Expanded Longitudinal Deformation Profile in Tunnel Excavations Considering Rock Mass Conditions via 3D Numerical Analyses

Abstract

In the convergence–confinement method, the longitudinal deformation profile (LDP) serves as a graphical representation of the actual tunnel convergence (both ahead of and behind the face); therefore, it is considered important for determining the distance of support installation from the face or the timing after excavation in this method. The LDP is a function of the rock mass quality, excavation size, and state of in situ stresses; thus, obtaining the LDP according to the rock mass conditions is essential for analyzing the complete behavior of convergence during tunnel excavation. The famous LDP shows that the best fit for the measured values of tunnel internal displacement reported simply expresses the ratio of the preceding displacement as approximately 0.3. This can lead to an error when predicting the ratio of the preceding displacement while neglecting the rock conditions; consequently, a complete tunnel behavior analysis cannot be realized. To avoid such error, the finite difference method software FLAC 3D is used to develop an expanded longitudinal deformation profile (ELDP) according to the rock mass conditions. The ELDP is represented by graphs featuring different shapes according to the rock mass rating (RMR), and the empirical formula of the LDP best fitted for the tunnel convergence measurement values is expanded. This expanded LDP formula is proposed in a generalized form, including the parameters α and β from the empirical equation. These parameters α and β are expressed as functions of the RMR and initial stress. Statistical analysis results of the 3D numerical analysis of 35 cases were analyzed in the ranges of α = 0.898–2.416 and β = 1.361–2.851; this result is based on the empirical formula of Hoek (1999) (α = 1.1, β = 1.7), which was expanded in the current study according to the rock quality and initial stress conditions.