Maturity Functions

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Maturity functions are used to calculate the rate of reaction (as a function of temperature) during cement hydration and track the evolution of concrete maturity over time. Maturity and equivalent age are generally interchangeable terms, both used to express the degree of hydration of cement. Maturity can then in turn be used to calculate the compressive strength of concrete, using the strength-maturity relationship (this is covered in more detail in the article “Curve fitting process and functions”).

ConcreteDNA is capable of using any maturity function to calculate the equivalent age of concrete over time. At present, 3 functions are available via ConcreteDNA (Nurse-Saul, Arrhenius & Sadgrove).

Nurse-Saul function

The Nurse-Saul function is one of the most commonly used maturity functions. It was first published in the UK in 1951 but is still in widespread use today, particularly in the US. It is one of two maturity functions listed in ASTM C1074 (Standard Practice for Estimating Concrete Strength by the Maturity Method). The parameter “datum temperature” is the theoretical temperature below which concrete ceases to gain maturity. This is often set as 0°C or -10°C, although a procedure to determine this experimentally is included in ASTM C1074 Appendix X1.2. Sometimes the Nurse-Saul function is used to express maturity as temperature-time factor (in units of °C.hours or similar) although this has generally been superseded by the concept of equivalent age now which uses different units.


Arrhenius function

The Arrhenius function was first published in 1977 by Freiesleben Hansen and Pedersen. It addresses one of the limitations of the Nurse-Saul function, by specifying the relationship between concrete temperature and the rate of reaction as non-linear. It also has a parameter known as “apparent activation energy” which represents the temperature sensitivity of the hydration reaction. Mixes with a high activation energy (such as mixes containing a high proportion of GGBS) react much slower in cool conditions and, conversely, much faster in warmer conditions. Mixes with a lower activation energy will not slow down so much in cool conditions but, conversely, will not accelerate as much in warm conditions. ASTM C1074 states that values of between 38,000J/mol and 45,000J/mol are commonly reported, but this can vary, particularly for mixes containing a proportion of supplementary cementitious materials such as GGBS or PFA. A procedure to determine this experimentally is included in ASTM C1074 Appendix X1.2


Sadgrove function

In 1971, the Weaver-Sadgrove function (more commonly referred to as the Sadgrove function) was published. It is a commonly used function in the UK, but is not referred to in ASTM C1074. Similarly to the Arrhenius function, the Sadgrove function aims to address the main shortcoming of Nurse-Saul function (ie. the linear relationship between temperature and maturity). Unlike the Arrhenius function, it does not have an additional parameter to allow it to be adapted to the temperature sensitivity of different mixes. Certain studies have shown it to be accurate for a wide range of mixes, including mixes containing up to 70% GGBS.

NB: Equivalent age is measured as time at a reference temperature. ConcreteDNA uses the units “Hours at 20°C”. This does not affect the applicability in other countries, or the accuracy of the calculations in any way. It is not generally exposed to users either, but is used by our back-end system in the calculation of compressive strength.

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