# Correlation of uniaxial compressive strength with the dynamic elastic modulus, P – wave velocity and S – wave velocity of different rock types

### Abstract

Knowing mechanical properties of rocks incorporated with ultrasonic waves velocities investigations provide a secure basis for mine modelling. Uniaxial compressive strength, dynamic elastic modulus and ultrasonic waves velocities are just some of the rock properties that indicate on presence of discontinuities, stratification and fissures of rocks. Determining the relationship of these rock properties testing the rock samples that are corresponding to different rock types extracted from different mineral deposits represents the core of this study.

In this paper, we statistically analyzed measured and calculated rock properties. We established the connection between these parameters creating empirical correlation equations. Using least squares method and simple linear regression analysis, we defined correlation coefficients and also developed empirical correlation equations.

### References

ALLISON P.D. (1998) Multiple regression: a primer. Thousand Oaks, Calif.: Pine Forge Press.

AŞCI M. et al. (2017) Correlation of physical and mechanical properties with ultrasonic pulse velocities of sandstones in Çenedağ, Kocaeli-Turkey. International Journal of Advanced Geosciences, 5 (2), pp. 109-115.

ANON (1979) Classification of rocks and soils for engineering geological mapping. Bulletin of the International Association of Engineering Geology, 19, pp. 364 – 371.

DIAMANTIS K. et al. (2011) Correlating wave velocities with physical, mechanical properties and petrographic characteristics of peridotites from the central Greece. Geotechnical and Geological Engineering, 29(6), pp. 1049-1062.

GHANI I.M.M. and AHMAD S. (2010) Stepwise multiple regression method to forecast fish landing. In: International Conference on Mathematics Education Research 2010, Procedia Social and Behavioral Sciences, 8, pp. 549 – 554.

GUERARD J. (2013) Introduction to financial forecasting in investment analysis. Springer.

INOUE M. and OHOMI M. (1981) Relation between uniaxial compressive strength and elastic wave velocity of soft rock. In: Proceedings of the International Symposium on Weak Rock, Tokyo, pp. 9–13.

KAHRAMAN S. (2001) Evaluation of simple methods for assessing the uniaxial compressive strength of rock. International Journal of Rock Mechanics and Mining Sciences, 38, pp. 981–994.

KELES T. (2018) Comparison of Classical Least Squares and Orthogonal Regression in Measurement Error Models. International Online Journal of Educational Sciences, 10 (3), pp. 200 – 214.

KISI O. and OZKAN C. (2017) A New Approach for Modeling Sediment-Discharge Relationship: Local Weighted Linear Regression. Water Resources Management, 31, pp. 1 – 23.

KOWAL R. (2016) The Efficiency of OLS Estimators of Structural Parameters in a Simple Linear Regression Model in the Calibration of the Averages Scheme. Folia Oeconomica Stetinensia, pp. 236 – 249.

KHANDELWAL M. and SINGH T.N. (2009) Correlating static properties of coal measures rock with P-wave velocity. International Journal of Coal Geology, 44, pp. 55- 60.

MAJSTOROVIĆ J. and CVETKOVIĆ M. (2004) Some results of stone testing as working environment by ultrasound. In: ECRBM '04 (European Conference on Raw Building Materials and Coal: New Perspectives), Sarajevo.

MINAEIAN B. and AHANGARI K. (2013) Estimation of uniaxial compressive strength based on P-wave and Schmidt hammer rebound using statistical method. Arabian Journal of Geosciences, 6, pp. 1925-1931.

NANGOLO C. and MUSINGWINI C. (2011) Empirical correlation of mineral commodity prices with exchange – traded mining stock prices. The Journal of the Southern African Institute of Mining and Metallurgy, 111, pp. 459 – 468.

PAPPALARDO G. et al. (2016) Geotechnical characterization of limestone employed for the reconstruction of a UNESCO world heritage baroque monument in southeastern Sicily (Italy). Engineering Geology, 212, pp. 86-97.

RAJABI A.M. et al. (2017) The New Empirical Formula to Estimate the Uniaxial Compressive Strength of Limestone; North of Saveh a Case Study. Journal of Engineering Geology, 11, No. 3, pp. 159-180.

SINGH M. P. (2018) Efficient Multi-site Statistical Downscaling Model for Climate Change. Thesis (PhD), Motilal Nehru National Institute Of Technology Allahabad Prayagraj.

SINGH T. N. et al. (2012) Correlation Between Point Load Index and Uniaxial Compressive Strength for Different Rock Types. Rock Mechanics and Rock Engineering, 45(2), pp. 259-264.

SHARMA P. K. and SINGH, T. N. (2008) A correlation between P-wave velocity, impact strength index, slake durability index and uniaxial compressive strength. Bulletin of Engineering Geology and the Environment, 67, pp. 17-22.

TUGRUL A. and ZARIF I. H. (1999) Correlating of mineralogical and textural, characteristics with engineering properties of selected granitic rocks from Turkey. Engineering Geology, 51, pp. 303-317.

YAGIZ S. (2011) P-wave velocity test for assessment of geotechnical properties of some rock materials. Bulletin of Materials Science, 34(4), pp. 947-953.

YASAR E. and ERDOGAN Y. (2004) Correlating sound velocity with the density, compressive strength and Young modulus of carbonate rocks. International Journal of Rock Mechanics and Mining Sciences, 41, pp. 871-875.

ZHANG L. (2005) Engineering properties of rocks. Oxford: Elsevier.

*Podzemni Radovi*, (34), 11-25. https://doi.org/10.5937/PodRad1934011M