Skip to main content
SpringerLink
Log in

Thermomechanical behavior of granite under 150 °C: experimental and numerical analysis

  • Original Article
  • Published:
Materials and Structures Aims and scope Submit manuscript

Abstract

A good durability of concrete under nuclear conditions is essential for the safe operating of nuclear powerplants. In this case, concrete is generally exposed to a relatively high range of temperature compared to ordinary situations, and the understanding of its thermomechanical behavior becomes required for a fair safety assessment. To achieve this objective, the thermomechanical behavior of the concrete components should be understood. Among these components, this paper focuses on aggregates due to their high proportion in concrete and the high heterogeneity. A granite sample is selected, and it is composed of quartz, plagioclase, K-feldspar, biotite and some minor phases of muscovite, zircon, chlorite, and fluorite. The CTE according to three orthogonal directions is measured and small difference is observed. According to the XRCT examination, the samples do not show any visible cracks. However, some voids surrounding heavy phases are detected before the heating process. To identify these heavy phases, SEM–EDS is used, and some micro cracks have been detected and linked to biotite and pargasite. The numerical estimation of the average of the high and low bounds underestimates the CTE compared to the experimental value. It is consistent with the pre-damaged state providing a higher strain for an equivalent thermic stress. Two-phase model composed from an inclusion inside a predominant phase is used to calculate the hydrostatic pressure. The combinations giving high pressure allow to identify the zones of weakness in the granite. It also shows a higher probability of cracking for the biotite and pargasite inclusions inside quartz.

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

Access this article

Log in via an institution

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

Similar content being viewed by others

Abbreviations

BSW:

Biological shield wall

CBS:

Concrete biological shield

CTE:

Coefficient of thermal expansion

HCP:

Hardened cement paste

NPP:

Nuclear powerplant

PPL:

Plane polarized light

RIVE:

Radiation-induced volumetric expansion

RVE:

Representative volume element

VRH:

Voigt reuss hill

XPL:

Cross polarized light

XRCT:

X-ray computed tomography

\({D}_{i}\) :

The diameter of the phase i (μm)

\({K}_{i}\) :

The bulk modulus of the phase i (GPa)

\({\mathrm{\alpha }}_{i}\) :

Coefficient of thermal expansion of the phase i (10–6/ °C)

\({\Phi }_{i}\) :

The volume fraction of the phase i

\(\Delta T\) :

The temperature increment (°C)

GoF:

Goodness of Fit defined as the ratio of Rwp and Rexp

Rexp :

The Expected R-factor corresponding to the best possible Rwp

RWP :

The Weighted Profile R-factor

References

  1. Naus DJ (2012) “Concrete,” in Comprehensive Nuclear Materials, pp. 407–431

  2. Samouh H, Soive A, Rozière E, Loukili A (2016) Experimental and numerical study of size effect on long-term drying behavior of concrete: influence of drying depth. Mater Struct 49(10):4029–4048

    Google Scholar 

  3. Samouh H, Rozière E, Wisniewski V, Loukili A (2017) Consequences of longer sealed curing on drying shrinkage, cracking and carbonation of concrete. Cem Concr Res 95:117–131

    Google Scholar 

  4. van Aardt JHP, Visser S (1977) Formation of hydrogarnets: Calcium hydroxide attack on clays and feldspars. Cem Concr Res 7(1):39–44

    Google Scholar 

  5. van Aardt JHP, Visser S (1977) Calcium hydroxide attack on feldspars and clays: possible relevance to cement-aggregate reactions. Cem Concr Res 7(6):643–648

    Google Scholar 

  6. Rymes J et al (2019) Long-term material properties of a thick concrete wall exposed to ordinary environmental conditions in a nuclear reactor building:the contribution of cement hydrates and feldspar interaction. J Adv Concr Technol 17(May):195–215

    Google Scholar 

  7. Samouh H, Rozière E, Loukili A (2018) Shape effect on drying behavior of cement-based materials: mechanisms and numerical analysis. Cem Concr Res 110(May):42–51

    Google Scholar 

  8. Samouh H, Rozière E, Loukili A (2017) The differential drying shrinkage effect on the concrete surface damage: experimental and numerical study. Cem Concr Res 102(December):212–224

    Google Scholar 

  9. Samouh H, Rozière E, Loukili A (2019) Experimental and numerical study of the relative humidity effect on drying shrinkage and cracking of self-consolidating concrete. Cem Concr Res 115(January):519–529

    Google Scholar 

  10. Maruyama I, Sasano H, Nishioka Y, Igarashi G (2014) Strength and Young’s modulus change in concrete due to long-term drying and heating up to 90°c. Cem Concr Res 66:48–63

    Google Scholar 

  11. Rozière E, Loukili A, El Hachem R, Grondin F (2009) Durability of concrete exposed to leaching and external sulphate attacks. Cem Concr Res 39(12):1188–1198

    Google Scholar 

  12. Rozière E, Loukili A, Cussigh F (2009) A performance based approach for durability of concrete exposed to carbonation. Constr Build Mater 23(1):190–199

    Google Scholar 

  13. Fillmore DL (2004) “Literature review of the effects of radiation and temperature on the aging of concrete,”

  14. Hilsdorf H, Kropp J, Koch H (1978) The effects of nuclear radiation on the mechanical properties of concrete. ACI Sp 55:223–251

    Google Scholar 

  15. Rosseel TM et al (2016) Review of the current state of knowledge on the effects of radiation on concrete. J Adv Concr Technol 14(7):368–383

    Google Scholar 

  16. Field KG, Remec I, Le Pape Y (2015) Radiation effects in concrete for nuclear power plants - Part I: quantification of radiation exposure and radiation effects. Nucl Eng Des 282:126–143

    Google Scholar 

  17. Kontani O, Sawada S, Maruyama I, Takizawa M, Sato O (2013) “Evaluation of irradiation effects on concrete structure-Gamma-ray irradiation tests on cement paste-,” in Proceedings of the ASME 2013 Power Conference POWER2013, Boston, Massachusetts, USA

  18. Golewski GL (2018) Evaluation of morphology and size of cracks of the interfacial transition zone (ITZ) in concrete containing fly ash (FA). J Hazard Mater 357:298–304

    Google Scholar 

  19. Akçaoǧlu T, Tokyay M, Çelik T (2005) Assessing the ITZ microcracking via scanning electron microscope and its effect on the failure behavior of concrete. Cem Concr Res 35(2):358–363

    Google Scholar 

  20. Maruyama I, Sasano H, Lin M (2016) Impact of aggregate properties on the development of shrinkage-induced cracking in concrete under restraint conditions. Cem Concr Res 85:82–101

    Google Scholar 

  21. Igarashi G, Maruyama I, Nishioka Y, Yoshida H (2015) Influence of mineral composition of siliceous rock on its volume change. Constr Build Mater 94:701–709

    Google Scholar 

  22. Maruyama I, Muto S (2016) Change in relative density of natural rock minerals due to electron irradiation. J Adv Concr Technol 14(11):706–716

    Google Scholar 

  23. Vu NL et al (2020) (2020) “Swelling of alpha-quartz induced by MeV ions irradiation: critical dose and swelling mechanism.” J Nucl Mater 539:152266

    Google Scholar 

  24. Luu VN et al (2021) Changes in properties of alpha-quartz and feldspars under 3 MeV Si-ion irradiation. J Nucl Mater 545:152734

    Google Scholar 

  25. Maruyama I et al (2017) Development of soundness assessment procedure for concrete members affected by neutron and gamma-ray irradiation. J Adv Concr Technol 15(9):440–523

    Google Scholar 

  26. Ishikawa S, Maruyama I, Takizawa M, Etoh J, Kontani O, Sawada S (2019) Hydrogen production and the stability of hardened cement paste under gamma irradiation. J Adv Concr Technol 17(12):673–685

    Google Scholar 

  27. Maruyama I et al (2017) Impact of gamma-ray irradiation on hardened white Portland cement pastes exposed to atmosphere. Cem Concr Res 108:59–71

    Google Scholar 

  28. Maruyama I, Igarashi G (2015) Numerical approach towards aging management of concrete structures: material strength evaluation in a massive concrete structure under one-sided heating. J Adv Concr Technol 13(11):500–527

    Google Scholar 

  29. Maruyama I, Igarashi G (2014) Cement reaction and resultant physical properties of cement paste. J Adv Concr Technol 12(6):200–213

    Google Scholar 

  30. Krishnan NMA, Le Pape Y, Sant G, Bauchy M (2018) Effect of irradiation on silicate aggregates’ density and stiffness. J Nucl Mater 512:126–136

    Google Scholar 

  31. Maruyama I, Lura P (2019) “Properties of early-age concrete relevant to cracking in massive concrete,” Cem Concr Res, 123, p. 105770

  32. Mindess S, Young JF, Darwin D (2002) Concrete

  33. Plevova E, Vaculikova L, Kozusnikova A, Ritz M, Simha MG (2016) Thermal expansion behaviour of granites. J Therm Anal Calorim 123(2):1555–1561

    Google Scholar 

  34. Zhao P, Feng ZJ (2019) Thermal deformation of granite under different temperature and pressure pathways. Adv Mater Sci Eng. https://doi.org/10.1155/2019/7869804

    Article  Google Scholar 

  35. Hockman A, Kessler DW (1934) Thermal and moisture expansion studies of some domestic granites. J Res Natl Bur Stand 44(4):395–410

    Google Scholar 

  36. Wong T-F, Brace WF (1979) Thermal expansion of rocks: some measurements at high pressure. Tectonophysics 57(2–4):95–117

    Google Scholar 

  37. Hobbs DW (1971) The dependence of the bulk modulus, Young’s modulus, creep, shrinkage and thermal expansion of concrete upon aggregate volume concentration. Matériaux Constr 4(2):107–114

    Google Scholar 

  38. CEN- EN 12407(2019) Natural stone test methods—Petrographic examination

  39. Larrea ML, Martig SR, Castro SM, Aliani PA, Bjerg EA, “Rock.AR—a point counting application for petrographic Thin Sections.”

  40. Electric Power Research Institute (2016) “Long-term operations: impact of radiation heating on pwr biological shield concrete, EPRI Report 3002008129,”

  41. Bruck PM, Esselman TC, Elaidi BM, Wall JJ, Wong EL (2019) Structural assessment of radiation damage in light water power reactor concrete biological shield walls. Nucl Eng Des 350(February):9–20

    Google Scholar 

  42. Osnes JD, Coates GK, Delong KB, Loken MC, WagnerRA (1984) “Expected repository environments in granite: Thermal environment,”

  43. Van der Molen I (1981) The shift of the α-β transition temperature of quartz associated with the thermal expansion of granite at high pressure. Tectonophysics 73(4):323–342

    Google Scholar 

  44. Sprunt ES, Brace WF (1974) Direct observation of microcavities in crystalline rocks. Int J Rock Mech Min Sci 11(4):139–150

    Google Scholar 

  45. Samouh H et al (2021) Modal analysis of rock forming minerals: contribution of XRD/rietveld analysis compared to the classic point counting method. J Adv Concr Technol 19(5):395–413

    Google Scholar 

  46. Lin W (2002) Permanent strain of thermal expansion and thermally induced microcracking in Inada granite. J Geophys Res Solid Earth. https://doi.org/10.1029/2001JB000648

    Article  Google Scholar 

  47. Homand-Etienne F, Houpert R (1989) Thermally induced microcracking in granites: characterization and analysis. Int J Rock Mech Min Sci 26(2):125–134

    Google Scholar 

  48. Vázquez P, Shushakova V, Gómez-Heras M (2015) Influence of mineralogy on granite decay induced by temperature increase: Experimental observations and stress simulation. Eng Geol 189:58–67

    Google Scholar 

  49. Calleja L, Ruiz De Argandoña VM (1985) Variación de la expansión térmica en rocas cristalinas. Trab Geol 15(12):307–315

    Google Scholar 

  50. Richter D, Simmons G (1974) Thermal expansion behavior of igneous rocks. Int J Rock Mech Min Sci 11(10):403–411

    Google Scholar 

  51. Walsh JB, Decker ER (1966) Effect of pressure and saturating fluid on the thermal conductivity of compact rock. J Geophys Res 71(12):3053–3061

    Google Scholar 

  52. Adams LH, Williamson ED (1923) On the compressibility of minerals and rocks at high pressures. J Franklin Inst 195(4):475–529

    Google Scholar 

  53. Wanne TS, Young RP (2008) Bonded-particle modeling of thermally fractured granite. Int J Rock Mech Min Sci 45(5):789–799

    Google Scholar 

  54. Huotari T, Kukkonen I (2004) “Thermal expansion properties of rocks:Literature survey and estimation of thermal expansion coefficient for Olkiluoto Mica Gneiss,”

  55. Adie AJ (1835) On the expansion of different kinds of stone from an increase of temperature with a description of the pyrometer used in making experiments. Prog Civ Eng 24(3):200–211

    Google Scholar 

  56. Dwivedi RD, Goel RK, Prasad VVR, Sinha A (2008) Thermo-mechanical properties of Indian and other granites. Int J Rock Mech Min Sci 45(3):303–315

    Google Scholar 

  57. Ramana YV, Sarma LP (1980) Thermal expansion of a few Indian granitic rocks. Phys Earth Planet Inter 22(1):36–41

    Google Scholar 

  58. Heyliger P, Ledbetter H, Kim S (2003) Elastic constants of natural quartz. J Acoust Soc Am 114(2):644–650

    Google Scholar 

  59. Brown JM (2015) Determination of Hashin-Shtrikman bounds on the isotropic effective elastic moduli of polycrystals of any symmetry. Comput Geosci 80:95–99

    Google Scholar 

  60. Angel RJ, Zhao J, Kaminsky W, Ross N, Waeselmann N, Brown JM (2016) The elastic tensor of monoclinic alkali feldspars. Am Mineral 101(5):1228–1231

    Google Scholar 

  61. Alexandrov (1974) “Microcline,” [Online]. Available: http://www.gm.univ-montp2.fr/PERSO/mainprice/W_data/CareWare_Unicef_Databases/MTEX_Elastic_Tensor_Files/Microcline_1974.m

  62. Moos D, Dvorkin J (1997) Application of theoretically derived rock physics relationships for clastic rocks to log data from the Wilmington Field, CA. Geophys Res Lett 24(3):329–332

    Google Scholar 

  63. Comboni D, Lotti P, Gatta GD, Merlini M, Liermann HP, Frost DJ (2018) Pargasite at high pressure and temperature. Phys Chem Miner 45(3):259–278

    Google Scholar 

  64. Roberts RB, White GK (1986) Thermal expansion of fluorites at high temperatures. J Phys C Solid State Phys 19(36):7167–7172

    Google Scholar 

  65. Speziale S, Duffy TS (2002) Single-crystal elastic constants of fluorite (CaF2) to 9.3 GPa. Phys Chem Miner 29(7):465–472

    Google Scholar 

  66. Peter Watt J (1987) POLYXSTAL a FORTRAN program to calculate average elastic properties of minerals from single-crystal elasticity data. Comput Geosci. https://doi.org/10.1016/0098-3004(87)90050-1

    Article  Google Scholar 

  67. Zanazzi P, Francesco Comodi P, Nazzareni S, Andreozzi G (2009) Thermal behaviour of chlorite: an in situ single-crystal and powder diffraction study. Eur J Mineral. https://doi.org/10.1127/0935-1221/2009/0021-1928

    Article  Google Scholar 

  68. Mookherjee M, Mainprice D (2014) Unusually large shear wave anisotropy for chlorite in subduction zone settings. Geophys Res Lett 10(April):1506–1513

    Google Scholar 

  69. Subbarao EC, Agrawal DK, McKinstry HA, Sallese CW, Roy R (1990) Thermal expansion of compounds of zircon structure. J Am Ceram Soc 73(5):1246–1252

    Google Scholar 

  70. Momenzadeh L, Belova IV (2020) Murch GE (2019) “Prediction of the lattice thermal conductivity of zircon and the cubic and monoclinic phases of zirconia by molecular dynamics simulation.” Comput Mater Sci 176:109522

    Google Scholar 

  71. Bruner WM (1979) Crack growth and the thermoelastic behaviour of rocks. J Geophys Res 84(B10):5578–5590

    Google Scholar 

  72. Thirumalai K, Demou SG (1974) Thermal expansion behavior of intact and thermally fractured mine rocks. AIP Conf Proc 17(60):60–71

    Google Scholar 

  73. Cooper HW, Simmons G (1977) The effect of cracks on the thermal expansion of rocks. Earth Planet Sci Lett 36(3):404–412

    Google Scholar 

  74. Wang F, Konietzky H (2019) Thermo-mechanical properties of granite at elevated temperatures and numerical simulation of thermal cracking. Rock Mech Rock Eng 52(10):3737–3755

    Google Scholar 

  75. Subbarao EC, Gokhale KVGK (1968) Thermal expansion of zircon. Jpn J Appl Phys 7:1126

    Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the support of Ministry of Economy, Trade, and Industry (METI) in Japan, through the Japan Concrete Aging Management Program on Irradiation Effects (JCAMP).

Funding

Ministry of Economy,Trade,and Industry (METI) in Japan,Japan Concrete Aging Management Program on Irradiation Effects (JCAMP).

Author information

Authors and Affiliations

  1. Department of Environmental Engineering and Architecture, Nagoya University, Nagoya, Japan

    Hamza Samouh & Ippei Maruyama

  2. Kajima Corporation, Tokyo, Japan

    Shunsuke Ishikawa

  3. Nuclear Power Department, Kajima Corporation, Tokyo, Japan

    Osamu Kontani

  4. Nagaoka University of Technology, Nagaoka, Niigata, Japan

    Kenta Murakami

  5. Aichi University, Nagoya, Japan

    Shoji Nishimoto

  6. Mitsubishi Research Institute, Inc, Tokyo, Japan

    Kiyoteru Suzuki

  7. Department of Architecture, The University of Tokyo, Tokyo, Japan

    Ippei Maruyama

Authors
  1. Hamza Samouh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shunsuke Ishikawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Osamu Kontani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kenta Murakami
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shoji Nishimoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Kiyoteru Suzuki
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Ippei Maruyama
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hamza Samouh.

Ethics declarations

Conflicts of interest

The authors declared that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Samouh, H., Ishikawa, S., Kontani, O. et al. Thermomechanical behavior of granite under 150 °C: experimental and numerical analysis. Mater Struct 54, 239 (2021). https://doi.org/10.1617/s11527-021-01830-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1617/s11527-021-01830-7

Keywords

Search

Navigation