Bayesian selection of regression model for probabilistic characterization of rock uniaxial compressive strength

Adeyemi E. Aladejare; Yu Wang

doi:10.7712/120215.4268.552

Bayesian selection of regression model for probabilistic characterization of rock uniaxial compressive strength

Adeyemi E. Aladejare^*
, Yu Wang

^*Corresponding author for this work

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

Abstract

Rock engineers and practitioners use regression equations/models between uniaxial compressive strength, UCS and point load index, Is₍₅₀₎ to estimate UCS when there is difficulty in direct determination of UCS from laboratory tests. Is₍₅₀₎ has been reported as an indirect measure of the compressive strength of rocks. However, there are many equations in the literature relating Is₍₅₀₎ to UCS for all rock types. Selecting the appropriate model for UCS estimation in a particular site/deposit becomes problematic. This is because UCS of rocks, like other geomechanical properties are products of different geological processes that rocks are subjected to, which makes them to be variable even within a formation or deposit. This study presents an approach for selecting regression equation for estimating UCS from Is₍₅₀₎, using only a limited number of Is₍₅₀₎ data obtained from a specific deposit or site. The approach works by comparing the occurrence probability of each model for a given set of observation (i.e. Is₍₅₀₎) data obtained from a site/deposit. The most appropriate model is the model with the highest occurrence probability for the given set of observation data. This approach is different from previous works that need both UCS and Is₍₅₀₎ data to draw comparison; instead it selects the appropriate model using the Is₍₅₀₎ data only. This is important because the time when there is need for selection and use of regression model is when the UCS data are not available. The selected model is then used in a Bayesian framework to integrate the prior knowledge about UCS with the limited number of site-specific Is₍₅₀₎ data available for probabilistic characterization of UCS. This is achieved by using Markov Chain Monte Carlo (MCMC) simulation to generate UCS samples from resulting posterior PDF of the Bayesian framework. Statistical analyses are then performed on the UCS samples to obtain its mean, standard deviation and full probabilistic distribution.

Original language	English
Title of host publication	UNCECOMP 2015 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering
Publisher	National Technical University of Athens
Pages	251-260
DOIs	https://doi.org/10.7712/120215.4268.552
Publication status	Published - 2015
Event	1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2015 - Hersonissos, Crete, United Kingdom Duration: 25 May 2015 → 27 May 2015 http://www.2015.uncecomp.org (unknown)

Conference

Conference	1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2015
Place	United Kingdom
City	Hersonissos, Crete
Period	25/05/15 → 27/05/15
Internet address	http://www.2015.uncecomp.org (unknown)

Research Keywords

Bayesian Framework
Markov Chain Monte Carlo Simulation
Occurrence Probability
Probabilistic Characterization
Regression Model
Site/Deposit

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@inproceedings{5805c53242174943b14968a5b4dc2403,

title = "Bayesian selection of regression model for probabilistic characterization of rock uniaxial compressive strength",

abstract = "Rock engineers and practitioners use regression equations/models between uniaxial compressive strength, UCS and point load index, Is(50) to estimate UCS when there is difficulty in direct determination of UCS from laboratory tests. Is(50) has been reported as an indirect measure of the compressive strength of rocks. However, there are many equations in the literature relating Is(50) to UCS for all rock types. Selecting the appropriate model for UCS estimation in a particular site/deposit becomes problematic. This is because UCS of rocks, like other geomechanical properties are products of different geological processes that rocks are subjected to, which makes them to be variable even within a formation or deposit. This study presents an approach for selecting regression equation for estimating UCS from Is(50), using only a limited number of Is(50) data obtained from a specific deposit or site. The approach works by comparing the occurrence probability of each model for a given set of observation (i.e. Is(50)) data obtained from a site/deposit. The most appropriate model is the model with the highest occurrence probability for the given set of observation data. This approach is different from previous works that need both UCS and Is(50) data to draw comparison; instead it selects the appropriate model using the Is(50) data only. This is important because the time when there is need for selection and use of regression model is when the UCS data are not available. The selected model is then used in a Bayesian framework to integrate the prior knowledge about UCS with the limited number of site-specific Is(50) data available for probabilistic characterization of UCS. This is achieved by using Markov Chain Monte Carlo (MCMC) simulation to generate UCS samples from resulting posterior PDF of the Bayesian framework. Statistical analyses are then performed on the UCS samples to obtain its mean, standard deviation and full probabilistic distribution.",

keywords = "Bayesian Framework, Markov Chain Monte Carlo Simulation, Occurrence Probability, Probabilistic Characterization, Regression Model, Site/Deposit",

author = "Aladejare, \{Adeyemi E.\} and Yu Wang",

year = "2015",

doi = "10.7712/120215.4268.552",

language = "English",

pages = "251--260",

booktitle = "UNCECOMP 2015 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering",

publisher = "National Technical University of Athens",

note = "1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2015 ; Conference date: 25-05-2015 Through 27-05-2015",

url = "http://www.2015.uncecomp.org",

}

Aladejare, AE & Wang, Y 2015, Bayesian selection of regression model for probabilistic characterization of rock uniaxial compressive strength. in UNCECOMP 2015 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering. National Technical University of Athens, pp. 251-260, 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2015, Hersonissos, Crete, United Kingdom, 25/05/15. https://doi.org/10.7712/120215.4268.552

Bayesian selection of regression model for probabilistic characterization of rock uniaxial compressive strength. / Aladejare, Adeyemi E.; Wang, Yu.
UNCECOMP 2015 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering. National Technical University of Athens, 2015. p. 251-260.

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Bayesian selection of regression model for probabilistic characterization of rock uniaxial compressive strength

AU - Aladejare, Adeyemi E.

AU - Wang, Yu

PY - 2015

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N2 - Rock engineers and practitioners use regression equations/models between uniaxial compressive strength, UCS and point load index, Is(50) to estimate UCS when there is difficulty in direct determination of UCS from laboratory tests. Is(50) has been reported as an indirect measure of the compressive strength of rocks. However, there are many equations in the literature relating Is(50) to UCS for all rock types. Selecting the appropriate model for UCS estimation in a particular site/deposit becomes problematic. This is because UCS of rocks, like other geomechanical properties are products of different geological processes that rocks are subjected to, which makes them to be variable even within a formation or deposit. This study presents an approach for selecting regression equation for estimating UCS from Is(50), using only a limited number of Is(50) data obtained from a specific deposit or site. The approach works by comparing the occurrence probability of each model for a given set of observation (i.e. Is(50)) data obtained from a site/deposit. The most appropriate model is the model with the highest occurrence probability for the given set of observation data. This approach is different from previous works that need both UCS and Is(50) data to draw comparison; instead it selects the appropriate model using the Is(50) data only. This is important because the time when there is need for selection and use of regression model is when the UCS data are not available. The selected model is then used in a Bayesian framework to integrate the prior knowledge about UCS with the limited number of site-specific Is(50) data available for probabilistic characterization of UCS. This is achieved by using Markov Chain Monte Carlo (MCMC) simulation to generate UCS samples from resulting posterior PDF of the Bayesian framework. Statistical analyses are then performed on the UCS samples to obtain its mean, standard deviation and full probabilistic distribution.

AB - Rock engineers and practitioners use regression equations/models between uniaxial compressive strength, UCS and point load index, Is(50) to estimate UCS when there is difficulty in direct determination of UCS from laboratory tests. Is(50) has been reported as an indirect measure of the compressive strength of rocks. However, there are many equations in the literature relating Is(50) to UCS for all rock types. Selecting the appropriate model for UCS estimation in a particular site/deposit becomes problematic. This is because UCS of rocks, like other geomechanical properties are products of different geological processes that rocks are subjected to, which makes them to be variable even within a formation or deposit. This study presents an approach for selecting regression equation for estimating UCS from Is(50), using only a limited number of Is(50) data obtained from a specific deposit or site. The approach works by comparing the occurrence probability of each model for a given set of observation (i.e. Is(50)) data obtained from a site/deposit. The most appropriate model is the model with the highest occurrence probability for the given set of observation data. This approach is different from previous works that need both UCS and Is(50) data to draw comparison; instead it selects the appropriate model using the Is(50) data only. This is important because the time when there is need for selection and use of regression model is when the UCS data are not available. The selected model is then used in a Bayesian framework to integrate the prior knowledge about UCS with the limited number of site-specific Is(50) data available for probabilistic characterization of UCS. This is achieved by using Markov Chain Monte Carlo (MCMC) simulation to generate UCS samples from resulting posterior PDF of the Bayesian framework. Statistical analyses are then performed on the UCS samples to obtain its mean, standard deviation and full probabilistic distribution.

KW - Bayesian Framework

KW - Markov Chain Monte Carlo Simulation

KW - Occurrence Probability

KW - Probabilistic Characterization

KW - Regression Model

KW - Site/Deposit

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DO - 10.7712/120215.4268.552

M3 - RGC 32 - Refereed conference paper (with host publication)

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BT - UNCECOMP 2015 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering

PB - National Technical University of Athens

T2 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2015

Y2 - 25 May 2015 through 27 May 2015

ER -

Bayesian selection of regression model for probabilistic characterization of rock uniaxial compressive strength

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