## 4 Conclusions  
(1) For closely spaced twin tunnels with staggered inlet and outlet, the air flow discharged from their air-exhausting tunnels would diffuse transversely toward the air-inlet tunnels under the influence of the negative-pressure zone at the inlet, even causing inverse flow and forming circulating air. Parameters including inlet air velocity \(u_{\text{in}}\), outlet air velocity \(u_{\text{out}}\), lateral distance of the tunnel portals \(d\), and staggered distance \(\Delta l\) were all important factors influencing the circulating air.  
(2) Both reducing inlet air velocity \(u_{\text{in}}\) and increasing outlet air velocity \(u_{\text{out}}\) and lateral distance d can reduce the impact of the negative-pressure zone at the tunnel entrance on the jet flow structure at the tunnel exit, thus weakening the circulating air.  
(3) When the inlet is placed behind or aligned with the outlet (staggered distance \(\Delta l\leq 0\)), under the influence of the negative-pressure zone at the inlet, the jet flow at the outlet deflects entirely. The shorter the longitudinal distance between the inlet and the outlet (the larger the \(\Delta l\)), the more the jet flow deflects; the quicker the jet flow maximum velocity \(u_{\text{max}}\) in the symmetry plane decreases, the higher the circulating air mixing ratio grows.  
(4) When the inlet is before the outlet (\(\Delta l>0\)), the inlet's negative-pressure zone hardly influences the decreasing law of maximum velocity \(u_{\text{max}}\) in the symmetry plane of jet flow between the inlet and the outlet but changes the decreasing law of the jet flow's \(u_{\text{max}}\) in other zones. With the increase of longitudinal distance between the inlet and the outlet (increase of \(\Delta l\)), the decreasing velocity of \(u_{max}\) manifests a law that is at first increasing and then decreasing. Thus, the circulating air mixing ratio also increases first and then decreases.  
(5) The quantitative relation formula of the circulating air mixing ratio for small-spaced twin tunnels with staggered inlet and outlet with air velocity ratio \(u_{\text{in}}/u_{\text{out}}\), lateral distance of the tunnel portals d, staggered distance \(\Delta l\), and tunnel portal hydraulic diameter \(D\) is created by sections. The predictions show a good correlation with measurements. This formula supplements the limitation of the circulating air mixing ratio prediction formula which can be applied only in tunnels with aligned inlet and outlet.  
(6) According to the relation model, predictions in the present research have a good correlation with measured results for tunnels with entrance slope gradients of \(15^{\circ}\) but do not relate well with those of \(20^{\circ}\), which indicates that the front slope gradient of the tunnel portal is also one of factors affecting the circulating air mixing ratio. More in-depth research and further discussions of this will be conducted in the future.  
Figure 17: Comparison of predicted circulating air mixing ratio \(\varphi_{\text{c}}\) with measured results.  
**Funding:** This research was funded by Natural Science Foundation of Zhejiang province (Study on ventilation characteristics and pollutant diffusion mechanisms of close-spaced bifurcated tunnels), Key Research and Development Project of Zhejiang Province (2018C03029), and the Fundamental Research Funds for the Central Universities (Nos. 2017 QNA4023).  
**Conflicts of Interest:** The authors declare no conflict of interest.