Shotcrete lining is one of the most frequently used tunneling supports. As shotcrete lining is placed near the excavation face, the radial pressure on the lining develops when the excavation face advances through time. Furthermore, the mechanical properties of shotcrete lining increases over time, which make the problem more complicated. This paper presents a new analytical-numerical method which can solve the convoluted interaction of shotcrete lining and surrounding rock mass. In this work, by using a general equation indicating the structural behavior of shotcrete lining, the expression of radial pressure inside the lining versus radial wall displacement is obtained. The proposed method develops the reaction curve of the supported tunnel considering the effect of shotcrete hardening, the face advancement rate, and therefore the gradual loading on tunnel lining; thus, the reaction curve of the supported tunnel substitutes for the ground response curve and shotcrete lining reaction curve. Inasmuch as the interaction problem has numerous parameters, in no way is it possible to obtain an analytical solution. As most of the existing elasto-plastic solutions for tunnel problems in Hoek-Brown media consider an intact rock, because of numerical nature of the proposed method, the interaction of shotcrete lining with the generalized Hoek-Brown materials is also possible. Finally, an example has illustrated how this method works.


Tunnel excavation disturbs the state of stress and the ground stiffness around the opening. Ground-support interaction is a consequence of resistance with which the support reacts against the movement of the surrounding ground into the excavated opening. Estimation of the support required to stabilize a tunnel opening, especially in the vicinity of the tunnel face, is an essentially 4 dimensional problem. Since the behavior of the rock mass is time-dependent, the tunnel problem is no longer three dimensional. Moreover, as the properties of the surrounding ground has significant effect on the loads acting on a liner, the ground support interaction is not just a structural problem and requires thorough understanding of both the ground and support behaviors. The study of the interaction between support structures can easily be carried out by simplified plane strain models, which are strongly dependent on the assumed degree of ground stress relief at the time of lining installation. The ‘convergence-confinement’ method (CCM), based on the simplified assumption of a circular tunnel in a hydrostatic stress field, is such a tool (AFTES, [1]). This method is discussed later in detail. Nowadays shotcrete lining is widely used as a first and fundamental support element for tunnels driven by conventional excavation methods in rock masses. The shotcrete lining is generally applied near the tunnel face when a part of the load that is distributed around the excavation is carried by the face itself. As the tunnel face advances, by decreasing the face effect, the gradual loading of shotcrete lining takes place which is coincident with an increase in mechanical properties of shotcrete lining; therefore, the most critical point may occur before the full strength of shotcrete is reached.

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