Find out the Mobilized Stiffness in Hardening Soil Model

Dear Omar,

What exactly would be mobilized stiffness? Strength is something that can be mobilized, but stiffness? And what stiffness would you be interested in....Young's modulus, 1D compression stiffness, deviatoric stiffness, shear stiffness, bulk modulus, etc. 

In PLAXIS Output under the Stresses menu and the submenu "State parameters" you can plot Eur, which is in principle the only stiffness the HS model has. If the soil is normally consolidated it will have a lot of plastic deformation as well, but that doesn't translate to a stiffness parameter. 

So the reason that in most advanced models it is not possible to see a plot or table with "the stiffness" is because it is undefined what exactly "the stiffness" is, apart from the elastic part of the deformation (Eur in HS/HSS models).

With kind regards,

Dennis Waterman

Hi Dennis

Thanks for taking the time to reply to my question. If you check the stiffness matrix calculated at the start (and end) of the phase at the integration point, you would get half the stiffnesses you mentioned. I am not interested in plotting the input I provided as a user (via the state parameters), but rather in plotting the stiffness(es) that the model end up using. If that is varying from increment to increment due to plasticity, then at least providing it at the start (and end) of the phase would suffice.

Is there a paper that describes the formulation of the HS or HSS model precisely? I was under the impression that those models will select the modulus from the 3 input that the user provides (Eur, E50, Eoed) depending on the stress path, but you are saying that it is all Eur. Every time I read about these models' description on this forum, I discover something new. It would be helpful to clarify this, if possible, because those models are becoming more and more vague for me and I am (and many others in my company) starting to be reluctant to use them as I do not understand what they do.

Thank you

Dear Omar,

It is not vague at all, the HS and HSS model follow the widely used concept of yield surfaces and plasticity that is described in many books.

The only stiffness matrix that exists is the elastic stiffness matrix which is made up by Eur and G0 (in case of HSS). The values of E50 and Eoed are not directly used by the model: they are only used initially to determine the shape of the yield surfaces as well as the hardening rules of the yield surfaces.
The stiffness matrix determines the elastic strain in a stress point, the yield surfaces and their hardening rules determine the plastic strain in a stress point. 

The Material Models Manual of PLAXIS describe the formulation of both models. But we're also quite open on how it works when we explain it during courses and workshops. More fundamentally there are many books on yield surfaces and plasticity, but most of them end up being quite mathematical. Though "Soil behaviour and Critical State Soil Mechanics" from David Muir Wood is a very comprehensible book on this topic.

Your last reasoning I find interesting. I'm quite sure that 99% of the people that drive a car have no idea or understanding of how a car works, but they still succesfully drive them (well, ok, considering the amount of accidents we may argue on the rate of succes).

With kind regards,

Dennis Waterman

Thanks Dennis

I would appreciate if you can direct me to an original reference describing the detailed formulation of the HSS model (in more detail than the overview provided in the manuals). I can be a user that provides input and then has faith in results without questionning them, but that's not how i do modelling. I, and many other phds in my company, like to verify things and make sure that the constitutive behavior matches the soil behavior of the material i am modelling. 

With best regards!

Dear Omar,

The orginal publication is the PhD work of Dr. Thomas Benz. You may be still able to download it from the website of the University of Stuttgart as they used to have all PhD works available for download.

With kind regards,

Dennis Waterman

Thank you!

Thank you!