# Behaviour of Horseshoe-Shaped Tunnel Subjected to Different In Situ Stress Fields
## 5 Conclusions  
This paper presents parametric stability analysis of underground tunnel opening with a focus on two major factors, namely state of in situ stress field and tunnel depth below surface. The results of this sensitivity analysis are used to evaluate the tunnel performance in terms of state of stress-deformation into rock mass after tunnel opening has been excavated. Six failure evaluation criteria have been used herein in this study, namely ratios of tunnel walls convergence, roof sag, floor heave, rock strength, stress concentration, induced-stress and depth of yielding zones into rock mass around tunnel opening. The results indicate that the ratios of wall convergence, roof sag and floor heave increase as both in situ stress and tunnel depth below surface increase. More specifically:  
* The maximum increase in the ratio of wall convergence (e.g., RWCR = \(-\)0.07% and LWCR = 0.034%) is monitored at tunnel perimeter (e.g., at zero-meter lateral distances from the tunnel boundary or key points #2 and #3), in situ stress ratio of 2.5 and tunnel depth of 250 m.
* Additionally, the maximum ratio of roof sag (e.g., RSR = \(-\)0.096%) and floor heave (e.g., FHR = 0.028%) is obtained at tunnel boundary (e.g., reference points#1 and #4, respectively), in situ stress ratio of 2.5 and tunnel depth of 250 m below surface. However, the performance of tunnel opening is satisfactory (e.g., WCR \(<\) 1.5%, RSR \(<\) 0.5% and FHR \(<\) 0.5%). * Additionally, the induced-stresses around tunnel opening increase as both in situ stress ratio and tunnel depth below surface increase. The maximum induced-stress (e.g., \(-\)11 MPa) is found around tunnel left wall at in situ stress ratio of 2.5 and tunnel depth of 250 m below surface. * The stress concentration (SCF) around tunnel opening decreases as both in situ stress ratio and tunnel depth increase. The maximum SCF is found at the tunnel floor (e.g., SCF = 1.23) and depth of 50 m, while the lowest SCF is found at the tunnel left wall (e.g., SCF = 0.15) and depth of 250 m.  
In addition, the strength of rock (SF) around tunnel back deteriorates as in situ stress ratio increases (e.g., SF = 0.95 at K = 2.5), while it deteriorates around the tunnel roof, floor and right wall as tunnel depth increases (e.g., SF = 0.95 at depth = 250 m). Additionally, there is discontinuity in the strength contours of rock around the tunnel when they are intersected by rock joints. * In addition, the depth of yielding zones increases in the rock surrounding tunnel roof (e.g., length of yield zones = 2.32 m) and floor (e.g., length of yield zones = 2.68 m) when in situ stress ratio (e.g., K = 2.5) and depth below surface increase (e.g., depth = 250 m). However, the yielding zones, around tunnel roof (e.g., 1.65 m, 1.93 m & 2.32 m) and floor (e.g., 2.28 m, 2.28 m & 2.68 m), only extend beyond the anchorage length of rock support (e.g., length > 1.5 m) when the tunnel depths reach 150, 200 and 250 ms. Moreover, the normal stress, shear stress and shear displacement along rock yielded joint that runs below tunnel opening at various in situ stress ratios and tunnel depths have been presented and discussed. The results reveal that:  
* The normal stress (e.g., 11.29 Mpa) along the rock yielded joint that passes beneath tunnel opening (e.g., at the centre of tunnel opening) is sharply dropped (e.g., 0.92 Mpa) and the direction of shear stress (e.g., +8.32 Mpa) is reversed (e.g., \(-\)2.64 Mpa) after the joints pass in the vicinity of the tunnel opening. * The latter (e.g., reversal direction of shear stress) indicates slip occurrence which causes inward shear displacement (e.g., maximum shear displacement = 0.0011 m at depth of 250 m) of rock on the underside of the plane of weakness. Conceptualization, W.R.A. and M.A.M.A. ; methodology, W.R.A., M.A.M.A. and J.-G.K.; software, W.R.A., M.A.M.A. and A.K.M. ; validation, W.R.A., A.K.A.H. and M.A.M.A. ; formal analysis, W.R.A., M.A.M.A. and J.-G.K.; investigation, M.A.M.A., A.K.A.H. and A.K.M. ; resources, J.-G.K. and W.R.A.