Proportioning footings for uniform settlement

Proportioning for uniform settlement means choosing the plan size of each footing so that all footings of a structure settle by about the same amount, even though their loads differ. This keeps the differential settlement and the angular distortion within the permitted limits.

Procedure

1. Collect loads. Find the load at every column: dead load plus the part of the live load that acts permanently (about 25% to 50%, as per usual practice). This is the load that causes long-term settlement.
2. Fix the allowable total settlement $S_{all}$ (for example 25 mm in sand, 40 mm in clay) and the allowable differential settlement.
3. Soil data. From the borehole log, SPT or plate load test, find the settlement characteristics of the soil (modulus of compressibility, $C_c$, $e_0$, $\sigma'_{vo}$).
4. Trial sizes. Assume sizes with equal soil pressure $q = Q/A$ (equal pressure is the first trial for sand) and check bearing capacity with $FS \ge 3$.
5. Compute settlement of each footing.
   • In sand: from the Terzaghi–Peck or Meyerhof curves, find the pressure that gives $S_{all}$ for each width $B$. The settlement increases with $B$, so for a given settlement the larger footing must carry a lower pressure than a smaller one.
   • In clay: find the stress increase $\Delta\sigma$ at mid-depth of the compressible layer for each footing and compute $S_c = \dfrac{C_c H}{1+e_0}\log\dfrac{\sigma'_{vo}+\Delta\sigma}{\sigma'_{vo}}$.
6. Revise. Increase the width of footings that settle more and reduce the width of those that settle less. Because a wide footing stresses a deeper zone, heavily loaded footings need a lower contact pressure to settle equally.
7. Repeat until all footings give nearly the same settlement, and finally check shear (bearing capacity) failure for each.

The final design gives different contact pressures for different footings, but equal settlements.