# Prediction of uniaxial compressive strength of carbonate rocks from nondestructive tests using multivariate regression and LS-SVM methods

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## Abstract

Uniaxial compressive strength (UCS) value of a rock material is one of the most important design parameters in engineering practice and related fields of geosciences. Through this importance, prediction of UCS values of rock materials from nondestructive quicker and simpler tests are widely preferred. The aim of this study is to predict the UCS values of five carbonate rock groups including marble, dolomite, two limestones, and travertine from longitudinal ultrasonic wave velocity (Vp), Schmidt hardness rebound number (SHR), and cubic sample sizes (*L*). For this aim, a total of 90 cubic samples with 7, 9, and 11 cm edge sizes were prepared. Chemical, petrographical, and basic physical properties of the sample groups were investigated. After Vp and SHR values, UCS values of all samples were determined. By using multivariate regression analyses (MR), different UCS prediction equations from *dry unit weight (γ*_{d}*)*, Vp, SHR, and also *L* values were proposed. Prediction performances of proposed model in which Vp, SHR, and *L* are input parameters was also analyzed by least square support vector machines (LS-SVM) method. Prediction performances of the MR and LS-SVM models were analyzed by coefficient of determination (*R*^{2}), efficiency (*E*), and root mean square error (RMSE) performance measures. These values were calculated as 0.867, 0.799, and 16.616 respectively for the LS-SVM model and 0.781, 0.749, and 18.561 respectively for the MR model. The LS-SVM method was found to be successful in the prediction of the UCS values from nondestructive test data of carbonate rocks.

## Keywords

Uniaxial compressive strength Schmidt hammer rebound values Ultrasonic wave velocity Carbonate rocks LS-SVM method## Notes

### Acknowledgements

The author wishes to express his sincere gratitude to geological engineers Ozan Düdükçü and Emin Deymeci from Ece and Çoban Marble Companies in Denizli, Turkey, respectively, for their support in sample supply and preparation. The author also wishes to express his kind regards to Dr. Fatih Dikbaş for English language editing of the manuscript.

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