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Geotechnical Dewatering & Slope Stabilization, Casagrande Electro-Osmosis in Soft Clays

Casagrande Electro-Osmotic Clay Dewatering & Power Formula

Calculate Electric Voltage Gradient ie = V/L (V/m), Electro-Osmotic Cathode Water Flow Qe (L/h), DC Rectifier Ohmic Power (kW), and Specific Dewatering Energy (kWh/m³).

Vacuum wellpoints fail completely in fat marine clay (`k_h = 10^-10` m/s)—yet a 50 V/m DC electric field pumps pore water 10,000x faster!

Hydraulic conductivity `k_h` collapses with grain diameter squared (`10^{-9}` to `10^{-11}` m/s in soft sensitive clays and silts, rendering gravity/vacuum wells useless!). Leo Casagrande discovered that **Coefficient of Electro-Osmotic Permeability `k_e` is remarkably constant (`~4.0–6.0 * 10^{-9}` m²/(s·V)) across almost ALL fine soils** because mobile hydrated cations inside negatively charged clay double-layers drag pore water from steel/EKG Anodes (`+`) into pumped Cathode Wells (`-`)! Applying DC Voltage `V` across Electrode Spacing `L` (m -> **Electric Field `i_e = V / L`** V/m) over Cross-Sectional Clay Area `A` (m²) drives **Electro-Osmotic Flow `Q_e = k_e * i_e * A`** (`m³/s`, `* 3.6 * 10^6` = `L/h`), while Bulk Soil Electrical Conductivity `sigma_e` (`S/m`) dissipates **DC Rectifier Power `P_{DC} = (sigma_e * (V^2 / L) * A) / 1,000`** (`kW`)—revealing that **Specific Energy `E_w = P_{DC} / Q_{e,m3/h}` (`kWh/m³`) scales linearly with `V`!**

Verify on a Sensitive Marine-Clay Excavation Cut Stabilization—DC_Rectifier_Voltage `V` = 90.0 V (B2), Anode-to-Cathode_Spacing `L` = 1.80 m (B3 -> Voltage Gradient `i_e = 50.0` V/m in E2), Electro-Osmotic_Permeability `k_e` = 5.0 (`x 10^-9` m²/(s·V), B4), Treated_Cross-Section `A` = 24.0 m² (B5), and Pore-Fluid_Clay_Conductivity `sigma_e` = 0.085 S/m (B6): Pumped Cathode Seepage reaches `21.60` L/h (E3), DC Power draws `9.18` kW (E4), and Specific Energy equals `425.0` kWh/m³ of extracted pore water (E5)!

Casagrande Electro-Osmosis KPI (L=1.8 m, ke=5.0e-9, A=24 m², sigma=0.085 S/m, V=90 vs 140 V)FormulaVerified Output
Electric Field Gradient ie (V/m)DC_Voltage_V / Electrode_Spacing_L_m50.0 V/m (77.8 V/m desiccation risk @ 140 V!)
Cathode Water Extraction Qe (L/h)(ke_e9 * 1e-9) * ie * Area_m2 * 3,600,00021.60 L/h (33.60 L/h @ 140 V)
DC Rectifier Load P_DC (kW)(sigma_S_m * (V^2 / L_m) * Area_m2) / 10009.18 kW (22.21 kW = V^2 Ohmic heating!)
Specific Dewatering Energy (kWh/m³)DC_Power_kW / (Water_Flow_L_h / 1000)425.0 kWh/m³ (661.1 kWh/m³ @ 140 V)

Casagrande Electro-Osmotic Seepage Law & Ohmic Soil Heating Power Formula

Validate `DC_Voltage V` in `[10, 250]` V, `Spacing L` in `[0.5, 6.0]` m, `k_e` in `[0.5, 15.0]` (`x 10^-9`), `Area A > 1` m², and `Conductivity sigma_e` in `[0.005, 1.50]` S/m!

=LET(vd_c, B2, ls_m, B3, ke_n, B4 * 0.000000001, ac_m, B5, sg_s, B6, ie_v, vd_c / ls_m, qe_m, ke_n * ie_v * ac_m * 3600, pk_w, (sg_s * (vd_c ^ 2) * ac_m) / (ls_m * 1000), IF(OR(vd_c < 10, vd_c > 250, ls_m < 0.5, ls_m > 6, B4 < 0.5, B4 > 15, ac_m <= 1, sg_s < 0.005, sg_s > 1.5), "Invalid EO Input", ROUND(pk_w / qe_m, 1)))

Excessive 140 V Anode Heating & V^2 Power Penalty Check (Set DC Voltage B2 = 140 V)

Boost rectifier voltage from `90` to `140` V (`B2 = 140`, Field Gradient E2 = `77.8` V/m > `60` V/m Casagrande anode-drying ceiling!): Water Flow E3 rises `+55.6%` to `33.60` L/h, YET DC Power E4 jumps `+142%` (`(140/90)^2`) to `22.21` kW and Specific Energy E5 climbs to `661.1` kWh/m³—baking and cracking clay around the anodes so electrical contact resistance spikes!

=IF(ISTEXT(E5), E5, ROUND((B6 * (B2 ^ 2) * B5) / (B3 * 1000), 2))

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