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Classification of the intact carbonate and silicate rocks based on their degree of thermal cracking using discriminant analysis

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Abstract

Discriminant analysis is a multivariate statistical tool that generates a discriminant function to predict about the group membership of sampled experimental data. In this study, discriminant analysis was performed using IBM SPSS software package (version 23) to discriminate between pre-defined groups of measured dynamic properties of thermally treated selected carbonate and silicate rocks. The range of temperature variations was selected from 35 °C (laboratory temperature) to 200 °C to estimate the change in dynamic properties including Q-factor (Q), resonance frequency (Fr), elastic Young’s modulus (Ed), damping ratio (ξ), and specific damping capacity (Ψ) by using the “Erudite Resonance Frequency Meter” apparatus in accordance with ASTM C215 test procedure. The test results revealed significant variations in the values of Q, Fr, Ed, ξ, and Ψ with the rise in temperature. The measured dynamic properties of selected sedimentary rocks were classified into 2 discrete groups based on their extent of thermal treatment (i.e., 35–100 °C and 100–200 °C). Discriminant analysis–based classification results showed the sensitivity level of 86.70% and specificity level of 100.00% between predicted and original group membership. The estimated model hit ratio of 92.00% found better than maximum chance criterion and proportional chance criterion that indicates the high level of significance of classification results. Q-statistic results also satisfied the high prediction accuracy of discriminant function. The outcomes of this study could provide useful references in the classification and characterization of experimental data related to geotechnical and geomechanical studies.

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References

  • Ahmed MF, Waqas U, Arshad M, Rogers JD (2018) Effect of heat treatment on the dynamic properties of selected rock types taken from the Salt Range in Pakistan. Arab J Geosci 11(22):728

    Google Scholar 

  • Bauer SJ, Johnson B (1979) Effects of slow uniform heating on the physical properties of the westerly and charcoal granites. In: Proceedings of a 20th symposium on rock mechanics Austin, Texas: ASCE, New York, pp 7–18

  • Brotons V, Tomás R, Ivorra S, Alarcón JC (2013) Temperature influence on the physical and mechanical properties of a porous rock: San Julian’s calcarenite. Eng Geol 167:117–127

    Google Scholar 

  • Chaki S, Takarli M, Agbodjan WP (2008) Influence of thermal damage on physical properties of a granite rock: porosity, permeability and ultrasonic wave evolutions. Constr Build Mater 22:1456–1461

    Google Scholar 

  • Chakrabarti B, Yates T, Lewry A (1996) Effect of fire damage on natural stonework in buildings. Constr Build Mater 10(7):539–544

    Google Scholar 

  • Davis JC (2014) Statistics and data analysis in geology. Wiley, New York

    Google Scholar 

  • Du-Shouji MM, Haohua C, Yiping Q (2003) The study on longitudinal wave characteristics of granite after high temperature. Chin J Rock Mech Eng 22(11):1803–1806

    Google Scholar 

  • Freire-Lista DM, Fort R, Varas-Muriel MJ (2016) Thermal stress-induced microcracking in building granite. Eng Geol 206:83–93

    Google Scholar 

  • Ghazi S, Sohail HJ, Hanif T, Masood FR (2017) Petrography of the early Permian (assilian) Tobra formation, eastern Salt Range, Potwar basin, Pakistan: implications on provenance, tectonic settings and environment of deposition. Arab J Earth Sci 4(2):6

    Google Scholar 

  • Heap MJ, Baud P, Meredith PG (2009) Influence of temperature on brittle creep in sandstones. Geophys Res Lett 36(19)

  • Inserra C, Biwa S, Chen Y (2009) Nonlinear ultrasonic characterization of thermally damaged westerly granite. Jpn J Appl Phys 48(7S):07GD03

    Google Scholar 

  • Jaba E, Jemna D, Viorică D, Balan CB (2007) Discriminant analysis in the study of romanian regional economic development. Analele Stiinţifice ale Universităţii “Alexandru Ioan Cuza” din Iaşi, Tomul LIV, Ştiinţe Economice 184: 147–153

  • Kramer SL (1996) Geotechnical earthquake engineering, vol 569. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Kranz RL, Harris WJ, Carter NL (1982) Static fatigue of granite at 200°C. Geophys Res Lett 9(1):1–4

    Google Scholar 

  • Lachenbruch PA (1975) Zero-mean difference discrimination and the absolute linear discriminant function. Biometrika 62(2):397–401

    Google Scholar 

  • Mahanta B, Singh TN, Ranjith PG (2016) Influence of thermal treatment on the mode I fracture toughness of certain Indian rocks. Eng Geol 210:103–114

    Google Scholar 

  • Mardoukhi A, Mardoukhi Y, Hokka M, Kuokkala VT (2017) Effects of heat shock on the dynamic tensile behavior of granitic rocks. Rock Mech Rock Eng 50(5):1171–1182

    Google Scholar 

  • Martínez-Martínez J, Benavente D, García-del-Cura MA (2012) Comparison of the static and dynamic elastic modulus in carbonate rocks. Bull Eng Geol Environ 71(2):263–268

    Google Scholar 

  • Murru A, Freire-Lista DM, Fort R, Varas-Muriel MJ, Meloni P (2018) Evaluation of post-thermal shock effects in Carrara marble and Santa Caterina di Pittinuri limestone. Constr Build Mater 186:1200–1211

    Google Scholar 

  • Nasseri MHB, Schubnel A, Young RP (2007) Coupled evolutions of fracture toughness and elastic wave velocities at a high crack density in thermally treated westerly granite. Int J Rock Mech Min Sci 44(4):601–616

    Google Scholar 

  • Peng J, Rong G, Cai M, Yao MD, Zhou CB (2016) Physical and mechanical behaviors of a thermal-damaged coarse marble under uniaxial compression. Eng Geol 200:88–93

    Google Scholar 

  • Pimienta L, Klitzsch N, Clauser C (2018) Comparison of thermal and elastic properties of sandstones: experiments and theoretical insights. Geothermics 76:60–73

    Google Scholar 

  • Potter PE, Shimp NF, Witters J (1963) Trace elements in marine and fresh-water argillaceous sediments. Geochim Cosmochim Acta 27(6):669–694

    Google Scholar 

  • Ramayah T, Ahmad NH, Halim HA, Zainal SRM, Lo MC (2010) Discriminant analysis: an illustrated example. Afr J Bus Manage 4(9):1654–1667

    Google Scholar 

  • Rao QH, Wang Z, Xie HF, Xie Q (2007) Experimental study of mechanical properties of sandstone at high temperatures. J Cent S Univ Technol 14:478–483

    Google Scholar 

  • Sameeni SJ (2009) The Salt Range. In Paleo-Parks: the protection and conservation of fossil sites worldwide. Université de Bretagne occidentale Département des sciences de la terre, pp 65-73

  • Shah SMI (2009) Stratigraphy of Pakistan, GSP Memoirs Vol. 22. Ministry of Petroleum and Natural Resources, Government of Pakistan

  • Siratovich PA, Villeneuve MC, Cole JW, Kennedy BM, Bégué F (2015) Saturated heating and quenching of three crustal rocks and implications for thermal stimulation of permeability in geothermal reservoirs. Int J Rock Mech Min Sci 80:265–280

    Google Scholar 

  • Takarli M, Prince-Agbodjan W (2008) Temperature effects on physical properties and mechanical behavior of granite: an experimental investigation of material damage. J ASTM Int 5(3)

  • Tian H, Kempka T, Xu NX, Ziegler M (2012) Physical properties of sandstones after high-temperature treatment. Rock Mech Rock Eng 45(6):1113–1117

    Google Scholar 

  • Torok A, Hajpál M (2005) Effect of temperature changes on the mineralogy and physical properties of sandstones. A laboratory study. Int J Rest Build Mon 11(4):211

    Google Scholar 

  • Wang HF, Heard HC (1985) Prediction of elastic moduli via crack density in pressurized and thermally stressed rock. J Geophys Res 90(B12):342–350

    Google Scholar 

  • Waqas U, Ahmed MF, Rogers JD (2018) Effect of loading frequencies on the dynamic properties of thermally treated rock samples. In 52nd US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association

  • Yang J, Fu LY, Zhang W, Wang Z (2019) Mechanical property and thermal damage factor of limestone at high temperature. Int J Rock Mech Min Sci 117:11–19

    Google Scholar 

  • Yin TB, Li XB, Zhou ZL, Hong L, Ye ZY (2007) Study on mechanical properties of post-high-temperature sandstone. Chin J Undergr Sp Eng 3(6):1060–1063

    Google Scholar 

  • Yin T, Li X, Cao W, Xia K (2015) Effects of thermal treatment on the tensile strength of Laurentian granite using Brazilian test. Rock Mech Rock Eng 48(6):2213–2223

    Google Scholar 

  • Zhang Y, Zhang X, ZHAO YS (2005) Process of sandstone thermal cracking (in Chinese). Chin J Geophys 48(3):656–659

    Google Scholar 

Download references

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Correspondence to Umer Waqas.

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Waqas, U., Ahmed, M.F. & Arshad, M. Classification of the intact carbonate and silicate rocks based on their degree of thermal cracking using discriminant analysis. Bull Eng Geol Environ 79, 2607–2619 (2020). https://doi.org/10.1007/s10064-020-01727-9

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