Civil, Structural & Geotechnical Engineering
Glover-Dumm Transient Drain Spacing Formula: Falling Water Table Drawdown m_0 to m_t
Calculate subsurface drain spacing L (m) required to lower a storm/irrigation water-table mound from m_0 to m_t within t days using R. E. Glover and L. D. Dumm’s (1954, USBR) Boussinesq diffusion solution.
Design irrigated arid-zone drains to drop the root-zone water table 30 cm inside 2–4 days!
In humid climates with frequent drizzle, Hooghoudt’s steady-state formula applies; in arid irrigated lands or intense episodic monsoons, each irrigation pulse raises the midpoint water table abruptly to m_0 above drain level, and crop roots suffocate unless the water table drops down to m_t within t days (e.g., from m_0 = 1.00 m to m_t = 0.70 m within t = 3 days)!
Solving the linearized 1D Boussinesq groundwater diffusion PDE dm/dt = (K * D / mu) * d^2m/dx^2 for a fourth-degree parabolic initial water table (Dumm, 1960 / US Bureau of Reclamation), the Glover-Dumm Transient Drain Spacing Equation is L = PI() * SQRT((K * D * t) / (mu * LN(1.16 * (m_0 / m_t)))), where K (m/day) is hydraulic conductivity, D = d_e + 0.5 * m_0 (m) is average saturated transmissivity thickness, and mu (dimensionless, e.g., 0.05–0.12) is drainable pore space (specific yield)!
| Glover-Dumm Design Parameter | Field Value | Physical Role in Drawdown |
|---|---|---|
| Hydraulic Conductivity K & Avg Thickness D | K = 1.10 m/d, D = 1.90 m | Aquifer Transmissivity T = K * D = 2.09 m^2/d |
| Drainable Porosity (Specific Yield) mu | mu = 0.06 (6%) | Hydraulic Diffusivity K*D/mu = 34.83 m^2/d |
| Required Drawdown m_0 -> m_t in Time t | 1.00 m -> 0.70 m in 3.0 days | LN(1.16 * 1.4286) = 0.5051 -> L = 45.19 m |
Glover-Dumm (USBR Fourth-Degree Parabola) Transient Drain Spacing L (m)
Evaluates PI() * SQRT((K * D * t) / (mu * LN(1.16 * (m_0 / m_t)))) across K (B2 m/day), average flow thickness D (B3 m), drainable porosity mu (B4, 0 < mu < 0.5), time t (B5 days), initial mound m_0 (B6 m), and target mound m_t (B7 m, requiring 1.16 * m_0 / m_t > 1 and m_t < m_0).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B4 >= 0.5, B5 <= 0, B6 <= 0, B7 <= 0, B7 >= B6), "Invalid Glover-Dumm Aquifer, Porosity, or Drawdown Inputs (Requires 0 < m_t < m_0)", ROUND(PI() * SQRT((B2 * B3 * B5) / (B4 * LN(1.16 * (B6 / B7)))), 2))Predicted Midpoint Water-Table Height m_t (m) at Fixed Spacing L = 40 m
Inverts Glover-Dumm to predict remaining mound height 1.16 * m_0 * EXP(-(PI()^2 * K * D * t) / (mu * 40^2)) after t days at 40 m spacing.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B4 >= 0.5, B5 <= 0, B6 <= 0), "Invalid Glover-Dumm Inputs", ROUND(1.16 * B6 * EXP(-((PI() ^ 2) * B2 * B3 * B5) / (B4 * (40 ^ 2))), 3))Try the example
Use the original values or change them to test your understanding.