular importance in the interior of mass concrete.
Two opposing effects can be produced. As reaction between water and the unhydrated cement proceeds, the actual volume of the solid increases. This causes stresses through the set structure and results in expansion. At later ages, the water available for the reaction will
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decrease, resulting in self-desiccation of the cement paste and a shrinkage ranging from 0.001 to more than 0.015 percent.[28]
2.3.6 Volume Changes due to Moisture Changes
Although the mechanism of volume change that occurs during moisture change is not fully understood, much has been learned to provide useful information for engineering purposes.
When concrete is dried, the first water to be removed causes no changes in volume. This is considered to be free water held in rather large “pores”. With continued drying, shrinkage becomes quite large and at equilibrium in 50 percent RH values in excess of 0.10 percent have been recorded for some concretes. Shrinkage values for neat cement paste have been observed in excess of 0.40 percent; the difference of this value from that of concrete is due to various restraints. A large portion of concrete is made up of relatively inert aggregate (from 3 to 7 times the weight of cement) and this, together with reinforcement, reduces shrinkage. In addition to internal restraints, some restraint arises from non-uniform shrinkage within the concrete member itself. [26] Moisture loss takes place on the surface so that a moisture gradient is established. The resultant differential shrinkage is associated with internal stresses, tensile near the surfaced and compressive is the core, and the result in warping or cracking.
2.3.7 Effect of Cement and Water Contents on Shrinkage
Water content is probably the largest single factor influencing the shrinkage of paste and concrete. Typical shrinkage values for concrete specimens with a 5 to 1 aggregate-cement ratio are 0.04, 0.06, 0.075 and 0.085 percent for water-cement ratio of 0.4, 0.5, 0.6 and 0.7,
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respectively. One of the reasons is that the density and composition of calcium silicate formed at different water-cement ratios may be slightly different. In general, higher cement content increases the shrinkage of concrete; the relative shrinkages of neat paste, mortar and concrete may be of the order of about 5, 2, and 1. For given materials, however, and uniform water content, the shrinkage of concrete varies little for a wide range of cement contents; a richer mix will have a lower water-cement ratio and these factors offset each other. [22]
2.3.8 Effect of Microcracking
The drying creep strain sCd(t,t’,to), also called the stress-induced shrinkage, includes the effects of microcracking (or cracking) and of pore humidity rate on the apparent creep viscosities, both of which are almost equally important.[29] In a specimen under sufficient compression the observed shrinkage is much closer to the true material shrinkage (free shrinkage of a small element) than in a load-free specimen. The reason is that the shrinkage observed on a load-free specimen is significantly offset by microcracking.
This is true also of the final values, because microcracking is largely irreversible (the cracking, once formed, cannot close completely). This phenomenon causes the average cross section shrinkage to depend on stress, which is taken into account by the term sCd(t,t’,to).
The microcracking can be enhanced by restraint which reduces the shrinkage strain; the term sCd(t,t’,to) is essential for realistic calculation of shrinkage stress in restrained concrete beams or slabs.[29]
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2.3.9 Effect of Fly Ash on Creep Properties of Concrete
Data on creep of fly ash concrete are limited. Lohtia et al. reported the results of studies on creep and creep recovery of plain and fly ash concretes under stress/strength of 20 and 35%. The concretes were made by replacing cement with equal weights of fly ash in the range of 0-25%. From this work, they drew the following conclusions: [20]
+ Replacement of 15% of cement by fly ash was found the optimum for strength, elasticity, shrinkage, and creep for the fly ash concretes studied.
+ Creep versus time curves for plain and fly ash concretes were similar, with creep linearly related to the logarithm of time.
+ Increase in creep with ≤15% fly ash content was negligible. However, slightly higher creep took place at fly ash contents of >15%.
+ The creep coefficients were similar for concrete with fly ash contents in the range of 0-25%.
+ Creep recovery was 22-43% of the corresponding 150days creep. For cement replacement >15%, the creep recovery was smaller. No definite trend of creep recovery as a function of stress/strength was observed.
In another study, Ghosh and Timusk examined bituminous fly ash of different carbon contents and fineness values in concrete at nominal strength levels of 20, 35, and 55 MPa (water/cement of 1.0, 0.4, and 0.2, respectively). Each concrete was proportioned for equivalent strength at 28 d. Fly ash concretes showed less creep in the majority of
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specimens than the reference concretes showed. This attributed to a relatively higher rate of strength gain after the time of loading for the fly ash concretes than for the reference concretes.
Yuan and Cook reported the data from studies of strength concrete containing a high-calcium fly ash. This paper shows that concrete containing 30-50% fly ash exhibited more creep than either the control concrete or a concrete with 20% fly ash. [20]
Gifford and Ward examined lean mass concrete and concluded that fly ash reduces creep, as a result of a number of factors including the following:
+ Fly ash increases the elastic modulus.
+ Fly ash contributes to the total aggregate and reduces the volume of paste available to creep.
Investigation by Bamforth on mass concrete showed that a reduction in creep of ~50% can be obtained when cement replaced by ~30% fly ash. However, the results of Nasser and Al-Manaseer’s work showed that there was an increase in creep of ~15% in concrete containing 20% fly ash and other admixtures. In another study, the same authors examined the creep of sealed and unsealed concrete made with ASTM type I cement containing 50%
Saskatchewan fly ash. They tested the concrete specimens at different stress/strength and measured their creep of concrete made with 50% lignite fly ash was a linear function of stress/strength. The creep of this concrete was lower than that of plain concrete by ~13%
for the unsealed and ~39% for the sealed specimens. In addition, they found that the ratio of
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creep values of sealed and unsealed concrete was about 2.44 for plain concrete and 3.67 for concrete with 50% fly ash.
In a CANMET investigation, the creep-strain data for control and fly ash concretes were compared. This research shows the creep strains after 91days of initial moist curing. All fly ash concretes are shown to produce consistently lower creep strains than the control concrete. The strain reduction, which in most cases varies between 20 and 45%, does not appear to be related to the type of ash. [20]
2.4 Prediction of Shrinkage and Creep
2.4.1 CEB-FIP Model Code 1990 (Europe)
CEB-FIP Model is the result of a comprehensive revision to the original model code of 1978, which was produced jointly by the Comité Euro-International du Béton (CEB) and the Fédération International de la Précontrainte (FIP). [30] Model Code 1990 has more detailed guidelines and explanations than national codes and can be used as a basis for them. It has already influenced the codification work that is being carried out both nationally and internationally and will continue to do so. With the publication of Eurocode 2: Part 1 as a draft pre-standard, this document is a useful reference during the consultative period before Eurocode 2 becomes a European standard. It may be of use to anyone involved in codification work on concrete.
(1) Shrinkage model:
Variables: the shape variables, cement type, relative humidity, temperature, compressive strength.
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The total shrinkage or swelling strains may be calculated from:
(2-2)
Where: is the notional shrinkage coefficient.
is the coefficient to describe the development of shrinkage with time is the age of concrete (days)
is the age of concrete (days) at the beginning of shrinkage or swelling.
The notional shrinkage coefficient may be obtained from:
(2-3)
⁄ (2-4)
{
{
( ) (2-5)
* + ⁄ (2-6)
Where h0 is the average thickness:
; (2-7)
;
Ac : Section area. u : Circumference.
32 (2) Creep model:
Variables: the shape variables, cement type, relative humidity, temperature, compressive strength.
Model:
(2-8)
(2-9)
⁄
⁄ ⁄ (2-10)
⁄ (2-11)
; t’ (days) (2-12)
The effect of type of cement on the creep coefficient of concrete may be taken into account by modifying the age at loading t’ according to equation:
[ ( ) ] (2-13)
{
for slowly hardening cements SL for normal or rapid hardening cements N and R for rapid hardening high strength cements RS
* + (2-14)
[ ( ) ] (2-15)
33 2.4.2 GL2000 (Canada)
Gardner and Lockman (2001) presented the GL2000 model which is a modified form of the earlier GZ model Gardner and Zhao (1993). [31] The model requires the information available at the time of structural analysis and design of the structure, namely the 28 days specified concrete strength, the concrete strength at loading, element size, and the relative humidity. For this model:
(1) Shrinkage model:
34 (2) Creep model:
Variables: relative humidity (h), shape ratio (V/S), cement types, dry and age, age of loading, elastic modulus, and so on.
Model:
Creep coefficient at time t:
2.4.3 B3 Model (United States)
In 1995, RILEM TC-107-GCS recommended the B3 model which is based on the statistical analysis of creep and shrinkage data in a computerized data bank involving about 15,000 data points and about 100 test series. The model is an improved version of the earlier models namely BP model (Bazant and Panula 1978a,b,c) and BP-KX model (Bazant and Kim 1991a,b). The prediction of material parameters of B3 model is restricted to the
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Portland cement concretes, having a 28-day mean cylinder compressive strength varying from 17 to 70 MPa, w/c ratio 0.30–0.85, a/c ratio 2.5–13.5 and cement content 160–720 kg/m3. For this model: [32~34]
(1) Shrinkage model:
Variables: specimen size, dry age, strength, water, conservation of the environment, cement type and relative humidity.
Model:
36 total aggregate amount of the limit drying shrinkage.
Model: J(t,t’) = [q1 + C0(t,t’) + Cd(t,t’,t0)] /MPa (2-27)
37
n
m
t t
t t t
Z ( , ' ) ( ' )
ln 1 ( ' )
(2-33)r(t’) = 1.7(t’)0.12 + 8 (2-34)
m = 0.5 n = 0.1
q3 = 0.29 q2 (w/c)4 (2-35)
q4 = 20.3 × 10-6(a/c)-0.7 (2-36)
Cd(t,t’,t0) = q5[exp{-8H(t)} − exp{-8H(t’)}]1/2 (2-37)
-1 6 0.6
5
0.757
cm28 sh10
q f
(2-38)
H(t) = 1 − (1−RH)S(t) (2-39)
2.4.4 FIB 2000
Previous prediction model introducing above are only talking about the nature of materials and ratio, such as mixing water, cement content, water cement ratio, or the total aggregate volume and specimen size, but that is not enough to predict the shrinkage and creep in the modern concretes, which contain other cementitious materials. However, FIB2000 prediction model [35] is the model to predict for the added part of the slag and silica fume in high early strength concrete. For this model:
(1) Shrinkage model:
Variables: specimen size, dry age, strength and relative humidity
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Model: (2-40)
Where: (2-41)
(2-42)
(2-43)
Where a, b, c, and d are given by Carlos Videla and Cristian Gaedicke, a large amount of experimental data by regression analysis, coefficients have to be confirmed. The values are in order of 0.0379, 0.5, 7.209 and 0.12.
2.4.5 AASHTO LRFD (2004)
(1) Shrinkage model: [36]
Variables: specimen size, loading age, curing period, intensity and relative humidity
Model: esh = 480×10-6ktdkskhskf (2-44)
39 t: loading age (days)
(2-49)
V/S: shape ratio
H: relative humidity (%) (2) Creep model:
Model: (2-50)
Where: (2-51)
(2-52)
ti: curing time
2.4.6 CCL Model 2001
According to the research of Lu Jing-Wen, in 2001, [37] this model base on the GL2000 and B3 model by collecting large quantities of concrete shrinkage data and rewritten for strength between 210kgf/cm2 ~ 840kgf/cm2 of concrete. This model is based on local materials of Taiwan. The results shall also be useful to those that use aggregates with similar characteristics as those in Taiwan.
(1) Shrinkage model:
Shrinkage strain equation:
1 3
sh t shuSa RH KS t
(2-53)
td la s hc f
Ψ(t,t ') 1.90K K K K K
Khc 1.56 0.008H
0.118
la i
K t
40 Where:
εshu limited shrinkage for standard aggregate:
1.02 2.13
25385 / / 420 /
shu w c a c m m
(2-54)
w/c is the water-cement ratio; a/c is the aggregate/cement ratio.
Sa : the effect of aggregate on Young’s Modulus (E)
2.05 1
Sae (2-55)
α is the ratio of actual elastic modulus of normal concrete according to ACI363 (Eexp./EACI363), when the actual elastic modulus and compressive strength of concrete is unknown, choose α=0.9 and Sa=1.23
1 RH
3is the humidity factor; RH is the relative humidity (%)K is the coefficient of affection of different cement, using Model B3 coefficient.
Cement type K
Type I 1.00
Type II 0.85
Type III 1.15
S(t) is the normalized shrinkage curve.
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V/S ratio for the volume and surface area, in units of mm
(2) Creep model:
J(t,t’)=[q1+C0(t,t’)+Cd(t,t’,t0)]/MPa (2-57)
Where: C0(t,t’) is basic creep variable;
Where: C0(t,t’) is basic creep variable;