On the Thermal Stresses Due to Weathering in Natural Stones
Abstract
:1. Introduction
2. Fundamentals and Methodology
2.1. Solar Radiation
2.2. Heat Flux
2.3. Inner Temperature
2.4. Induced Thermal Stresses
2D Formulation
3. Results and Discussion
3.1. Temperature
3.2. Stresses Due to Daily Variation of Temperature
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
diffuse air mass | - | |
B | building plan width | (m) |
c | constant | - |
clock time | (h) | |
d | declination angle | (C) |
correction for daylight savings time | (h) | |
E | Young’s modulus | (GPa) |
equation of time | (minutes) | |
Grashof number | - | |
h | hour angle | () |
convection heat-transfer coefficient for inside surface | (W/m·K) | |
convection heat-transfer coefficient for outside surface | (W/m·K) | |
extraterrestrial radiant flux | (W/m) | |
diffuse horizontal irradiance | (W/m) | |
solar constant | (W/m) | |
diffuse solar radiation | (W/m) | |
direct solar radiation | (W/m) | |
reflected solar radiation | (W/m) | |
total solar radiation | (W/m) | |
k | thermal conductivity | (K/m·K) |
air thermal conductivity | (K/m·K) | |
l | latitude | () |
building plan length | (m) | |
L | thickness of material | (m) |
equivalent length | (m) | |
longitude | () | |
standard meridian for the local time zone | (W/m) | |
local solar time | (h) | |
m | air mass | - |
Fourier coefficient | (C) | |
n | day of the year | - |
n | constant | - |
Fourier coefficient | (C) | |
Nusselt number | - | |
Prandtl number | - | |
convection flux | (W/m) | |
solar radiation flux | (W/m) | |
gray body radiation flux | (W/m) | |
Reynolds number | - | |
T | period of a periodic function | (h) |
outside dry-bulb temperature | (C) | |
sol-air temperature | (C) | |
harmonic coefficient | (C) | |
mean value of sol-air temperature | (C) | |
indoor dry-bulb temperature | (C) | |
wall surface temperature | (C) | |
inside wall surface temperature | (C) | |
U | heat transmission coefficient | (W/m·C) |
universal coordinated time | (h) | |
factor | (W/m·C) | |
Y | correction factor of the direct solar radiation | - |
factor | - | |
factor | - | |
dimensionless thickness | - | |
thermal expansion coefficient | (m/s) | |
solar absorptivity | - | |
angle of incidence | () | |
time | (h) | |
temperature | () | |
wind direction | (m/s) | |
beam optical depths | - | |
diffuse optical depths | - | |
solar altitude | () | |
surface–solar azimuth angle | () | |
angular correction | () | |
azimuth angle | () | |
surface azimuth | () | |
angle | () | |
viscosity | (Pa·s) | |
surface emissivity | - | |
angular velocity | (rad/h) | |
Stefan–Boltzmann constant | (W/m·K) | |
factor | (m) | |
normal stress in y direction | (kPa) | |
infrared radiation correction factor | (W/m) | |
surface tilt angle | () | |
temperature function | - | |
lag angle | () | |
Poisson’s ratio | - |
Appendix A
Time | Wind Velocity (m/s) | Wind Direction | Relative Humidity (%) |
---|---|---|---|
23:50 | 2.04 | SSW | 82 |
0:50 | 1.53 | Variable | 82 |
1:50 | 0 | - | 82 |
2:50 | 0 | - | 82 |
3:50 | 0 | - | 77 |
4:50 | 2.55 | S | 82 |
5:50 | 1.02 | Variable | 82 |
6:50 | 2.04 | SSW | 82 |
7:50 | 2.55 | SSW | 82 |
8:50 | 1.02 | Variable | 56 |
9:50 | 0.51 | Variable | 46 |
10:50 | 2.55 | NE | 50 |
11:50 | 6.12 | NE | 60 |
12:50 | 6.12 | NNE | 64 |
12:55 | 7.14 | N | 63 |
13:10 | 10.2 | W | 67 |
13:18 | 7.14 | NNW | 87 |
13:50 | 5.1 | N | 93 |
14:26 | 2.55 | SSW | 87 |
14:50 | 1.53 | Variable | 82 |
15:50 | 3.06 | NNW | 72 |
16:50 | 4.08 | NNW | 59 |
17:50 | 1.02 | Variable | 59 |
18:50 | 1.53 | Variable | 63 |
19:50 | 0 | - | 67 |
20:50 | 1.53 | Variable | 72 |
21:50 | 1.53 | Variable | 77 |
22:50 | 0.51 | Variable | 82 |
23:50 | 0 | - | 82 |
References
- Bedon, C.; Zhang, X.; Santos, F.; Honfi, D.; Kozłowski, M.; Arrigoni, M.; Figuli, L.; Lange, D. Performance of structural glass facades under extreme loads—Design methods, existing research, current issues and trends. Constr. Build. Mater. 2018, 163, 921–937. [Google Scholar] [CrossRef]
- Friedrich, D. Effects from natural weathering on long-term structural performance of wood-polymer composite cladding in the building envelope. J. Build. Eng. 2019, 23, 68–76. [Google Scholar] [CrossRef]
- Hawila, A.A.W.; Merabtine, A.; Troussier, N.; Bennacer, R. Combined use of dynamic building simulation and metamodeling to optimize glass facades for thermal comfort. Build. Environ. 2019, 157, 47–63. [Google Scholar] [CrossRef]
- Hua, L.; Shen, J.; Chena, Y.; Lan, Q.; Liu, J. Wipe-on and durable self-cleaning coating for glass facade. Thin Solid Film. 2020, 697. [Google Scholar] [CrossRef]
- Alenka, M.; Tadeja, M.; Ana, M. 3D visualization and quantification of bowing marble microstructure. Constr. Build. Mater. 2009, 23, 2380–2385. [Google Scholar] [CrossRef]
- Marini, P.; Bellopede, R. Bowing of marble slabs: Evolution and correlation with mechanical decay. Constr. Build. Mater. 2009, 23, 2599–2605. [Google Scholar] [CrossRef]
- Tschegg, E.K. Environmental influences on damage and destruction of the structure of marble. Int. J. Rock Mech. Min. Sci. 2016, 89, 250–258. [Google Scholar] [CrossRef]
- Grelk, B.; Christiansen, C.; Schouenborg, B.; Malaga, K. Durability of Marble Cladding—A Comprehensive Literature Review. J. ASTM Int. 2007, 4, 19. [Google Scholar] [CrossRef]
- Schouenborg, B.; Grelk, B.; Malaga, K. Testing and Assessment of Marble and Limestone (TEAM)—Important Results from a Large European Research Project on Cladding Panels. J. ASTM Int. 2007, 4, 1–14. [Google Scholar] [CrossRef]
- Ito, W.H.; Ferrero, A.M.; Vagnon, F.; Migliazza, M.R.; de Queiroz, P.I.B. Thermomechanical numerical analysis of bowing in marble slabs. In Proceedings of the 14th International Congress on Rock Mechanics and Rock Engineering, Foz Do Iguassu, Brazil, 13–18 September 2019; pp. 2649–2657. [Google Scholar]
- Ito, W.H.; Ferrero, A.M.; de Queiroz, P.I.B. Numerical analysis of bowing phenomenon due to thermal stresses in marble slabs. Materials 2020, 13, 4367. [Google Scholar] [CrossRef]
- Weiss, T.; Siegesmund, S.; Fuller, E.R., Jr. Thermal degradation of marble: Indications from finite-element modelling. Build. Environ. 2003, 38, 1251–1260. [Google Scholar] [CrossRef]
- Ferrero, A.M.; Migliazza, M.; Spagnoli, A.; Zucali, M. Micromechanics of intergranular cracking due to anisotropic thermal expansion in calcite marbles. Eng. Fract. Mech. 2014, 130, 42–52. [Google Scholar] [CrossRef]
- Weiss, T.; Siegesmund, S.; Fuller, E.R., Jr. Thermal stresses and microcracking in calcite and dolomite marbles via finite element modelling. Geol. Soc. 2002, 205. [Google Scholar]
- Royer-Carfagni, G.F. On the thermal degradation of marble. Int. J. Rock Mech. Min. Sci. 1999, 36, 119–126. [Google Scholar] [CrossRef]
- Scherer, G. Internal stress and cracking in stone and masonry. In Measuring Monitoring and Modeling Concrete Properties; Springer: Berlin/Heidelberg, Germany, 2006; pp. 633–641. [Google Scholar]
- Hudson, J.A.; Cosgrove, J.W. Deterioration of building stones and stone buildings. In Understanding Building Stones and Stone Buildings; CRC Press: London, UK, 2019; pp. 328–332. [Google Scholar]
- European Commission. Testing and Assessment of Marble and Limestone; Final Technical Report; EC-Project: TEAM—G5RD-CT-2000-00233; European Commission: Brussels, Belgium, 2005. [Google Scholar]
- Vagnon, F.; Colombero, C.; Colombo, F.; Comina, C.; Ferrero, A.M.; Mandrone, G.; Vinciguerra, S.C. Effects of thermal treatment on physical and mechanical properties of Valdieri Marble—NW Italy. Int. J. Rock Mech. Min. Sci. 2019, 116, 75–86. [Google Scholar] [CrossRef]
- Weydt, L.M.; Bar, K.; Colombero, C.; Comina, C.; Deb, P.; Lepillier, B.; Mandrone, G.; Milsch, H.; Rochelle, C.A.; Vagnon, F.; et al. Outcrop analogue study to determine reservoir properties of the Los Humeros and Acoculco geothermal fields, Mexico. Adv. Geosci. 2018, 45, 281–287. [Google Scholar] [CrossRef] [Green Version]
- Comite Europeen de Normalisation. Natural Stone Test Methods. Determination of Resistance of Marble to Thermal and Moisture Cycles; EN 16306; Comite Europeen de Normalisation: Brussels, Belgium, 2013. [Google Scholar]
- Malaga, K.; Shouernborg, B.; Grelk, B. Bowing and expansion of natural stone panels: Marble and limestone testing and assessment. Mater. Constr. 2008, 58, 97–112. [Google Scholar] [CrossRef] [Green Version]
- Siegesmund, S.; Ullemeyer, K.; Weiss, T.; Tschegg, E.K. Physical weathering of marbles caused by anisotropic thermal expansion. Int. J. Earth Sci. 2000, 89, 170–182. [Google Scholar] [CrossRef]
- Li, C.; Wei, J.; Li, C. Influence of foliage thickness on thermal performance of green façades in hot and humid climate. Energy Build. 2019, 199, 72–87. [Google Scholar] [CrossRef]
- Mackiewicz, P. Thermal stress analysis of jointed plane in concrete pavements. Appl. Therm. Eng. 2014, 73, 1169–1176. [Google Scholar] [CrossRef]
- Naboni, E.; Milella, A.; Vadalà, R.; Fiorito, F. On the localised climate change mitigation potential of building facades. Energy Build. 2020, 224, 110284. [Google Scholar] [CrossRef]
- Stazi, F.; Ulpiani, G.; Pergolini, M.; Perna, C.; D’Orazio, M. The role of wall layers properties on the thermal performance of ventilated facades: Experimental investigation on narrow-cavity design. Energy Build. 2020, 209, 109622. [Google Scholar] [CrossRef]
- Kuehn, T.H.; Ramsey, J.W.; Threlkeld, J.I. Thermal Environmental Engineering, 3rd ed.; Prentice-Hall: Upper Saddle River, NJ, USA, 1998; pp. 381–414. [Google Scholar]
- Stephenson, D.G. Equations for solar heat gain through windows. Sol. Energy 1965, 9, 81–86. [Google Scholar] [CrossRef] [Green Version]
- Threlkeld, J.L. Solar irradiation of surfaces on clear days. ASHRAE Trans. 1963, 69, 24. [Google Scholar]
- ASHRAE. Fundamentals; I-P Edition; ASHRAE: Atlanta, GA, USA, 2017. [Google Scholar]
- ASHRAE Climatic Design Conditions. Available online: http://ashrae-meteo.info/v2.0/index.php?lat=42.43&lng=14.20&place=%27%27&wmo=162300&ashrae_version=2009 (accessed on 7 December 2020).
- Iqbal, M. An Introduction to Solar Radiation; Academic Press: Montreal, QC, Canada, 1983. [Google Scholar]
- Kasten, F.; Young, T. Revised optical air mass tables and approximation formula. Appl. Opt. 1989, 28, 4735–4738. [Google Scholar] [CrossRef]
- Whitaker, S. Elementary Heat Transfer Analysis; Pergamon: New York, NY, USA, 1976. [Google Scholar]
- Ozisik, M.N. Heat Transfer: A Basic Approach; McGraw-Hill: New York, NY, USA, 1985. [Google Scholar]
- McAdams, W.H. Hear Transmission, 3rd ed.; McGraw-Hill: New York, NY, USA, 1954. [Google Scholar]
- BSI. BS 8298: Code of Practice for Design and Installation of Natural Stone Cladding and Lining; BSI: London, UK, 2010. [Google Scholar]
- Johns, D.J. Two-dimension formulations and solutions. In Thermal Stress Analyses; Pergamon Press: London, UK, 1965; pp. 21–32. [Google Scholar]
- Ferrero, A.M.; Migliazza, M.; Spagnoli, A. Theoretical modelling of bowing in cracked marble slabs under cyclic thermal loading. Constr. Build. Mater. 2009, 23, 2151–2159. [Google Scholar] [CrossRef]
- Bergman, T.L.; Lavigne, A.S.; Incropera, F.P.; Dewitt, D.P. Fundamentals of Heat and Mass Transfer, 7th ed.; John Wiley and Sons: Hoboken, NJ, USA, 2011. [Google Scholar]
- Rosso, F.; Pisello, A.L.; Jin, W.; Ghandehari, M.; Cotana, F.; Ferrero, M. Cool Marble Building Envelopes: The Effect of Aging on Energy Performance and Aesthetics. Sustainability 2016, 8, 753. [Google Scholar] [CrossRef] [Green Version]
- Costa, A.A.M.N. Study on the Contribution of Thermal Mass Indoors Placed on Windowsills and Jambs. Master’s Thesis, Faculty of Engineering of the University of Porto, Porto, Portugal, 2017. [Google Scholar]
- Bellopede, R.; Zichella, L.; Marini, P. Marble durability assessment by means of total optical porosity and adjacent grain analysis. Key Eng. Mater. 2020, 848, 35–47. [Google Scholar] [CrossRef]
Symbol | Parameter | Value | Unit | Ref. |
---|---|---|---|---|
k | Thermal conductivity | 2.9 | [41] | |
Emissivity | 0.95 | - | [42,43] | |
c | Specific heat capacity | 870 | J/kg·K | [43] |
Density | 2785 | [43] | ||
Solar absorptivity | 0.44 | - | [43] | |
Thermal expansion coefficient | C | [40] | ||
E | Young modulus | 52.4 | GPa | [40] |
Poisson’s ratio | 0.16 | - | [40] |
Symbol | Parameter | Value | Unit | Ref. |
---|---|---|---|---|
B | Building plan width | 10 | m | |
Building plan length | 15 | m | ||
Surface azimuth | 194.28 | |||
L | Thickness | 0.03 | m | |
Daylight savings time | 1 | - | ||
Universal coordinated time | 1 | - | ||
Beam optical depths | 0.494 | - | [32] | |
Diffuse optical depths | 1.935 | - | [32] | |
Heat-transfer coefficient (outside) | 22 | |||
Heat-transfer coefficient (inside) | 3 |
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Ito, W.H.; Scussiato, T.; Vagnon, F.; Ferrero, A.M.; Migliazza, M.R.; Ramis, J.; de Queiroz, P.I.B. On the Thermal Stresses Due to Weathering in Natural Stones. Appl. Sci. 2021, 11, 1188. https://doi.org/10.3390/app11031188
Ito WH, Scussiato T, Vagnon F, Ferrero AM, Migliazza MR, Ramis J, de Queiroz PIB. On the Thermal Stresses Due to Weathering in Natural Stones. Applied Sciences. 2021; 11(3):1188. https://doi.org/10.3390/app11031188
Chicago/Turabian StyleIto, William Hideki, Talita Scussiato, Federico Vagnon, Anna Maria Ferrero, Maria Rita Migliazza, Jacqueline Ramis, and Paulo Ivo Braga de Queiroz. 2021. "On the Thermal Stresses Due to Weathering in Natural Stones" Applied Sciences 11, no. 3: 1188. https://doi.org/10.3390/app11031188
APA StyleIto, W. H., Scussiato, T., Vagnon, F., Ferrero, A. M., Migliazza, M. R., Ramis, J., & de Queiroz, P. I. B. (2021). On the Thermal Stresses Due to Weathering in Natural Stones. Applied Sciences, 11(3), 1188. https://doi.org/10.3390/app11031188