## 4 Discussion  
The aforementioned results were obtained under the premise that joint development is not considered. In practice, joints will develop, and adjacent joints will connect and merge under mechanical loading. However, this study focuses on the effect of existing joints on the tensile properties.  
The change in the number of joints can be considered as a change in the degree of development of fractures of the rock mass. Then, the geological strength index (_GSI_) is introduced [10]. _GSI_ is generally used to calculate the strength and Young's modulus of a rock mass through laboratory rock mechanics properties and rock mass structural surface parameters. Figure 17[38] is a _GSI_ quantization table based on rock mass structures and surface features of the structures.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(n\) & \(\sigma_{t}\) **(MPa)** & \(E_{t}\) **(GPa)** \\ \hline \(n=2\) & 0.93 & 0.73 \\ \(n=4\) & 0.93 & 0.58 \\ \(n=6\) & 0.93 & 0.50 \\ \(n=8\) & 0.93 & 0.44 \\ \(n=10\) & 0.93 & 0.38 \\ \(n=12\) & 0.93 & 0.34 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Mechanical behaviors of rock specimens with different numbers of intersection joints.  
Figure 16: The relationship between \(n\) and \(E_{t}\) under the different values of \(\beta\).  
For rocks with a uniaxial compressive strength (\(\sigma_{ci}\)) \(<\) 100 MPa, the elastic modulus of a rock mass (\(E_{t}\)) is estimated from the following equation [39]:  
\[E_{t}=\left(1-\frac{D}{2}\right)\sqrt{\frac{\sigma_{ci}}{100}}\times 10^{(\frac{GS +10}{40})} \tag{1}\]  
where \(\sigma_{ci}\) is the uniaxial compressive strength of intact rock, and \(D\) is a factor that depends on the degree of disturbance to which the rock mass has been subjected by blast damage and stress relaxation. When \(D=0\), the relationships between \(E_{t}\) and \(GSI\) under the conditions of different values of \(\sigma_{ci}\) are shown in Figure 18a. With the increase of the development of rock mass fissures, the Young's moduli decline notably. The degradation patterns with the number of parallel and intersection joints are illustrated in Figures 19a and 20a, respectively, which agree with the numerical results presented in the previous sections.  
Figure 17: Quantitative chart of the geological strength index (\(GSI\)).  
Figure 19: Effect of the number of parallel fractures on \(E_{t}\) and \(\sigma_{t}\). (**a**) Effect of the number of fractures on \(E_{t}\),(**b**) Effect of the number of fractures on \(\sigma_{t}\).  
Figure 20: Effect of the number of intersecting parallel fractures on \(E_{t}\) and \(\sigma_{t}\). (**a**) Effect of the number of fractures on \(E_{t}\) (**b**) Effect of the number of fractures on \(\sigma_{t}\).  
According to the generalized Hoek-Brown peak strength criterion [40], the tensile strength of a rock mass is:  
\[\sigma_{t}=-s\sigma_{ci}/m_{b} \tag{2}\]  
where \(m_{b}\) is the reduced value of the material constant \(m_{i}\) for the rock mass, and is given by:  
\[.m_{b}=m_{i}\exp[\left({GSI-100}\right)/(28-14D)] \tag{3}\]  
and \(s\) is the rock mass constants, given by:  
\[s=\exp[\left({GSI-100}\right)/(9-3D)] \tag{4}\]  
When \(D=0\), the relationships between \(\sigma_{t}\) and \(GSI\) under the conditions of different values of \(\sigma_{ci}\) are shown in Figure 18b. In a certain interval, the influence on the tensile strength is negligible with the increase of the development of rock mass fissures. Then, the rationalities of the conclusion in this paper were proved, as illustrated in Figures 19b and 20b.