The hydraulic gradient is the change in hydraulic head (in metres) divided by the distance over which it occurs (in metres).
The hydraulic gradient of water flowing through rock determines the flow rate. It also determines the ability of the rock to resist deterioration due to the flow. When an unlined tunnel (or shaft) carries water close to the upstream wall of a powerhouse, the water permeates the surrounding rock. As a result, the ground water pressure around the unlined tunnel is equal to the water pressure in the tunnel. The powerhouse is at atmospheric pressure, so the pressure in the rock at the upstream wall of the powerhouse is atmospheric.
To prevent damaging hydraulic gradients in the rock, the tunnel is lined with steel for a certain distance upstream of the powerhouse. Then:
Safe Hydraulic Gradient, SHG = (Tunnel internal pressure in metres, H) / (length of the steel liner, in metres, L).
Benson’s criteria are used to select a safe hydraulic gradient, based on the quality of the surrounding rock. Then:
Length of steel liner, L = H / SHG
This criterion is also used to design the length of concrete plugs, which are constructed in water tunnels to close off construction adits.