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18-Geom-B3 Networks and Precise Engineering Surveys · December 2018

Question 10 of 12: Shaft Plumbing — Orientation and Coordinate Transfer through Two Shafts

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format: Closed-book, 3 hours, calculator permitted. TEN questions constitute a complete paper — Part A: all of #1–#8; Part B: one of #9/#10; Part C: one of #11/#12. All twelve questions are solved here for completeness. Most answers are essay-format; Q5, Q6 and Q9 carry short verified numeric illustrations.

Reference texts: Wolf, Ghilani & De Blij, Elementary Surveying: An Introduction to Geomatics (15th ed., Pearson); Mikhail & Gracie, Analysis and Adjustment of Survey Measurements (Van Nostrand, 1981); Kavanagh & Slattery, Surveying with Construction Applications; Hofmann-Wellenhof, Lichtenegger & Wasle, GNSS (Springer, 2008); Kahmen & Faig, Surveying (de Gruyter); Chrzanowski et al. on deformation analysis; USACE Structural Deformation Surveying (EM 1110-2-1009); ISO 17123 field-test procedures. Canadian frame throughout (NAD83(CSRS), CGVD2013).

Question 10 (Part B): Shaft Plumbing — Orientation and Coordinate Transfer through Two Shafts (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

To control an underground tunnel, the surface coordinate system and azimuth must be carried down into the workings. Shaft plumbing transfers position (and, with two shafts, orientation) vertically down a shaft by physically defining the shaft-bottom point directly beneath a surface point.

surfaceunderground driftShaft 1Shaft 2surface baseline (known azimuth)underground baseline (= surface azimuth)orientation transferred via shaft pair → no gyrotheodolite needed
Figure 10 — Two-shaft plumbing: plumb points are transferred down each shaft; the line joining the two underground points reproduces the long, strong surface baseline, giving a well-determined underground azimuth without a gyro.

The plumbing itself. Each shaft is plumbed by suspending heavy plumb wires (weighted, damped in oil to steady them) from surface points down the shaft, or by an optical/laser plumb (auto-plumb) or a precise zenith/nadir plummet. The surface end of each wire is coordinated by the surface network; the wire then defines a point of the same horizontal coordinates at the shaft bottom, transferring $X,Y$ (and, by measuring wire length or by levelling, $Z$) underground.

Two-shaft orientation transfer. With two separate shafts, a plumb point is established at the bottom of each. Since both surface points are known, the surface azimuth of the line joining them is known. Transferring both points underground reproduces that same line — now with a long baseline (the horizontal separation of the two shafts) — so the underground azimuth is fixed directly and strongly:

  1. Coordinate both shaft-top points on the surface network and compute the surface azimuth $A_{12}$ and distance between them.
  2. Plumb each shaft to establish the two corresponding underground points $1',2'$ with the same horizontal coordinates.
  3. Run a connecting traverse underground between the two plumb points $1'$ and $2'$ (they are generally not intervisible), computing it first with an assumed starting azimuth. This gives a provisional underground azimuth $A'_{12}$ and length $L'$ of the line $1'\!-\!2'$.
  4. Rotate the traverse onto the surface line. The orientation correction is $\Delta A=A_{12}-A'_{12}$; add $\Delta A$ to every traverse azimuth and recompute the coordinates from $1'$, so that $1'\!-\!2'$ takes the surface azimuth $A_{12}$. The length check $L'-L$ tests the plumbing and the traverse, and any residual coordinate misclosure at $2'$ is distributed. Tie the underground traverse to this oriented baseline. Because the baseline is long, the azimuth uncertainty $\sigma_A\approx\sigma_{\text{lateral}}/L$ is small, giving a strong orientation for the whole tunnel.

Why two shafts are preferred. A single shaft can transfer coordinates but its two plumb wires are only metres apart, so the underground azimuth derived from them is weak (the short in-shaft base amplifies plumbing error) and must be strengthened by a Weisbach triangle (a small, nearly-straight triangle between the two wires and a near instrument). Two shafts give a base equal to the horizontal separation of the shafts (typically hundreds of metres, against a few metres inside one shaft), so the orientation is far more reliable — this is the classical strength of two-shaft plumbing, and it needs no gyrotheodolite.