## 2 Materials and Methods  
The proposed method is based on [13], which evaluates the strength of the cement-based concrete by the Nurse-Saul maturity method. The above method was previously determined based only on the principle of temperature accumulation over time (see Equation (1)). \[M(t)=\sum(T_{a}-T_{0})\Delta t \tag{1}\]  
where:  
\(M(t)\)--the temperature-time factor at age \(t\), degree-days or degree-hours;  
\(\Delta t\)--a time interval, days or hours;  
\(T_{a}\)--average concrete temperature during time interval \(\Delta t\), \({}^{\circ}\)C;  
\(T_{0}\)--datum temperature, \({}^{\circ}\)C.  
The Nurse-Saul method for calculating the maturity of concrete has been improved by including the parameter of ambient humidity and ambient temperature in the basic formula of maturity. Here, the impact of internal humidity in a gaseous stage was not considered as, according to the system equilibrium theory, the inner pores always tend to be fully saturated. In addition, depending on changes in temperature and pressure, processes of evaporation or condensation occur so that the moisture remains fully saturated in closed pores [20]. Thereby, the maturity gains a complex sense and is referred to as complex maturity \(M_{c}\), which includes 3 parameters: internal temperature (IT), ambient temperature (AT) and ambient relative humidity (ARH), which may be expressed by Equation (2). \[M_{c}=\sum M_{i}\overline{\gamma}_{i}=M_{IT}\cdot\overline{\gamma}_{IT}+M_{AT }\cdot\overline{\gamma}_{AT}+M_{ARH}\cdot\overline{\gamma}_{ARH} \tag{2}\]  
\[M_{IT}=M(t);\quad M_{AT}=\sum(AT\cdot\Delta t);\quad M_{ARH}=\sum(ARH\cdot \Delta t); \tag{3}\]where: \(i\)--parameters affecting the concrete strength gain, such as IT, AT, and ARH; \(M_{i}\)--maturity of \(i\) parameter, such as IT, AT, and ARH, expressed by Equation (3). \(\overline{\gamma}_{i}\)--average weight of \(i\) parameter for 28 days of curing that is calculated by Equation (4) below. \[\overline{\gamma}_{i}=\frac{1}{28}\sum_{t=1}^{28}\gamma_{i,t} \tag{4}\]  
Regarding the aforementioned IT, AT, and ARH, Equation (4) may be extended in Equation (5):  
\[\overline{\gamma}_{IT}=\frac{1}{28}\sum_{t=1}^{28}\gamma_{IT,t};\quad\overline {\gamma}_{AT}=\frac{1}{28}\sum_{t=1}^{28}\gamma_{AT,t};\quad\overline{\gamma}_ {ARH}=\frac{1}{28}\sum_{t=1}^{28}\gamma_{ARH,t}; \tag{5}\]  
Here, the value of the weight of the \(i\) parameter (namely IT, AT, and ARH) at the age of \(t\) (\(\gamma_{i,t}\)) is calculated by Equation (6) below. \[\gamma_{i,t}=\frac{|r_{i,t}|}{\sum|r_{i,t}|} \tag{6}\]  
where: \(r_{i,t}\)--is a correlation coefficient between the \(i\) parameter (IT, AT, and ARH) and the strength of the concrete at curing age of \(t\) (from 1 to 28 days). It should be noted that the sum of the weights is always equal to 1 (Equation (7)). \[\sum\gamma_{i,t}=\sum\overline{\gamma}_{i}=1 \tag{7}\]  
By monitoring the internal and ambient temperature and relative humidity for 28 days every 0.5 h and obtaining the compressive strength (CS) for certain types of concrete mixture at each period of time (Table 1), it is possible to calculate the maturities corresponding to each parameter (Table 2) and to determine the trend line for the complex maturity-strength relationship. To examine the proposed concept: a batch of cement-based concrete mixture of class B25 and grade M350 was retrieved from an operating concrete mixture manufacturing plant. The concrete mixture was used to prepare 17 vertical cylindrical samples with a diameter of 15 cm and a height of 15 cm [21], 15 cubes with an edge size of 10 cm [14] and 2 boxes 50 \(\times\) 50 \(\times\) 50 cm in size [22] at once, depicting the real structures on the site. All the samples and boxes were kept at the same temperature and humidity conditions. For compression testing on the 1 st, 3 rd, 7 th, 14 th and 28 th days, 15 cylindrical and 15 cubic samples were prepared to be used in batches, three pieces at a time.