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Bulletin of Engineering Geology and the Environment

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01-01-2024 | Original Paper

The application of small sample theory and confidence interval method to determine the representative mean Leeb rebound hardness value

Authors: Saleh Ghadernejad, Kamran Esmaeili

Published in: Bulletin of Engineering Geology and the Environment | Issue 1/2024

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Abstract

The Leeb rebound hardness (LRH) test is a fast, non-destructive, and portable technique widely used to assess rock hardness in the field of rock engineering. However, no universally approved standard or testing method for measuring the representative mean Leeb rebound hardness value (HLD) exists. Hence, this research aimed to propose a method for measuring the representative mean HLD value and assess the effects of ambient temperature and geochemistry on the mean HLD value. The literature review revealed that regardless of the selected number of LRH measurements, the existing testing approaches could be classified as single impact, repeated impact, or hybrid dynamic hardness methods. The results of an extensive laboratory testing program on 16 different rock samples showed that only the single-impact method could result in a representative mean HLD value. Afterward, an integrated statistical technique called small sample theory and associated confidence interval was used to address the appropriate number of LRH measurements leading to a representative mean HLD value. Statistical analyses showed that it is impossible to determine a unique predefined number of LRH measurements leading to a representative mean HLD value in general. Instead, one could consider an error level and a confidence interval level and must perform the test until the small sample theory’s conditions are satisfied. Furthermore, while it was observed that the ambient temperature has no clear effect on the representative mean HLD value, the geochemistry analysis demonstrated that certain geochemical elements could control the mean and variation of the measured HLD values.

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Title: The application of small sample theory and confidence interval method to determine the representative mean Leeb rebound hardness value
Authors: Saleh Ghadernejad
Kamran Esmaeili
Publication date: 01-01-2024
Publisher: Springer Berlin Heidelberg
Published in: Bulletin of Engineering Geology and the Environment / Issue 1/2024
Print ISSN: 1435-9529
Electronic ISSN: 1435-9537
DOI: https://doi.org/10.1007/s10064-023-03512-w

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