Top-Down Excavation Shoring, FHWA GEC-7 Grouted Soil-Nail Wall Pullout & Spacing
Soil-Nail Wall Grout Pullout Capacity & Spacing Formula
Calculate Ultimate Grout-Soil Bond Pullout Qu (kN), FHWA ASD Allowable Pullout Resistance (FS = 2.0, kN), Tributary Facing Nail Load (kN), and Pullout Factor of Safety.
Only the nail length BEHIND the active failure wedge resists pullout—counting total drilled bar length double-counts the sliding soil!
Top-down shotcrete **Grouted Soil-Nail Shoring** drills rotary/auger holes of Diameter `D_{dh}` (`100–200` mm) on Horizontal x Vertical Grid `S_h * S_v` (`m²`) and encapsulates Grade 520 threaded steel bars in neat cement grout. Under **FHWA GEC-7 (`FHWA-NHI-14-007`)**, any nail segment inside the Rankine/Coulomb active wedge moves *with* the sliding block—so pullout resistance comes EXCLUSIVELY from **Resistant-Zone Bond Length `L_p`** (`m`, behind the slip surface) mobilizing Ultimate Grout-to-Ground Bond Stress `q_u` (`kPa`, verified by sacrificial field pullout jack testing!): **Ultimate Pullout Capacity `Q_u = PI() * (D_{dh} / 1,000) * L_p * q_u`** (`kN`), **ASD Allowable Pullout `Q_{all} = 0.50 * Q_u`** (`FS_P = 2.0`), opposing **Tributary Nail Service Load `T_{service} = sigma_a * S_h * S_v`** (`kN`) with **Pullout Safety Factor `FS = Q_u / T_{service} >= 2.0`**!
Verify on a Highway Cut Soil-Nail Shoring Row in Dense Glacial Till—Drillhole_Diameter `D_{dh}` = 150 mm (B2), Behind-Slip_Bond_Length `L_p` = 5.50 m (B3), Field-Verified_Ultimate_Bond `q_u` = 140.0 kPa (B4), Grid_Spacings `S_h` = 1.50 m (B5) x `S_v` = 1.50 m (B6), and Design_Lateral_Earth_Pressure `sigma_a` = 36.0 kPa (B7): Ultimate Pullout reaches `362.9` kN (E2), ASD Allowable equals `181.4` kN (E3) vs Tributary Nail Demand `81.0` kN (E4), yielding a robust `FS = 4.48 >= 2.0` (E5)!
| FHWA GEC-7 Soil-Nail KPI (Ddh=150 mm, Grid 1.5x1.5 m, sigma_a=36 kPa) | Formula | Verified Output |
|---|---|---|
| Ultimate Bond Pullout Qu (kN) | PI() * (Ddh_mm / 1000) * Lp_m * qu_kPa | 362.9 kN (128.2 kN @ soft clay seam!) |
| Allowable ASD Pullout Q_all (kN) | 0.50 * Ultimate_Pullout_Qu_kN (FS=2.0) | 181.4 kN (64.1 kN < 81 kN @ clay seam!) |
| Tributary Nail Demand T_serv (kN) | Earth_Pressure_kPa * Sh_m * Sv_m | 81.0 kN |
| Pullout Factor of Safety FS | Ultimate_Pullout_Qu / Tributary_Demand_T | 4.48 (1.58 < 2.0 FAIL @ clay seam!) |
FHWA GEC-7 Resistant-Zone Bond Pullout & Tributary Grid Safety Factor Formula
Validate `Drillhole D_{dh}` in `[75, 350]` mm, `Bond_Length L_p > 0.5` m, `Bond_Stress q_u > 15` kPa, `Spacings S_h, S_v` in `[0.5, 3.0]` m, and `Earth_Pressure sigma_a > 2` kPa!
=LET(dd_m, B2 / 1000, lp_m, B3, qu_k, B4, sh_m, B5, sv_m, B6, sa_k, B7, qu_n, PI() * dd_m * lp_m * qu_k, ts_n, sa_k * sh_m * sv_m, IF(OR(B2 < 75, B2 > 350, lp_m <= 0.5, qu_k <= 15, sh_m < 0.5, sh_m > 3, sv_m < 0.5, sv_m > 3, sa_k <= 2), "Invalid Soil-Nail Input", ROUND(qu_n / ts_n, 2)))Shortened Bond Zone in Stiff Clay Lens (Lp = 3.2 m, qu = 85 kPa) Pullout Rejection Check
Hit a slickensided clay lens (`q_u` B4 = 85 kPa) with shortened bond zone (`L_p` B3 = 3.2 m): Ultimate Pullout E2 drops to `128.2` kN (`Q_{all} = 64.1` kN in E3 `< 81.0` kN demand!), pushing `FS` E5 down to **`1.58 < 2.0`**—requiring tightened `1.1` m nail spacing or deeper `6.5` m nails before excavating the next `1.5` m bench!
=IF(ISTEXT(E5), E5, ROUND(PI() * (B2 / 1000) * B3 * B4, 1))Try the example
Use the original values or change them to test your understanding.