--- title: "Culmann's method, active, with surcharge" subject: "Foundation Engineering" chapter: 3 key: "semester_5/foundation_engineering:culmann-active-surcharge" source: https://www.bctengineer.com/q/semester_5/foundation_engineering/culmann-active-surcharge site: BCT Engineering --- # Culmann's method, active, with surcharge Foundation Engineering · Chapter 3: Lateral Earth Pressure Theories and Retaining Walls - Asked in: 2079 Bhadra, 5 marks; 2076 Chaitra, 5 marks; 2073 Shrawan, 8 marks (asked 3 times) - Video: [Culmann's Method for Active Condition](https://www.youtube.com/watch?v=mKoXwh5VEUo) — Ekeeda - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/culmann-active-surcharge - Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-3 ## Question Describe the step by step procedure of Culmann's method of determining active thrust behind a retaining wall carrying an inclined backfill with line load/surcharge, with the help of a sketch. Explain how surcharge affects earth pressure in the active state. ## Short answer Draw wall, φ-line BD, pressure line BE, trial planes. Wedge weights including surcharge are plotted on BD; lines parallel to BE intersect planes to form the Culmann curve. The tangent parallel to BD gives Pa. Surcharge adds uniform pressure Ka q, raising resultant above H/3 and increasing overturning moment. ## Answer Culmann's method is a graphical wedge method that finds the active thrust on a wall for any backfill surface, including inclined backfill and surcharge. #### Procedure (cohesionless backfill with inclined surface and line load) 1. Draw the wall $AB$ and the backfill surface to scale. Mark the heel $B$. 2. Draw the **$\phi$-line $BD$** from $B$ at angle $\phi$ to the horizontal. 3. Draw the **pressure line $BE$** from $B$ at angle $\psi = \theta-\delta$ above $BD$, where $\theta$ is the angle the wall back makes with the horizontal (on the fill side) and $\delta$ is wall friction. 4. Draw several trial failure planes $BC_1, BC_2, \dots$ from $B$ to points on the ground surface. 5. Compute the weight $W_1, W_2,\dots$ of each trial wedge $ABC_i$ per metre. **If a line load $Q$ lies inside a wedge, add $Q$ to that wedge's weight**; for a uniform surcharge $q$, add $q\times$(horizontal width of the wedge) to the weight. 6. Choose a scale of force and mark $W_i$ along $BD$: $b_1, b_2, \dots$ 7. From each $b_i$ draw a line parallel to $BE$ to meet the corresponding trial plane $BC_i$ at $c_i$. 8. Join $c_1 c_2 \dots$ to get the **Culmann curve**. The step in the curve at the line load position shows the effect of $Q$ (jump when the plane passes beyond $Q$). 9. Draw a tangent to the curve parallel to $BD$. The ordinate from the point of tangency $c_m$ to $BD$, parallel to $BE$, scaled by the force scale, is the **active thrust $P_a$** (maximum). 10. The critical failure plane is $BC_m$; $P_a$ acts at $H/3$ above the base (uniform fill) at angle $\delta$ to the normal to the wall. ```text Q (line load) A v ground surface |\______________________ C1 C2 Cm C3 | .. | .. ... Culmann | .. curve | .. / B +--------/---> b1 b2 bm b3 (weights on BD) BD at phi, BE at psi from BD ``` #### Effect of surcharge on active pressure - A uniform surcharge $q$ is equivalent to an extra soil height $h_e = q/\gamma$. It adds a **uniform** (rectangular) pressure $\Delta p_a = K_a q$ over the whole height, so the total thrust increases by $K_a q H$. - The resultant thrust moves **higher** than $H/3$ because the pressure distribution changes from triangular to trapezoidal, increasing the overturning moment. - A line load adds a localised pressure on the wall (a discontinuity in the Culmann curve) and increases the thrust only when the load is within the sliding wedge; the closer to the wall the larger the effect. - Hence surcharges (traffic, buildings) must always be included in wall design. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In Culmann's method, the pressure line BE is drawn at what angle from the phi-line BD? A. psi = theta - delta B. psi = 90 - phi C. psi = phi + delta D. psi = 45 + phi/2 Answer: A. BD is at phi to the horizontal and BE at psi = theta - delta above BD, where theta is the wall back angle and delta wall friction. (Key point: Phi-line and pressure line) 2. How is a line load Q handled when a trial wedge contains it? A. Ignored B. Q is added to that wedge's weight C. Q is subtracted from the weight D. Q is applied at the heel only Answer: B. If the line load lies inside a wedge, Q is added to that wedge's weight before plotting. (Key point: Line load in wedge weight) 3. How is the active thrust Pa found from the Culmann curve? A. Minimum ordinate to BD B. Tangent parallel to BD; ordinate at the point of tangency (maximum) measured parallel to BE, scaled C. Length of BD D. The average of all ordinates Answer: B. A tangent parallel to BD touches at cm; the ordinate cm-bm parallel to BE is the maximum, giving Pa. (Key point: Reading Pa) 4. How does a uniform surcharge q affect active pressure? A. Adds a triangular pressure only at the base B. Adds a uniform pressure Ka q over the height, increasing thrust by Ka q H and raising the resultant above H/3 C. Reduces the thrust D. Moves the resultant below H/3 Answer: B. The diagram changes from triangular to trapezoidal; thrust increases and acts higher than H/3, increasing overturning moment. (Key point: Effect of uniform surcharge) ## 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 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, 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, 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× - [Culmann's method, active, cohesionless](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aculmann-active-plain) — Foundation Engineering, chapter 3 - [Active thrust, 6 m wall, sand over clay](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Atwo-layer-wall-6m-sand-clay) — Foundation Engineering, chapter 3, asked 4× ## Related in other subjects - [Inclined smooth pipe with wall shear limit](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Asmooth-pipe-inclined-wall-shear-limit) — Hydraulics, chapter 1 - [Short note: Retaining wall](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Ashort-retaining-wall) — Building Technology, chapter 3, asked 2× - [Parapet wall, gravity and counterfort retaining walls](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Aparapet-retaining-counterfort) — Building Technology, chapter 3 - [Short note: Basement and retaining wall](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Ashort-basement-retaining-wall) — Building Technology, chapter 3