Dear all,
(HS small) is a modification of the hardening soil model that accounts for the increased stiffness of soils at small strains. At low strain levels, most soils exhibit a higher stiffness than at engineering strain levels, and this stiffness varies non-linearly with strain. There are additional two additional material parameters, i.e. G0ref and γ0.7. G0ref is the small-strain shear modulus and γ0.7 is the strain level at which the shear modulus has reduced to about 70% of the small-strain shear modulus. In the absence of laboratory and field tests, some correlations are available in the literature for sand soils using relative density (Brinkgreve et al. (2010)).
Dear Abdirahman,
The Gmax = G0ref and indeed it can be obtained by as you mentioned by geophysics tests (measuring the shear wave velocity Vs).
There are different correlations for γ0.7 published online along with some suggested values. Of course, this highly depends on the soil you are interested in and whether that has similar behaviour.
Below you can find another correlation from Benz (2007):
Thank You Stefanos Papavasileiou