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Drained vs Undrained

Drained vs Undrained

Drained vs Undrained

I'm reviewing a report on the stability of a railway embankment that is at least 100 years old.  The embankment is some 6m high, 7m wide at crest, with 1V:1.4H (~36degr.) sideslopes and is comprised of firm to stiff clay overlying weaker bedrock.  Some 0.6m of ballast is present on the top below the rails.  Permanent groundwater table is well below the embankment base. There are no known instability problems.

A recent slope analysis of the embankment used both drained and undrained approach. Drained to represent the long term conditions (c=o, fric=27degr.) and undrained (c=50kPa, fric=0) to apparently simulate loading due to trains. Obviously, for the drained case the Fs is less than 1 for shallow slip surfaces but just above unity for deeper slip surfaces. Undrained results provided higher Fs leading to a paradox where the embankment is more stable when loaded by trains.

My question is where does the cohesion of 50kPa sudenly comes from - isn't cohesion an inherent property of the material and its moisture content, rather than being related solely to the weight of the train? Furthermore, would not the ballast distribute the train load in such manner that in a depth of some 1.5-2m the stress increase would be insignificant and, as such, drained conditions would prevail?

Sorry if this is an obvious question....


RE: Drained vs Undrained


The cohesion value we use to describe soil strength is not an inherent property of the soil, but rather an artifact of the assumption that a curved strength envelope can be represented as a straight line.  The cohesion is literally the y-intercept of that "idealized" linear strength envelope.  The tangent of the friction angle is slope of that straight line.

The approach that the geotechnical consultant took appears to be standard practice for many parts of the U.S.  For loading conditions that are slow (with respect to the time that it would take for excess porewater pressures to drain from the embankment), we will use a "drained" type of analysis with a higher friction angle and lower cohesion (most often selecting zero cohesion).  This case is the embankment without the train.  For loading conditions that are so rapid that any excess pore pressures that would be present in the soils would not have a chance to drain, we will perform an undrained analysis and generally select strength parameters, cohesion and friction angle, from a strength test that is run rapidly without the ability of pore pressures to dissipate.  this is the case of the embankment with the train.

The reason why the results you have may seem to be contradictory may be that the clays in the embankment are unsaturated (have high suction values) and that choosing zero cohesion may be significantly underpredicting the actual strength for the longterm case.  One approach to handling the effect of suction is to select a cohesion that reflects the effect of the suction.  There are various ways to do this.

If you would like to have a more realistic estimate of the stability of the slope over the longterm, I would suggest that you get in contact with the geotechnical consultant that wrote the report and ask him/her to assess the potential that the clays in the embankment may be unsaturated and have suction values.

If the consultant is unable to make such an assessment, there are various suction experts that would be able to assist you.

On another note, the embankment has been in place for about 100 years and it hasn't shown signs of instability yet your report tells you that in the long run it is supposed to be less stable.  This should tell you that one or more parts of the puzzle are not yet in place.

The results of any slope stability analysis should reflect the actual conditions and performance of the embankment.

Good Luck

Glen Andersen
BBC&M Engineering, Inc.
Cleveland, Ohio

RE: Drained vs Undrained

Glenn provided an excellent discussion.  Let me add a few comments to supplement his.

The use of a φ = 27° and c = 0 was probably too severe, resulting in the apparent contradiction.  If the factor of safety was really near unity, then a fair number of slope failures would have manifested themselves because the soil's strength properties will vary spatially as well as over time.  

How much of the slope would have failed?  You could get an indication of the likely risk of failure using probabilistic methods to evaluate the risk of failure using the assumed φ = 27° and c = 0 drained strength parameters.

I suggest that you check out a paper titled Factor of Safety and Reliability in Geotechnical Engineering, by J. Michael Duncan, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 127 No 8, August 2001.  And be sure to read all the discussions - and Duncan's closure - of the paper.  This will give you a realistic - and usable - guide to selecting appropriate factors of safety, evaluating risk, and assessing the appropriateness of the parameters that were provided to you.

Please see FAQ731-376  by VPL for tips on how to make the best use of Eng-Tips Fora.

RE: Drained vs Undrained


Can you give us an update of where your project stands?

RE: Drained vs Undrained

We won't likely hear from BXB12 anytime soon; he hasn't logged on since signing up...

Please see FAQ731-376  by VPL for tips on how to make the best use of Eng-Tips Fora.

RE: Drained vs Undrained


Thank you for your valuable responses.  As for the project, there is not much new to report at this stage...

But to use this opportunity and broaden my horizons, Glen when switching from drained to undrained conditions would you carry out a stress distribution analysis within the unsaturated slope/embankment with respect to the imposed loading to outline an area where to change your parameters?

One would also think that the sleepers and the 0.6m (2 feet) of ballast would spread the load laterally and reduce stress increase in the underlying clay - or am I way out on this...  

Thanks in advance

RE: Drained vs Undrained


Perhaps the best way to handle the change in soil parameters (from the drained to the undrained case) is to change all of the parameters in the embankment at once and to allow the critical failure surface to be found wherever it wants to be.  If there are zones of weakness in the embankment, generally we can expect that the failure surface will pass through these.

In terms of stress distributions in an embankment, the elastic type stress distribution analysis that we normally use is based upon continuum mechanics.  When a failure plane occurs in an embankment, it represents a discontinuity and the stresses in its immediate vicinity will be different from those estimated using elastic types of analyses.  Soil parameters that are selected for a slope stability analysis should be chosen to reflect the "best rational estimate" of conditions that would bring the embankment closest to failure.  These are generally not known before the analysis, so trial and error procedures are used.

The stress "spreading" that you are describing does infact occur.  If we were to formulate the slope stability problem using a continuum type model with soil parameters that can vary with position in the soil mass and as a function of the stress path (change in stresses) and strain path, we would get closer to the situation that you are alluding to.  Such an approach is generally overkill.  Only in circumstances with factors of safety that are low and where small changes in factor of safety can have a significant impact on the project economics would a continuum-based formulation possibly be justified.  Such appears not to be the case for your problem.  Am I correct?

For common slope stability analyses, we use slope stability programs that search for critical surfaces (assumed failure planes) in the soil mass based on soil properties that are independent of how the "failure state" is achieved.  Through the judicious selection of the soil strength parameters, we can generally put ourselves in the ball park of reasonable solutions.  My comments in my earlier response to this thread were intended to imply that the strength parameters selected previously could be refined to get results that more closely mimic your performance observations.

These slope stability programs do not give an exact solution, so the geotechnical engineer needs to perform a parametric study and use actual embankment performance information before concluding what a factor of safety would be.

I hope this helps.


RE: Drained vs Undrained

Thanks for your valuable response. It is always a pleasure to walk away from a discussion with increased knowledge.  From the project economics sense, and as far as I am aware from the risk perspective, you are correct to assume that a more sophisticated stress analysis is not required.

All the best in your work,

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