Sunday, November 16, 2014

Waterjetting 27b - Drilling rock under stress

Last time I opened discussion on the topic of cutting a material that contained high levels of stress. This is a more common situation when working with rock, since – as a general rule of thumb – the vertical stress on a rock increases by 1 psi, for every foot deeper one goes into the earth. Thus, for example, if one goes down around 700 feet, the depth of a number of coal mines, then the background pressure on that rock is some 700 psi due to the weight of the rock that is pressing on it from above.

Now I should also mention that this is only a general rule, because, over the millennia, the rocks move, are split by earthquakes, overlain by volcanic eruptions and many other events that make that generalized statement less accurate for any given location. And one factor is that, if there weren’t such movements, then the natural horizontal stress on the undisturbed rock would be about a quarter of the vertical stress (the ratio is known as Poisson’s ratio, though usually derived for the resulting strain on the material, rather than the driving stress).

What one often finds, when these values are measured, is that the horizontal stress is higher than the above simple calculation would suggest. Which is a long way of saying that it is often difficult, without making a measurement, to know exactly what stress a rock is actually undergoing when found underground. But if some of the rock is removed (because it contains valuable ore) then the stress field redistributes, and some of the simpler assumptions come back into play. And we found that out when we drilled these holes:

Figure 1. Oval holes drilled into a lead-bearing sandstone;

You can see that we were drilling oval holes. The drill we were using used two high-pressure (10,000 psi) waterjets that were rotating at constant speed as we fed the drill into the rock. (And I’ll discuss the drill design and other stress effects in the next post). The small dark spots in the rock are galena, and as I will discuss in some future post, we were able to separate the galena from the sandstone at the drill, in part because of the way the waterjets penetrate, as I will discuss below.

Figure 2. Waterjet drill penetrating sandstone at up to 12 ft/min.

The region of the mine we were working in was around 700 ft. deep, and had been previously mined. Roughly half the rock volume had been removed, over a relatively large surface area, so that the pillars that were remaining were carrying roughly twice the load that they were before mining took place. On the other hand, since the rock on either side of the pillars had been removed, the vertical load was all that was acting on the rock within the body of the pillar, where we were drilling the holes. So very crudely the vertical stress, before we started drilling was around 1,500 psi in the rock.

Now, to explain why the holes are oval rather than round, consider that a waterjet works by getting into the cracks that exist in the rock, pressurizing the fluid and causing the crack to grow until it meets other cracks that together free a small piece of the rock mass. In this case the rock is made up of grains of sandstone and galena which have boundary cracks around each particle. By growing the cracks using this process, the rock is broken out into the individual grains of sand and galena.

But when the rock puts pressure on the rock, so the cracks are squeezed closed, and the water finds it harder to penetrate into them. This happens to the rock on the sides of the hole. As it is being formed, the load that was being carried by the rock being removed transfers to the rock on either side of the hole. Because the load is vertical this means that the jets find it harder to penetrate the rock on either side of the hole, and the horizontal diameter of the hole is therefore less than it would be otherwise.

Figure 3. Lines showing equal stress magnitude around a hole drilled into a rock loaded vertically. (This is purely representative and does not carry a scale, the lines are of diminishing intensity as they move away from the hole.)

On the other hand, as the load from the overlying rock moves out to either side of the hole, it comes off the rock at the top and bottom of the hole, and those cracks get larger, and were no longer being squeezed shut. As a result the jets found it easier to penetrate into the rock, and the vertical diameter of the hole is thus larger than it would be otherwise.

Put these two together and the result was that the jet drilled holes that were oval in shape, as shown in Figure 1.

As one way of making sure that this was really the cause of the change in hole shape, we used the waterjets to cut a slot around the perimeter of a part of the rock in the pillar. By making a horizontal cut above the slab that this outlined, we removed the vertical loading that the rock was seeing due to the overlying rock.

With no external loads on the rock, from either direction, it was as easy for the jets to cut into the rock in all directions, and, as a result, the holes that the jet drilled were round.

Figure 4. Round holes drilled in unstressed rock near the block of holes shown in Figure 1.

Again, while the effects are much larger when shown in cutting and drilling rock, the effects would be similar if we were cutting material that was under other internal stresses and which were then cut by a jet in a shop or other surface facility.

In the above case we were working in a mine where there was free access to the rock, the situation changes if we had been trying to drill down from the surface, and that will be the topic of the next post. In passing it should be noted that the waterjet drill was not only quieter, but also less powerful and smaller than the existing mechanical drill, and it could drill the rock faster.

Figure 5. Comparison of mechanical drill (upper) and the waterjet drilling equivalent (lower) on a drilling rig underground in a lead mine.(You need to look closely to see the drilling rod that is shown in Figure 2.)


  1. 12 ft/min. Impressive.

    I wonder if you couldn't put an array of these on a tunnel boring machine? The machine boring the tunnel in Seattle is reported to move at 35 ft (10 m) per day. Your machine would go through rock fine and it would seem positively fly through clay or sandstone.

    Thanks for your blog it's very informative.

    1. In the new post I have explained the design, but the short answer to your question is yes it can be done.

  2. Seattle had some mysterious object stop its drilling. (Last I heard). Like all good boondoggles its just a bit of fun to be had.
    I would think removing the waste would be a big part of the time involved in drilling as big a hole as the Seattle tunnel.

    1. Last I heard IIRC they found the problem and have bypassed it.

  3. Just thinking out loud. It may not be practical to use water jets for tunnels but if you could get it to work the speed might be worth the headaches. I know that mud is kept under pressure while the wheels crack the rock on the face on traditional tunnel boring machines. If shields were used to hold the tunnel up the pressure from the rock face could be used to help cut. The water from the jets would help wash away the face debris. I've been reading your articles on bits with water jets. Could a kerf, like this,

    be cut then the tool would have very little pressure needed to break the stone? Spin the jet like a circular saw to make the kerfs. I'm assuming the cost is in the pumps so adding more jets is not as costly. Those tool steel?/plow steel? cutters have got to be expensive. Especially when you only get a few feet worth of cutting out of one.
    The real advantage is cost. Each tunnel boring machine seems to be custom made. Each piece, each wheel, each bearing etc. has to all be engineered together. If instead you made hexagonal sections with water jets and material clearing bits build like chisels in each section then bolting sections together to get whatever size bit you need. Also you would save money on rock crushing. The material would already be in small pieces. Cost could be much lower.

    Anyways thanks for your blog it's very good. I guess I'm one of those strange people that can be entertained by learning about cutting rock. :)

  4. There are so many facets to an answer to tunneling, and the big problem is often the joints in the rock, and the water content. Modern methods of ground support, including drilling holes around the projected edge of the tunnel and filling them with cement before taking out the central core is one way of doing this.

    Over the course of this series I have discussed some ways of doing this, see for example,, which discusses the work done under Minneapolis.

  5. This type of drilling machines is set up for big industrial projects. The heavy pressure drilling machines can manage the oil pressure between high to low while working.

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