Civil, Structural & Geotechnical Engineering
Bouwer-Rice Unconfined Aquifer Slug-Test Formula: Hydraulic Conductivity K (m/day)
Determine in-situ unconfined or partially penetrating monitoring-well hydraulic conductivity K = (r_c^2 * LN(R_e / r_w)) / (2 * L_e * t) * LN(y_0 / y_t) using Herman Bouwer and R. C. Rice’s (1976) slug-recovery method.
Estimate aquifer hydraulic conductivity from a single monitoring well without pumping contaminated groundwater!
At contaminated environmental sites where multi-well pumping tests would require treating thousands of gallons of purged water, hydrogeologists displace the static water level instantaneously by y_0 using a solid mechanical slug (or pneumatic pressure step) and record residual head displacement y_t over seconds! Derived by Herman Bouwer and R. C. Rice (1976, Water Resources Research) via electrical-resistance network analogs for unconfined and partially penetrating wells, hydraulic conductivity is K = ((r_c^2 * LN(R_e / r_w)) / (2 * L_e)) * (1 / t) * LN(y_0 / y_t)!
Here r_c is standpipe casing radius where water level rises/falls (corrected for drained filter-pack porosity when the water table straddles the screen), r_w is borehole + gravel-pack radius, L_e is submerged screen length, and dimensionless geometry factor LN(R_e / r_w) accounts for radial flow convergence into partial or full screen penetrations (multiplying m/s by 86,400 converts directly to m/day!).
| Bouwer-Rice Slug Parameter | Field Value | Evaluated Contribution |
|---|---|---|
| Standpipe Casing Radius r_c | 0.050 m | r_c^2 = 0.0025 m^2 |
| Dimensionless Radial Geometry Factor LN(R_e / r_w) | 2.65 | From Bouwer-Rice A, B, C curves |
| Submerged Screen Length L_e & Time t | L_e = 3.0 m, t = 40 s | 2 * L_e * t = 240 m·s |
| Head Recovery Ratio y_0 / y_t (0.80 m -> 0.20 m) | LN(4.0) = 1.3863 | K = 3.3063 m/day |
Bouwer-Rice Hydraulic Conductivity K in m/day (86,400 s/day Conversion)
Evaluates 86400 * ((r_c^2 * LN_Re_rw) / (2 * L_e * t)) * LN(y_0 / y_t) across r_c (B2 m), LN(R_e / r_w) (B3), L_e (B4 m), elapsed time t (B5 s), initial displacement y_0 (B6 m), and residual displacement y_t (B7 m, with 0 < y_t < y_0).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= 0, B7 >= B6), "Invalid Slug-Test Geometry or Non-Decaying Head (Requires 0 < y_t < y_0)", ROUND(86400 * ((B2 ^ 2) * B3 / (2 * B4 * B5)) * LN(B6 / B7), 4))Normalized Residual Head Ratio y_t / y_0 (Semi-Log Plot Ordinate)
Computes ROUND(y_t / y_0, 4); Bouwer & Rice recommend fitting the straight-line segment across y_t / y_0 between ~0.20 and 0.30 to avoid early filter-pack drainage artifacts.
=IF(OR(B6 <= 0, B7 <= 0, B7 >= B6), "Requires 0 < y_t < y_0", ROUND(B7 / B6, 4))Try the example
Use the original values or change them to test your understanding.