---
title: "Culmann's method, active, cohesionless"
subject: "Foundation Engineering"
chapter: 3
key: "semester_5/foundation_engineering:culmann-active-plain"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/culmann-active-plain
site: BCT Engineering
---

# Culmann's method, active, cohesionless

Foundation Engineering · Chapter 3: Lateral Earth Pressure Theories and Retaining Walls

- Asked in: 2081 Bhadra, 4 marks
- Video: [CULMANN GRAPHICAL METHOD | ACTIVE EARTH PRESSURE | FOUNDATION CHAPTER 2 | MOST IMPORTANT](https://www.youtube.com/watch?v=P0b-PcEqrhE) — Sudip Dhakal
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/culmann-active-plain
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-3

## Question

Explain with neat sketch the step by step procedure for Culmann's graphical method of active earth pressure without surcharge load for cohesionless soil.

## Short answer

Draw wall, φ-line BD, pressure line BE at ψ=θ−δ. From heel draw trial planes, compute wedge weights W=γA. Plot W on BD, draw lines parallel to BE to intersect planes, forming the Culmann curve. Tangent parallel to BD gives maximum ordinate Pa, acting at H/3, inclined at δ to the wall normal.

## Answer

Culmann's graphical method for active thrust on a wall with a cohesionless backfill and no surcharge:

1. Draw the wall $AB$ and the backfill surface to scale and 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 $B$ making angle $\psi = \theta-\delta$ with $BD$ ($\theta$ = wall back angle with horizontal, $\delta$ = wall friction).
4. Draw trial failure planes $BC_1, BC_2, BC_3,\dots$ from $B$ to the ground surface.
5. Find the area of each wedge $ABC_i$ and its weight $W_i = \gamma\times\text{area}$ per metre run.
6. To a suitable scale, mark $W_1, W_2, W_3,\dots$ on $BD$ as $b_1, b_2, b_3,\dots$
7. From each $b_i$ draw a line parallel to $BE$ to meet $BC_i$ at $c_i$.
8. Join $c_1, c_2, c_3,\dots$ with a smooth curve (Culmann curve).
9. Draw a tangent to the curve parallel to $BD$; let it touch at $c_m$.
10. Draw $c_m b_m$ parallel to $BE$ to meet $BD$. Its length, converted by the force scale, is the **active thrust $P_a$**. $BC_m$ is the critical failure plane.
11. $P_a$ acts at $H/3$ above the base of the wall, inclined at $\delta$ to the wall normal.

```text
    A |\                      ground
      |  \_____________________ C1 C2 Cm C3
      |     curve ..  .
      |        ..  /
    B +---b1--b2--bm--b3--> D   (phi from horizontal)
          BE at psi from BD, weights on BD
```

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In Culmann's active method, the phi-line BD is drawn from the heel B:
   A. Vertically
   B. At angle phi to the horizontal
   C. At angle phi to the wall
   D. At 45 degrees
   Answer: B. BD is at angle phi to the horizontal. (Key point: Phi-line)

2. Weight of each trial wedge is calculated as:
   A. gamma x area per metre run
   B. gamma x height
   C. Ka x gamma x H
   D. c x area
   Answer: A. W_i = gamma x area of wedge ABCi per metre run. (Key point: Wedge weight)

3. Pa is obtained from:
   A. The ordinate cm-bm (parallel to BE) at the point where the tangent parallel to BD touches the curve
   B. The shortest distance from B to the curve
   C. The sum of all Wi
   D. The length BC
   Answer: A. The tangent parallel to BD touches at cm; cm-bm scaled gives Pa and BCm is the critical plane. (Key point: Reading Pa)

4. Pa acts at:
   A. H/2 above the base, horizontally
   B. H/3 above the base, inclined at delta to the wall normal
   C. At the top of the wall
   D. 2H/3 above the base
   Answer: B. For uniform cohesionless fill with no surcharge, Pa acts at H/3 at angle delta to the normal. (Key point: Point of action)

## Related in Foundation Engineering

- [Culmann's method, active, with surcharge](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aculmann-active-surcharge) — Foundation Engineering, chapter 3, asked 3×
- [Culmann's method for passive pressure](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aculmann-passive) — Foundation Engineering, chapter 3, asked 2×
- [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
- [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 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
- [Anchored sheet pile, free earth procedure](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aanchored-sheet-pile-free-earth-procedure) — Foundation Engineering, chapter 5