The use of Ultimate Limit States in Bridge Foundation Design

[VoyageofDiscovery]

Hi Focht3 and Ron,

Continuing our discussion wrt ultimate, to explain why this seemingly absurd question.

In Canada, I believe based on Meyerhoff's specific yet controversial work in this area, the recent bridge design code is adopting an Ulimate Limit State design method philosophy, while leaving the ASD behind, and I am having a hard time getting my head around this. Though in the past version of the code, it covered the ultimate philosphy, it was not widely accepted and there was a provision in the code that mentioned that engineering judgement should still be exercised.

I have found that by designing with ultimate values, I end up with significantly smaller footings for my shallow foundations. I am really having a hard time swallowing this idea but when competing in this area it makes all the difference.

Regards

VOD

 

[Focht3]

I'm not familiar with the code or your reference to Meyerhof. Are there on-line references?



Please see FAQ731-376 for great suggestions on how to make the best use of Eng-Tips Fora. See faq158-922 for recommendations regarding the question, "How Do You Evaluate Fill Settlement Beneath Structures?"

 

[VoyageofDiscovery]

I am afraid not, I have seen his findings in the Canadian Geotechnical Journal. If you want to see it, I believe I have a paper somewhere, and you could get it through an inter-library loan at your local public library.

Regards

VOD

 

[GAFenton]

Sorry this reply is 9 months late, I just joined today.

The Canadian (Ontario) Highway Bridge Design Code, whose foundation provisions are based in large part on Meyerhof's excellent work, is currently calibrated from older ASD codes (as specified also by Meyerhof and others). What this means is that you should be getting pretty much the same footing sizes as you used to get using ASD. If you are not, then please let me know how the current code is leading to this unconservative result. My design computations indicate that the CHBDC has about average conservatism amongst world-wide (english) codes.

The reason for going to an LSD philosophy is two-fold; 1) to harmonize with structural codes, and 2) to allow for future economies when we actually take full advantage of risk-based design. Hopefully, you will see these economies correctly implemented soon (e.g. a couple of years).

 

[BigH]

I'm going to jump in a bit so that VAD can put in his dollar - but few foundations ever fail by shear but are based on the settlement criteria. If I remember right, you do this fancy calculation for bearing capacity - then you have to look at the service limits. Chances are that the bearing capacity (allowable) will give more settlement than you want at serviceability levels. Then we are stuck going to calculations of settlement again. But then the question begs - what method of computation are you to use? I've seen the same examples get widely divergent settlements - so if you base your bearing pressures on a specific settlement, depending on the method used, you will get widely divergent bearing pressures. Probably will end up where you would have in the first place without all that bearing capacity analysis. I (luckily) haven't had to do this LRFD yet, but . . . It is in the EuroCode 7; and Tomlinson's latest revision of his tome on Foundation Design and construction covers the LRFD stuff.

 

[ashjun]

I dont know if this is the case, but just a thought. For the design of pile mat (that is a temporary raft over the ground so that rigs can be driven over them safely) the design usually accounts for the factored load (factor applied to the rig load, critical position, etc.) while the soil strength is taken as the ultimate. The precaution taken is to estimate the weakest strength the soils can have in the area and not the average.
The second point is a bit questionable because how to be sure that of all the boreholes that have been investigated, how can one be sure of the critical parameters that may exist at the site?

My argument to the employer when I was given the problem what that the designs have been made by the structural engineer and perhaps the geotech guys were not consulted in this. It didnt pave through though.

Rgds

 

[GAFenton]

I have three comments relating to BigH and Ashjun's comments;

1) as BigH indicates, settlement does usually govern the design of a shallow foundation and the various settlement calculation methods do often lead to quite different results (unfortunately).
In addition, LRFD provisions haven't been developed for settlement design. Which is to say, settlement design currently proceeds pretty well as it has for decades with load and resistance factors set to 1.0. Since Voyage's question relates to the ultimate limit state (eg bearing failure), settlement is presumably not the problem he is worried about.

2) as indicated by ashjun, the specification of soil properties is also very poorly defined in all codes that I have reviewed. This is a very important issue and a major letdown on the current codes. In general the "characteristic" soil property is defined as "a cautious estimate of the value affecting the occurrence of the limit state." (Eurocode 7), or "the characteristic value is a cautious estimate that is close to, but not greater than, the mean value" (Australian Standard AS 4678). Australian Standard AS 5100.3 says "the characteristic value of a geotechnical parameter should be a conservatively assessed value of that parameter". In North America, NCHRP507, NCHRP343, NCHRP12-55, and the Canadian Foundation Engineering Manual (1992) make no attempt to define the characteristic soil value, so NA is a bit behind AU and EU (lets get going here!).

But clearly the codes are pretty much out to lunch on this issue. If we all stuck with one clear definition, we might be able to actually get somewhere.

My recommendation is to use a geometric average of soil properties as the cautious "characteristic value". The geometric average is obtained by computing the n'th root of the product of the n soil property values. For example, if 5 lab samples yield cohesion estimates of 13, 31, 34, 25, and 28, then the geometric average would be

5th root of 13*31*34*25*28 = (9591400)^(1/5) = 24.9

Note that the geometric average tends towards the lower values (e.g. if one of your cohesion measurements is zero, the geometric ave is zero, which makes sense since failure generally takes the weakest path). Conversely, the arithmetic average of these five observations is

(1/5)(13+31+34+25+28) = 26.2

which is larger than the geometric average.

There are a number of other advantages to the geometric average, all of which point to its being a natural "cautious" (or "conservative") estimate of the mean soil property.

3) I'm wondering what calculation VoyageofDiscovery was actually making. When I consider the bearing capacity design of a footing with DL = 3700, LL = 1000, c' = 100, phi' = 30 degrees, and using the Canadian Highway Bridge Design Code with dead load factor = 1.25, live load factor = 1.5, and total bearing resistance factor of 0.5, I get a required footing area of 4.064. This is almost exactly in the middle of the pack when compared to the Denmark (1965), US (NCHRP and ANSI A58), Australian, and Eurocode7 results. (I should also point out that the 1992 Canadian Foundation Engineering Manual gave the most conservative required area, 5.217, and the US ANSI A58 the least conservative area, 2.836).
Perhaps Voyage could check this result with his own interpretation?

 

[BigH]

GA - you get a nice on your note. [green]Well done!![/green] I have one point that should be made. In soil strata, you do not always get "uniform" or "linear increasing" engineering properties (e.g., Su, Es). We have, especially in clays, situations of dessication where a middle part of a layer is weaker than the upper part and the lower part. In many siutations, [blue]it is this weaker zone that should form the basis of design[/blue] and not necessarily the "average" value although GAFenton's geometric average favours a lower value. In such cases, you might need to break a geologic stratum down into substrata. I don't have access to the various codes mentioned and was wondering if GAFenton have any web sites in which parts of such could be downloaded? I take it you are in Canada - likely Ontario - do you stay with the Ontario Bridge Code or favour the CGF Manual?

 

[VAD]

Just a few responses

The NA codes are not behind rather they are ahead by not trying to codify how parameters are chosen. To do this would be allowing anyone to provide parameters for the design of foundations. Geotechnical Engineering recommendations result from a dedicated study of this discipline.

I would personally desist from recommending what approach- geometric average or arithmetic average to use. This should be decided upon by the geotechnical engineer. There maybe very good reasons as well for using the lowest or the highest values. However, with the growing practice of geotechnical engineers hardly ever again looking at testing and or test data and going out in the field to observe drilling and sampling procedures, I can see why some prefer to use statistical principles.

The NA codes realize that the judgement of the geotechnical engineer is important in choosing parameters, which it should be. Of course some would choose the lowest value. No two doctors prescribe the same treatment as often diagnosis is not the same - fact of life.

I see no reason why all the codes should be the same. People develop different ideas depending on the type of testing done in a jurisdiction and understanding of the geological make up of the ground. It would be nice I suppose to have a universal system but there are too many variables.

The attractive aspect of the LRFD in my opinion is that it allows us to examine the behaviour of the foundation under a variety of loading conditions that the structure may be possibly subjected to and understand how our foundation is expected to behave. In the past to account for these possible load combinations we often used a 33% to 40 % increases in stresses as a compensation. This often worked well, but we did not understand or rather concieve how our foundation was likely to behave and wheteher the approach/ method used in obtaining the ultimate resistance was realistic. I am not saying that we even fully understand the simplest case. For example, when do we invoke local or general shear calculations etc.

Note that load factors are not numbers that are cast in stone. The premise for these values has to be understood. The code srecognize this and also allows for judgement to be used. This would be a discussion between the geotech and structural engineer. Load Factors calibrated for Interstate Highways are not the same that should be used for other roadways unless certain conditions apply. Here is where I think that some problems lie as we do not want to do different than what we see in print.

The AASHTO and Canadian codes give load factors that are less than 1 and exoplanation of how they shoud be used.

I think that our problems with the design lie nore with the understanding of the structural load factors to be used rather than in the determination of the geotechnical resistance. One of the reasons for varying foundation sizes etc. The factors that are used to obtain geotechnical resistance are basically the reciprocal of the factor of safeties that have been traditionally used over the years by geotech engineers with possibly some slight refinement.

I attended a seminar in Nova Scotia Tech on the Canadaian Foundation Manual when the ULS concept was incorporated in the manual. Geoff Meyerhoff explained that was all to the calibration i.e bascially the same time honoured FOSs were converted to resistance factors as those were what had proven successful over the years.

This does not mean that you cannot use a factor of 0.7 rather than 0.5 where the Code says 0.5. If you do not want to state that then simply modifiy your ultimate resistance value. You are in charge and it is your judgement. You also take the liability. It all comes down to the parameters chosen and the method used to obtain the ultimate resistance. Yes indeed there are numerous answers depending on what we choose. Some can push the edge others may be simply afraid.

In terms of settlement, the load factors used are 1.0 as overloads are generally treated as transient in relation to bridge structures. Some other situations may require that overloads be used. Every problem needs to be examined.

The day of the geotech engineer providing information without knowing fully how the structural engineer is going to use same is drifting by. Loads and resistances must go hand in hand. Despite the grey area of load factors, there is an opportunity with the LRFD design approach for the geotech engineer not to provide a "standard geotechnical report" as in the past but to become intricately involved with the process.

How many times have you not wondered how the recommendations you made are being used? How may times have you not wondered what magnitude of loads are being applied to your foundation. How may times have you not wondered whether your design was too conservative or unconservative? Now is your chance to get involved.

If you remember that Ralph Peck was a structural engineer then a geotechnical engineer, you may realize that he advocates that a geotechnical engineer must have a good appreciation for loads that are to be applied to the foundation if he is going to provide suitable recommendations.

Regards

 

[BigH]

Good points VAD! - I knew you'd come through. But, as with a thread in the foundation side; let's hope that the design firms will let the geotechs in on the development. Too often the geotechnical investigation is done before loadings are approximately known. If we are to have this 'hand-in-hand' approach, then it must truly be an interactive venture.

 

[GAFenton]

BigH, do those pancakes come with maple syrup??? If so, I could eat a good deal more than 3!!

You and VAD have clearly identified many of the problems with developing a half-decent geotechnical design code.

BigH:

The weaker zone should indeed form the basis of design. My point re the geometric average is that given a pile of data about a site (we should all be so lucky), the geotechnical engineer has several possible ways to characterize the site. I'm interested to know: when you have data (CPT, lab, whatever) from a "layer", what sort of average do you use to characterize that layer?

Consider the following problem: if a uniform load is applied to the surface of a perfectly horizontally layered soil then the settlement depends on a harmonic average of the soil layer elastic moduli (see, e.g., Schmertman's formula and write it as settlement = (stress*depth)/E_eff... E_eff is a harmonic average of the layer moduli). Alternatively, if the soil is perfectly layered VERTICALLY, then the settlement of a (rigid) foundation depends on the arithmetic average of the elastic moduli. There are no formula for this case because it hardly ever happens.

Note that the geometric average lies between the arithmetic and harmonic averages.

Since soils are almost never vertically layered, and only sometimes perfectly horizontally layered, the arithmetic average (the one we mostly use) should be almost never used, and the harmonic average sometimes used. This suggests that, in the lack of detailed knowledge about the layering, that the geometric average is a reasonable choice. It is also a "cautious estimate of the mean", as specified by several codes. The use of the geometric average to specify soil properties has also been found to be reasonable in areas such as flow, bearing capacity, and slope stability (in all cases, the "weakest path" principle exists).

In the above argument, I am really just suggesting that if you have no overwhelming reason to use the arithmetic average, you might want to consider the advantages of the geometric average in general practice as a "cautious estimate of the mean".

Regarding your last few questions: I'm in Nova Scotia (well, actually, I'm in Australia right now, but normally I'm in NS), I'm on the Canadian Highway Bridge Design Code (Foundations) Committee. I don't favour this code over CFEM (2005, if it ever appears) at this point - I am merely looking for the best solution. Regarding downloading codes... unfortunately, most codes are now both expensive and protective. You can find the NCHRP and FHWA reports at

http://www.engmath.dal.ca/risk/publications.html

under "Related Publications". Contact me directly for more information. I expect you can figure out how.

VAD:

I agree completely that the codification of geotechnical parameters directly is not a good thing. There is absolutely no question in my mind that geotechnical insight should govern designs. As you know, geotechnical engineering involves many uncertainties that can only be properly captured by experience. Have you read Steve Vick's book "Degrees of Belief: Subjective Probability and Engineering"? I highly recommend it.

However, the problem is this: How can a geotechnical design code be formulated if everything is to be left up to the geotechnical engineer? Is that what the structural engineers did?

I would have no objection to NOT working on a geotechnical design code if all geotechnical engineers were equally experienced and if all geotechnical engineers were happy to operate solely on the basis of past accumulated experience. However, we have to face the fact that our (e.g. your) years of experience and your ability to extend that experience to new problems can only be passed to the next generation by an equal number of years of experience under the current educational scheme.

Structural engineers use their code to pass on a great deal of their experience. Can we not make use of the same model?

I am not suggesting that we develop a code which eliminates subjective thought and the benefit of experience. I am suggesting that we need a code which 1) guides the inexperienced, 2) allows input from research to help extend experience to new problems, 3) allows geotechnical engineers to be on the same playing field as structural engineers.

Your input is definitely essential. I think that you and I and all geo-engineers need to come up with a design code which bows to experience but which guides the inexperienced (for the safety of us all!) and allows for the input of new research results so that we can produce competive yet safe designs. The trick is to embody your experience along with that of others from around the world while remaining open-minded, yet logically critical, during the process. It is hard not to be blinded by what we know.


Regards,

(Imagine two beer glasses clinking)

------------------------------------------------
Appendix: Various Common Averages

- the arithmetic average, the most common, pays no
attention to magnitude
- the geometric average, a little more complicated, is
influenced by low values,
- the harmonic average (see Schmertman) is strongly
dominated by low values.

Arithmetic Ave:
n
x_a = (1/n) sum x_i
i=1

Geometric Ave:

x_g = n'th root of (x_1 * x_2 * ... x_n)

n
= exp{(1/n) sum ln(x_i) }
i=1

Harmonic Ave:
n
x_h = 1/[(1/n) sum 1/x_i]
i=1

 

[BigH]

GAFenton - the "pancakes" are my way of giving "snaps" - or "clapping"! Good ol' Quebec Maple Syrup would be nice over here in India!

 

[VoyageofDiscovery]

Hi GAFenton,

My discrepancy between the two methods was in the earthquake load case wrt bearing pressure and sliding. I should have mentioned that earlier.

Regards

VOD