Table of Contents

## Concrete mix :

Concrete mix is the heterogeneous mixture consisting of coarse aggregate, fine aggregate, cement and water as the main ingredients. Grade of concrete is the designation of the concrete mix which is indicated according to its cube compressive strength at 28 days. Concrete mix is categories into two types: nominal mix and design mix.

**Nominal mix of concrete:**

Based on the nominal mix, different grade of concrete are

Grade | Proportion |

M5 | 1:5:10 |

M7.5 | 1:4:8 |

M10 | 1:3:6 |

M15 | 1:2:4 |

M20 | 1:1.5:3 |

M25 | 1:1:2 |

The proportion given is the ratio of cement, fine aggregate and coarse aggregate. Above M25, we can’t use nominal mix, we should go through design mix.

**Concrete mix design:**

Here we discuss concrete mix design based on the indian standard. Some of the codes used for concrete mix design are IS 456:2000 and IS 10462:2019

**Step 1: Calculate target strength**

Target strength is that strength of concrete for which concrete mix is designed. The concrete mix has to be proportioned for higher target mean compressive strength f^{’}_{ck} in order that not more than the specified proportion of test results are likely to fall below the characteristic strength.

Target strength f^{’}_{ck} = f_{ck} + 1.65 S or

f^{’}_{ck} = f_{ck}+ X

whichever is higher.

where

f^{’}_{ck} = target mean compressive strength at 28 days, in N/mm2;

f_{ck} = characteristic compressive strength at 28 days, in N/mm2;

S = standard deviation, in N/mm2 and

X = a factor that depend on the grade of concrete

To constitute an acceptable results for calculation of standard deviation, the minimum number of samples for test strength shall be not less than 30.

If the number of samples or the test results are not sufficient for a particular grade of concrete , the value of standard deviation given in Table below should be taken for the proportioning of mix in the first instance.

[Table 1 & 2 of IS 10262:2019]

S.N | Grade of concrete | Assumed standard deviation | Value of X |

1 | M10 & M15 | 3.5 | 5.0 |

2 | M20 & M25 | 4.0 | 5.5 |

3 | M30 – M60 | 5.0 | 6.5 |

4 | M65 & above | 6.0 | 8.0 |

**Step 2: Estimation of Air Content:**

Approximate amount of entrapped air to be expected in normal (non-air-entrained) concrete is given as,

[Table 3 of IS 10262:2009]

S. N | Nominal max. size of aggregate | Entrapped air as percentage of volume of concrete |

1 | 10 | 1.5 |

2 | 20 | 1.0 |

3 | 40 | 0.8 |

**Step 3: Calculate w/c ratio based on target strength and required workability**.

Water cement ratio w/c is the ratio which is calculated by dividing the mass of mixing water by the mass of cement. The free water-cement ratio aphrdi.ap.gov.in

The given table below is for normal weight aggregate of maximum nominal size 20 mm.

[Table 5 of IS 456:2000]

S.N | Exposure condition | Min. grade of reinforced concrete | Max. w/c ratio | Min. cement Kg/m^{3} |

1 | Mild | M20 | 0.55 | 300 |

2 | Moderate | M25 | 0.50 | 300 |

3 | Severe | M30 | 0.45 | 320 |

4 | Very severe | M35 | 0.45 | 340 |

5 | Extreme | M40 | 0.40 | 360 |

**Step 4: Calculate water content based on max size of aggregate and durability condition**

The water content in the concrete is influenced by different factor such as shape, size and texture of aggregate, workability, w/c ratio, chemical admixture and environmental conditions.

Water content per cubic meter of Concrete for nominal maximum size of aggregate:

[Table 4 of IS 10262:2019]

S.N | Nominal maximum size of aggregate mm | Water content kg |

1 | 10 | 208 |

2 | 20 | 186 |

3 | 40 | 165 |

Water content corresponding to saturated surface dry aggregate.

The water content in the table 4 is for angular coarse aggregate and for 50mm slump. The estimated water can be reduced by

10 kg for sub-angular aggregate

15 kg for gravel with some crushed particles

20 kg for rounded aggregate

For desired workability other than slump value 50 mm, the required water content may be increased or decreased by about 3 percent for each increase or decrease of 25 mm slump.

The calculated water content can be reduced by use of chemical admixture conforming to IS 9103. At the appropriate dosages of water reducing admixture or super plasticizing admixture, the water content is usually decreased by 5 to 10 percent and 20 to 30 percent and above respectively.

**Step 5: Calculate the cement content from the w/c ratio and free water content**

The cement and supplementary cementitious materials content per unit volume of concrete may be calculated from the free water-cement ratio and the quantity of cement per unit volume of concrete. The minimum quantity of cement required per unit volume of concrete is given in step 3. [Table 5 of IS456:2000]

Adjustment to min. cement content for aggregate other than 20mm

S.N | Nominal max. size of aggregate | Adjustment to min. cement content kg/m^{3} |

1 | 10 | +40 |

2 | 20 | 0 |

3 | 40 | -30 |

**Step 6: Calculate the proportion of aggregate**

[Table 5 of IS10262:2019] Volume of coarse Aggregate per Unit Volume of Total Aggregate for Different Zones of Fine

Aggregate for Water-Cement/Water-Cementitious Materials Ratio of 0.50

Approximate values for this aggregate volume are given in Table 5 for a water-cement/water cementitious materials ratio of 0.5, which may be suitably adjusted for other ratios, the proportion of volume of coarse aggregates to that of total aggregates is increased at the rate of 0.01 for every decrease in water-cement/cementitious materials ratio by 0.05 and decreased at the rate of 0.01 for every increase in water cement ratio by 0.05

Requirement for the concrete mix design are

IS 456: 2000 and IS 10262: 2009

**Example 1: Mix design of M30 grade of concrete**

**STIPULATIONS FOR PROPORTIONING**

a) Grade designation: M30

b) Type of cement: OPC 43 grade conforming to IS 269

c) Maximum nominal size of aggregate: 20 mm

d) Minimum cement content and maximum water-cement ratio to be adopted and/or: Severe (for reinforced concrete)

Exposure conditions as per Table 3 and Table 5 of IS 456

e) Workability: 75 mm (slump)

f) Method of concrete placing: Chute (Non pump able)

g) Degree of site control: Good

h) Type of aggregate: Crushed angular aggregate

j) Maximum cement content not including fly ash: 450 kg/m3

k) Chemical admixture type: Superplasticizer – normal

**TEST DATA FOR MATERIALS**

a) Cement used: OPC 43 grade conforming to IS 269

b) Specific gravity of cement: 2.88

c) Chemical admixture: Superplasticizer conforming to IS 9103

d) Specific gravity of

1) Coarse aggregate [at saturated surface dry: 2.74 (SSD) Condtion]

2) Fine aggregate [at saturated surface dry: 2.65 (SSD) Condtion]

3) Chemical admixture: 1.145

e) Water absorption

1) Coarse aggregate: 0.5 percent

2) Fine aggregate: 1.0 percent

f) Moisture content of aggregate [As per IS 2386 (Part 3)]

1) Coarse aggregate: Nil

2) Fine aggregate : Nil

**Step 1: Calculate target strength of mix**

The target strength of concrete mix is given by

f ’ck = fck+1.65 S or

f ’ck = fck + X

whichever is higher.

From Table 2, standard deviation, S = 5 N/mm2.

From Table 1, X = 6.5.

Therefore, target strength using both equations, that is,

a) f ’ck = fck+1.65 S = 30+1.65 × 5 = 38.25 N/mm2

b) f ’ck = fck + 6.5 = 30 + 6.5 = 36.5 N/mm2

The higher value is to be adopted. Therefore, target strength will be 38.25 N/mm2 as 38.25 N/mm2 > 36.5 N/mm2.

**Step 2: Estimation of Air Content:**

From Table 3, the approximate amount of entrapped air to be expected in normal (non-air-entrained) concrete is 1.0 percent for 20 mm nominal maximum size of aggregate.

**Step 3: Calculate w/c ratio based on target strength and required workability**.

From Fig. 1, the free water-cement ratio required for the target strength of 38.25 N/mm2 is 0.42 for OPC 43 grade curve. This is lower than the maximum value of 0.45 prescribed for ‘severe’ exposure for reinforced concrete as per Table 5 of IS 456.

0.42< 0.45, hence O.K.

**Step 4: Calculate water content based on max size of aggregate and durability condition**

From Table 4, water content = 186 kg (for 50 mm slump) for 20 mm aggregate.

Estimated water content for 75 mm slump

= 186 + 3/100 *186

= 191.58 kg

As superplasticizer is used, the water content may be reduced. Based on trial data, the water content reduction of 23 percent is considered while using superplasticizer at the rate 1.0 percent by weight of cement.

Hence the water content

= 191.58 × 0.77

= 148 kg

**Step 5. Calculation of cement content**

Water-cement ratio = 0.36

Cement content = 148/0.36

= 411.11 kg/m3 ̴ 412 kg/m3

From Table 5 of IS 456, minimum cement content for ‘severe’ exposure condition = 320 kg/m3

412 kg/m3> 320 kg/m3, hence, O.K.

**Step 6. Proportion of volume of coarse aggregate and fine aggregate content:**

From Table 5, the proportionate volume of coarse aggregate corresponding to 20 mm size aggregate and fine aggregate (Zone II) for water-cement ratio of 0.50 = 0.62.

In the present case water-cement ratio is 0.42.

Therefore, To decrease the volume of fine aggregate content, it is required to increase the volume of coarse aggregate. To make water-cement ratio lower by 0.08, the proportion of coarse aggregate content should be increased by 0.016 (at the rate of 0.01 for every ± 0.05 change in water-cement ratio). Therefore, corrected proportion of volume of coarse aggregate for the water-cement ratio of 0.42 = 0.62 + 0.016 = 0.636.

Volume of fine aggregate content = 1 – 0.636 = 0.364

**MIX CALCULATIONS**

The mix calculations per unit volume of concrete shall be as follows:

a) Total volume = 1 m3

b) Volume of entrapped air in wet concrete = 0.01 m3

c) Volume of cement = Mass of cement / (Specific gravity of cement * 1000)

= 412 / (2.88 * 1000)

= 0.143 m^{3}

d) Volume of water = Mass of water / (specific gravity of water * 1000)

= 148 / (1*1000)

= 0.148 m^{3}

e) Volume of chemical admixture (superplasticizer) @ 1% of mass of cementitious materials

= mass of chemical admixture / (specific gravity of chemical admixture * 1000)

= 4.12 / (1.145 * 1000)

= 0.0036 m^{3}

f) Volume of all aggregates = [(a-b) – (c+d+e)]

= [(1- 0.01) – (0.143 + 0.148 + 0.0036)]

= 0.695 m^{3}

g) Mass of coarse aggregate = f * volume * specific gravity of coarse aggregate * 1000

= 0.695 * 0.636 *2.74 *1000

= 1216.85 kg

h) Mass of fine aggregate = f * volume * specific gravity of fine aggregate * 1000

= 0.695 * 0.364 * 2.65 *1000

= 670.4 kg

**Adjustment for field condition (if the coarse and fine aggregate are in dry condition)**

Fine aggregate (dry);

Weight of F.A = 670.4 / (1+1/100)

= 663.37 kg

Coarse aggregate (dry)

Weight of coarse aggregate = 1216.85 / (1+0.5/100)

= 1210.80 kg

The extra water to be added for absorption in coarse and fine aggregate,

For coarse aggregate = mass of coarse aggregate in (SSD condition – dry condition)

= 1216.85 – 1210.8

= 6.05 kg

For fine aggregate = mass of fine aggregate in (SSD condition – dry condition)

= 670.4 – 663.37

= 7.03 kg

The estimated requirement for added water, therefore, becomes = 148 + 6.05 + 7.03

= 161.08 kg

**Mix proportion after adjustment:**

Cement = 412 kg

Water to be added = 161.08 kg

Fine aggregate = 663.37 kg

Coarse aggregate = 1210.8 kg

Chemical admixture = 4.12 kg

Free cement- water ration = 0.42

The slump should be measured and the water content and doses of admixture shall be adjusted for achieving the required slump based on trial.

With variation of water-cement ratio by 10 percent, two more trial shall be carried out and the graph between the water-cement ratio. And their corresponding strength shall be plotted to work out the mix-proportion for the given target strength for field trials. However durability condition should be met.

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