Foundation Engineering / Immediate settlement of shallow foundations
The elastic calculation
Rigid, flexible, and which number you are comparing.
Lesson review: expert verification remains open
This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.
Corrections checked in this pass
- Recalculated the elastic settlement examples with the exact flexible-centre influence. Rigid non-square results remain unavailable.
Checks needed for project use
- A geotechnical reviewer must confirm drainage and stress basis, bearing-factor formulation, correlations and settlement influence factors. Partial factors and project-specific ground conditions are outside these teaching checks.
- Select modulus for drainage, stress and strain; layering/embedment excluded. Rigid non-square influence remains unavailable until a verified shape-dependent solution is selected.
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesWhy this matters
Settlement calculations require a stiffness model as well as the applied pressure and foundation geometry. This lesson uses a simplified elastic estimate to show how those inputs affect movement.
By the end of this lesson you should be able to
- Compute elastic settlement for a footing on a deep uniform layer
- Apply the rigid and flexible cases correctly
- Identify which input carries the uncertainty
What it calculates: Elastic settlement for the selected drained or undrained stiffness and Poisson ratio
- Net bearing pressure (kPa)
- B
- Foundation width (m)
- Poisson's ratio — 0.5 undrained, 0.2–0.3 drained (—)
- If
- Influence factor for shape and rigidity (—)
- E
- Young's modulus of the soil (kPa)
This assumes
- Homogeneous, isotropic, linearly elastic soil — none of which soil is
- A layer deep relative to the foundation, so the half-space idealisation holds
In plain terms: Settlement rises in proportion to pressure and to width, and falls in proportion to stiffness. Because E appears alone in the denominator, the answer is only ever as good as the modulus.
Rigid or flexible changes both the shape of the settlement and the number you should quote.
A flexible foundation — a thin raft, an embankment, a tank base — applies uniform pressure and settles into a dish, deepest at the centre. A rigid foundation settles uniformly and applies a non-uniform pressure instead, concentrating it at the edges.
For a 3 m square footing carrying 120 kPa on soil with E = 20 MPa, the flexible centre settles 18.4 mm and the rigid square is about 16.2 mm, using the approximate factor 0.99 tabulated in FHWA GEC6, Table 5-12. The flexible centre uses the exact rectangle integral. The comparison matters: quoting a flexible-centre settlement against a limit written for uniform movement compares two different quantities.
Now the part that dominates everything. Halve the modulus in that example, from 20 MPa to 10 MPa, and settlement goes from 18.4 mm to 36.8 mm — an exact doubling, since E appears linearly in the denominator.
The uncertainty in E depends on the tests, strain range and ground variability. The factor-of-two change here is a sensitivity example, not a universal uncertainty bound. Establish a defensible stiffness range before refining small geometric corrections.
Practice
A flexible 3.0 m square foundation carries a net pressure of 120 kPa on soil with E = 20 MPa and ν = 0.3. The settlement is 18.4 mm. If the modulus turns out to be 10 MPa, what is the settlement, in mm?
Check yourself
A rigid pad and a flexible raft apply the same net pressure over the same plan area on the same ground. How do they differ?