Friday 25 March 2016

Quibans 24 - Tunnels

From the Cambridge News:
University of Cambridge study to tackle Cambridge transport – including tunnels and driverless cars

Some of the world's best transport engineers are turning their eyes to solving Cambridge congestion. Things like tunnels and innovative new vehicles are all on the table for the study commissioned by the University of Cambridge.
Professor Lord Mair is the university's head of civil and environmental engineering and one of the world's foremost experts on tunnels, having been involved with projects such as HS2 and Crossrail.
He told the News: "This is going to be a feasibility study which I think will really change the way Cambridge thinks about congestion and how people move around the city.
"Our remit is to look at options. It might be more or less direct, it could involve some underground, it could involve some overground. It could go within the city centre, and that would probably be underground.
"The important thing is, the ground conditions are very favourable for creating economic tunnels, particularly if they're relatively small in diameter." Lord Mair added that smaller tunnels of say 4 metres in width would cost about a quarter of those 8 metres in width, with the costs reducing as a greater proportion the narrower the tunnels got.

  • The obvious question is why a tunnel of half the width would cost about a quarter as much.
  • We could work out the cross-sectional area of a circular tunnel of width 8m and one of width 4m, and could also do the same for a square tunnel of widths 8m and then of 4m.  
  • Having established that the area is a quarter, why would this affect the cost?  (A quarter as much soil to dispose of, etc.)
  • Why might it not be a quarter of the cost?  
    • There are fixed costs that would be the same regardless of the width of the tunnel (eg survey costs, buying land, diverting streams, legal costs, etc).
    • The inside of the tunnel needs to be lined with concrete blocks.  How is this affected by halving the width?  Work out the perimeter of the circular tunnels (8m and 4m) and of the square tunnels.  
    • The calculation before is only approximate.  Look at the diagrams below and work out the area of the concrete if it is 30cm thick.
    • The smaller digging machine might not be a quarter of the cost.
    • You might not need a quarter of the people to run the machine.
    • The bigger machine might work more slowly so it takes longer.
    • Any others?  
  • Is a 4-metre tunnel big enough for 2-way traffic?  High enough for buses?  How small could the tunnels get?

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