Ground Improvement, Soft Marine Clay & Prefabricated Wick Drains
Barron Radial Consolidation Vertical Wick Drain Time Formula
Calculate Drain Spacing Ratio n = d_e / d_w, Exact Barron Geometric Factor F(n), Radial Consolidation Time Factor T_r, and Surcharge Waiting Time to Target Consolidation (Months).
Why Prefabricated Vertical Drains (PVDs) compress 20-year marine-clay settlements into 8 months!
Thick saturated marine clay deposits under airport runways, port container yards, and highway embankments take decades to consolidate vertically (t proportional to H_dr^2 / c_v), yet horizontal varved silt seams give Horizontal Coefficient of Consolidation c_h = 2x to 5x higher than c_v AND stitching Prefabricated Vertical Wick Drains (equivalent diameter d_w ~ 0.05–0.07 m) on a triangular/square grid shrinks drainage cylinder diameter to d_e = 1.2–2.5 m! Under Barron’s Exact Equal-Strain Radial Consolidation Solution with Spacing Ratio n = d_e / d_w, Geometric Resistance Factor is F(n) = ((n^2) / (n^2 - 1)) * LN(n) - (3 * n^2 - 1) / (4 * n^2), Radial Time Factor is T_r = (F(n) / 8) * LN(1 / (1 - U_r)), and Surcharge Waiting Time is t_years = ((d_e^2) * T_r) / c_h!
Verify on a Port Reclamation Surcharge Grid—Influence_Zone_Diameter d_e = 1.50 m (B2), Equivalent_Wick_Diameter d_w = 0.06 m (100x4 mm strip drain, B3 -> Spacing Ratio n = 25.00 in E2), Horizontal_Consolidation_Coeff c_h = 2.40 m²/yr (B4), and Target_Radial_Consolidation U_r = 0.90 (90.0%, B5): Exact Barron Factor F(25) hits 2.4744 (E3), Radial Time Factor T_r equals 0.7122 (E4), and Time to 90% Radial Consolidation equals 8.01 months (E5)!
| Barron Wick Drain KPI (de = 1.50 m, dw = 0.06 m, ch = 2.40 m²/yr, Ur = 90%) | Formula | Verified Output |
|---|---|---|
| Drain Spacing Ratio n (de / dw) | Influence_Dia_de / Equivalent_Drain_dw | 25.00 (40.00 @ de = 2.40 m) |
| Exact Barron Factor F(n) | (n^2/(n^2-1))*LN(n) - (3*n^2-1)/(4*n^2) | 2.4744 (2.9413 @ de = 2.40 m) |
| Radial Time Factor T_r | (F(n) / 8) * LN(1 / (1 - Ur)) | 0.7122 (0.8466 @ de = 2.40 m) |
| Waiting Time to Target Ur (Months) | ((de^2 * T_r) / ch_m2_yr) * 12 | 8.01 mo (24.38 mo @ de = 2.40 m!) |
Exact Barron Equal-Strain Radial Consolidation Time Formula
Validate d_w > 0, Spacing_Ratio n = d_e / d_w >= 5, c_h > 0, and Target_Consolidation U_r strictly in (0.05, 0.999)!
=LET(de_m, B2, dw_m, B3, ch_y, B4, ur_f, B5, IF(OR(dw_m <= 0, de_m < 5 * dw_m, ch_y <= 0, ur_f <= 0.05, ur_f >= 0.999), "Invalid Wick Drain Input", LET(nr_t, de_m / dw_m, n2_s, nr_t ^ 2, fn_b, (n2_s / (n2_s - 1)) * LN(nr_t) - (3 * n2_s - 1) / (4 * n2_s), tr_f, (fn_b / 8) * LN(1 / (1 - ur_f)), ROUND((((de_m ^ 2) * tr_f) / ch_y) * 12, 2))))Wider Drain Grid nonlinear d_e^2 * F(n) Schedule Penalty Check (Set d_e = 2.40 m)
Widen Influence_Diameter B2 by 60% from 1.50 m to 2.40 m to cut wick installation footage: because consolidation time scales with BOTH d_e^2 (2.56x) AND higher F(40) = 2.9413 (E3), Surcharge Waiting Time E5 triples from 8.01 months to 24.38 months!
=IF(ISTEXT(E5), E5, LET(nr_t, B2 / B3, n2_s, nr_t ^ 2, ROUND((n2_s / (n2_s - 1)) * LN(nr_t) - (3 * n2_s - 1) / (4 * n2_s), 4)))Try the example
Use the original values or change them to test your understanding.