Target mean strength for M25 concrete mix design

f'ck is the higher of fck + 1.65s and fck + X.

Worked answer.

Why design above f_ck. The characteristic strength f_ck is defined as the strength below which not more than 5% of test results are expected to fall. Concrete strength varies from batch to batch, roughly following a normal distribution. To keep only 5% of results below f_ck, the mean strength must be set higher. For a normal distribution, 5% of values lie below the mean minus 1.65 standard deviations.

IS 10262:2019 rule. The target mean strength is the higher of:

• f'ck = f_ck + 1.65s
• f'ck = f_ck + X

Step 1: Values for M25 without site data.

• f_ck = 25 MPa.
• Assumed standard deviation s = 4.0 MPa (Table 2, for M20 and M25).
• Factor X = 5.5 (Table 1, for M20 and M25).

Step 2: Calculate both.

• f_ck + 1.65s = 25 + 1.65 × 4.0 = 25 + 6.6 = 31.6 MPa
• f_ck + X = 25 + 5.5 = 30.5 MPa

Step 3: Take the higher. Target mean strength = 31.6 MPa.

Check. With mean 31.6 and s = 4.0, the value 1.65 standard deviations below the mean is 31.6 − 6.6 = 25.0 MPa, which is exactly f_ck. So about 5% of cubes are expected below 25 MPa, consistent with the definition.

Practical notes

• Once at least 30 test results are available from the site, the actual standard deviation should replace the assumed value. Better quality control gives a lower s and a more economical mix.
• The "X" check was added in the 2019 revision so that the margin is not too small when the standard deviation is low.
• The target strength is then used to choose the water-cement ratio from the relevant curves, subject to the maximum w/c limits for durability in IS 456.

Common mistake. Designing the mix directly for 25 MPa. Then about half the cubes would fail the acceptance criteria.

Likely follow-up. "What are the values for M30?" s = 5.0 MPa and X = 6.5, giving f'ck = max(30 + 8.25, 36.5) = 38.25 MPa.