Module 9 · Lesson 9.2
Which stiffness?
The number that decides the answer, and how to choose it.
Why this matters
If settlement is proportional to 1/E, then choosing E is the settlement calculation. Everything else is arithmetic. It is worth understanding why a single value of E does not really exist.
Soil stiffness is strain-dependent, and strongly so. At very small strains — below about 0.001% — soil is far stiffer than most engineers expect, and this small-strain stiffness is what governs ground movements around well-designed structures. As strain rises the stiffness falls away along a characteristic decay curve, and by the time a laboratory triaxial specimen is at 1% strain it may be showing a fifth of its small-strain value.
A working foundation typically imposes strains of the order of 0.01% to 0.1%. That is well below conventional laboratory measurement and well above the small-strain plateau — squarely on the steep part of the curve.
Drained or undrained is the other decision, and it follows from the timescale.
Immediate settlement in clay is an undrained process: no volume change, so ν = 0.5 and the relevant stiffness is the undrained modulus. Consolidation settlement follows afterwards, and Module 10 deals with it.
In sand the distinction largely disappears, because drainage is fast enough that settlement is essentially complete by the end of construction. This is why sand settlement is treated as immediate and why the awkward long-term component belongs to clay.
Check yourself
Why does a modulus from a conventional triaxial test usually overpredict foundation settlement?
Try it
Settlement and the modulus
The algebra is easy. Halve the modulus and see what happens to the answer.
Foundation
- Settlement
- 18.3 mm
- Rigid would be
- 17.1 mm
- Difference
- 7 %
- Settlement if E is half
- 36.7 mm
Halving E exactly doubles the settlement, because E appears alone in the denominator. Soil stiffness is rarely known to better than a factor of two — so the answer carries that factor before shape, rigidity or layering are even considered.
Summary
- Settlement is proportional to q, to B, and to 1/E — so E dominates
- Halving the modulus doubled the settlement, from 18.3 mm to 36.7 mm
- Soil stiffness falls steeply with strain; a foundation works at 0.01–0.1%
- A conventional triaxial modulus is measured too far along that curve and overpredicts movement
- Back-analysis of a comparable structure often beats any test result
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint