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Back analysis for FOS

Back analysis for FOS

Back analysis for FOS


A steep embankment (about 38deg and 23m high) made of sand + sandstone spalls is to be assessed for stability. EFCP and boring indicated initial medium dense sand+cobbles up to 5m and then dense with sandstone boulders. In theory material is cohesionless, but there seems to be apprent cohesion. (no Water table). Slope-W analysis with phi angle only (33 for MD sand and 39 deg for D sand+boulders) gives shallow failures with FOS near to one. Slope has not shown any distress for the past 20+ years. Sides have some vegetation. This suggests FOS sould be higher than one. The parameters derived from EFCP and boring + SPT are seem to be too low.

Is it reasonable
1. to have higher phi angle for sand+boulders, say 40 or 42
2. to have high phi for MD sand in the order of 34deg to compensate cobbles
2. to include some cohesion, say 5 ~ 10kPa for sany layers
   (there are some silts and clays in the sand)

Any ideas greatly appreciated.

RE: Back analysis for FOS

As for parameters, the 33 & 39 degree phi angles appear about right.  I would be careful using higher values because of the cobbles as the sand in the sandstone cobbles may not be any stronger than the weathered sand from the sandstone.  I agree with your last item of using a little cohesion to account for the silts and clays.  This will not significantly effect the deeper slides, but will greatly effect the shallow surface slides that the software is finding.

As for your overall analysis, you cannot do a "backin" analysis of a stable slope.  The only way to "backin" the soil parameters is to know the factor of safety which requires that you have a slide and therefore know that the FOS=1.0.  Since the slope is stable all you know is that the FOS>1.0.

RE: Back analysis for FOS

Thanks for the reply.
AS you said the only thing known is FOS>1.0.
If it has failed, parameters could be back calculated.
However, to estimate what margin FOS is higher needs some
experience I suppose. If it is say, 1.1, is it
possible the slope to show some distress, say
some creep movement within the potential slip circle?.
Industry standard for a stable slope requires FOS to be 1.3 to 1.5.
Can a circular slip be expected in sandy fill with
little cohesion?.   

RE: Back analysis for FOS

Yes you could estimate that the FOS is 1.1 and then do a back analysis, but why?  All you would be doing is estimating strengths based on an estimated FOS.

As for the question of whether a slope with a FOS of 1.1 would show creep movement, I would say no.  By definition, there is no movement when the FOS is greater than 1.0, however, while the overall slope may be at 1.0 there may be areas along the slope that are lower, i.e. 1.0 that could exibit movement.  I just would not expect that in an otherwise stable slope showing no signs of movement.

As for your comment about the industry standard for a stable slope requiring a FOS of 1.3 to 1.5, be careful.  I have had clients who were perfectly happy with a 1.2 and I have clients who would not live with less than 1.5.  It also depends on the conditions being analyized, i.e. is it a normal operating or an extream condition.

Lastly, I would expect a shallow surface slide in sands with little to no cohesion.  As the amount of cohesion increases, I would expect the depth of the slide plane to increase.  Run this through your computer model and compare the resulting critical failure surfaces.

Good luck.

RE: Back analysis for FOS

I don't know what software package you are using for the analysis, but you should be able to change the initiation and termination points, or put in some limitations so that the shallow failures will not be calculated.  The vegetation and its root system is probably providing additional strength for surficial stability, so these potential failure surfaces are not of interest.

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