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A Predictive Model for Class II Rocks Post Peak Modulus Using Stochastic and Backward Multivariate Methods

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Abstract

The post peak modulus of hard brittle Class II rocks are the least studied geo-mechanical properties of rocks. This is because of the difficulty associated with its determination. The Brazilian tensile strength, pre-failure mechanical properties, ultra-sonic pulse velocity and the mineralogical properties of the rocks were determined. The post peak moduli were determined under brittle uniaxial compression process. Predictive equations were developed for the estimation of the post peak modulus using backward multivariate and stochastic analysis of the rocks properties. The result of analysis show that the post peak modulus depends on the Poisson’s ratio and the quartz content of rocks. As the values of duo increases the magnitude of the post peak modulus decreases. Therefore, maximum possible magnitude of post peak modulus will be for mafic rocks with zero quartz content and low value of Poisson’s ratio. While low magnitude of post peak modulus will be for felsic rocks of high proportion of quartz content and high Poisson’s ratio. The backward multivariate analysis has a coefficient of correlation of 0.903 while the correlation coefficient was improved to 0.999 by stochastically modelling the relationship using normal distribution probability function for Poisson’s ratio and exponential distribution function for quartz content. The Mean Absolute Percentage Error (MAPE) was used as performance indicator to assess the predictive performance of the models. The stochastic model shows excellent performance with MAPE of 0.5% while the backward multivariate statistics model has MAPE of 0.9%. Both the backward multivariate and stochastic models are excellent prediction models.

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  1. Department of Mining Engineering, Federal University of Technology, P.M.B. 704, Akure, Nigeria

    V. A. Akinbinu

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  1. V. A. Akinbinu
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Akinbinu, V.A. A Predictive Model for Class II Rocks Post Peak Modulus Using Stochastic and Backward Multivariate Methods. Geotech Geol Eng 40, 443–456 (2022). https://doi.org/10.1007/s10706-021-01907-8

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