# Fracture Behaviour of Concrete with Reactive Magnesium Oxide as Alternative Binder
## 2 Materials and Methods
### Experimental Procedure
#### 2.1.3 Tests  
Fracture energy is the quantity of energy required for the propagation of crack through a unitary area. This property is strongly related to the tensile behaviour of the material. Thus, to better analyze the results obtained in the fracture energy test, other mechanical properties of concrete were analyzed (compressive strength, splitting tensile strength, and modulus of elasticity) after 28 days of curing in a wet chamber. The compressive strength of hardened specimens was evaluated according to EN 12390-3 [36]. This test was performed on four specimens of 150 \(\times\) 150 \(\times\) 150 mm. The splitting tensile strength test followed the method presented in EN 12390-6 [37]. This test was performed on three cylindrical specimens of 150 mm diameter \(\times\) 300 mm high. The test procedure used to determine the secant modulus of elasticity is described in LNEC E 397 [38]. This test was performed on two cylindrical specimens of 150 mm diameter \(\times\) 300 mm high.  
The fracture energy (\(\mathrm{G_{F}}\)) was determined using the wedge splitting test (WST) [39], following the procedure described in NT BUILD 511 [40]. WST was performed on four cubic samples of 150 \(\times\) 150 \(\times\) 150 mm tested after 28 days of curing in a wet chamber. \(\mathrm{G_{F}}\) is determined as the average area under the curve of the splitting force-crack mouth opening displacement (CMOD). This method minimizes the effect of weight on the fracture energy, in contrast to other methods [39; 40; 41; 42]. The geometric configuration of the specimens was generated using special moulds in the casting, the guides and the starting notches were made after 15 days of wet curing using a 1 mm diamond saw as shown in Figure 2a,b. The test procedure applies a vertical force (\(\mathrm{F_{v}}\)) at a deformation speed of 0.006 mm/sec that divides the test specimen into two sections. During the test, CMOD was continuously measured with a clip gauge as \(\mathrm{F_{v}}\) increased. After the test, the depth and width of the split surface (\(\mathrm{A_{lig}}\)) were measured.  
Figure 1: Water/binder ratio of each mix concrete (**a**); Abrams cone consistency according to the MgO content (**b**).  
The preparation steps to perform WST are illustrated in Figure 3. The splitting force (\(\rm F_{sp}\)) was determined from WST using Equation (3), where \(\alpha\) is the angle between the wedge and the vertical load line. The area of the splitting force-COMD curve is the energy dissipated during the fracture, \(\rm W_{f,CMOD}\), and is normalized with respect to the total split surface (\(\rm A_{lig}\)) to complement the fracture. This intermediate specific fracture energy is denoted \(\rm G_{F}\) (\(\rm kN/mm\)) and is determined from the test result through Equation (4) [39; 40; 42].  
The double K fracture and the double \(\rm G_{F}\) fracture criteria are based on asymptotic linear superposition, maintaining the relationship of the linear elastic fracture mechanics valid at all points of the splitting force-CMOD envelope. Therefore, the effective double \(\rm K_{I}\) fracture is obtained in terms of equivalent stress intensity factors using the double \(\rm G_{F}\) fracture model. Equation (5) relates the two criteria: double \(\rm K_{I}\) fracture model and double \(\rm G_{F}\) fracture model [43].  
\[\rm F_{sp}=\frac{\rm F_{V}}{2\tan(\alpha)} \tag{3}\]  
\[\rm G_{F}=\frac{\rm W_{f,CMOD}}{\rm A_{lig}} \tag{4}\]  
\[\rm K_{I}=(\rm G_{F}E_{cm})^{\frac{1}{2}} \tag{5}\]  
Figure 2: Illustration of the specimens’ geometry: front view (**a**); top view (**b**).