Abstract
The Valley of the Kings (KV) is located within a large funerary landscape called the Theban Necropolis, in Luxor, Egypt. In 2018, our team started to monitor the transient conditions of a 15 m rock column of micritic limestone above the tomb KV42 and a fracture located at the west end of the column (lateral fracture), registering thermo-mechanical displacements with a crack metre, infrared thermographic sensor, and a weather station. The data from April 2018 to May 2021 showed seasonal fluctuations in the rock surface temperature (RST) from 12°C (winter) to 45°C (summer), as well as an average reversible fracture opening (FO) rate of 1 mm/year. The measured average thermo-mechanical ratio of FO to RST was 0.05 mm/°C. Data collected at the site were used to calibrate a finite difference model in FLAC®8.0 for thermo-mechanical simulations. The results showed a correlation (R2) of 0.8 between measured data and elastic isotropic mechanical constitutive model results, with a ratio of FO to RST equal to 0.03 mm/°C and rates of reversible displacements of 0.8 mm/year, whereas the average irreversible displacement for the monitored period of 2018–2021 was 0.2 mm/year. The insights from this study can help provide a preservation approach for this area of the UNESCO World Heritage site and also enhance our understanding of environmentally driven long-term fracture growth mechanisms, such as thermo-mechanical fatigue. In the future, such insights could become more important as the global and local magnitude of daily and annual temperature fluctuations continue to increase.
Highlights
-
Our team conducts fieldwork in the Valley of the Kings (Luxor, Egypt), monitoring a rock column of 15 m which is attached at the bottom to the adjacent cliff. Cyclic behaviour of temperature and fracture opening were registered between April 2018 and May 2021, at a ratio of 0.05 mm/°C. The fracture opening trend increased throughout the monitored period at rates of 0.2 mm/year, showing irreversible deformation of the rock column.
-
Thermo-mechanical numerical model in FLAC (R) software intended to fit the observed data, under elastic conditions with an R2 of 0.8. The thermal inputs showed that thermal regions change in extension, associated to the shading patterns from the cliffs and hills around the rock column. For FLAC simulations, the ratio between fracture opening and rock surface temperature is 0.03 mm/°C.
-
Because of the cyclic nature of the displacement with the rock temperature, thermally assisted deformations are relevant to determine stability of the rock mass. This is impacted by the presence of joints, affecting the stability and the heat transfer process inwards the column. This could explain differences between observed and simulated data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
Not applicable.
Abbreviations
- AT:
-
Air temperature
- ANI:
-
Anisotropic
- E:
-
Young’s modulus
- FDM:
-
Finite differences model
- Fm:
-
Formation
- FO:
-
Fracture opening
- GSI:
-
Geological strength index
- IRT:
-
Infrared thermography
- ISO:
-
Isotropic
- HS#:
-
Horizontal survey number 1, 2, 3 or 4, on numerical model in FLAC®
- J#:
-
Joint number 1, 2 or 3 measured on rock column above KV42
- KV:
-
Valley of the Kings
- KV42:
-
Tomb KV42 in the Valley of the Kings
- KV62:
-
Tomb KV62 in the Valley of the Kings
- LR:
-
Low region, linear thermal boundary
- m a.s.l:
-
Meter above (mean) sea level
- MR:
-
Middle region, linear thermal boundary
- PA:
-
Orientation parallel to rock bedding
- PE:
-
Orientation perpendicular to rock bedding
- RH:
-
Relative humidity
- RT:
-
Rock temperature
- RST:
-
Rock surface temperature
- S#:
-
Slab number 1, 2 or 3 identified on rock column above KV42
- SR:
-
Sun radiation
- TR:
-
Top region, linear thermal boundary
- VS#:
-
Vertical survey number 1, 2 or 3, on numerical model in FLAC®
- UCS:
-
Uniaxial compressive strength
- υ :
-
Poisson’s ratio
- WD:
-
Wind direction
- WS:
-
Wind speed
References
Aboelkhair H, Morsy M, El Afandi G (2019) Assessment of agroclimatology NASA POWER reanalysis datasets for temperature types and relative humidity at 2 m against ground observations over Egypt. Adv Space Res. https://doi.org/10.1016/j.asr.2019.03.032
Alcaíno-Olivares R, Perras MA, Ziegler M, Maissen J (2019) Cliff stability at tomb KV42 in the Valley of the Kings, Egypt: a first approach to numerical modelling and site investigation. In: Proceedings of the 53rd US rock mechanics/geomechanics symposium
Alcaíno-Olivares R, Perras MA, Ziegler M, Leith K (2020) Thermo-mechanical cliff stability at tomb KV42 in the Valley of the Kings, Egypt. In: Proceeding of 5th World Landslide Forum. https://doi.org/10.1007/978-3-030-60196-6_38
Alcaíno-Olivares R, Ziegler M, Bickel S, Ismaiel HAH, Leith K, Perras MA (2022) Rock mechanical laboratory testing of Thebes Limestone Formation (Member I), Valley of the Kings, Luxor, Egypt. Geotechnics. https://doi.org/10.3390/geotechnics2040040
Alcaíno-Olivares R, Leith K, Ziegler M, Perras MA (2021) Thermo-mechanical fatigue cracking of the bedrock on an island in the Baltic Sea. In Proceedings of the GeoNiagara 2021. Niagara Falls, Canada. September 2021
Algarni S, Nutter D (2015) Survey of sky effective temperature models applicable to building envelope radiant heat transfer. ASHRAE Trans. https://doi.org/10.13140/RG.2.1.4212.5526
Atkinson BK (1984) Subcritical crack growth in geological materials. J Geophys Res Solid Earth. https://doi.org/10.1029/JB089iB06p04077
Bakun-Mazor D, Hatzor YH, Glaser SD, Santamarina JC (2013) Thermally vs seismically induced block displacements in Masada rock slopes. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2013.03.005
Bentz D (2000) A computer model to predict the surface temperature and time-of-wetness of concrete pavements and bridge decks, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg. https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=860286. Accessed 10 March 2021
Bottelin P, Levy C, Baillet L, Jongmans D, Gueguen P (2013) Modal and thermal analysis of Les Arches unstable rock column (Vercors massif, French Alps). Geophys J Int. https://doi.org/10.1093/gji/ggt046
Burton H (ca. 1910) Valley of the Kings: steps leading to tomb of Thutmose III. The Metropolitan Museum of Art, Department of Egyptian Art Archives, photo T3130
pers. comm. Campbell Scientific Inc. 2019. Helio Scientific Egypt, a Campbell Scientific partner. https://www.campbellsci.com/helio-scientific Accessed 15 June 2019
Collins BD, Stock GM (2016) Rockfall triggering by cyclic thermal stressing of exfoliation fractures. Nat Comm. https://doi.org/10.1038/ngeo2686
Collins BD, Stock GM, Eppes MC, Lexiw SW, Corbett SC, Smith JB (2018) Thermal influences on spontaneous rock dome exfoliation. Nat Comm. https://doi.org/10.1038/s41467-017-02728-1
Cross SW (2008a) Report on the stability of a section of cliff face in the Valley of the Kings. Unpublished
Cross SW (2008b) The hydrology of the valley of the kings. J Egypt Archaeol. https://doi.org/10.2307/40345878
Dorn A (2015) The hydrology of the valley of the kings: weather, rainfall, drainage patterns, and flood protection in antiquity. In: Wilkinson R, Weeks K (eds) The Oxford handbook of the valley of the kings. Oxford University Press, Oxford, pp 30–38
Ecomatik (2019) Circumference Dendrometer (Type DC-3). User manual. https://ecomatik.de/en/products/growth-and-plant-water-status-dendrometer/circumference-dc/ Accessed 10 December 2022.
Egyptian Meteorological Authority EMA (2021) Scientific Research Department. https://nwp.gov.eg/ Accessed 15 March 2021.
El-Hagrsy RM, Gado TA, Rashwan IMH (2018) Climate change effects on annual rainfall characteristics in Egypt. In: 21st International Water Technology Conference
Fiorucci M, Marmoni G, Martino S, Mazzanti P (2018) Thermal response of jointed rock masses inferred from infrared thermographic surveying (Acuto test-site, Italy). Sensors. https://doi.org/10.3390/s18072221
Freiman SW (1984) Effects of chemical environments on slow crack growth in glasses and ceramics. J Geophys Res Solid Earth. https://doi.org/10.1029/JB089iB06p04072
Gasc-Barbier M, Merrien-Soukatchoff V, Virely D (2021) The role of natural thermal cycles on a limestone cliff mechanical behaviour. Eng Geol. https://doi.org/10.1016/j.enggeo.2021.106293
Gischig V, Amann F, Moore JR, Loew S, Eisenbeiss H, Stempfhuber W (2011) Composite rock slope kinematics at the current Randa instability, Switzerland, based on remote sensing and numerical modelling. Eng Geol. https://doi.org/10.1016/j.enggeo.2010.11.006
Google Earth Pro (2022) Valley of the Kings 25◦44′ 24.5′′ N, 32◦36′ 05′′ E, Elevation 200 m. Terrain Layer. Imagery Date 23rd January 2022. http://www.earth.google.com Accessed 15 September 2022
Grechi G, Fiorucci M, Marmoni GM, Martino S (2021) 3D Thermal monitoring of jointed rock masses through infrared thermography and photogrammetry. Remote Sens. https://doi.org/10.3390/rs13050957
Grechi G (2022) Nonlinear strain effects induced by thermal forcing on jointed rock masses. Ph. D. thesis, Sapienza University of Rome
Greif V, Sassa K, Fukuoka H (2006) Failure mechanism in an extremely slow rock slide at Bitchu-Matsuyama castle site (Japan). Landslides. https://doi.org/10.1007/s10346-005-0013-0
Guerin A, Jaboyedoff M, Collins BD, Derron MH, Stock GM, Matasci B, Boesiger M, Lefeuvre C, Podladchikov YY (2019) Detection of rock bridges by infrared thermal imaging and modelling. Sci Rep Nat Res. https://doi.org/10.1038/s41598-019-49336-1
Gunzburger Y, Merrien-Soukatchoff V, Guglielmi Y (2005) Influence of daily surface temperature fluctuations on rock slope stability: case study of the Rochers de Valabres slope (France). Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2004.11.003
Hall K, Thorn CE (2014) Thermal fatigue and thermal shock in bedrock: an attempt to unravel the geomorphic processes and products. Geomorphology. https://doi.org/10.1016/j.geomorph.2013.09.022
Hassan HM, Panza GF, Romanelli F, ElGabry MN (2017) Insight on seismic hazard studies for Egypt. Eng Geol. https://doi.org/10.1016/j.enggeo.2017.01.029
IPCC (2014) Climate Change 2014: synthesis report of the sixth assessment. https://www.ipcc.ch/report/sixth-assessment-report-cycle. Accessed 20 March 2022
Ishikawa M, Kurashige Y, Hirakawa K (2004) Analysis of crack movements observed in an alpine bedrock cliff. Earth Surf Process Landforms J Br Geomorphol Res Group. https://doi.org/10.1002/esp.1076
Itasca Consulting Group, Inc (2019) FLAC—fast lagrangian analysis of continua, Ver. 8.1. Minneapolis: Itasca
Karakhanyan A, Avagyan A, Sourouzian H (2010) Archaeoseismological studies at the temple of Amenhotep III. Ancient Earthquakes, The Geological Society of America, Luxor. https://doi.org/10.1130/2010.2471(17)
Libelium (2022) Smart Agriculture PRO, Agriculture sensor guide. https://development.libelium.com/agriculture-sensor-guide/sensors. Accessed 10 December 2022.
Lukovic M, Ziegler M, Aaron J, Perras MA (2021) Rockfall susceptibility and runout in the Valley of the Kings. In Natural Hazards. https://doi.org/10.1007/s11069-021-04954-9
Maissen J (2019) The fractured rock cliff above KV42, Valley of the Kings, Egypt. Master’s Thesis, Swiss Federal Institute of Technology Zurich
Marmoni GM, Fiorucci M, Grechi G, Martino S (2020) Modelling of thermo-mechanical effects in a rock quarry wall induced by near-surface temperature fluctuations. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2020.104440
McLane J, Wüst R (2000) Flood hazards and protection measures in the Valley of the Kings. CRM Wash 23:35–38
Meteoblue (2020) Meteoblue, University of Basel. www.meteoblue.com. Accessed 15 June 2020
Mohamed AEEA, El-Hadidy M, Deif A, Elenean KA (2012) Seismic hazard studies in Egypt. NRIAG J Astronomy Geophys. https://doi.org/10.1016/j.nrjag.2012.12.008
Mufundirwa A, Fujii Y, Kodama N, Kodama JI (2011) Analysis of natural rock slope deformations under temperature variation: a case from a cool temperate region in Japan. Cold Reg Sci Technol. https://doi.org/10.1016/j.coldregions.2010.11.003
Nara Y, Yamanaka H, Oe Y, Kaneko K (2013) Influence of temperature and water on subcritical crack growth parameters and long-term strength for igneous rocks. Geophys J Int. https://doi.org/10.1093/gji/ggs116
Nara Y, Kashiwaya K, Nishida Y, Ii T (2017) Influence of surrounding environment on subcritical crack growth in marble. Tectonophysics. https://doi.org/10.1016/j.tecto.2017.04.008
Nashwan MS, Shahid S, Wang X (2019) Assessment of satellite-based precipitation measurement products over the hot desert climate of Egypt. Remote Sens. https://doi.org/10.3390/rs11050555
Ogiso Y, Sumi T, Kantoush S, Saber M, Abdel-Fattah M (2017) Risk assessment of flash floods in theValley of the Kings, Egypt. DPRI Annuals 60(B)
Paulose P (2020) Mapping and numerical modelling of flash flood hazard in the alley of the Kings (Luxor, Egypt). Master’s Thesis, Swiss Federal Institute of Technology Zurich
Potyondy DO (2007) Simulating stress corrosion with a bonded-particle model for rock. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2006.10.002
Reeves N, Wilkinson RH (2008) The complete Valley of the Kings, tombs and treasures of Egypt’s greatest pharaohs. Thames and Hudson, New York
Said R (1990) The geology of Egypt. Routledge, Abingdon
Vargas E, Velloso RQ, Chávez LE, Gusmão L, Do Amaral CP (2013) On the effect of thermally induced stresses in failures of some rock slopes in Rio de Janeiro Brazil. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-012-0247-9
Villarraga C, Vaunat J, Virely D, Gasc M (2021) Effect of thermal cycles on rock cliff deformation. Monitoring and interpretation. IOP Confer Ser Earth Environ Sci. https://doi.org/10.1088/1755-1315/833/1/012152
Vlcko J, Greif V, Grof V, Jezny M, Petro L, Brcek M (2009) Rock displacement and thermal expansion study at historic heritage sites in Slovakia. Environ Geol. https://doi.org/10.1007/s00254-008-1672-7
Vlcko J, Brček M, Greif V (2014) Deformations dynamics in response to seasonal temperature oscillations: an example from Pravcicka Brana rock arch (Czech Republic). In WLF 2013: Landslide risk mitigation. https://doi.org/10.1007/978-3-319-04996-0_55
Weeks KR, Hetherington NJ (2006) The Valley of the Kings, Luxor, Egypt. Site management masterplan. The Theban Mapping Project, Cairo
Wilkinson RH, Weeks KR (2016) The Oxford handbook of the Valley of the Kings. Oxford University Press, Oxford
Willockx S (2011) The last of the experimental royal tombs in the Valley of the Kings: KV42 and KV34. Ancient Egypt. https://www.egyptology.nl/. Accessed 10 August 2019
Woodman J, Ougier-Simonin A, Stavrou A, Vazaios I, Murphy W, Thomas ME, Reeves HJ (2021) Laboratory experiments and grain based discrete element numerical simulations investigating the thermo-mechanical behaviour of sandstone. Geotech Geol Eng. https://doi.org/10.1007/s10706-021-01794-z
Wüst R (1995) Geologisch-geotechnische untersuchungen im Thebanischen Gebirge, Teil Sud, Luxor, Agypten. Master’s Thesis, University of Bern
Acknowledgements
The authors would like to express their gratitude to the University of Basel Kings’ Valley Project and project Life Histories of Theban Tombs for their contribution and interest in this research. We particularly thank Andrea Loprieno-Gnirs and Elina Paulin-Grothe for their great support, and the Permanent Committee of the Supreme Council of Antiquities in Cairo for permission to carry out the works at the site. Mahmoud Ibrahim kindly assisted with the administrative planning of our field seasons, and Rais Abd el-Hamid Osman gave on-site technical and logistic support. Matjaz Kacicnik provided visual resources. We also thank Jasmin Maissen and Pushpendra Sharma for contributing with technical assistance in this project, as well as Derek Hayden, Alexandra Innanen and Bora Suda for their aid during the construction of sensor and setting systems. We also acknowledge Helio Scientific for allowing us to use their environmental data collected above tomb KV62 in the Valley of the Kings, as well as to meteoblue for their simulated data from 1985 for the Luxor region. The Metropolitan Museum of Art of New York City has granted access to the Harry Burton’s archives, so we recognise the contribution from Aude Semat and the Egyptian Art members at the MET to this research. Finally, we highlight the support in part from Natural Sciences and Engineering Research Council of Canada (NSERC) through the Discovery Grant program [RGPIN-2018-05918] and in part by funding from the Government of Canada’s New Frontiers in Research Fund (NFRF), [NFRF-2020-00893].
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no competing interests related to data acquisition, analysis, and discussion derived from the present work; involving either conflict of interests or breaching the Code of Ethics from their individual institutions.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix A
Appendix A
See Fig. 17.
Thermal boundary derived function, coupling monthly and daily variations. The rock surface temperature was calculated with Bentz (2000) model, using local weather data. The boundary function time-series plot shows the average trend of measured rock surface temperature, along with the calculated and derived function. Derived hourly values for January and July are displayed to show expected fluctuations within a day. Scatter plots of derived rock surface temperature function values and calculated rock temperatures are displayed, including the correlation factor R2 between both time-series for a top boundary, b middle boundary and c lower boundary. Location of boundaries is presented in Fig. 6 and Fig. 9
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.
About this article
Cite this article
Alcaíno-Olivares, R., Ziegler, M., Bickel, S. et al. Monitoring and Modelling the Thermally Assisted Deformation of a Rock Column Above Tomb KV42 in the Valley of the Kings, Egypt. Rock Mech Rock Eng 56, 8255–8288 (2023). https://doi.org/10.1007/s00603-023-03458-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00603-023-03458-1