Let's assume I want to build a subway system. I dig two subway stations and now I start digging a tunnel from both of these endpoints simultaneously.
How can I ensure that the two tunnels dug from the different endpoints meet in the middle? I don't believe I can use GPS underground. What methods do professionals use to ensure that the two tunnels meet? Are there some positioning technologies that work underground?
The alignment of a tunnel constructed from two ends and meeting somewhere is the middle is achieved via old fashioned surveying methods.
If the tunnel breaks through to the surface, surveying stations are accurately established on the surface of the Earth at each end of the tunnel. These days GPS surveying techniques would most likely be used for that.
Once the surface surveying stations have been established, surveying stations are established underground, as the tunnel progresses from each end.
Prior to the use of lasers and electronic distance measuring devices, theodolites & tape measures were used to take surveying measurements so that co-ordinates could be assigned to each underground surveying station. These days, total stations tend to be used to undertake the measurements.
To ensure the alignment of the tunnel is true, gyrotheodolites will be used periodically to check the position of the underground surveying stations. These use a gyroscope to determine the orientation of true north.
If the tunnel will not break through to the surface, vertical shafts must be first constructed by which people and equipment can be lowered to access the shaft. Unlike tunnels that break through to the surface, where people can walk from the surface into the underground tunnel, surveying lines and stations cannot be taken directly underground.
To establish the first surveying station underground two plumb bobs need to be lowered down, at least one shaft. From the surface the co-ordinates of each plumb bob line can be determined. This gives a surveying plane that can be transferred underground. From this, the first underground surveying station will be established and the remainder of the underground surveying technique will be the same a for a tunnel that breaks through to the surface.
It is not an easy answer... depends.
Basically, depends on the length of the tunnel.
For a short tunnel, let´s say 5 km, it is just a matter to create a grid on the surface, in top of the tunnel to give coordinates to both entries. Later on, the guide of the tunnel is made by total stations (theodolites anciently) by several methods: English traverse methodology (place benchmarks on pairs, make a traverse until the front of the tunnel in let´s say, par benchmarks and return back on the ones still not used... the problem of it is the turning on the front, but for 5 km is ok), English traverse plus axis (it is the same idea plus an open traverse on the axis of the tunnel, that one allows a better compensation and better results), traverse grids (instead to make observations on just traverse, the observations are made on small 4 point benchmarks grids... that ones is the best and most accurate methodology)
For a long tunnel, the English traverse is not enough, and you should use the 2nd and 3rd methodology.
Anyhow... The study of it should be done before begin, because you can find some surprises... For example, on the Eurotunnel, this question was raised during the construction, and within a few kilometers, the deviation was huge (>50 cm) in both entries (France and England). This deviation was corrected during the remaining tunnel.
There are another factors that are not considered, that it is not just direction... In long tunnels (>25 km) the "gravity" (plumb) it is not the same, so, if you follow the level from both entries, the tunnel will not match on level, and that one should be corrected against the system you are using (normally ellipsoid).
Gyrotheodolites are ok to know the North, but they can not guarantee coordinates, just alignment. So if your coordinates are not matching with a gyrotheodolite... what will you do?
@Fred... the "plumb" system fro tunnels it is just when you are accessing by shafts and when there is no way to place benchmarks or optical plumbs. It is very inaccurate and risky if you down know how to "plumb". Vertical shafts are ok when you have small cover and you have a tunnel without water on top (undersea or under-river tunnels).
This is more for a historical aspect (not about state of the art)
If you search for Eupalinian aqueduct on Wikipedia, you will find a reference for the first tunnel excavated from both ends through the use of geometry (and it is actually the second ever excavated in recorded history).
The tunnel was approximately 1 km long and it was build in 6th century BC (approximately 2600 years ago) - long before GPS or any fancy instrumentation.
In the Wikipedia article, there is a fairly detailed description of how Eupalinos used a "mountain line" to create a guide which then compared to the direction of the tunnel.
