--- title: "Active thrust, 6 m wall, sand over clay" subject: "Foundation Engineering" chapter: 3 key: "semester_5/foundation_engineering:two-layer-wall-6m-sand-clay" source: https://www.bctengineer.com/q/semester_5/foundation_engineering/two-layer-wall-6m-sand-clay site: BCT Engineering --- # Active thrust, 6 m wall, sand over clay Foundation Engineering · Chapter 3: Lateral Earth Pressure Theories and Retaining Walls - Asked in: 2082 Bhadra, 6 marks - Video: [Rankine's Active Earth Pressure Distribution on Three Layered Soil with Water Table and Surcharge](https://www.youtube.com/watch?v=vyVz6HhquuI) — Master Civil Engineering - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/two-layer-wall-6m-sand-clay - Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-3 ## Question A retaining wall of 6 m high has two layers of backfill. The soil supported consists of 3 m sand ($\gamma = 17.5\ \text{kN/m}^3$, $\phi = 30^\circ$) overlying saturated sandy clay ($\gamma = 19\ \text{kN/m}^3$, $\phi = 30^\circ$, $c = 10\ \text{kN/m}^2$). The ground water table is at the upper surface of the sandy clay. Draw the distribution of active pressure on the wall and calculate the total thrust per meter of the wall and its point of application. ## Short answer Using Rankine theory, active pressures are computed for sand (Ka=0.333) and saturated clay (Ka=0.333, c=10 kN/m²) with water pressure. Total thrust is 102.0 kN/m, acting horizontally at 1.86 m above the base. ## Answer **Assumptions:** smooth vertical wall, horizontal backfill, Rankine theory; sand above the water table is taken at the given unit weight; the clay is saturated, so the effective stress uses $\gamma' = \gamma_{sat} - \gamma_w = 19.00 - 9.81 = 9.19\ \text{kN/m}^3$. **Coefficients** $$ \begin{aligned} K_{a1} &= \tan^2(45^\circ-30^\circ/2) = 0.3333 \\ K_{a2} &= \tan^2(45^\circ-30^\circ/2) = 0.3333,\quad 2c\sqrt{K_{a2}} = 2\times10\times0.5774 = 11.55\ \text{kN/m}^2 \end{aligned} $$ **Pressures (kN/m$^2$)** - Sand, top: $0$. - Sand, bottom ($z=3$ m): $p = K_{a1}\gamma H_1 = 0.3333\times17.5\times3 = 17.50$. - Clay, top: $\sigma_v' = 17.5\times3 = 52.50$, so $p = 0.3333\times52.50 - 11.55 = 5.95$. - Clay, bottom ($z=6$ m): $\sigma_v' = 52.50 + 9.19\times3 = 80.07$, so $p = 0.3333\times80.07 - 11.55 = 15.14$. - Water pressure at the base: $u = 9.81\times3 = 29.43$ (zero at the water table). ```text 0 --| |\ sand | \ | \ WT -|---17.50 | eff 5.95 clay | \ | \ eff 15.14 base|-----> + water 29.43 ``` **Forces per metre run and lever arms about the base** | Part | Force (kN/m) | Arm above base (m) | Moment (kN m/m) | |---|---|---|---| | Sand triangle | 26.25 | 4.000 | 105.00 | | Clay, rectangle | 17.86 | 1.500 | 26.79 | | Clay, triangle | 13.78 | 1.000 | 13.78 | | Water pressure | 44.14 | 1.000 | 44.14 | | **Total** | **102.04** | | **189.72** | $$ \bar y = \frac{\sum M}{\sum F} = \frac{189.72}{102.04} = 1.86\ \text{m above the base} $$ **Answer: total thrust $P = 102.0$ kN/m (water included), acting horizontally at 1.86 m above the base of the wall.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For the saturated clay below the water table, the effective unit weight used is: A. 19 kN/m3 B. 9.19 kN/m3 C. 9.81 kN/m3 D. 28.8 kN/m3 Answer: B. gamma' = 19 - 9.81 = 9.19 kN/m3, and water pressure is added separately. (Key point: Effective unit weight) 2. Active pressure at the bottom of the sand (3 m) is: A. 52.5 kN/m2 B. 17.50 kN/m2 C. 5.95 kN/m2 D. 29.43 kN/m2 Answer: B. 0.3333 x 17.5 x 3 = 17.50. (Key point: Pressure at base of sand) 3. At the top of the clay, p = Ka sigma_v' - 2c sqrt(Ka) = A. 17.5 kN/m2 B. 5.95 kN/m2 C. -11.55 kN/m2 D. 15.14 kN/m2 Answer: B. 0.3333 x 52.5 - 11.55 = 5.95. (Key point: Clay top pressure) 4. Water pressure at the wall base (3 m below WT) is: A. 29.43 kN/m2 B. 58.9 kN/m2 C. 0 D. 9.19 kN/m2 Answer: A. u = 9.81 x 3 = 29.43, giving thrust 44.14 kN/m; total P = 102.0 kN/m at 1.86 m. (Key point: Water pressure) ## Close variants set in other exams - [Active thrust, 7.5 m wall, 3 m sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Atwo-layer-wall-7-5m-3m-sand) — Foundation Engineering, chapter 3, asked 4× - [Active thrust, 7.5 m wall, 4.5 m sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Atwo-layer-wall-7-5m-4-5m-sand) — Foundation Engineering, chapter 3, asked 4× - [Active thrust, 7.5 m wall, 5 m sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Atwo-layer-wall-7-5m-5m-sand) — Foundation Engineering, chapter 3, asked 4× ## Related in Foundation Engineering - [Active thrust with surcharge and water table](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-6m-surcharge-water-table) — Foundation Engineering, chapter 3 - [Active pressure, sloping backfill and water table](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-sheet-pipe-sloping-backfill) — Foundation Engineering, chapter 3 - [Active pressure, 8 m wall, table of layers](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-8m-two-layer-table) — Foundation Engineering, chapter 3 - [Stability of gravity wall, two layers](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Astability-gravity-wall-two-layer) — Foundation Engineering, chapter 3 - [Passive thrust on retaining wall back](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-passive-thrust-two-layer) — Foundation Engineering, chapter 3 - [Active pressure on wall, cohesive soil](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acohesive-wall-pressure-diagram) — Foundation Engineering, chapter 3 ## Related in other subjects - [Clay over sand, effective stress at depths](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aclay-sand-profile-effective-stress-depths) — Soil Mechanics, chapter 6 - [Uniform sand, water table 2 m, capillary](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Auniform-sand-effective-stress-capillary) — Soil Mechanics, chapter 6 - [Primary settlement, sand over clay, 110 kPa](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aprimary-settlement-sand-clay-110kpa) — Soil Mechanics, chapter 9 - [Two-layer sand, plot stresses (bulk 18)](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Atwo-layer-sand-stress-plot) — Soil Mechanics, chapter 6