# Numerical Studies on Rockbursts in Tunnels with High In Situ Stresses and Geothermally Rich Areas
## 5 Discussion  
### Effect of the Convective Heat Transfer Coefficient  
Timely ventilation and heat dissipation are the keys to ensuring project progress in tunnels in geothermally rich areas. Fans are often used for ventilation and cooling, and the number of fans and the wind speed also affect the convective heat transfer coefficient. Based on the selection basis of the heat transfer coefficient proposed by [PERSON] et al. [23] and [PERSON] et al. [24], the analysis values of the heat transfer coefficient are set as follows: natural ventilation of \(5\,W\cdot\mathrm{m}^{-2}\cdot\mathrm{K}^{-1}\), and forced convection of \(15,25,35,\) and \(45\,W\cdot\mathrm{m}^{-2}\cdot\mathrm{K}^{-1}\)  
Figure 11: Distribution of temperature and the maximum and minimum principal stresses in tunnels with 5 and 10 m radii at different times. (**a**) Minimum principal stress in tunnel (R = 5 m) when \(t\) = 0 h (The value in the red frame is the maximum of the minimum principal stress (compressive)). (**a**’) Minimum principal stress in tunnel (R = 10 m) when \(t\) = 0 h (The value in the red frame is the maximum of the minimum principal stress (compressive)). (**b**) Minimum principal stress in tunnel (R = 5 m) when \(t\) = 24 h. (**b**’) Minimum principal stress in tunnel (R = 10 m) when \(t\) = 24 h. (**c**) Maximum principal stress in tunnel (R = 5 m) when \(t\) = 0 h. (**c**’) Maximum principal stress in tunnel (R = 10 m) when \(t\) = 0 h. (**d**) Maximum principal stress in tunnel (R = 5 m) when \(t\) = 24 h (The value in the red frame is the maximum of the maximum principal stress (tensile)). (**d**’) Maximum principal stress in tunnel (R = 10 m) when \(t\) = 24 h (The value in the red frame is the maximum of the maximum principal stress (tensile)). (**e**) Distribution of temperature in tunnel (R = 5 m) when \(t\) = 24 h. (**e**’) Distribution of temperature in tunnel (R = 10 m) when \(t\) = 24 h.  
Figure 12a shows the temperature change of the tunnel wall within 24 h of cooling foe different heat transfer coefficients. The decrease in the tunnel wall temperature during cooling is not linear, and the greater the heat transfer coefficient is, the greater the temperature reduction on the tunnel wall within the same time. Compared with that of forced ventilation (h = 15, 25, 35, and 45 W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\)), the cooling capacity of natural ventilation (h = 5 W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\)) is much worse. Under all conditions, the cooling rate of the tunnel wall is high at first (\(t\) = 0-3 h), then gradually decreases (t = 3-12 h), and finally tends to be stable (\(t\) = 12-24 h). Figure 12b shows the internal temperature range of the surrounding rock for different heat transfer coefficients at \(t\) = 24 h. The greater the heat transfer coefficient is, the greater the temperature difference formed per unit length (the greater the thermal gradient) and the more obvious the effect of thermal stress [17]. Figure 12c shows that after cooling for 24 h, the maximum compressive stress (locations of concentrated stress are the same as the results of Section 4) decreases, and the maximum tensile stress increases with increasing heat transfer coefficient. When the heat transfer coefficient is 5 W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\), the maximum compressive stress is 53.9 MPa, which is only 1.7 MPa higher than that when the heat transfer coefficient is 45 W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\) (52.2 MPa). However, when the heat transfer coefficient is 45 W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\), the maximum tensile stress is 28 MPa, which is 18 MPa higher than that when the heat transfer coefficient is 5 W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\) (10 MPa). This indicates that, combined with the previous results (Section 4), the reduction in maximum compressive stress caused by cooling is not very obvious (the inhibitory effect on rockbursts is not enhanced) in the later stage of tunnel ventilation.