Rock Mechanics

Tunnels and earthquakes have a special relationship.

In university, I went through UofT Engineering Science, and I specialized in Geophysics. It was more of a leftover choice, after I eliminated everything else! About the only thing you could do with this option was go into the oil exploration industry, so for my third year summer, I went to Calgary to work for an oil company.

I hated it! The only good thing was that I went into the mountains every weekend to look at the rocks. I love rocks! After that summer, the oil boom collapsed, and I had to look for another job anyway. I needed a career change, so I did my Masters degree in Rock Mechanics.

The most amazing thing about rocks, is that all rocks have a very similar friction angle. Their 'cohesion', however, varies from ultra-hard granite, to near-sand. Also, rocks are marvelously fractal, meaning that they behave mostly the same, from a very small scale to a very large scale.

My very first work, when I got out of university, was to look at underground structures - tunnels and caverns. It's a bit different to design infrastructure tunnels, than mining. In mining you can take slow, controlled failure, because you can re-excavate access tunnels. In fact, continuous movement is the norm in mines, simply because you are excavating all around and changing the stress fields.

I was looking at the dynamic stability of these tunnels and caverns, particularly for nuclear plants and waste repositories. The waste repository has the difficult problem of excess heat from the fuel bundles, thus it is always heating up, thus the stresses are always changing. On the other hand, a nuclear plant water intake tunnel is quite the simple thing; it should stand up long enough to slap in a thick concrete lining. Nothing much 'dynamic' about these tunnels!

Besides standing up to heat, there is the added problem of low-probability and time-distant events for a nuclear waste repository. Actually anything is better than having the waste hang around in concrete cans, but the 'people' demand 'million year' time frames, simply because someone (in the distant future) could theoretically dig into an ultra-deep repository and start eating the nuclear fuel.

As you see, there is little rationality in the nuclear waste biz, but it leads to fun things such as determining what happens during the next ice age. (No matter that those cans on the surface all get ground up and spat out!).

Rock mechanics has been mostly concerned with rock failure under the following-load of gravity. If your tunnel doesn't fall down on your head, you're happy! What I was studying 30 years ago, was the impact of earthquakes on caverns and tunnels.

Underground workings have generally done very well with seismic shaking. They do not resonate, and thus, are not very amenable to conventional seismic analysis, which I think sucks, anyway! For underground structures, I had to go into a totally different type of analysis, which is just now being applied to buildings, thanks to cheap computing!

Probably the best way to look at the seismic performance of underground things, is to use the methodology of 'Experience Data', which I used extensively for nuclear plants. Around the world, there have been many tunnels and mines exposed to strong ground motion. The performance has varied from very good, to very bad. "It never rains, but it pours!". If a tunnel fails during an earthquake, it can flood within seconds!

I went into the analysis of what actually happens to a tunnel during an earthquake. The earthquake source radiates seismic waves, which is easy to model with a wave propagation program. What I discovered 30 years ago, was the variation of peak seismic stress with distance. Although there is virtually no limit to peak stress in the near-field, seismic waves that propagate a decent distance, cannot be non-linear. In other words, the peak stress disturbance must go down to the level where it does not interact with the rock! This is extremely important, and saves us a lot during earthquakes.

Nobody had actually measured the peak stresses of a passing seismic wave, so I needed to go for another measurement. I did some computer modeling, and some research, and came to the conclusion that Peak Ground Velocity (PGV) offered a good correlation with peak stress. The only problem was, at the time, nobody gave a damn about PGV.

30 years ago, the seismic world was totally dominated by California. Strong ground motions, correlation with damage, etc, was all from the deep soil basins. The whole concept of Standard Response Spectrum and modal seismic analysis was due to the fact that basin motions were low-frequency, long rumbling things. In this world, the measurement of Peak Ground Acceleration (PGA), expressed as a percentage of g, was all the rage.

I knew there was something wrong here. We had sent a crew, measuring stresses at the recent Miramichi earthquake, and had found something unusual. The crews reported that the ground was crackling with small earthquakes after the main event. Some would really thump the drill rig! I knew that if you had measured the PGA, you would get around 1g, but clearly these things had no energy to damage. I was convinced that PGA was a useless measure for the rest of the world!

When I went back to computer modeling, I found there was no physical limit to PGA, since you could just increase the frequency, and PGA would go through the roof! It was only in California, where the frequencies were forced to be low, that it was valid.

Thus, began my great campaign to wipe PGA off the seismic map! After 30 years, there is now some glimmer of hope! But I digress, as usual. My next step was to see if there was some limit to PGV on rock, and thus a limit on peak stress. As well, I had to determine if there was some indication of how much peak stress was required to damage a tunnel or cavern.

At the time, 30 years ago, PGV was never recorded, let alone discussed. So I made a study of the Modified Mercalli Index, which had recently been tied to PGV, and was the best surrogate. The PGV approximately doubled for every jump in the MMI, and I began to collect stories about the several point difference between rock and soil.

Thus began my classic report Seismic Ground Motion on Rock and Soil (which I loved!). In that report, I looked very hard for situations where there were both rock and soil reports of ground shaking. It was difficult, since nobody ever reported where there wasn't any damage!

I was lucky to find this absolutely inspirational book in the old library at Hydro (since kaput!): Freeman,J.R., 1932. Earthquake Damage and Earthquake Insurance. He was a total rationalist, and looked at actually earthquake damage and non-damage. (I should have stolen that damn book!).

He noted that there was no damage on Telegraph Hill (solid rock), and buildings designed with a flat 10% lateral load did quite well. The difference in intensity between the hill, and the landfill harbour was about 5 points! Later, I had the opportunity to walk the Hill, and view the harbour, but I digress.

I had lots of stories, for example the 1944 Cornwall earthquake. On the Leda clay, people couldn't stand up, and there was extensive damage. But according to my old grandfather-in-law, there was nothing on the highlands (hard till). The 1925 St. Lawrence earthquake devastated the river lowlands, but didn't wake the guests at the Chateau, nor plink off any icicles!

After this, I concluded that PGV was exceedingly low on solid ground (rock or hard till), and soft sludge could amplify by a factor of 10 to 100 times!

I, therefore, went with a max of about 5 cm/s on rock for Eastern North America (ENA), and set about to check the stress levels for this PGV. As well, I had to determine the 'sensitivity' of the rock to stress changes.

Having determined that there were generally low PGV's for solid rock, I was prepared to slide to home plate, by going back to Rock Mechanics! This subject is mostly about the behaviour of cracked, wet rock, which is exactly what have in earthquakes.

I was running a finite-differences wave propagation computer code, which I had written myself. In it, I could view traveling seismic waves, look at the generated stresses, and bounce waves off tunnels! All in all, better than Nintendo! Best of all, I could make the rock properties non-linear, and I found that if I introduced the tiniest non-linearity, the wave propagation would fail.

What's the source of true non-linearity in rock? It's when the stress disturbance of the wave causes some energy absorption in the rock. This can come from water flow in and out of pores, or sliding along a fracture. I was most interested in what could induce rock to slide.

That was fairly easy to look at, since you can't really disturb rock without making a ton of micro-seismic noise, and the South African gold mines had been wired up for sound, a long time ago. They had the great ability to actually generate earthquakes, and you could see the effect by mining through it afterward! In general, I found that the micro-crack damage zone was very confined to the actually slipped fault, and the seismic waves only induced rock failure, at a distance, if things were extremely unstable.

My next step was to estimate how close my target rock (Eastern North America, ENA) was to failure. This would also help determine the maximum induced stress, for if you knew what could cause micro-slippage, you would have another confirmation, along with the low PGV. For that, I ventured into Grand Geology, and Induced Seismicity!

I was working on the sub-theory that propagating seismic waves could only carry a little bit of stress, due to the general weakness of the rock. For that to hold, the basement of ENA would have to be at its Limit State, which means it is as close to failure as you can get, and still be relatively stable.

At the time there was a lot of evidence in favour, and subsequent papers continue to support this. Essentially, we have an ancient craton, that has been pushed and pulled to a great extent over the last billion years. It would get greatly pushed (compressed) in between expansion cycles, when it was over cold mantle. It would be pulled (tension) when the heat built up underneath, and the continents were splitting up again.

Currently, we are in a big cold trough, and the craton has settled in. This puts it a generally high compressive state. You can see that whenever the water head is increased by about 10 m (induced earthquakes), you get earthquakes, or when a large extent of rock is removed (as in quarrying), of about 3 m.

Into this mix came glaciation, which had a tremendous effect on the rock. Although a uniform ice load would merely act as a big wet blanket, the ice loading is far from uniform. During surges, and retreats, it builds up a very high shear stress, combined with high water pressures being injected into the rock. I don't think that anyone has appreciated this, except moi!

Although the glaciation relieved some stress, it also shattered the rock, through hydrofracturing (which is the splitting of rock through injected fluid pressure). My prediction from this, was that we would see extensively fractured rock down to about 1 km, at relatively low stress, then we would see unfractured rock at very high compressive stress. In other words, the measured stress increased with the rock's ability to hold it.

I was lucky to have this sub-theory tested with the construction of the mostly useless URL (Underground Research Laboratory), which was a great "FEED ME!" AECL gift. This mine went about 1 km down, where they encountered great big 'sub-horizontal' features, which were essentially underground rivers hooked to the surface. Seeing that this was probably not a good thing (except for Bruce!), they proceeded to go under these rivers.

What they encountered was extremely high stresses. So much so that the rock virtually exploded when touched! We really couldn't put used fuel here because of all the heat produced, and the rock would be shattered within a decade! Thus, URL ended both with a bang, and a whimper!

So, in the end I had good justification that the maximum stress from a seismic wave was only about an atmosphere, and the PGV was limited to about 5 cm/sec. This was scarcely enough to spill a coffee in a mine, and shows how even large earthquakes mostly do nothing to mines. Still, I was determined to model it in a computer, because that was fun!

I've always tended to approach analysis slightly differently than most people at the old company. They always wanted to go for the 'Big One' that proved a political point, such as 'the reactor is safe'. I always called that 'Snow, by analysis'. I used analysis to improve the fundamental science, since I knew what uncertainties were (as opposed to them!), and I wanted to see the effects of 'what if's'.

I love working with wave propagation model (no, not that kind!) This is the most fun a dynamics person can have cheaply! My first work was with code I had written myself, and then I eventually went to commercial code. But for that, you needed powerful Linux computers, and not the namby-pamby Windows crap that bureaucracies like to buy! Needless to say, in modern times, I overran the computing power I had, and became bored. Still, I learned something.

With my simple wave modeling, I showed that the tunnel was a small fraction of the seismic wavelength, and did no 'funny stuff'. To show funny stuff, I propagated into beds of soft soil, and saw tremendous amplifications!

I concluded, that under normal, well-designed conditions, a tunnel had nothing to fear from earthquakes, and this has been proven out in the field. But what of poorly designed underground structures? They had a serious problem...

Thus I created (just now!), Harold list of tunneling bo-bo's:

-Don't rely on grout! Any water channels get reactivated by seismic motions. The tiniest amount of differential movement can shatter grout. Many tunnels have been instantly flooded after an earthquake.

-Don't have open zones, or major fractures near your cavern. Earthquakes can suddenly change the regional groundwater flow. Seismic ground motion from very far away can dramatically affect well levels, and even blast natural gas into the air.

-Build in a lot of margin. The stress impact of an earthquake is less than the stress changes you would expect over the life of the cavern. It has to be designed so that there is no chance of spontaneous failure, or rockbursts.