SANICLAY-B (2018) how to calculate Dep

Dear fellows,

I have been working on coding SANICLAY-B model (2018) . Now I have one question in terms of this model. But I am stuck now. I have two questions.
The related paper can be found here. https://www.researchgate.net/publication/257410668_SANICLAY-B_a_plasticity_model_for_cyclic_response_of_clays

First one is to calculate stress tensor from strain tensor with this model, an elasto-plastic matrix Dep is required. In order to calculate Dep, I need the derivation of loading and potential functions, f and g, over the stress state. But in the SANICLAY-B model, first I am not sure what the loading function f is. It seems it is not clearly defined. Second, the plastic potential function, G now is related to the image stress instead of the true state of stress. Therefore, I am asking how to correctly calculate the two derivations to get stress from strain tensor or maybe there is another way to do it?
Thank you so much for your time.
I really appreciate it.
Warm Regards,

Steve