Concrete Proportioning

[Type text] Proportioning of concrete mixes 2010 - 2011 – I

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CE 251 Construction Materials Instructor: Sudhir Misra

Handout

Proportioning of concrete mixes

1.0 INTRODUCTION Rapidly growing use of mineral and chemical admixtures, better understanding of the chemistry of cement hydration and structural behavior of concrete has made the task of proportioning concrete mixes a very important step in the overall process of design and construction of concrete structures. It should be pointed out that improvement in the understanding of the different material and structural aspects of concrete has led to development and utilization of special concretes, which will be taken up for discussion at a later stage in this course. An effort has been made in this note to place in perspective the basic methodology of proportioning normal concrete mixes. Attention has been focused on concrete used in reinforced concrete, where fresh concrete when placed in the formwork is vibrated and works its way around the reinforcing bars and fills the formwork. Figure 1 is a representation of the cross-section of reinforced concrete also showing the schematic representation of the ‘transition zone’ between the paste and coarse aggregates, and, the CSH gel, with pores and hydration products. Figure 2 shows a further simplified view of the heterogeneous concrete where all the constituents have been ‘lumped’ at one place. Now, proportioning of concrete basically entails finding an appropriate combination of relative amounts of sand, water, coarse aggregate and cement, so that the resulting concrete,

has the required properties in the fresh state,

has the required properties in the hardened state

meets durability requirements depending on the structure and the environment, and

meets any other requirements such as those on setting time, etc. In other words, proportioning should be carried out in a manner that the properties of concrete are satisfied in the fresh and hardened state and also any other conditions stipulated, in terms of setting time, durability, etc. are also satisfied. 2.0 PROPORTIONING OF NORMAL CONCRETE In very simple terms, concrete can be looked upon as a conglomerate rock – consisting of large ‘aggregate’ particles embedded in a matrix of ‘mortar’. Now, mortar can itself be looked upon as finer aggregate particles (sand) embedded in the matrix of ‘paste’ and paste is the mixture of water and cement. Hence in the context of cement concrete, it is common to define ‘paste’, ‘mortar’ and ‘concrete’ as given in Table 1. Any difficulty in the definitions given in Table 1, arising from the presence of mineral admixtures within the concrete matrix should, in principle, be resolved on the basis of the particle size distribution on the mineral admixture. For example, finely ground flyash or granulated blast furnace slag, which are also expected to participate in the hydration reactions, may be counted as part of the paste phase. However, depending upon the sizes involved, coarse fraction of slag may be counted as fine or coarse aggregates.

2.1 Required properties of concrete in the fresh and hardened state

Concrete is required to meet specific properties in the fresh state. Given the variation in the sizes of the particles (from say cement ranging in microns to coarse aggregate which could be as large as say 40 mm), and the specific gravity of the particles, concrete behaves as a non-Newtonian fluid. The following are some of the properties that the concrete is required to meet in the fresh state:

a) Workability b) Air content c) Others (such as segregation resistance, setting time, flowability, etc.)


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It should also be noted that concrete of different workability is required depending upon factors such as the structural member to be cast, whether the concrete is placed in situ or is precast, the extent of congestion of reinforcement in the member (as per design requirements). Table 2 of this document is reproduced from IS 456-2000, and gives the workability requirements for different kinds of structural members. As far as air content in concrete is concerned, the subject of entrapped versus entrained air and the benefits of use air-entrained concrete, has been dealt with in greater detail elsewhere. Here it should be reiterated that using air-entrained has been made is mandatory in cases when concrete is exposed to cycles of freezing and thawing. Table 3 is also reproduced from IS 456-2000 giving details of the required air entrainment for different concretes. Further, though compressive strength is usually the basic quality that is sought in hardened concrete, depending on the situation and concrete, other properties such as toughness, flexural strength, creep and shrinkage, etc could also be sought. In addition to specific requirements for fresh and hardened concrete, codes and specifications often lay down requirements on parameters such as water-cement ratio, cement content, etc. These are specified with the basic intention and understanding that by placing limits on the (maximum) water-cement ratio and (minimum) cement content, durability of concrete structures, especially in harsh environment. In certain cases codes may place a limit on the maximum amount of cement in the concrete matrix, or require the use (or forbid the use) of a certain type of cement, and so on. At times, specific limits are also laid down on the temperature of fresh concrete, allowed temperature rise on account of hydration of cement, or the setting time of concrete. In any case, it needs to be ensured that the final concrete is such that it satisfies ALL requirements.

2.2 Procedure for proportioning concrete mixes

As mentioned above the exercise of proportioning a concrete mix boils down to determination of relative amounts of constituent materials such that the resulting concrete meets ALL requirements – be it in the fresh or hardened state, or externally imposed restrictions. A brief description of the different steps in the proess is given below. As mentioned above, the basic issue is to find for one cubic meter, the relative volumes of air, water, cement and fine and coarse aggregates, Va, Vw, Vc, Vfa, Vca, such that (1) the concrete meets the required conditions, and, (2) the sum of Va, Vw, Vc, Vfa, and Vca is one cubic meter (1000 liters). It should be noted that it is desirable that the amounts of constituents is given in terms of kgs per cubic meter, though the process itself involves calculations of relative volumes, for the sake of convenience and to facilitate understanding. Step 1: Assume an air content: Depending on whether the concrete is AE or non-AE, it may be taken as the specified value or between 1 and 2%, depending on the shape and size of aggregates, etc. Table 4 gives the values that may be assumed in the case of non air-entrained concrete as per IS 10262. Step 2: Determination of water content: Unit water content of concrete is the most important factor that affects the workability of concrete and the basic unit water-slump relationship is schematically shown in Figure 3. The actual variation is obviously very complex and depends upon several factors including the maximum size, particle size distribution and other characteristics of the aggregates used, fineness of cement, environmental conditions, etc. Thus, the relationship should either be known from past experience, or established through basic experiments carried out at different unit water content. A tabular representation of the unit water demand depending on the maximum size of the aggregate is given in Table 5. For simplicity, the specific gravity of water may be taken as unity and thus the volume of water (Vw) in Figure 2 is known. Step 3: Determination of cement content: Having determined the water content above, the cement content can be determined easily if the water-cement ratio is known. Typically, this ratio is estimated from the required compressive strength of the concrete. It is important to note designers typically work with the characteristic compressive strength, which is the strength with a 95% probability of exceedance, as discussed in greater detail elsewhere. However, the proportioning of the concrete mix should be based on the target compressive strength appropriately determined from the characteristic strength, assuming a suitable standard deviation depending upon the extent of quality control expected. IS 456-2000 recommends using a formulation of (fck + 1.65 σ) to estimate the required target strength, where fck and σ are the characteristic strength and the likely standard deviation in strength values. The factor 1.65 comes from the assumption of


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compressive strength being normally distributed about a mean with a standard deviation of σ and allowing a 95% exceedance of characteristic strength. In the absence of other information from the site, the values given in Table 6 may be used as a guideline to estimate σ. Some other specifications also follow an alternative approach to estimating the target compressive strength using a multiplying overdesign factor, which is related to the expected coefficient of variation in strength. Figure 4 shows an example of the variation of this factor, and as an illustrative example, the over design factor in case the coefficient of variation is expected to be 15%, is about 1.33. Thus, the target strength for an M20 concrete using this approach would be 1.33 x 20 = 26.6 MPa. Further, in principle, it may be assumed that the compressive strength of concrete is related principally to the water-cement ratio, and Figure 5 shows a representation of this relationship, though several other factors such as the age of concrete, curing and testing conditions, nature of the constituent materials, etc. also play a significant role. Now, Figure 5(a) gives a schematic representation of the variation of concrete strength with the water-cement ratio. Further, it can be seen that the suggested variation shown in Figure 5b clearly shows the dependence of strength on factors such as the properties of cement, etc. It should also be noted that the ordinate in Figures 5a and 5b is the actual strength of the concrete. In case the water-cement ratio vs. strength relationship is not known, basic experiments should be carried out by varying the water-cement ratio to establish the relationship. Thus, after determining the target compressive strength as outlined above, and using the strength versus water-cement ratio variation, the required water-cement ratio can be determined, and since water content has already been determined in Step 2 above, the cement content can be determined. However, since the water-cement ratio is generally expressed by mass, the specific gravity of cement needs to be used to estimate the volume of cement (Vc) as shown in Figure 2. Steps 4 and 5: Determination of fine and coarse aggregate volume: Having determined the volumes of air, water and cement in the concrete, and using the model suggested in Figure 2, the total volume of fine and coarse aggregate (Vfa+Vca) in liters can be estimated from [1000 – (Va + Vw + Vc)], using Va, Vw , Vc also in liters (per 1000 liters or a cubic meter). The volumes fractions of fine aggregate (sand) and coarse aggregate are usually given in terms of ‘s/a’, which is the volume faction of sand in the total aggregate content. This parameter (s/a) varies with the maximum size of the coarse aggregate used, and representative values for the different sizes is given in Table 7. It should be noted that as the maximum size of the aggregate increases, the total surface area of the coarse aggregate is reduced, and hence a lesser amount of mortar is required to coat these aggregates, and hence a recommended decrease in the s/a. Finally, since it is desirable that the proportions of the different materials be given in terms of kgs/m3, the volumes of the fine and coarse aggregates should be converted to mass, using their respective specific gravities.

2.3 Illustrative example of proportioning concrete

On the basis of the steps given above, an illustrative example is worked out in Table 8 In the example we work with trying to proportion a concrete for the following conditions:

Slump = 8 cm

Air content = 5%

Characteristic compressive strength = 20 MPa Further the following information is provided:

a) Specific gravity of cement, sand and coarse aggregate may be taken to be 3.10, 2.61 and 2.68 respectively.

b) Water demand on the basis of the slump-unit water content relationship for the required slump is 160kg/m3

c) The standard deviation in the strength values may be taken as 4 MPa d) the actual compressive strength of concrete at water-cement ratios of 48% and 52% may be taken to

be 30MPa and 24 MPa, respectively. e) in cases when the water-cement ratio is between 48% and 52%, s/a may be taken to be a constant at

36%


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Notes:

1. The assumptions and relationships given are only illustrative in nature and a lot of effort is required in real life, before they can be established.

2. the table also gives explanations for the different steps, and can be followed in light of the discussion above. 3. It should be noted that the concrete proportioned above is air-entrained concrete, and the air content is taken as

5%. Now, this obviously involves the use of air-entraining admixtures, and in order to complete the exercise, the amount of the agent also needs to be specified. This aspect of the proportioning has not been taken up here, and is dealt with in another handout.

The resulting mix is thus proportioned to have 160kgs of water, 320kgs of cement, 645kgs of sand and 1178 kgs of coarse aggregate. Obviously given the nature of the excerise, there is no reason to really believe that this concrete will have the required slump, air content and strength. This issue of ‘adjustments’ in the mix design is addressed in the following section.

2.4 Adjustments in proportions of concrete mixes

As mentioned above, since the initial values used for proportioning, such as those used in the above example, are based primarily of experience, it cannot be assured that the (fresh) concrete actually meets the specifications in terms of slump and/or air. Also, it is very likely that the actual strength obtained may necessitate a change in the water-cement ratio to be used. Thus, after the initial mixing has been carried out, it is very likely that changes in the basic parameters used, i.e. W and s/a, are required. As mentioned above, in certain cases a change in the w/c may also be called for. These changes will, obviously change the overall balance of the constituent components and guidelines are required on how a change in one of the parameters should be handled as far as other parameters are concerned. A summary of a typical example of such a guideline is given in Table 9. Implementation of the guidelines given in this table is shown in the following example, which may be taken as an extension of the case cited above. Example Required air content = 5% Required slump = 8cm Actual air content = 4% Actual slump = 9 cm Thus, what we require a change in air content (+1%), and a change in slump (-1cm). Now, from Table 9, it can be seen that:

a) For decreasing the slump by 1 cm, no adjustment is required in the s/a, though the water content needs to be reduced by 1.2%, and,

b) For a 1% increase in the air content, the s/a may be reduced by (0.5 to 1.0%), and the water content needs to be reduced by 3%.

The net result can thus be taken to be a reduction of 1% in the s/a, and a reduction of 1.8% in (+ 1.2 – 3.0 = -1.8) the water content. Thus, the basic parameters for the modified mix design can be written as:

W = 160 – 2.9 = 157.1 liters (say 157liters) S/a = 36 – 1 = 35%

For the sake of simplicity no change in the strength (or water-cement ratio) has been accounted for in this example, though it can be easily accounted for if appropriate data is available. Further, again for simplicity, the effects have been taken to be linear and algebraic, which may not actually be the case. However, the approximation helps us arrive at an acceptable design of the mix, and the fine-tuning is usually carried out using conditions closer to those at site. (Please note that the proportioning exercise is often first carried out in the laboratory to narrow down the choices, and get an idea of the actual materials that will be used at site. Having done that, the exercise is repeated in the field to verify the results and finally decide the mix. This two stage process often needs to be followed as there are unavoidable differences in the mixing procedures in the laboratory and the actual batching plant – for example, in the laboratory, the mixing is carried out using smaller mixers than the ones used in the field and that changes the properties of the mixed concrete as the energy used during mixing is quite different. Similarly, the temperature and humidity conditions in the laboratory tests could be different, and the real properties should be determined under field conditions.)


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Further, following the steps already outlined above, the modified concrete proportions it can found out as outlined below:

From step 1, A = 50 liters From step 2, W = 157 liters From step 3, C = 314kgs, which is equivalent to (314/3.10) = 100 liters Thus, volume of aggregate, i.e. fine and coarse, is equal to (1000 – 50 – 157 – 100) or 693 liters From step 4, the amount of fine aggregate = 0.35 * 693 = 242.55 liters (or 633.06kgs) From step 5, the mount of coarse aggregate = 0.65 * 693 = 450.45 liters (or 1207.21kgs)

Also, though not addresses in detail, changes also need to be made in the dosage of the air-entraining admixture, as an increase of 1% air is sought. This should be carried out according to the specifications and literature available for the admixture being used. 3.0 SOME OTHER ISSUES OF CONCERN

3.1 Batching by volume versus batching by weight

The discussion above focused on the relative proportioning of the different constituents in terms of kgs/m3. Difficulty is often experienced at sites where smaller mixers with a capacity of say 100 liters are used, and facilities for appropriate weighing machines are not readily available. This is especially true in the Indian construction scenario where labour intensive methods of construction are used, and the labour is often unskilled. Now, since the specific gravity of water may be usually taken as one, and cement is available in bags having 50kgs (sometimes 40 kgs) cement, these two materials are basically batched by weight. Difficulty is encountered with proportioning fine and coarse aggregates, and Figure 6 shows a typical box often used to batch these materials. Indeed depending upon the proportions arrived at, the actual size of the box (in terms of the length, breadth and height) is determined, and the number of boxes of a particular material are worked out. Now, in principle, there is no difficulty in proportioning the aggregates by volume – as the relative amounts are arrived at basically on a volumetric basis. However, volumetric batching is not a desirable practice for the following reasons, and the IS 456 permits very restricted use of volume batching only under special supervision.

1. It is very difficult to ensure that the boxes are filled in a proper manner and excess material is removed every time before the material is fed into the hopper of the concrete mixer.

2. There is virtually no way that any control can be exercised on the extent of compaction of the material being put into the box. Thus the mass of aggregates being actually used is not clearly defined.

3. It is difficult to account for the presence of water in the aggregates, especially in the case of fine aggregates because of the phenomenon of ‘bulking’, which refers to the change in ‘apparent’ volume of sand upon absorption of water (or drying).

4. The chances of mis-proportioning a batch increase as multiple boxes of sand and coarse aggregate need to be used (say for each bag of cement), and a mistake in counting the number of boxes loaded can easily be made.

3.2 Nominal mix versus design mix

This discussion is also relevant almost only in the Indian context, where specifications such as IS 456 provide for use of a ‘nominal’ mix to achieve a certain grade of concrete. The idea of providing for such a mix is to short cut the process of proportioning concrete using the properties of the specific material being used at a site (as outlined in this handout) and providing a ‘ready made’ mix proportion. Table 10 gives the details of the ‘nominal mixes’ provided for in IS 456. As can be seen from the table 10, nominal mix proportions are available for only upto M20 grade of concrete. Now, coupled with the provision that only concrete conforming to M20 and above can be used in


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reinforced concrete work, it is clear that the only nominal mix that can be used in reinforced concrete construction is for M20 concrete. Like in the case of volumetric batching, use of nominal mix in concrete construction is also fraught with several pitfalls, and should be resorted to only when unavoidable. For example, there is no clear guideline on the water-cement ratio, and as can be seen from Table 10, only a ‘maximum’ water content of 30kg is given per bag (50kg) of cement, which gives a water-cement ratio for M20 concrete to be 0.6. Further, since the properties of the materials being used are not often properly tested, and the problem could be compounded by the fact that even the actual strength of concrete may not be determined (since it may be assumed that a particular nominal mix yields a certain grade of concrete)

Table 1 Defining paste, mortar and concrete in normal concrete

Term Constituents Comments

Paste Cement + water Extremely fine particles such as flyash, ground granulated blast furnace slag, silica fume etc. could be considered part of the paste phase in cases when these admixtures are used.

Mortar Paste + fine aggregate In the context of concrete engineering, particles smaller than 4.75 mm are generally considered fine aggregates, whereas those larger than that size are referred to as coarse aggregate.

Concrete Mortar + coarse aggregate

Table 2: Workability requirements for concrete to be used in different structural members

Table 3 Air entrainment required depending upon nominal maximum size of aggregate (mm) [IS 456-2000]

Nominal maximum size of aggregate (mm) 20 40

Entrained air (%) 5±1 4±1


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Table 4 Assumed air entrapment in non AE concrete depending upon maximum size of aggregate

Nominal maximum size of aggregate (mm) 10 20 40

Entrapped air (%) 3.0 2.0 1.0

Table 5 Suggested unit water content depending on the maximum size of the aggregate.

Nominal maximum size of aggregate (mm)

10 20 40

Unit water content (kg/m3) # 208 186 165

# please note that the given water content is for a given level of workability, and if a different level is required, suitable modifications in the mix need to be made. Also the values are for saturated surface dry aggregates, and appropriate corrections need to be made in other situations. Sometimes, a modification in the above table can also be introduced in terms of the grade of concrete required – for example, it may be stated that for grades higher than M35, the water content may be taken as 180 for 20mm aggregates.

Table 6 Assumed values of standard deviation (N/mm2) depending upon the grade of concrete

Grades of concrete M 10, M 15 M 20, M 25 M 30, M 35, M 40, M 45, M 50

Assumed std. dev# 3.5 4.0 5.0

# Please note that the actual value also depends on the extent of quality control at site Table 7 Suggested s/a ratio depending on the maximum size of the aggregate.

Nominal maximum size of aggregate (mm)

10 20 40

s/a (%) by absolute volume # 40 35 30

# please note that the given s/a is for a given level of workability, and if a different level is required, suitable modifications in the mix need to be made. The s/a ratio is also sensitive to the particle size distribution of both the coarse and the fine aggregate, and their shapes, and the figures given here are only a very rough guide.

Table _8_ Basic procedure for proportioning of normal concrete.

Step Description Comments

Setting basic parameters

1 Determine the target compressive to be (20 + 1.65 * 4) i.e., 26.8MPa, say 27 MPa

Standard deviation given to be 4 MPa in (c) above

2 Unit water content may be taken to be 160kg/m3 Information in (b) above

3 s/a may be taken as 36% Information in (e) above

Proportioning for 1000liters (1 m3)

4 A = 50 liters Step 1: given that the air content in fresh concrete is 5%

5 W = 160 liters Step 2

6 Using w/c = 50% and (5) above, C = 320kgs. This is equivalent to (320/3.10) = 103.2 liters

Step 3, and using specific gravity of cement as given in information (a)

7 Total volume of aggregate, i.e. (Vfa+Vca), = [1000 – 50 – 160 – 103.2] or 686.8 liters

Steps 4 and 5. Using the s/a and the specific gravities of fine and coarse aggregates

8 Vfa = 0.36 * 686.8 = 247.2 liters, which is equivalent to 645.2 kgs

9 Vca= 0.64 * 686.8 = 439.6 liters, which is equivalent to 1178 kgs

10 Final proportions: W = 160kg; C = 320kg; Fine aggregate = 645.2 kgs and coarse aggregate = 1178 kgs


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11 Check: [50 + 160 + (320/3.14) + (645.2/2.61) + (1178/2.68)] should be 1000

Table 9: Suggested changes in water content and s/a for adjustments in slump, FM, etc.

Table 10: Proportions for nominal mixes in concrete


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Figure 1b: cross-section of reinforced concrete also showing the schematic representation of the ‘transition zone’ between the paste and coarse aggregates, and, the CSH gel, with pores and hydration products.


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Figure 2: Simplified model of heterogeneous concrete

Models showing constituent elements

AIR


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Unit water content (kg/m3)

Slu

mp

Slopes depend on

aggregates properties, etc.

Figure 3 Unit water

content vs slump

Figure 4: Over-design factor vs expected

coefficient of variation


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Water-cement ratio

Co

mp

res

siv

e s

tren

gth

Depending upon age,

type of cement, etc.

Figure 5a : Schematic

representation of variation

of compressive strength of

concrete with water-cement

ratio

Figure 5b: variation of

compressive strength of concrete

with water-cement ratio at

different ages

Figure 6 : Wooden boxes often used

for measuring sand and aggregate by

volume. The dimensions of the box

are adjusted to give a certain

predetermined volume.

Concrete Proportioning

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