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Geostudio/exit angle

Geostudio/exit angle

Geostudio/exit angle

I came across the following frase "Slip surface exit angle is steeper than 45 degrees" while doing a very simple stability analyse with Geostudio/SlopeW.
The solution couldn´t converge/An unrealistically small factor of safety, I presume?

My geomechanics book tells me that the maximum exit angle
is about 66.7 degrees(when load is applied to a horisontal soil surface and the soil is homogenous cohesion soil).

Why can´t I calculate bigger/steeper angle´s?
Is this only with Geostudio/SlopeW or is it the same with other programs?

Or should I just get a better geomechanics book?

Very thankful for all replies(hope you understood the question)
Yours Ville Vallaton (Dennis the Menace in english)

RE: Geostudio/exit angle

While I'm not familure with SlopeW, I have seen similar messages with other software pacakages.  Most give this as a warrning message that the solution is likely not correct, but will give you the calculated FS anyway.  I expect that there is a problem with the combination of slope geometry and soil parameters, most likely the soil has a relatively high cohesion when compared to the height of the slope.  This results in high calculated negative side forces and the math goes to pot.

With respect to your question about 66.7 degrees, that is for a footing, a condition that most slope stability programs are not really made to handle.  

If you want, post some more info. and I'll take a look.

RE: Geostudio/exit angle

Are you possibly trying to develope a circular failure surface when the Block Type of failure along a predefined surface would be appropriate?  Remember that you are allowed to create a fairly wide and varying sliding surface using Slope/W.

RE: Geostudio/exit angle

Hello GeoPaveTraffic and thank You for Your reply!

The problem is, that the program won´t calculate/give any FS value for exit angles bigger than 45 degrees.

I will give more detail´s concerning my geomechanics book:

The case in the book is dealing with bearing capacity(Yes I know, that´s not slope stability) with a horisontal (=flat) ground, homogeneous cohesion soil(no friction angle) and a linear load(for example footing) applied to the surface.

In the book it is shown how the maximum circular-shaped slope is being calculated. The maximum valued angle for the the whole segment of the slip surface is 133.5 degrees, so from there I have calculated the angle I was talking about earlier(=about 66.7 degrees).

My biggest question is, is it somehow not allowed(=geotechnical theory says so...) to calculate circular slip surfaces with exit angles steeper
than 45 degrees?

Anyhow, thanks again. Hope I could characterise/describe my
problem properly.

Ville Vallaton

RE: Geostudio/exit angle

Hello also emmgjld and thank You too!

First when I heared my customer making this statement, I immediately thought also that:"Yes, I can do steeper(=bigger)
angles than 45 degrees. If not with the normal(grid and radius, for example by turning the radius), then with block-specified. If not with block specified then with fully-specified and so on."

But when trying to analyse very simple problem with all the possible options(also fully specified), I couldn´t get anykind of value for the FS.

So like I wrote in the message to Geopavetraffic, I´m mainly
interested(at the moment) is it somehow illegal to calculate
these kind of FS:s/slip surfaces?

Ville Vallaton

RE: Geostudio/exit angle


You have not provided us enough information on what you are trying to analize.  Are you trying to recreate the problem from your text book?  If so, a slope stability program is simply not the correct tool for the job.  If it is a true slope stability problem, give us some more information.

RE: Geostudio/exit angle

Also, please advise name of your geomechanics book.  If I remember correctly, since tan(alpha) - the tangent to the slope of the angle to the slice in question - is greater than 45 degrees, the effect of tan(alpha) getting large quickly is there.  e.g., tan(50) = 1.2, tan(60) = 1.7, tan(70) = 2.7.  This may/does skew the results to the effect.  I remember way back in the 70s when we did this by hand, it was always advised to keep the exit angle to less than 45deg.

RE: Geostudio/exit angle

emmgjld: Yes I´ve contacted GeoSlope and yes I also think they are very reponsive too. I´m getting answer´s next week from the creator´s of the software.

GeoPaveTraffic: Yes, you are right. I haven´t provided enough information. I´m not trying to analyze a problem from a text book. I´m mainly trying to answer a question my customer asked me.

I was only desperate after finding out that I can´t calculate these kind of problem´s and then thougth that this web-site would be good place to ask advice.

I´m only trying to find out two things:
1. Why there are these kind of limitation´s in the software(creators of the software will answer this question)
2. Are there any geotecnical/theoretical/practical "laws" why this shouldn´t be done(an answer I hoped to get from this web-site)

BigH: It´s a Finnish handbook(written in Finnish). In fact one person in GeoSlope asked me to send them a copy of it, so if I will do it(translation and sending) I can send it to You too.

Thank You all for Your patience...
Although maybe not a big/important geotechnical problem for anybody, I´m still curious to learn why is it so.

Ville Vallaton

RE: Geostudio/exit angle

In answer to you second question, there is no theoretical reason that I can think of as why you should not be able to do what you are attempting.  However, there are some very real practical reasons:

1.  Slope stability and bearing capacity (what you are really analyzing) are three dimensional problems.  The software must make assumptions when dealing with this.

2.  To achieve numerical convergence, the software/programs make assumptions about what kind of problem it is likely to see so that the software "guess'" in the correct direction and works toward a solution.

3.  Most if not all slope stability software programs divide the possible failure zone into slices.  The forces on these slices are then determined, one of these forces is the between slice side force.  Depending on the solution method implemented by the software, different assumptions are made about these side forces; i.e. (if I'm remembering correctly) if Spencer’s method is used the side force angle and magnitude are calculated to achieve zero moment whereas Bishops simplified method assumes all side forces act horizontally.  There are many other methods as well.

You should really be able to look at the detailed output of the software and be able to determine why it was unable to converge on an answer.  I'm still betting it was calculating negative side forces whit the final failure surface and the software is designed not to allow that condition.  If you are not getting detailed output from the software, try to figure out the setting to turn it on.  If the software does not allow such a setting, I would use a different package.

It is very important that anyone using a slope stability software package (or any engineering software package) understand what the software is doing and how it is doing it.  If you can't look at the output and determine all of the forces on each slice that makes up the failure surface, I would not use the software.  Remember, you as the engineer are responsible for your design, not the maker of the software.

RE: Geostudio/exit angle

Yes, there are mechanical reasons why the steep exit angles would be disallowed.

Ran into the same problem with simplified Bishop method.  I dug out some notes I made 20 years ago when that was all I used.  A similar thing probably happens for Spencer or whatever you are using now.

For each slice, simplified Bishop calculates:

F-resisting = [c'b+(w-ub)tan(phi')] * sec(alpha) /


where b is slice width, u is pore pressure, w is slice weight, and alpha is the slice inclination angle, positive at the top of the slide, and negative for exit portion of circle (or whatever shape).  The value of the part inside the last [] goes negative if alpha is a large negative.  Alpha = 60, phi' = 35, FS = 1.2 will make that happen. A negative resisting force probably violates the laws of thermodynamics.  This phenomenon has panicked at least 2 or 3 engineers over the years.

A steeply inclined exit can also cause you to calculate side forces higher than Coulomb passive.  If that happens, you probably don't have the critical surface, unless there is some physical constraint on the exit, like a rock outcropping.  (Coulomb passive is basically the resistance provided by a wedge of soil being pushed ahead of the retaining wall acting as a dozer blade.  The angle of the passive wedge is the one with the overall lowest resistance, 45-phi'/2.)  For a slope stability problem, the maximum angle won't be exactly 45-phi'/2, but pretty close.  I expect that's the basis for SLOPE/w's objections.

Some programs (UTEXAS2?) let you specify a limit on the exit angle.

Bon chance!

RE: Geostudio/exit angle

Hello Everyone,

Ever since version 5.13 of SLOPE/W was released (December, 2002), trial slip surfaces analyzed with exit angles greater than 45° have been considered invalid. Since this time, some engineers have wondered why this restriction was implemented. In response, GEO-SLOPE's engineers have written a detailed technical note to discuss the theoretical basis behind the enhancement.

The underlying rationale to limit the exit angle is based on earth pressure theory. In a slope stability analysis the toe (or exit area) is analogous to a zone of passive pressure conditions, which should have a maximum inclined angle of around (45°-Ø/2). If Ø=0, the maximum angle would therefore be 45°.

One of the main concerns prior to the implementation of the exit angle restriction, was that it became possible for physically inadmissible slopes to be presented as the critical slip surface with very low factors of safety. Without looking beyond the factor of safety, it became difficult to make a sound engineering decision about why the presented slip surface should be dismissed and another accepted as being more reasonable.

The technical note outlines the various theoretical reasons for restricting the maximum exit angle and encourages engineers to thoroughly examine all the slip surface information presented in a slope stability analysis and to look beyond the computed factor of safety.

You can find the note on our website at http://www.geo-slope.com/res/Slip%20Surface%20Exit%20Angles_April06.pdf


Paul Bryden
Sales & Marketing Manager
GEO-SLOPE International Ltd.
Calgary, Alberta, CANADA

RE: Geostudio/exit angle

Thank You Paul(Lori and John too) for your
replies and thorough answers to my question.

I´m now having more profound conversation´s with my
customer and they seem(at the moment) to accept/approve the statement´s You have given.

Yours Dennis the Menace

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