During 2019 Plaxis User Meeting in İstanbul, I have presented a detailed discussion on Hardening Soil Model. The presentation was really welcomed by the audience and in fact, later on, I have been invited to two other companies for the same presentation. This short post will be a summary of that presentation.
Hardening Soil model (will be called HS from now on) was presented in an excellent conference for 10th year of Plaxis in a paper called The hardening soil model: Formulation and Verification by Schanz, Vermeer and Bonnier. However, HS is tightly bonded to previous studies on the literature such as Lade, Tatsuoka and Ishihara, Cam-Clay model, Kondner and Zelasko, Jardine, Duncan and Chang, Al Tabbaa, Simson et. al.
Hardening behaviour of soils is shown on the experiments on Tatsuoka and Ishihara (1978) on sand samples. On each cycle, yield starts on the previous cycle’s maximum stress. We will see that later on on the preconsolidation pressure concept of HS.
Tatsuoka & Ishihara (1978)
Vermeer (1978) defines a hardening parameter to expand the yield surface which is also an integral part of the HS model.
The yield surface moves in conjunction with some measure for the plastic strains which is called the hardening parameter.
He clearly describes the hardening effect on the soils with the following:
The concept of a yield locus or yield surface is felt to be the most important concept of plasticity theory. It is a surface in stress space (a curve in the p, q-plane) separating stress states which can be reached elastically (the elastic domain) from those which can only be obtained after plastic deformation or cannot be achieved at all.
Vermeer (1978)
Hardening means that yield surface is not fixed as described in Plaxis Material Manual. There are two types of hardening:
Let’s take a look at these concepts.
According to Plaxis Material Manual, shear hardening is used to model irreversible strains due to primary deviatoric loading. If we ignore the fancy functions for calculating strain, simply it can be defined as the ratio of failure divided by the E50. So, here comes the difference between each stiffness modulus in HS. E50 if used for shear deformations. (Also, Eu is used in the formulations.)
Primary deviatoric loading is used everywhere in HS literature. However, I went over 875 google results 2 years ago and there are only two definition. One of them is given in first sentence of this chapter and other is “When subjected to primary deviatoric loading, soil shows a decreasing stiffness”. This is a concept deriven from Kondner (1963) and Duncan and Chang (1963): Hyperbolic relationship between deviatoric stress and stiffness. Primary simply means virgin loading. Deviatoric loading is same as we know from triaxial test.
Duncan & Chang (1967)
To simplify;