Deep Foundations & Seismic Underpinning, FHWA Drilled & Grouted Micropile Design
Drilled & Grouted Micropile Bond & Structural Load Formula
Calculate Ultimate Grout-to-Ground Bond Capacity (kN), Allowable Geotechnical Bond Load (FS = 2.0, kN), Composite Casing+Grout Structural Capacity (kN), and Governing Load.
Small-diameter micropiles ignore end-bearing completely—and switch from geotechnical skin-friction failure in sand to structural steel yielding in bedrock!
Low-headroom seismic retrofits and bridge underpins install **Small-Diameter (`150–300` mm) Drilled & Pressure-Grouted Micropiles** (`FHWA-NHI-05-039`) using high-yield API N80 steel casing (`F_y = 552` MPa, Steel Area `A_s` mm²) filled with neat cement grout (`f’_c = 30–40` MPa, Core Area `A_g` mm²). Because a `200` mm tip has tiny area (`0.031` m²), FHWA design neglects tip bearing (`Q_{tip} = 0`) and evaluates TWO competing axial limit states: (1) **Geotechnical Grout-to-Ground Side Bond** along Uncased Bond Length `L_b` (m) of Diameter `D_b` (mm) at Nominal Bond Strength `alpha_{bond}` (`kPa`): **`P_{G,ult} = alpha_{bond} * PI() * (D_b / 1,000) * L_b`** (`kN`) and **Allowable Bond `P_{G,all} = 0.50 * P_{G,ult}`** (`FS = 2.0`), vs (2) **FHWA ASD Plunging/Cased Structural Compression `P_{c,all} = (0.47 * F_y * A_s + 0.40 * f’_c * A_g) / 1,000`** (`kN`), with **`MIN(P_{G,all}, P_{c,all})`** governing!
Verify on a Type B Pressure-Grouted Dense-Sand Micropile—Bond-Zone_Diameter `D_b` = 200 mm (B2), Bond_Length `L_b` = 9.0 m (B3), Pressure-Grouted_Sand_Bond `alpha_{bond}` = 320 kPa (B4), API_N80_Casing_+_Bar_Steel `A_s` = 3,420 mm² (B5) at `F_y` = 552 MPa (B6), and Internal_Grout_Area `A_g` = 24,800 mm² (B7) at `f’_c` = 35 MPa (B8): Ultimate Bond reaches `1,809.6` kN (E2), Allowable Geotechnical Bond equals `904.8` kN (E3) vs Structural Capacity `1,234.5` kN (E4)—so Geotechnical Bond governs at `904.8` kN (E5)!
| FHWA Micropile Limit-State KPI (Db=200 mm, Lb=9.0 m, N80 Steel, alpha=320 vs 680 kPa) | Formula | Verified Output |
|---|---|---|
| Ultimate Grout-Ground Bond (kN) | alpha_kPa * PI() * (Db_mm / 1000) * Lb_m | 1,809.6 kN (3,845.3 kN in granite!) |
| Allowable Geotech Bond PG_all (kN) | 0.50 * Ultimate_Bond_kN (FS=2.0) | 904.8 kN (1,922.7 kN in granite) |
| Allowable Structural Pc_all (kN) | (0.47 * Fy * As + 0.40 * fc * Ag) / 1000 | 1,234.5 kN |
| Governing Micropile Capacity (kN) | MIN(Allowable_Bond, Allowable_Structural) | 904.8 kN (switches to 1,234.5 kN in rock!) |
FHWA Dual-Envelope Geotechnical Bond vs Composite Casing Compression Formula
Validate `Bond_Diam D_b` in `[100, 400]` mm, `Bond_Length L_b > 1.0` m, `Bond_Stress alpha > 30` kPa, `Steel_Area A_s > 200` mm², `Steel_Yield F_y` in `[250, 700]` MPa, `Grout_Area A_g > 2,000` mm², and `Grout f’_c` in `[20, 60]` MPa!
=LET(db_m, B2 / 1000, lb_m, B3, ab_k, B4, as_m, B5, fy_m, B6, ag_m, B7, fc_m, B8, pg_a, 0.5 * ab_k * PI() * db_m * lb_m, pc_a, (0.47 * fy_m * as_m + 0.4 * fc_m * ag_m) / 1000, IF(OR(B2 < 100, B2 > 400, lb_m <= 1, ab_k <= 30, as_m <= 200, fy_m < 250, fy_m > 700, ag_m <= 2000, fc_m < 20, fc_m > 60), "Invalid Micropile Input", ROUND(MIN(pg_a, pc_a), 1)))Sound Granite Rock Socket (alpha = 680 kPa) Structural Casing Ceiling Switch Check (Set Bond B4 = 680 kPa)
Socket the identical `9.0` m bond zone into sound granite (`alpha_{bond}` B4 = 680 kPa): Allowable Geotech Bond E3 surges to `1,922.7` kN, so `MIN(...)` in E5 caps Governing Capacity cleanly at **`1,234.5` kN**—proving further rock drilling is wasted money unless casing wall thickness or center-bar steel area `A_s` is increased!
=IF(ISTEXT(E5), E5, ROUND((0.47 * B6 * B5 + 0.4 * B8 * B7) / 1000, 1))Try the example
Use the original values or change them to test your understanding.