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(Finite) statistical size effects on compressive strength

Weiss, Jérôme and Girard, Luca and Gimbert, Florent and Amitrano, David and Vandembroucq, Damien (2014) (Finite) statistical size effects on compressive strength. Proceedings of the National Academy of Sciences of the United States of America, 111 (17). pp. 6231-6236. ISSN 0027-8424. PMCID PMC4035992. doi:10.1073/pnas.1403500111.

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The larger structures are, the lower their mechanical strength. Already discussed by Leonardo da Vinci and Edmé Mariotte several centuries ago, size effects on strength remain of crucial importance in modern engineering for the elaboration of safety regulations in structural design or the extrapolation of laboratory results to geophysical field scales. Under tensile loading, statistical size effects are traditionally modeled with a weakest-link approach. One of its prominent results is a prediction of vanishing strength at large scales that can be quantified in the framework of extreme value statistics. Despite a frequent use outside its range of validity, this approach remains the dominant tool in the field of statistical size effects. Here we focus on compressive failure, which concerns a wide range of geophysical and geotechnical situations. We show on historical and recent experimental data that weakest-link predictions are not obeyed. In particular, the mechanical strength saturates at a nonzero value toward large scales. Accounting explicitly for the elastic interactions between defects during the damage process, we build a formal analogy of compressive failure with the depinning transition of an elastic manifold. This critical transition interpretation naturally entails finite-size scaling laws for the mean strength and its associated variability. Theoretical predictions are in remarkable agreement with measurements reported for various materials such as rocks, ice, coal, or concrete. This formalism, which can also be extended to the flowing instability of granular media under multiaxial compression, has important practical consequences for future design rules.

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Gimbert, Florent0000-0001-7350-3563
Additional Information:© 2014 National Academy of Sciences. Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved March 19, 2014 (received for review February 27, 2014) S. Zapperi, D. Bonamy, and an anonymous reviewer are acknowledged for interesting discussions and suggestions. All numerical simulations were performed at Service Commun de Calcul Intensif CIMENT Grenoble. J.W. and D.V. acknowledge the hospitality of the Aspen Center for Physics, which is supported by National Science Foundation Grant PHY-1066293, as the seminal ideas of this work came up during their stay at the Center. Author contributions: J.W., D.A., and D.V. designed research; J.W., L.G., F.G., D.A., and D.V. performed research; J.W., L.G., and F.G. analyzed data; and J.W. and D.V. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. This article contains supporting information online at
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Issue or Number:17
PubMed Central ID:PMC4035992
Record Number:CaltechAUTHORS:20140604-110901117
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Official Citation:Jérôme Weiss, Lucas Girard, Florent Gimbert, David Amitrano, and Damien Vandembroucq (Finite) statistical size effects on compressive strength PNAS 2014 111 (17) 6231-6236; published ahead of print April 14, 2014, doi:10.1073/pnas.1403500111
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:46074
Deposited By: Ruth Sustaita
Deposited On:04 Jun 2014 21:57
Last Modified:10 Nov 2021 17:20

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