Hydraulic design of tunnel; alignment criteria

Hydraulic design of a tunnel

It is the selection of the shape, size and slope of the tunnel so that the design discharge flows with an acceptable velocity and head loss, and so that the cost is the minimum.

1. Determine the design discharge $Q$ and select the type: free-flow (non-pressure) or pressure tunnel.
2. Choose the velocity: about 1.5-2.5 m/s for unlined and 2.5-4 m/s for lined tunnels (up to 5-6 m/s for pressure tunnels).
3. Size: $A=Q/V$; for circular, $D=\sqrt{4A/\pi}$. The economic diameter is found by optimisation (cost of the tunnel against the value of the energy lost).
4. Head loss: Manning $V=\frac{1}{n}R^{2/3}S^{1/2}$ ($n=0.013-0.015$ concrete, $0.03-0.04$ unlined rock) or Darcy-Weisbach; add the local losses (entry, bends, transitions).
5. For a free-flow tunnel, provide an air space of 15-20% of the area, a bed slope of 1:500-1:1000, and keep $Fr$ below 0.7 (not near 1) to avoid unstable flow.
6. For a pressure tunnel, the hydraulic grade line (including water hammer/surge) must stay above the crown, with a minimum rock cover.

Selection of tunnel alignment

• Shortest and straightest route possible (lowest cost and head loss), with gentle bends.
• Good geology: avoid faults, shear zones, weak and water-bearing rock and landslide areas; cross the weak zones at right angles; avoid squeezing and swelling rock.
• Adequate rock cover so that the internal pressure cannot burst the rock: the vertical rock cover must satisfy the Norwegian criterion $C_{RM}\ge\dfrac{h_s\gamma_w F}{\gamma_r\cos\beta}$ ($h_s$ = static head, $F\approx1.3$, $\beta$ = slope of the ground).
• Portals and adits: stable slopes at the portals and adits at suitable intervals for faster construction; access roads.
• Ground water and inflow: avoid high water pressure and heavy inflow zones.
• Connection with the intake, surge tank and powerhouse so that the layout (surge shaft and penstock) is simple, with a sufficient head and low cost.
• Environment and safety: avoid damage to settlements and existing structures.