Three-centred Arch

The 'Three-centred arch' is a common drift design method which can be selected as a Profile Shape option in the Centreline to Solid (form) form.

The following diagram shows the parameters and how they are included in the calculation to arrive at a three-centred arch shape.

The three-centred arch calculation is as follows

  1. Inputs are the designed drift excavation width (B1) and the designed drift excavation height (H1).
  2. Draw a horizontal line ab with length of B1; draw another horizontal line cd above it with the same length and offset from line ab by H1+B1/3. Make a vertical line ef with a length of 0.692 B1 starting from point e which is the midpoint of the line cd.
  3. Make point f the centre with a radius of 0.692 B1 and draw an arc hg anticlockwise with an angle of 66 degrees and 82 seconds starting from an azimuth of 33 degree 41 seconds.
  4. Point i is on line hf, a distance of 0.262 B1 offset from point h. Make point i the centre with a radius of 0.262 B1 and create an anticlockwise arc with an angle of 56 degrees and 19 seconds, starting from point h and ending at point j.
  5. Point k is on the line gf, a distance of 0.262 B1 offset from point g. Make point k the centre with a radius of 0.262 B1 and create a clockwise arc with an angle of 56 degrees and 19 seconds, starting from point g and ending at point l.
  6. Make point j the starting point and draw a vertical line down to point m. The length of the line jm is H1. Making point l the starting point and draw a vertical line down to point n. The length of the line ln is H1.
  7. The closed area consists of lines ln, nm, mj and arcs jh, hg, and gl. Together they comprise a 'three-centred arch'.