Bayesian data analysis to quantify the uncertainty of intact rock strength
One of the main difficulties in the geotechnical design process lies in dealing with uncertainty. Uncertainty is associated with natural variation of properties, and the imprecision and unpredictability caused by insufficient information on parameters or models. Probabilistic methods are normally us...
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| Format: | Article |
| Language: | English |
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Elsevier
2018-02-01
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| Series: | Journal of Rock Mechanics and Geotechnical Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S167477551730149X |
| _version_ | 1818840108829245440 |
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| author | Luis Fernando Contreras Edwin T. Brown Marc Ruest |
| author_facet | Luis Fernando Contreras Edwin T. Brown Marc Ruest |
| author_sort | Luis Fernando Contreras |
| collection | DOAJ |
| description | One of the main difficulties in the geotechnical design process lies in dealing with uncertainty. Uncertainty is associated with natural variation of properties, and the imprecision and unpredictability caused by insufficient information on parameters or models. Probabilistic methods are normally used to quantify uncertainty. However, the frequentist approach commonly used for this purpose has some drawbacks. First, it lacks a formal framework for incorporating knowledge not represented by data. Second, it has limitations in providing a proper measure of the confidence of parameters inferred from data. The Bayesian approach offers a better framework for treating uncertainty in geotechnical design. The advantages of the Bayesian approach for uncertainty quantification are highlighted in this paper with the Bayesian regression analysis of laboratory test data to infer the intact rock strength parameters σci and mi used in the Hoek–Brown strength criterion. Two case examples are used to illustrate different aspects of the Bayesian methodology and to contrast the approach with a frequentist approach represented by the nonlinear least squares (NLLS) method. The paper discusses the use of a Student's t-distribution versus a normal distribution to handle outliers, the consideration of absolute versus relative residuals, and the comparison of quality of fitting results based on standard errors and Bayes factors. Uncertainty quantification with confidence and prediction intervals of the frequentist approach is compared with that based on scatter plots and bands of fitted envelopes of the Bayesian approach. Finally, the Bayesian method is extended to consider two improvements of the fitting analysis. The first is the case in which the Hoek–Brown parameter, a, is treated as a variable to improve the fitting in the triaxial region. The second is the incorporation of the uncertainty in the estimation of the direct tensile strength from Brazilian test results within the overall evaluation of the intact rock strength. |
| first_indexed | 2024-12-19T04:04:57Z |
| format | Article |
| id | doaj.art-a414a1ee7714442bbed43d3079d5f31b |
| institution | Directory Open Access Journal |
| issn | 1674-7755 |
| language | English |
| last_indexed | 2024-12-19T04:04:57Z |
| publishDate | 2018-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Rock Mechanics and Geotechnical Engineering |
| spelling | doaj.art-a414a1ee7714442bbed43d3079d5f31b2022-12-21T20:36:33ZengElsevierJournal of Rock Mechanics and Geotechnical Engineering1674-77552018-02-01101113110.1016/j.jrmge.2017.07.008Bayesian data analysis to quantify the uncertainty of intact rock strengthLuis Fernando Contreras0Edwin T. Brown1Marc Ruest2The University of Queensland, St Lucia Campus, Brisbane, QLD 4072, AustraliaGolder Associates Pty. Ltd., Brisbane, AustraliaThe University of Queensland, St Lucia Campus, Brisbane, QLD 4072, AustraliaOne of the main difficulties in the geotechnical design process lies in dealing with uncertainty. Uncertainty is associated with natural variation of properties, and the imprecision and unpredictability caused by insufficient information on parameters or models. Probabilistic methods are normally used to quantify uncertainty. However, the frequentist approach commonly used for this purpose has some drawbacks. First, it lacks a formal framework for incorporating knowledge not represented by data. Second, it has limitations in providing a proper measure of the confidence of parameters inferred from data. The Bayesian approach offers a better framework for treating uncertainty in geotechnical design. The advantages of the Bayesian approach for uncertainty quantification are highlighted in this paper with the Bayesian regression analysis of laboratory test data to infer the intact rock strength parameters σci and mi used in the Hoek–Brown strength criterion. Two case examples are used to illustrate different aspects of the Bayesian methodology and to contrast the approach with a frequentist approach represented by the nonlinear least squares (NLLS) method. The paper discusses the use of a Student's t-distribution versus a normal distribution to handle outliers, the consideration of absolute versus relative residuals, and the comparison of quality of fitting results based on standard errors and Bayes factors. Uncertainty quantification with confidence and prediction intervals of the frequentist approach is compared with that based on scatter plots and bands of fitted envelopes of the Bayesian approach. Finally, the Bayesian method is extended to consider two improvements of the fitting analysis. The first is the case in which the Hoek–Brown parameter, a, is treated as a variable to improve the fitting in the triaxial region. The second is the incorporation of the uncertainty in the estimation of the direct tensile strength from Brazilian test results within the overall evaluation of the intact rock strength.http://www.sciencedirect.com/science/article/pii/S167477551730149XUncertaintyIntact rock strengthBayesian analysisHoek–Brown criterion |
| spellingShingle | Luis Fernando Contreras Edwin T. Brown Marc Ruest Bayesian data analysis to quantify the uncertainty of intact rock strength Journal of Rock Mechanics and Geotechnical Engineering Uncertainty Intact rock strength Bayesian analysis Hoek–Brown criterion |
| title | Bayesian data analysis to quantify the uncertainty of intact rock strength |
| title_full | Bayesian data analysis to quantify the uncertainty of intact rock strength |
| title_fullStr | Bayesian data analysis to quantify the uncertainty of intact rock strength |
| title_full_unstemmed | Bayesian data analysis to quantify the uncertainty of intact rock strength |
| title_short | Bayesian data analysis to quantify the uncertainty of intact rock strength |
| title_sort | bayesian data analysis to quantify the uncertainty of intact rock strength |
| topic | Uncertainty Intact rock strength Bayesian analysis Hoek–Brown criterion |
| url | http://www.sciencedirect.com/science/article/pii/S167477551730149X |
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