You may also be interested in reading this article:

Name of Author: Roberts, A.W.

Company Affiliation: University of Newcastle

Title of Article: 100 Years of Janssen

Published in Journal: bulk solids handling

Year: 1995 Volume: 15 Number: 3 Page: 369

Type of Article: Original Article

Fields of Interest: Silos, Bins and Domes

Article published in 'The Best of ...' book: A/2000 Part IV (Silos, Hoppers, Bins & Domes - Parts I, II, III & IV)

I am sure somone will offer the original article.

Reinhard H. Wöhlbier ■

You can find the original 1895 Janssen article as PDF under

http://www.phy.duke.edu/~msperl/Janssen/

together with a recent translation.

Matthias Sperl ■

The subject of Janssen's work is of special interest to me. The point is that for many years, I carried out extensive theoretical research on static and dynamic wall pressures of granular materials in silos in view of the stochasticity of mechanical characteristics of these materials (the term dynamic means here that the wall pressures are exerted by a granular material moving in a silo during its discharge). To this end, I developed new deterministic and stochastic mathematical models of wall pressures of granular materials in silos based on the classical theory of elasticity. My works in this field were published in 1981-1991 in the Russian journals:

1.1. Granik V.T. "A Theory of Dynamic Wall Pressures of Bulk Materials in Silos." Structural Mechanics and Design of Structures, 1981, 5, 37-40. (in Russian)

1.2. Granik V.T. "Dynamic Wall Pressures of a Granular Medium Flow in a Silo." Structural Mechanics and Design of Structures, 1983, 4, 34-39. (in Russian)

1.3. Granik V.T. "A Stochastic Theory of Bulk Material Wall Pressures in a Silo Shell." Physico-Technical Problems of Mining. The Academy of Sciences of the USSR. The Siberian Division, 1984, 2, 35-42. (in Russian)

1.4. Granik V.T. "Dynamics of Granular Flow in a Silo Shell at the Variable Coefficient of Medium Wall Friction." Structural Mechanics and Design of Structures, 1985, 5, 39-43. (in Russian)

1.5. Granik V.T. "Dynamic Wall Pressures of a Granular Medium Flow in a Vertical Prismatic Shell." Proceedings of the Academy of Sciences of the Armenian SSR. Mechanics, 1986, XXXIX, 4, 48-59. (in Russian)

1.6. Granik V.T. "Statistical Dynamics of Granular Flows in Vertical Shells." Structural Mechanics and Design of Structures, 1986, 5, 43-47. (in Russian)

1.7. Granik V.T. "A Stochastic Variant of Granular Medium Mechanics." Applied Mechanics. The Academy of Sciences of the Ukrainian SSR, 1986, XXII, 3, 84-91. (in Russian)

1.8. Granik V.T., Gaevskaya G.A. "Determination of Internal Forces in a Cylindrical Silo Shell Exerted by Stochastic Pressures of a Granular Flow." Structural Mechanics and Design of Structures, 1987, 2, 51-55. (in Russian)

1.9. Granik V.T. "The Design-Basis Wall Loads for the Silo Shells Exerted by Stochastic Pressures of Granular Flows." Structural Mechanics and Design of Structures, 1991, 4, 78-84. (in Russian)

These studies have resulted in a series of theoretical formulae and supplementary graphs for the static and dynamic (both deterministic and stochastic) wall pressures of granular materials in silos which are easy to employ since they are almost as simple as the well-known Janssen equation. The theoretical results are corroborated by numerous experimental data and can be used in a more precise and reliable silo design.

It is also worth mentioning that my research on the wall pressures of granular materials in silos had initially been preceded by and was later going hand in hand with developing a new non-classical mechanics of granular media allowing for their discrete microstructure:

2.1. Granik V.T. "Microstructural Mechanics of Granular Media." Technical Report IM/MGU 78-241, 1978. Institute of Mechanics. Moscow State University, USSR, 73 pages. (in Russian)

2.2. Vladimir T. Granik. "Microstructural Mechanics of Granular Media. 1. The Principles of Theory." Report No. UCB/SEMM 92/02, March 1992. Department of Civil Engineering, University of California, Berkeley, California, USA, 18 pages.

2.3. Vladimir T. Granik and Mauro Ferrari. "Microstruc-tural Mechanics of Granular Media." Mechanics of Materials, 1993, 15, 301-322.

2.4. Vladimir T. Granik and Mauro Ferrari. "Multi-Scale Homogenization of Granular Media." ASME Composite Material Technology Symposium. Houston, USA. Eds. D. Hui, T.J. Kozik, O.O. Ochoa. 1993, PD-Vol. 53, 217-222.

Subsequently, in collaboration with my colleagues from UC Berkeley, USA, I have extended the microstructural mechanics of granular media to cover any deformable solids in view of their intrinsically discrete microstructure. The corresponding theory called Doublet Mechanics (DM) has been published, together with its various applications, in the monograph

3.1. Advances in Doublet Mechanics. Eds: M. Ferrari, V.T. Granik, A. Imam, J.C. Nadeau. Springer, 1997, 216 pages. Heidelberg, New York.

Note that in two simplest cases, DM involves no structural parameters and reduces to either the Cauchy non-couple classical theory of elasticity or the Cosserat couple elasticity model.

Being far more comprehensive and precise than the above elasticity theories, DM makes it possible to gain new insights into the mechanical behavior (and to obtain otherwise impossible solutions to a variety of mechanical problems) of materials with microstructure. An illustration of such a solution is given in the aforementioned publications 2.1-2.4 and 3.1 (pages 165-170) considering, in particular, the traditional Flamant problem of the internal stresses in a semi-infinite plate of isotropic material subjected to external pressure of a penetrating point force on the straight boundary.

Accordingly, DM can be used for dealing with a wide range of still unsolved problems of wall pressures of granular media in silos in view of these media's discrete microstructure.

I hope that the above information – should you consider it worth posting somehow – may attract attention of and be useful to some members of the worldwide powder & bulk solids handling & processing community.

In conclusion, I am pleased to tell you that I greatly appreciate the work you're doing. The importance of this work cannot be overestimated. I wish you the best and remain

Sincerely yours,

Vladimir T. Granik

Doctor of Technical Sciences and Professor of Structural Mechanics

Formerly at

The University of California, Berkeley, USA ■