Montecarlo and FORM

[Mccoy]

I came across the following article abstract, which would seem to support my suspicion of FOSM and FORM methods, when indiscriminately applied. The authors found that Montecarlo (quasi-exact) solutions and FORM (Taylor series approximation) were substantially different when applying shallow foundations bearing capacity formula, in view of the nonlinear function(s) involved and the non-normal distribution functions assigned to variables.
Montecarlo method, when carried out with a high number of simulations and a reliable random number generator, is recognized to be the reference (subject to very small error). I do not know why, but Montecarlo has been slow to catch on in geotechnical engineering, where FOSM-FORM approximations are preferred (as it results evident also from the Christian and Baecher's book).

Author(s): Y. Honjo1 | S. Amatya2
doi: 10.1680/geot.2005.55.6.479

Géotechnique

Print ISSN: 0016-8505
Volume: 55 | Issue: 6
Cover date: August 2005
Page(s): 479-491
Abstract text
Partial safety factors for square footings for highway bridges resting on granular soils have been determined based on reliability analyses. Some example cases are chosen based on a database which includes detailed information of 1869 actually constructed highway bridge pier shallow foundations in one fiscal year in Japan. The designs obtained, using calculations based on the bearing capacity equations by Meyerhof and by Brinch Hansen as modified by Vesic, are compared. The uncertainties involved in the bearing capacity equations are investigated through a comprehensive literature review. The seismic forces determined from the peaks over threshold analysis and fitted to a general Pareto distribution have been considered. The first-order reliability method (FORM) and Monte Carlo simulations (MCS) are employed to determine and compare the 100-year failure probabilities of the shallow foundations designed. It is found that FORM gives a considerably lower failure probability than MCS. Finally, partial factors obtained using calculations based on the two bearing capacity equations are carefully reviewed. It is found that the design value method used to determine partial factors by FORM does not appropriately give either the partial factors or the failure probability for the case of shallow foundation design where the performance function is highly non-linear and some of the basic variables follow distributions that are far from the normal distribution.

 

[jdonville]

McCoy,

I will preface this by stating that my familiarity with explicit probability-based analysis methods is fleeting at best - possibly to my detriment.

I suspect that MC methods are slow to catch on due to the fact that many commercial software analysis packages, if not most, are deterministic and do not easily or explicitly support the representation of input parameters as probability distributions.

Additionally, I suspect that even though add-in software for spreadsheet calculations (@Risk, for example) is available, there are several reasons why these methods have not been adopted:

1) The additional cost and learning curve to climb to incorporate them into existing methods of analysis (applies equally well to software vendors as well as practitioners).

2) No explicit requirement or even "official" encouragement to use these approaches in some jurisdictions (including North America).

3) Many engineers will use a 'good enough' approach that is conceptually easy to perform (and that has historical momentum) rather than investing in (or demanding from vendors) newer, more rigorous methods. A big, fat factor of safety can hide a multitude of deterministic sins.

Jeff


Jeffrey T. Donville, PE
TTL Associates, Inc.

http://www.ttlassoc.com

The views or opinions expressed by me are my own and do not necessarily reflect the views or opinions of my employer.

 

[MRM]

I could've sworn I contributed to this post when it was new. Did the post get pulled for some reason, did I respond to an entirely different thread, or did I dream posting to this thread one night?? My dreams are sometimes rather vivid...

 

[BigH]

MRM et. al.: I've never pulled a post or been requested to - and would never intend to unless so over the top!

Do you have the published paper yet? Did they give you some 'prints'. If so, I'd love to have a 'signed' copy - first edition, eh??

 

[Mccoy]

MRM:
Do you refer to the similar but not identical thread: "limit state design" ?

Maybe I should have replied to that instead of opening a new one.

 

[MRM]

Mccoy,
I think you're right. The "limit state design" sounds familar. I should check on that... I'll review what's new and try to add something meaningful to the FORM/Montecarlo discussion.

BigH,
Almost! It's going to appear in the May edition (this May). I understand I'll see something by mid April. Thanks once again for your help on that paper, along with SlideRuleEra and VAD. Your comments gave me a lot of good info. Unfortunately, I wasn't able to directly incorporate your great suggestions in this one since everything happened concurrently; ASTM accepting it, and you guys reviewing it. I know that your comments will help with future papers though.

Sorry about getting off track. Hope all is well with everyone!