Cantilever Sheet Pile Wall Penetration Depth
Rankine coefficients, active force, and the embedment that balances moments about the toe.
Example
You enter
- Retained height above dredge line (ft) 12
- Soil friction angle phi (degrees) 32
- Soil unit weight (lb/cu ft) 120
- Increase on theoretical depth (%) 30
- Allowable bending stress (psi) 30000
You get
- Active pressure coefficient Ka 0.3073
- Passive pressure coefficient Kp 3.2546
- Active force 2654.71
- Theoretical embedment 10.03 ft
- Design embedment 13.04 ft -- 1.09 times the retained height
- Total pile length 25.0417
- Embedment share (%) 52.08
- Depth to maximum moment 5.32 ft below the dredge line, not at it
- Maximum moment 22,128 ft-lb per foot of wall
- Section modulus required 8.9 in^3 per foot of wall
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
ScopeIncreased by the conventional 20 to 40% that USS calls the margin. The worked 12 ft wall needs a 25 ft pile, 52% of it below the excavation. Deflection often governs instead and this does not compute it.
Formula or tableKa = tan^2(45 - phi/2); Kp = tan^2(45 + phi/2); Pa = 0.5 Ka gamma H^2 at H/3; embedment from moments about the toe on the gross pressures, Kp D^3 = Ka (H + D)^3; max moment where shear is zero, z = H sqrt(Ka) / (sqrt(Kp) - sqrt(Ka)); S = M / allowable stress.
Source and editionRankine earth pressure with the simplified (Blum) cantilever moment balance, increased by the conventional 20 to 40% (USS Steel Sheet Piling Design Manual). The geotechnical report, the applicable building code, and the design engineer govern.
Free accessRankine's relations are public; the soil parameters come from the site's own investigation.
What governsEstimate. AHJ and licensed professional govern.
API field namesretained_height_ft, friction_angle_deg, unit_weight_pcf, increase_factor_pct, allowable_stress_psi, ka, kp, active_force_plf, theoretical_depth_ft, design_depth_ft, total_length_ft, embedment_share_pct, depth_to_max_moment_ft, max_moment_ftlb_per_ft, section_modulus_in3_per_ft
- Soil drained granular, no surcharge, and no water differential across the wallspec-v1831 scope
- Deflection NOT computed, and frequently the criterion that governs; a flexible wall can move inches while the section is well inside its capacitydesign engineer