Sheet Pile Wall Design

Calculation

1. 1Rankine coefficients at the ground surface
   K_a = \tan^2\!\left(45° - \frac{\varphi}{2}\right), \quad K_p = \tan^2\!\left(45° + \frac{\varphi}{2}\right)
   K_a = 0.333, \quad K_p = 3
   K_a=0.333
2. 2Theoretical embedment, moment equilibrium about the toe
   \sum M_{toe} = 0 \Rightarrow D_0
   D_0 = 12.205 \text{ m}
   D_0=12.205 m
3. 3Design embedment, 1.20 × theoretical
   D = (\text{depth factor}) \times D_0
   D = 1.200 \times 12.205 = 14.646
   D=14.646 m
4. 4Maximum bending moment
   M_{max} = \max|M(z)|
   M_{max} = 1671.9 \text{ at } z = 13.400 \text{ m}
   M_{max}=1671.9 kN·m

Assumptions

• Rankine active/passive earth pressure, the unified c–φ form: σa = max(σ'v·Ka − 2c√Ka, 0), σp = σ'v·Kp + 2c√Kp.
• Free earth support: the toe (cantilever) or the anchor/lowest brace (anchored) is the point the governing equilibrium equation takes moments about.
• A double-anchor wall uses a tributary load split (everything above the upper brace, plus half the block between the two braces, goes to the upper brace) — a preliminary idealisation of a statically indeterminate structure, not a full analysis.