Terzaghi's trap door experiment

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.

        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.