SpringerLink
Log in

Soft computing approaches for evaluating the slake durability index of rocks

  • Original Paper
  • Published:
Arabian Journal of Geosciences Aims and scope Submit manuscript

Abstract

In this research, some predictive models were constructed for estimating the slake durability index of sedimentary rocks. Sandstone, limestone, travertine and conglomerate were collected as studied rocks, and comprehensive laboratory investigations such as mineralogical study and geotechnical properties including dry unit weight, porosity, Schmidt rebound hardness, P-wave velocity, uniaxial compressive strength and slake durability index were determined based on standard procedures. Results of mineralogy studies and XRD analysis showed studied rock samples are dominantly composed of quartz and calcite with different textures. The durability test, up to three cycles, was performed in fluids with different pH conditions. Based on the results, the slake durability index is affected by the pH of the test fluids, and in initial cycles, the decreasing rate of slake durability index is higher than the end cycles. Also, in most of the samples, a constant pattern exists between the slake durability index and pH of the testing solutions so that the weight loss increases with decreasing pH from 7 to 4. Soft computing techniques including multiple regression analysis (MRA), artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) were developed for estimating SDI for pH = 7 and 4 conditions. Experimental equations were obtained by MRA with correlation coefficients from 0.74 to 0.85 that show porosity, Schmidt hardness, P-wave velocity and UCS are the good parameters for estimating the SDI2 of rocks. In order to evaluate the performance of predictive models, some statistical coefficients, including R, RMSE, VAF, MAPE and PI were also calculated. ANFIS models have the best coefficients, and the results demonstrate that the ANN models are efficient when compared to MRA. Therefore, all methods obtained acceptable results, but the ANN and ANFIS are more reliable methods for estimating the SDI of rocks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Abbreviations

SS:

Sandstone sample

LS:

Limestone sample

TS:

Travertine sample

CS:

Conglomerate sample

γ dry :

Dry unit weight (g/cm3)

n :

Porosity (%)

H S :

Schmidt rebound hardness

V P :

Primary wave velocity (m/s)

UCS:

Uniaxial compressive strength (MPa)

SDI:

Slake-durability index (%)

XRD:

X-ray diffraction

MRA:

Multiple regression analysis

ANN:

Artificial neural network

ANFIS:

Adaptive neuro-fuzzy inference system

R :

Correlation coefficient

R 2 :

Coefficient of determination

RMSE:

Root mean square error

VAF:

Coefficient values account for

MAPE:

Mean absolute percentage error

PI:

Performance index

References

  • Abdullah GMS, El al AA, Radwan AE, Qadri T, Aly N (2022) The influence of carbonate texture and rock composition on durability cycles and geomechanical aspects of carbonate rocks. Acta Geotech. https://doi.org/10.1007/s11440-022-01561-1

    Article  Google Scholar 

  • Admassu Y, Hamdan H, Gautam T (2016) Multivariate statistical approach to re-evaluate the slake durability index test (ASTM 4644–08). Eng Geol 209:12–20

    Article  Google Scholar 

  • Afolagboye LO, Owoyemi OO, Akinola OO (2022) Effect of pH condition and different solution on the slake durability of granitic rocks. Geotech Geol Eng. https://doi.org/10.1007/s10706-022-02312-5

    Article  Google Scholar 

  • Ahmad M, Ansari MK, Singh R, Sharma LK, Singh TN (2017) Assessment of durability and weathering state of some igneous and metamorphic rocks using micropetrographic index and rock durability indicators: a case study. Geotech Geol Eng 35:827–842

    Article  Google Scholar 

  • Ahmed I, Basharat M, Sousa L, Mughal MS (2021) Evaluation of building and dimension stone using physico-mechanical and petrographic properties: a case study from the Kohistan and Ladakh batholith, Northern Pakistan. Environ Earth Sci 80. https://doi.org/10.1007/s12665-021-10007-y

  • Aladejare AE, Alofe ED, Onifade M, Lawal AI, Ozoji TM, Zhang Z (2021) Empirical estimation of uniaxial compressive strength of rock: database of simple, multiple, and artificial intelligence-based regressions. Geotech Geol Eng 39:4427–4455

    Article  Google Scholar 

  • Ankara H, Kandemir SY, Cicek C (2015) Compression of slake durability index (SDI) values of sphere and rounded marl samples. Procedia Earth Planet Sci 15:93–98

    Article  Google Scholar 

  • Arman H (2021) Correlation of uniaxial compressive strength with indirect tensile strength (Brazilian) and 2nd cycle of slake durability index for evaporitic rocks. Geotech Geol Eng 39:1583–1590

    Article  Google Scholar 

  • Arman H, Hussein S, Abouhaligah HEY, Osman M, Baloch MA, Hag DBA, Algaishi HAA (2019) Predicting weathering characteristics of carbonate rocks under different geo-environmental conditions. IOP Conf Ser: Earth Environ Sci 362:012016. https://doi.org/10.1088/1755-1315/362/1/012016

    Article  Google Scholar 

  • ASTM (1990) Standard test method for slake durability of shales and similar weak rocks (D4644). Annual Book of ASTM Standards, vol. 4.08. ASTM, Philadelphia

  • ASTM (1995) Standard test method for unconfined compressive strength of intact rock core specimens. ASTM standards on disc 04.08; Designation D2938

  • ASTM (1996) Standard test method for laboratory determination of pulse velocities and ultrasonic elastic constants of rock. Designation: D2845–D2895

  • ASTM (2001) Standard test method for determination of rock hardness by rebound hammer method. D5873 ASTM Philadelphia Pa

  • ASTM (2009) Standard guide for petrographic examination of dimension Stone (C1721). Book Standards, Vol 04.07

  • Bishop C (1995) Neural networks for pattern recognition. Oxford Press, New York

    Google Scholar 

  • Cargill JS, Shakoor A (1990) Evaluation of empirical methods for measuring the uniaxial compressive strength of rock. Int J Rock Mech Min Sci 27:495–503

    Article  Google Scholar 

  • Ceryan N (2021) Prediction of Young’s modulus of weathered igneous rocks using GRNN, RVM, and MPMR models with a new index. J Mt Sci 18:233–251

    Article  Google Scholar 

  • Cetin H, Laman M, Ertunc A (2000) Settlement and slaking problems in the world’s fourth largest rock-fill dam, the Ataturk Dam in Turkey. Eng Geol 56:225–242

    Article  Google Scholar 

  • Dhakal G, Yoneda T, Kato M, Kaneko K (2002) Slake durability and mineralogical properties of some pyroclastic and sedimentary rocks. Eng Geol 65:31–45

    Article  Google Scholar 

  • Diamantis K, Fereidooni D, Khajevand R, Migiros G (2021) Effect of textural characteristics on engineering properties of some sedimentary rocks. J Cent South Univ 28:926–938

    Article  Google Scholar 

  • Dunham RJ (1962) Classification of carbonate rocks according to depositional texture. Classification of carbonate rocks, WE Ham. AAPG Mem 1:108–121

    Google Scholar 

  • El Aal AA, Kahraman S (2017a) Estimation of durability aspects of Al Masjid Al-Haram marble, Makkah city, Saudi Arabia. Geotech Geol Eng 35:2763–2779

    Article  Google Scholar 

  • El Aal AA, Kahraman S (2017b) Indirect methods to predict the abrasion resistance and slake durability of marbles. J Molec Eng Mat 5(3):1–11

    Google Scholar 

  • Fereidooni D, Khajevand R (2018) Correlations between slake-durability index and engineering properties of some travertine samples under wetting-drying cycles. Geotech Geol Eng 36:1071–1089

    Google Scholar 

  • Fereidooni D, Khajevand R (2019) Utilization of the accelerated weathering test method for evaluating the durability of sedimentary rocks. Bull Eng Geol Environ 78:2697–2716

    Article  Google Scholar 

  • Folk RL (1959) Practical petrographic classification of limestones. Am Assoc Petrol Geol Bull 43:1–38

    Google Scholar 

  • Franklin JA, Chandra A (1972) The slake durability test. Int J Rock Mech Min Sci 9(1):325–341

    Article  Google Scholar 

  • Gamble JC (1971) Durability–plasticity classification of shales and other argillaceous rocks. Ph.D. Thesis, University of Illinois, Urabana

  • Gautam TP, Shakoor A (2016) Comparing the slaking of clay-bearing rocks under laboratory conditions to slaking under natural climatic conditions. Rock Mech Rock Eng 49:19–31

    Article  Google Scholar 

  • Ghobadi MH, Kapelehe M (2017) The influence of pH of water and chemical composition on the durability of different rocks from Qom formation, East and Northeast of Hamedan, Iran. J Eng Geol 10:3699–3718

    Article  Google Scholar 

  • Ghobadi MH, Momeni AA (2011) Assessment of granitic rocks degradability susceptive to acid solutions in urban area. Environ Earth Sci 65:753–760

    Article  Google Scholar 

  • Ghobadi MH, Mousavi S (2014) The effect of pH and salty solutions on durability of sandstones of the Aghajari Formation in Khouzestan province, southwest of Iran. Arab J Geosci 7:641–653

    Article  Google Scholar 

  • Goodman RE (1989) Introduction to rock mechanics, 2nd edn. John Wiley & Sons Publication, New York

    Google Scholar 

  • Gokceoglu C, Ulusay R, Sonmez H (2000) Factors affecting the durability of selected weak and clay-bearing rocks from Turkey, with particular emphasis on the influence of the number of drying and wetting cycles. Eng Geol 57:215–237

    Article  Google Scholar 

  • Gratchev I, Pathiranagei SV, Kim DH (2019) Strength properties of fresh and weathered rocks subjected to wetting-drying cycles. Geomech Geophys Geo-Energy Geo-Resour 5:211–221

    Article  Google Scholar 

  • GSI (Geological Society of Iran) (1977) Geological quadrangle map of Iran, No. 6862, Scale 1:100000, Printed by Offset Press Inc. Tehran

  • Gupta V, Ahmed I (2007) The effect of pH of water and mineralogical properties on the slake durability (degradability) of different rocks from the Lesser Himalaya, India. Eng Geol l 95:79–87

    Article  Google Scholar 

  • Gurney K (2009) An introduction to neural networks. UCL Press, New York

    Google Scholar 

  • Heidari M, Mohseni H, Jalali SH (2018) Prediction of uniaxial compressive strength of some sedimentary rocks by fuzzy and regression models. Geotech Geol Eng 36:401–412

    Article  Google Scholar 

  • Hemeda S, Pitilakis K (2010) Serapeum temple and the ancient annex daughter library in Alexandria, Egypt: geotechnical–geophysical investigations and stability analysis under static and seismic conditions. Eng Geol 113:33–43

    Article  Google Scholar 

  • IAEG (1979) Classification of rocks and soils for engineering geological map**, Report by the IAEG Commission on Engineering Geological Map**. Bulletin of IAEG 24:235–274

    Google Scholar 

  • IBM Corp. Released 2019 (2019) IBM SPSS Statistics for Windows, version 24.0. Armonk, NY: IBM Corp

  • ISRM (1979) Suggested method for determination of the slake durability index. Int J Rock Mech Min Sci Geomech Abstr 16:154–156

    Google Scholar 

  • ISRM (1981) Suggested methods for determining hardness and abrasiveness of rocks, Part 3. Commission on standardization of laboratory and field tests 101–112

  • ISRM (2007) The blue book: the complete ISRM suggested methods for rock characterization, testing and monitoring, 1974–2006, compilation arranged by the ISRM Turkish National Group, Ankara, Turkey, R. Ulusay and J. A. Hudson, Eds., Kazan Offset Press, Ankara

  • Jain AK, Jianchang M, Mohiuddin KM (1996) Artificial neural networks: a tutorial. Computer 29(3):1–44

    Article  Google Scholar 

  • Jang JSR (1993) ANFIS: adaptive network-based fuzzy inference systems. IEEE Trans Sys Man Cybern 23:665–685

    Article  Google Scholar 

  • Jensen LR, Friis H, Fundal E, Moller P, Jespersen M (2010) Analysis of limestone micromechanical properties by optical microscopy. Eng Geol 110(3):43–50

    Article  Google Scholar 

  • Johnson RB, DeGraff JV (1988) Principles of engineering geology. Wiley, New York, p 497

    Google Scholar 

  • Kahraman S, Fener M, Gunaydin O (2017) Estimating the uniaxial compressive strength of pyroclastic rocks from the slake durability index. Bull Eng Geol Environ 76:1107–1115

    Article  Google Scholar 

  • Kaunda R (2014) New artificial neural networks for true triaxial stress state analysis and demonstration of intermediate principal stress effects on intact rock strength. J Rock Mech Geotech Eng 6:338–347

    Article  Google Scholar 

  • Kayabali K, Beyaz T, Kolay E (2006) The effect of the pH of the testing liquid on the slake durability of gypsum. Bull Eng Geol Environ 65:65–71

    Article  Google Scholar 

  • 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 Infra Solu 4. https://doi.org/10.1007/s41062-019-0201-8

  • Khanlari GR, Heidari M, Noori M, Momeni A (2016) The effect of petrographic characteristics on engineering properties of conglomerates from famenin region, northeast of Hamedan, Iran. Rock Mech Rock Eng 49(7):2609–2621

    Article  Google Scholar 

  • Kolay E, Kayabali K, Tasdemir Y (2010) Modeling the slake durability index using regression analysis, artificial neural networks and adaptive neuro-fuzzy methods. Bull Eng Geol Environ 69:275–286

    Article  Google Scholar 

  • Koncagul EC, Santi PM (1999) Predicting the unconfined compressive strength of the Breathitt shale using slake durability, shore hardness and rock structural properties. Int J Rock Mech Min Sci 36:39–153

    Article  Google Scholar 

  • Koralegedara NH, Maynard JB (2017) Chemical, mineralogical and textural properties of the Kope Formation mudstones: how they affect its durability. Eng Geol 228:312–322

    Article  Google Scholar 

  • Kumar BR, Vardhan H, Govindaraj M, Vijay GS (2013) Regression analysis and ANN models to predict rock properties from sound levels produced during drilling. Int J Rock Mech Min Sci 58:61–72

    Article  Google Scholar 

  • Liu X, Song Y, **a Z, Chen R (2020) Assessing the slake durability of red stratum sandstone in different solution environments by a novel dual rotation test. Eng Geol 267. https://doi.org/10.1016/j.enggeo.2020.105503

  • MATLAB and Statistical Toolbox Released 2020b the MathWorks (2020), Inc., Natick, Massachusetts, United States

  • Meng J, Pan J (2007) Correlation between petrographic characteristics and failure duration in clastic rocks. Eng Geol 89:258–265

    Article  Google Scholar 

  • Mishra DA, Srigyan M, Basu A, Rokade PJ (2015) Soft computing methods for estimating the uniaxial compressive strength of intact rock from index tests. Int J Rock Mech Min Sci 80:418–424

    Article  Google Scholar 

  • Momeni A, Hashemi SS, Khanlari GR, Heidari M (2017) The effect of weathering on durability and deformability properties of granitoid rocks. Bull Eng Geol Environ 76(3):1037–1049

    Article  Google Scholar 

  • Monticelli JP, Ribeiro R, Futai M (2020) Relationship between durability index and uniaxial compressive strength of a gneissic rock at different weathering grades. Bull Eng Geol Environ 79:1381–1397

    Article  Google Scholar 

  • Moradian ZA, Ghazvinian AH, Ahmadi M, Behnia M (2010) Predicting slake durability index of soft sandstone using indirect tests. Int J Rock Mech Min Sci 47:666–671

    Article  Google Scholar 

  • Nielsen RH (1998) Neurocomputing: picking the human brain. IEEE Spectr 25:36–41

    Article  Google Scholar 

  • Rahimi MR, Mohammadi SD, Beydokhti AT (2020) Effects of mineral composition and texture on durability of sulfate rocks in Gachsaran Formation, Iran. Geotech Geol Eng 38:2619–2637

    Article  Google Scholar 

  • Selen L, Panthi KK, Vistnes G (2020) An analysis on the slaking and disintegration extent of weak rock mass of the water tunnels for hydropower project using modified slake durability test. Bull Eng Geol Environ 79:1919–1937

    Article  Google Scholar 

  • Sharma PK, Singh TN (2008) A correlation between P-wave velocity, impact strength index, slake durability index and uniaxial compressive strength. Bull Eng Geol Environ 67:17–22

    Article  Google Scholar 

  • Singh T, Sharma P, Khandelwal M (2007) Effect of pH on the physico-mechanical properties of marble. Bull Eng Geol Environ 66(1):81–87

    Article  Google Scholar 

  • Singh TN, Verma AK, Singh V, Sahu A (2005) Slake durability study of shaly rock and its predictions. Environ Geol 47:246–253

    Article  Google Scholar 

  • Sousa L, Menningen J, Lόpez-doncel R, Siegesmund S (2021) Petrophysical properties of limestone: influence on behaviour under different environmental conditions and applications. Environ Earth Sci 80. https://doi.org/10.1007/s12665-021-10064-3

  • Sousa L, Siegesmund S, Wedekind W (2018) Salt weathering in granitoids: an overview on the controlling factors. Environ Earth Sci 77. https://doi.org/10.1007/s12665-018-7669-y

  • Sousa LMO (2014) Petrophysical properties and durability of granites employed as building stone: a comprehensive evaluation. Bull Eng Geol Environ 73:569–588

    Article  Google Scholar 

  • Suparta W, Alhasa KM (2016) Modeling of precipitable water vapor using an adaptive neuro-fuzzy inference system in the absence of the GPS network. J App Meteo Climat 55(10):2283–2300

    Article  Google Scholar 

  • Takagi T, Sugeno M (1985) Fuzzy identification of systems and its application to modeling and control. IEEE Trans Syst Man Cybern 15(1):116–132

    Article  Google Scholar 

  • Tang H, Tan CK, Yi Z (2007) Neural networks: computational models and applications. Stud Com Intell 53. Springer, Berlin

  • Tang ZC, Zhang QZ, Zhang Y (2021) Cyclic drying-wetting effect on shear behaviors of red sandstone fracture. Rock Mech Rock Eng 54:2595–2613

    Article  Google Scholar 

  • Tasdemir Y, Kolay E, Kayabali K (2013) Comparison of three artificial neural network approaches for estimating of slake durability index. Environ Earth Sci 68:23–31

    Article  Google Scholar 

  • Wang T, Zhang H, Gamage RP, Zhao W, Ge J, Li Y (2020) The evaluation criteria for rock brittleness based on double-body analysis under uniaxial compression. Geomech Geophys Geo-Energ Geo-Resour 6:49. https://doi.org/10.1007/s40948-020-00165-x

    Article  Google Scholar 

  • Yagiz S (2011) Correlation between slake durability and rock properties for some carbonate rocks. Bull Eng Geol Environ 70:377–383

    Article  Google Scholar 

  • Yagiz S (2018) The effect of pH of the testing liquid on the degradability of carbonate rocks. Geotech Geol Eng 36:2351–2363

    Article  Google Scholar 

  • Yang Y, Zhang T (2022) Effects of water intrusion on thermal conductivity and durability of carbonaceous rocks. Soils Found 62. https://doi.org/10.1016/j.sandf.2021.101102

  • Yavuz AB, Kaputoglu SA, Çolak M, Tanyu BF (2017) Durability assessments of rare green andesites widely used as building stones in Buca (Izmir), Turkey. Environ Earth Sci 76:211–216

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Information Control 8(3):338–353

    Article  Google Scholar 

  • Zhu J, Deng H (2019) Durability classification of red beds rocks in central Yunnan based on particle size distribution and slaking procedure. J Mt Sci 16(3):714–724

    Article  Google Scholar 

Download references

Acknowledgements

The author likes to express his thanks to Mr. P. Khajevand for the English editing.

Author information

Authors and Affiliations

  1. School of Earth Science, Damghan University, Damghan, Semnan, Iran

    Reza Khajevand

Authors
  1. Reza Khajevand
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reza Khajevand.

Ethics declarations

Ethical approval

This article does not contain any studies with human participants.

Conflict of interest

The author declares no competing interests.

Additional information

Responsible Editor: Zeynal Abiddin Erguler

Highlights

• This study aims to evaluate the SDI of rocks in different pH conditions, including 7, 5.5 and 4, and assess the effect of petrography, physical and mechanical properties.

• Mineralogy and texture of the rocks were studied by thin section and XRD analysis; also, physical and mechanical properties including γdry, n, VP, HS and UCS were determined.

• The results indicated that the decreasing rate of SDI in the initial cycles is higher than the end cycles, and weight loss increases with decreasing the pH from 7 to 4.

• Proposed some experimental equations for estimating the SDI by multiple regression analysis for pH = 7 and 4 with correlation coefficients in the range of 0.74 to 0.85.

• Performance of MRA, ANN and ANFIS models was assessed by some statistical coefficients, including R, RMSE, VAF, MAPE and PI.

• The results indicated that the ANFIS models have the best coefficients and the ANN models are efficient when compared to MRA for estimating the SDI of the rocks.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khajevand, R. Soft computing approaches for evaluating the slake durability index of rocks. Arab J Geosci 15, 1698 (2022). https://doi.org/10.1007/s12517-022-10997-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12517-022-10997-4

Keywords

Search

Navigation