Skip to main content
main-content
Top

Hint

Swipe to navigate through the articles of this issue

Published in: Geotechnical and Geological Engineering 8/2022

27-05-2022 | Original Paper

Development of Statistical Models to Predict the Mechanical Properties of Some Metamorphic Rocks from P-Wave Velocity and Certain Physical Properties

Authors: Hari Om Singh, Tariq Anwar Ansari, T. N. Singh, K. H. Singh

Published in: Geotechnical and Geological Engineering | Issue 8/2022

Login to get access
share
SHARE

Abstract

Strength and elastic properties of rocks have vital importance for the design of structures in several rock engineering projects. Additionally, these parameters are extensively used in numerical modelling to envisage the mechanical behavior of rock before failure and their relevance to geotechnical characteristics in slope stability. This study was intended to predict the geomechanical properties of three different metamorphic rocks using simple and multiple regression analysis. The predictive models and their correlation coefficients were established and well discussed for P-wave velocity and different physico-mechanical parameters. Initially, simple regression analysis was performed and then the authenticity of the result was also validated by student’s ‘t’ and ‘F’ test. Further, 13 different empirical models were developed to predict the strength and elastic properties of these rocks through multiple regression analysis. The predicted values estimated from these models show a deterministic and closely associated result with the observed values. Analysis of variance of these rock-mechanics data was also compared to check the confidence of multiple regression models. The coefficient of determination (R2), the root mean square error (RMSE), the mean absolute percentage error (MAPE), and the variance account for (VAF) of these empirical equations were estimated and compared to quantify the performance of the models. The comparative result of statistical indices (R2, RMSE, MAPE, VAF) revealed negligible error in developed models with high prediction performance and may be accepted for empirical models to predict the mechanical properties.
Literature
go back to reference Allison PD (1999) Multiple regression. Pine Forge Press, Thousand Oaks, CA Allison PD (1999) Multiple regression. Pine Forge Press, Thousand Oaks, CA
go back to reference Altindag R (2012) Correlation between P-wave velocity and some mechanical properties for sedimentary rocks. South Afr Inst Min Metall 112:229–237 Altindag R (2012) Correlation between P-wave velocity and some mechanical properties for sedimentary rocks. South Afr Inst Min Metall 112:229–237
go back to reference Auden JB (1937) Structure of Himalaya in Garhwal Red. GSI 72:403–433 Auden JB (1937) Structure of Himalaya in Garhwal Red. GSI 72:403–433
go back to reference Chawre B (2018) Correlations between ultrasonic pulse wave velocities and rock properties of quartz-mica schist. J Rock Mech Geotech Eng 10(3):594–602 CrossRef Chawre B (2018) Correlations between ultrasonic pulse wave velocities and rock properties of quartz-mica schist. J Rock Mech Geotech Eng 10(3):594–602 CrossRef
go back to reference Franklin JA (1979) Suggest methods for determining water content, porosity, density, absorption and related properties and swelling and slake-durability index properties. Int J Rock Mech Min Sci Geomech Abstr 16:141–156 Franklin JA (1979) Suggest methods for determining water content, porosity, density, absorption and related properties and swelling and slake-durability index properties. Int J Rock Mech Min Sci Geomech Abstr 16:141–156
go back to reference Golberg MA, Cho HA (2010) Introduction to regression analysis. WIT Press, Cambridge Golberg MA, Cho HA (2010) Introduction to regression analysis. WIT Press, Cambridge
go back to reference International Society for Rock Mechanics (ISRM). Commission on Standardization of Laboratory and Field Tests (1979) Suggested methods for determining water content, porosity, density, absorption and related properties and swelling and slake-durability index properties: Pergamon. International Society for Rock Mechanics (ISRM). Commission on Standardization of Laboratory and Field Tests (1979) Suggested methods for determining water content, porosity, density, absorption and related properties and swelling and slake-durability index properties: Pergamon.
go back to reference Jech J, Babuska V (1985) Quantitative correlation of velocity anisotropy with the distribution of microcracks in rocks. In: Kapicka A, Kropacek V, Pros Z (eds) Physical properties of the mineral system of the earth's interior. Union Czech. Math. Phys., Prague, 175–183 Jech J, Babuska V (1985) Quantitative correlation of velocity anisotropy with the distribution of microcracks in rocks. In: Kapicka A, Kropacek V, Pros Z (eds) Physical properties of the mineral system of the earth's interior. Union Czech. Math. Phys., Prague, 175–183
go back to reference Ji S, Li L, Motra HB, Wuttke F, Sun S, Michibayashi K, Salisbury MH (2018) Poisson's ratio and auxetic properties of natural rocks. J Geophys Res Solid Earth 123(2):1161–1185 Ji S, Li L, Motra HB, Wuttke F, Sun S, Michibayashi K, Salisbury MH (2018) Poisson's ratio and auxetic properties of natural rocks. J Geophys Res Solid Earth 123(2):1161–1185
go back to reference Kahraman S, Yeken T (2008) Determination of physical properties of carbonate rocks from P-wave velocity. Bull Eng Geol Env 67(2):277–281 CrossRef Kahraman S, Yeken T (2008) Determination of physical properties of carbonate rocks from P-wave velocity. Bull Eng Geol Env 67(2):277–281 CrossRef
go back to reference Khajevand R, Fereidooni D (2019) Utilization of the point load and block punch strengths to predict the mechanical properties of several rock samples using regression analysis methods. Innov Infrastruct Sol 4(1):1–14 CrossRef Khajevand R, Fereidooni D (2019) Utilization of the point load and block punch strengths to predict the mechanical properties of several rock samples using regression analysis methods. Innov Infrastruct Sol 4(1):1–14 CrossRef
go back to reference Khandelwal M (2013) Correlating P-wave velocity with the physico-mechanical properties of different rocks. Pure Appl Geophys 170(4):507–514 CrossRef Khandelwal M (2013) Correlating P-wave velocity with the physico-mechanical properties of different rocks. Pure Appl Geophys 170(4):507–514 CrossRef
go back to reference Kurtulus CE, Bozkurt A, Endes H (2012) Physical and mechanical properties of serpentinized ultrabasic rocks in NW Turkey. Pure Appl Geophys 169(7):1205–1215 CrossRef Kurtulus CE, Bozkurt A, Endes H (2012) Physical and mechanical properties of serpentinized ultrabasic rocks in NW Turkey. Pure Appl Geophys 169(7):1205–1215 CrossRef
go back to reference Kurtuluş C, Sertçelik F, Sertçelik I (2016) Correlating physico-mechanical properties of intact rocks with P-wave velocity. Acta Geod Geoph 51(3):571–582 CrossRef Kurtuluş C, Sertçelik F, Sertçelik I (2016) Correlating physico-mechanical properties of intact rocks with P-wave velocity. Acta Geod Geoph 51(3):571–582 CrossRef
go back to reference Moradian ZA, Behnia M (2009) Predicting the uniaxial compressive strength and static Young’s modulus of intact sedimentary rocks using the ultrasonic test. Int J Geomech 9(1):14–19 CrossRef Moradian ZA, Behnia M (2009) Predicting the uniaxial compressive strength and static Young’s modulus of intact sedimentary rocks using the ultrasonic test. Int J Geomech 9(1):14–19 CrossRef
go back to reference Orús-Lacort M, Jouis C (2014) Simple regression model. Conference on Simple linear regression analysis Orús-Lacort M, Jouis C (2014) Simple regression model. Conference on Simple linear regression analysis
go back to reference Sachpazis CI (1990) Correlating Schmidth hardness with compressive strength and Young’s modulus carbonate rocks. Bull Int Ass Engng Geol 42:75–83 CrossRef Sachpazis CI (1990) Correlating Schmidth hardness with compressive strength and Young’s modulus carbonate rocks. Bull Int Ass Engng Geol 42:75–83 CrossRef
go back to reference Sarkar K, Vishal V, Singh TN (2012) An empirical correlation of index geomechanical parameters with the compressional wave velocity. Geotech Geol Eng 30(2):469–479 CrossRef Sarkar K, Vishal V, Singh TN (2012) An empirical correlation of index geomechanical parameters with the compressional wave velocity. Geotech Geol Eng 30(2):469–479 CrossRef
go back to reference Sharma PK, Singh TN (2008) A correlation between P-wave velocity, impact strength index, slake durability index and uniaxial compressive strength. Bull Eng Geol Env 67(1):17–22 CrossRef Sharma PK, Singh TN (2008) A correlation between P-wave velocity, impact strength index, slake durability index and uniaxial compressive strength. Bull Eng Geol Env 67(1):17–22 CrossRef
go back to reference Sharma LK, Vishal V, Singh TN (2017) Developing novel models using neural networks and fuzzy systems for the prediction of strength of rocks from key geomechanical properties. Measurement 102:158–169 CrossRef Sharma LK, Vishal V, Singh TN (2017) Developing novel models using neural networks and fuzzy systems for the prediction of strength of rocks from key geomechanical properties. Measurement 102:158–169 CrossRef
go back to reference Ulusay R, Türeli K, Ider MH (1994) Prediction of engineering properties of a selected litharenite sandstone from its petrographic characteristics using correlation and multivariate statistical techniques. Eng Geol 38(1–2):135–157 CrossRef Ulusay R, Türeli K, Ider MH (1994) Prediction of engineering properties of a selected litharenite sandstone from its petrographic characteristics using correlation and multivariate statistical techniques. Eng Geol 38(1–2):135–157 CrossRef
go back to reference Valdiya KS (1980) The two intracrustal boundary thrusts of the Himalaya. Tectonophysics 66(4):323–348 CrossRef Valdiya KS (1980) The two intracrustal boundary thrusts of the Himalaya. Tectonophysics 66(4):323–348 CrossRef
go back to reference Vasconcelos G, Lourenço PB, Alves CA, Pamplona J (2007) Prediction of the mechanical properties of granites by ultrasonic pulse velocity and Schmidt hammer hardness. Vasconcelos G, Lourenço PB, Alves CA, Pamplona J (2007) Prediction of the mechanical properties of granites by ultrasonic pulse velocity and Schmidt hammer hardness.
go back to reference Wilson AH (1980) Stability of underground working in the soft rocks of coal measures. Ph.D. Thesis, University of Nothingam. Wilson AH (1980) Stability of underground working in the soft rocks of coal measures. Ph.D. Thesis, University of Nothingam.
go back to reference Xie H, Pei J, Zuo J, Zhang R (2011) Investigation of mechanical properties of fractured marbles by uniaxial compression tests. J Rock Mech Geotech Eng 3(4):302–313 CrossRef Xie H, Pei J, Zuo J, Zhang R (2011) Investigation of mechanical properties of fractured marbles by uniaxial compression tests. J Rock Mech Geotech Eng 3(4):302–313 CrossRef
go back to reference Yagiz S (2011) P-wave velocity test for assessment of geotechnical properties of some rock materials. Bull Mater Sci 34(4):947 CrossRef Yagiz S (2011) P-wave velocity test for assessment of geotechnical properties of some rock materials. Bull Mater Sci 34(4):947 CrossRef
go back to reference Yasar E, Erdogan Y (2004) Correlating sound velocity with the density, compressive strength and Young’s modulus of carbonate rocks. Int J Rock Mech Min Sci 41(5):871–875 CrossRef Yasar E, Erdogan Y (2004) Correlating sound velocity with the density, compressive strength and Young’s modulus of carbonate rocks. Int J Rock Mech Min Sci 41(5):871–875 CrossRef
go back to reference Yilmaz I, Yuksek G (2009) Prediction of the strength and elasticity modulus of gypsum using multiple regression, ANN, and ANFIS models. Int J Rock Mech Min Sci 46(4):803–810 CrossRef Yilmaz I, Yuksek G (2009) Prediction of the strength and elasticity modulus of gypsum using multiple regression, ANN, and ANFIS models. Int J Rock Mech Min Sci 46(4):803–810 CrossRef
go back to reference Yilmaz I, Kaynar O (2011) Multiple regression, ANN (RBF, MLP) and ANFIS models for prediction of swell potential of clayey soils. Expert Syst Appl 38(5):5958–5966 CrossRef Yilmaz I, Kaynar O (2011) Multiple regression, ANN (RBF, MLP) and ANFIS models for prediction of swell potential of clayey soils. Expert Syst Appl 38(5):5958–5966 CrossRef
go back to reference Zukui L, Xinxu Z, Jinhai Z, Daixu T, Yongsong T, Jing Y, Yanqing L (2001) The experiment investigation of the correlation of acoustic logging and rock mechanical and engineering characteristics. Frontiers of Rock Mechanics and Sustainable Development in the 21st Century. Sijing, Bingiun, Zangkui (eds.), 89–92. Zukui L, Xinxu Z, Jinhai Z, Daixu T, Yongsong T, Jing Y, Yanqing L (2001) The experiment investigation of the correlation of acoustic logging and rock mechanical and engineering characteristics. Frontiers of Rock Mechanics and Sustainable Development in the 21st Century. Sijing, Bingiun, Zangkui (eds.), 89–92.
Metadata
Title
Development of Statistical Models to Predict the Mechanical Properties of Some Metamorphic Rocks from P-Wave Velocity and Certain Physical Properties
Authors
Hari Om Singh
Tariq Anwar Ansari
T. N. Singh
K. H. Singh
Publication date
27-05-2022
Publisher
Springer International Publishing
Published in
Geotechnical and Geological Engineering / Issue 8/2022
Print ISSN: 0960-3182
Electronic ISSN: 1573-1529
DOI
https://doi.org/10.1007/s10706-022-02155-0

Other articles of this Issue 8/2022

Geotechnical and Geological Engineering 8/2022 Go to the issue