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Q: granular materia; ( Answered 5 out of 5 stars,   0 Comments )
Subject: granular materia;
Category: Science > Physics
Asked by: laza-ga
List Price: $20.00
Posted: 29 Jan 2003 03:22 PST
Expires: 28 Feb 2003 03:22 PST
Question ID: 149887
I want to find out the relationship and explanation of arch formations
in granular materials or silo.
1.relationship between arch height and angle of repose of silos
2.relationship between arch size and silo openings
3.relationship bewtween number of arches and silo angle of repose,
height etc.
simple formulas are also welcome

Clarification of Question by laza-ga on 30 Jan 2003 03:52 PST
I want to find out the relationship and explanation of arch formations 
in granular materials (grains, sands etc) and especially in silos . 
1.relationship between arch height and angle of repose of silos 
2.relationship between arch size and silo openings 
3.relationship bewtween number of arches and silo angle of repose, 
height etc. 
simple formulas are also welcome and especially rules of thumb.

Request for Question Clarification by hedgie-ga on 30 Jan 2003 22:30 PST
      your an interesting question can be understood two ways:
  1) solve this problem of the physics of the granular materials
  2) find out what has been published on the web about this problem

 1) can be done, but would exceed the $20 effort and result, I guess,
    in a computer model, rather then just a formula.
 2) can be done, but may not provide a complete explanation and description.

    Which one are you after?

Clarification of Question by laza-ga on 31 Jan 2003 00:45 PST
i am not interested in a computer model,as this will not help me
understand the arch formation, but i am interested in finding a
relation of proportions, simple rules of thumb or equations. i have
found net publications which do not clarify the arche proportions so i
am not interested in net publications unless they directly answer my
question. As far as effort and fee, if the results satisfy my answer i
would be willing to raise the fee, again provided the answer is what i
am looking for.

Request for Question Clarification by hedgie-ga on 31 Jan 2003 19:57 PST
Thanks for the clarification. 
Few more questions, please:

  In your  point   3. relationship bewtween number of arches ..

    You mean 'how often arches happen' (for given material etc)
    not some multi-arch geometry, right?

    Would it be enough to find the source of information 
     So that you would have to get the book or article and study it
      to get the desired understanding?

      Are your familiar with Jenike method?

Clarification of Question by laza-ga on 01 Feb 2003 02:33 PST
1.i am interested in the foemation of arches in respect to their
geometry i.i. height span geometry that this collapses etc. i.e. the
limits of arch formation
2.If a multi arch geometry is discovered then great, but it is not a
3.ideally a rule of thumb or a simple eqation is needed, if this is
found within an article, please notify me!
4.yes i am know the jenike method although seferal articles seem very
unclear and do not explain the full method but refer or have extracts
to it, if the jenike method answers the proportions question, then it
could be what i am looking for.
thanks for the help!
Subject: Re: granular materia;
Answered By: hedgie-ga on 01 Feb 2003 04:24 PST
Rated:5 out of 5 stars
OK laza
          I have found some 'rules of thumb' describing  when
 jamming happens, i.e. when arcs  form. I will include
  some additional information, both to provide  terminology
  for eventual further study or questions and as search terms
  for additional web searches.

  This - Rheology of granular materials - is a vast topic which has
both scientific (physics-based) and engineering aspects (typical in

  I will limit the references to the physics aspect of it, since they
 use complex  equations and simulations, but will mentions few.
 The reason for this is that  you mentioned 'explanation' as one of
the goals.
 The stress contours which are shown in some of these physics studies
 eventualy determine shapes of the arcs. Pictures may give you some
 for what is happening inside of the silo and also what is involved in
 solving that kind of the equations (by FE method). You do not have to
 make the computer runs yourself.

1) First a paper on a model system (very simplified system) which
 to some very simple rules:

 We study experimentally the jamming phenomenon of granular
 flow of monodisperse disks of D = 5  mm diameter
  in a two-dimensional hopper with opening R.
  The jamming probability J(d) is measured where d[equivalent]R/D.
   We found that J(d) decreases from 1 to zero when d increases from 2
to 5. From observing the disk configurations of the arch in the
jamming events, the jamming probability can be explained
quantitatively by treating the arch as the trajectory of a restricted
random walker.
 2000 The American Physical Society

   The tone of this article is a bit overdone.
 The work is not that pioneering, other stidies were done,
 nor unique but two things are of interest here:
a) a rule:
" No jams occurred when the opening was five times larger than the
disk diameter, but jams invariably occurred when the opening was twice
the disk diameter .."
b) the concept of the  Jam probability J(d) . 
  I think that what you mean by 'Number of arches' -is 'arches which
happen under a given regime per month' or something like that. It was
not quite clear from the question 3 nor from your explanation.
 It is ulikely that there will be some arc profile with multiple
minima, so I assume that you are after 'Jam probability' which is the
same as
'average frequency of the arc formation'  OK? 

 The paper itself, paper in  Phys. Rev. Lett. 85, 5659 
is available on-line but at a cost. That's not unusual in engineering
applications and that (business aspect) may explain why Jenike method
is not  described on line. Jenike's company is giving courses on it,
as well solving the practical cases as consultants.(I can give the
link to their site, as well as references to books which explain the
method, an ASTM standard costs $35
and describe instruments used to characterise the materials). 

 Jenike's method  calculates the J - the probability of arc formation
for a given hopper or silo and material  It does not
calculates the shape of the arc. That can only be calculated by the FE
method - using computer - and we will not go into that.

2) This web article may be interesting (?)
 It has a diagram on the stress conditions and references to more
technical papers.

3) This has experimental determination of the arc shape
for different materials - aand description of  instrument.
(We do not consider irregual shape 'multi-arcs' (see above) right?

4) This is fairly technical paper
You may skip the equations, at look at Fig.9, 14, 15  which is giving
the stress countours and mobility of grains profiles. These will
shape of arcs. Also eq. 1 on page 56 may be quite useful. It
determines flow rate, which becomes zero when arc is formed.  Rule is
that this happen when
 D approaches k *d.  The values of k and definitinxs of d and D are

Finaly, the rules of thumb I promised:

a) flow rate (and so arc formation) is independent of the H 
provided H> 2.5 * W 
(W= width of the cylinfer, D = aperture size  H= head in the hopper)
and W> 2.5 * D  and W > D+30*d

d is the grain size. 
These rules are hidden on page 4405 in the intro of the above paper.
 Please do remember that there are many other parameters, such as
conditioning,.. which modify the real situation, as described e.g.
  conditioning of material
        Rules of thumb are often good only for specific martials and
 for which hey were developed.

5) This paper also is quite complex, but Figures provide some insights

 6) Here is a paper which describes the material properties
 These determine 'angle of repose' and flowability. There are diagrams
to determine the some such properties and flowability from that angle.

7)  This model (described in reference 2, in Journal Nature) is
perhaps the
     best mix of theory and simplicity for your application:
 Simple model --Scalar Arching Model [5]
  In a certain (quasi linear) limit, the model is completely soluble,
and has allowed us to obtain a remarkable fit of the experimental data
with only one free parameter [2].

   I hope I have provided useful information and would appreciate some
feedback, either as rating or as request for clarification. In a case
like this, when there is a lot of info available, it is not always
to guess from a short question what is useful and what not.


Clarification of Answer by hedgie-ga on 03 Feb 2003 04:23 PST
In the last reference, #7 The URL of the paper got lost.
The paper is available on line, for free. Just click on
a format, ps or pdf you want.

It may look complex, but provides an explanation of
what is going on inside hopper. Arches are constantly
forming and collapsing in the bulk of the material.

Most of them transfer the weight of the grains to the wall,
sometimes they stop the flow.
laza-ga rated this answer:5 out of 5 stars and gave an additional tip of: $5.00
thumbs up! the last url was what i was looking for, the second message
containing url worked, so it was good that you double checked the

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