For 15 cm cube compressive strength at 7 days, what should be the minimum ratio f7(M 20) : f7(M 40) expected from standard curing and testing?

Introduction / Context:
Early-age compressive strength (e.g., at 7 days) is often used to track quality and predict 28-day results. For normal concretes cured under standard conditions, strength tends to scale proportionally across grades at the same age, allowing simple ratios to be inferred between different characteristic grades.

Given Data / Assumptions:

• Compare 7-day strengths of M 20 and M 40 (same curing regime).
• Assume typical maturity/strength-gain curves (similar cement type, no special admixture effects).
• Seek a minimum ratio reflecting proportional scaling across grades.

Concept / Approach:

At any given early age, strengths of different grades are approximately proportional to their 28-day characteristics if mix design methodology is consistent. Hence, f7(M 20) : f7(M 40) ≈ 20 : 40 = 1 : 2 → a ratio of 1/2 as a reasonable lower bound.

Step-by-Step Solution:

Verification / Alternative check:

Empirical curves often show f7 ≈ 0.60–0.70 of f28 for OPC systems; if both grades follow similar curves, the ratio between grades at 7 days mirrors the 28-day ratio, supporting 1/2.

Why Other Options Are Wrong:

• 1/3: Too low; implies unusually poor early strength for M 20 relative to M 40.
• 3/2 or 2.0: Inverted; would suggest M 20 stronger than M 40 at 7 days.
• 3/4: Overestimates relative M 20 strength compared to M 40 at early age.

Common Pitfalls:

• Comparing cubes with different curing or cement types, which skews ratios.
• Ignoring that absolute early-age strengths depend on temperature and admixtures.

Final Answer:

1/2