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

**Requirements for concrete mix design**

- The grade designation giving the characteristic strength requirement of concrete.
- The type of cement influences the rate of development of compressive strength of concrete.
- Maximum nominal size of aggregates to be used in concrete may be as large as possible within the limits prescribed by IS 456:2000.
- The cement content is to be limited from shrinkage, cracking and creep.
- The workability of concrete for satisfactory placing and compaction is related to the size and shape of section, quantity and spacing of reinforcement and technique used for transportation, placing and compaction.

**Procedure for Concrete Mix Design as per IS 456 : 2000**

1. Determine the mean target strength ft from the specified characteristic compressive strength at 28-day fck and the level of quality control.

f_{t} = f_{ck} + 1.65 S

where S is the standard deviation obtained from the Table of approximate contents given after the design mix.

2. Obtain the water cement ratio for the desired mean target using the empirical relationship between compressive strength and water cement ratio so chosen is checked against the limiting water cement ratio. The water cement ratio so chosen is checked against the limiting water cement ratio for the requirements of durability given in table and adopts the lower of the two values.

3. Estimate the amount of entrapped air for maximum nominal size of the aggregate from the table.

4. Select the water content, for the required workability and maximum size of aggregates (for aggregates in saturated surface dry condition) from table.

5. Determine the percentage of fine aggregate in total aggregate by absolute volume from table for the concrete using crushed coarse aggregate.

6. Adjust the values of water content and percentage of sand as provided in the table for any difference in workability, water cement ratio, grading of fine aggregate and for rounded aggregate the values are given in table.

7. Calculate the cement content form the water-cement ratio and the final water content as arrived after adjustment. Check the cement against the minimum cement content from the requirements of the durability, and greater of the two values is adopted.

8. From the quantities of water and cement per unit volume of concrete and the percentage of sand already determined in steps 6 and 7 above, calculate the content of coarse and fine aggregates per unit volume of concrete from the following relations:

where V = absolute volume of concrete = gross volume (1m^{3}) minus the volume of entrapped air

Sc = specific gravity of cement

W = Mass of water per cubic meter of concrete, kg

C = mass of cement per cubic meter of concrete, kg

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

fa, Ca = total masses of fine and coarse aggregates, per cubic meter of concrete, respectively, kg, and

S_{fa}, S_{ca} = specific gravity of saturated surface dry fine and coarse aggregates, respectively

9. Determine the concrete mix proportions for the first trial mix.

10. Prepare the concrete using the calculated proportions and cast three cubes of 150 mm size and test them wet after 28-days moist curing and check for the strength.

11. Prepare trial mixes with suitable adjustments till the final mix proportions are arrived at.

## Concrete Mix Design Example – M50 Grade Concrete

Grade Designation = M-50

Type of cement = O.P.C-43 grade

Brand of cement = Vikram ( Grasim )

Admixture = Sika [Sikament 170 ( H ) ]

Fine Aggregate = Zone-II

**Sp. Gravity**

Cement = 3.15

Fine Aggregate = 2.61

Coarse Aggregate (20mm) = 2.65

Coarse Aggregate (10mm) = 2.66

Minimum Cement (As per contract) =400 kg / m^{3}

Maximum water cement ratio (As per contract) = 0.45

**Concrete Mix Design Calculation**

**1. Target Mean Strength = 50 + ( 5 X 1.65 ) = 58.25 Mpa**

**2. Selection of water cement ratio:**

Assume water cement ratio = 0.35

**3. Calculation of water content:**

Approximate water content for 20mm max. Size of aggregate = 180 kg /m^{3} (As per Table No. 5 , IS : 10262 ). As plasticizer is proposed we can reduce water content by 20%.

Now water content = 180 X 0.8 = 144 kg /m^{3}

**4. Calculation of cement content:**

Water cement ratio = 0.35

Water content per m^{3} of concrete = 144 kg

Cement content = 144/0.35 = 411.4 kg / m^{3}

Say cement content = 412 kg / m^{3} (As per contract Minimum cement content 400 kg / m^{3} )

Hence O.K.

**5. Calculation of Sand & Coarse Aggregate Quantities:**

Volume of concrete = 1 m^{3}

Volume of cement = 412 / ( 3.15 X 1000 ) = 0.1308 m^{3}

Volume of water = 144 / ( 1 X 1000 ) = 0.1440 m^{3}

Volume of Admixture = 4.994 / (1.145 X 1000 ) = 0.0043 m^{3}

Total weight of other materials except coarse aggregate = 0.1308 + 0.1440 +0.0043 = 0.2791 m^{3}

Volume of coarse and fine aggregate = 1 – 0.2791 = 0.7209 m^{3}

Volume of F.A. = 0.7209 X 0.33 = 0.2379 m^{3} (Assuming 33% by volume of total aggregate )

Volume of C.A. = 0.7209 – 0.2379 = 0.4830 m^{3}

Therefore weight of F.A. = 0.2379 X 2.61 X 1000 = 620.919 kg/ m^{3}

Say weight of F.A. = 621 kg/ m^{3}

Therefore weight of C.A. = 0.4830 X 2.655 X 1000 = 1282.365 kg/ m^{3}

Say weight of C.A. = 1284 kg/ m^{3}

Considering 20 mm: 10mm = 0.55: 0.45

20mm = 706 kg .

10mm = 578 kg .

Hence Mix details per m^{3}

Increasing cement, water, admixture by 2.5% for this trial

Cement = 412 X 1.025 = 422 kg

Water = 144 X 1.025 = 147.6 kg

Fine aggregate = 621 kg

Coarse aggregate 20 mm = 706 kg

Coarse aggregate 10 mm = 578 kg

Admixture = 1.2 % by weight of cement = 5.064 kg.

**Water: cement: F.A.: C.A. = 0.35: 1: 1.472: 3.043 **

**Observations from Concrete Mix Design**

A. Mix was cohesive and homogeneous.

B. Slump = 120 mm

C. No. of cube casted = 9 Nos.

7 days average compressive strength = 52.07 MPa.

28 days average compressive strength = 62.52 MPa which is greater than 58.25MPa

Hence the mix accepted.

**Percentage strength of concrete at various ages**

The strength of concrete increases with age. Table shows the strength of concrete different ages in comparison with the strength at 28 days.

Age | Strength per cent |

1 day | 16% |

3 days | 40% |

7 days | 65% |

14 days | 90% |

28 days | 99% |

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