 # Determining Concrete Strength: The Common Methods of Maturity

There are different methods to determine concrete maturity. Over the years, the methods have been refined further and further parameters have been added. We have compiled the most common methods and their functions for you:
• Maturity according to Saul (also Saul/Nurse)
• The Freiesleben Hansen & Pedersen method according to Arrhenius
• The weighted maturity according to de Vree
At the end of the article you will also find a table where you can compare the differences at a glance.

## 1. Degree of maturity according to Saul (also Saul/Nurse)

This function is considered the oldest and simplest method for determining concrete maturity. Its basic assumption is as follows: “Concrete of the same mix has approximately the same strength at the same maturity, regardless of the combination of temperature and time leading to that maturity (A.G.A. Saul 1951).” The rate of strength development is a linear function of temperature. The maturity index – also called the “temperature-time factor” – is expressed in units of °C-hours or °C-days. Saul further assumed that concrete does not harden further at a temperature of minus 10 degrees Celsius.

## The formula is as follows: Explanation: M = maturity index in (°C days). T = average temperature during the time interval (°C) T0 = reference temperature ∆ = time interval
The temperature-time factor is also shown in this graph.
The temperature-time factor (at a given age t*) is equal to the area under the concrete temperature curve to the reference temperature (T₀). The reference temperature is the temperature at which the strength development of the concrete stops. While Saul – see above – sets this at minus 10 degrees Celsius, zero is also often chosen as the reference temperature.
What Saul did not take into account: concrete maturity would have to increase disproportionately at higher temperatures. In addition, the influence of the cement type is not taken into account. Nevertheless, the determination of the degree of maturity according to Saul was included in the ASTM C1074 standard in 1987 and is still one of the most frequently used methods in the USA and Canada

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## The Freiesleben Hansen & Pedersen method according to Arrhenius

Saul’s method reaches its limits particularly at temperatures outside the range between zero and 40 degrees Celsius. The Danes, Per Freiesleben Hansen and Erik Jørgen Pedersen, have therefore developed it further. To do so, they refer to the Arrhenius equation, named after Svante Arrhenius. It describes approximately a quantitative temperature dependence in chemical processes. The Freiesleben Hansen & Pedersen method is based on the assumption that the speed of strength development is exponentially related to temperature. In other words, the higher the temperature, the faster the strength development and vice versa. For this purpose, it includes the activation energy, i.e. the minimum energy required by a molecule to participate in a chemical reaction. The value of the activation energy depends on various factors. These include:
• The composition of the cement and its fineness
• The mixing ratio between water and cement
• The degree of hydration
The maturity index in this case is referred to as the equivalent age and is expressed in units of hours at 20 °C or days at 20 °C.

## The formula is as follows: Explanation:  Te: equivalent age E: activation energy R? T: average temperature during ∆ Tr: reference temperature ∆t: time interval
Since its introduction in 1977, the Freiesleben Hansen & Pedersen method has been widely used, especially in Europe, to determine an accurate prediction of the concrete strength on site.

## The weighted maturity according to de Vree

The term “weighted maturity”, which indicates the hardening contribution of a young concrete per hour, was coined by the Dutchman de Vree. Here, the temperature-dependent hardening behavior of concrete is taken into account, as is the type of cement.  For this, two new factors come into play:
• the C-value/weighting factor for the cement type, which depends on the cement composition
• the nk value, which represents a nonlinear effect of temperature on strength development
Especially at higher temperatures, the actual strength development and thus the degree of maturity, can be determined even better on this basis. C: C-value of the cement Nk: temperature-dependent parameter for the curing interval
The graph below shows the relationship between weighted maturity and compressive strength in the temperature range from 5 to 65 °C for a concrete mix: ## For certain cement types, these C values are recommended:

C = 1.25 for CEM I 32.5R, CEM I 52.5, CEM I 52.5R, and CEM II/B-V 32.5R. C = 1.65 for CEM III/B 42.5 LH HS C = 1.60 for CEM II/B 42.5 LH HS plus C = 1.0 for CEM III/A 52.5 and CEM V/A 42.5

## Overview of the different methods for determining the maturity level Even in long-term applications, i.e. after the actual concrete maturity has been completed, monitoring the concrete quality is useful. Learn more about how ConcR sensors can benefit you in this regard by contacting us today!
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