This model demonstrates the use of the Dupuit-Forchheimer equation to estimate groundwater inflows to a mine pit within an unconfined aquifer. The radius of influence is solved iteratively using the binary search algorithm.
A mine pit can be simplified, geometrically, to a cylinder of radius effectively equivalent to its irregular size and shape. Regional groundwater inflows to an open pit can be estimated using the method first developed by Dupuit (1863), improved by Forchheimer (1930) and described as the Dupuit-Forchheimer equation for radial flow conditions for an unconfined aquifer.
Q = pK * ( h02 - hw2 ) / ln( (R + rw) / rw )
K is the hydraulic conductivity of the rock mass
h0 is the pre-mining groundwater level above the base of the aquifer
hw is the base of the pit floor above the base of the aquifer
rw is the pit diameter
R is the radius of influence
The Dupuit-Forchheimer equation does not account for rainfall recharge when estimating likely pit inflows. The maximum radius of influence can therefore be estimated based on the rainfall recharge in the area and with the assumption that the inflow in the pit will eventually reach equilibrium with the rainfall recharge.
Q = Rainfall Recharge * p * R2
Model Contributed by:
Jaco Grobler with Golder Associates
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