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Rock Mechanics Letters

Open Access Research Article

The Conundrum of the Crack Initiation Stress of Rock Type Material – II. The Second Derivative Method

by Dimitrios Papadomarkakis 1,*
1
Laboratory of Tunneling, School of Mining and Metallurgical Engineering, National Technical University of Athens, Zografou Campus, Athens, Greece
*
Author to whom correspondence should be addressed.
RML  2025 2(3):22; https://doi.org/10.70425/rml.202503.22
Received: 18 July 2025 / Accepted: 7 August 2025 / Published Online: 9 August 2025
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Abstract

In part II of this study, a second method for the prediction of the crack initiation stress was sug-gested. The new technique is based on an elementary mathematical calculus theory. Particularly, the one that supports that the points where the second derivative of a function is equal to zero can be considered as possible inflection points of the function. The proposed Second Derivative meth-od fulfilled all the necessary criteria, that were mentioned in part I, so that it can further advance the research field. The method was applied to ten rock specimens, specifically eight marbles and two vesicular basalts, that were subjected to uniaxial compressive tests. The predicted crack initi-ation stresses from the new method were compared with those obtained from the established techniques of the existing literature. The new method had very close results with all other utilized methods for the marbles, thus meaning that the proposed Second Derivative technique can accu-rately and consistently determine the onset of stable crack growth for that rock type. On the con-trary, the new method displayed a poor correlation with the other techniques for the two basalts, hence indicating that further tests need to be conducted in the future for that rock type.

Keywords: Crack initiation; Crack damage; Uniaxial compressive tests; Brittle fracture;
Copyright: © 2025 by Papadomarkakis. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) (Creative Commons Attribution 4.0 International License). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
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ACS Style
Papadomarkakis, D. The Conundrum of the Crack Initiation Stress of Rock Type Material – II. The Second Derivative Method. Rock Mechanics Letters, 2025, 2, 22. doi:10.70425/rml.202503.22
AMA Style
Papadomarkakis D. The Conundrum of the Crack Initiation Stress of Rock Type Material – II. The Second Derivative Method. Rock Mechanics Letters; 2025, 2(3):22. doi:10.70425/rml.202503.22
Chicago/Turabian Style
Papadomarkakis, Dimitrios 2025. "The Conundrum of the Crack Initiation Stress of Rock Type Material – II. The Second Derivative Method" Rock Mechanics Letters 2, no.3:22. doi:10.70425/rml.202503.22
APA Style
Papadomarkakis, D. (2025). The Conundrum of the Crack Initiation Stress of Rock Type Material – II. The Second Derivative Method. Rock Mechanics Letters, 2(3), 22. doi:10.70425/rml.202503.22

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