Which of the following represents the CORRECT expression for maturity (M) of a concrete sample?
Correct Answer: A. M = Σ(Time × Temperature)
📚 Detailed Explanation: Maturity Formula M = Σ(Time × Temperature)
Why A (M = Σ[Time × Temperature]) is correct: The Nurse-Saul maturity function defines maturity as the summation (over all time intervals) of the product of time and temperature (relative to a datum temperature). In its general form M = Σ[Δt × (T − T0)]. When written in simplified/general notation as in the question, the maturity is expressed as the summation of (Time × Temperature) — a product, not a quotient or sum.
Full Maturity Formulas
| Formula | Name | Expression | Notes |
|---|---|---|---|
| Nurse-Saul | Most common in practice | M = Σ[Δt × (T − T0)] | T0 = datum temperature (−10°C or −11°C); linear temperature effect |
| Freiesleben Hansen & Pedersen (FHP) | Equivalent age method | te = Σ[Δt × exp(E/R × (1/Tref − 1/T))] | Accounts for non-linear (Arrhenius) temperature effect; more accurate |
Why Other Expressions Are Wrong
| Expression | Mathematical Form | Why Wrong |
|---|---|---|
| A. Σ(Time × Temperature) | Summation of products | Correct — maturity is the sum of (time × temperature) increments |
| B. Σ(Time ÷ Temperature) | Summation of quotients | Wrong: dividing time by temperature has no physical meaning in hydration kinetics |
| C. Σ(Temperature ÷ Time) | Summation of quotients (reversed) | Wrong: rate-type expression; does not represent cumulative maturity index |
| D. Σ(Time + Temperature) | Summation of sums | Wrong: adding time and temperature is dimensionally inconsistent (days + °C) and has no physical basis |
Application Example (from Q9)
M = Σ[Δt × (T – T0)]
= Σ[Time × Effective Temperature]
= Σ[Time × Effective Temperature]
For constant conditions:
M = 28 days × (15°C – (-11°C))
M = 28 × 26
M = 728 °C·days
For variable temperature curing (realistic site condition):
M = Δt1 × (T1 – T0) + Δt2 × (T2 – T0) + …
(sum each time interval's product separately, then add)
- Maturity = M = Σ(Time × Temperature) — summation of products of time and temperature increments.
- The maturity concept (ASTM C1074) allows in-situ strength estimation by tracking temperature history.