2. Groundwater Flow

MINEDW evaluates potential inflows and pore-pressure distributions near open-pit and underground mining operations. The software applies to diverse climatic, geologic, and hydrogeologic settings. This section describes the computational formulation for simulating groundwater systems in MINEDW.

Groundwater flow in MINEDW follows the three-dimensional flow equation:

(2.1)\[\frac{\partial}{\partial x}\left(K'_{xx} k_R \frac{\partial h}{\partial x}\right) + \frac{\partial}{\partial y}\left(K'_{yy} k_R \frac{\partial h}{\partial y}\right) + \frac{\partial}{\partial z}\left(K'_{zz} \frac{\partial h}{\partial z}\right) - S_s' \frac{\partial h}{\partial t} - W = 0\]

Where:

  • \(h\) = hydraulic head [L],

  • \(K'_{xx}\) = effective hydraulic conductivity in the x-direction [LT⁻¹],

  • \(K'_{yy}\) = effective hydraulic conductivity in the y-direction [LT⁻¹],

  • \(K'_{zz}\) = effective hydraulic conductivity in the z-direction [LT⁻¹],

  • \(k_R\) = relative hydraulic conductivity [L⁰],

  • \(S_s'\) = effective specific storage, a parameter that accounts for specific storage and specific yield [L⁻¹],

  • \(W\) = source-sink discharge per unit volume [T⁻¹],

  • \(x\) = coordinate in the x-direction [L],

  • \(y\) = coordinate in the y-direction [L],

  • \(z\) = coordinate in the z-direction [L],

  • \(t\) = time [T],

  • \(S_s\) = specific storage [L⁻¹],

  • \(S_y\) = specific yield at the phreatic surface [L⁰],

  • \(V\) = specified volume of media [L³], and

  • \(A\) = area of the phreatic surface within the specified volume of water [L²]

The governing equation assumes the coordinate system aligns with the principal components of the hydraulic conductivity tensor (\(K\)).

The following sections detail key components and parameters of the groundwater flow equation: