MIX DESIGN CONCEPT

Mix design of concrete is the process of selecting the required ingredients of concrete and finding their relative proportions with the aim of producing an economical concrete of certain strength and durability.

It has been discussed earlier that concrete is based on two phases, viz., aggregate phase and paste phase. Workability of the concrete depends on the lubricating effect of the paste phase. The strength of concrete is predominantly governed by the aggregate paste and the contribution by the paste phase is limited. But the permeability of concrete is based on the quality and continuity of the paste phase. Further, the paste phase fully contributes to the control of drying shrinkage of the concrete.

For a given set of materials, the four factors to be considered in the design of concrete mix are:

1. Water–cement ratio or cement content
2. Cement–aggregate ratio
3. Gradation of aggregate
4. Consistency

In general, all the four factors are inter-related and can not be dealt with individually to get the best concrete. However, two or three factors are fixed and the others are adjusted to get the required workability and economy.

The water–cement ratio represents the dilution of the paste, and cement concrete depends on the amount of paste. The gradation of the aggregate is done by adjusting the quantity of given fine and coarse aggregates. The required consistency or workability is obtained on the site of placement of concrete.

The effort in proportioning is to use a minimum quantity of paste which will lubricate the mixture while fresh, harden afterwards, will bind the aggregate particles together and fill the space between them. Excess cement should be avoided as it leads to greater cost, high shrinkage, high permeability, and more weathering. All these defects can be nullified by proper gradation.

There are over twelve mix designs of which two are explained, viz., the American Concrete Institute Method and the Bureau of Indian Standards Method. These two methods are popular in India.

8.7.1 American Concrete Institute (ACI) Method of Mix Design

This method has been used since 1944 and has undergone several revisions continuously. It has developed an identical procedure for angular or rounded aggregates, regular or light-weight aggregates and air-entrained or non-air-entrained concretes. The ACI mix design is based on certain factors which are established by field experience on large works. The factors are as follows:

1. The fresh concrete of a given slump with a well-graded aggregate (of a given maximum size) will have constant total water content irrespective of variations in water–cement ratio and cement content.
2. It considers the relationship that the optimum dry-rodded volume of coarse aggregate per unit volume of concrete is based on its maximum size and the fineness modulus of the fine aggregate (Table 8.3) irrespective of the shape of the particles.
3. Irrespective of the method of compaction, there is a definite percentage of air that exists which is inversely proportional to the maximum size of the aggregate.

Table 8.3 Dry bulk volume of concrete aggregate per unit volume of concrete

Source: ACI 211.1–91.

Reproduced with permission from the American Concrete Institute, Farmington Hills, MI (www.concrete.org)

The following step-by-step procedure has to be adopted:

1. All the required data, viz., (i) given modulus of the selected fine aggregate, (ii) unit weight of dry-rodded coarse aggregate, (iii) specific gravity of coarse and fine aggregates in SSD condition, (iv) absorption characteristics of both coarse and fine aggregates and (v) specific gravity of cement.
2. The maximum size of the aggregate has to be decided. Generally 20 mm and 10 mm are recommended for RCC and pre-stressed concrete work, respectively.
3. Workability has to be decided based on the slump depending on the work. General guidance may be taken from Table 8.4.Table 8.4 Recommended value of slump for different worksSource: ACI 211.1–91.Reproduced with permission from the American Concrete Institute, Farmington Hills, MI (www.concrete.org)Note: Upper limit of the slump may be increased by 20 mm for compaction by hand.
4. Based on the selected slump and maximum of aggregate, the total water in kg/m³ of concrete can be read from Table 8.5. Also the amount of accidentally entrapped air in non-air-entrained concrete may be obtained from Table 8.5.Table 8.5 Approximate water content requirement for mixing and air content for different workabilities and nominal maximum size of aggregates.Source: ACI 211.1–1994.Reproduced with permission from the American Concrete Institute, Farmington Hills, MI (www.concrete.org)
5. The cement content is calculated by dividing the total water content by the water–cement ratio.
6. The bulk volume of dry-rodded coarse aggregate per unit volume of concrete is selected from Table 8.5 for the particular maximum size of coarse aggregate and the fineness modulus of fine aggregate.
7. On multiplying the bulk volume by bulk density, the weight of the coarse aggregate in one cubic meter of concrete can be calculated.
8. With the knowledge of the specific gravity of coarse aggregate, the solid volume of the coarse aggregate in a cubic meter can be calculated.
9. Similarly, the solid volume of cement, water, and volume of air is calculated in one cubic meter of concrete.
10. The solid volume of sand is calculated by subtracting the volumes of cement, coarse aggregate, water and entrapped air from the total volume.
11. The weight of the fine aggregate is calculated by multiplying the solid volume of the fine aggregate by the specific gravity of the fine aggregate.

8.7.2 Bureau of Indian Standards (BIS) Method of Mix Design

Bureau of Indian Standards (BIS) has recommended a Mix Design Concept mainly based on the research works performed in national laboratories. This method can be applied for both medium-strength and high-strength concretes. The step-by-step approach of the BIS mix design is given below.

1. The target mean compressive  strength at 28 days is given by = f_ck + tSwhere f_ck = characteristic compressive strengtht = a statistical valueS = the standard deviation
2. It is desirable to establish a relationship between concrete strength and water–cement ratio at the site. If such a relationship is not available the water–cement ratio corresponding to the target strength may be determined from the relationship given in Table 8.6. It is possible to design in an effective way if the strength of the cement is incorporated in the concrete mix. This is done in the BIS design. Thus, if the 28-days strength is known, the water–cement ratio can be obtained from Fig. 8.1.Table 8.6 Strength and water–cement ratioSource: ACI 211.1–91.Reproduced with permission from the American Concrete Institute, Farmington Hills, MI (www.concrete.org)
3. The air content can be obtained from Table 8.7 for the normal size of the aggregate used.Table 8.7 Approximate air content Figure 8.1 Relationship between free water–cement ratio and concrete strength for different cement strengthsTable 8.8 Approximate sand and water content per m³Source: IS: 10262–82.
4. The water content and percentage of sand are determined from Table 8.8 for medium-strength (less than M 35 grade) and high-strength (greater than M 35 grade) concrete.
5. The cement content per unit volume of concrete is obtained asMass of cement = The cement calculated from the above relationship has to be checked against the minimum cement content requirement for durability from Table 8.9, and the greater of the two has to be taken.Table 8.9 Details for different exposures of concreteSource: IS: 456–2000.
6. The quantity of aggregate can be calculated from the following relationship:(8.1)(8.2)where V = absolute volume of fresh concrete= (gross volume) – (volume of entrapped air) m³W = mass of water per m³ of concrete, kgC = mass of cement per m³ of concrete, kgS_c = specific gravity of cementP = ratio of fine aggregate to total aggregate by absolute volumef_a, c_a = total masses of fine and coarse aggregates per m³ of concrete, respectively, kgS_fa, S_ca = specific quantities of saturated, surface-dry fine aggregate and coarse aggregate, respectively.
7. The mix proportions have been calculated based on the assumption that the aggregates are saturated and surface dry. When there is any deviation, necessary correction has to be incorporated.
8. The above calculated mix properties have to be checked by means of trial batches.
9. First the workability is checked, this forms Mix No. 1. If the measured workability is different from the assumed one, then the water content is changed (Table 8.10), and the whole mix design is modified keeping the new water–cement ratio constant.(b) A minor adjustment in the aggregate quantity may be made to improve the finishing quality or freedom from bleeding and segregation. This forms Mix. No. 2.(c) Now the water–cement ratio is changed by ±10% and the mix proportion is recalculated. This will form trial Mix Nos. 3 and 4.(d) Testing for trial Mix Nos. 2, 3 and 4 are done simultaneously.(f) These test results will provide adequate information including the relationship between compressive strength and water–cement ratio from which the correct mix proportion can be arrived at.

Table 8.10 Adjustment of value in water content and sand percentage for other conditions

Source: IS: 10262–82.