# How can I determine the radius of turn a 4.6m diameter Tunnel Boring Machine could have? (im building fictional underground labs in the desert)

I have chosen this kind of Tunnel Boring Machine to make the tunnels (4.6m diameter). The curvature of the tunnels depends on the radius of turn the machine has.

The idea is to build underground tunnels which contain botanical labs inside them. Since it is an architecture project, the labs are connected between them through a network of tunnels. This network must not be too deep into the ground, since it is necesarry to have some light entrances for the place. If it is of any use, the labs are the ends of this network, so they are placed closer to the surface. This means the network is not flat. Labs are meant to look like Aires Mateus' Monsaraz house.

• I suppose it's a related question : worldbuilding.stackexchange.com/q/250937/80336 Commented Nov 5, 2023 at 16:45
• @OliviaBD As it's very unclear what you're actually doing, I'd like to remind that worldbuilding is not about building in the real-world, but fictional ones (ie. novels, movies, games...). It would be hazardous to do something from a fictional world in the real-one, to say the least. You should check twice you're asking on the good site (see tour, help center and recent questions list). If you're sure, it will be wise to clarify this to us you're building something fictional. Commented Nov 5, 2023 at 16:57
• P.S. On a flat plain as shown in the illustration, one would want to consider the relative costs and merits of a using the cut-and-cover method instead of a boring machine. It could go much faster (depending on the depth of the tunnel), and it would allow for much wider tunnels with much tighter turns. Commented Nov 5, 2023 at 19:14
• Please remember to do your homework, Olivia. It took me seconds to find a reasonable answer via Google. (Find "TBMs can make turns" in the article. My Google search was '"TBM" turning radius'.)
– JBH
Commented Nov 5, 2023 at 21:14
• My first thought is, if you are going to make tunnels in a desert which are not going to be very deep, why use a tunnel boring machine? That is way more expensive, takes longer to create the tunnel, and limits how your tunnels look like. And unless you want to labs in awkward narrow tubes, you're going to dig out the labs themselves anyway. Commented Nov 6, 2023 at 12:49

## 4 Answers

Larger TBMs naturally can't bore curves as sharp as smaller ones can. An example of the first, from this article :

The 9.53-m diameter CREG machine completed a challenging portion of the project that included a tight 90-m radius curved drive.

A smaller machine, however, like the TERRATEC S48 EPBM,* which is of a slightly smaller radius than your preferred one (namely 3.2 meters), "excavated a sharp 32m-radius curve as it exited the project’s launch shaft to negotiate the piles of an adjacent expressway ramp".
The article continues:

To achieve this challenging curved alignment, the EPBM was manufactured with an extreme X-type articulation system that provides a maximum articulation angle of 6.6-degrees.

(The X-type articulation system refers to how segments of the machine rotate around a central point, and not around a point on the outer wall [see this image].)

I'm not sure where the line is drawn, but the preview to this paper mentions so-called Tight Radius Curve Tunnel Boring Machines, TBMs "that are designed to execute extremely tight radius curves":

Improvements to TBM designs [in Japan] now mean that manufacturers can supply machines that can execute curves under 10 mR.

* An 'Earth Pressure Balance Shield Machine'

(Tunnel boring is quite different if made in soft rock or soil, or hard rock. This answer considers the latter case)

The curvature radius depends on the TBM design. The simplest TBMs (Kellys) almost cannot curve at all. Otherwise, a difference from true of up to 2-3° can be usually obtained, which for a 4.6m diameter means a curvature radius of about 100m (if I didn't botch the numbers) with a "off the shelf" machine (assuming you can talk of OTS when speaking of TBMs).

There are semi-custom machines with a radius as low as 70 meters or lower. With a diameter of 9.53m, you have the 972 CREG waterjet hard rock tunnel borer that is designed for (and succeeded in) boring 90m-radius tunnels.

Waterjet-assisted borers have more leeway than normal TBMs because they do not rely on hydraulic pressure from martinets to push the drilling bits against the rock; rather they use water cutting. This means that the whole machine can be more flexible and needn't be as close as possible to a single solid hunk of metal.

There are also experiments on both gyrotronic borers using dense beams of millimeter-wave microwave radiation, and "bladeless" borers with waterjets; both open a series of circular cuts in the rock, then pneumatic "feather-and-wedge" rock splitters are driven in the cut and used to crack the circular crowns. Both these designs need no pressure on the boring head, so the latter might consist in just a flat disc whose axis can be rotated at will, giving an effective curvature radius of zero (as long as you don't curve too often: the rest of the TBM must fit too). The rest of the machine has to be appropriately designed with flexibly-joined sections.

So, since this is worldbuilding, I'd say you can justify whatever radius you're most comfortable with.

• I believe the energy consumption of gyrotronic borers make them prohibitive for bore diameters over a couple hundred millimeters. Basically you'd need a full scale nuclear power plant hooked up to the thing to bore a tunnel suitable for something like a train. They do have several advantages over existing boring technologies, but their energy efficiency seems to be very poor. Commented Nov 6, 2023 at 16:51
• @Crazymoomin and you're right, of course. Gyrotronic borers would not be used to create the bore itself, but rather the holes where the wedges would go in order to shatter the rock. I imagine you'd have several small gyrotronic heads drilling a circle of holes, then water would go in to cool the rock (and thermally crack it maybe), finally the wedges would shatter a circular crown of rock. Commented Nov 6, 2023 at 17:46
• I guess that could work, but that would negate many of the advantages of gyrotronic boring, such as being able to deal with high temperatures and a lack of tool wear. Commented Nov 7, 2023 at 7:44

If it's present-day, then this likely isn't a question for this site, but just a question of fact, best answered by going to primary sources. This is the kinda thing that, as authors, we should do ALL THE TIME, just like reporters.

The obvious thing is to contact the people who will know, and manufacture the TBMs. Click the little envelope icon on the top right of Herrenknecht's homepage, and say something like "Hi, I'm writing a story about some fictional labs that have been dug out using your machines. I want to make it realistic, so could you tell me the tightest turn radius of the m-1070m EPB4000ah model?" (I picked that one because it has 4.6m excavation, 3.6m finished tunnel radius, but go for whatever model you think best).

If your tale is set any distance in the future, though, I see no worldbuilding reason that the engineering challenges associated with drilling any angle you want for your narrative could not be assumed to have been resolved. Still worth contacting Herrenknecht to establish a max value for the angle, then you can reduce it as you feel appropriate for your story.

(I'm no TBM engineer, nor do I have any special knowledge in this area, so take what follows with a pinch of salt)

If you're cutting curves, the limit seems to be a factor of:

• how long your segments are, plus
• the maximum angle between each segment.

Another limit is:

• the maximum angle that the cutting head can be turned to, and still be pressed against the cutting face, and still have the area between it and the TBM be fully braced.

The constraints on these are not necessarily entirely engineering limits, since smaller-diameter TBMs can be created, with shorter segment lengths.

But SOME engineering limits exist. Let's say that you're lining the tunnel in 4.5m-long sections of reinforced-concrete liner, 30 cm thick. Each segment needs (as a vague back-of-the-envelope guess) about 100 metric tons of liner.

If you're creating that liner in slabs of a quarter circle, 4.5m x 7.5m x 0.30m, that's about 25 metric tons of concrete, and there'll definitely be engineering limits on the minimum size of the equipment that passes that up the TBM, and places it against the wall, while also leaving room for other TBM requirements to be passed through it like a conveyor for disposal of waste material, coolant, lubricant, humans, replacement teeth and other repair parts and consumables, air flow, etc.

But there's no reason to have the concrete that large, other than to save time. You can make the liner in smaller parts, by reducing the sizes of the concrete sections. At an extreme, you could line the tunnels with bricks (and there're plenty of large brick-lined tunnels out there in the real world: brick performs excellently under compression!). It becomes a time-and-complexity tradeoff.

A curve in the tunnel would require shaving the respective angle off the bricks/blocks and tossing the dust and offcuts onto the conveyor of waste material, or having them be cast in precisely the right dimensions well in advance, and passed in for placement in precisely the correct sequence (which is how I believe it was done for the Channel Tunnel's large concrete sections, or so I vaguely remember hearing on some TV program about it).

In an ideal world, and for your maximum narrative freedom, you'd have the TBM-segment length be less than your tunnel width, the max angle between each TBM-segment be 90, and be able to have the cutting head be able to bore at 90 degrees to the main body.

At that point, you can bore whatever tunnels you wish.

The "making a 90 degree T-junction" thing could be a bit of an exercise: cut the crosspiece of the T past the junction, then back up leaving the main boring head in place against the cutting face at the far end of the T, so that smaller boring machines can be passed through the body of the main TBM, to expand the junction enough for the cutting head to then be pulled back and rotated to 90 degrees, or whatever angle required.

Keeping everything braced while doing all that, then placing the liner, might be the most significant engineering challenges there. That could be reduced if your site was specifically selected to be self-supporting rock with no sections of muddy, watery soil. But if you're looking at the EPB (Earth Pressure Balance) TBMs, then you're probably talking about digging through soft, cohesive soils.

This network must not be too deep into the ground

### Frame challenge: A tunnel boring machine is almost certainly not the tool for the job

A tunnel boring machine is intended for use deep enough underground that digging down to that depth from above is impractical. If you can get light shafts down to that depth (or at least light shafts which actually achieve anything), then almost by definition you're not deep enough to need a tunnel boring machine.

As per this link, for anything up to 10-12m deep it's much more economical to use the cut-and-cover method. Simply dig yourself a trench, install the tunnel structure, and cover it up again.