Concrete mix design is required to achieve target strength in
structures. Concrete Mix design of M20, M25, M30 grade of concrete can be
calculated from example below.
CONCRETE MIX DESIGN CALCULATION FOR M20 M25 M30 WITH EXAMPLE
Data Required for Concrete Mix Design
(i) Concrete Mix Design Stipulation
(a) Characteristic compressive strength required in the field at 28 days grade
designation — M 25
(b) Nominal maximum size of aggregate — 20 mm
(c) Shape of CA — Angular
(d) Degree of workability required at site — 50-75 mm (slump)
(e) Degree of quality control available at site — As per IS:456
(f) Type of exposure the structure will be subjected to (as defined in
IS: 456) — Mild
(g) Type of cement: PSC conforming IS:455
(h) Method of concrete placing: pump able concrete
(ii) Test data of material (to be 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) Aggregate are assumed to be in saturated surface dry condition.
(e) Fine aggregates confirm to Zone II of IS – 383
Procedure for Concrete Mix Design of M25 Grade Concrete
Step 1 — Determination Of Target Strength
Himsworth constant for 5% risk factor is 1.65. In this case standard
deviation is taken from IS:456 against M 20 is 4.0.
ftarget = fck + 1.65 x S = 25 +
1.65 x 4.0 = 31.6 N/mm2
Where,
S = standard deviation in N/mm2 = 4 (as per table -1 of IS 10262- 2009)
Step 2 — Selection of water / cement ratio:-
From Table 5 of IS 456, (page no 20)
Maximum water-cement ratio for Mild exposure condition = 0.55
Based on experience, adopt water-cement ratio as 0.5.
0.5<0.55, hence OK.
Step 3 — Selection of Water Content
From Table 2 of IS 10262- 2009,
Maximum water content = 186 Kg (for Nominal maximum size of aggregate —
20 mm)
Table for Correction in water content
|
Parameters
|
Values as per Standard reference condition
|
Values as per Present Problem
|
Departure
|
Correction in Water Content
|
|
Slump
|
25-50 mm
|
50-75
|
25
|
(+3/25) x 25 = +3
|
|
Shape of Aggregate
|
Angular
|
Angular
|
Nil
|
–
|
|
|
|
Total
|
+3
|
Estimated water content = 186+ (3/100) x 186 = 191.6 kg /m3
Step 4 — Selection of Cement Content
Water-cement ratio = 0.5
Corrected water content = 191.6 kg /m3
Cement content =
From Table 5 of IS 456,
Minimum cement Content for mild exposure condition = 300 kg/m3
383.2 kg/m3 > 300 kg/m3, hence, OK.
This value is to be checked for durability requirement from IS: 456.
In the present example against mild exposure and for the case of
reinforced concrete the minimum cement content is 300 kg/m3 which is less than
383.2 kg/m3. Hence cement content adopted = 383.2 kg/m3.
As per clause 8.2.4.2 of IS: 456
Maximum cement content = 450 kg/m3.
Step 5: Estimation of Coarse Aggregate proportion:-
From Table 3 of IS 10262- 2009,
For Nominal maximum size of aggregate = 20 mm,
Zone of fine aggregate = Zone II
And For w/c = 0.5
Volume of coarse aggregate per unit volume of total aggregate = 0.62
Table for correction in
estimation of coarse aggregate proportion
|
Parameter
|
Values
as per Standard reference condition
|
Values
as per present problem
|
Departure
|
Correction
in Coarse Aggregate proportion
|
Remarks
|
|
W/c
|
0.5
|
0.5
|
Nil
|
–
|
See
Note 1
|
|
Workability
|
–
|
pump
able concrete
|
–
|
-10%
|
See
Note 2
|
|
|
|
Total
|
-10%
|
|
Note 1: For every ±0.05 change in w/c, the coarse aggregate proportion
is to be changed by 0.01. If the w/c is less than 0.5 (standard value), volume
of coarse aggregate is required to be increased to reduce the fine aggregate
content. If the w/c is more than 0.5, volume of coarse aggregate is to be
reduced to increase the fine aggregate content. If coarse aggregate is not
angular, volume of coarse aggregate may be required to be increased suitably,
based on experience.
Note 2: For pump able concrete or congested reinforcement the coarse
aggregate proportion may be reduced up to 10%.
Hence,
Volume of coarse aggregate per unit volume of total aggregate = 0.62 x
90% = 0.558
Volume of fine aggregate = 1 – 0.558 = 0.442
Step 6: Estimation of the mix ingredients
a) Volume of concrete = 1 m3
b) Volume of cement = (Mass of cement / Specific gravity of cement) x
(1/100)
= (383.2/3.15) x (1/1000) = 0.122 m3
c) Volume of water = (Mass of water / Specific gravity of water) x
(1/1000)
= (191.6/1) x (1/1000) = 0.1916 m3
d) Volume of total aggregates = a – (b + c ) = 1 – (0.122 + 0.1916) =
0.6864 m3
e) Mass of coarse aggregates = 0.6864 x 0.558 x 2.84 x 1000 = 1087.75
kg/m3
f) Mass of fine aggregates = 0.6864 x 0.442 x 2.64 x 1000 = 800.94
kg/m3
Concrete Mix proportions for Trial Mix 1
Cement = 383.2 kg/m3
Water = 191.6 kg/m3
Fine aggregates = 800.94 kg/m3
Coarse aggregate = 1087.75 kg/m3
W/c = 0.5
For trial -1 casting of concrete in lab, to check its properties.
It will satisfy durability & economy.
For casting trial -1, mass of ingredients required will be calculated
for 4 no’s cube assuming 25% wastage.
Volume of concrete required for 4 cubes = 4 x (0.153 x1.25) = 0.016878
m3
Cement = (383.2 x 0.016878) kg/m3 = 6.47 kg
Water = (191.6 x 0.016878) kg/m3 =3.23 kg
Coarse aggregate = (1087.75 x 0.016878) kg/m3 =18.36 kg
Fine aggregates = (800.94 x 0.016878) kg/m3 = 13.52 kg
Step 7: Correction due to absorbing / moist aggregate:-
Since the aggregate is saturated surface dry condition hence no
correction is required.
Step 8: Concrete Trial Mixes:-
Concrete Trial Mix 1:
The mix proportion as calculated in Step 6 forms trial mix1. With this
proportion, concrete is manufactured and tested for fresh concrete properties
requirement i.e. workability, bleeding and finishing qualities.
In this case,
Slump value = 25 mm
Compaction Factor = 0.844
So, from slump test we can say,
Mix is cohesive, workable and had a true slump of about 25 mm and it is
free from segregation and bleeding.
Desired slump = 50-75 mm
So modifications are needed in trial mix 1 to arrive at the desired
workability.
Concrete Trial Mix 2:
To increase the workability from 25 mm to 50-75 mm an increase in water
content by +3% is to be made.
The corrected water content = 191.6 x 1.03 = 197.4 kg.
As mentioned earlier to adjust fresh concrete properties the water
cement ratio will not be changed. Hence
Cement Content = (197.4/0.5) = 394.8 kg/m3
Which also satisfies durability requirement.
Volume of all in aggregate = 1 – [{394.8/(3.15×1000)} + {197.4/(1 x
1000)}] = 0.6773 m3
Mass of coarse aggregate = 0.6773 x 0.558 x 2.84 x 1000 = 1073.33 kg/m3
Mass of fine aggregate = 0.6773 x 0.442 x 2.64 x 1000 = 790.3 kg/m3
Concrete Mix Proportions for Trial Mix 2
Cement = 384.8 kg/m3
Water = 197.4 kg/m3
Fine aggregate =790.3 kg/m3
Coarse aggregate = 1073.33 kg/m3
For casting trial -2, mass of ingredients required will be calculated
for 4 no’s cube assuming 25% wastage.
Volume of concrete required for 4 cubes = 4 x (0.153 x1.25) = 0.016878
m3
Cement = (384.8 x 0.016878) kg/m3 = 6.66 kg
Water = (197.4 x 0.016878) kg/m3 =3.33 kg
Coarse aggregate = (1073.33 x 0.016878) kg/m3 =18.11 kg
Fine aggregates = (790.3 x 0.016878) kg/m3 = 13.34 kg
In this case,
Slump value = 60 mm
Compaction Factor = 0.852
So, from slump test we can say,
Mix is very cohesive, workable and had a true slump of about 60 mm.
It virtually flowed during vibration but did not exhibit any
segregation and bleeding.
Desired slump = 50-75 mm
So , it has achieved desired workability by satisfying the requirement
of 50-75 mm slump value .
Now , we need to go for trial mix-3 .
Concrete Trial Mix 3:
In case of trial mix 3 water cement ratio is varied by +10% keeping water
content constant. In the present example water cement ratio is raised to 0.55
from 0.5.
An increase of 0.05 in the w/c will entail a reduction in the coarse
aggregate fraction by 0.01.
Hence the coarse aggregate as percentage of total aggregate = 0.558 –
0.01 = 0.548
W/c = 0.55
Water content will be kept constant.
Cement content = (197.4/0.55) = 358.9 kg/m3
Hence, volume of all in aggregate = 1 – [{(358.9/(3.15 x 1000)} +
(197.4/1000)] =0.688 m3
Mass of coarse aggregate = 0.688 x 0.548 x 2.84 x 1000 = 1070.75 kg/m3
Mass of fine aggregate = 0.688 x 0.452 x 2.64 x 1000 = 821 kg/m3
Concrete Mix Proportions of Trial Mix 3
Cement = 358.9 kg/m3
Water = 197.4 kg/m3
FA = 821 kg/m3
CA = 1070.75 kg/m3
For casting trial -3, mass of ingredients required will be calculated
for 4 no’s cube assuming 25% wastage.
Volume of concrete required for 4 cubes = 4 x (0.153 x1.25) = 0.016878
m3
Cement = (358.9 x 0.016878) kg/m3 = 6.06 kg
Water = (197.4 x 0.016878) kg/m3 =3.33 kg
Coarse aggregate = (1070.75 x 0.016878) kg/m3 =18.07 kg
Fine aggregates = (821 x 0.016878) kg/m3 = 13.85 kg
In this case,
Slump value = 75 mm
Compaction Factor = 0.89
So, from slump test we can say,
Mix is stable, cohesive, and workable and had a true slump of about 75
mm.
Desired slump = 50-75 mm
So , it has achieved desired workability by satisfying the requirement
of 50-75 mm slump value .
Now , we need to go for trial mix-4.
Concrete Trial Mix 4:
In this case water / cement ratio is decreased by 10% keeping water
content constant.
W/c = 0.45
A reduction of 0.05 in w/c will entail and increase of coarse aggregate
fraction by 0.01.
Coarse aggregate fraction = 0.558 +.01 =.568
W/c = 0.45 and water content = 197.4 kg/m3
Cement content = (197.4/0.45) = 438.7 kg/m3
Volume of all in aggregate = 1 – [{438.7/(3.15 x 1000)} + (197.4/1000)]
= 0.664 m3
Mass of coarse aggregate = 0.664 x 0.568 x 2.84 x 1000 = 1071.11 kg/m3
Mass of fine aggregate = 0.664 x 0.432 x 2.64 x 1000 = 757.28 kg/m3
Concrete Mix Proportions of Trial Mix 4
Cement = 438.7 kg/m3
Water = 197.4 kg/m3
FA = 757.28 kg/m3
CA = 1071.11 kg/m3
For casting trial -4, mass of ingredients required will be calculated
for 4 no’s cube assuming 25% wastage.
Volume of concrete required for 4 cubes = 4 x (0.153 x1.25) = 0.016878
m3
Cement = (438.7 x 0.016878) kg/m3 = 7.4 kg
Water = (197.4 x 0.016878) kg/m3 =3.33 kg
Coarse aggregate = (1071.11 x 0.016878) kg/m3 =18.07 kg
Fine aggregates = (757.28 x 0.016878) kg/m3 = 12.78 kg
A local correction due to moisture condition of aggregate is again
applied on this proportions. With corrected proportions three concrete cubes
are cast and tested for 28 days compressive strength.
A summary of all the trial mixes is given in the following Table.
Recommended mix proportion of ingredients for grade of concrete M25:
From Compressive Strength vs. c/w graph for target strength 31.6 MPa we
get,
W/c = 0.44
water content = 197.4 kg/m3
Cement content = (197.4/0.44) = 448.6 kg/m3
Volume of all in aggregate = 1 –
[{448.6/(3.15 x 1000)} + (197.4/1000)] = 0.660 m3
A reduction of 0.05 in w/c will entail and increase of coarse aggregate
fraction by 0.01.
Coarse aggregate fraction = 0.558 +.01 =.568
Volume of fine aggregate = 1 – 0.568 = 0.432
Mass of coarse aggregate = 0.660 x 0.568 x 2.84 x 1000 = 1064.65 kg/m3
Mass of fine aggregate = 0.660 x 0.432 x 2.64 x 1000 = 752.71 kg/m3
