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how to get factor of safety of slope based on finite element analysisHelpful Member!(9) 

ananan88 (Civil/Environmental)
7 Jul 04 12:32
Dear friends:
I'm using some finite element softwares such as ADINA\ANSYS to analysis the stability of a slope. Although I can calculate the stress and strain of each elements,I don't know how to calculate the whole safety factor of a slope.Do I need to draw many slip surfaces and calculate each of the safety factors and then find the mininum value?How to programming it?
Thank you for your help!
Helpful Member!(2)  kwalton (Geotechnical)
9 Jul 04 5:12
I am not familiar with the FE programme you are using.  However, I use Phase2 from Rocscience so can tell you how it is done in that software.  I presume you are using Mohr Coulomb strength parameters c & phi.  (Phase also allows the use of Hoek-Brown parameters) The material type needs to be set to plastic, not elastic (it will then analyse both elastic and plastic deformation).  It should then give you the ooption of imputing c & phi in addition to the elastic parameters.  You will then need to adjust c & phi by strength reduction, dividing c & tan phi by a factor representing the factor of safety, e.g. 1.2 until the programme cannot converge the algorithm, i.e. it cannot achieve elastic equilibrium.  It should tell you that this cannot be achieved.  This is also accompanied by a rapid increase in the maximum deformation.  At this stage the model has effectively failed and you will see significant movement on the total deformation plot.  You should also see the failure plane by viewing maximum shear strain.  You will need to play about with the strength factors until you see roughly what the factor of safety is then you can home in on the relevant c & phi.  The factor of safety is the strength reduction factor for failure, i.e. if you have used a strength reduction factor of 1.2, the factor of safety is 1.2.  If you visit the rocscience site they have some useful papers on strength reduction you can download (No, I don't work for them)

K Walton
Helpful Member!(3)  Focht3 (Geotechnical)
10 Jul 04 16:47
I couldn't disagree more with the approach proffered by kwalton.  That's a dangerous approach that can give very misleading results - not the least of which is the location of the surface with the minimum factor of safety.

The factor of safety is generally defined as the available resisting force divided by the driving force.  By "adjusting" the cohesion and phi values, you alter the location of the critical surface.  This approach also does not properly account for the phreatic surface, and would be virtually impossible to do with multiple soil layers.

I have never attempted a slope stability analysis using FE software.  I see no advantage (for most, if not all, design assignments) given the relatively "mature" state of our knowledge regarding slope stability.  Why aren't you using "traditional" slope stability software?

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?"

Helpful Member!  BigH (Geotechnical)
11 Jul 04 0:08
I agree with my esteemed Colleague Focht3!   Unless there are some very very special considerations, it doesn't seem worth it and the normal methods are quite fine, well documented and are considered quite satisfactory.
  I will bring to your attention, as interest, an article by Seo and Swan in ASCE J or Geo and GeoEnviro Engr May 2001, Vol 127, No.5 - "Load-Factor Stability Analysis of Embnakments on Saturated Soil Deposits".  They used FEM analyses and also compared to an actual case history from France.
kwalton (Geotechnical)
14 Jul 04 7:32
Bit of a put down from Focht3 & BigH! wenandsky88 was asking for the technique and I have explained it, (perhaps not as well as I might have).  

With regard to changing the location of the failure surface, assuming that the slope is stable, there will be no failure surface anyway at the input parameters, we are merely generating a theoretical failure if the material were weaker. c and tan(phi) are reduced by the same amount each time, thereby maintaining their relative values.

Multiple layers can be catered for by reducing each layer by the same amount.  I have done this on some complex multiple strata and it has given very sensible results.  FE is only another tool and should be used with sound engineering judgement.

Geotechnical FE programmes allow the input of phreatic surfaces, Ru etc. and I have no reason to doubt that the various programmes available treat this in the correct manner.

I don't have access to the paper in ASCE and a synopsis of the conclusions would be useful.  Did they compare FE and limit equilibrium results?  There is a wealth of published data supporting the technique. e.g. Griffiths & Lane (Geotechnique 49, 1999) say  "The FE method.........has been shown to be a reliable and robust method for assessing the factor of safety of slopes......The widespread use of this method should now be seriously considered by geotechnical practitioners as a more powerful alternative to traditional limit equilibrium methods"
kwalton (Geotechnical)
14 Jul 04 7:36
Before I get pulled up, yes, I have just realised that I refered to the "failure surface" when Focht3 refered to the "critical surface".
kwalton (Geotechnical)
15 Jul 04 8:05
I have been giving some more thought to Focht3's comments re the location of the critical surface and conclude that these comments apply equally to limit equilibrium analysis.  In plastc FE analysis, you are generating the potential failure surface, not the critical failure surface.  With limit equilibrium methods, the critical surface is the surface with the lowest factor of safety for the input parameters, not necessarily the surface that would fail.  Failure would only occur for one or more of the following reasons:

lower shear strength
greater water pressure
external loading
wrong mode of failure

In any event it is likely that the failure surface would not be the same as the critical surface for the very reasons that Focht3 states with regard to FE analysis.  At least with FE analysis wrong mode of failure should not be as big an issue since no preconception of the mode of failure is required (but requires sound judgement and evaluation as with any geotechnical problem).
Focht3 (Geotechnical)
17 Jul 04 10:06

First, no "put down" was intended - sorry you took it that way.  This isn't personal -

I'd suggest that you read Ralph Peck's letter to Karl Terzaghi about their collaboration on their text book.  (Some of their correspondence can be found in the "Judgment in Geotechnical Engineering" book.)  And re-read some of Terzaghi's letters to Peck - he was pretty hard on some Ralph's ideas and occasional fuzzy thinking.  My comments are in the same vein.  I will continue to be tough, because I firmly believe that you are very wrong on this point.  But my criticisms have to do with the approach, not you.  

First, my assumptions.  To me, the original question has to do with design and does not involve the evaluation of a slope failure.

Quote (wenandsky88):

Dear friends:
I'm using some finite element softwares such as ADINA\ANSYS to analysis the stability of a slope. Although I can calculate the stress and strain of each elements,I don't know how to calculate the whole safety factor of a slope. Do I need to draw many slip surfaces and calculate each of the safety factors and then find the minimum value? How to programming it?
Thank you for your help!
  If you know the failure surface, then varying the soil strengths until you reach incipient failure is fine - as long as "the" surface is in agreement with your knowledge of the failure.  But this is easier - and faster - to do with limit state programs.  FE does not offer any real advantage for this type of analysis, unless you are looking at reinforcing the slope with drilled piers, soil nails, etc.  Then it has some merit.

For evaluating stable slopes, the FE approach you have described (Which I will call the kFE method) is not equivalent to a traditional limit equilibrium analysis.  To understand why I say this, consider the following: if I were to follow your logic and perform a limit equilibrium analysis - with search for "the" critical surface - I would reduce the soil strengths until I found a slip surface with a factor of safety of 1.0.  (I'll call this the kLS method.)  But that would not be the appropriate critical surface, since the soil properties no longer represent the "true" soil conditions.  (I don't want this discussion to drift into a discussion of what the "true" properties are - yet.)  The critical surface obtained by the kLS method would, in almost every case, be very different from that obtained using the well established limit state approach used by most of us.  You have a very high probability of getting the wrong answer by using the kFE method to evaluate stable slopes -

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?"

JOR1 (Civil/Environmental)
5 Aug 04 16:59

I see that there is a debate about slope stability and finite element.

Actually, in finite element any soil model coupled with the c-phi reduction technique will give the same results. For example, if the softening-hardening model is used with the c-phi reduction it will give the same result as the mohr-coloumb method. As a result, strength reduction method  requires only three soil parameters (phi, c, and gama). Remember that the limit equilibrium needs the same parametr.
In a study by Griffiths (Griffiths, D.V., Lane, P.A. (1999). “Slope stability analysis by finite elements” Geotechnique, 49(3), 387-403.) he showed that finite element method is more accurate for several cases. For example when there is a sloped  weak layer underlaying a stiff layer. For other cases where the geometry is simple, limit equilibrium (rigourus methods like morgenstern-price) has the same power as finite element (2D analysis and 3D analysis).
I did a research recently on Finite element and limit equilibrium methods. It seems that the most critical point in the analysis (assuming simple geometries that do not need finite element)is the searching technique used in the limit equilibrium methods. A powerful search technique is the MONTE-CARLO technique. The power comes from the optimized slip surfaces created each run (can be up to millions in less than a minute).
Another good reference is by Duncan (Duncan, J. M. (1996). “ State of the art: limit equilibrium and finite element analysis of slopes.” Journal of Geotechnical Engineering, 122(7), 557-596.) who summarizes the state-of art practice in slope stability analysis.

Wish this will help in the debate.


gandersen (Geotechnical)
6 Aug 04 7:41
I have been following the discussion on the use of continuum based numerical methods versus limit equilibrium methods for slope stability analysis and have really appreciated the references that have been given.  We are getting ready to evaluate the capacity of an existing bridge pier for I-90 in Cleveland and plan on working with both methods.  We are tasked with estimating the current Factor of Safety or capacity and the future Factor of Safety or capacity with various changes in load conditions.

I would appreciate other's opinions about the use of the one versus the other and any actual experiences where they have been compared.

BigH (Geotechnical)
6 Aug 04 15:06
Glen - one thing to consider and I am sure that you will - at the time of the initial embankment construction, the factor of safety was based, most likely on the undrained shear strengths in the soils investigation.  Now, with the embankment having been there for many years (most have, if I remember I-90 correctly), is that the embankment will have consolidated the clay and you may now have higher operative undrained shear strengths if you are going that way.  N. Som wrote a note in ASCE years ago (I have a scanned copy) on estimation of the increase in Su due to loading.  Just a thought as you get started.
Helpful Member!  TerraBoy (Civil/Environmental)
12 Aug 04 9:36
In response to gandersen/Glen's question about FE versus LE, I would say that you have to look at each method as a tool.  I think LE tells you about "failure."  All it does is compute a driving force and a resisting force and divide one by the other to give you a FOS.  This gives you an idea about if it is going to fail.  I still have some questions about just what failure mechanisms LE can identify (see a new post in this forum).  FE gives you stresses and strains.  You get a stress a some point, you have identified a stress/strain relationship, and you get a resulting strain.  You have to be careful when you start getting large strains, because your soil model's stress/strain relationship may not apply any more.  

Should they give you the same answer?  I'm not sure.  I have seen some published stuff where they do, I have seen some actual projects where they do, I have also seen some projects where they do not.  There is a whole lot of input that goes into making each method's output and it is quite likely that some of the problem is in the input.  Our ability to analyze far exceeds our ability to characterize.

Both methods are useful, both have advantages and disadvantages, but in the end both are just tools.  Both are essentially dumb.  They can do more calculations in seconds than we could do in years (or something like that).  But neither has intelligence or judgement and that, in my experience, is what is usually needed when you look at the results of each method.  
Helpful Member!  SmokeyBear (Geotechnical)
31 Aug 04 5:33
I see a debate about LE and numerical methods and can't help but respond.
On a recent long term study we looked ast both LE, FE and FD analyses in nauseating detail and browsed various references. The upshot was:
The latitude for error is greately reduced when all conditions for equilibrium, including moment equilibrium, are satisfied i.e. Morgenstern & Price, Spencer, Janbu's Generalised procedure and Sarma '73 (not Sarma '79.)
Extensive studies (Duncan et al)compare rigorous LE and FE and suggest the difference in FoS computed by any of these methods is less than 12%.  
It is reasonable to conclude that the middle of this range is the best value that can be calculated and if a method is used whiuch satisfies all conditions of equilibrium, the calculated FoS will differ by no more than +/-6%.
Note that the range of uncertainty in evaluating shear strength may be much higher.
Numerical methods which satisfy all conditions of equilibrium give the same value of FoS (+/-6% from the best obtainable value).
The FE strength reduction method discussed in this forum, with large deformations used as an indicator of instability, is essentially the same definition of FoS used in LE methods and hence should result in the same FoS as LE methods. Where it did not, I would prefer to use the LE result because of longer experience with this method and a lower likelihood of significant numerical inaccuracy.
The huge benefit of FE/FD is that for complex material conditions, the stress changes provide strain levels and hence provide a "picture" of the potential failure surface/s. LE methods don't.

As has been said before, both LE and numerical methods are valuable tools and we should embrace both (whether Peck and Terzaghi agree or not---apologies to Focht3)
gandersen (Geotechnical)
31 Aug 04 8:42

Thank you for the thoughtful post.  Is it possible to get a copy of the report/study that you are refering to?  It sounds extremely interesting.  We are starting a study on a large slide in Cleveland, Ohio (USA) and would appreciate any input that we can get.


Glen Andersen, Sc.D., P.E.
BBC&M Engineering, Inc.
Cleveland, Ohio

Focht3 (Geotechnical)
31 Aug 04 10:47
Yes - I would like to see the results as well.

Please don't misunderstand my previous comments: I did not mean to give the impression that FEA isn't useful.  The thrust of my argument is that a "strength reduction" approach with FEA will give misleading results.  While one can easily reduce all cohesion values by a constant factor, applying the same factor for frictional resistance is neither obvious nor intuitive.  Particularly when multiple strata and water tables are involved.  LE programs are designed to deal with a global factor of safety by the way the problem is formulated; FEA is not.

And I think that Terzaghi would be amazed by some of our achievements, SmokeyBear - and very annoyed by some of our repetition of mistakes of prior generations of engineers.  He was absolutely critical of fuzzy thinking.  I have had the privilege to know a few of his former students, and they say that he was quite a taskmaster in this regard.  He was not above "dressing down" engineers in public -

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?"

BigH (Geotechnical)
31 Aug 04 15:51
As to Focht3's point on repition of past mistakes ... I find it quite interesting how little most of the newer engineers know of Bjerrum (other than his vane shear strength modification factor), Skempton, Casagrande(s), Hutchinson, Tshebotarioff, Krynine, Judd, Golder, Bishop, Chellis, etc.  My adice to you all is to pick up their books - even though they may be more than 30 years old.  You will find they taught through real projects (especially see Tshebotarioff in this regard) and not idealized situations like the new breed of books and course lectures (via downloads of internet). They talk of failures that really happened. While I can understand the desire to do the FE/FD analyses, I would suggest that for the vast majority of all cases by practicing engineers, the normal Bishops, Janbu, etc. are quite fine - this is the point that I belive Focht3 and I have put out.
SmokeyBear (Geotechnical)
31 Aug 04 21:14
ganderson-results of the study are not published. It was undertaken for a major litigation case. However, I would run LE programs like UTexas, SlopeW with Monte Carlo simulation to assess properties; then FE or FD analysis using strength reduction assessment for FoS. If results are within +/-6% you are probably close to the best obtaiable value and can move on to forward analysis. Duncan 1996 (refer Jor1) is terrific.
TerraBoy - if you are concerned with large strains try FLAC a FD code. It remains numerically stable under very large strains.
Focht3 - I cautiously/respectfully take issue with your statement "..a strength reduction approach with FEA will give misleading results."
Under LE we slam in c and phi values which we know are correct???, set up a search routine and press the button. The program makes varying assumptions about interslice forces and produces a FoS.
Under numerical methods, we at least can look at things like strain, strain compatibility, displacement vectors etc. It helps us visualise the problem and potential failure surfaces. I question why strength reduction is considered more error prone than material categorisation based on all to often limited SI and lab testing.
Note I do not advocate one or the other, merely the use of both to help us understand what may be happening. I repeat that if LE and FE/FD give different results, I would lean towards LE because of longer experience with this method.

BigH - There is always a need to assess the appropriate degree of analytical sophistication. However, checking your work by different methodologies is appealing. The cost and time to utilise numerical methods, together with LE techniques is, I would consider, low and provides value added solutions. It also allows, or forces people to think about the problem rather than just stick it in a program and push a button.
BigH (Geotechnical)
1 Sep 04 15:18
SmokeyBear - agree with your last statement; Focht3 (I am sure) and I have both done more than our share of Bishops analyses by hand - so, yes, we have thought of the problems many times over.  How many of the younger - computer literate - engineers have ever take a problem (other than the required problem in University) and done it by hand with the Table as, say, per Terzaghi and Peck?  Learning that slope stability in sand embankments on hard soils gives the infinite slope situation the hard way - can be an eye opener.  Sadly, sometimes (take it as me) I don't have the greenbacks to own all the computer programs myself - and, when you are in a very large company - they have other needs than G-Slope especially for a guy overseas!
Best regards and
kwalton (Geotechnical)
7 Sep 04 10:58
I would like to pick up a point that Smokeybear hinted upon, particularly with regard to non-circular failure.  In LE methods we have to define a critical surface and then analyse that.  In other words we have to decide on the critical surface before we run the analysis.  Yes, we can (and should) consider a number of different surfaces but are we always sure that we have considered the correct one?  Slight differences in defining the critical surface can have significant influence on the FOS.  FE does not require any such assumptions.  I also agree (and I am sure everyone else will) with Smokeybear re the strength parameters we input.

Focht3 - Re difficulty of using strength reduction on phi.  We apply the same strength reduction to both cohesion and friction.  We apply the factor directly to c but apply it to tan(phi) for friction which will therefore mainatain the ratio of c & phi.

geotechman (Geotechnical)
4 Mar 05 15:50
kwalton wrote: "You will then need to adjust c & phi by strength reduction, dividing c & tan phi by a factor representing the factor of safety, e.g. 1.2 until the programme cannot converge the algorithm, i.e. it cannot achieve elastic equilibrium.  It should tell you that this cannot be achieved."

My question is how to adjust the SRF. Is it adjusted automatically? I have not found the place adjusting c & phi or SRF in the program.    
kwalton (Geotechnical)
22 Mar 05 11:22
That will depend on the software.  I have been using Phase2 (Rocscience) and my version does not do SRF automatically.  I have to work out c & phi for each run then change the Mohr Coulomb parameters each time.  I understand that the next version of the software will incorporate automatic generation of SRF parameters.  Other software may already include this facility. (Don't forget to divide tan phi by FOS then take tan-1)
gamadot (Geotechnical)
2 Jul 05 15:29
I agree with great suggestions from kwalton. I have few misconceptions about shear strength reduction(SSR) technique.I hope that a clarification can be found at this site.For starting an analysis with SSR we need to know some value of c and phi and we keep reducing these two values by a same factor until non convergenec is achieved.So the final c and phi value depends upon the start value.In my case i have a bunch of experimental values of c and phi obtained from undisturbed, remoulded and direct shear and triaxial shear test which were used as a starting value in SSR.Since the experimental values are widely varying and hence the final values from SSR are. Can anyone tell me which value to be considered as the strength parameters prevailing at the time of slope failure.
kwalton (Geotechnical)
8 Aug 05 4:49
To gamadot:

The problem is just the same whether you are undertaking Finite Element or Limit Equilibrium analysis.  You have to decide on realistic strength & density parameters to start with and go with those unless you are undertaking probability analysis.  You need to consider the nature of the material, likely failure mode and the spread of parameters obtained from the varying test methods.  You probably have too much information!  Professor Jennings from Witwatersrand in South Africa once said to me when we were doing some large scale plate loading tests "Only do one test then you only have one answer".  He was saying it "tongue in cheek" but it does acknowledge the difficulty of deciding on appropriate parameters.
Helpful Member!  Rocscience (Geotechnical)
3 Nov 05 15:10
Phase2 version 6 by Rocscience offers fully automated finite element slope stability analysis, using the SSR (shear strength reduction) method. With one mouse click you can determine the critical strength reduction factor (safety factor) of a slope. The SSR analysis in Phase2 can be used with Mohr-Coulomb or non-linear Hoek-Brown materials, and can be applied to soil or rock slopes.
The validity of the SSR results produced by Phase2 has been well documented. The SSR method produces results which are identical or very comparable to limit equilibrium slope stability results. Over 30 verification examples are documented in the Phase2 SSR Verification Manual. Models can be easily built in Phase2 or imported from Slide (limit equilibrium slope stability program).
For more information see

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