Soil Sub-grade reaction, ks

Hi all,

To calculate the ks, we can provide prescribed displacement of 25mm on the footing in Plaxis 2D and get the bearing pressure for that and calculate the ks. I have some questions regarding ks.

01. Based on the Bowles equation, he requested to use ultimate bearing capacity instead of allowable bearing capacity, what is the reason for that?

02. Does footing stiffness (width of the footing depend on the ks value as higher B , higher stress bulb => less ks value) is influenced in the ks value of the soil? if so can you explain? (Based on Vesic equation the relationship of stiffness of the footing can be approximated to 1 and provide more basic ks = Es / (B(1-vs*vs)) equation)

03. What is the best and most accepted correlation of ks values used for the analysis in the industry?

04. Can be get these types of relationship in Plaxis 2D? (i tried some but couldn't get). If can please tell how?

05. I did the analysis in Plaxis 2D check how the pressure was taken by center and edge of the footing in cohesionless soil using line displacement option and the result is shown below. 

Here i need to know why after some displacement, pressure at the edge of the footing didn't take that (shear failure) while center extended far?

If see the failure surface of the footing in cohesive soil it comes as below

and this is the failure surface of footings in cohesion less soil

Thanks.

  • Ok i'll have a go at this.

    I'm not a big proponent of springs (i.e coefficients of subgrade reaction), and if they are used I'd keep the soil behavior as elastic. It seems that your questions have to do with plastic yielding of the soil.

    01. If the Bowles statement your referring to is about these images then ultimate bearing capacity is more appropriate because the types of pressure distributions, especially those for cohesionless soils  occur in a plastically yielding materials. 

    02. The footing stiffness and size (rigid or flexible definitely) has an influence on the bearing pressure, so it reasons that it has an influence on ks. But according to the Vesic equation the 12th root of the foundation stiffness is approximately 1 so the influence is not that great. But this is for elastic behavior!

    03. For linear elastic behavior, I'm guessing the Vesic equation above. 

    04. I have produced the linear elastic versions of these diagrams using Plaxis and they match closed form solutions almost perfect. I'd try match the linear elastic solutions first  show that you have the meshing and interfaces figured out. (I just did one for rocking deformation on a circular rigid smooth footing and it matched the closed form solution almost exact).

    05. Your figure shows for the elastic part of the loading the  pressures at the edge is greater than the center, this is true for a rigid footing. Line displacement would be a perfectly rigid footing. Then when the edge soil reaches the maximum shear stress it can sustain it plastically deforms and any additional load is resisted by increase in stress in the center.

    The edge fails first because the shear stresses are higher at the edge,  for the case of cohensionless soil the shear strength at the edge also is less than at the center because the horizontal stress (confinement) is less.

    But the interpretation of combining Ks and plasticity in this manner is very confusing.

    Martin

    Answer Verified By: Dennis Waterman 

  • Dear Mr. Martin,

    Thanks for the reply and sharing great knowledge. 

     I'm keen to know about the "plastic"term. Here I modeled using MC model which is perfectly elastic and plastic. So if the soil reaches its maximum elastic capacity and enters into the plastic region which means does the soil going to fail ?

    My second question is what happened at the point when soil meeting the high stiffness concrete base or footing (here at the meeting point there is a vast change in the stiffness)?

    Third question is how to differentiate whether the footing is rigid or flexible?

    Final question is when we are modelling a non-suspended slab using a program with dealing with sub-grade modulus (for example Staad Pro one of the Bentley product), how we can allocate the sub grade values based on the type of soil and type of footings (rigid or flexible)? because we can't provide as a same value for springs specially for flexible footings. 

    Thanks.

  • Plaxis is all about the "plastic" term. If fail is defined as the end of elastic response then soils fail all the time, but that's perfectly fine and completely normal and does not mean the footing fails. Just normal soil behavior.

    Where the soil meets the high stiffness concrete is where the soil-structure interaction takes place that lead to all these different pressure distributions. The stiff concrete is able to redistribute the stresses from failed soil areas to none failed areas. 

    In Plaxis you don't have to decide whether the footing is flexible or ridged because the stiffness of the footing and the soil are entered as parameters. In the plots you're not applying a contact pressure, just apply the load to the footing and Plaxis will calculate the contact pressure distribution based on the stiffness.

    In answer to your final question I'd use Plaxis for the soil deformation part and Staad for the structural part. I would get the initial load distributions from STAAD, apply them in Plaxis, Get the load /displacement springs from Plaxis, and send them back to Staad. Then recalculate the load distribution from Staad, and use them in Plaxis to get a new set of springs. After a few iterations the loads and the deflections should match. Plaxis actually developed a script to do this once, the loads in Plaxis become linked to the springs in Staad. Staad updates the loads, and Plaxis updates the springs.

    Martin