# Calculations for Concrete Mix

Concrete mix design is the way toward deciding right extents of concrete, sand and totals for concrete to accomplish target quality of concrete.

The Advantages of concrete mix design is that it gives the correct extents of materials, along these lines making the concrete utilize affordable in accomplishing required quality of auxiliary members. As the amount of concrete required for colossal developments are tremendous, the economy in amount of materials, for example, concrete makes the undertaking development practical.

Concrete Mix design of M – 20, M – 25, M – 30 and higher evaluation of concrete can be determined from following advances:

Concrete Mix Design - Data Required for Mix Design of Concrete:

(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 by as per IS: 456
(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

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 confirm to Zone II of IS – 383

Procedure for M – 25 Concrete Mix Design

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.

ftarget = fck + 1.65 x S = 25 + 1.65 x 4.0 = 31.6 N/mm2
Where,
S = standard deviation (N/mm2) = 4 (Refer: IS 10262- 2009 table -1)

Step 2 — Determining water / cement ratio

[Reference: IS 456, (page no 20) Table 5]
Maximum water-cement ratio taken for Mild exposure condition = 0.55
Assume water-cement ratio as 0.50 for experiment base 0.5 < 0.55, hence it is OK.

Step 3 — Selection of Water Content for mix

[Reference: IS 10262- 2009 Table 2]

Maximum water content 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 /m3

Step 4 : Selection of Cement Content for mix

Water-cement ratio = 0.50
Corrected water content for mix = 191.6 kg /m3
[Refer IS 456 – 2000, Table 5]

Cement content =
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 requirement from IS: 456 – 2000

In this example for mild exposure and for the reinforced concrete the minimum cement content is 300 kg/m3 which are less than 383.2 kg/m3. Hence cement content adopted = 383.2 kg/m3.
[IS: 456: 2000, clause 8.2.4.2]
Maximum cement content for mix = 450 kg/m3.

Step 5: Estimation of Coarse Aggregate proportion for mix

Refer IS 10262- 2009, Table 3
For Nominal max. size of aggregate for mix = 20 mm,
Zone of fine aggregate = Zone II
And For w/c = 0.5

Volume of coarse aggregate per unit volume Concrete = 0.62

Note 1: For every ±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, volume of coarse aggregate is required to be increased to reduce the fine aggregate content in mix.

If the water cement ratio is more than 0.5, volume of coarse aggregate is to be reduced to increase the fine aggregate content. If coarse aggregate is not of angular shape, volume of coarse aggregate is required to be increased suitably, based on experience based)

Note 2: For pump able concrete or congested reinforcement in structure the coarse aggregate proportion may be reduced up to 10

Hence,
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 – 0.558 = 0.442

Step 6: Estimation of the mix Materials

a) Volume of concrete is taken = 1 m3
b) Volume of cement = (Weight of cement / Specific gravity of cement) x (1/100) = (383.2/3.15) x (1/1000) = 0.122 m3
c) Volume of water = (Weight of water / Specific gravity of water) x (1/1000) = (191.6/1) x (1/1000) = 0.1916 m3
d) Volume of aggregates = a – (b + c ) = 1 – (0.122 + 0.1916) = 0.6864 m3
e) Weight of coarse aggregates = 0.6864 x 0.558 x 2.84 x 1000 = 1087.75 kg/m3
f) Weight of fine aggregates = 0.6864 x 0.442 x 2.64 x 1000 = 800.94 kg/m3

Concrete Mix proportions for Concrete Trial Mix – 1

1. Cement = 383.2 kg/m3
2. Water = 191.6 kg/m3
3. Fine aggregates = 800.94 kg/m3
4. Coarse aggregate = 1087.75 kg/m3
5. W/c = 0.5

For trial -1 of concrete in the lab & to check its properties. It will satisfy durability & economy. For making trial -1, mass of ingredients required will be calculated for 4 no’s cube assuming 25% wastage.

1. Volume of concrete required for Making 4 cubes = 4 x (0.153 x1.25) = 0.016878 m3
2. Wt. of Cement = (383.2 x 0.016878) kg/m3 = 6.47 kg
3. Wt. of Water = (191.6 x 0.016878) kg/m3 =3.23 kg
4. Wt. of Coarse aggregate = (1087.75 x 0.016878) kg/m3 =18.36 kg
5. Wt. of Fine aggregates = (800.94 x 0.016878) kg/m3 = 13.52 kg

Step 7: Correction for absorption / moisture of aggregate

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

Step 8: Concrete Trial Mixes

Concrete Trial Mix 1: The mix proportion determined in Step 6 Make trail mix -1 & with this proportion, concrete is manufactured and tested for fresh concrete properties requirements like workability, bleeding and finishing qualities.

In this Trial Mix,
Slump value = 25 mm
Compaction Factor = 0.844

From the Mix Slump test, the concrete is workable and has a true slump of about 25 mm and it is free from segregation and bleeding.
required slump = 50-75 mm

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/m3

Which also needs to satisfy durability requirements.

1. Volume of aggregate in Concrete = 1 – [{394.8/(3.15×1000)} + {197.4/(1 x 1000)}] = 0.6773 m3
2. Weight of coarse aggregate = 0.6773 x 0.558 x 2.84 x 1000 = 1073.33 kg/m3
3. Weight of fine aggregate = 0.6773 x 0.442 x 2.64 x 1000 = 790.3 kg/m3

Concrete Mix Proportions for Trial Mix 2

1. Weight of Cement = 384.8 kg/m3
2. Weight of Water = 197.4 kg/m3
3. Weight of Fine aggregate =790.3 kg/m3
4. Weight of Coarse aggregate = 1073.33 kg/m3

For making trial -2, Weight of material required will be calculated for 4 no’s cube assuming 25% wastage.

1. Volume of concrete required for 4 cubecasting = 4 x (0.153 x1.25) = 0.016878 m3
2. Weight of Cement = (384.8 x 0.016878) kg/m3 = 6.66 kg
3. Weight of Water = (197.4 x 0.016878) kg/m3 =3.33 kg
4. Weight of Coarse aggregate = (1073.33 x 0.016878) kg/m3 =18.11 kg
5. Weight of Fine aggregates = (790.3 x 0.016878) kg/m3 = 13.34 kg

In this trial Mix,

1. Slump value for mix = 60 mm
2. 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 = 50-75 mm

So, it satisfied the desired workability by satisfying the requirement of 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 water content constant.
Water cement ratio = 0.45

As a reduction of 0.05 in w/c, we have to increase the coarse aggregate fraction by 0.01.

1. Coarse aggregate fraction in mix = 0.558 +0.01 =0.568
2. W/c = 0.45 and water content for mix = 197.4 kg/m3
3. Cement content for mix = (197.4/0.45) = 438.7 kg/m3
4. Volume aggregate in total volume of concrete = 1 – [{438.7/(3.15 x 1000)} + (197.4/1000)] = 0.664 m3
5. Weight of coarse aggregate = 0.664 x 0.568 x 2.84 x 1000 = 1071.11 kg/m3
6. Weight of fine aggregate = 0.664 x 0.432 x 2.64 x 1000 = 757.28 kg/m3

Recommended mix Weight of ingredients for grade of concrete M25: For Compressive Strength of concrete vs. C/W graph for target strength 31.6 MPa , we found

1. Water cement ratio = 0.44
2. Weight of water content = 197.4 kg/m3
3. Weight of Cement content = (197.4/0.44) = 448.6 kg/m3
4. Volume of aggregate in total volume of concrete = 1 – [{448.6/(3.15 x 1000)} + (197.4/1000)] = 0.660 m3

A reduction of 0.05 in w/c, we have to increase the coarse aggregate fraction by 0.01.

1. Coarse aggregate volume = 0.558 +0.01 =0.568
2. Volume of fine aggregate in mix = 1 – 0.568 = 0.432
3. Weight of coarse aggregate = 0.660 x 0.568 x 2.84 x 1000 = 1064.65 kg/m3