--- title: "Cantilever sheet pile, simplified method" subject: "Foundation Engineering" chapter: 5 key: "semester_5/foundation_engineering:cantilever-sheet-pile-backfill-3m" source: https://www.bctengineer.com/q/semester_5/foundation_engineering/cantilever-sheet-pile-backfill-3m site: BCT Engineering --- # Cantilever sheet pile, simplified method Foundation Engineering · Chapter 5: Flexible Retaining Structures and Coffer Dams - Asked in: 2074 Asoj, 5 marks - Video: [[Numerical 1- Simplified Method] Cantilever Sheet Pile in Cohesionless Soil | Foundation Engineering](https://www.youtube.com/watch?v=NZQpCk7kSXI) — Abhash Acharya - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/cantilever-sheet-pile-backfill-3m - Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-5 ## Question A cantilever sheet pile wall is driven into sand deposit having friction angle $35^\circ$ and bulk unit weight $22\ \text{kN/m}^3$. One side of the sheet pile was backfilled to 3 m height. The backfill material is cohesionless sand having $\phi = 32^\circ$ and bulk unit weight of $18\ \text{kN/m}^3$. Using the simplified method determine the depth of penetration needed for the sheet pile to retain the backfill. Provide a safety factor of 2 for the passive resistance. The water table is below the base of the sheet pile. ## Short answer By applying a factor of safety of 2 to passive resistance and equating moments about the pile tip, the required penetration depth is 3.10 m below the 3 m backfill level. ## Answer **Data:** deposit (in which the pile is driven): $\phi_2 = 35^\circ$, $\gamma_2 = 22$ kN/m$^3$. Backfill 3 m high on one side: $\phi_1 = 32^\circ$, $\gamma_1 = 18$ kN/m$^3$. $FS = 2$ on passive resistance. Water table below the pile tip. Simplified method: moments about the pile tip. **Coefficients** $$ K_{a1} = \tan^2(45^\circ-16^\circ) = 0.3073,\quad K_{a2} = \tan^2(45^\circ-17.5^\circ) = 0.2710,\quad K_p = \tan^2(45^\circ+17.5^\circ) = 3.6902 $$ **Active pressures (back, depth $z$ from the top of the backfill; the dredge line is at $z=3$)** - Backfill ($0 \le z \le 3$): $p = K_{a1}\gamma_1 z$, giving 16.59 kN/m$^2$ at 3 m. - Below 3 m (in the deposit): $p = K_{a2}\,[18\times3 + 22(z-3)] = 14.63 + 5.962(z-3)$ kN/m$^2$. **Passive pressure (front, depth $y$ below the dredge line)** $$ p_p = \frac{K_p\gamma_2 y}{FS} = \frac{3.690\times22\,y}{2} = 40.59\,y\ \text{kN/m}^2 $$ **Moments about the tip** (embedment $D$): the active moment is $$ M_a(D) = \int_0^{3+D} p_a\,(3+D-z)\,dz $$ and the passive moment is $M_p = \tfrac16\,(K_p\gamma_2/FS)\,D^3 = 6.765\,D^3$. Solving $M_a = M_p$ by trial and error gives $$ D = 3.10\ \text{m}:\qquad M_a = 202.4,\quad M_p = 202.4\ \text{kN m/m} $$ (active force 99.0 kN/m, passive force 195.6 kN/m). **Answer: required depth of penetration $D \approx 3.10$ m** below the 3 m backfill (dredge) level. Since $FS = 2$ is already applied to the passive resistance, no further increase is needed; the total pile length is about 6.1 m. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which K_a is used for the pressure from the backfill zone (0 to 3 m)? A. K_a2 = 0.2710 from phi = 35 B. K_a1 = 0.3073 from phi = 32 and gamma = 18 C. K_p = 3.69 D. 0.3333 Answer: B. Backfill (phi = 32, gamma = 18) uses K_a1; the deposit below uses K_a2. (Key point: Which soil parameters) 2. How is active pressure computed below 3 m? A. K_a1 x gamma_1 x z B. K_a2 x (18x3 + 22(z-3)) C. K_p x gamma_2 x y D. Zero Answer: B. Below the dredge line the overburden is 18x3 plus 22 per metre, multiplied by K_a2. (Key point: Active pressure below dredge line) 3. How is FS = 2 applied? A. Active pressure doubled B. D doubled C. Passive pressure divided by 2: K_p gamma y /2 D. Ignored Answer: C. Passive resistance is reduced by FS: 3.69x22y/2 = 40.59y. (Key point: Factor of safety) 4. What is the depth of penetration, and is a further increase needed? A. About 3.10 m, and no further increase since FS is already on passive B. About 3.10 m, increase by 20% C. About 6.1 m below dredge D. About 1.5 m Answer: A. Moments about the tip give D = 3.10 m; FS is already included so no extra increase is applied. 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