Generalized Illustrative Example on Concrete Mix Design

The Design for Concrete Mix of Grade M20

Input

Characteristic Compressive Strength f_ck                 20 N/mm²

Maximum Aggregate Size                                       20 mm

Specific Gravity of Cement                                     3.15        (Lab Test Data)

Specific Gravity of Coarse Aggregate                     2.60        (Lab Test Data)

Specific Gravity of Fine Aggregate                          2.60        (Lab Test Data)

Calculation Part

Target Mean Compressive Strength f_ck’ = f_ck + t.s, Where

“t” is a statistic, generally taken as 1.65, where not more than 5% (1 in 20) results are expected to fall. That means, if 20 tests were conducted, only 1 test is expected to show low result.

“s” is standard deviation, depends on the expected degree of quality. In general, for “Good” degree of quality, the value of “s” is as shown in Table 1.

Grade	M10	M15	M20	M25	M30	M35	M40	M45	M50	M55	M60
fck	10	15	20	25	30	35	40	45	50	55	60
t	1.65	1.65	1.65	1.65	1.65	1.65	1.65	1.65	1.65	1.65	1.65
s	2.3	3.5	4.6	5.3	6.0	6.3	6.6	7.0	7.4	7.7	7.8
fck’	13.80	20.78	27.59	33.75	39.90	45.40	50.89	56.55	62.21	67.71	72.87
w/c	0.65	0.60	0.50	0.45	0.35	0.30	0.30	0.30	0.30	0.30	0.30

Table 1: Tabular representation of Standard Deviation, Target Mean Compressive Strength and Water-Cement ratio for different grades of concrete.

Therefore, f_ck’ = 27.59 N/mm², and using this, the water-cement ratio (w/c) is determined using the graphical relation which can be approximately tabulated as shown in Table 1.

Therefore, w/c = 0.50.

From Table 2, for 20mm nominal maximum size of aggregate, entrapped air = 2%, water content = 186 kg and fine aggregate (sand) content = 35% for M20 grade concrete.

Nominal Size of Aggregate	Entrapped Air	M10, M15, M20, M25, M30, M35		M40, M45, M50, M55, M60
		Water Content	Fine Aggregate	Water Content	Fine Aggregate
10 mm	3%	208 kg	40%	200 kg	28%
20 mm	2%	186 kg	35%	180 kg	25%
40 mm	1%	165 kg	30%	-	-

Table 2: Tabular representation of Entrapped air, Water content and Fine aggregate for different nominal maximum size of aggregates and for different grades of concrete. The entrapped air and water content are for one cubic meter of concrete whereas fine aggregate is percentage of total aggregate content.

w/c ratio = 0.50 and water content = 186 kg, therefore cement content = 372 kg.

The calculation of fine and coarse aggregate content is done by using the following formulae

Where

V             absolute volume of concrete (gross volume minus entrapped air) = 1 – 0.02 = 0.98 cum

Ww        weight of water = 186 kg

Sw          specific gravity of water = 1

Wc          weight of cement = 372 kg

Sc            specific gravity of cement = 3.15

Pfa         percentage of fine aggregate = 35%

Wfa        weight of fine aggregate

Sfa          specific gravity of fine aggregate = 2.60

Wca       weight of course aggregate

Sca         specific gravity of coarse aggregate = 2.60

Implies, Wfa = 615 kg and Wca = 1,142 kg

Therefore, the mix becomes

Water                                   = 186 kg

Cement                                 = 372 kg

Fine Aggregate (Sand)           = 615 kg

Coarse Aggregate                  = 1,142 kg

If cement is considered as 1 part, then sand is 1.65 parts and Coarse aggregate is 3.07 parts, hence, the proportion is 1 : 1.65 : 3.07.

Note: This is the most generalized procedure for designing a concrete mix. However, for accurate proportions, factors such as: gradation, water absorption, surface moisture of fine and coarse aggregates, compaction factor etc., should be taken into account.