###### Abstract  
The maturity method is deservedly considered one of the reliable indirect methods for determining the strength at the early stages of concrete curing. The main parameter in the calculation is the internal temperature of concrete that accumulates during the chemical reaction of concrete curing, while external factors such as ambient temperature and relative humidity are fallaciously omitted. In this work, the complex maturity method was developed based on ASTM C1074, accounting for the influence of ambient temperature and relative humidity and coefficients indicating their influence weight. The laboratory testing to measure the concrete strength by compression method and non-destructive sclerometer method were performed on concrete samples according to ASTM C109, GOST 22690, and GOST 10180. According to the calibration dependence of the existing and proposed methods results in comparison with the strength of cubic samples, the highest coefficient of determination R\({}^{2}\) = 0.976 was revealed for temperatures, although [8] specified that the core compressive strength from the mid-section was within \(\pm\)15% of the predicted values and core results from the bottom section were generally higher than the predicted values. Ref. [9] has reviewed and studied the rate of temperature increase during concrete curing in detail, but also predicted the strength gain over the curing and tested a wide range of test settings for ambient temperature and different concrete mixtures. Ref. [10] considered various curing conditions in the laboratory and on-site, where he evaluated the strength-maturity relationship by Nurse-Saul and Arrhenius maturity functions, and stated that the considered methods are only accurate for the first 7 days of concrete curing. [PERSON]. [11; 12] carried out the experimental and modelling study on the influence of curing temperature (T) and relative humidity (RH) on the compressive strength gain of cement mortars and determined that both of the parameters affect the strengthening rate, especially at the curing period. Despite the fact that numerous attempts have been made to account for the influence of external parameters such as ambient temperature and humidity, there is no unified method for calculating the complex maturity to date, which would most accurately convey the state of concrete strength during the curing. Thus, it turns out that ambient relative humidity and ambient temperature significantly affect the maturity and strength relationship of concrete; however, this process was overlooked in [13; 14], and in other sources [15; 16; 17; 18; 19]. The main parameter in the calculations is the internal temperature of the concrete that accumulates during the chemical reaction of concrete maturation, while external factors such as ambient temperature and relative humidity were wrongly ignored.  
The purpose of this study is to develop a detailed methodology to calculate the complex maturity, accounting for the external and internal parameters such as internal and ambient temperature and ambient relative humidity, which would weigh the influence ratio of each parameter and most accurately convey the relationship of gained strength with the maturity of concrete over curing time. A complex maturity method was developed based on ASTM C1074, accounting for the influence of ambient temperature and relative humidity, as well as coefficients indicating their influence on weight.