Prediction of the Angle of Repose from Materials Failure Theory
Publication: Journal of Engineering Mechanics
Volume 147, Issue 10
Abstract
A fundamental materials failure theory is used to predict the angle of repose for granular solids. This long-existing classical problem is now solved. The solution only requires two properties: (1) the uniaxial compressive strength of the aggregate and (2) the effective grain size. There are no adjustable parameters. When subjected to the specified gravity field, the angle of repose between the free surface and the horizontal datum is uniquely determined. The results are compatible with observations existing in nature and with specific cases involving materials products in granular forms. The general failure theory is specialized to the limiting case of a cohesionless materials form in order to consummate the solution to the problem. The significance of this work for all isotropic materials failure problems is assessed in the final section.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
No data, models, or code were generated or used during this study.
References
Al-Hashemi, H. B., and O. B. Al-Amoudi. 2018. “A review on the angle of repose.” Powder Technol. 330 (May): 397–417. https://doi.org/10.1016/j.powtec.2018.02.003.
Christensen, R. M. 2013. The theory of materials failure. Oxford, UK: Oxford University Press.
Christensen, R. M. 2019. “The ductility number Nd provides a rigorous measure for the ductility of materials failure.” J. Appl. Mech. 86 (4): 041001. https://doi.org/10.1115/1.4042291.
Christensen, R. M., Z. Li, and H. Gao. 2018. “An evaluation of the failure modes transition and the Christensen ductile/brittle failure theory using molecular dynamics.” Proc. R. Soc. A 474 (2219): 20180361. https://doi.org/10.1098/rspa.2018.0361.
Christensen, R. M., Z. Li, and H. Gao. 2019. “An independent derivation and verification of the voids nucleation failure mechanism: Significance for materials failure.” Proc. R. Soc. A 475 (2222): 20180755. https://doi.org/10.1098/rspa.2018.0755.
Duran, J. 2000. Sands, powders, and grains: An introduction to the physics of granular materials. New York: Springer.
Dury, C. M., G. H. Ristow, J. I. Moss, and M. Nakagawa. 1998. “Boundary effects on the angle of repose in rotating cylinders.” Phys. Rev. E 57 (4): 4491–4497. https://doi.org/10.1103/PhysRevE.57.4491.
Glover, T. J. 2017. Desk reference. 4th ed. Anchorage, AK: Sequoia Publishing.
Kou, B., Y. Cao, J. Li, C. Xia, Z. Li, H. Dong, A. Zhang, I. Zhang, W. Kob, and Y. Wang. 2017. “Granular materials flow like complex fluids.” Nature 551 (7680): 360–363. https://doi.org/10.1038/nature24062.
Love, A. E. H. 1927. A treatise on the mathematical theory of elasticity. Cambridge, UK: Cambridge University Press.
Mohr, O. 1900. “Welche umstände bedingen die elastizitätsgrenz und den bruch eines materials.” Z. Ver. Dtsch. Ing. 44: 1524–1530.
Nelson, E. 1955. “Measurement of the repose angle of a tablet granulation.” J. Am. Pharm. Assoc. 44 (7): 435–437. https://doi.org/10.1002/jps.3030440714.
Pitanga, H. N., J. P. Gourc, and O. M. Vilar. 2009. “Interface shear strength of geosynthetics: Evaluation and analysis of inclined plane tests.” Geotext. Geomembr. 27 (6): 435–446. https://doi.org/10.1016/j.geotexmem.2009.05.003.
Powers, M. C. 1953. “A new roundness scale of sedimentary particles.” J. Sediment. Res. 23 (2): 117–119.
Schulze, D. 1996. “Measuring powder flowability: A comparison of test methods. Part II.” Powder Bulk Eng. 10: 17–28.
Senetakis, K., M. R. Coop, and M. C. Todisco. 2013. “The inter-particle coefficient of friction at the contacts of Leighton Buzzard sand quartz minerals.” Soil Found. 53 (5): 746–755. https://doi.org/10.1016/j.sandf.2013.08.012.
von Karman, T. V. 1912. “Festigkeitsversuche unter allseitigem Drunk.” In Vol. 118 of Metteilungen Forschungsarbeit Gebiet Ingenieurs, 27–68. Oxford, UK: Oxford University Press.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 147 • Issue 10 • October 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Mar 31, 2021
Accepted: May 4, 2021
Published online: Jul 27, 2021
Published in print: Oct 1, 2021
Discussion open until: Dec 27, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Homogeneous and Isotropic Materials Failure Theory: A Critical Appraisal, Journal of Applied Mechanics, 10.1115/1.4052798, 89, 1, (2021).
- Richard M. Christensen, The Three Controlling Modes of Failure in Homogeneous and Isotropic Materials With Proof Thereof Through Critical Plane Stress Conditions, Journal of Applied Mechanics, 10.1115/1.4052507, 89, 1, (2021).