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Tunnel Lining Design 24-1 Tunnel Lining Design In this tutorial, Phase2 tutorial, Phase2 is is used to design a reinforced concrete tunnel liner. The complete model can be found in the Tutorial 24 Tunnel Lining Design.fez file located in the Examples > Tutorials folder in your Phase2 installation installation folder.
Topics covered • Reinforced concrete liners • 3D tunnel simulation • Distributed loads – field stress vector option • Support capacity curves • GSI calculator Phase2 v.7.0 Tutorial Manual Tunnel Lining Design 24-2 Problem A circular tunnel of radius 4m is to be constructed in Schist at a depth of 550m. The in-situ stress field has been measured with the major in-plane principal stress equal to 30 MPa, the minor in-plane principal stress equal to 15 MPa and the out-of-plane stress equal to 25 MPa. The major principal stress is horizontal and the minor principal stress is vertical. The strength of the Schist can be represented by the Generalized HoekBrown failure criterion with the uniaxial compressive strength of the intact rock equal to 50 MPa, the GSI equal to 50 and mi equal to 10. To compute the rock mass deformation modulus, the modulus ratio (MR) is assumed to be 400. The support is to be installed 2m from the tunnel face.
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The goal of this tutorial is to design a reinforced concrete lining with a factor of safety greater than 1.4. To design a support system, the following three steps must be performed: 1. Determine the amount of tunnel wall deformation prior to support installation. As a tunnel is excavated, there is a certain amount of deformation, usually 35-45% of the final tunnel wall deformation, before the support can be installed.
Determini Determining ng this deformation can be done using either a) observed field values, or b) numerically from 3D finite-element models or axisymmetric finite-element models, or c) by using empirical relationships such as those proposed by Panet or Vlachopoulos and Diederichs. Using either the internal pressure reduction method, or the modulus reduction method (see tutorial 18), determine the internal pressure or modulus that yields the amount of tunnel wall deformation at the point of and prior to support installation.
This is the value determined in step 1. Build a model that relaxes the boundary to the calculated amount in step 2 using either an internal pressure or modulus. Add the support and determine whether a) the tunnel is stable, b) the tunnel wall deformation meets the specified requirements, and c) the tunnel lining meets certain factor of safety requirements. If any of these conditions are not met, choose a different support system and run the analysis again. Model The first step is to determine the amount of tunnel wall deformation prior to support installation. For this tutorial, we’ll use the relationship proposed by Vlachopoulos and Diederichs.
The Vlachopoulos and Diederichs method is documented in Appendix 1 of the Kersten Lecture by Hoek, Carranza-Torres, Diederichs and Corkum. The paper is in the Hoek’s published papers area on the Rocscience website: Phase2 v.7.0 Tutorial Manual Tunnel Lining Design 24-3 This method requires that we build a model of the tunnel and determine a) the deformation far from the tunnel face using a simple plane strain analysis, and b) for the same model determine the plastic zone radius. In this tutorial we’ll start by building a single model that also combines step 2 with step 1. We’ll build a plane strain model that relaxes an internal pressure pressure on the tunnel boundary from a value equal to the applied in-situ stress to zero.
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