Significant depth and isobar

Significant depth is the depth below a foundation up to which the increase in vertical stress due to the load is large enough to cause significant settlement. Below it the stress increase is negligible. It is commonly taken as the depth at which the vertical stress increase falls to 10% of the contact pressure ($0.1\,q$), or 20% of $q$ in some practice (or where $\Delta\sigma_z = 0.1\,\sigma'_{v0}$ for the overburden).

Importance:

• It fixes the depth of exploration (boreholes should reach at least this depth).
• It fixes the soil thickness to be included in settlement and consolidation calculations. Layers below it can be neglected.
• For footings, the depth is approximately $1.5B$ to $2B$ for a square footing and $4B$ to $6B$ for a strip footing.

Construction of an isobar for significant depth

An isobar is a contour of equal vertical stress.

1. Select the stress level, e.g. $\Delta\sigma_z = 0.1\,q$.
2. For a chosen set of depths $z$ below the footing, compute $\Delta\sigma_z$ at various horizontal distances $x$ from the centre using Boussinesq or the strip/circular/rectangular footing equations (or charts).
3. At each depth, mark the points where $\Delta\sigma_z = 0.1\,q$ on both sides of the axis.
4. Join the points by a smooth curve to get a bulb-shaped isobar.
5. The depth of the lowest point of the 0.1q isobar, on the axis, is the significant depth.

   |<---- B ---->|
   ▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇  q
    (   0.5 q   )
     (  0.2 q  )
      ( 0.1 q )  <-- isobar
        \___/    significant depth below this