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What is the yield strength assumed in calculations of the steel sets?

Your question about the grade of steel used in the support calculation for RocSupport takes me back a very long way to the work that I did with Ted Brown in about 1975 for the book "Underground Excavations in Rock". The calculation of the stiffness and capacity of blocked steel sets is given on page 254 (Second edition). The yield strength of the steel was assumed to be 245 MPa and the Young's modulus 207 GPa. The resulting support capacity curves for different tunnel radii are given on page 269.

I have not revisited these calculations for many years although I have used the curves in a couple of more recent papers. Note that we seldom use blocked steel sets today and the most recent calculations have assumed very small angles between blocking in order to simulate the modern practice of embedding steel sets into shotcrete. I believe that the accuracy of the calculations is consistent with the accuracy of the convergence confinement calculations. I no longer use these calculations except for very general indications of tunnel behaviour. In terms of our modern understanding of tunnel support mechanics in weak ground, I believe that these calculations are completely inadequate, particularly for non-circular tunnels in anisotropic stress fields, and I prefer to use numerical methods for critical problems.

In designing tunnel support today, I would use two- or three-dimensional numerical models to determine the extent of progressive rock mass failure during each stage in the excavation process. The model would also include rock bolts, if these are used, and passive support in the form of shotcrete, embedded steel sets or reinforced concrete. This passive lining would be represented by beam elements to allow calculation of the axial thrust, bending moments and shear forces in the lining. These would then be compared with moment- thrust and/or shear-thrust capacity calculations for the shotcrete, concrete or steel sets or lattice girders or some combination of these elements.

(Answer provided by Dr. Evert Hoek, Evert Hoek Consulting Engineer Inc.)

How is the deformation at the tunnel face calculated in RocSupport?

In RocSupport for deformation at the tunnel face, two values are reported: wall displacement and tunnel convergence. The following two references are the basis for the deformation calculations:

Carranza-Torres, C. (2004). Elastoplastic solution of tunnel problems using the generalized form of the Hoek–Brown failure criterion. International Journal of Rock Mechanics and Mining Sciences, Proceedings of the ISRM SINOROCK 2004 Symposium, edited by J.A. Hudson and Xia-Ting Feng, Volume 41, Issue 3.

Duncan Fama, M. E. (1993). Numerical Modeling of Yield Zones in Weak Rock. In: Hudson JA, editor. Comprehensive Rock Engineering, 2. Oxford: Pergamon, 1993. p. 49-75

Where can I find more information on ground reaction curves?

The best reference for ground reaction curves is Evert Hoek's Practical Rock Engineering chapter on Tunnels in Weak Rock.

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