Gravity and Gradients of Long Tunnels

Effects of disturbances in the local gravity field of the earth on gradients of long tunnels is explored and a simple method of locating any particular geopotential horizon in a pilot shaft suggested, using Prey's formula and geopotential or relative geopotential numbers. Little difficulty with gradients of long tunnels need be anticipated from naturally occurring gravity anomalies, even if these are as large as 500 mgals. As long as height differencing is involved, determination of shaft depths to given level surfaces remains simple. The 51-mile long Orange-Fish Tunnel (currently under construction, 1969) in South Africa's Cape Province is chosen as a practical example. It is shown that the invert level of the Tunnel's No. 2 Shaft only needs a correction of −0.15 ft relative to the inlet end of the tunnel 14 miles away. Such correction will create no engineering problem in maintaining the 1 in 2,000 gradient of the tunnel or in construction of the concrete lining.