A new numerical approach to the hyperstatic reaction method for segmental tunnel linings

Abstract

SUMMARYThis paper proposes a numerical approach to the hyperstatic reaction method (HRM) for the analysis of segmental tunnel linings. The influence of segmental joints has been considered directly using a fixity ratio that is determined on the basis of the rotational stiffness. The parameters necessary for the calculation are presented. A specific implementation has been developed using a FEM framework. This code is able to consider the three-dimensional (3D) effect of segment joints in successive rings on the tunnel lining behaviour. The present HRM allows one to take an arbitrary distribution of segment joints along the tunnel boundary into consideration. In addition, the rotational stiffness of segment joints has been simulated using nonlinear behaviour, as it is closer to the true behaviour of a joint than linear or bilinear behaviour.The numerical results of three hypotheses on ring interaction, which allow the 3D effect of a segmental tunnel lining to be taken into account, have been compared with data obtained from the shield-driven tunnel of the Bologna-Florence high-speed railway line project. The numerical results presented in the paper show that the proposed HRM can be used to effectively estimate the behaviour of a segmental tunnel lining.

The Determination of the Tunnel Structure Loads Through the Analysis of the Interaction between the Void and the Support Using the Convergence-Confinement Method

“…The load acting on the support structure is of fundamental importance to proceed with the evaluation of the stress conditions that develop inside the support: Such an evaluation, which can be conducted through analytical methods (for example the Einstein and Schwartz (1979) method or that of the hyperstatic reaction (Oreste, 2007;Do et al, 2014c), leads to a confirmation of the initial hypotheses on the considered support (typology and dimensions) or to the necessity of varying the typology and/or the geometry of the support in relation to an excessive or lack of strength with reference to the σ Req load to which the support is subjected.…”

“…3 makes it possible to make a quick estimation of the load acting on a support structure, even through interpolation for intermediate values from among those explicitly considered, without needing to conduct specific calculations through the convergence-confinement method. The knowledge of such load values can then be useful for a preliminary dimensioning of a support structure using commonly adopted analytical methods, such as the Einstein and Schwartz (1979) method or the hyperstatic reaction method (Oreste, 2007;Do et al, 2014c).…”

“…The most common support dimensioning methods that are based on analytical approaches, such as the hyperstatic reaction method (Oreste, 2007;Do et al, 2014c) and the Einstein and Schwartz (1979) method, are very fast to use and allow parametric analyses, which are very useful in the preliminary design phases, to be developed. Moreover, these methods, because of the velocity that can be reached in the definition of the calculation model, in the development of the calculations and in the interpretation of the results, make it possible to develop probabilistic analysis (Oreste, 2005a), which are very useful in the geotechnics field, due to the elevated uncertainty that generally characterizes the ground parameters.…”

Behaviour of segmental tunnel linings under seismic loads studied with the hyperstatic reaction method

“…This paper has the aim of proposing the use of a numerical procedure to the hyperstatic reaction method (HRM) in order to analyse of segmental tunnel linings exposed to seismic loads. This method has been developed on the basis of the HRM that was proposed by Oreste [14], and then developed by Do et al [15,16]. Seismic loads are determined on the basis of in-plane shear stresses which were introduced in the works of Peinzen and Wu [3] and El Naggar et al [13].…”

Simplified Analysis of the Lining Behavior During Earthquakes in Deep Rock Tunnels

“…In recent times, many analytical methods have been developed in the tunneling field, to resolve static problems of great importance (Oreste, 2007;Do et al, 2014c). The analytical methods require computing time remarkably low and permit, therefore, to develop parametric analyzes (Oreste, 2014b;2014c), probabilistic ones (Oreste, 2005a) or back-analysis (Oreste, 2005b), all very useful in the design phase or during the construction of a tunnel.…”