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Angle of Repose versus internal friction angle

Angle of Repose versus internal friction angle

I am in the process of designing storage buildings for road salt. The hiring firm is a DOT and has set the properties of the salt as follows:
density = 100pcf
internal fricition angle = 34 degrees
angle of repose = 34 degrees

AS I am sure you have already concluded, using the same angle of repose as the internal friction angle in Rankine's equation yeilds a very high Ka. A reduction to and angle of repose to just 33.4 degrees yields a Ka almost 20% smaller.

I have (2) questions:
1. Is it possible for the angle of repose to match the internal friction angle of a non-compacted granular material?
2. Are there any references out there that either correlate angle of repose and internal angle of friction that would carry enough clout to challenge a DOT? If not, are there any industry standards out there that carry enough clout to challenge a DOT?

Thanks for any help you can provide.

RE: Angle of Repose versus internal friction angle

Why not measure them both using a couple of samples of the material?

RE: Angle of Repose versus internal friction angle

Angle of repose is generally very close to angle of internal friction.  For soft angular particles (rock salt perhaps), repose could be a few degrees higher than what you would measure for internal friction in a triax test or direct shear test under 500 lb/ft^2 normal stress, due to particle crushing.

Why do you want to fight the DOT on this, unless they are doing something obviously wrong?  You're taking on liability for using different material properties without having testing to back you up, for no additional profit?  If you think you could save them a pile of money, then propose a testing program.

RE: Angle of Repose versus internal friction angle

Not that I have experience with road salt individual physical properties for design, but I know in water softeners it can develop a crusty situation and hang up, which probably is good from a lateral pressure standpoint.

Since it is likely that there are storage buildings for salt in your area also, I'd visit a few sites and ask about experiences with salt storage.  For one, those guys unloading the last parts of the pile are likely to put imp[act pressure against the walls with the buckets of the equipment.

A community I was with decided to go for some concrete blocks as the base parts of the wall due to this possibility, but with treated timber walls above.  Most of the salt storage buildings I have seen are glorified pole buildings with creosote treated poles set in the ground. Also our DNR requires the salt to be on a concrete slab with a curb all the way around.

RE: Angle of Repose versus internal friction angle

The schedule attached to this project precludes the ability to test the material.  As i am sure you can imagine, a 20%+ reduction in lateral force per member greatly reduces all of the material required to construct these buildings and does greatly increase profit.  I am not looking to take on any liability by not using the material properties they provided, I am looking for reasonable resources that realte repose to internal friction angle so that they will approve a different angle to be used.  If none exisits then I will move on to some of the other options to reduce material use.


RE: Angle of Repose versus internal friction angle

Where I live (Zaragoza, Spain) these buildings are made of reinforced concrete; walls are 1 ft thick, mat maybe more, and surfaces are protected with about 1 inch of protective material against the effects of abrasion and corrossion. Through repeated application of protective layers they are expected to reach normal design life, say 50 to 75 years. It must be noted that the region is not much wet (220 mm of rain a year). Since the material is normally dumped from trucks and moved using front-loaders the height of salt is not much, and active pressure on the walls is scarcely a concern, or at least not a worrying one; apex of the salt mounds maybe are some 5 meters or 6 from the mat in some cases and may be 3 to 5 more times.  

RE: Angle of Repose versus internal friction angle

For a coarse material, not well graded, dry material, the angle of repose nearly matches the angle of internal friction.  A couple books that I know of may actually verify the DOT, which is not what you want: Design of Tubular Structures by Troitsky (a section on bins); Design of Bins (or something like this) by Gaylord & Gaylord.

RE: Angle of Repose versus internal friction angle

Lucky Luciano - What is the geometry of the wall you are analyzing, like this?

           *   <-Slope@repose
 | <- Wall

This is the only way I can think of right away for the active pressure to be sensitive to both repose AND phi' as separate variables.

It's not this:

 | *    *    *    *    *
 |      Level or slope flatter than repose
 | <- Wall


RE: Angle of Repose versus internal friction angle

The angle of repose, as I was taught and understand it, refers to the maximum stable slope of a non-compacted granular fill that, if exceeded, will cause the material to destabilize, and the slope will seek it's natural angle of repose where it is stable.

This can be illustrated by watching a dump truck dump a load of granular material. The slope of the resulting stable pile is the "Angle of Repose" for that specific granular material.

This angle is very important in determining the maximum slope of excavated material stored near the excavation as well as the slope of the sides of the excavation itself for safety reasons, and determining if excavation supports are required by design in absence of specific codes or regulations.

RE: Angle of Repose versus internal friction angle

Also, in addition to my last posting, I would like to ad that the internal friction angle, Phi, for compacted granular material is derived from a laboratory confined shear test of the material in question, and could possibly be equal to the Angle of Repose, but the two values are not one in the same, as I'm sure you know. I have never encountered a situation where the angle of repose is required in an equation by definition of the variables, but I have used it for calculation of surcharge loads of stored, unconfined granular material.

The number you gave for Phi is very close to the value I, and many of my associated assume for granular materials (30 - 33) in the absence of a geotechnical report. As both a structural and geotechnical engineer with laboratory experience, I am often required to generate my own geotechnical information by performing all required geotechnical manual calculations, which I prefer to do using a program called Mathcad, so I can see the effect my assumed value of Phi has on other related variables being calculated to be sure they make sense and are reasonable. That way, I don't have to keep redoing calculations in a manual iterative process, which is too time consuming for most project budgets.

My approach allows me to change variables in a function or equation and see the effect it has on subsequent operations as I make the change, as well as the final result in real time, automatically. I get a better overall perspective on the calculation than I do on paper.

RE: Angle of Repose versus internal friction angle

I have a book titled "Retaining Walls" by M & A Reimbert published by Trans Tech. In it the authors use the angle of repose over the internal friction angle. There are many experiments to make their case. There are in direct conflict with Rankine and Coulomb throughout the book.

RE: Angle of Repose versus internal friction angle

I've never designed a project using salt as a backfill but just thinking of this as a granular material, that won't crush into smaller particles, then it seems pretty reasonable that the internal friction angle about equals the angle of repose for this loose material.  If this were a compacted salt pile then it could be argued that there would be a peak shear strength, associated with dilation during shear, greater than the angle of repose (loose fill dumped in a pile).

RE: Angle of Repose versus internal friction angle

cap4000 - I only have volume 2 of that publication, but throughout it they keep saying alpha is approximately equal to phi.  Are you saying that their experiments are precise enough to distinguish between the two?  If they make that claim, I don't buy it.  The values are too close together and the mathematical models are too crude for that.  Besides, the models they use all involve internal friction, and only make sense for phi.

In parts of volume 2 discussing backfills at angle of repose, they do use alpha quite a bit, in order to avoid having to include both alpha and phi (which they repeatedly say are approximately equal).

RE: Angle of Repose versus internal friction angle


I only have the 1974 Volume 1. On page 148 "Charts for Determining Thrust" it uses the angle of repose. I have over 15 retaining wall books and Reimbert is the only one that uses angle of repose. Nonetheless its a great book.   

RE: Angle of Repose versus internal friction angle

In 2008, I designed a "Salt Storage Shed" for the City of Ellsworth, ME. I have to agree with dgillette when he/she points out that, if you have been supplied with the values for Phi and the Angle of Repose, and you use something different, then you are assuming the liability for that information. I didn't have the luxury of being supplied with anything (not even boring logs) for my project.

The City wanted the foundation walls to extend 8'-0" above finish grade, and act as retaining walls as well as the framed building foundation. As a result, I designed the foundation as a two sided retaining wall, which was required to retain both soil from the exterior grade, and the salt pile (actually a sand / salt mix) on the inside.

As I recall, the the internal friction angle, Phi, was obviously different for the outside retained soil, the sand / salt mixture, and the in situ soil at the base of the retaining wall / foundation. Phi for the soil at the base of the retaining wall footing was used in determining the summation of resistance against sliding, and was unrelated to either retained material in my case. Phi for the outside retained material was also different from the sand / salt mixture retained from the inside of the building. In my case, the angle of repose, which is not necessarily the same as the angle "Alpha", which denotes the slope of material being retained (and is illustrated by the "Slope@Repose" diagram above by dgillette, only it isn't necessarily equal to the Angle of Repose in most cases), was never used, and neither was Alpha due to the construction and final conditions. Since all the soil I was dealing with, except the sand / salt material, was permanently compacted and level, neither Alpha or the Angle of Repose was ever used on the wall / foundation I designed to calculate lateral force coefficients to determine the design moments on the walls, footings, or the overturning moments and sliding force / resistance. But Phi certainly was.

In the absence of ground water in my design for the below grade and outside compacted retained material, I elected to assume a value of PHI which gave me a value of ka=0.33, which past experience has shown to be conservative for many designs in my area of the country, and is confirmed by both peer review and tabulated values in a soils text I use frequently, as well as by my associates.

With all that said, if you have been provided with values for Phi and other required design values by "others", then by all means, use them without question, and you will not assume any liability for no apparent reason, as dgillette points out. That is probably the best advice if it applies to your situation.

RE: Angle of Repose versus internal friction angle

I disagree with geostability's last paragraph.  Consider the soil values provided in the geotech report.  Determine if you agree with them.  Were they based on testing or just conservatively pulled out of the air (which happens often)?  What values do you believe to be correct based on the information you were provided or upon new information you need to obtain.  Ultimately, you will be responsible for the design (and the soil values).  You can't say you aren't responsible just because you blindly used someone else's soil values.  You could wind up in court sitting across from the geotech report's author, pointing fingers at each other.

RE: Angle of Repose versus internal friction angle

Hi PEinc.  My point was that Luciano should not take on liability by trying to bump up phi or reduce alpha (i.e., angle of repose) of the salt (to produce smaller loads, thereby saving the client money on the structure) without DS or tx, UNLESS there is an identifiable error in the information provided.  If they had told him 20 or 44 degrees, that could be a red flag.  If they had told him 30 or 35 instead of 34, that would be entirely believable.  He would be most unwise to argue for better salt properties than the DOT reported without actual data to back him up.  There may well be a geotech report, but there was no salt testing or budget for it, so is it unreasonable for him to use the values the DOT reported (which constitute the loadings on the wall)?

Geostability - As used in the Reimbert book brought up by CAP4000, alpha is the angle of repose.  The fill slope is designated as alpha', which seems like odd notation to use, but that's how they did it.  (This is not the alpha in tan(alpha= sin(phi) from CSSM.)

RE: Angle of Repose versus internal friction angle


Can you verify that the Reimbert book indicates a much lower Ka than Rankine. He does not use salt but he uses wheat, rice, river sand and plastic granules to dispute both Rankine and Coulomb.

RE: Angle of Repose versus internal friction angle

I only have v. II, "Study of Passive Resistance in Foundation Structures."

To tell you the truth, I bought it in 1986 or earlier from Publishers Central Bureau or one of those places that sell excess stock of books.  I have barely looked at it, in part because I have not done much work on retaining walls (except recently, with seismic loads), and when I have, I've used Coulomb, and just once, Sokolovski for passive load in an unusual case.

Won't have time to study up on it any time in the near future, because of the work they pay me to do and a research report I agreed to review.


RE: Angle of Repose versus internal friction angle

Clarification:  Coulomb and Sokolovski were for statically loaded walls only.  Didn't intend to imply I was using them for seismically loaded walls.  Those are a whole 'nother can of worms.

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