# Behaviour of Horseshoe-Shaped Tunnel Subjected to Different In Situ Stress Fields
###### Abstract  
At great depths, tunnel openings experience a tectonic stress field rather than overburden stress. This paper aims to examine the impact of different in situ stress ratios and multiple tunnel depths below the surface on the excavation induced-stresses and displacements around tunnel openings. Thus, a series of models has been built, using a two-dimensional elasto-plastic finite-elements code, RS2D, to conduct parametric stability analysis. The performance of tunnel opening is examined by evaluating the induced stress-deformation around the opening. The results indicate that ratio of wall convergence, roof sag and floor heave increase as in situ stress ratio and tunnel depth below surface increase. Additionally, the induced-stresses increase as depth and state of in situ stress increase. In addition, the extent of yielding zones into rock mass around tunnel roof and floor deteriorates as tunnel depth and in situ stress ratio increase. Moreover, the normal stress along rock joints is sharply dropped when joints pass in the vicinity of tunnel opening (e.g., centre of opening). As well, the direction of shear stress along joints is reversed. Consequently, inward shear displacement of rock, on the underside of the weakness plane, is produced as a result of slip occurrence. in situ stress ratio; tunnel depth; tunnel parametric stability analysis; finite-elements +
Footnote †: journal: Applied sciences  
failure mechanism (e.g., stress-deformation response) is mainly affected by the in situ stress field (e.g., magnitude and direction). Consequently, high induced-stress may cause severe damage to the rock mass surrounding the tunnel opening and therefore leads to detrimental performance effects [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. Additionally, an effective support system will not be efficiently designed unless rock mass properties, around the opening, are well-addressed in advance (e.g., before excavating the tunnel opening). Excavating an opening into rock mass disrupts the initial state of stress before opening has been introduced. Thereby, new stress regime is induced in the vicinity of the opening. Such stress (e.g., induced) is directly related to the in situ stress that primarily depends on the depth of overburden, weight of overlying rock, presence of geological features and the characteristics of rock mass. Consequently, a tremendous hazard may result due to high in situ stress, particularly at great depths. Alternatively, brittle or shear failure may result if the rock surrounding the tunnel opening is overstressed. Thus, it is strongly recommended to specify the magnitude and direction of in situ stress to evaluate their effect on stability of underground openings [25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. As mentioned beforehand, the stability assessment of underground openings is inevitably a prerequisite for the rational design of large underground excavations in rock (e.g., to determine whether they stand-up without the need for secondary support or not) [39; 40; 41]. Such stability is significantly affected by many factors such as: rock mass properties (e.g., cohesion, friction angle, modulus of deformation and presence of discontinuities), opening geometry (e.g., shape and size) and stress state surrounding the openings. Experimental, analytical (empirical) and numerical methods can be employed to investigate the state of stress-displacement around the openings. Each method has its merits and shortcomings. However, the latter (e.g., numerical simulation) is the most robust, reliable and effective method [42; 43; 44]. Therefore, it has been more frequently adopted in practice to evaluate the stability of underground openings and to design rock support systems. In addition, many authors [45; 46; 47; 48] have said that the numerical analysis is necessary to investigate the mechanical behaviour of rock mass surrounding the tunnel opening, if the tunnelling problem is not axisymmetric (e.g., tunnel cross-section is not circular or in situ stress field is not hydrostatic).