Vertical pressure under conical stockpile 4

[sdz]

Does anyone know how to calculate the vertical pressure under a conical stockpile?
I believe it should be somewhere between the average; density * 1/3 height; and the "hydrostatic" value; density * height.

 

[PXC]

I have had equations for conical and strip loads in the past but I can not find them now. Recently, I have been creating an FEA solid model to get the pressure, and simply using linear elastic elements rather than soil elements. I am a bit suspicious of this approach as I have never had the time to research it fully. Nevertheless, it gives pressures that look right, and can be used for all those cases where there are no standard solutions such as a semi conical stockpile, and even pressures on buried structures below the stockpile.

I ran a simple conical model and it gave the maximum internal pressure of k x max height x specific weight where k = 0.67 for a slope of 35°, and k = 0.58 for a slope of 45°.

 

[jhardy1]

Clause 6.2.3 of AS 3774 “Loads on Bulk Solids Containers” gives the following initial vertical pressures for a “Squat” container. Pressures under a simple conical pile should be similar:

The MEAN vertical pressure on a horizontal plane is given by:

Pvi = gamma * z (kPa)

Where gamma is the unit weight of the bulk material
(NOTE: Unit WEIGHT in kN/m3 NOT bulk DENSITY in kg/m3!!)
And z is measured vertically down from the centroid of the cone (i.e. use H/3 where H is the height of the cone)

The variation of vertical pressure distribution across the base is given by:

Pvix = 1.25 * Pvi * (1 – 1.6 * (x / Dc) ^ 2)) (kPa)

Where x is radial coordinate (metres) and Dc is the container diameter (metres) (i.e. use base diameter of the cone)

Therefore, the maximum pressure at the centre of the base of the pile (x = 0)is:

Pvix max = 1.25 * (gamma * H / 3)
= 0.417 * gamma * H (kPa)

And the minimum effective vertical pressure at the toe of the pile (x = Dc / 2) is:

Pvix min = 1.25 * (gamma * H / 3) * (1 – 1.6 * 0.5 ^ 2)
= 0.25 * gamma * H (kPa)

Vertical pressure variation is parabolic across the radius.

Hope this helps!

 

[BigH]

Get a copy of Polous and Davis Book: Elastic Solutions for Soils and Rocks (or something like that). It has solutions for vertical, horizontal and shear distributions under just about any shape you want - not just at the surface but with depth as well for purposes of settlement estimations, etc.

 

[sdz]

Thanks for your help, guys. From other reading I have been doing I think somewhere about 0.67 * unit weight * height will be appropriate for a stockpile at roughly angle of repose.
I am aware of AS3774 but think it might not be appropriate in this situation.
I will try to find "Elastic Solutions for Soil and Rock Mechanics", by H. G. Poulos, E. H. Davis, although Amazon lists it as being out of print.
I have also read that there can be a pressure dip at the center with resulting rise of pressure at some radial distance. Under a stockpile pressures can vary as material is drawn off by reclaim from a tunnel under the stockpile.

 

[BigH]

Let me know if you have a problem at library or university library - bohica@indiatimes.com

 

[Focht3]

There is a paperback version of the book that's out now; I'm not sure where you can buy it, though. My copy came from one of the authors -



Please see FAQ731-376 for great suggestions on how to make the best use of Eng-Tips Fora.

 

[aggman]

I have a question in regards to this post as I have often struggled with these loads and here is my reasoning. Correct me if I am wrong, but the H. G. Poulos, E. H. Davis book has a chart in it, but it only gives you a reduction if you are some distance below the base of the pile. For the typical reclaim bunker, reclaim tunnel, the pile actually would encase the structure. In this case you would not be some distance below the base of the pile. If this is the case, do you still see a reduction or not? The structure is not in some sort of dug out tunnel either, so I don't think that the AASHTO specs for buried conduits really applies either. But on the other hand it seems that their should be some sort of a reduction for the rock friction. I have designed 5 or 6 of these types of structures, and have always used the pressure as force times height times density, which I felt was conservative, if not very conservative. I would just like to get some opinions in regards to this, as I have struggled with this many times before. I just always felt that I could not dig up enough information to prove to myself that the loads are reduced, although logically you would think so.

Thanks for your input...

 

[BigH]

Aggman - my first attempt would be to use the base of the pile as the datum. Poulos and Davis gives you charts for vertical (horizontal and shear) stresses beneath the pile. Now if you have a "void", using the concept of "add and subtract" in elastic half space, you would determine the "negative stresses" of the void at the pile density, then subtract the effects of this at each of the points within your half-space. It can be time consuming, for sure. You do this, say for embankments - use a "conical" strip, calculate the pressure, then subtract off a conical strip corresponding to the "width" of the embankment.

 

[sdz]

I have received some advice from Dr W McBride of Newcastle Uni, Australia. His advice is that measured pressures under the center of a conical stockpile can be 70% of hydrostatic at the centre but this pressure may apply over a distance up to 30% of stockpile radius and be hydrostatic outside that. This is an envelope of the varying pressures that can occur during the construction, reclaim, and refilling of the stockpile.

Bear in mind that this is a preliminary result and further research might modify the result.

What can be said is that a stockpile is definately not a static, isotropic, linear elastic structure.