## 2 Experimental Procedure
### Estimation of Stress Intensity Factors  
The method for estimating mode I and mixed-mode I-II stress intensity factors is proposed here, based on the displacement fields determined via the DIC method. The displacement fields around a crack tip of the concrete specimen are expressed as Equation (3):  
\[\left\{ \begin{array}{l}u_{x}\\ u_{y}\end{array} \right\} =\sum\limits_{n=1}^{\infty}\frac{A_{\rm II}}{2\mathcal{C}_{t}}r^{ n/2}\left\{ \begin{array}{l}\kappa\cos\frac{\eta}{2}\theta-\frac{\eta}{2}\cos( \frac{\eta}{2}-2)\theta+\left\{\frac{\eta}{2}+\left(-1\right)^{n}\right\} \cos\frac{\eta}{2}\theta\\ \kappa\sin\frac{\eta}{2}\theta+\frac{\eta}{2}\sin(\frac{\eta}{2}-2)\theta- \left\{\frac{\eta}{2}+\left(-1\right)^{n}\right\}\sin\frac{\eta}{2}\theta\\ \kappa\sin\frac{\eta}{2}\theta-\frac{\eta}{2}\sin(\frac{\eta}{2}-2)\theta+ \left\{\frac{\eta}{2}-\left(-1\right)^{n}\right\}\sin\frac{\eta}{2}\theta\\ -\kappa\cos\frac{\eta}{2}\theta-\frac{\eta}{2}\cos(\frac{\eta}{2}-2)\theta+ \left\{\frac{\eta}{2}-\left(-1\right)^{n}\right\}\cos\frac{\eta}{2}\theta \end{array} \right\} \tag{3}\]  
The \(u_{x}\) and \(u_{y}\) are the displacement components in the specimen considered, and \(G\) is shear modulus. The \(\kappa\) is \((3-\mu)/(1+\mu)\) for plane stress, and \(r\) and \(\theta\) are the polar coordinates around a crack tip, as shown in Figure 2.  
In the series solutions, the coefficient of the first terms \(A_{\rm II}\) and \(A_{\rm III}\) are related to stress intensity factors \(K_{\rm I}\) and \(K_{\rm II}\) of mode I and mode II through the relations of Equation (4). \[A_{\rm II}=\frac{K_{\rm I}}{\sqrt{2\pi}},\,A_{\rm III}=-\frac{K_{\rm II}}{ \sqrt{2\pi}} \tag{4}\]  
For the cases of mode I fracture, the displacement component of the specimen is perpendicular to the crack surface. This means that the \(u_{y}\) displacement field can be generally used to determine the stress intensity factors. In mixed-mode cases, however, the dominant displacement component for the crack can't be predicted before analysis. Therefore, radial \(u_{r}\) and circumferential displacement components \(u_{\theta}\) on a polar coordinate system are used in this study to transform Cartesian displacements \(u_{x}\) and \(u_{y}\). The displacements \(u_{r}\) and \(u_{\theta}\) are obtained as Equation (5):  
Figure 2: Coordinate system around a crack tip. \[\left\{ \begin{array}{c}u_{r}\\ u_{\theta}\end{array} \right\}=\left[ \begin{array}{c}\cos\theta\sin\theta\\ -\sin\theta\ \cos\theta\end{array} \right]\left\{ \begin{array}{c}u_{x}\\ u_{y}\end{array} \right\} \tag{5}\]  
The displacement fields in Equation (5) can, hence, be rewritten as Equation (6):  
\[\left\{ \begin{array}{c}u_{x}\\ u_{y}\end{array} \right\}=\sum\limits_{n=1}^{N}A_{\text{In}}\left\{ \begin{array} []{c}f_{\text{In}}(r,\theta)\\ g_{\text{In}}(r,\theta)\end{array} \right\}-\sum\limits_{n=1}^{N}A_{\text{In} }\left\{ \begin{array}{c}f_{\text{In}}(r,\theta)\\ g_{\text{In}}(r,\theta)\end{array} \right\} \tag{6}\]  
The \(N\) is the number of terms of the series expansion of the displacement field. From Equations (5) and (6) with rigid-body displacements taken into account, the displacement fields can be expressed as Equations (7) and (8):  
\[