I think that Bishop's simplified method of slices is the best method followed by Morgenstern Price method.

There are 2 groups of limit equilibrium methods; the ones called rigorous methods which consider the force and momentum equations to compute FS, and the non-rigorous methods which consider only force (x and/or y axis) or momentum equations.

Among the former you have Spencer, Morgenstern-Price and Sarma as examples. Janbu, Bishop are some examples of the latter.

Having said that, rigorous methods should be used as a more reliable estimation of the true FS (this isn't just my opinion, some authors state the same).

And from my experience, non-rigurous methods tend to give more conservative results in comparison to the its rigorous counterpart.

For more details, go to the book 'Soil Strength and Slope Stability, Duncan and Wright. It has a comprehensive chapter of slope stability that you shouldn't miss!

Regards,

Morgenstern-Price and Spencer are mathematically more rigorous methods which include all

inter-slice forces and satisfy all equations of statics. The other LEM methods such as Ordinary, Bishop's simplified and Janbu's simplified methods ignore inter-slice shear forces for determination FS of the slopes. Therefore, Morgenstern-Price and Spencer methods are recommended to be used for estimation of a more reliable safety factor of the slope. Regards.

I agree with the conclusions in the previous three posts/replies. Given that the first differs from the second and third, that may seem odd. However, if one considers that a more conservative result for the FS might be considered "best," then it makes complete sense. Conservatism is sometimes desired, or a virtue. A more accurate prediction of the FS might be an over prediction. If the true factor of safety is 1.01 and Bishop's method gives a result of 0.8 and Spencer's method gives a result of 1.15 the accuracy isn't as important as the conclusion. (In my experience, so great a difference between those methods is unusual. My hypothetical numbers are merely for the purposes of illustration. A more realistic outcome would be for Bishop's to give 1.15 and Spencer's to give 1.21 with the true value being unknown and unknowable.)

I do want to make a more global comment.

All LEMs are mathematical models of reality. We should never lose sight of that fact. It will not always be the case that the "more rigorous" (i.e. more complex) model will give results that better match reality than a "less rigorous" (i.e. less complex) model. The proper argument in favor or any model is a careful, objective assessment of how well it matches reality. How rigorous or complex it might be is only important in that it gives us hope that it might better match reality as it is developed. All models are finite and incomplete approximations of reality. If the omission of two factors happens to have the effect of balancing each other, adding in one of the two will not be an improvement. Even adding in both of them might not be an improvement if our ability to quantify those factors and include them is inaccurate, imprecise, or just incorrect.

I used spencer's method which provide the good result. So, I suggest for it.

• Bishop's method --> Only for circular slip surface.
• Spencer and Morgenstern-Price --> For any type of slip surface.
• Janbu's methods --> For shallow and elongated slip surface.
• Sarma's method --> For slip surfaces that initiates as circular and continues planar.
• Seed and Sultan & Lowe and Karafiath --> For multiplanar slip surfaces.

You can use Spencer's or Morgenstern-Price's methods with confidence.

To decide which method/s is/are best, we should consult another method different than LEMs. FEM models employing SSR technique gives the right answer. Sometimes, the failure surface of a slope can be more complex, it would not be enough to define failure surface with a simple circular form. Therefore, I usually employ two methods together in my analysis. Then, I have a chance to compare for deciding which one is the correct.

Method Assumptions

• Bishop's method --> Resultant interslice forces are horizontal. There are no interslice shear forces.
• Morgenstern-Price --> The direction of the resultant interslice forces is defined using an arbitrary function.
• Spencer --> The resultant interslice forces have constant slope throughout the sliding mass.
• Janbu's methods --> Resultant interslice forces are horizontal. An empirical correction factor is used to account for interslice shear forces.
• Sarma's method --> The shear strength criterion is applied to the shears on the sides and bottom of each slice. The inclinations of the slice interfaces are varied until a critical criterion is met.
• Lowe and Karafiath --> The direction of the resultant interslice force is equal to the average of the ground surface and the slope of the base of each slice.

Therefore, I feel the performance of each method depends on its underlining assumption and the situation/condition for which it is to be used. It is somewhat difficult to arbitrary conclude on any of the methods.

I think, it depends on the proposed slip surface in the slope under ınvestigation.

Hi,

Please read my paper regarding comparison of results between fem and lem methods

https://doi.org/10.14256/JCE.1030.2014

In most cases, strict methods (Spencer etc.) are more preferable. However, there are cases when they yield unrealistic result. In particular it belongs to rocky slopes when sliding of the landslide block happens on a crack (system of cracks), taking into account anisotropy of durability in the rocky massif. In this case it is preferable to use the methods based on balance of forces (for example Yanbu). It is always more correct to use several methods and to carry out the analysis of results on realness (both according to FoS, and under the provision of a surface of shift).

All aforesaid belongs to a case when calculations are made with optimization of a surface of sliding. The result, besides a calculation method, is defined by an optimization method. Now the majority of methods of optimization of a surface of sliding are a little suitable for use in when calculating stability of slopes in anisotropic (jointed) rocky massifs

SLOPE/W computes the factor of safety of earth and rock slopes. SLOPE/W can effectively analyze both simple and complex problems for a variety of slip surface shapes, pore-water pressure conditions, soil properties, analysis methods and loading conditions. Using limit equilibrium, SLOPE/W can model heterogeneous soil types, complex stratigraphic and slip surface geometry, and variable pore-water pressure conditions using a large selection of soil models. Analyses can be performed using deterministic or probabilistic input parameters. Stresses computed by a finite element stress analysis may be used in addition to the limit equilibrium computations for the most complete slope stability analysis available. With this comprehensive range of features, SLOPE/W can be used to analyze almost any slope stability problem you will encounter in your geotechnical, civil, and mining engineering projects.

• However the FOS of a slope can also be computed with FLAC by reducing the soil shear strength in stages until the slope fails.

Always it is better to check the variation of Fs values by using two methods. For circular slip surfaces Bishop simplified method of slices and for any other slip surfaces Spenser and Mosgenstern method can be used to see the variation of results.

For the seismoinduced landslides - method Sarma

Inside the Framework of LEM type of analysis the Rigorous methods should be preferred with respect the Simplified methods. The method that gives more stable numerical solution of Fs are usually the Spencer method and Morgestern-Price method, and Sarma's methods. Rigorous Janbu method is valid as well but gives sometimes unstable numerical solution. Analysis based on software that generate only potencial sliding surface with circular shape should be avoided. The best practice is generate general shape potencial sliding surfaces. Most of the software awailable are commercial licence softwares. But exist at least a full freeware software for it.

For anisotropic rocks with optimization of a surface of sliding, strict methods (the Spencer method and Morgenstern-Price method) can yield not realistic result. Perhaps it is connected with a problem of optimization of a surface of sliding in anisotropic rocks. However, in this case, even the simple method of Yanbu is more preferable.

The best method LEM depends on the slope boundary conditions and type of material (i.e soil vs rock) some good answers have been provided already. We have better tools to assess a factor of safety. LEM should be used as a screening tool only. The obvious alternative to LEM is finite elements (geostudio offers an alternative to calculate stresses using FE, then run a classic LEM, a waste of time in my view) or finite differences. Both using the strength reduction strategies. Again, strength reduction results would be material dependent (better for soils than rocks). Back to LEM, when looking at 3D problems you find that geostudio for example is not even launching a pure 3D LEM, rockscience did with their slide3, I think Geostudio made the right move. LEM has been stretched by software companies beyond its initial capabilities by adding features that improve its results not by much. A well trained user can do far more with simpler modeld. A strength envelope in 3D is not as simple as people image and usually requires a bit of computational effort to do so. For slope stability only the best tool available today is Limit Analysis (LA) the only commercial software I am aware uses it is Optum. There are several advantages of using LA vs LEM. Min 1:00 in the video link below provide some insights on the initial question regarding LEM techniques. Good luck

https://www.youtube.com/watch?v=9kMHkuLTyIM

I am a bit late seeing and joining this question. I have a question to the geotechnical community as a whole. I have often wondered about the stress transformation at the base of the slices in all these famous methods. Do they just use the classic equations with the sin 2beta and cos 2beta terms for converting local principal stresses to the shear and normal components presumably needed to compare with the locally available (and perhaps non-linear) shear strengths? A problem could be that many /even most geotechnical materials we deal with from compact sand, OC clay, rockfill, slopes in rock masses etc are dilatant at failure. As far as I have understood - and please correct if wrong (but Harry Poulos once agreed too) the stress transformation is really supposed to be within an isotropic continuum, with no slip surface, no dilation, in fact no discontinuity there at all. We discovered almost 40 years ago in Terra Tek (Bakhtar and Barton, 1984) that you apparently have to add the mobilized dilation angle to the sin 2beta and to the cos 2beta terms (......sin (2beta + dn mob) etc...) to get the transformation that agrees with large scale shear test results. Has dn mob for the relevant materials been incorporated in slices methods, or not? When non-dilatant materials presumably less or not important.

The phrase posted by Neil Bar " The best method, is ultimately the one that best represents actual conditions in the field, and validation with other methods such as finite element is advisable." is of extreme importance because make a perfect synthesis of what each model should do..

If the model do not reproduce what we observe in field then it May be not appropriate, or may be that ahs been used in incorrect form or with wrong parameters..

The rule Thrash IN -->Trash OUT always is valid..

The LE and FEM method require more parameters with respect LEM to be applied. More parameters may increase the risk associated to parametric uncertainty and then consequences in the model results..

Many thanks to Nick Barton for his Post. Dilatancy is frequently a forgot issue in the shear strength assessment.. In many Geomaterials it has a key role and it is not limited only to shear strength along of discontinuities.

Any way the initial question was: " Which is the best LEM method for determination of Slope Stability ? "

The coupling with blocky DEM maybe better.

This link talk about:

Slope Stability Evaluations by Limit Equilibrium and Finite Element Methods https://core.ac.uk/download/pdf/30817581.pdf

Bishop's Simplified method is the best LEM method for slope stability. The accuracy is best. Can be compared result with Morgenstern-Price Method.

For general case, Bishop's simplified method is one of best methods for LEM.

In most cases all the simplified LEM methods aren't able to consider in appropriate way additional resisting forces induced by presence of stabilizing structures as: Piles/Piers, nails, geodrids/geoesyentetics, anchored steel wire mesh, inclined external surcharge. Neglect the interslice forces and moments and in particular the effects on them produced by reaction forces due to the stabilizing structures may produce unreliable results when simplified methods are chosen. Vary issues are still open : the use and misuse of simplified method), the use and misuse of circular (only) sliding surfaces and... many others.

Dear geotechnical community! Those who use these LEM method-of-slices techniques and have favourite ones, and perhaps, as in the discussions, claiming a 'most accurate' one, have reasons for their preferences of course. But what about the stress transformation question raised earlier? Is the material dilatancy (or not) taken into account in the transformations of sigma 1 and 2 into tau and sigma n (or not) beneath the slices....and should it be? If it should be then the process becomes iterative. Is this not a nice Ph.D. topic for someone? (A presumed step beyond the nice studies already cited in the links kindly given).

Many thanks to Nick Barton for his reply. There are a lot of open issues in slope stability analysis models. The points indicated by Nick are really important as: the role of Dilatancy, and curved failure envelope on the assessment of tau and Sigma N. Yes it is usually an implicit relationship and it should be solved iteratively.. I suppose (hope) that are many peoples working on these topic. In my research activity I tried to approach at these points using both GHB + JRC in rock mass stability analysis, for continuous + discontinuous domains. It a difficult task but several advances can be found in the literature. Anyway if we back to the main theme of this chat I believe that the best model (LEM or not) is the model that produce the best result reproducing real observations of collapsed slopes.

Nowadays, the most important advances in the LEM world is the search methods to find the most critical slip surface used together with the LEM approaches. These methods are Metahueristic methods such as Cuckoo Search, Particle Swarm, Simulated annealing from other fields brought to the geotechnical applications. The value of the LEM methods to be combined with the new search methods becomes more important (these are all non-circular methods). Our studies showed that, for complicated models, simplified Bishop method cannot give good results. Janbu method gives the lower-bound for the factor of safety. The best methods that give similar answer to even FEM analysis are Spencer and Morgenstern Price methods. I hope that helps.

Dear Sina!

I expected an answer from you:

The best LEM method is RLEM.

Igor Fomenko LOL, thanks Igor.

RLEM is the combination of the advanced LEM and Spatial statistics. It is the best indeed.

Dear Kobid,

See the following paper about LEMs:

Article Discontinuous rock slope stability analysis by limit equilib...

Bests,