The concrete is widely used construction material. The main ingredient of the concrete is cement, aggregates, water and admixtures. Due to the varying properties of the materials used in concrete, the design of concrete is not an easy task. The various methods of mix design are applied for determining the qualities & quantity of concrete. The objective of designing a mix is to produce a concrete of required strength, durability and workability as economically as possible. In our country, generally Indian Standard Institution (ISI) concrete design method is preferred and hence has been discussed. The use of Indian standard institution (ISI) concrete design method is illustrated with the aid of an example.

## Introduction

The compressive strength of hardened concrete depends upon many factors, e.g. quality and quantity of cement, water and aggregates; batching and mixing; placing, compaction and curing. The actual cost of concrete is related to the cost of materials required for producing a minimum mean strength called characteristic strength which is specified by the structure engineer. This depends on the quality control measures, but it is a fact that the quality control adds to the concrete cost. The extent of quality control is often an economic compromise, and depends on the size and type of job. The cost of labor depends on the workability of mix, e.g., a concrete mix of inadequate workability may result in a high cost of labour to obtain a degree of compaction with available equipment. So it is obligatory to resort to mix design for high rise/ strength structures.

## Requirements of Concrete Mix Design

a) The minimum compressive strength required from structural point of view.

b) The adequate workability necessary for full compaction

c) Maximum water-cement ratio and/or maximum cement content to give adequate durability for site conditions

d) Maximum cement content to avoid shrinkage cracking due to temperature in mass concrete.

## Factors Affecting the Choice of Mix Proportions

- Compressive strength

It is one of the most important properties of concrete and influences many other describable properties of the hardened concrete. The mean compressive strength required after 28 days, determines the nominal water-cement ratio of the mix. The other factor affecting the strength of concrete are age, cured and degree of compaction.

- Workability

The degree of workability required depends on three factors i.e. size of the section, the amount of reinforcement, and the method of compaction to be used. For the narrow and complicated section with numerous corners or inaccessible parts, the concrete must have a high workability so that full compaction can be achieved

- Durability

The durability of concrete is its resistance to the aggressive environmental conditions. High strength concrete is generally more durable as compared to low strength concrete. When the high strength is not required but the conditions of exposure are severe in such situations, high durability is vital. To meet the durability requirement, the mix design is the necessity.

- Maximum nominal size of aggregate

The compressive strength tends to increase with the decrease in size of aggregate whereas the workability of concrete increases with increase in maximum size of the aggregate.

- Grading and type of aggregate

The grading of aggregate influences the mix proportions for a specified workability and water-cement ratio. Coarser the grading, leaner will be mixed which can be used. An important feature of a satisfactory aggregate is the uniformity of the grading which can be achieved by mixing different size fractions.

- Quality Control

The degree of control can be judged statistically by the variations in test results. The variation in strength results is due to lack of control of accuracy in batching, mixing, placing, curing and testing. The lower the difference between the mean and minimum strengths of the mix lower will be the cement-content required. The factor controlling this difference is called as quality control.

- Mix Proportion designations

The common method of expressing the proportions of ingredients of a concrete mix is in the terms of parts or ratios of cement, fine and coarse aggregates e.g. a concrete mix of proportions 1:2:4 means that the mix contains one part of cement, two parts of fine aggregate and four parts of coarse aggregate. The proportions are either by volume or by mass. The water-cement ratio is usually expressed in mass.

## Information Required For Mix Design

- Grade of concrete
- Degree of workability
- Maximum temperature of fresh concrete
- Type of cement
- Minimum cement content
- Maximum water cement ratio
- Type of aggregates
- Maximum nominal size of aggregate
- Type of admixtures, if required
- Level of quality assurance
- Exposure condition
- Method of placing
- Degree of supervision

## Materials and Methods

**ISI Mix Design Method:-**

**Example:**Present investigation includes design of concrete mix (non-air entrained) for medium strength concrete. The guidelines given in various codes like SP: 23-1982, IS: 10262-1982 and IS: 456-2000 has been adopted for mix design of concrete.

Table 1 Coarse aggregate | ||||||

IS Sieve sizesmm | Analysis of coarse aggregate fraction (Percent passing) | Percent of different fractions | Conforming to Table 2 of IS : 383-1970 | |||

10mm | 20mm | I(50%) | II(50%) | Combined(100%) | ||

20 | 100 | 94.6 | 50 | 47.3 | 97.3 | |

10 | 56.2 | 0.40 | 28.1 | 0.2 | 28.3 | |

4.75 | 0.60 | 0 | 0.3 | 0 | 0.3 | |

2.36 | 0 | 0 |

Table 2 Fine aggregate | ||

Is Sieve sizes | Fine aggregate(Percent passing) | Conforming to grading zone II of Table 4 of IS : 383-1970 |

4.75 mm | 96 | |

2.36 mm | 86 | |

1.18 mm | 61 | |

600micron | 35.5 | |

300micron | 23.5 | |

150micron | 5.5 |

Table 3 Adjustment required in water content and sand (Reproduced from IS: 10262-1982: Table 6) | ||

Change in condition | Adjustment required in | |

Water content percent | percentage sand in total aggregate | |

For decrease in water-cement ratio by (0.60-0.50) that is 0.1 | 0 | -1.0 |

For increase in compacting factor (0.9-0.8) that is 0.10 | 3 | 0 |

For sand conforming to zone II of Table 4 of IS:383 | 0 | 0 |

Total | +3 percent | -1.0 |

Table 4 Approximate air content corresponding to nominal maximum size of aggregate (Reproduced from IS:10262-1982: Table 3) | |

Nominal maximum size of aggregate (mm) | Entrapped air, as percentage of volume of concrete |

10 | 3.0 |

20 | 2.0 |

40 | 1.0 |

For the present investigation, it is required to have characteristic compressive strength 40 N/mm^{2}. The compaction factor for the design mix is taken as 0.9. The maximum size of aggregate is 20 mm (angular). Type of exposure moderate and degree of quality control as very good.

**Test data for materials:** Cement used of 43 grade of OPC,

Company- Ultratech

Specific gravity of cement – 2.975

Specific gravity of aggregates:-

Coarse – 2.63

Fine – 2.62

Water absorption

Coarse aggregate – 0.5 percent

Fine aggregate – 1.0 percent

Free surface moisture

Coarse aggregate – nil

Fine aggregate- nil

Sieve analysis was done & results are given in Table 1 & Table 2, which satisfies the codal requirement of IS: 383-1970

**Target mean strength of concrete:** Tolerance factor (t) for very good quality control obtained from Table 2 of IS: 10262-1982 is 1.65 and standard deviation is 5.6 (obtained from Table 1 of IS: 10262-1982). The target mean strength for the specified characteristic strength is 40 + 5.6 x 1.65 = 49.24 N/mm^{2}

**Selection of water cement ratio:** From Figure 1 of IS: 10262-1982, the free water cement ratio required for the target mean strength of 49.24N/mm2 is 0.32. In this study, w/c ratio for all the specimens were kept constant (0.32). This is lower than the maximum value of 0.50 prescribed for moderate exposure.

**Selection of water and sand content:-** From Table 5 of IS:10262-1982, for 20mm nominal maximum size aggregate and sand conforming to grading Zone II, water content per cubic metre of concrete = 180 kg and sand content as percentage of total aggregate by absolute volume = 25%

For change in values in water-cement ratio, compacting factor and sand belonging to Zone II, the following adjustment is required as given in Table 3

Therefore, required sand content as percentage of total aggregate by absolute volume =25-1=24 percent.

Required water content = 180 + 180 x 3/100=185.40 liters/m^{3}

**Determination of cement content:-**

Water cement ratio = 0.32

Water= 185.40 liters/m^{3}

Cement=185.40/0.32=579.375kg/m^{3}

From Table 4, for the specified maximum size of aggregate of 20 mm, the amount of entrapped air in the wet concrete is 2 percent. Taking this into account and applying equations:-

V= [W+C/S_{c}+1/p. f_{a}/S_{fa}] x1/1000,

V= [W+C/S_{c}+1/1-p. C_{a}/S_{ca}] x1/1000

Where,

V = absolute volume of fresh concrete, which is equal to gross volume (m^{3})

minus the volume of entrapped air,

W = mass of water (kg) per m^{3} of concrete,

C = mass of cement (kg) per m^{3} of concrete,

S^{c} = specific gravity of cement,

p = ratio of fine aggregate to total aggregate by absolute volume,

f_{a}, C_{a} = specific gravities of saturated surface dry fine aggregate and

coarse aggregate respectively.

S_{fa}, S_{ca} = specific gravities of saturated surface dry fine aggregate and

coarse aggregate respectively.

0.98m^{3} = [185.4+ 579.375/2.975+1/0.2975xfa/2.62]x1/1000

0.98m^{3} = [185.4+579.375/2.975+1/0.7025xCa/2.63]x1/1000

or f_{a} = 467.58kg/m^{3}

C_{a} = 1108.52kg/m^{3}

The mix proportion then becomes as given in Table 5:

Table 5 Proportion of different materials | |||

Water | Cement | Fine aggregate | Coarse aggregate |

185.4 liters | 579.375 kg | 467.58 kg | 1108.52 kg |

0.32 | 1 | 0.81 | 1.91 |

**Actual quantities required for the mix per bag:** The mix is 0.32:1:0.81:1.919 (by mass). For 50kg of cement, the quantity of materials are worked out as below:

Cement = 50kg

Fine aggregate = 40.5kg

Coarse aggregate = 95.5kg

(Fraction I=47.75kg, Fraction II = 47.75kg)

(Fraction I =10mm, Fraction II = 20mm)

For water-cement ratio of 0.32, quantity of water=16 liters

Extra quantity of water to be added for absorption

in case of coarse aggregate, at 0.5 percent by mass = (+) 0.80 liters

Actual quantity of water to be added = 16.0+0.80= 16.80 liters

Actual quantity of sand required after allowing

for mass of free moisture = 40.5 kg

Actual quantity of coarse aggregate required:

Fraction I =47.75-0.385=47.365kg

Fraction II=47.75-0.385=47.365kg

Therefore, the actual quantities of different constituents required for the mix are:

Water: 16.80 kg

Cement: 50.00 kg

Fine aggregate :40.50 kg

Coarse aggregate Fraction I

: 47.365 kg

Fraction II : 47.365 kg

## Conclusion

- It is obligatory to design the mix for high strength concrete.
- Design mix for a site/construction results in economy.
- By designing a mix, we can achieve the required compressive strength and workability by consuming minimum quantity of concrete materials.
- It is suggested that all the contractors/builders should get the design mix done for bringing quality control in construction.

## Projects for which mix design was obligatory due to their high strength or/and height.

World’s Tallest Buildings | Dubai, d Aates (UAE) to become the world’s newest tallest tower. | Tallest building in Mumbai |

Modern day bridges | Longest Bridge in China, 22 miles |

**Anil Kumar Nanda**

Associate Professor & Head Surya School of Engg. & Tech. Surya World, Rajpura

**Jaspal Singh**

Professor & Head Civil Engg Department PAU Ludhiana

## References

- Gambhir, M.L.(1992) Concrete Manual, 4
^{th}ed., Dhanpat Rai & Sons, DELHI. - IS: 456 (2000) Code of Practice for Plain and Reinforced Concrete, Bureau of Indian Standards, New Delhi.
- IS: 10262 (1982) Concrete Mix Design, Bureau of Indian Standards, New Delhi.
- IS: 8112(1989) 43 Grade Ordinary Portland Cement Specification, Bureau of Indian Standards, New Delhi.
- IS : 383 (1970) Specification for coarse and fine aggregates, Bureau of Indian Standards, New Delhi.
- Jain, A.K.(2002) Reinforced Concrete, 6
^{th}ed., Nem Chand & Bros. Roorkee. - Neville, A.M. (1994) Properties of Concrete technology, 4th ed., Longman Scientific & Technical Essex, U.K.