Eurocode Characteristic values

[Mccoy]

I'm rising again this topic because the latest, final draft of EC7 and some reasoning at last made it clear to me a few things:

1) characteristic values can be chosen in different ways:
simply out of consolidated experience, without samples or tests.
Out of official tables or databases, with very cautious values of soil groups (Germany and Russia, maybe Switzerland are proceeding this way).
As a personal cautious estimate of values from tests or samples; the estimate is based on personal engineering judgment.
As a statistical analysis of data from tests/samples.

2) in case of characteristic values from statistical data analysis, you have to consider 2 cases:
a) limit state entails large soil volumes: k-value is the 5th percentile of the distribution of the mean, that is the monolateral confidence interval of the mean with alpha= 95%
b)limit state entails small volumes: k-value is the 5th percentile of the sample. Such value is usually smaller then the previous.

The rationale in this is that if a failure surface runs thru a large volume, fluctuations in the geotechnical parameters of interest tend to cancel out. Conversely, in small volumes (i.e.: pile tips) all you can have is a single fluctuation, so it is not the mean which governs, but the whole distribution.

To make things clear: assume a failure surface under a large footing has a fixed geometry, which does not vary according to location of more resistant and less resistant parts of soil ("homogeneous" layer). In this case the global resistance will be the sum of the resistances within small representative volumes of soil, divided by the number of such volumes which intersect the failure surface. That is, the arithmetic mean of resistance values along the surface. Since we have usually only a few samples or data, we have to account for epistemic uncertainty, so the average is not fixed, but is a distribution itself. The distribution of this average governs the limit state, and a conservative value of such distribution is its 5th percentile. With a minimum of 5-6 data, not too dispersed, such 5h percentile turns out not to be too distant from the mean value.

Then this value, the carachteristic value, shall have to be further reduced by means of a partial safety factor, to become a design value to be introduced in bearing capacity equations. Finally, there might be a global safety factor, according to the various design approaches.
You American guys are lucky that carachteristic values find no place in LRFD. Yet. Japan, China and Australia (New Zealand as well, I reckon) are adopting, or have already adopted in part, a system similar to Europe.

In the case where the failure surface is affected by less resistant volumes, then we should look into the distribution of the geometric mean or the harmonic mean (see Gordon Fenton explanations to BigH and Vad). But this is not going to be simple, we may have to use techniques such as the bootstrap or Bayesian analysis.

 

[BigH]

Will we all need to go back to school? Which is likely what the professors and others who propose such stuff want. I see geotechnical engineers going "nuts" over some of this stuff in many cases as bearing capacity actually governs only such a small percentage of foundation cases - it is the settlement that governs. Needing to "prove" something that is well known not to be needed to "prove". I'm trying to get a copy of the ER7. Seems like a dog's breakfast.
Ciao.

 

[dgillette]

Hi McCoy.

In 1) you list four different ways to arrive at characteristic values. Are those ways that engineers are capable of, or ways that are permitted under EC7?

Also, are Gordon Fenton's comments available on Eng-Tips somewhere? I'd like to see those. Regardless of what you may have heard, I don't actually consider statistical analysis to be a tool of the devil, and I'm trying to be open-minded. However, as we've discussed before, a simple statistical description like harmonic mean or 5th percentile may be too simplistic because it can't account for the geometry of the deposit. I'd much rather have an experienced eye looking at the data in 3D.

And let's not forget that other issue, bias and epistemic uncertainty about the measurements. Does EC7 provide any guidance?

 

[Mccoy]

Howard,
We are all familiar with foundation bearing capacity in static conditions. During seismic loads , though, situation is not so clearly defined. When the acceleration peaks out, vertical load is increased, the horizontal component as well, reducing the effective foundation area because of eccentricity and reducing bearing capacity because of load inclination. Exceptional ill luck might put together the quake and the big snowfall, or windstorm, or occupancy. And failure may thus occurr. So the failure condition might well in cases govern the calcs. This of course rules out the special cases where liquefaction settlements are predicted.
The eurocodes do not rule out engineering judgment, on the contrary it's one factor which is stressed out. You can weigh quantitatively and objectively the value of your judgment by years worked in the field, importance of projects, and so on. Nevertheless, I feel much more confident if my own judgment is backed up by consolidated statistical methods, described in authoritative technical literature. Furthermore, EC7 gives the same indications to figure out characteristic values for serviceability limit states. Only there is no safety factor.

Dave,
The thread I refer to is "The use of ultimate limit states in bridge foundation design", archived thread n. 256-96409. Gordon Fenton from Dalhousie is the one who calibrated Canadian LRFD for bridge foundations, and a recognized authority in random field theory, a disciple of Eric Vanmarke. He is part of the terzaghi foundation group, but has not logged in for a while, presumably he is very, very busy in his academical pursuits (if you have a look at his homepage you can have an idea).

The four different ways I've listed are those permitted by EC7.

I agree upon the geometry of deposit, layering, heterotipies and so on. As a matter of fact, characteristic values should be figured out for every single statistical population, that is every "homogeneous" layer or stringer, or lens or deposit.

EC7 speaks about bias, but provides no guidances, that being left to individual knowledge, expertise or practice. Epistemic uncertainty is automatically accounted for by the formula you use to calculate the 5th percentile of the distribution of the mean. it is accounted for in 2 ways: by the degrees of freedom of t-distribution, and by the dividend of the standard deviation:

Xk = Xaverage - t(1-alpha)(n-1)*(s/sqrt(n-1))

One interesting way to proceed would be, expecially where there are very few data at disposal, by belief functions, a field you have been studying in some depth but I have yet to.

At the end of it, engineers involved in Eurocode characteristic values calculations should not worry too much, in that, once the logic has been grasped, the math is straightforward and easily implemented on spreadsheets.