Abstract
The increase of bored tunnels in the entire world has raised the question how to design the tunnel structure in an efficient way. This paper proposes a numerical approach to the Hyperstatic Reaction Method (HRM) for analysing permanent tunnel linings. The permanent tunnel lining is known as main structure of tunnel maintenance during the time. The HRM is one of the analysis methods for tunnel lining in long term. In this paper, two dimensional numerical modelling is performed by considering hyperstatic reaction concepts. Loading is done after the calculation of long term loads, and ground reaction is simulated by springs. Designing is done for Manjil-Rudabar freeway project, Tunnel No. 2. The numerical analyses were performed for Operational Design Earthquake (ODE) and Maximum Design Earthquake (MDE) loading conditions. A new simplified approach is used for considering the effect of earthquake loading on the tunnel lining. Then, an interaction diagram between axial force and bending moment used for investigating the capacity of tunnel lining. The thickness of tunnel lining and armature are calculated for three sections based on induced forces in tunnel lining. These forces were different in every section according to the load combinations, rock mechanics properties, lining properties, and overburden. The numerical results showed that the forces in tunnel lining for MDE condition is approximately 50% more than ODE condition in earthquake loading. This numerical processing presented that the HRM is a proper, fast, and practical method for designing and analysing the tunnel lining.
Highlights
Numerical tunnel analysis is generally conducted for preliminary design with the two-dimensional beam-spring model, which consists of linear beam and spring elements to simulate the behaviour of lining and ground, respectively
The numerical modelling was performed based on section 3.2.2 under static and dynamic conditions (ODE & Maximum Design Earthquake (MDE)) for three tunnels sections by considering hyperstatic reaction concepts
The application of Hyperstatic Reaction Method (HRM) is presented for designing permanent tunnel lining in which two dimensional analyses can be considered
Summary
Numerical tunnel analysis is generally conducted for preliminary design with the two-dimensional beam-spring model, which consists of linear beam and spring elements to simulate the behaviour of lining and ground, respectively. When factors such as input parameters, boundary conditions, and ground loads are wellestimated, a simple model can give a good prediction which is comparable to or more accurate than results from complex models These facts enable the beam-spring model to usefully and approximately examine the state of the tunnel, and the model has been continuously used. As these are only generally known with a certain approximation, it is often necessary to carry out parametric or probabilistic type analyses in order to be able to completely describe the uncertainty on the stress state of the support structure. A real case study (Manjil-Rudabar freeway project, Tunnel No 2) is designed by this method
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