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Variability of intact rock mechanical properties for some metamorphic rock types and its implications on the number of test specimens

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Abstract

Intact rock strength and stiffness properties are commonly used in rock mass mechanical characterization, and their evaluation is usually based on laboratory tests. Due to the variability that affects strength and stiffness parameters, the determination of the number of laboratory-tested specimens required to obtain a reliable reference value is very useful. However, many studies reported in apposite literature focused only on the variability of strength parameters. This study investigates the variability of some of the most important strength and stiffness properties (unconfined compressive strength, indirect tensile strength, tangent and secant Young’s moduli, Poisson’s ratio) by applying statistical methods (statistical decision theory and statistical inference theory). A data set of 451 laboratory tests was used, performed on three rock types. The statistical analyses were applied with the aim of assessing how closely intact rock laboratory data follow a normal distribution and determining the minimum number of specimens required to obtain a reliable average value of the parameters in relation to a targeted precision index for a confidence level of 95 %. The results indicate that the minimum number of samples needed varies depending on rock and test types. Among the stiffness properties, tangent Young’s modulus has a lower variability than both the secant modulus and the Poisson’s ratio, whereas in terms of strength parameters, unconfined compressive strength is subject to greater variability than indirect tensile strength.

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Abbreviations

χ 2α :

Chi-squared tabulated critical value

χ 2 :

Chi-squared calculated value

α:

Significance level

f o :

Observed frequency

f e :

Theoretical or expected frequency

k :

Number of intervals or classes

m :

Number of the normal statistical distribution parameters calculated from the sample

df :

Degrees of freedom

n :

Sample size

μ:

Population mean

σ :

Population standard deviation

S :

Sample standard deviation

\( \bar{X} \) :

Sample mean

t β :

Student’s t distribution confidence coefficient

λ:

Student’s t distribution number of degrees of freedom

p :

Precision index

N :

Minimum number of specimens

σ c :

Unconfined compressive strength

σ t :

Indirect tensile strength

E t :

Tangent Young’s modulus

E s :

Secant Young’s modulus

v :

Poisson’s ratio

References

  • Al-Shayea NA (2004) Effects of testing methods and conditions on the elastic properties of limestone rock. Eng Geol 74:139–156. doi:10.1016/j.enggeo.2004.03.007

    Article  Google Scholar 

  • ASTM (1993) Soil and rock. Annual Book of ASTM Standards, 4.08, Philadelphia, Pennsylvania

  • ASTM (2001) American Society for Testing and Materials. ASTM Standards on Disc, 04.08. West Conshohocken, PA

  • ASTM (2003) E122-00 standard practice for calculating sample size to estimate, with a specified tolerable error, the average for characteristic of a lot or process. Book of Standards 14.02:27–31

  • British Standard Institution (1981) Code of practice for site investigations, BS 5930 HMSO, London

  • Cai M, Kaiser PK, Uno H, Tasaka Y, Minami M (2004) Estimation of rock mass deformation modulus and strength of jointed hard rock masses using the GSI system. Int J Rock Mech Min Sci 41:3–19. doi:10.1016/S1365-1609(03)00025-X

    Article  Google Scholar 

  • Duzgun HSB, Yucemen MS, Karpuz C (2002) A probabilistic model for the assessment of uncertainties in the shear strength of rock discontinuities. Int J Rock Mech Min Sci 39:743–754. doi:10.1016/S1365-1609(02)00050-3

    Article  Google Scholar 

  • Gercek H (2007) Poisson’s ratio values for rocks. Int J Rock Mech Min Sci 44:1–13. doi:10.1016/j.ijrmms.2006.04.011

    Article  Google Scholar 

  • Gill DE (1963) Uniaxial compression as an element in a classification of rocks. ME Thesis, McGill University

  • Gill DE, Corthésy R, Leite MH (2005a) Determining the minimal number of specimens for laboratory testing of rock properties. Eng Geol 78:29–51. doi:10.1016/j.enggeo.2004.10.005

    Article  Google Scholar 

  • Gill DE, Corthésy R, Leite MH (2005b) A statistical approach for determining practical rock strength and deformability values from laboratory tests. Eng Geol 78:53–67. doi:10.1016/j.enggeo.2004.10.006

    Article  Google Scholar 

  • Gokceoglu C, Sonmez H, Kayabasi A (2003) Predicting the deformation moduli of rock masses. Int J Rock Mech Min Sci 40:701–710. doi:10.1016/S1365-1609(03)00062-5

    Article  Google Scholar 

  • Grasso P, Xu S, Mahtab MA (1992) Problems and promises of index testing of rocks. In: Tillerson Wawersik (ed) Rock mechanics. Balkema, Rotterdam, pp 879–888

    Google Scholar 

  • Hawkins AB (1998) Aspects of rock strength. Bull Eng Geol Env 57:17–30. doi:10.1007/s100640050017

    Article  Google Scholar 

  • Hoek E (1998) Reliability of Hoek-Brown estimates of rock mass properties and their impact on design. Int J Rock Mech Min Sci 35:63–68. doi:10.1016/S0148-9062(97)00314-8

    Article  Google Scholar 

  • Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci Geomech Abstr 34:1165–1186. doi:10.1016/S1365-1609(97)80069-X

    Article  Google Scholar 

  • Hsu SC, Nelson PP (2002) Characterization of eagle ford shale. Eng Geol 67:169–183. doi:10.1016/S0013-7952(02)00151-5

    Article  Google Scholar 

  • ISRM (1978) Suggested method for petrographic description of rocks. Int J Rock Mech Min Sci 15:43–45

    Article  Google Scholar 

  • ISRM (1979) Suggested method for determining the uniaxial compressive strength and deformability of rock materials. Int J Rock Mech Min Sci Geomech Abs 16:135–140

    Google Scholar 

  • ISRM (1981) Brown ET (ed) Suggested methods for rock characterization, testing and monitoring. Pergamon Press, Oxford

  • Kim K, Gao H (1995) Probabilistic approaches to estimating variation in the mechanical properties of rock masses. Int J Rock Mech Min Sci Geomech Abstr 32:111–120. doi:10.1016/0148-9062(94)00032-X

    Article  Google Scholar 

  • Lama RD, Vutukuri VS (1978) Handbook on mechanical properties of rocks. Trans Tech Publications, Clausthal

    Google Scholar 

  • Liu H, Kou S, Lindqvist P (2005) Microscope rock texture characterization and simulation of rock aggregates properties. Project report SGU, Geological Survey of Sweden Project. pp 60–1362

  • Martínez-Martínez J, Benavente D, García-del-Cura MA (2011) Spatial attenuation: the most sensitive ultrasonic parameter for detecting petrographic features and decay processes in carbonate rocks. Eng Geol 119:84–95. doi:10.1016/j.enggeo.2011.02.002

    Article  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 Env 71:263–268. doi:10.1007/s10064-011-0399-y

    Article  Google Scholar 

  • Orr TLL (2000) Selection of characteristic values and partial factors in geotechnical designs to Eurocode 7. Comput Geotech 26:263–279. doi:10.1016/S0266-352X(99)00042-7

    Article  Google Scholar 

  • Pincus HJ (2003) Goodness of fit of six probability functions to some commonly used properties of rock. In: Proceedings of the 39th US Rock Mechanics Symposium, vol 2, pp 2757–2764

  • Přikryl R (2001) Some microstructural aspects of strength variation in rocks. Int J Rock Mech Min Sci 38:671–682. doi:10.1016/S1365-1609(01)00031-4

    Article  Google Scholar 

  • Přikryl R (2006) Assessment of rock geomechanical quality by quantitative rock fabric coefficients: limitations and possible source of misinterpretations. Eng Geol 87:149–162. doi:10.1016/j.enggeo.2006.05.011

    Article  Google Scholar 

  • Ruffolo MR, Shakoor A (2009) Variability of unconfined compressive strength in relation to number of test samples. Eng Geol 108:16–23. doi:10.1016/j.enggeo.2009.05.011

    Article  Google Scholar 

  • Sari M (2009) The stochastic assessment of strength and deformability characteristic for a pyroclastic rock mass. Int J Rock Mech Min Sci 46:613–626. doi:10.1016/j.ijrmms.2008.07.007

    Article  Google Scholar 

  • Sari M (2012) An improved method of fitting experimental data to the Hoek-Brown failure criterion. Eng Geol 127:27–35. doi:10.1016/j.enggeo.2011.12.011

    Article  Google Scholar 

  • Sari M (2015) Incorporating variability and/or uncertainty of rock mass properties into GSI and RMi systems using Monte Carlo method. In: Lollino G. et al. (ed) Engineering geology for society and territory. Springer International Publishing, pp 843–849. doi: 10.1007/978-3-319-09060-3_152

  • Sari M, Karpuz C (2006) Rock variability and establishing confining pressure levels for triaxial tests on rocks. Int J Rock Mech Min Sci 43:328–335. doi:10.1016/j.ijrmms.2005.06.010

    Article  Google Scholar 

  • Sonmez H, Gokceoglu C, Ulusay R (2004) Indirect determination of the modulus of deformation of rock masses based on GSI system. Int J Rock Mech Min Sci 41:849–857. doi:10.1016/j.ijrmms.2003.01.006

    Article  Google Scholar 

  • Spiegel MR, Stephens LJ (2008) Theory and problems of statistics, 4th edn. McGraw-Hill Inc, London

    Google Scholar 

  • Tandon RS, Gupta V (2013) The control of mineral constituents and textural characteristics on the petrophysical and mechanical (PM) properties of different rocks of the Himalaya. Eng Geol 153:125–143. doi:10.1016/j.enggeo.2012.11.005

    Article  Google Scholar 

  • Thuro K, Plinninger RJ, Zäh S, Schütz S (2001) Scale effects in rock strength properties. Part 1: unconfined compressive test and Brazilian test. In: ISRM regional symposium, EUROCK 2001, Rock mechanics—a challenge for society, Finland, pp 169–174

  • Yamaguchi U (1970) The number of test-pieces required to determine strength of rock. Int J Rock Mech Min Sci Geomech Abstr 7:209–227. doi:10.1016/0148-9062(70)90013-6

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank Salini-Impregilo S.p.A. and the Servizi Geotecnici Liguri S.r.l. Soil and rock mechanics laboratory staff (Vado Ligure, Italy) for providing the intact rock data. The authors also wish to thank the two anonymous referees for comments and suggestions that improved this paper.

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Authors and Affiliations

  1. Department of Earth, Environmental and Life Sciences, University of Genoa, Corso Europa 26, 16132, Genoa, Italy

    Giacomo Pepe, Andrea Cevasco & Laura Gaggero

  2. Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via Montallegro 1, 16145, Genoa, Italy

    Riccardo Berardi

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  1. Giacomo Pepe
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  2. Andrea Cevasco
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  3. Laura Gaggero
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Correspondence to Giacomo Pepe.

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Pepe, G., Cevasco, A., Gaggero, L. et al. Variability of intact rock mechanical properties for some metamorphic rock types and its implications on the number of test specimens. Bull Eng Geol Environ 76, 629–644 (2017). https://doi.org/10.1007/s10064-016-0912-4

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  • DOI: https://doi.org/10.1007/s10064-016-0912-4

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