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Chapter 11 — Stiffness & Stress–Strain

11.1 Why stiffness matters

Stiffness — how much a soil deforms for a given stress change — governs settlement, the distribution of load between structural elements, and the movement around excavations. It is measured by a modulus, and unlike strength, it is highly nonlinear and strain-dependent.

11.2 The elastic parameters

For small strains, soil is described by:

  • Young's modulus \(E\) — the slope of stress–strain in the loading direction.
  • Poisson's ratio \(\nu\) — the ratio of lateral to axial strain (typically 0.2–0.5; 0.5 for undrained).
  • Shear modulus \(G = E / [2(1+\nu)]\) — the resistance to shear distortion, often the most useful parameter for dynamic and small-strain problems.
  • Bulk modulus \(K\) — resistance to volumetric change.

11.3 Nonlinearity and strain level

Soil stiffness decreases as strain increases:

  • Very small strain (\(< 0.001\%\)) — maximum stiffness \(G_0\) or \(E_0\), measured by seismic methods (bender element, seismic CPT, MASW).
  • Small strain — relevant to machine foundations and dynamic loading.
  • Working strain (\(0.01–1\%\)) — relevant to most foundation settlement; stiffness is a fraction of \(G_0\).
  • Large strain — near failure; relevant to stability.

Design must use the modulus appropriate to the strain level of the problem — a common source of error is using a single "modulus" for all cases.

11.4 Obtaining modulus values

  • Laboratory — triaxial or oedometer tests give \(E\) or constrained modulus over a strain range.
  • Field — pressuremeter, dilatometer, plate load test, and seismic methods give in-situ values, often preferable because they avoid sampling disturbance.
  • Correlations — with SPT \(N\) or CPT tip resistance, useful as a first estimate.

11.5 Key takeaways

  • Stiffness governs settlement and load distribution.
  • Soil stiffness is nonlinear and strain-dependent — \(G_0\) at small strain, far lower near failure.
  • Use the modulus appropriate to the strain level of the problem.
  • Seismic methods give the small-strain modulus; field tests give working values.
  • Correlations with SPT/CPT are a starting point, not a substitute for testing.