The Longitudinal Deformation Profile (LDP) is a graphical representation of the radial displacement versus the distances to the tunnel face for an unsupported tunnel section. LDPs can be computed by numerical models. Also, Vlachopoulos and Diederichs [1] have proposed accurate expressions to calculate LDPs for tunnels excavated in elastic perfectly plastic (EPP) rock masses, as a function of the plastic radius that is induced by the excavation. On the other hand, average quality rock masses behave in a strain-softening (SS) manner. This behaviour produces different Ground Reaction Curves to those obtained for an equivalent EPP material. The aim of this paper is the analysis of LDPs using the numerical code FLAC3D. Comparing the LDPs of different quality rock masses under the same confinement, we have observed that the curves are less steep as the GSI of the rock mass diminishes. These differences increased as far as the confinement is greater. We have also found that the fact of accounting for SS behaviour affects LDPs significantly. Moreover, we have made simulations with different values of the dilatancy parameter for SS, and it seems that this parameter does not have great influence in the LDPs.
The estimation of the stresses involved in a tunnel excavation, the control of the deformation of the rock mass and the determination of the distance from the tunnel face where the installation of support and reinforcement is most efficient are key issues in underground tunneling. The face itself carries a significant portion of the load in its surroundings. This As the tunnel face advances, the support will have to carry a greater proportion of the load. Once the face has advanced far enough, there would be no face effect and the support and reinforcement system will be carrying the design load. Therefore, if the support is installed too close to the tunnel face, it would carry an excessive load and if it is installed too far from the tunnel face, excessive deformations may occur. The three basic components of the convergence-confinement method are:
the ground reaction curve (GRC);
the support characteristic curve (SCC); and
the LDP [2].
The LDP is a graphical representation of the radial displacement (tunnel wall deformation) versus the distances to the tunnel face for an unsupported tunnel section, behind and ahead of the tunnel face, along the axis of the tunnel. An accurate description of this LDP is needed to estimate the optimal distance to the face for installing the support. The profile of radial displacements along the axis of the tunnel can be computed by numerical models -for instance, FLAC3D [16]. Vlachopoulos and Diederichs (V&D, in what follows) [1] have performed a series of numerical simulations to determine the LDP for a wide range of EPP rock masses. This has led them to propose more accurate expressions to calculate LDPs, as a function of the plastic radius that is induced in the rock mass by the excavation (see section 1.2).
