Predicting elastic properties of intact rocks from index tests using multiple regression modelling

doi:10.1016/j.ijrmms.2004.08.005

International Journal of Rock Mechanics and Mining Sciences

Volume 42, Issue 2, February 2005, Pages 323-330

https://doi.org/10.1016/j.ijrmms.2004.08.005 Get rights and content

Introduction

As Bieniawski [1] reports, one of the important rock mechanics aspects for mining engineers is the determination of the uniaxial compressive strength of rocks. Moreover, Young's modulus (E) and Poisson's ratio $(ν)$ are important parameters for understanding the stress–strain behaviour. These parameters are crucial in tunnel design, or rock blasting and drilling, slope stability, pillar design, embankments and many other civil and mining operations. Goodman [2] points out that the strength tests always require careful test set-up and specimen preparation and thus index tests are useful only if the properties are reproducible from one laboratory to another and can be measured inexpensively. A recent trend is for estimating $σ_{c}$ from simple laboratory index tests. Many researchers have been conducting investigations to predict the Unconfined Compressive Strength (UCS) from non-destructive testing methods such as the sound velocity test. A great number of attempts have been made to predict the uniaxial compressive strength of the same type of rocks [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. However, the estimation of the most useful intact rock properties, Young's modulus and Poisson's ratio, was found to be less reported in the literature.

The basic idea behind the current research is to use multiple regression modelling to estimate the elastic properties of intact rocks. For this objective, nine different rock types have been tested according to the ISRM testing standards. These tests consist of the Schmidt Hammer Hardness test, Point Load Index test, Sound Velocity, Density ( $ρ$ ), Porosity (n) and UCS $(σ_{c})$ test. Each rock type has been subjected to the aforementioned six tests and their mean values, standard deviations and coefficient of variations (CoV) from each test were calculated accordingly. The CoVs have been calculated by dividing the standard deviations by the mean values.

There have been many simple models introduced to relate $σ_{c}$ to Schmidt hammer rebound (SHR) value , $σ_{c}$ to V_p, $σ_{c}$ to n, $σ_{c}$ to I_s₍₅₀₎ and so on [3], [4], [5], [8], [9], [10], [11], [12], [13], [14], [15]. However, for those who had established simple models only, R², i.e. the explanation capability of the dependant variable from information obtained via independent variables, was considered as a sufficient criterion. This is not adequate for use in mining and civil engineering applications because the R²s based on simple models cannot explain the total variability introduced by independent variables. In other words, they are less reliable models. Therefore, the use of a multiple regression model will be more accurate in appraising elastic properties of intact rocks.

Section snippets

The proposed method for prediction of the elastic properties of intact rocks

Elastic properties of rocks can be predicted by multiple regression modelling, the statistical methodology used to relate variables [16]. A variable termed the dependent or response variable is related to predictor or independent variable(s). The objective is to construct a regression model relating the dependent variable, y, to independent variable(s), $x_{1}, x_{2}, \dots, x_{p}$ .

The multiple regression model relating y to $x_{1}, x_{2}, \dots, x_{p}$ is $y_{i} = μ_{i} + ε_{i} = β_{0} + β_{1} x_{i 1} + β_{2} x_{i 2} + \dots + β_{p} x_{ip} + ε_{i},$ where $μ_{i}$ is the mean value of the

Experimental investigations

Rock blocks have been collected from different locations in the Malatya and Elazıg region in Eastern Anatolia. Rock blocks consisted of mainly marbles, limestones and dacite. Optical microscopy study has been conducted to define the composition, and mineralogical and textural characteristics of the rock samples to be tested. Thin section analysis results are given in Table 1. Using core drilling machines at the laboratory, NX size core samples have been taken from the blocks. The ELE core

Case study

A case study was then carried out to demonstrate the recommended method for predicting the elastic properties of intact rocks. The data set given in the experimental section was used for the case study. The SPSS for Windows was used for the modelling. In order to compare all reasonable regression models, a backward elimination procedure was used as the screening procedure. Then the independent variable having the absolute smallest t statistic was selected. If the t statistic was not significant

Results and conclusions

Multiple regression analysis is a powerful modelling technique. The method can be useful in such cases in which complex relations are involved. Also, multiple regression analysis can be the right method where more than one variable affects a rock property. Thus, using multiple regression analysis, elastic properties of rock can be evaluated.

The results obtained from the case study by means of multiple regression models also support the arguments outlined above. As can be seen in Fig. 1, Fig. 2,

Acknowledgements

Grateful acknowledgements are due to the Scientific Research Unit of Inonu University, Malatya, for providing financial support for the project (Project No: 2002/02). Many thanks go to Prof. Dr. Hüseyin Yalçın for his valuable petrographic study.

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Technical notePredicting elastic properties of intact rocks from index tests using multiple regression modelling

Introduction

Section snippets

The proposed method for prediction of the elastic properties of intact rocks

Experimental investigations

Case study

Results and conclusions

Acknowledgements

First page preview

Int J Rock Mech Min Sci

Int J Rock Mech Min Sci

Eng Geol

Int J Rock Mech Min Sci

Int J Rock Mech Min Sci Geomech Abstr

Int J Rock Mech Min Sci Geomech Abstr

Int J Rock Mech Min Sci Geomech Abstr

Int J Rock Mech Min Sci

Estimating the strength of rock materials

J S Afr Inst Min Metall

Introduction to rock mechanics

Influence of porosity and elastic modulus on uniaxial compressive strength in soft brittle porous sandstones

Rock Mech Rock Eng

Fuzzy model for the prediction of unconfined compressive strength of rock samples

Int J Rock Mech Min Sci

Technical note
Predicting elastic properties of intact rocks from index tests using multiple regression modelling