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# Which method is preferable when estimating safety factors? LEM or FEM?

## Which method is preferable when estimating safety factors? LEM or FEM?

(OP)
Hi,
I am investigating 3 different geometries of embankments. I' m both using PLAXIS and a conventional software based on method of slices (ex. SLOPE/W incorporating Morgenster-Price approach).
In all cases, PLAXIS gives always a lower S.F. In one case the difference is rather large. For example, one gets S.F.=1.55 using the method of slices, while he gets S.F.=1.38 using PLAXIS.

Here are my questions:

1) Is it a general tendency, FEM softwares to give lower S.F.s than softwares based on method of slices.?
2) If the first stands, how can this be explained? Is it possible that method of slices gives solutions close to upper bound (unsafe solution), while FEM gives solutions close to lower bound solutions? Is the "real" F.S. somewhere between the two different values and thus should we present both values commenting that those values are close to the two extremes?

Efty

### RE: Which method is preferable when estimating safety factors? LEM or FEM?

Building codes and typical practice are "calibrated" to the limit-equilibrium method.

When I've seen FLAC and Morgenstern-Price results from Slope/w compared, the difference has been just a few percent, not as big of a difference as you're seeing between PLAXIS and MP.  Have you looked at why the difference is so large, perhaps because you have large contrasts in strength and stiffness among materials in the PLAXIS model, and thus large differences in the percentages of the strength that are mobilized in PLAXIS?

Does the difference between 1.38 and 1.55 really matter?  Both are stable if the material properties and piez line are correct, and higher factor of safety doesn't protect against anything but errors in the analysis (or not being able to get the building permit).

### RE: Which method is preferable when estimating safety factors? LEM or FEM?

Unless I'm trying to calculate deflections, I always use a limit equilibrium method.  Unless specifically requested otherwise, I use the Spencer's Method.

How are you determining the FS from Plaxis?  While I don't personally run LEM models, I've never gotton a "warm fuzy feeling" from the engineers when I have had them ran and I ask for a SF from those runs.

### RE: Which method is preferable when estimating safety factors? LEM or FEM?

(OP)
Thanks for the useful replies.

GeoPaveTraffic, I also basically use LEM for estimating SF and PLAXIS or simple spreadsheets for the estimation of settlements and deflections.  Nevertheless, you can easily get a SF by running a simple "phi-c reduction" analysis when using PLAXIS. In this method, parameters tan(phi) and c are simultaneously reduced in steps by an increasing factor until a failure mechanism is formed. When the latter happens, the respective factor is considered to be the SF.

Dgillette, I did some runs while changing the deformation modulus E of the embankment (ex. E=15 and 50 MPa), but it seems that the SF is only governed by the phi and c parameters. However, I don't know, how the fact that Plaxis allows for both elastic and plastic behaviour affects SF.
It is also interesting that Plaxis failure zone is usually much larger than that derived by the LEM analysis.
I agree with you that when you have a value of 1.38 compared to a value of 1.55, there's not any problem; but what happens when you have 1.18 compared to 1.35 and the minimum SF allowed by the code you use is 1.30?
Thus, I don't know whether LEM analysis provide SFs that are adequately in the "safe side". And imagine that it is not always easy to find the proper "family" of circles that give the minimum SF, so you can be misled in your estimations.

### RE: Which method is preferable when estimating safety factors? LEM or FEM?

There was a long discussion about the pros and cons of LE vs FE slope stability on this forum a few years ago.  Dr. John Krahn (CEO of GEO-SLOPE) posted his own response in one of GEO-SLOPE's monthly newsletters.

Nate Hekman
GEO-SLOPE International Ltd.

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