---
title: "Proportioning footings for uniform settlement"
subject: "Foundation Engineering"
chapter: 6
key: "semester_5/foundation_engineering:proportion-footings-uniform-settlement"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/proportion-footings-uniform-settlement
site: BCT Engineering
---

# Proportioning footings for uniform settlement

Foundation Engineering · Chapter 6: Bearing Capacity and Settlement of Shallow Foundations

- Asked in: 2079 Bhadra, 3 marks; 2074 Chaitra, 4 marks (asked 2 times)
- Video: [Uniform/Differential Settlement, Angular Distortion & Tilt| Geotechnical | Settlement of Foundations](https://www.youtube.com/watch?v=ar-mcw7ix30) — Geotechnical Engineering Consultancy
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/proportion-footings-uniform-settlement
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-6

## Question

Describe the procedure (steps) for proportioning of footings for uniform settlement.

## Short answer

Collect permanent column loads and fix allowable total and differential settlement. Obtain soil settlement parameters. Assume trial footing sizes with equal soil pressure, check bearing capacity. Compute settlement of each footing: in sand, use Terzaghi-Peck or Meyerhof curves relating pressure to width for the given settlement; in clay, use consolidation settlement formula. Revise widths—increase for footings settling more, decrease for those settling less—until settlements are nearly equal. The final design yields different contact pressures but uniform settlement.

## Answer

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.

## Check yourself

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

1. Which load is used to proportion for settlement?
   A. Dead load only plus no live load
   B. Dead load plus part of live load acting permanently (25-50%)
   C. Full live load plus wind
   D. Ultimate load
   Answer: B. Long-term settlement is caused by dead load plus the sustained part of the live load. (Key point: Design load)

2. In sand, for equal settlement, how must a large footing compare with a small one?
   A. Higher pressure
   B. Same pressure
   C. It must carry lower contact pressure
   D. Unrelated
   Answer: C. Settlement grows with B in sand, so larger footings need lower pressure for the same settlement. (Key point: Sand footings)

3. How is settlement of each footing on clay computed?
   A. S = Cc H/(1+e0) log((sigma_vo + delta sigma)/sigma_vo) with delta sigma at mid-depth
   B. S = q B
   C. From N-value only
   D. From bearing capacity
   Answer: A. Consolidation formula with stress increase at layer mid-depth is used. (Key point: Clay settlement)

4. What is the final result of the procedure?
   A. Equal contact pressures and different settlements
   B. Equal pressures and equal settlements
   C. Different contact pressures but nearly equal settlements
   D. Different footing loads
   Answer: C. Footings are resized iteratively until settlements are nearly equal, giving different pressures; shear failure is then checked. (Key point: Outcome)

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