Understanding 2008 Kresten Lecture

As described in Week 5's blog, 2008 Kresten Lecture by Hoek et al was one of the discussion point during last week. According to our Professor Daniele Peila, this is the best paper (on Tunnel design) ever written [dot]! That was instigating enough to make us extra curious to read this paper ;)

This paper is available at Hoek's corner. This paper presents two detailed case studies which could serve as guidelines for Tunnel designers. This paper uses the derivation of equation for capacity curves presented in Carranza-Torres et al (2009) - discussed in Week 6 blog post. This post highlights the critical features addressed in this paper:

• While using 2D numerical model, it should be noted that analysis section near the excavation face is a 3D problem however it can be simulated in 2D environment by means of deformation control process. This process consists of three steps:

• Step 1: Calculate deformation for different Inclusion modulus (in steps) and prepare characteristic curve as shown in Figure 7 of the paper. In addition, for deep tunnels (as in case study 2 of this paper), we also need to determine maximum plastic radius (unsupported condition), using a plane strain analysis.
• Step 2: Prepare Longitudinal deformation profile for the tunnel (this can be done based on Appendix 1 of the paper, my spreadsheet on support interaction curve could be used as a starting point. This could also be done using commercially available software RocSupport by RocScience). Axis symmetric continuum model could also be used for this purpose.
• Step 3: Based on the distance of installation of support (and Longitudinal deformation profile), determine the deformation already realized in the tunnel. This value can further used to determine the corresponding inclusion modulus required for 2D simulation.

• Another important issue addressed in this paper is about choosing shotcrete properties. Authors suggest to use support capacity curves (based on Carranza-Torres et al 2009), instead of Concrete codes for their design and presents the shotcrete strength development curve developed by Melbye and Garshol (2000).
• Contribution of shotcrete in long term load carrying capacity is dicussed in the paper and recommendations from ITA Guidelines for Design of Tunnels (1988) is cited for the conditions under which shotcrete's strength could be used for final lining design.
• Authors have suggested to use Elastic capacity curves proposed by  Carranza-Torres et al (2009) even for final lining design and have justified by comparing with the results from structural program Response 2000 (based on modified compression field theory -Vecchio and Collins, 1986).
• Convergence confinement analysis is explained for a yielding support system using the second case study.

Appendix 1 and Appendix 2 are essential excerpts from the papers by Vlachopoulos et. al (2009) and  Carranza-Torres (2009).

References:

[1] Hoek, Evert, et al. "The 2008 Kersten Lecture Integration of geotechnical and structural design in tunneling." 56th Annual Geotechnical Engineering Conference. 2008 (available for educational purpose at: Hoek's Corner)

[2] Vlachopoulos, N., and M. S. Diederichs. "Improved longitudinal displacement profiles for convergence confinement analysis of deep tunnels." Rock mechanics and rock engineering 42.2 (2009): 131-146.

[3] Carranza-Torres, C., and M. Diederichs. "Mechanical analysis of circular liners with particular reference to composite supports. For example, liners consisting of shotcrete and steel sets." Tunnelling and Underground Space Technology 24.5 (2009): 506-532.