Dear ma'am,

pl refer following papers.

All the best

http://www.ejge.com/2013/Ppr2013.199alr.pdf

https://www.rocscience.com/documents/hoek/corner/11_Insitu_and_induced_stresses.pdf

http://www.umich.edu/~gs265/tunnel.htm

https://www.hindawi.com/journals/mpe/2015/230126/

https://elearning.just.edu.jo/jjce/issues/paper.php?p=2887.pdf

Dear Kundan, 

Thank you very much. I appreciate your sharing. Going through them.

A traditional and most practical rock load calculations can be performed on the basis of Terzaghi's Rock Load Classification Table (Table 6.1.21 in the attached paper). This table divides the rock loading into 9 distinct classes of rock from from Hard and Intact Rock to Swelling Rock and gives simple formulae for calculation of rock loads on a tunnel support. The limitations of this method are given in my paper published in JGGE Journal of ASCE:.

Modeling Ground-Shell Contact Forces in NATM Tunneling, Based on 3D Displacement Measurements

Article in Journal of Geotechnical and Geoenvironmental Engineering 139(3):444-457 · March 2013

DOI: 10.1061/(ASCE)GT.1943-5606.0000791

Hope it will work. Please feel free to contact for more details.

 Dear Shafi,

Thank you for your assistance and reference, I appreciate it.

Joan! If you look back - not quite so far as Terzaghi - to the origins of the Q-system of rock mass classification and tunnel or cavern support (Barton et al 1974), and to a much more recent illustrated Q-manual (Barton and Grimstad, 2014) you will find that tunnel support capacity requirements can be related to a simple empirical equation (p.209, 1974) which was derived from an analysis of bolting and anchoring capacity applied at numerous caverns and tunnels.The original equation, involving the negative cube-root of the Q-value and the typical joint roughness Jr, gives a match to case records over a big range of Q. Unlike in Terzaghi's steel-sets-and-wooden-blocking times, a scale effect is not experienced when using 'modern' bolting and fibre-reinforced shotcrete, but is still experienced when using deformation-inviting steel sets or lattice girders. You will find that the combined bolting and shotcrete design chart in the Q-system gives a more direct practical answer to your query, based on thousands of case records. It turns out that the original support capacity equation is roughly inverse to the deformation modulus equation, so support capacity requirements are roughly inverse to the estimate of deformation modulus. See www.nickbarton.com downloads.

Dear Nick, 

Thank you for such great insights and wealth of resources. I took long to respond because I needed to go through a couple of the resources- they were most useful. Thank you.

By any chance, are there tunnel supports you may have designed based on underground rock loads, the required support capacity to withstand the forces and acceptable factors of safety. Chart approximations are mostly geological methods but my research is on geotechnical considerations.

Are there any equations developed to calculate underground rock loads?  

I look forward to your further sharing and great insights please. Thank you.

Joan, Nick Barton is the pioneer of Q-System of tunnel lining design and has a life long experience in tunneling. We shall feel proud that he has joined our question session.

However, so far as I kn ow, the Barton's method of lining design is meant for (applicable to) a single-layer of  lining / support (called NMT and mostly used in Norway and some other countries). There is another method of tunnel support which is based on two-layers lining / support (called NATM and used in Austria, Pakistan and other parts of the world). You has to first decide whether you are going for a single layer support and a double-layer one. You may then use the corresponding method of rock load support.

Regards

Oh yes, its such a great opportunity and a humble priviledge for a giant in the field such as Nick Barton would share from a wealth of knowledge and experience. 

I am thrilled! Thank you all.

Please be sparing with your sentiments! But actually single shell tunnel and cavern support (basically permanent B + S(fr) using Q or RMR empirical means, considering all the hydropower tunnels and caverns, and mining roadways , and transport tunnels in less rich counries, is probably more dominant in the world than the double-shell and more costly and time-consuming NATM. The latter also often includes the deformation-inviting lattice-girder phase: how can we design for this insecure period (prior to concrete lining) when there are poorly tackled problems with over-break?

We may not think single-shell competes with double-shell, because of all the reporting in tunnelling magazines of prominent NATM projects. The widespread 'single-shell' work goes unreported because it is so widespread and contractors and consultants have moved on to their next projects. So it is good to have ways to estimate B+S(fr) quantities and maybe check with equations, i.e. the bolt capacity needs (and anchors in caverns).

When 'numerically' dimensioning, remember that modellers like uniform loads, and no over-break and uniform thickness liners. This is seldom the reality.  It is more interesting to adress the use of bolts and shotcrete where the lining is following the over-break, in a more economic manner. Even a thin layer of S(fr) reduces the load on bolts considerably - so the bolt capacity formulae of long ago are conservative.

Dear Nick Barton,

You may be true in saying that globally single-shell tunnels / caverns are more dominant that double-shell ones. But we do not have any statistical data in the support of this claim, probably as you told due to non-reporting of single-shell projects.

For lattice-girders, both the increasing strength of hydrating shotcrete and the decreasing deformation of inward moving excavated ground are predictable on a temporal scale. These predictions can be used in the design of lattice-girders.

So far as the uniform load for tunnel modelers is concerned, the use of primary shotcrete shell converts the rather non-uniform load of freshly excavated ground into a more uniform load because of its ductility.

Still, I think we need to explore the merits and demerits of both the single- and double-shell tunneling in more detail. For that, if you agree, I would like to initiate a new question on the forum of Researchgate and invite the world renown experts in tunneling to give their opinions.

With best regards 

You can refer to papers of Prof. Hoek about tunneling and your purpose.