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

This 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. Copyright © 2014 John Wiley & Sons, Ltd.     

2D Tunnel Numerical Investigation: The Influence of the Simplified Excavation Method on Tunnel Behaviour

Tunnel excavation is a three-dimensional (3D) problem. However, despite recent advances in computing resources, 3D models are still computationally inefficient and two-dimensional (2D) simulations are therefore often used. Modelling the tunnelling process in a 2D plane strain analysis requires a specific approach that allows a 3D tunnelling effect to be taken into consideration. As far as the urban tunnels are concerned, most cases reported in the literature have focused on estimating the applicability of these equivalent approaches that are based on the evaluation of the settlement that develops on the ground surface, without considering the influence of segment joints. The main objective of this study was to provide a 2D numerical investigation to highlight the influence of two equivalent approaches, that is, the convergence-confinement method (CCM) and the volume loss method (VLM), on the behaviour of a tunnel built in an urban area, in terms of not only the surface settlement but also the structural lining forces, taking into account the effect of segment joints. A technique that can be used to simulate the tunnel wall displacement process, based on the principles of the VLM, has been developed using the FLAC^3D finite difference program (Itasca in FLAC fast Lagrangian analysis of continua, version 4.0; User’s manual, http.itascacg.com, 2009). A comparison with 3D numerical results has been introduced to estimate the precision of these 2D equivalent approaches. The results have shown a significant influence of the tunnel boundary deconfinement technique and segment joints on the tunnel lining behaviour and surface settlements. The structural forces obtained by means of the CCM are often smaller than those determined with the VLM for the same surface settlement. Generally, the structural lining forces determined by the CCM are in better agreement with the 3D numerical results than the ones obtained with the VLM. However, in order to obtain an accurate estimation of the structural forces, the impact of the construction loads during tunnelling should be taken into account.     

Shear modulus and damping ratio of grouted sand

An experimental comparative study of three different grouted sands in terms of their effects on the values of two dynamic properties is presented. The dynamic properties studied are the shear modulus and the damping ratio which are determined with resonant column tests and cyclic triaxial tests. The behaviour of a pure Fontainebleau sand is compared with the behaviour of a Fontainebleau sand grouted with a silicate grout, a micro-fine cement grout and a mineral grout. The effects of the grouting treatment, the type of grout, the confining pressure, and the strains, on the shear modulus and the damping ratio are studied. The test results have shown that grouting improves the stiffness of the sand especially for small strains. Whatever the type of material, confining stress improves the shear modulus whereas it has a negligible effect on the damping ratio. When strain increases, the shear modulus decreases and the damping ratio increases.     

Three-dimensional numerical simulation for mechanized tunnelling in soft ground: the influence of the joint pattern

The main purpose of this study was to provide a three-dimensional numerical model, which would allow the tunnel lining behaviour and the displacement field surrounding the tunnel to be evaluated. Most of the processes that occur during mechanized excavation have been simulated in this model. The influence of the lining joint pattern, including segmental lining joints and their connections, has in particular been taken into consideration. The impact of the processes during mechanized excavation, such as the grouting pressure and the jacking forces in the structural forces induced in the tunnel lining, has been presented. These values depend on the tunnel advancement. However, a negligible influence of the joint pattern on the ground displacement field surrounding the tunnel has been observed. Generally, a variation in the structural forces in successive rings along the tunnel axis has been found in a staggered segmental lining, indicating the necessity of simulating the joints in the tunnel lining and using a full three-dimensional numerical model to obtain an accurate estimation. In addition, the considerable influence of the coupling effect between successive rings on the lining behaviour has been highlighted.     

The origin of wide-angle tailed radio galaxies

To investigate the origins of wide-angle tailed radio sources (WATs), we have compiled a sample of these systems in Abell clusters for which X-ray data exist. Contrary to conventional wisdom, the WATs are found to be significantly displaced from the X-ray centroids of their host clusters. The bends in the radio jets of WATs are found to be oriented preferentially such that they point directly away from or toward the cluster centre, with more of the former than the latter. If this morphology is attributed to ram pressure, then the WATs are on primarily radial orbits, with more approaching the X-ray centroid than receding. There is also some evidence that the incoming WATs are on average further from the X-ray centroid than the outgoing ones. All of these observations strongly support a scenario in which WATs are created in cluster mergers.     

Interactions of radio galaxies and the intracluster medium in Abell 160 and Abell 2462

We present Chandra and Very Large Array observations of two galaxy clusters, Abell 160 and Abell 2462, whose brightest cluster galaxies (BCGs) host wide angle tailed radio galaxies (WATs). We search for evidence of interactions between the radio emission and the hot, X-ray emitting gas, and we test various jet termination models. We find that both clusters have cool BCGs at the cluster centre, and that the scale of these cores (∼30–40 kpc for both sources) is of approximately the same scale as the length of the radio jets. For both sources, the jet flaring point is coincident with a steepening in the host cluster's temperature gradient, and similar results are found for 3C 465 and Hydra A. However, none of the published models of WAT formation offers a satisfactory explanation as to why this may be the case. Therefore, it is unclear what causes the sudden transition between the jet and the plume. Without accurate modelling, we cannot ascertain whether the steepening of the temperature gradient is the main cause of the transition, or merely a tracer of an underlying process.