# Behaviour of Horseshoe-Shaped Tunnel Subjected to Different In Situ Stress Fields
## 4 Discussion  
Case I represents an examination of the effect of in situ stress ratio on tunnel opening performance. In the light of rock mass deformation results, it can be said that the performance of tunnel opening is satisfactory (e.g., maximum WCR in the tunnel walls \(<\) 1.5%, RSR \(<\) 0.5% and FHR \(<\) 0.5%). Alternatively, the maximum deformations ratios occur at in situ stress ratio K of 25 in tunnel right wall (RWCR), left wall (LWCR), roof sag (RSR) and floor heave (FHR) are \(-\)0.0148%, 0.0046%, \(-\)0.0148% and \(-\)0.01006%, respectively. As the in situ stress increases, the shear stress increases. For instances, the minimum shear stresses along rock joints, when they pass the tunnel opening, are \(-\)0.26 MPa and \(-\)0.707 MPa at in situ stress ratios K of 25 and 0.5, respectively. Additionally, the shear stress ranges from \(-\)0.26 MPa to 1.52 MPa at \"K\" equals 2.5, while it ranges from \(-\)0.707 MPa to 0.102 MPa when \"K\" equals 0.5. Thereby, the reversal of shear stress indicates slip occurrence. Such slip causes inward shear displacement of rock on the underside of the plane of weakness. In addition, shear displacements increase as in situ stress K increases. For instances, the shear displacements along rock joints are \(-\)4.52 \(\times\) 10\({}^{-5}\) and \(-\)1.71 \(\times\) 10\({}^{-5}\) ms at in situ stress ratio K of 0.5 and 2.5, respectively. Shear displacement ranges from \(-\)4.52 \(\times\) 10\({}^{-5}\) m to 6.83 \(\times\) 10\({}^{-6}\) m at in situ stress ratio K of 0.5 and it ranges from \(-\)1.71 \(\times\) 10\({}^{-5}\) m to 0.00024 m when in situ stress ratio equals to 2.5. Irrespective of these insignificant shear amplitudes. They do, but nevertheless, demonstrate the incidence of a slip. In other words, rock mass rotation is expected to be associated with shear displacement. Case II investigates the effect of tunnel depth below the surface on its stability performance. It can be shown that, as depth extends below surface, the ratio of convergence increases. The maximum RWCR is found at tunnel depth of 250 m (e.g., measured at zero distance from key point #3 on tunnel perimeter) is \(-\)0.07%. The maximum LWCR is 0.0344% at tunnel depth of 250 m (e.g., monitored at zero distance from key point #2 on tunnel boundary). However, these results reveal that the ratio of convergence increases as depth extends below surface, but stability of tunnel is still satisfactory (e.g., WCR \(<\) 1.50%). The maximum roof sag ratio (e.g., RSR \(=\)\(-\)0.096%) is found at zero-meter vertical distance from the tunnel boundary (e.g., key point #1), while the maximum ratio of floor heave (FHR \(=\) 0.028%) is measured at zero-meter vertical distance from the tunnel floor boundary (e.g., reference point #4). The tunnel unsatisfactory performance is reached when the roof sag ratio (RSR \(>\) 0.5%) and floor heave ratio (FHR \(>\) 0.5%) exceed 0.5%. Therefore, according to the obtained results, tunnel opening is still stable. In terms of induced stress, rock mass around the tunnel would fail in tension (e.g., brittle shear failure). At tunnel  
Figure 25: Shear displacement along a rock yielded joint that runs beneath the tunnel opening at different tunnel depth below surface. depth of 50 m, the induced-stresses around tunnel roof/back, floor, right wall (RW) and left wall (LW) are 0.13, 0.57, \(-\)0.62 MPa and \(-\)2.31 MPa, while, at 250 m tunnel depth, they become \(-\)9.9 MPa, \(-\)8.9 MPa, \(-\)6.9 MPa and \(-\)11 MPa, respectively. The induced-stresses indicate the failure mechanism of rock mass. Induced stress values that are negative may indicate high in situ stresses, especially at great depths. Compressive stress is indicated by the negative sign. The state of equilibrium and uniformly distributed in situ stresses are disturbed after excavating the tunnel opening. As a result, an elasto-plastic deformation occurs following the removal of rock mass within the tunnel. The shape of the underground opening determines whether in situ stresses are distributed uniformly or not.