In this article we will discuss about:- 1. Introduction to Strength of Hardened Concrete 2. Type of Porosity for Strengthening Hardened Concrete 3. Influence of Gel/Space Ratio 4. Accelerated Curing Test to Prevent Drying of Concrete 5. Maturity Concept 6. Effect of Different Water/Cement Ratios 7. Conditions for Application of Water Cement Law.
Introduction to Strength of Hardened Concrete:
The compressive strength of hardened concrete is one of the most important and useful properties of concrete. In most of the structural uses, the concrete is used mainly to resist the compressive stresses. In situations where the shear or tension strength is of importance, the compressive strength is usually used as a measure of these properties. Thus the concrete making properties of ingredients of the mix are usually measured in terms of the compressive strength. It is also used as a qualitative measure of other properties of hardened concrete.
No exact qualitative relationship between the compressive strength and other properties like tensile strength, flexural strength, modulus of elasticity, wear resistance, permeability and fire resistance exists. However some statistical or empirical relations have been established between them to be used in the field work. These relations give only approximate value of these properties. It should be noted that the indicated strength of concrete increases as the size of specimen decreases, whereas modulus of elasticity decreases.
Thus modulus of elasticity does not follow the compressive strength. In situations where concrete is subjected to freezing and thawing, the compressive strength does not indicate the other useful properties of the concrete. Concrete containing about 6% air entrainment is relatively weaker in compressive strength, but on the other hand it has been found to be more durable than dense and strong concrete.
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The strength of concrete is the measure of its resistance to rupture. Strength of concrete may be measured as strength in tension, strength in compression, in flexural or in shear. All these strengths indicate a particular method of testing.
When concrete fails under compressive load, the failure is essentially a mixture of crushing and shear failure. The mechanics of failure resisting concrete generates cohesion and internal friction both. The development of cohesion and internal friction in concrete simultaneously is a function of single parameter water/cement ratio.
For given cement and aggregate the strength developed by workable, properly placed mix of ingredients is affected by the following factors:
(a) Water/cement ratio
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(b) Cement/aggregate ratio
(c) Maximum size of aggregate
(d) Surface texture, shape, grading, strength etc. of aggregate particles.
Out of the above factors, water/cement ratio is the prime factor affecting the strength of concrete. The other factors influence the water/cement ratio, thus influencing the strength indirectly.
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Water/Cement Ratio:
Water/cement ratio can be expressed in terms of weight and volume too. In terms of weight, the quantity of water to be used per unit weight of cement (1 kg) is known as water/cement ratio. If 500 grams of water is used per kg of cement then the water/cement ratio will be 0.5. Normally water/cement ratio more than 1.0 is not used. In terms of volume water used in liters per bag of cement (50 kg) is taken as water/cement ratio by volume.
Suppose 25 liters of water is used per bag of cement, then again water/cement ratio will be 0.5. Actually water/cement ratio is an index of the strength of concrete. The strength of concrete mainly depends upon the strength of the cement paste, and the cement paste strength depends upon the dilution of cement pate. In other words the strength of cement paste increases with cement content and decreases with water and air content.
For a fully compacted concrete, its strength is taken to be inversely proportional water/cement ratio. A typical curve of strength versus water/cement ratio is shown in Fig.8.1.
Abram’s Water/Cement Law:
More importance to concrete properties was attached after the First World War and more stress was given for the development of cheap construction materials. Keeping this aim in view Duff Abram carried out extensive experiments and on the basis of his experimental results he proposed a relation between the compressive strength of concrete and water/cement ratio in 1919, which is known as water/cement ratio law, which is reproduced below as-
where,
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fc = concrete cylinder (15 x 30 cm) strength at 28 days after proper curing
K1 & K2 = constants
x = water/cement ratio.
He suggested empirically the values for K1 as 984 and for K2 as 7 in M.K.S. units
ABRAM’S water/cement ratio law states that the strength of concrete is only dependent on water/cement ratio provided the mix is workable.
The numerical values for K1 and K2 may vary with the type of cement and aggregate, method of curing, age of concrete at which strength is desired, and mode of testing etc. Thus these values are variable. Due to the advancement in cement technology, the better quality cement is available now. Hence the compressive strength given by equation 8.2 can be assumed as 7 days strength and 28 days strength can be assumed as-
This relation was found true for a fully compacted concrete. Later it has been found that water/cement ratio law holds equally good for tensile strength, resistance of concrete to wear, bond between concrete and steel, resistance to weather influence and water tightness etc. i.e., the decrease in water/cement ratio improves the above properties. This is particularly more important in respect of water tightness. To obtain plastic mixtures, more water is required than can be permanently combined with cement even on longer curing.
Some water remains uncombined and leaves voids after it evaporates. Thus the quantity of water and the extent of curing both affect the water tightness of concrete. After ABRAM many researchers put forth their theories, but none of them could stand the test of time and disappeared slowly. However ABRAM’S water/cement ratio law stood the test of time and is held valid even today. Though some modifications have been suggested but the truth of statement remains unchanged.
Although Abram established his law independently, but it is a special case of a general rule formulated by Ferret in 1896.
He expressed the compressive strength of concrete as-
where fc is strength of concrete, c, w and a are absolute volumes of cement, water, and air respectively and K is a constant.
The water/cement ratio determines the porosity of the hardened cement paste at any stage of hydration. Thus the water/cement ratio and the degree of compaction both affect the volume of voids in concrete and that is why volume of air in concrete has been included in Ferret’s equation.
The relation between strength of concrete and total volume of voids is not a unique property of concrete, but in other brittle material also in which water leaves pores behind in the same way. For example the strength of plaster also is a direct function of its voids. If the strength of different materials is expressed as a fraction of the strength at zero porosity, many materials such as steel, iron, alumina etc., confirm the same relation between the relative strength and porosity Fig.8.2.
Type of Porosity for Strengthening Hardened Concrete:
Porosity may be divided into the following groups:
1. Gel Porosity:
It is the ratio of the volume of gel pores to the total volume of hydrated cement paste.
2. Capillary Porosity:
It is the ratio of the volume of the capillary pores to the total volume of hydrated cement paste. Capillary pores are much larger than gel pores.
3. Total Porosity of Cement Paste:
It is the ratio of the sum of volumes of gel pores and capillary pores to the total volume of cement paste.
4. Concrete Porosity:
It is independent of whether the capillary pores are full of water or empty and has some entrapped air in it.
The influence of volume of pores on strength can be expressed as fc = fco (1 – p)n where fc is strength of concrete at porosity p, while fco denotes concrete strength at zero porosity and is a coefficient which need not be a constant. From test-results it has been observed that there is a direct relation between strength and porosity of concrete, but the exact form of this relation has not yet been established. It is straight line relation between the strength and log of porosity.
Fig.8.1 shows that the range of validity of the water/cement ration law is limited. At the lower water/cement ratio, when full compaction is no longer possible, the curve ceases to be followed. The actual position of the point of departure depends on the means of compaction available. It is also evident that mixes with very low water/cement ratios and with extremely high cement content exhibit retrogression of strength, particularly when large size aggregate is used. Thus in this type of mix, at later ages a lower water/cement ratio would not produce higher strength.
This may be due to the stresses induced by shrinkage, whose restraint by aggregate particles causes loss of bond between the aggregate and cement paste. Theoretically the lesser the water/cement ratio, higher should be the strength, but as stated above it is not true, below a certain water/cement ratio, full compaction of concrete is not possible. It has been shown by broken lines in Fig.8.1 In practice water/cement ratio is the largest single factor which influence the strength of fully compacted concrete.
From Fig.8.1 it can be seen that lower water/cement ratio can be used when the concrete is vibrated to get higher strength, where comparatively higher water/cement ratio is required than hand competed concrete, thus when the water/cement ratio is lower than the practical limit, the strength of concrete falls rapidly due to introduction of air voids.
Fig. 8.4 shows a relation between compressive strength and cement/water ratio which gives a straight-line in the range of cement/water ratio between about 1.2 and 2.5.
Whose equation may be as-
S = A + [B (C/W)]
where,
S = compressive strength in kg/cm2
A = constant value = – 24
B = constant value = 267
C/W = cement/water ratio by weight
However this relation is true for a particular given cement only and in any practical case the actual relation between the strength and cement/water ratio should be determined.
However according to Gilkey, the strength developed by a workable and properly placed concrete is influenced by the following factors:
1. Ratio of cement to mixing water
2. Ratio of cement to aggregate
3. Grading, surface texture, shape, strength and stiffness of aggregate particles
4. Maximum size of aggregate.
However factors (2) to (4) are of lesser importance than factor (1) for aggregates upto 38 mm in size. The plot of strength of concrete and water/cement ratio is approximately a hyperbola. This relation is true for concrete made with any given type of aggregate and at any age, while the relation between strength and cement/water ratio is approximately linear (straight line) in the range of cement/water ratios between about 1.2 and 2.5, which is more convenient to use than water/cement ratio curve.
Influence of Gel/Space Ratio on Strength of Hardened Concrete:
According to T.C. Powers the influence of water/cement ratio on strength does not truly constitute a law as the water/cement rule does not include many necessary conditions for its validity. In particular, strength at any water/cement ratio depends on the degree of hydration of cement, its chemical and physical properties, temperature at which hydration takes place, air content of concrete, change in effective water/cement ratio and formation of capillaries or fissures formed due to bleeding etc. Thus it will be more correct to correlate strength to the concentration of the solid products of hydration of cement in the space available for these products.
Powers and Brownyard have established the relation between the strength development and the gel/space ratio. This ratio is defined as the ratio of the volume of hydrated cement paste to the sum of the volumes of hydrated cement and the capillary pores.
Hydrated cement occupies about 2.15 times its original volume i.e. more than twice its original volume. In the following calculations the increase of volume is assumed as 2.06. Though all the hydrated material is not gel, yet as an approximation it is considered as such.
Power’s experiments showed that a relationship of the type fc = Axb could be established, where fc is concrete strength and x is gel/space ratio where A and b are constants which depend on the type of cement. The constant A represents the intrinsic or maximum strength of gel in Newton/mm2 when x = 1, for the type of cement and type of specimen used. From his study he suggested the value of A as 240. b = 3. Thus strength fc = 240 x3. The strength calculated from the power’s equation holds good for an Ideal case for the type of cement and specimen used by him. The relationship between strength and gel/space ratio is shown in Fig. 8.5.
It may be pointed out here that the relationship between the strength and water/cement ratio holds good primarily for 28 days strength for fully compacted concrete, whereas the relationship between the strength of concrete and gel/space ratio is independent of age.
Gel/space ratio can be calculated at any age for any degree or fraction of hydration of cement as follows:
Case I:
Calculations for gel/space ratio for complete hydration
Let,
C = weight of cement in grams
Vc = specific volume of cement = 0.319 ml/gram
w0 = volume of water mixed in ml (c.c.)
Assuming that on hydration 1 ml cement will produce 2.06 ml of gel.
Then volume of gel = C x 0.319 x 2.06
= 0.657 C
Total space available = vol. of gel + vol. of water
= 0.319 C + w0
... Gel/space ratio x = volume of gel/vol. of space = [0.657 C/(0.319 C + w0)] …(1)
Case II:
Calculation of gel/space ratio for partial hydration
Let,
α = fraction of hydrated cement
Volume of gel = α x C x 0.319 x 2.06 = 0.657 α C
Total space available = C . Vc . α + w0 = C x 0.319 . α + w0
... Gel/space ratio x = [(0.319 x 2.06 x C x α)/(0.319 C . α + w0)]
Example 1:
Calculate the gel/space ratio and theoretical strength of a concrete sample made with 600 gram of cement with 0.5 water/cement ratio on full hydration and at 70% hydration.
Solution:
(i) for full hydration
(a) Weight of cement = 600 gram
For 0.5 water/cement ratio, weight of water = 300 gram
Theoretical strength of concrete = 240 (0.8)3 = 123 MPa
(ii) Gel space ratio for 70% hydration
Earlier IS Code 456-1978 considered age factor and allowed the design stress in lower columns in multi-story buildings. Earlier only type of cement governed by IS 269-1976 was used in which after 28 days appreciable increase in strength was considered. After gradation of ordinary Portland cement, the present day cements particularly 53 grade cements are grounds very fine. Thus the increase in strength after 28 days is nominal. In well cured concrete, the development of strength will take place within 28 days. Thus the allowance of age factor generally is not necessary.
Thus IS 456-2000 has revised this clause The revised clause states that normally the gain in strength beyond 28 day’s depends upon grade, type of cement, curing and environmental conditions. Thus the design should be based on 28 days characteristic strength of concrete, unless there is an evidence to justify a higher strength for a particular structure due to age. However British Code has suggested the age factor for permissible compressive stress in concrete as shown in Table 8.1.
The grade of concrete as per IS 456-2000 is shown in Table 8.2 below:
Many a times the knowledge of strength of concrete becomes necessary to forecast the strength of the structure and it may prove futile to wait for 28 days. In this direction many researchers have attempted to forecast or correlated 28 days strength from 1, 3 or 7 days strength.
The relationship between the strength at lower age and 28 days strength depends upon the following factors:
1. Compound composition of cement.
2. Fineness of cement.
3. Temperature of curing etc.
Further, mixes with low water/cement ratio gain strength more rapidly than that of higher water/cement ratio concrete. This may happen presumably due to the fact that in low water/cement ratio concrete, the voids in between cement particles are less or they are held closer than that of higher water/cement ratio concrete, forming thicker gel, which results in more strength.
Capillary pores are much larger than gel pores. In partially hydrated cement, the paste contains an interconnected system of capillary pores, resulting in increased permeability, lower strength and more prone to freezing and thawing and chemical attack. These problems are avoided if the hydration of cement is high as the capillary pore system would be segmented by higher hydration. The minimum period of curing required for the segmentation of capillary pores is shown in Table 2.6.
Researchers in Germany have suggested following relations between 7 and 28 days compressive strength of concrete.
1. σ28 = 1.4 σ7 + 150 and σ28 = 1.7 σ7 + 850
where σ is expressed in lbs/cm2 (1 lbs/cm2 = 0.0727 kg/cm2)
2. This relation is of the type f28 = K2 (f1)k1 where f28 and f7 are the concrete strength at 28 and 7 days respectively and K1 and K2 are coefficients which are different for different cements and curing conditions. The value of K1 varies from 0.3 to 0.8 and that of K2 from 3 to 6.
Prof. King suggested a quick method of estimating 28 days strength after its cast. This method gives results which have a good correlation with field results. This method is known as Accelerated curing test method.
Accelerated Curing Test to Prevent Drying of Concrete:
In this test the standard cubes of 15 cm x 15 cm x 15cm are cast and covered at top with plates. To prevent drying of concrete, the joints are sealed with special grease. Within 30 minutes of adding water, the effectively sealed cubes are placed in an air tight oven. The oven now is switched on. The temperature of the oven is brought to 93°C in about 60 minutes. The temperature of the oven is maintained at 93°C for 5 hours. After 5 hours curing at 93°C temperature, the cubes are removed from oven, mould removed, cooled to room temperature and tested. The test should be completed within 30 minutes.
The strength of concrete is determined by this method within 7 hours of casting. This accelerated strength shows good relationship with normally cured concrete at 7 days and 28 days. This relationship is shown in Fig. 8.6.
Factors Affecting the Results:
One of the main factors that affect the rate of gain of strength is the fineness of cement. It has been observed that particles of cements over 40 micron in size contribute to the compressive strength of concrete only over long periods, while particles lower than 25 to 30 micron contribute to 28 days strength. The particles smaller than 20 to 25 micron contribute to 7 days strength. The particles smaller than 5 to 7 micron contribute to 1 to 2 days strength. The relative gain of strength with time of concrete prepared with different water/cement ratio using ordinary port-land cement is shown in Fig. 8.7.
Maturity Concept for Strength of Hardened Concrete:
Temperature during the early period of hydration also influences the rate of gain of strength of concrete. As the strength development of concrete depends on time and temperature both, it can be said that the strength of concrete is a function of summation of product of time and temperature. This summation is called the maturity of concrete.
Thus,
Maturity of concrete = ∑ (time x temperature)
The temperature is reckoned from an origin lying between – 12 and – 10°C. Experimentally it has been observed that hydration of concrete continues to take place upto about – 11°C, Thus – 11°C is taken as the datum time for computing maturity.
Maturity is measured in degree centigrade 70 hours (°C hours) or degree centigrade day (°C day). If the graph between the strength of concrete and logarithm of maturity is drawn, it will be a straight line as shown in Fig.8.8.
A sample of concrete cured at 18°C for 28 50 days is assumed as fully matured concrete. Its maturity would be
= 28 x 24 [18 – (–11)]
= 28 x 24 x 29 = 19480°C h
However in standard calculations of maturity of fully cured concrete is taken as 19800°C h. This discrepancy is due to the fact that the exact value of datum is not known.
If the period is broken into smaller intervals and the corresponding temperature is recorded for each small interval of time, the summation of the product of time and temperature will give ail accurate result.
Maturity concept is useful for estimating the strength of concrete at any other maturity as a percentage of strength of concrete of known maturity. For the calculation of concrete at any maturity as a percentage of fully matured concrete plowmen has suggested the following relation.
Strength at any maturity as a % of strength at a maturity of-
19800° Ch = A + B log10 (maturity/1000)
The values of coefficient A & B depend on the strength of concrete.
These values are shown in Table 8.3 below:
If the values of A and B are plotted against the cube strength at the maturity of 19800°C h, a straight line relationship will be obtained indicating that they are directly proportional to the strength. Plowman has divided the length into four zones as shown table 8.3 and assigned the values of A and B for each Zone. The maturity equation holds goods for initial temperature of concrete less than 38°C.
Effect of Different Water/Cement Ratios on Strength:
From experimental data it has been found that for no un-hydrated cement to be left and no capillary pores to be left there should be sufficient water in the mix. The least quantity of this water corresponds to 0.38 water/cement ratio by weight. Thus for water/cement ratio less than 0.38 complete hydration is not possible. From workability consideration this water/cement ration is found as 0.4.
At a water/cement ratio of 0.4, mix has sufficient water for hydration as well as for providing ease in compaction. At this water/cement the ‘gel’ formed is of good physical structure being dense. At higher water/cement ratio the ‘gel’ is formed of poor physical structure probably more porous resulting in lower strength of concrete at different age is shown in Fig.8.15.
Conditions for Application of Water Cement Law:
Water-cement law is applicable under the following conditions:
1. Internal moisture condition of hydration of cement should continue till the concrete gains full strength.
2. Concrete should be cured under standard temperature.
3. Size of concrete specimen should be same.
4. Test should be done at the same age.