Mound Beneath Rectangular Recharge Area

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Groundwater Mound Beneath Rectangular Recharge Area

Hantush (1967) presented the following equations for predicting the maximum height of the water table beneath a rectangular recharge area:

h_m² - h_i² = Z_m(t) = (2w/K)ntS*(0.5A/(4nt)^1/2,0.5B/(4nt)^1/2) . . . . . (1)

n = Kb/e . . . . . (2)

b = 0.5[h_i(0) + h(t)] . . . . . (3)

where h_m is maximum height of mound above aquifer base (i.e., maximum saturated thickness of aquifer beneath recharge area); h_i is initial height of water table above aquifer base (i.e., initial saturated thickness of aquifer); K and e are hydraulic conductivity and storativity (specific yield) of aquifer, respectively; w is constant rate of percolation from rectangular recharge area of length A and width B; b is a constant of linearization; and the function S* is an integral expression (see Hantush 1967). The aquifer is unconfined and assumed to have infinite extent.

If infiltration ends at time t=t₀, Hantush (1967) applied the principle of superposition to compute the decay of the mound as follows:

h_m² - h_i² = Z_m(t) - Z_m(t-t₀) . . . . . (4)

Equation (1) is nonlinear owing to the definition of b in Equation (3); however, the solution is readily obtained by successive approximation.

Example: Growth and decay of groundwater mound beneath a rectangular recharge area (A = 100 ft, B = 100 ft) assuming K = 0.1 ft/day, e = 0.1, h_i = 10 ft and w = 0.01 ft/day. Decay of mound begins after 100 days.

Groundwater Mounding Calculator for Rectangular Recharge Area

Hydraulic Conductivity (K) =	[L/T]
Specific Yield (e) =	[dimensionless]
Initial Saturated Thickness (h_i) =	[L]
Length of Recharge Area (A) =	[L]
Width of Recharge Area (B) =	[L]
Recharge Rate (w) =	[L/T]
Time (t) =	[T] (t > t₀)
Compute Decay
Time When Infiltration Stops (t₀) =	[T] (0 < t₀ < t)

Use consistent units for the above input parameters. For example, enter K in m/day and t in days to compute h_m in m. Compute the recharge rate using w = q/(A*B) where q is the volumetric recharge rate [L³/T].

Groundwater Mounding Calculator developed by Glenn M. Duffield, HydroSOLVE, Inc.
Support for this page provided by Todd Engineers.

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