How Much Stronger Does Concrete Get After 28 Days? Fitting the ACI 209 and CEB-FIP Strength-Gain Functions to 557 Paired Observations, with Asymptotic Comparisons and the Effect of Slag and Fly Ash

Design codes predict compressive strength at any age from the 28-day strength with a one- or two-parameter function: the hyperbola t/(a + bt) of ACI 209R-92 and the exponential exp(s(1 − sqrt(28/t))) of the CEB-FIP Model Code 1990 and fib Model Code 2010. I fit both to 557 ratios f(t)/f(28) from 178 mixes in the UCI Concrete Compressive Strength data set (Yeh 1998), where the same mix was tested at 28 days and at another age between 1 and 365 days. I prove that the CEB coefficient is identified by the 7-day ratio alone, s = −ln g(7), that the ACI form with g(28) = 1 has g(7) = 1/(4 − 3b), and that the two forms approach their long-term limits at different rates (1/t against 1/sqrt(t)), so the CEB form predicts more late-age gain. The fitted CEB coefficient is 0.427 (long-term limit 1.53 times the 28-day strength), well above the code values of 0.20 to 0.38, and the code curves give errors 15–33% larger than the fitted ones. Mixes containing slag or fly ash have s = 0.452 against 0.366 for Portland cement alone (difference 0.086, mix bootstrap interval 0.032 to 0.142). The median 7-day ratio is 0.630, below the ACI code value of 0.70, and the median 365-day ratio is 1.206, which the fitted CEB curve overpredicts (1.362), as the asymptotic result implies.