Cantilever Sheet Pile Wall Penetration Depth

Rankine coefficients, active force, and the embedment that balances moments about the toe.

Run the calculator

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 8.19 ft
Design embedment 10.64 ft -- 0.89 times the retained height
Total pile length 22.644
Embedment share (%) 47.0057
Depth to maximum moment 3.87 ft below the dredge line, not at it
Maximum moment 17476 ft-lb per foot of wall
Section modulus required 7.0 in^3 per foot of wall

Details, formula, and sources

Increased by the conventional allowance for the net-pressure simplification. The worked 12 ft wall needs a 23 ft pile, 47% of it below the excavation. Deflection often governs instead and this does not compute it.

Ka = tan^2(45 - phi/2); Kp = tan^2(45 + phi/2); Pa = 0.5 Ka gamma H^2 at H/3; embedment from (Kp - Ka) gamma D^3 / 6 = Pa (D + H/3); max moment where net shear is zero; S = M / allowable stress.

Rankine earth pressure with the cantilever net-pressure simplification, increased by the conventional 20 to 40% for that idealisation. The geotechnical report, the applicable building code, and the design engineer govern.

Rankine's relations are public; the soil parameters come from the site's own investigation.

Estimate. AHJ and licensed professional govern.

Field names used by the API: retained_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