Mix design concrete is a crucial process in the concrete making that involves determining the proportions and ingredients of concrete to achieve the desired strength, workability, durability, and other properties. It is essential to design a concrete mix that meets the specific requirements of a construction project.

The mix design of concrete takes into account various factors such as the compressive strength required, the type and size of aggregates, the water-cement ratio, the shape of coarse aggregates, the workability needed, the exposure conditions, and the type of cement used. These factors play a crucial role in determining the performance and longevity of the concrete structure.

**Mix Design of Concrete**

The calculate mix design for concrete following step to be followed.

**Data Required Mix Design**

**i.** **Design Data**

(a) Characteristic compressive strength of concrete required at end of 28 days = M 25

(b) Nominal maximum size of aggregate used = 20 mm

(c) Shape of Coarse Aggregate = Angular

(d) Required workability at site = 50-75 mm (slump Value)

(e) Quality control is done as per IS: 456 – 2000

(f) Type of exposure Condition of concrete (as defined in IS: 456) = Mild

(g) Type of cement used = PSC conforming IS: 456 – 2000

(h) Method of placing Concrete on Site = pumpable concrete

**(ii) Material testing data (determined in the laboratory)**

(a) Specific gravity of cement = 3.15

(b) Specific gravity of FA = 2.64

(c) Specific gravity of CA = 2.84

(d) Aggregates are assumed to be having surface dry conditions**.**

(e) Fine aggregates are confirmed to Zone II of IS â€“ 383

## Mix Design of Concrete Procedure

The following steps are to be followed for concrete mix design calculation,

**Step-1 Determining the Target Strength of Concrete**

Himsworth constant for 5% risk factor is 1.65 & standard deviation is taken from IS: 456 2000 for M – 25 Grade of concrete is 4.0.

**f**_{target}** = f**_{ck}** + 1.65 x S**

= 25 + 1.65 x 4.0 = 31.6 N/mm^{2}

Where,

S = Standard Deviation (N/mm^{2}) = 4 (Refer: IS 10262- 2009 table -1)

**Step-2 Determining Water-Cement ratio**

Refer: IS 456, (page no 20) Table 5

Maximum water-cement ratio taken for Mild exposure condition = 0.55

Assume the water-cement ratio as 0.50 for the experiment base

0.5 < 0.55, hence it is OK.

**Step-3 Selection of Water Content for Mix**

**Refer: IS 10262- 2009 Table 2**

Maximum water content is taken = 186 Kg (maximum size of aggregate = 20 mm)Correction in water content is

Estimated water content for mix = 186+ (3/100) x 186 = 191.6 kg /m^{3}

**Step-4 Selection of Cement Content for Mix**

- Water-cement ratio = 0.50
- Corrected water content for mix
^{3} - Refer to IS 456 â€“ 2000, Table 5
- Minimum cement Content required for mild exposure condition = 300 kg/m3
- 383.2 kg/m3 > 300 kg/m3, hence, OK.
- This value is required to be checked for durability requirements
- In this example for mild exposure and for reinforced concrete, the minimum cement content is 300 kg/m3 which is less than 383.2 kg/m
^{3}. Hence cement content adopted = 383.2 kg/m^{3}. - IS: 456: 2000, clause 8.2.4.2
- Maximum cement content for mix = 450 kg/m
^{3}.

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**Step-5 Estimation of Coarse Aggregate Proportion for Mix **

Refer to IS 10262- 2009, Table 3

- For Nominal max. size of aggregate for mix = 20 mm,
- Zone of fine aggregate
- And For w/c
- The volume of coarse aggregate per unit volume of Concrete

**Table for Correction in Estimation of Coarse Aggregate Proportion**

(Note 1: For every Â±0.05 increase or decrease change in w/c, the coarse aggregate proportion is to be changed by 0.01. If the w/c is less than 0.5.)

The volume of coarse aggregate is required to be increased to reduce the fine aggregate content in the mix. If the water-cement ratio is more than 0.5, the volume of coarse aggregate is to be reduced to increase the fine aggregate content.

If the coarse aggregate is not of an angular shape, the volume of coarse aggregate is required to be increased suitably, based on experience-based.)

**(**Note 2: For pumpable concrete or congested reinforcement in structure the coarse aggregate proportion may be reduced up to 10%)

Hence, the Volume of coarse aggregate per unit volume of total Volume of concrete = 0.62 x 90% = 0.558

Volume of fine aggregate in mix = 1 â€“ 0.558 = 0.442

**Step-6 Estimation of the Mix Materials **

** **The volume of concrete is taken = 1 m^{3}

Volume of cement = (Weight of cement / Specific gravity of cement) x (1/100) = (383.2/3.15) x (1/1000) = 0.122 m^{3}

The volume of water = (Weight of water / Specific gravity of water) x (1/1000)

= (191.6/1) x (1/1000) = 0.1916 m^{3}

Volume of aggregates =** **a â€“ (b + c ) = 1 â€“ (0.122 + 0.1916) = 0.6864 m^{3}

Weight of coarse aggregates = 0.6864 x 0.558 x 2.84 x 1000 = 1087.75 kg/m^{3}

Weight of fine aggregates =** **0.6864 x 0.442 x 2.64 x 1000 = 800.94 kg/m^{3}

**Concrete Mix Proportions for Concrete Trial Mix -1**

- Cement = 383.2 kg/m
^{3} - Water = 191.6 kg/m
^{3} - Fine aggregates
^{3} - Coarse aggregate = 1087.75 kg/m
^{3} - W/c = 0.5
- For trial -1 of concrete in the
- It will satisfy durability
- For making trial -1, the mass of ingredients required will be calculated for 4 noâ€™s cubes assuming 25% wastage.
- Volume of concrete required for Making 4 cubes = 4 x (0.15
^{3 }x1.25) = 0.016878 m^{3} - Wt. of Cement = (383.2 x 0.016878) kg/m
^{3}= 6.47 kg - Wt. of Water = (191.6 x 0.016878) kg/m
^{3}=3.23 kg - Wt. of Coarse aggregate = (1087.75 x 0.016878) kg/m
^{3}=18.36 kg - Wt. of Fine aggregates = (800.94 x 0.016878) kg/m
^{3 =}13.52 kg

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**Step-7 Correction for Absorption / Moisture of Aggregate**

As we assumed the aggregate is a saturated surface dry condition, therefore no correction is required.

**Step-8 Concrete Trail Mixes**

**Concrete Trial Mix 1**

- The
- In this Trial Mix,
- Slump value
- Compaction Factor
- From the Mix Slum test, the concrete is workable and had a true slump of about 25 mm and it is free from segregation
- Required slump
- So modifications and changes are needed in trial mix 1 to get the desired workability.

**Concrete Trial Mix 2**

- To increase the workability of concrete mix from 25 mm to 50-75 mm an increase in water content by +3% is to be made.
- The corrected water content for mix = 191.6 x 1.03 = 197.4 kg.
- As mentioned earlier to adjust fresh concrete properties the water-cement ratio should not be changed. Hence
- Cement Content = (197.4/0.5) = 394.8 kg/m
^{3} - Which also need to satisfy durability requirement.
- Volume of aggregate in Concrete = 1 â€“ [{394.8/(3.15Ã—1000)} + {197.4/(1 x 1000)}] = 0.6773 m
^{3} - Weight of coarse aggregate
^{3} - Weight of fine aggregate = 0.6773 x 0.442 x 2.64 x 1000 = 790.3 kg/m
^{3}

**Concrete Mix Proportions for Trial Mix 2**

- Weight of Cement = 384.8 kg/m
^{3} - Weight of Water = 197.4 kg/m
^{3} - Weight of Fine aggregate =790.3 kg/m
^{3} - Weight of Coarse aggregate
^{3} - For making trial -2, the Weight of material required will be calculated for 4 noâ€™s cubes assuming 25% wastage.
- Volume of concrete required for 4 cubecasting = 4 x (0.153 x1.25) = 0.016878 m3
- Weight of Cement = (384.8 x 0.016878) kg/m3 = 6.66 kg
- Weight of Water = (197.4 x 0.016878) kg/m3 =3.33 kg
- Weight of Coarse aggregate = (1073.33 x 0.016878) kg/m3 =18.11 kg
- Weight of Fine aggregates
- In this trial Mix,
- Slump value for mix = 60 mm
- Compaction Factor for mix = 0.852
- So, from the results of the slump of Mix, the concrete is workable and had a true slump of about 60 mm.
- Required slump
- So, it satisfied the desired workability by satisfying the requirement of a 50-75 mm slump value.
- Now, we have to go for trial mix-3

**Concrete Trial Mix 3 **

- In this trial mix water/cement ratio is to be decreased by 10% keeping the water content constant.
- Water cement ratio = 0.45
- With the reduction of 0.05 in w/c, we have to increase of coarse aggregate fraction
- Coarse aggregate fraction in mix = 0.558 +0.01 =0.568
- W/c = 0.45 and water content for mix = 197.4 kg/m
^{3} - Cement content
^{3} - Volume aggregate in total volume of concrete
^{3} - Weight of coarse aggregate = 0.664 x 0.568 x 2.84 x 1000 = 1071.11 kg/m
^{3} - Weight of fine aggregate = 0.664 x 0.432 x 2.64 x 1000 = 757.28 kg/m
^{3}

## M 25 Mix Design

For the** Compressive Strength of concrete **vs. C/W graph for a target strength of 31.6 MPa, we found

- Water cement ratio = 0.44
- Weight of water content = 197.4 kg/m
^{3} - Weight of Cement content = (197.4/0.44) = 448.6 kg/m
^{3} - The volume of aggregate in a total volume of concrete = 1 â€“ [{448.6/(3.15 x 1000)} + (197.4/1000)] = 0.660 m
^{3}With a reduction of 0.05 in w/c, we have to increase of coarse aggregate fraction by 0.01. - Coarse aggregate volume = 0.558 +0.01 = 0.568 m
^{3} - Volume of fine aggregate in mix = 1 â€“ 0.568 =
^{3} - Weight of coarse aggregate = 0.660 x 0.568 x 2.84 x 1000 =
^{3} - Weight of fine aggregate = 0.660 x 0.432 x 2.64 x 1000 = 752.71 kg/m
^{3}

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