Dear Padmanabhan,

Please find the attached pages from US NAVY design Manual, and also the link to another useful paper

best wishes

http://cedb.asce.org/cgi/WWWdisplay.cgi?7100930

In hardening hyperbolic soil behaviour laws such as 'hardening soil' or 'hardening soil with small strain stiffness' in Plaxis, the Young modulus is stress-dependent. In the attached equation, c' is the effective cohesion, phi' is the effective friction angle, pref is a reference stress level, m is depending on soil type (usually 0.5 for sands, 1 for clays, in between for silts) and sigma3 is the minor principal stress in the soil. In a horizontally-layered soil, you can consider that sigma3 is the horizontal stress, related to the vertical stress by K0. According to Jaky's formula, K0 is equal to 1-sin(phi'). You can therefore compute the variation of the Young modulus with depth, provided you know it at a given depth... You can find references on the topic in the Plaxis Manual, or see the attached link...

http://kb.plaxis.nl/sites/kb.plaxis.nl/files/kb-publications/The%20Hardening%20Soil%20Model%20-%20Formulation%20and%20Verfication.pdf

You can see my paper 

Thank you very much for your response.

Is the formula given is also applicable for Mohr-Columb soil model in Plaxis.

In Plaxis, you can manualy input the stiffness increase in MC model

https://www.google.rs/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CCIQFjABahUKEwj4_4-2wpzJAhXCkSwKHevUBcg&url=http%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fdownload%3Fdoi%3D10.1.1.455.4781%26rep%3Drep1%26type%3Dpdf&usg=AFQjCNGDjHgu4PzpAAwr5Cxs5V3K5IK3RA&sig2=aJ8hT3S3feddlRzgFWmXqA&cad=rja

Gazetas G. (1984) 3 soil model for piles. its incorporate in EC 8.

Dear Shri.Le Chi Hung, 

Thank you for your response. The equation given in the Red book Foundation Design, is it for calculation of Youngs Modulus at a particular depth? How can I vary this Youngs Moulus with depth using the same equation in Plaxis?  How I will get Modular ratio? In present case I have estimated E value say for all the layers with the correlations using SPT N values. Now I need to find the effect of increase of E over depth for an excavation problem. Kindly guide me,. 

Thank you very much  Mr.Le Chi Hung. As  I have got E from Bowles relations, i had used the relation sig_p (sig_m'/sig_p)^m, to  find the increment of E with depth. Hope this is correct approach. 

Hi Mr. Lyer,

I wondered, what value you should input to Plaxis while using MC model for the increase of Young Modulus ?

thanks 

you can use the method proposed by Seed and Idriss (1970): 

For sand:

Follow report UCB/GT/80-81 by Duncan et al. 1980

Hi Mr. Ihsan Qasim,

Can you please share the reference of the method proposed by Seed and Idriss(1970) as you have mentioned in your answer??? I am looking for that.

Thanks.

Muhammad Bilal Adeel, below is the link to the paper.

https://ro.uow.edu.au/cgi/viewcontent.cgi?article=5670&context=eispapers

Le Chi Hung