7.4 Hardening Soil Model with Small⁃strain Stiffne...
The original Hardening Soil model assumes elastic material behavior during unloading and reloading.However，the strain range in which soils can be considered truly elastic，i.e.where they recover from applied straining almost completely，is very small.With increasing strain amplitude，soil stiffness decays non⁃linearly.Plotting soil stiffness against log（strain）yields characteristic S shaped stiffness reduction curves.Figure 7.9 gives an example of such a stiffness reduction curve.It also outlines the characteristic shear strains that can be measured near geotechnical structures and the applicable strain ranges of laboratory tests.It turns out that at the minimum strain which can be reliably measured in classical laboratory tests，i.e.triaxial tests and oedometer tests without special instrumentation，soil stiffness is often decreased to less than half of its initial value.
Figure 7.9 Characteristic stiffness⁃strain behaviour of soil with typical strain ranges for laboratory tests and structures（after Atkinson and Sallfors 1991）
The soil stiffness that should be used in the analysis of geotechnical structures is not the one that relates to the strain range at the end of construction according to Figure 7.9.Instead，very small⁃strain soil stiffness and its non⁃linear dependency on strain amplitude should be properly taken into account.In addition to all features of the Hardening Soil model，the Hardening oil model with small⁃strain stiffness offers the possibility to do so.In fact，only two additional parameters are needed to describe the variation of stiffness with strain：
•the initial or very small⁃strain shear modulus G0.
•the shear strain levelγ0.7 at which the secant shear modulus Gs is reduced to about 70% of G0.