About Cantilever Sheet Pile Wall Calculator
This cantilever sheet pile wall calculator estimates the required embedment depth and maximum bending moment for a steel sheet pile retaining a height H of cohesionless soil. It uses Rankine earth-pressure coefficients and a simplified net-pressure moment balance taken about the toe of the pile.
A cantilever sheet pile derives all its support from passive resistance of the soil below the dredge (excavation) line. The tool finds the theoretical penetration d0 by equating the active driving moment to the passive resisting moment about the toe, then increases it to a design depth D = 1.2 to 1.3 times d0 to account for the approximations of the simplified cantilever solution. Enter consistent SI units (metres, kN/m^3, degrees, kPa).
How It Works
- Compute Rankine coefficients Ka = tan^2(45 - phi/2) and Kp = tan^2(45 + phi/2), and a design passive coefficient Kp/FS.
- Build the active pressure on the retained side over the full height (H + D) including any uniform surcharge, and the passive pressure on the excavated side over the embedment depth.
- Solve for the theoretical depth d0 by taking moments about the toe: passive resisting moment equals active driving moment.
- Apply the design factor to obtain D = factor × d0, then locate the depth below the dredge line where the net shear is zero and evaluate the maximum bending moment there.
Worked Example
A cantilever sheet pile retains H = 5 m of dry sand with gamma = 18 kN/m^3, phi = 30 degrees, no surcharge, FS = 1.0 on the passive side, and a design factor of 1.3. Rankine coefficients are Ka = tan^2(30) = 0.333 and Kp = tan^2(60) = 3.0. The active pressure at the dredge line is Ka·gamma·H = 0.333 × 18 × 5 = 30 kPa and the active thrust above the dredge line is 0.5 × 0.333 × 18 × 5^2 = 75 kN/m. Equating the passive and active moments about the toe gives a theoretical depth d0 = 4.629 m, so the design depth is D = 1.3 × 4.629 = 6.018 m and the total pile length is 11.018 m. The net shear is zero 2.5 m below the dredge line, where the maximum bending moment is 281.25 kN·m per metre run.
Formulas
- Rankine earth-pressure coefficients
Ka = tan^2(45 - phi/2), Kp = tan^2(45 + phi/2), Kp_design = Kp / FS- Active and passive pressures
pa(y) = Ka (q + gamma y); pp(d) = Kp_design gamma d- Theoretical depth (moment balance about toe)
Pp (D/3) = Pa * arm_a solved for D = d0- Design depth and maximum moment
D = designFactor * d0; M_max evaluated at the depth of zero net shear below the dredge line
Standards & References
- USS Steel Sheet Piling Design Manual
- Rankine earth-pressure theory (1857)
- Das, Principles of Foundation Engineering
- BS 8002 / EN 1997 (Eurocode 7) for earth-retaining structures
Frequently Asked Questions
What simplifying assumptions does this cantilever sheet pile calculator make?
It assumes a homogeneous, cohesionless soil (c = 0), Rankine coefficients for a smooth vertical wall with level backfill, and a net-pressure moment balance about the toe. The design depth is the theoretical depth multiplied by 1.2 to 1.3 to approximate the rigorous fixed-earth cantilever solution. A water table below the dredge line is not modelled in this simplified version.
Why is the design embedment depth larger than the theoretical depth d0?
The theoretical depth d0 from a simple moment balance is the minimum penetration for equilibrium. Real cantilever walls need extra penetration to develop the reaction below the pivot point that the simplified analysis omits, so the depth is increased by 20 to 30 percent (a factor of 1.2 to 1.3) to give the design depth D.
How is the factor of safety applied?
The factor of safety is applied to the passive resistance by dividing the passive coefficient by FS (Kp_design = Kp / FS). This reduces the available resisting pressure, so a higher FS produces a deeper required embedment. A value of FS between 1.5 and 2.0 on passive resistance is common in practice.
Where does the maximum bending moment occur?
In a cantilever sheet pile the maximum bending moment occurs below the dredge line, at the depth where the net horizontal shear is zero. The calculator locates that point and integrates the active and passive pressure blocks above it to report the maximum moment per metre run of wall.