## 2 Updated NTNU Drill and Blast Prediction Model  
The NTNU D&B model consists of three models for the blast design, advance rate, and excavation cost models. Among these, the advance rate model can estimate the advance rate of tunnel excavation, including drilling, charging, loading and hauling, scaling, and regular rock supports, such as shotcrete and rock bolts, for tunnel cross-sections between 10-120 m\({}^{2}\)[22; 26]. The tunnel geometry, blast design parameters (drillhole diameter and length and type of explosives), and rock properties (i.e., blastability and wear quality) are considered in the model. For a fast calculation of the advance rate and excavation cost, a simulation tool, TUNSIM (Tunnel Simulation), was developed as an Excel spreadsheet [26], with which the effect of variation in any input parameter related to the advance rate and excavation cost could be calculated. Since the NTNU model is an empirical model established through investigations on the time spent on detailed operation activities, the time calculation for every operation is performed by the combination of detailed sub-operation time as depicted in Figure 1.  
The analysis of the construction time and advance rate in the TUNSIM; however, is available only for the excavation, without considering the rock supports and installations in the tunnel [28]. In addition, even though the rock properties such as the Rock Blastability Index (SPR of \"SPRengbarhet\" in Norwegian, rock blastability), Drilling Rate Index (DRI), and Vickers Hardness Number Rock (VHNR) that are produced from lab tests are used in the model, the effects of the rock mass quality, which is generally used in a tunnel by the Q-value or RMR, are not considered. Thus, in this study, TUNSIM-Q, updated in 2009 [29; 30] and based on project reports of NTNU [31; 32], is used, where the effects of rock properties such as SPR, DRI, VHNR, as well as the rock mass quality in the Q-value, can be considered. In addition, the usual tunnel supports and various installation methods such as shotcrete, rock bolts, steel ribs, forepooling, water protection, and concrete lining, etc., were included in the updated model. Meanwhile, the construction method of a Korean tunnel that is analysed for this study is different from the one of a Norwegian tunnel, which is the basis of the NTNU model, as well as for the tunnel sizes. For example, rock mass classification is conducted by the Q-value, and a concrete lining is installed for an extremely poor rock mass quality in Norway. On the other hand, the rock mass quality is classified by RMR, and a concrete lining is always installed for the whole length of a tunnel in Korea. Additionally, the amount and kinds of tunnel supports are different. Hence, the NTNU model is slightly modified for this study. Initial SPR, DRI and VHNR are automatically given according to the rock mass quality (Q-value) in the Excel simulation sheets unless they are provided by the user, and the variation of Q-values in the model influences the initial SPR, round/drill length and others factors, as shown in Figure 2.  
Scheme 3 needs to break the rock to a certain degree of fragmentation, where 50% of the blasted rock size is under 250 mm (d\({}_{50}\) = 250 mm) [22]. Furthermore, the variation of SPR leads to the adjustment in time of the number of charge holes, time determinant charging time, incidental lost time, and scaling time. The variation in round/drill length results in an adjustment of the time for drilling and moving to the other holes, as well as the volume of the blasted muck pile. Figure 1: Typical examples of the NTNU advance rate prediction model (Modified from [23]) and TUNSIM-Q. The DRI is determined from the brittleness value, which is a measure of the rock resistance from repeated impacts until crushing, and the SJ value, which is a measure of the rock resistance to miniature drill penetration (surface hardness) [23]. The DRI affects the penetration rate of the charge holes and rock bolt holes in the model.