Nowadays they use a device called a total station. If you’ve ever seen a worker beside the road looking into a device on a tripod, that looks like a complicated camera, that’s a total station. They are computerized devices that can really precisely measure the angles and distances between points.
The surveyors will establish a “benchmark,” which is a point whose coordinates are known to a high degree of precision – like, within 2 mm. The design will be based off of that benchmark. As the tunnel progresses, the surveyors will regularly mark out on the ground what is the correct direction for the workers to dig, based off of the benchmark and using a total station.
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