Estimating rock strength parameters across varied failure criteria: Application of spreadsheet and R-based orthogonal regression to triaxial test data

Triaxial tests, a staple in rock engineering, are labor-intensive, sample-demanding, and costly, making their optimization highly advantageous. These tests are essential for characterizing rock strength, and by adopting a failure criterion, they allow for the derivation of criterion parameters throu...

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Main Authors: Roberto Úcar, Luis Arlegui, Norly Belandria, Francisco Torrijo
Format: Article
Language:English
Published: Elsevier 2025-08-01
Series:Journal of Rock Mechanics and Geotechnical Engineering
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Online Access:http://www.sciencedirect.com/science/article/pii/S167477552400550X
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author Roberto Úcar
Luis Arlegui
Norly Belandria
Francisco Torrijo
author_facet Roberto Úcar
Luis Arlegui
Norly Belandria
Francisco Torrijo
author_sort Roberto Úcar
collection DOAJ
description Triaxial tests, a staple in rock engineering, are labor-intensive, sample-demanding, and costly, making their optimization highly advantageous. These tests are essential for characterizing rock strength, and by adopting a failure criterion, they allow for the derivation of criterion parameters through regression, facilitating their integration into modeling programs. In this study, we introduce the application of an underutilized statistical technique—orthogonal regression— well-suited for analyzing triaxial test data. Additionally, we present an innovation in this technique by minimizing the Euclidean distance while incorporating orthogonality between vectors as a constraint, for the case of orthogonal linear regression. Also, we consider the Modified Least Squares method. We exemplify this approach by developing the necessary equations to apply the Mohr-Coulomb, Murrell, Hoek-Brown, and Úcar criteria, and implement these equations in both spreadsheet calculations and R scripts. Finally, we demonstrate the technique's application using five datasets of varied lithologies from specialized literature, showcasing its versatility and effectiveness.
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series Journal of Rock Mechanics and Geotechnical Engineering
spelling doaj-art-ca1af1be18a74fd8bb5e403525f9c6ac2025-08-20T03:40:41ZengElsevierJournal of Rock Mechanics and Geotechnical Engineering1674-77552025-08-011784685469910.1016/j.jrmge.2024.11.024Estimating rock strength parameters across varied failure criteria: Application of spreadsheet and R-based orthogonal regression to triaxial test dataRoberto Úcar0Luis Arlegui1Norly Belandria2Francisco Torrijo3Affiliation Universidad de Los Andes, Venezuela; Corresponding author.Affiliation Universidad de Zaragoza, Spain; Corresponding author.Affiliation Universidad de Los Andes, Venezuela; Affiliation Universidad de Zaragoza, SpainAffiliation Universitat Politècnica de València, SpainTriaxial tests, a staple in rock engineering, are labor-intensive, sample-demanding, and costly, making their optimization highly advantageous. These tests are essential for characterizing rock strength, and by adopting a failure criterion, they allow for the derivation of criterion parameters through regression, facilitating their integration into modeling programs. In this study, we introduce the application of an underutilized statistical technique—orthogonal regression— well-suited for analyzing triaxial test data. Additionally, we present an innovation in this technique by minimizing the Euclidean distance while incorporating orthogonality between vectors as a constraint, for the case of orthogonal linear regression. Also, we consider the Modified Least Squares method. We exemplify this approach by developing the necessary equations to apply the Mohr-Coulomb, Murrell, Hoek-Brown, and Úcar criteria, and implement these equations in both spreadsheet calculations and R scripts. Finally, we demonstrate the technique's application using five datasets of varied lithologies from specialized literature, showcasing its versatility and effectiveness.http://www.sciencedirect.com/science/article/pii/S167477552400550XRock failure criteriaNonlinear regressionOrthogonal regressionTriaxial testingDot product
spellingShingle Roberto Úcar
Luis Arlegui
Norly Belandria
Francisco Torrijo
Estimating rock strength parameters across varied failure criteria: Application of spreadsheet and R-based orthogonal regression to triaxial test data
Journal of Rock Mechanics and Geotechnical Engineering
Rock failure criteria
Nonlinear regression
Orthogonal regression
Triaxial testing
Dot product
title Estimating rock strength parameters across varied failure criteria: Application of spreadsheet and R-based orthogonal regression to triaxial test data
title_full Estimating rock strength parameters across varied failure criteria: Application of spreadsheet and R-based orthogonal regression to triaxial test data
title_fullStr Estimating rock strength parameters across varied failure criteria: Application of spreadsheet and R-based orthogonal regression to triaxial test data
title_full_unstemmed Estimating rock strength parameters across varied failure criteria: Application of spreadsheet and R-based orthogonal regression to triaxial test data
title_short Estimating rock strength parameters across varied failure criteria: Application of spreadsheet and R-based orthogonal regression to triaxial test data
title_sort estimating rock strength parameters across varied failure criteria application of spreadsheet and r based orthogonal regression to triaxial test data
topic Rock failure criteria
Nonlinear regression
Orthogonal regression
Triaxial testing
Dot product
url http://www.sciencedirect.com/science/article/pii/S167477552400550X
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AT norlybelandria estimatingrockstrengthparametersacrossvariedfailurecriteriaapplicationofspreadsheetandrbasedorthogonalregressiontotriaxialtestdata
AT franciscotorrijo estimatingrockstrengthparametersacrossvariedfailurecriteriaapplicationofspreadsheetandrbasedorthogonalregressiontotriaxialtestdata