## 2 Experimental Program
### Experimental Methods
#### 2.4.3 Fracture Performance Test  
The fracture performance test of concrete was carried out by the \"Norm for fracture test of hydraulic concrete\" (DL/T5332-2005) [37]. The concrete specimen size was 100 mm \(\times\) 100 mm \(\times\) 515 mm. The WAW-1000 electro-hydraulic servo universal testing machine was used. A three-point bending loading device was adopted, whose loading pad was a steel bar of 120 mm \(\times\) 10 mm \(\times\) 5 mm. A load sensor of model JLBU-30 was adopted, whose measuring range was 30 kN. The YHD-30 displacement sensor was used to record  
Figure 4: Schematic diagram of flexural resistance test. the mid-span deflection of the specimen. The clip extensometer fixed by a 0.5 mm blade on both sides of the prefabricated crack of the specimen was used to measure the crack mouth opening displacement (CMOD) value of concrete crack tensile opening displacement. A DH3818Y static strain tester was used to collect the above data. Before the test, it was necessary to record the parameters, such as the size, quality, and length of the prefabricated crack of the specimen. Then, the specimen was installed on the supports. A steel sheet was pasted at the bottom of the other side of the specimen to install the displacement sensor, and then a loading pad and load sensor were placed on the top of the specimen. The test loading device is shown in Figure 5. The equipment was started during the test, and the data acquisition system was open when the load sensor was almost in contact with the loading device. The equipment was loaded at a rate of 0.1 mm/min until the specimen was destroyed. The initial fracture toughness, instable fracture toughness, and fracture energy were calculated using the double-K fracture model [37; 38]. The initial fracture toughness, \(K^{\text{Q}}_{\text{IC}}\)(MPa.m\({}^{1/2}\)), and instable fracture toughness, \(K^{\text{S}}_{\text{IC}}\)(MPa.m\({}^{1/2}\)), were calculated by Equation (3) and Equation (4), respectively. The initial fracture toughness is:  
\[K^{\text{Q}}_{\text{IC}}=\frac{1.5(F_{\text{Q}}+0.5 mg\times 10^{-2})\times 10^{-3} S\sqrt{a_{\text{c}}}}{th^{2}}f(\alpha) \tag{3}\]  
The instable fracture toughness is:  
\[K^{\text{S}}_{\text{IC}}=\frac{1.5(F_{\text{max}}+0.5 mg\times 10^{-2})\times 10^{- 3}S\sqrt{a_{\text{c}}}}{th^{2}}f(\alpha) \tag{4}\]  
where _f(\(\alpha\))_ is calculated according to Equation (5):  
\[f(\alpha)=\frac{1.99-\alpha(1-\alpha)(2.15-3.93\alpha+2.7\alpha^{2})}{(1+2 \alpha)(1-\alpha)^{1.5}};\alpha=\frac{a_{\text{c}}}{h} \tag{5}\]  
where \(F_{\text{Q}}\) (kN) is the initial cracking load; \(F_{\text{max}}\) (kN) is the maximum load; \(m\) (kg) is the quality of the specimen between the beam supports; \(g\) is the acceleration of gravity, which is 9.81 m/s\({}^{2}\); \(t\) (m) is the thickness of the specimen; \(h\) (m) is the height of the specimen. \(a_{\text{c}}\) (m) is the effective crack length, which is calculated by Equation (6):  
\[\alpha_{\text{c}}=\frac{2}{\pi}(h+h_{0})\text{arctan}\sqrt{\frac{tEV_{\text{ c}}}{32.6F_{\text{max}}}-0.1135}-h_{0} \tag{6}\]  
Figure 5: Schematic diagram of fracture test. where \(h_{0}\) (m) is the thickness of the blade steel plate; \(V_{\rm c}\) (\(\upmu\)m) is the critical value of crack opening displacement. \(a_{0}\) (m) is the initial crack length; \(E\) (GPa) is the calculated elastic modulus, which is calculated by Equation (7):  
\[E=\frac{1}{tc_{i}}[3.70+32.60\tan^{2}(\frac{\pi}{2}\frac{a_{0}+h_{0}}{h+h_{0}})] \tag{7}\]  
where \(a_{0}\) (m) is the initial crack length; \(c_{i}=V_{\rm i}/F_{\rm i}\) (\(\upmu\)m/kN) is calculated from any point in the straight segment of the rising section of the \(F\)-\(V\) curve. The fracture energy is expressed by the area that is enclosed by the load-deflection curve (\(F\)-\(\delta\) curve) of the three-point bending test, i.e., the energy required for crack growth per unit area.