A Typical Mix-Design procedure for say, M40 (40 N/mm²) Grade of Concrete.

The Codes generally used are IS-456, IS-9103 & SP-23 (latest versions) along with relevant contract specs.

1)      Design Stipulation:

a)      f_ck at 28 days = 40 N/mm²

b)      Max. size of aggregates = 20mm

c)      Degree of workability = Compaction Factor of 0.95 & Slump of 100 to 150 mm as per IS-456.

d)      Shape of aggregates = angular

e)      Degree of Quality Control = very good

f)       Type of exposure = Moderate (or choose as per site condition)

g)      Max. water/cement (w/c) ratio = 0.50 (refer IS-456)

h)      Minimum cement content = say 300 kg ( refer IS-456 & contract specification & adopt the higher of the two)

Note: In this design, coarse aggregates considered is a blend of 20mm as well as 12 mm aggregates blended at a ration of 60:40 i.e. 60% 20mm & 40% 12mm aggregates. This is a commonly adopted practice in various sites. In stead of 12mm, some use 12.5mm or 10mm aggregates also.

2)      Test data for materials:

a)      Grade of cement = OPC 43 grade (commonly used)

b)      Specific gravity of cement = say, 3.15

c)      Size of coarse aggregates = 20mm; Specific gravity of C.A. = say, 2.9; Water absorption = say, 0.45% (actual sp. gr. & water absorption are to be determined at site-laboratory periodically as per Inspection Test Plan)

d)      Size of coarse aggregates = 12mm; Specific gravity of C.A. = say, 2.87; Water absorption = say, 0.75% (actual sp. gr. & water absorption are to be determined at site laboratory periodically as per Inspection Test Plan)

e)      Fine aggregates used is River sand of say, Zone-1. Specific gravity of F.A. = say, 2.65; Water absorption = say, 1.15% (actual sp. gr. & water absorption are to be determined at site laboratory periodically as per Inspection Test Plan)

3)      Mix calculation:

a)      Target Mean Strength = f_ck^ =  f_ck  + 1.65S = 40 + 1.65 x 5 = 48.25 N/mm²

Where S is a factor specified for various degree of Quality Control & in this case, for degree of quality control = very high, S = 5.

b)      As per SP-23, for 20mm down coarse aggregates & Zone-II fine aggregates water required for the mix is 180 litres & percentage of fine aggregates is 25% for w/c ratio 0.35 & C.F. 0.80. (Note that these are the standards stipulations and any variation from these would need correction as described below. The actual site conditions will generally always vary from these stipulations e.g. in stead of ideal Zone-II sand, only Zone-I or Zone-III sands are available in site, or the w/c ration adopted at site is 0.40 in stead of 0.35 as stipulated above etc. So, that’s okay as long as the necessary correction are induced)

After the above three steps one can proceed to the Trial-mix stage in order to arrive at the right or optimum mix-design for the particular mix, in this case M40. For that, several trials (usually 3 to 4) are conducted at laboratory adopting various w/c ratio & cement contents on trial basis as described below:

Trial-Mix No.-1

a)      w/c ratio:  Let us adopt a  w/c ratio of  0.37 (it is less than max. w/c ratio prescribed by IS-456 which is 0.50 in this case and hence safe). So, the w/c ratio is now 0.37, sand is Zone-I & C.F. is 0.95 (refer Design Stipulation above). But the standard conditions mentioned as in point b) above are w/c of 0.35 & sand of ideal Zone-II. Hence, some corrections need to be done as specified by the code itself:

                                                                     Water content                       % of sand

For sand conforming to Zone-I                           0                                   (+)1.5%

For increase of C.F by 0.15                             (+) 4.5%                                 0

(0.95 – 0.80 = 0.15)

For increase in w/c ratio by 0.02                         0                                   (+) 0.4%

(0.37 – 0.35 = 0.02)

——————————————————————————————————

Net correction to be induced =                        (+) 4.5%                           (+)1.9%

Therefore, % of sand 25 + 1.9 = 26.9%

As a result, % of C.A. = 100 – 26.9 = 73.1%

In case of concrete to be poured by pumping & not manually, then it is convenient to reduce C.A. by 10% as per ACI 221 for practical reasons. This correction need not be done for manually poured concrete. In this case, pumped concrete is considered.

Therefore, modified % of C.A. now comes to = 73.1 – 10% of 73.1 = 65.79%

Accordingly, modified % of C.A. now comes to = 100 – 65.79 = 34.21% = say, 34%.

Now, referring to the all-in-one aggregates combined curve, it suggests a slightly high 37% of  F.A.(sand) for reasons like better pumpability and cohesiveness. This is also called the ratio of F.A. to total aggregates i.e. 0.37.

Now, corrected Water Content = 180 + 4.5% of 180 = 180 + 8.1 = 188.1 liters.

According to IS-9103 & ASTM-C494, with addition of super plasticisers water content can be reduced by 20 to 25% with a dosage of 0.9 to 1.2% of the cement content. This is convenient as lesser w/c is desirable for higher strength and at the same time it ensures desired workability as well.

Let water content reduction of 20% be considered for strength purpose by addition of 1% super plasticiser,

Hence, final water content = 188.1 – 20% of 188.1 = 150.48 = say 150 liters or kg.

b)      Cement content = (water content)/(w.c ratio) = 150/0.37 = 405.41 kg.

This is higher than minimum cement content, 300 kg, required for M40 as per IS-456, hence safe. If contract specification asks for a higher min. content then in stead of 300kg, that figure needs to be considered for min content check purpose, A higher figure than the calculated one could be adopted to be on the safer side. In this case, calculated fig. is 405.41 kg & let 425 kg be the adopted cement content.

So, for the finally adopted cement content of 425 kg, the actual water content would be now = 425 x w/c ratio = 425 x 0.37 = 157.25 liters or kg.

c)      As per SP-23, Volume of entrapped air in 1 M³ of fresh concrete for 20mm max. size C.A. = 2%.

Hence, Absolute volume of  1 M³ fresh concrete = gross vol. of 1 M³ of fresh concrete – entrapped air (i.e. 2% of 1 M³) = 0.98 M³ .

d)      Calculation of Volumes of F.A. & C.A.:

      V= [ W + C/S_c + A/S_a + 1/P x F_a/S_fa ] x 1/1000  ………… Eq.1

      V= [ W + C/S_c + A/S_a + 1/(1-P) x C_a/S_ca ] x 1/1000  ………Eq.2

Where, V= Absolute vol. of 1 M³ fresh concrete =  0.98 M³      

      W = mass of water per M³ of concrete = 425 x 0.37 = 157.25.

       C = mass of cement per M³ of concrete = 425kg.

       S_c = specific gravity of cement = say, 3.15.

       A = mass of admixture = 4.25kg.

       S_a = specific gravity of admixture(super plasticiser) = say, 1.18.

       P = ratio of F.A. to total aggregates = 0.37.

       S_fa = specific gravity of F.A. in saturated surface dry (S.S.D.) condition = say, 2.65.

       S_ca = sp.gr. of C.A. in saturated surface dry (S.S.D.) condition = say,2.89(for 20mm)

                                                                                                                    = say,2.87(for 12mm)

Now, for F.A., putting values in Eq.1,

          V =  [W + C/S_c + A/S_a + 1/P x F_a/S_fa ] x 1/1000

   i.e.  0.98 = [157.25 + 425/3.15 + 4.25/1.18 + 1/0.37 x F_a/2.65] x 1/1000.

Hence,  F_a = say, 684 kg

for C.A. proportion of 20mm & 12mm aggregates in the combined grading is 60:40.

Hence, for C.A., putting values in Eq.2,

           V= [ W + C/S_c + A/S_a + 1/(1-P) x C_a/S_ca ] x 1/1000

For 20mm,  0.98 = [157.25 + 425/3.15 + 4.25/1.18 + 1/0.63*.60 x C_a/2.89] x 1/1000

           C_a = say, 747 kg (20mm)

For 12mm,  0.98 = [157.25 + 425/3.15 + 4.25/1.18 + 1/0.63*.40 x C_a/2.87] x 1/1000

           C_a = say, 495 kg (12mm).

So, mix details for Trial Mix No.1:

Cement = 425 kg,  Water = 157.25 liters or kg,  20mm CA = 747 kg,  12mm CA = 495 kg,  F.A. = 684 kg,  Admixture = 4.25 kg.

Trial-Mix No.-2:

For trial 2, consider a w/c ratio of say, 0.36 & a cement content of say, 435 kg. Then all the steps for TM No.1 are to be repeated and the above quantities are to be arrived at.

Trial-Mix No.-3:

For trial 3, consider a w/c ratio of say, 0.37 & a cement content of say, 415 kg. Then all the steps for TM No.1 are to be repeated and the above quantities are to be arrived at.

Similarly any number of trials can be done by repeating the above procedure. Generally 3 trials are sufficient.

Now, for all the above three trials cube tests are conducted in laboratory to determine the 7 days & 28 days strengths for each trial mix. The results should meet the strength requirement i.e. the 28 days cube strength should be at least f_ck^ which is 48.25 N/mm² as calculated in the beginning in this case. The 7 days strength should not be less than ⅔ times the 28 days strength. Adopt the mix which meets both the criteria as the final mix for the purpose of casting. In case all the trials meet the strength criteria, then the one with the least cement content (in this case TM No.3) could be adopted as it would be economic.

Finally, Batch Correction needs to be done as in the above equations i.e. Eq.1 & Eq.2, the aggregates are assumed to be in Saturated Surface Dry (SSD) condition i.e. they are fully saturated & hence can not absorb any further water when aggregates are mixed with water in plants or mixture machines. In reality that is not the case and both CA & FA will hardly be fully saturated and hence would suck water from the added quantity of water & thus changing the w/c ratio. To avoid that batch correction is necessary & for that actual moisture contents of all the aggregates are determined in laboratory for all the trial mixes. Then correction is done as shown in the table below: