Architectural and geotechnical aspects affecting earthquake resilience for the antique Egyptian Khufu pyramid

www.nature.com/scientificreports OPEN Architectural and geotechnical aspects affecting earthquake resilience for the antique Egyptian Khufu pyramid Mohamed ELGabry1,5, Ayman Hamed2, Sakuji Yoshimura3, Hesham M. Hussein1,4,5, Mohamed Maklad1 & Asem Salama4 The Great Pyramid of Khufu, completed during Egypt’s Old Kingdom (2600–2450 BCE), exhibits the architectural expertise of ancient Pharaonic Egypt. To understand the structural longevity and earthquake resilience of this iconic monument, we carried out a comprehensive ambient noise survey employing horizontal-to-vertical spectral ratio (HVSR) analysis at 37 measurement points distributed throughout the pyramid’s internal chambers, construction blocks, and adjacent soil. Our analysis reveals several critical findings. First, the pyramid exhibits uniform fundamental frequencies (2.0– 2.6 Hz) with an average of ~ 2.3 Hz across all structural elements, indicating exceptional homogeneity in dynamic characteristics. Second, this frequency band differs significantly from that of the surrounding soil (~ 0.6 Hz), preventing resonance amplification through soil-structure interaction—a key mechanism protecting the monument during seismic activity. Third, seismic relative amplification increases systematically with elevation up to 48.68 m, but diminishes substantially within the pressure-relieving chambers (48.86–61.07 m), demonstrating how their geometry actively reduces seismic response. Finally, seismic vulnerability assessment of the subsurface foundation yields a low value (kg = 8.2), confirming excellent bearing capacity and minimal earthquake-induced risk. The low seismic vulnerability index estimated for the foundation soils suggests that any future earthquakes are likely to produce only limited damage to the main pyramid body. These findings present compelling quantitative evidence that ancient Egyptian architects possessed profound geotechnical understanding, optimising structure design and site characterisation to assure millennial-scale stability against seismic hazards. Keywords Khufu pyramid, Horizontal to the vertical spectral ratio (HVSR), Amplification, Fundamental frequency, Egyptian old kingdom The Khufu pyramid, or Pyramid of Cheops, was the oldest Pyramid constructed in the northwestern part of the Giza plateau in Cairo during the Old Kingdom (Fig. 1)1,2. provided a comprehensive account of the architectural design of the Pyramid of Khufu (Fig. 2). The pyramid was originally constructed to a height of 146.59 m, with a base length of approximately 230.33 m per side and a slope angle of 51° 50′ 40"1–3. However, current measurements indicate that the present height is about 137 m, reflecting the loss of the original casing stones and apex over time3,4. According to1,2, the pyramid’s structure consists of a core and a casing of horizontal stones, with supporting blocks interspersed throughout. The Great Pyramid is estimated to contain around 2,300,000 stone blocks, each carefully positioned to achieve its monumental scale and stability1,2,4. Internally, Khufu’s pyramid features eight principal elements: the main entrance with descending passage, the entrance created by Caliph alMa’mun’s workmen, the Subterranean Chamber, the Grand Gallery, the Queen’s Chamber, the King’s Chamber, the relieving chambers, and the shafts1–3,5. This intricate arrangement highlights the advanced engineering and architectural planning characteristic of Old Kingdom pyramid construction1–4. 1Egyptian National Data Center (ENDC), National Research Institute of Astronomy and Geophysics (NRIAG), Helwan, Cairo 11421, Egypt. 2Faculty of Petroleum and Mining Engineering, Suez University, Suez, Egypt. 3Institute of Egyptian Archaeology, Higashi Nippon International University, Iwaki, Japan. 4General Seismology Laboratory, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan, Cairo 11421, Egypt. 5African Disaster Mitigation Research Center (ADMiR), Cairo, Egypt. email: Scientific Reports | (2026) 16:14032 | https://doi.org/10.1038/s41598-026-49962-6 1 www.nature.com/scientificreports/ Fig. 1. Location map of the Great Khufu Pyramid, Landsat image updated in July 2020 (Google Earth database). Fig. 2. Sketch showing the structure of the Khufu Pyramid. The pyramid area has been affected by numerous earthquakes within an epicentral radius of 80 km, without any serious damage to the main body of the Khufu pyramid over 4600 years. The largest reported earthquake event was on 7 August 1847 with an estimated magnitude of 6.86. This event was located near El-Fayoum, ~ 70 km from the Giza pyramids. Later, on 12 October 1992, an earthquake with a magnitude of 5.8 struck Giza again. During this event, several casing stones fell from the top parts of the pyramids7. Desoky and Hendawy8 examined the pyramid’s architecture and shape from a civil engineering perspective. They noted that most of the mass is concentrated near the ground and gradually decreases toward the top. The symmetrical design also suggests good balance and centralised mass distribution. They summarized out these features as: (a) Smart design that channels vibration forces safely through the structure; (b) Solid torsion resistance and stiffness to avoid uneven stress; (c) Good damping that calms down shaking and helps prevent resonance; (d) Low height-to-base ratio keeping it stable against tipping; (e) Both centres of mass and resistance are located at, or close to, the same point. This will cause the elimination/ reduction of torsion. (f) Plan dense footprint that resists overturning well; (g) No re-entrant corners to avoid stress buildup; (h) Existence of lateral Scientific Reports | (2026) 16:14032 | https://doi.org/10.1038/s41598-026-49962-6 2 www.nature.com/scientificreports/ resisting components along the Perimeter of the structure. This will produce a structural layout with high rigidity and strength. One of the main parameters which control the dynamic response of a structure is the interaction between natural frequencies inside the structure and the surrounding ground. The dynamic response is defined as the oscillation of the building at a certain vibration frequency as a result of the dynamic motion of an earthquake9. This phenomenon is one of the most significant factors governing structural damage during an earthquake. We also examine the relationship between the relative amplification factor of the pyramid’s various structural elements and the different heights of these elements. Ambient noise is simply a natural signal, consisting of an assemblage of body waves and surface waves which exist everywhere10. These signals may exist either because of human activities, oceanic waves or climatic changes11. The advanced applications of Ambient noise (HVSR) utilised in various studies for multiple purposes are based on Nakamura’s foundational research12, including HVSR reliability, ambient vibrations in historical monuments, soil-structure inter (...truncated)