Wanted - Advice from Civil Engineer

[Bob Mehew]

I'm in the process of writing a note on the history of the BCA Anchor scheme and need some 'professional advice' on the relationship between anchor depth, rock strength and the appropriate separation of anchors so as to avoid overlapping cones of stress. My problem is I recollect getting hold of a figure of twice the depth for spacing of resin bonded anchors in limestone but have lost the basis for that information. (I think it came from doing calculations using a piece of free software provided by Fischer Fixings which is no longer available. I know it is not a simple relationship and such notes I have are now incomprehensible.) So I'm after a quotable source for providing a guide on the minimum separation of anchors / distance between anchor and edge to maintain maximum strength of each anchor. As there is interest in placing anchors in other rocks which are mined, I would like to get a feel for a moderate range of rocks. Please PM me if you think you can help.

And yes I know it is more a engineering than science question.

 

[Cantclimbtom]

Based on a body of knowledge from empirical/observation and experience rather than calculation and aimed at climbers and canyoners as well rather than only cavers, you might find useful resource here. PDF download

https://hownot2.com/blogs/bolting-bible

 

[Bob Mehew]

Thanks for the pointer but https://hownot2.com/blogs/bolting-bible/bolting-bible-book-of-holes indicates his opinion has no firm basis. I was looking for something more scientific.

 

[asheshouse]

The 2xdepth recommendation is based on the assumption that the failure cone of a single anchor has 45deg sides, so radius of failure cone = anchor depth. So to avoid failure cones intersecting the spacing has to be 2xdepth.

 

[ChrisB]

Message sent, Bob

 

[andrewmcleod]

I suspect that in these cases all that really matters is the empirical, rather than the theoretical, i.e. what the manufacturer says after its own testing to guarantee the rated strength of the anchor (when in the approved compressive strength of concrete etc)... Certainly Fischer anchors (at least the through bolts) certifications include plenty of stuff stating what the minimal allowable distance between anchors (and distance from edges) is.

Obviously this is more difficult for non-commercial anchors such as the IC anchor which aren't sold and don't come with a comprehensive set of manufacturer instructions (or the volume of testing that a major manufacturer like Fischer can do).

There is no magic distance after which anchors will suddenly cease to affect each other, and putting them close together will not instantly result in anchors pulling out; it all depends (now that's an engineering answer if ever there was one ) It will also depend enormously on the rock - I suspect a rock with bedding parallel to the surface will have very different characteristics to one with bedding perpendicular to the surface.

 

[Cantclimbtom]

The 2xdepth recommendation is based on the assumption that the failure cone of a single anchor has 45deg sides, so radius of failure cone = anchor depth. So to avoid failure cones intersecting the spacing has to be 2xdepth.

45 degrees is very convenient for rules of thumb. I've used the same, for things like assumed loading from the bottom of a footing of a wall in clay soil so as minimise risk of damage to a clay pipe drain by getting the bottom of the footing deep enough that the drain isn't inside the "cone".

I'm sure this works nicely in test cubes of concrete and other non real life scenarios but is a total nonsense bolting rock IMHO because if there are already in situ fractures in the rock (maybe not visible at surface or revealed by hammer rapping) then placing anchors that close and there's a good chance they'll be in the same "bad" rock area

For example a Petzl P36GS 10mm bolt specifies a drill depth of 70mm so doubling that you'd have centres of 2 bolts only 140mm apart. Would you feel happy with them so close? If there was a fault/fracture in the rock there's a good chance they'd both be affected.

However a rule of thumb (not scientific/calculated) is to place drill centres at least 4x the bolt length apart to reduce the odds of both landing in the same fault. Rather than theoretical cone calculation.

Maybe it's because I originally studied as an engineer (general/civil) that I respect years of hard earned lessons above physicists' theoretical maths because a lump of rock in a cutting or a drive in a mine (or a cave) isn't going to be a fault free perfectly homogeneous substrate and frankly that 45 degrees has just been plucked out of the air anyway. </ObnoxiousRant>

 

[Steve Clark]

Hilti have some comprehensive manuals and software that you could take a look at.

The posts above highlight the important point though. Rules will only get you so far. You could cast a concrete block large enough to pass all the rules for a 50kN resin anchor and find you can lift it off the ground at 0.5kN. In a more extreme example there were probably lots of pegs and a few bolts in the Bonati Pillar.

 

[Bob Mehew]

Many thanks for the range of answers. We became fully aware of the problem with the integrity of the rock when doing some testing in the floor of Horseshoe Quarry in Derbyshire. It was belatedly pointed out to us the quarry ceased working at this level because the limestone bed had changed to a weaker and thinner bed. That was further reinforced by tests done on natural exposures of limestone which produced better results than those from a quarry of the same limestone. And also by some spectacular failures when using boulders in a quarry, see image. I'll not get into other rocks save to say that in slate, a few tests in both the Cleavage plane and the Pillar plane demonstrated the need for care. But perhaps the most memorable result comes from a test done in 2007 in an oolite mine where the anchor was pulled out at 6kN (issue 9 of Speleology).

The prompt for the request was rereading an old Fischer manual (their Technical Internal handbook). At Section 2.5.3.1 it states "With concrete cone failure the ... failure load increases proportionally to the square root of the concrete strength." (Of course the ultimate load can be limited by the strength of other materials in the system.) At Sec 2.5.3.2 it goes onto state "The increase in the ultimate load is proportional to the anchorage depth to the power of 1.5". And at Sec 2.5.3.3 it states "The failure cone develops from the area of undercut or expansion at an angle of approximately 35° to the concrete surface. This results in the concrete failure cone‘s surface diameter being 3 times the anchor‘s embedment depth." So the radius is 1.5 times the depth which is an angle of just under 60 degrees to the cone's axis, not 45 degrees from the rule of thumb of twice separation. Given concrete is normally quite a lot weaker than limestone, I would have expected the cone's angle to be smaller for a weaker rock. (Though the Fisher quotes are about undercut and expansion anchors, not resin.) So I am left confused and hence my request to get back into the science of the topic.

 

[Tricky Dicky]

I've sent you some design guidance to BS8110 and EC2 which relates to bolts in concrete.

 

[Steve Clark]

Another thing to consider is the pull-out test method. For bigger / deeper anchors I've often thought that the typical hydraulic test rig 'legs' could influence the potential failure cone if they are not far enough apart. If they are within the cone, there are some more internal forces in the rock that could artificially increase the failure load, compared to a pure tension.

Shear loads on bolts, which are far more common than pure tension pull-out in most caving situations, the failure mode is different again and more difficult to test using a standard hydraulic rig.

 

[Bob Mehew]

Another thing to consider is the pull-out test method. For bigger / deeper anchors I've often thought that the typical hydraulic test rig 'legs' could influence the potential failure cone if they are not far enough apart. If they are within the cone, there are some more internal forces in the rock that could artificially increase the failure load, compared to a pure tension.

Shear loads on bolts, which are far more common than pure tension pull-out in most caving situations, the failure mode is different again and more difficult to test using a standard hydraulic rig.

The BCA anchor puller was sized so as to place the feet well outside the size of the cone, see photo. Most test rigs are designed for checking non permanent fixed anchors prior to their use to 6kN as per the PPE anchor standard EN 795. (BCA did this for a few years until we had problems with surplus surface resin spalling. Though DCA continue to do a post installation check.) There was a rig which could pull at angles of up to around 75 degrees from the axial direction. Sadly it was lost following the tragic death of the guy who built it. He did produce a small amount of data which gave encouraging results that the force to extract a resin anchor increased as the angle from the axial axis increased. More recently, Simon Wilson did do some work on shear loading, see https://cncc.org.uk/equipment/ic-anchor/ .

 

[Bob Mehew]

Right, I have had some very useful pointers from Tricky Dicky - many thanks - which have lead me back into the world of standards. It appears that BS8110-1:1997 was one source of the advice that the full cone angle was 90 degrees and hence the spacing between anchors needs to be at least twice the anchor depth if one is not to reduce the strength of the anchor. (I use the phrase 'full cone angle' to differentiate it from the half cone angle which is used to compute the radius of the base of the cone.) That was overtaken by Eurocode 2 in 2004 which endorsed EN 1992-1-1 which retained the 90 degree value. However, Eurocode 2 was updated in 2018 by a revision to the standard to EN 1992-4:2018. EN 1992-4:2018 changed the value of the full cone angle to just under 110 degrees which gives a value of spacing between anchors of three times the anchor depth.

I should emphasise that the Eurocode is more about how to compute the strength of the group of anchors if they are placed in a configuration where the spacing between anchors is less than three times the anchor depth. That computation appears to be based on using the degree of overlap of the cones, that is, ignoring that part of the rock which is shared by two (or more) anchors. Whilst this approach may seem a bit crude, it apparently works. Though I should say the same process is used for all anchors be they undercut, expansion or bonded (as in BCA's use of resin bonded anchors). And I should also point out that the Eurocode does also provide the process for allowing for weaker rock and such like. The other point of significance is that the Eurocode treats the calculations dealing with anchors near to edges in the same way. So placing an anchor within 1.5 times its depth to an edge will inherently weaken the anchor.

Having said all that, it is worth emphasising that the bonded anchors used by the BCA scheme do have a moderately high strength when compared to the potential force created by a falling caver on an SRT rope. Results from recent testing anchors suggest an average value of around 37kN (with the 5% fractile value being 21kN). Rope test work indicates possible peak forces of under 20kN using a steel test mass. There is not any evidence on how much of the peak force would be mitigated by replacing the steel mass by a human body (which is more squishy) so there is a moderate amount of capacity left. In any case, cavers should be using two anchors to belay their rope so the second anchor should hold the caver if the first fails. Though it is unlikely that the caver would escape being hurt by the forces involved. But that's a topic for another thread.

 

[andrewmcleod]

Most of my ropes will fail (with a knot in) long before 20kN anyway
(the 8mm at ~10kN, the 7mm at 8kN :O )