BEaring Capacity on Saturated Clay 4

[tkvail]

When determining bearing capacity of a shallow foundation on saturated clay one would use the the formula:
q=Cu*Nc +Gamma*D

But how do you account for a varying Cu when it depends on depth(z)?
i.e. Su=10+20z

 

[jdonville]

tkvail,

In order to account for variable undrained shear strength with depth, you can discretize the soil column into layers of "constant" su. I sometimes discretize to layers as thin as the sampling interval, if conditions are appropriate.

AASHTO HB-17 (Standard Specifications for Highway Bridges) has approaches for dealing with layered soils (2 layer systems). You could apply the equations iteratively / recursively to your soil profile.

Alternately, you could discretize the soil into layers and check the bearing capacity of each layer using Boussinesq or Westergaard pressures due to your foundation. It's fairly straightforward to implement in a spreadsheet.

In the example you cite, the shear strength is increasing with depth, so the su value at the bearing grade will provide a somewhat conservative estimate of the bearing capacity.

BigH (and anyone else), please set us all back on the path to righteousness and cosmic harmony if I'm off the mark here. I'm sure that Terzaghi and Peck (and perhaps Mesri) also have something to say on the subject.

Hope this is helpful.

Jeff


Jeffrey T. Donville, PE
TTL Associates, Inc.

http://www.ttlassoc.com

 

[GeoPaveTraffic]

I generally agree with Jeff. One comment, most of the time the bearing capacity in clays is not limited by bearing capacity failure, but by settlement. So unless you have an unusual situation, pick a Su in the lower third or so of that indicated by the exploration and laboratory testing program and use that for all calcualtions.

Some unusual conditions that might require other analysis could be: cases where settlement is not an issue, greatly different Su values, and Su values that decrease with depth.

In these cases, I generally, analyze the footing for the upper most layer assuming that the layer does not end with depth. Size the footing, then check the next lower layer assuming Boussinesq, Westergaard or even 2:1 pressure distribution. Then repeat for each additional layer. If the pressure is to high for one of the lower layers then you have to start over.

 

[BigH]

First, one must have a "scale" of the foundation with which you are dealing. Look at the classical shape of a bearing capacity failure and you will find, I believe that the depth of any of the failure surface is within the distance of approximately 0.7B where B is the width of the foundation. I would then focus on the undrained shear strengths within this zone. I trust that the formula you give is an "example" for I suggest that it may be way off mark - if, for instance, z is in m, and Su is in kPa, you get astronomical increases in each metre of depth and this isn't "correct". For the most part, Suz = Su + 0.22 (to 0.25)*UWt*H. For UWt = 18kN/m3, you get Suz = Su + 4.5H. If the depth of influence is 2 to 2.5m, you would get only 9 to 11 kPa over and above the original Su. I have seen theoretical solutions of this - but I would go by the average Su value over the zone of the failure. For a 3m wide footing, you would only have to consider about 2 to 2.5m below the foundation level. Of course, you could "compute" the length of the failure surface appropriate to each discrete zone and estimate it this way - but I doubt that you would really need to do this. Again, I would think that the average value of Su would be okay.
Of course, the above assumes (as does the original post of (Su + 20H)) that you are founding on normally consolidated clay soil, and not with a dessicated crust. If you have a dessicated crust, then you would use a couple of theories for layered soil (as per jdonville - such as Button) to get the "layered" bearing capacity. In this case, I would "equalize" the Su value in the crust and in the underlying clay.
As a bit of an aside, I would suggest that you could look up Bjerrum's paper on an edge failure of a large tank (London Conference of ISSMFE now ISSMGE) back in 1957. He goes through an exercise of showing how the crust, decrease in Su and then increase has an effect on the bearing of the tank foundation. Interesting and still valid historic paper.
I will, though, look to see if I can find the more "correct" approach.