PSI - Issue 73

Sushant Chaudhary et al. / Procedia Structural Integrity 73 (2025) 19–26 Pratanu Ghosh / Structural Integrity Procedia 00 (2025) 000–000

23 5

3.2.3.1. Hyperbolic function

= . ( − 0 ) 1+ ( − 0 )

(3)

Where, Mo = maturity index when strength development is assumed to begin (°C·hr or hr), and k = rate constant, initial slope of strength-maturity curve (1/(°C·hr) or 1/hr). 3.2.3.2. Logarithmic function = + log ( ) (4) Where, a, b = constants (mixture dependent) 3.2.3.3. Exponential function: = . − ( ) (5) Where, S = compressive strength at maturity M (psi), S u = limiting compressive strength (psi), M = maturity index (°C·hr or hr), t = characteristic time constant (°C·hr or hr), and = shape parameter. Carino [1991] found that equations (3) and (5) fit very well to the strength-maturity data, producing almost identical curves, while equation (4) underestimates strength around 5 days and gives inaccurate results for late ages, as the equation estimates ever-increasing strength values with increasing maturity. 4. Results and Discussion 4.1. Maturity functions The temperature history up to 28 days for each mixture obtained from the maturity sensors was used to calculate the Time-Temperature Factor (TTF) and Equivalent Age (t e ) using equations (1) and (2). Average temperature (T a ) was calculated for the time interval (∆t) of 0.5 h our, specified temperature (T s ) was taken as 23 0 C (296 K), and datum temperature(T 0 ) and activation energy (Q) was taken as 0 0 C (32 0 F) and (37500 J/mol) respectively, which is discussed more in Section 4.2. The maturity functions were then plotted against the actual compressive strength measured on 1, 3, 7, 14, and 28 days, as shown in Figures 2 and 3 for all binary mixtures. The best-fit equation obtained from the graphs, as shown in Figures 2 and 3, also known as the Strength Maturity (S-M) relationship, was then used to estimate the compressive strength of the mixture for any given day.

0 10 20 30 40 50 60

y = 10.89ln(x) - 54.01 y = 11.88ln(x) - 64.77 y = 8.97ln(x) - 45.08

y = 6.19ln(x) - 20.59 y = 9.18ln(x) - 46.14 y = 11.5ln(x) - 55.07

Compressive Strength (MPa)

0

2000

4000

6000

8000

10000

12000

14000

TTF (C-hr) 100 TII-V 90 TII-V/ 10 Z 85 TII-V/ 15 Z 80 TII-V/ 20 Z 75 TII-V/ 25 Z 70 TII-V/ 30 Z

Figure 2: Nurse-Saul maturity function for all binary mixtures