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Rock Mechanics Letters

Open Access Research Article

The Conundrum of the Crack Initiation Stress of Rock Type Material – I. The Trapezoid Rule 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):20; https://doi.org/10.70425/rml.202503.20
Received: 17 July 2025 / Accepted: 28 July 2025 / Published Online: 3 August 2025
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Abstract

In part I of this study, the great practical importance of the onset of stable crack growth was out-lined, since several researchers have supported that it can serve as a more realistic estimation of the in-situ spalling strength of the rock mass, in comparison with the more frequently used uniaxi-al compressive strength. Moreover, a short review was also provided regarding the empirical techniques that have been proposed in the last six decades for the prediction of the crack initiation stress. The main criticism of each method was also mentioned. Subsequently, a new method was proposed, based on the Trapezoid Rule, an elementary calculus approximation technique. The lat-ter technique possesses a strong and robust physical explanation, easy application, and complete objectiveness. The Trapezoid Rule method was applied to ten rock specimens, eight marbles and two vesicular basalts, that were subjected to uniaxial compressive tests. The results of the newly suggested method were compared to those obtained using the established methods of the existing literature. Ultimately, it displayed exceptionally close results with all other methods for the ten specimens, thus indicating that it can accurately and consistently predict the crack initiation stress for the two rock types.

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 – I. The Trapezoid Rule Method. Rock Mechanics Letters, 2025, 2, 20. doi:10.70425/rml.202503.20
AMA Style
Papadomarkakis D. The Conundrum of the Crack Initiation Stress of Rock Type Material – I. The Trapezoid Rule Method. Rock Mechanics Letters; 2025, 2(3):20. doi:10.70425/rml.202503.20
Chicago/Turabian Style
Papadomarkakis, Dimitrios 2025. "The Conundrum of the Crack Initiation Stress of Rock Type Material – I. The Trapezoid Rule Method" Rock Mechanics Letters 2, no.3:20. doi:10.70425/rml.202503.20
APA Style
Papadomarkakis, D. (2025). The Conundrum of the Crack Initiation Stress of Rock Type Material – I. The Trapezoid Rule Method. Rock Mechanics Letters, 2(3), 20. doi:10.70425/rml.202503.20

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