SHOTCRETE ARCHES

[NEMINING]

Hello,

I'm a rock mechanics engineer and I would like to calculate my factor of safety of shotcrete arches holding a certain rock weight. The shotcrete arches have the same profile as the excavation drift (15'W x 15'H) but has an arch in it in the back. The shotcrete thickness in the shoulders of the tunnel is approx 10" and 4" in the walls (see sketch).

I was able to calculate the factor of safety of the support by taking into account shotcrete only by diving the capacity of shear resistance of shotcrete along the failure perimeter by the load of the rock on the support system. However, this is conservative because I'm not taking into account the effect of the steel reinforcement. Could you give me guidance on how to account for the steel reinforcement in case of shearing along the shoulder due to the load of the rock on top. I'm sure it's a simple material resistance calculation but I can't quite remember my old course back in university.

Thanks,

 

[bridgebuster]

Based on your sketch you could treat it as a concrete rigid frame bridge, pinned at the bottom of the legs.

The Army Corps of Engineers has a manual on tunnel design: EM 1110-2-2901

 

[BUGGAR]

How are you figuring your rock loading? It must be self-supporting before shotcreting. Do you have rock that presents a uniformly distributed load as shown?

 

[NEMINING]

I looked into The Army Corps of Engineers tunnel design: EM 1110-2-2901, and I couldn't find my answer. Thanks for your suggestion bridgebuster

Good Question Buggar !

When we blast the first round, the rock is still self-supporting. We apply shotcrete arches and then we move ahead and blast the other round. Because I know the jointing in the rock and the geometry, after 2-3 rounds, the rock may not be supporting itself creating a rockoverhang, that's why we apply these reinforced shotcrete arches with advance.

I know the likely geometry of the unstable rock, that way I can calculate my loading. In this case, I assume uniform loading.

I just don't know how to calculate the formula of factor of safety for a rigid frame with concrete and steel reinforcement subjected to loading...

Thanks,

 

[BAretired]

Not much point having 10" depth at the haunch if there is only 4" depth in the column unless the rock on each side is preventing rotation of the beam ends. Normally, the depth of column at the top is the same as the depth of haunch because, in a rigid frame, the moments are equal in the beam and column where they meet.

The solution depends on the assumed boundary conditions, but it seems to me the column will be acting essentially in axial compression with an insignificant bending moment. The assumption of a hinge at the bottom of the legs is not realistic. The assumption of a hinge at the underside of haunch may be realistic, but it means that you will have very large horizontal forces to be resisted by the rock which, depending on the properties of the rock, may be excessive.

BA

 

[NEMINING]

BAretired, thanks for the reply

I'm not concerned about the horizontal forces on the rock, as the rock we are dealing with is massive and has a high UCS (UCS>180 MPa). I'm more worried about exceeding the shear strength of the reinforced shotcrete arch at the haunch. So that's why I would like to know what would be my shear forces there, my bending moment and see if the used materials (shotcrete + steel) are able to withstand that shearing.

Any insights/tips how to do that ?

Thanks,

 

[BUGGAR]

In the tunnels I've been involved in (hardrock, but blocky after blasting), we used large safety factors, like 5 or more on working stress. As you advance your tunnel, miners are going back and forth to the face through your supports. In my tunneling design, I always went for the overkill (opposite pun intended).
And think of the cost of a dig out if you misjudge the rock load.

Where is your tunnel? Are you rock-bolting?

 

[NEMINING]

Buggar,

I'm also being really conservative here. Not only i'm applying our normal rock-bolting support, but because of this particular case, I'm adding shotcrete + steel reinforcement. Remember, i'm talking about a good rock quality here (RMR>75). I just want to know that in case all my assumptions turn to be worst case scenario. what would be my factor of safety with this support system.

I'm well aware of the cost... and we are one of the safest sites in the world. I've been designing ground support system for over 10 years now. I just want to have a engineered calculation for these shotcrete arches, which by the way work pretty good.

Thanks,

 

[KootK]

Based on the proportions of the "arch", my thoughts are as follows:

1) You're not getting squat for frame action out of the connection to those 4" walls.

2) I doubt that the member would have any hope of resisting the applied loads as a beam element (classic flexure and shear).

3) I think that your best bet is to identify a true arch within the concrete provided and assess capacity based on the compression strength of that arch.

4) The arch just mentioned will require competent thrust capacity in the adjacent rock. It sounds as though you do indeed have that.

5) Conceived of as the arch just described, shear and moment should be non-issues, at least for truly uniform loads.

6) I know a thing or two about structures but I don't know jack about tunnels. Bear that in mind.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[hokie66]

The concrete will just serve as lining for the rock arch. Erosion control, if you will. The steel can be left out of the shotcrete, unless you intend to tie it in some way to rock bolts.

As KootK said, the concrete will not work as a rigid frame, or as a beam.

 

[miningman]

Cant comment on the theoretical aspects of this discussion but the tunnel dimensions here are quite small and if the RMR and UCS values are as quoted , then the thicknesses of shotcrete seem really excessive. Those dimensions would be what I would expect to apply in a block caving situation , with RMR and UCS only about 20% of the values you are dealing with. And I've got a sneaking suspicion you are not blasting a flat back but a definite arch. That will significantly affect any theoretical analysis. Without giving away any confidential info, are you in a mine or a civil tunnel?? Where geographicaly ??