---
title: "Terzaghi's trap door experiment"
subject: "Foundation Engineering"
chapter: 4
key: "semester_5/foundation_engineering:terzaghi-trap-door"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/terzaghi-trap-door
site: BCT Engineering
---

# Terzaghi's trap door experiment

Foundation Engineering · Chapter 4: Arching in Soils and Braced Cuts

- Asked in: 2081 Bhadra, 4 marks; 2079 Bhadra, 2 marks; 2075 Chaitra, 2 marks; 2076 Asoj, 2 marks (asked 4 times)
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/terzaghi-trap-door
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-4

## Question

Draw the complete diagram of Terzaghi's trap door experiment and explain Terzaghi's arching theory; why is arching in soil important in geotechnical engineering?

## Short answer

Terzaghi's trap-door test showed that yielding of a narrow strip reduces vertical pressure well below overburden as shear planes transfer load to fixed sides. Arching is essential for designing tunnel linings, buried pipes, braced excavations, and flexible retaining walls where soil–structure interaction controls loads.

## Answer

#### Terzaghi's trap door experiment
A long rectangular box is filled with dry sand. At its base there is a narrow strip (trap door) of width $2b$ that can be lowered while the rest of the base is fixed. The vertical pressure on the door is measured as it is lowered.

```text
        sand surface
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~
   |  \                 /  |
   |   \  sliding wedge /   |   shear planes
   |    \             /    |   (nearly vertical,
   |_____\___________/_____|   curving at the top)
   fixed  |  trap door |  fixed
          |<---- 2b -->|
             v moves down
```

#### Observations
1. Before any movement the pressure on the door is the full overburden $\gamma z$.
2. As the door moves down by a small amount, the pressure on it **falls rapidly** to a minimum (about 0.4 to 0.5 of the overburden pressure or less).
3. The pressure on the adjacent fixed base **rises** correspondingly, so the total load is unchanged.
4. If the door continues to move, the pressure on it stays nearly constant at this reduced value (the load is carried by the arch).

#### Terzaghi's arching theory
When the strip yields, the soil above the door tries to settle. The adjacent soil resists it by shear along the vertical planes through the door edges. These shear forces carry part of the weight, so the load on the door is less than the weight of soil above it. For a door of half-width $b$ at depth $z$ with a surcharge $q$:
$$
\sigma_v = \frac{b\,(\gamma - c/b)}{K\tan\phi}\left(1 - e^{-K\tan\phi\, z/b}\right) + q\,e^{-K\tan\phi\, z/b}
$$
where $K$ is the lateral pressure coefficient (about 1.0) and $\phi$ the angle of friction. For large $z$ the pressure no longer increases with depth: it reaches a limit.

#### Importance in geotechnical engineering
- Design of tunnels and underground conduits (loads on linings and pipes).
- Pressure on braced excavations: apparent pressure diagrams differ from Rankine's triangle.
- Flexible retaining structures such as sheet piles and anchored walls.
- Loads on piles and pile caps, bin and silo pressures, and loads on culverts or buried pipes.

## Check yourself

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

1. When the door is lowered slightly, what happens to the pressure on it?
   A. It rises
   B. It falls rapidly to about 0.4-0.5 of overburden or less
   C. It stays same
   D. It becomes zero immediately
   Answer: B. Arching shifts load to the adjacent fixed base. (Key point: Trap door observation)

2. What happens to pressure on the fixed parts?
   A. It rises, so total load is unchanged
   B. It falls
   C. It is zero
   D. It is unchanged
   Answer: A. The load is transferred by shear, not lost. (Key point: Load on adjacent base)

3. How does the soil above the door get support?
   A. Shear along the near-vertical planes at the door edges
   B. Buoyancy
   C. Surface tension
   D. Compaction
   Answer: A. Shear forces carry part of the weight, so door load is less than overburden. (Key point: Mechanism)

4. For large depth z, what does Terzaghi's expression give?
   A. Pressure increases forever
   B. A limiting pressure that no longer increases with depth
   C. Zero pressure
   D. Pressure equal to gamma z
   Answer: B. The exponential terms vanish, leaving a constant value. (Key point: Limit at depth)

## Related in Foundation Engineering

- [Arching in soil and its requirements](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aarching-requirements) — Foundation Engineering, chapter 4, asked 8×
- [Terzaghi's bearing capacity theory](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aterzaghi-theory-assumptions) — Foundation Engineering, chapter 6
- [Arching and heave of bottom of cut](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aheave-bottom-cut-soft-clay) — Foundation Engineering, chapter 4
- [Terzaghi lateral stability, light well](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awell-lateral-stability-light-derive) — Foundation Engineering, chapter 9
- [Strut loads, 8 m cut in sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Astrut-loads-8m-cut-sand) — Foundation Engineering, chapter 4
- [Allowable load of 400 mm pile, layered soil](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-400mm-layered-soil-chart) — Foundation Engineering, chapter 8

## Related in other subjects

- [Trap door; firewalls and ACL](https://www.bctengineer.com/question.md?key=semester_6%2Foperating_system%3Atrapdoor-firewall-acl) — Operating System, chapter 8
- [Derive Terzaghi 1D consolidation theory](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aterzaghi-1d-consolidation-derivation) — Soil Mechanics, chapter 9, asked 2×
- [Important properties of civil engineering materials](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Aimportant-properties-civil-materials) — Civil Engineering Materials, chapter 1, asked 8×
- [Settling basin trap efficiency (Camp's diagram)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Asettling-basin-camp-diagram-80cumec) — Hydropower Engineering, chapter 5