## 6 Conclusions  
In order to undergo economical and efficient excavation process by using the non-vibrational rock splitting method, the increase in borehole spacing values plays a great role. For this purpose, discrete element analysis of this method was performed using PFC\({}^{\text{2D}}\) code and feasible borehole spacing values to be used in different types of intact rock are proposed in this study. The concept of Representative Elementary Volume was used to simulate intact rocks based on their unconfined compressive strength and modulus ratio concept. The modulus ratio is defined as the ratio of Young's modulus to unconfined compressive strength of intact rock. Based on unconfined compressive strength, the intact rock was classified into soft rock, normal rock, and hard rock and their respective UCS values were used as 50, 100 and 150 MPa. Based on modulus ratio concept, the three intact rock types were further classified into high modulus ratio (550:1), average modulus ratio (300:1), and low modulus ratio (150:1). Rock splitting models were prepared for different types of intact rock and maximum borehole spacing values were recorded in each case by performing rock splitting process using 20 mm splitting width and 1.4 m borehole depth. The numerical analysis results show that increased values of borehole  
Figure 17: Effect of borehole depth on maximum borehole spacing values at different intact rock strengths (high modulus ratio).  
spacing can be used for all rock types when the intact rock has average modulus ratio and high modulus ratio. The maximum borehole spacing results for low modulus ratio were obtained slightly less than the typically used values. Therefore, it is important to consider the modulus ratio of the intact rock when the non-vibrational rock splitting method is used for excavation purposes. Furthermore, numerical simulations were performed to analyze the effects of borehole depth on maximum borehole spacing in all types of intact rock. Three different borehole depths of 1.4 m, 1.3 m and 1.2 m were analyzed using splitting width of 20 mm. The results show that decreasing the borehole depth value in rock splitting process can generally be useful by resulting in the use of increased borehole spacing values for all types of intact rocks. This study is mainly based on the discrete element analysis of the rock splitting process and maximum borehole spacing values in different strengths of intact rock are proposed to be used in non-vibrational rock splitting method. However, the presence of joints and pre-existing fractures as well as the in-situ stresses need to be considered for the future studies. Furthermore, the numerical analysis results obtained in this study also need to be compared with the field testing results or physical model test results.  
This research was supported by Development of Design and Construction Technology for Double Deck Tunnel in Great Depth Underground Space (14 SCIP-B088624-01) from Construction Technology Research Program funded by Ministry of Land, Infrastructure and Transport of Korean government.  
[PERSON] and [PERSON] conceived the main idea. [PERSON] designed the experimental technique and performed the numerical simulations. [PERSON] and [PERSON] wrote the paper.  
The authors declare no conflict of interest.