--- title: "Culmann's method for passive pressure" subject: "Foundation Engineering" chapter: 3 key: "semester_5/foundation_engineering:culmann-passive" source: https://www.bctengineer.com/q/semester_5/foundation_engineering/culmann-passive site: BCT Engineering --- # Culmann's method for passive pressure Foundation Engineering · Chapter 3: Lateral Earth Pressure Theories and Retaining Walls - Asked in: 2080 Bhadra, 6 marks; 2074 Asoj, 6 marks (asked 2 times) - Video: [Culmann Graphical Method | Passive earth pressure | Foundation Engineering](https://www.youtube.com/watch?v=nT8wdCxdQ3c) — Sudip Dhakal - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/culmann-passive - Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-3 ## Question Explain with a neat sketch the step by step procedure for Culmann's graphical method of passive earth pressure. ## Short answer Draw wall, φ-line BD below horizontal on the opposite side, pressure line BE at ψ = θ+δ. Plot trial wedge weights on BD; lines parallel to BE intersect planes to form the curve. The tangent parallel to BD yields the minimum ordinate, which is the passive resistance Pp, acting at H/3 above the base. ## Answer Culmann's passive method finds the minimum passive resistance by trial wedges in front of the wall. #### Procedure 1. Draw the wall $AB$, the backfill surface in front of the wall and the heel/toe $B$ to scale. 2. Draw the **$\phi$-line $BD$** from $B$ at angle $\phi$ to the horizontal, but on the **opposite side** from the active case (below the horizontal, going into the soil), because the resultant of the failure plane tilts the other way in the passive state. 3. Draw the **pressure line $BE$** from $B$ at angle $\psi = \theta+\delta$ to $BD$, where $\theta$ is the angle of the wall back with the horizontal and $\delta$ the wall friction (the thrust acts on the other side of the normal in the passive state). 4. Draw trial failure planes $BC_1, BC_2, BC_3,\dots$ from $B$ to the ground surface, in front of the wall. 5. Calculate the weight $W_i$ of each trial wedge $ABC_i$ (per metre), adding any surcharge on it. 6. Mark $W_i$ to a scale on $BD$ to get points $b_1, b_2, \dots$ 7. Through each $b_i$ draw a line parallel to $BE$ to cut the trial plane $BC_i$ at $c_i$. 8. Join $c_1 c_2 c_3 \dots$ to obtain the **Culmann curve**. 9. Draw a tangent to the curve parallel to $BD$ on the side closest to $BD$. The **minimum** distance from the curve to $BD$, measured parallel to $BE$ and multiplied by the force scale, gives the **passive resistance $P_p$**. (Passive failure occurs along the plane giving the least resistance, so the minimum ordinate is taken, whereas it is the maximum for active.) 10. The critical plane is $BC_m$; $P_p$ acts at one-third of the height above the base. ```text A ____ ground surface ___ C3 C2 Cm C1 | \ | \_ trial planes B +----+-----> b1 b2 bm b3 (W on BD, below horizontal) BE at psi = theta + delta from BD P_p = minimum ordinate of Culmann curve ``` ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the phi-line BD drawn in the passive case compared to the active case? A. Same side as active B. On the opposite side, below the horizontal into the soil C. Vertical D. Along the wall Answer: B. In the passive state the resultant tilts the other way, so BD is drawn on the opposite side. (Key point: Phi-line in passive) 2. The pressure line BE in the passive method is at angle: A. psi = theta - delta B. psi = theta + delta from BD C. psi = phi D. psi = 45 - phi/2 Answer: B. The thrust acts on the other side of the normal, so psi = theta + delta. (Key point: Pressure line angle) 3. Which ordinate of the Culmann curve gives Pp? A. The maximum ordinate B. The minimum ordinate C. The average D. The ordinate at the first trial wedge Answer: B. Passive failure occurs along the plane of least resistance, so the minimum ordinate is taken (maximum for active). (Key point: Minimum ordinate) 4. After computing wedge weights Wi, what is done? A. Wi is marked on BD, lines parallel to BE are drawn from each bi to meet BCi at ci, and the ci are joined B. Wi is marked on BE and lines parallel to BD drawn C. Wi is plotted on the wall D. Wi is divided by the height Answer: A. Weights are set off on BD and lines parallel to BE meet the trial planes to form the curve. (Key point: Wedge construction) ## Related in Foundation Engineering - [Culmann's method, active, cohesionless](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aculmann-active-plain) — Foundation Engineering, chapter 3 - [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× - [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 - [Earth pressure coefficients and types](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aearth-pressure-coefficients-types) — Foundation Engineering, chapter 3, asked 2× - [Wall movement versus earth pressure plot](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-movement-pressure-plot) — Foundation Engineering, chapter 3 - [Why design for active pressure only](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apassive-pressure-neglect) — Foundation Engineering, chapter 3, asked 4× ## Related in other subjects - [Procedure for developing a project proposal](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aproposal-procedure-develop) — Project Engineering, chapter 2, asked 4× - [Rigid pavement thickness by IRC procedure](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Arigid-thickness-irc-procedure) — Transportation Engineering II, chapter 2 - [Second-order transducer frequency and step response](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Asecond-order-transducer-numerical) — Instrumentation and Measurement, chapter 4