## 2 Materials and Methods
### Static Fracture Tests  
As mentioned above, three-point bending (3 PB) tests were carried out to determine the selected mechanical fracture characteristics of the investigated composite with alkali-activated slag matrix. The above-mentioned prismatic specimens were provided with an initial notch one day before fracture tests were performed. The central edge notch with a nominal depth of about 1/3 of the specimen's height was made by a diamond blade saw. The span length was set to 120 mm. The specimens were tested at different ages of their hardening, namely at the age of 40, 160, and 530 days. Fracture tests were conducted using the stiff multi-purpose mechanical testing machine LabTest 6.250 with the load range of 0\(-\)250 kN. An arrangement of a static 3 PB fracture test is shown in Figure 4a. The loading process was governed by a constant increment of displacement of 0.02 mm/min during the whole course of testing. The vertical displacement (midspan deflection) \(d\) was measured using the inductive sensor mounted in a special measurement frame placed on the specimens (see Figure 4b). Crack mouth opening displacement (_CMOD_) was measured using a strain gauge mounted between blades fixed on the bottom surface of the test specimens, close to the initial notch (see Figure 4b). The outcome of each test is a vertical force \(F\) vs. \(d\) diagram and \(F\) vs. _CMOD_ diagram. The diagrams recorded during the tests were processed to obtain the correct input values for consecutive diagram evaluations using the selected fracture models described below. In this case, the modification of diagrams covered the elimination of duplicate points, the shifting of the origin of the coordinate system, the smoothing of the diagram, and the reduction of the number of points. The processing of recorded diagrams was performed in GTDiPS software [28], which is based on advanced transformation methods used for the processing of extensive point sequences. The \(F-d\) and \(F-CMOD\) diagrams after the above-mentioned corrections for investigated ages of specimens are introduced in Figure 5.  
Figure 4: Arrangement of static fracture test (**a**), fracture test configuration in three-point bending (3 PB) (**b**) including the measurement frame (1), and the sensors for measuring the midspan deflection (2) and the crack mouth opening displacement (3). Note that in the case of \(F-CMOD\) diagrams, only their part until a peak load is used for consecutive evaluation. Therefore, only the details of these parts are introduced in Figure 5d-f.  
Figure 5: \(F-d\) diagrams (**a–c**) and \(F-CMOD\) diagrams (**d–f**) from 3 PB fracture test for investigated ages of specimens: 40, 160 and 530 days, respectively. 2.4.1. Direct Evaluation of Mechanical Fracture Parameters from \(F-d\) Diagrams  
The value of static modulus of elasticity was calculated from the initial part of the recorded \(F-d\) diagrams according to Stibor [29]:  
\[E=\frac{F_{i}}{4 Bd_{i}}\bigg{(}\frac{S}{W}\bigg{)}^{3}\bigg{[}1-0.387\frac{W}{S}+ 12.13\bigg{(}\frac{W}{S}\bigg{)}^{2.5}\bigg{]}+\frac{9}{2}\frac{F_{i}}{Bd_{i}} \bigg{(}\frac{S}{W}\bigg{)}^{2}F_{1}(\alpha_{0}) \tag{4}\]  
where \(F_{i}\) is the vertical force in the ascending linear part of the diagram, \(B\) is the specimen width, \(d_{i}\) is the midspan deflection corresponding to the force \(F_{i}\), \(W\) is the specimen height, \(S\) is the span length (see Figure 2b), and  
\[F_{1}(\alpha_{0})=\int\limits_{0}^{\alpha_{0}}xY^{2}(x)dx \tag{5}\]  
where \(\alpha_{0}=a_{0}/W\) is the relative notch depth (\(a_{0}\) is the initial notch depth), and \(Y(x)\) is the geometry function for the 3 PB configuration proposed by [PERSON] and [PERSON] [20]:  
\[Y(\alpha_{0})=1.93-3.07\alpha_{0}+14.53{\kappa_{0}}^{2}-25.11{\alpha_{0}}^{3 }+25.80{\alpha_{0}}^{4}. \tag{6}\]  
Several adaptations of linear elastic fracture mechanics (LEFM) have been proposed to consider the non-linear behavior of quasi-brittle materials in an approximate manner.