Rock Mass - Tunnel Support Interaction Analysis

This post presents a spreadsheet which can be used to perform parametric studies of support interaction (based on the book "Support Underground Excavations in Hard Rock", E.Hoek et. al, A.A. Balikema Publishers). 

This calculation considers circular tunnel subjected to hydrostatic stress field in which horizontal and vertical stresses are equal. Kirshch's elastic closed form solution os one of the commonly used analytical solution and is used for this spreadsheet. Although this is never a real case but as the author suggests,"a great deal can be learned by carrying out parametric studies in which different combinations of in situ stress levels, rock mass strengths and support characteristics are evaluated". Also, this solution is considered to be a good tool for a "Sanity check" of the results obtained from numerical analysis[4].

Download support_interaction_analysis here.

Snapshot of the Support Interaction Curve.

The calculation has following support systems available in the spreadsheet for parametric studies.

• 16mm dia - Very light rock bolts
• 19mm dia - Light rock bolts
• 25mm dia - Medium rock bolts
• 34mm dia - Heavy rock bolts
• 50mm thick, 1 day old shotcrete
• 50mm thick, 28 day old shotcrete
• 300mm thick, 28 day old shotcrete
• 6I12, Light steel sets @ 1.5m spacing
• 8I23, Medium steel sets @ 1.5m spacing
• 12W65, Heavy steel sets @ 1.5m spacing

Maximum pressure and maximum elastic displacement of the above support systems are based on Hoek and Brown [2] and Brady and Brown [3]. Note that, in all cases, the supports are assumed to act over the entire surface of the tunnel walls. In other words, the shotcrete and concrete linings are closed rings; the steel sets are complete circles; and the mechanically anchored rockbolts are installed in a regular pattern which completely surrounds the tunnel.

I hope to post similar spreadsheet soon which can be used to draw support interaction curves for user defined rockbolts, shotcrete, concrete linings and steel sets.

References:
[1] E.Hoek et. al, "Support Underground Excavations in Hard Rock", A.A. Balikema Publishers, The Netherlands
[2] Hoek, E. and Brown, E.T. 1980. Empirical strength criterion for rock masses. J. Geotech. Engng Div., ASCE 106(GT9), 1013-1035
[3] Brady, B.H.G. and Brown, E.T. 1985. Rock mechanics for underground mining. London: Allen and Unwin, USA. This book is available at Mr. Partha Das Sharma's blog: http://miningandblasting.wordpress.com/
[4] Chapter 6, Technical Manual for Design and Construction of Road Tunnels (FHWA-NHI-10-034), Washington, December 2009.