Structural pathology and vulnerability assessment of monolithic stone columns at El Ashmonein Site, Egypt

Abstract

This study assesses the structural vulnerability of ancient monolithic granite columns at the El-Ashmonein site in Minia, Egypt, focusing on seismic and flood risks. Using Finite Element Modeling (FEM), modal analysis, and in situ surveys, both sound and decayed columns were analyzed. Seismic simulations showed top displacements of 2.44 cm in sound columns and 3.34 cm in decayed ones, a 37% increase due to degradation. Modal analysis revealed a longer fundamental period (0.58 s) and lower frequency (1.73 Hz) in decayed columns, raising resonance risk. Flood simulations with water depths of 1–3 m showed maximum lateral deformations of up to 20.7 cm in decayed columns, exceeding their sliding resistance at 3 m depth. These results highlighted the heightened vulnerability of deteriorated columns and emphasize the need for integrated conservation strategies. A simulation-based model for interventive conservation was proposed to enhance structural resilience against seismic and flood hazards.

Introduction

Structural analysis is essential in the study of columns as these elements often serve as the primary load-bearing structures in historical, monumental and modern buildings. Columns are particularly susceptible to stresses and forces that can lead to various forms of damage, including cracking, bending, and eventual structural failure^1,2,3. A thorough understanding of their dynamic behavior under different loading conditions is important for assessing their stability, especially when considering the potential impact of seismic forces, material aging, and environmental factors. As many ancient structures, including monuments and temples, feature columns as central structural components, understanding their responses under such conditions helps in preservation and restoration efforts⁴. In this regard, several studies highlight the importance of modal analysis in understanding the structural behavior of columns. Modal analysis allows researchers to examine how columns respond to dynamic forces by identifying natural frequencies and corresponding vibration modes. This method has been widely used to study both modern and ancient columns providing results relate to how they may behave under different loading conditions. For instance, Chopra⁵ and Fajfar⁶ describe modal analysis as a fundamental tool for understanding seismic responses, emphasizing that the primary modes of vibration in columns and structures significantly influence their structural resistance. The first few modes of vibration typically define the overall behavior, while higher modes correspond to localized deformations and internal stresses dynamic behavior of columns is influenced not only by their material properties but also by their geometry and boundary conditions. Furthermore, studies by Timoshenko and Gere⁷ provide foundational knowledge on the effects of slenderness ratio, material stiffness and boundary constraints on the buckling behavior of columns. This work established that slender columns are more vulnerable to buckling, while shorter, stiffer columns can withstand higher loads before failure. In addition, modal analysis has been further refined by applying finite element modeling (FEM) to assess the dynamic properties of complex columnar structures with irregular shapes or deteriorated materials⁸.

Environmental factors such as weathering and aging can alter the mechanical properties of column materials, which in turn affects their natural frequencies and vibration modes. For instance, research by Sarhosis et al.⁹ demonstrates that material decay and degradation due to weathering can lead to increased flexibility and reduced stiffness in ancient columns. This makes them more susceptible to seismic forces, as they exhibit longer vibration periods and lower natural frequencies. Such results highlight the importance of evaluating columns in both their sound and decayed states to ensure the structural safety. Archeological columns particularly those in seismic regions, are highly vulnerable to earthquakes due to their age, material degradation and structural characteristics. These columns are often constructed of stone or masonry, materials that are particularly brittle under dynamic forces. In this sense, Psycharis¹⁰ illustrates that stone columns, unlike modern reinforced concrete, lack the ductility needed to withstand lateral seismic forces, making them susceptible to cracking and toppling. Further, the absence of reinforcement and connection between column segments exacerbates instability, as individual blocks may displace during seismic activity¹¹. Additionally, Kappos and Scott¹² show that the fundamental modes of vibration are important in determining a column’s response to seismic forces. For ancient columns, the first few vibration modes often correspond to high lateral sway, which can lead to severe displacement or even collapse.

Moreover, studies using finite element modeling (FEM) have provided how vibration modes in decayed or weathered columns and structures change over time, typically showing increased fundamental periods due to material loss, which results in greater deformations during seismic events¹³. Furthermore, the seismic resilience of archeological columns is further compromised by material degradation, such as cracks, microfissures and weathering. According to a study by Shi et al.¹⁴, degradation reduces the column’s stiffness, increases its flexibility, and changes its natural frequencies, making it more responsive to seismic forces. This reduced stiffness can cause the column to resonate with seismic waves, resulting in amplified vibrations that may induce critical structural deformations. This phenomenon has been documented in earthquake-susceptible regions like the Mediterranean, where ancient stone structures have shown considerable damage following seismic events¹⁵.

On the other hand, flooding presents another threat to archeological structures and columns through hydrostatic pressure effects, which can destabilize foundations and weaken the structural base¹⁶. Hydrostatic pressure from floodwaters applies lateral forces to columns and other structures, potentially causing tilting, cracking, partial or full collapse, particularly in those with eroded or weakened bases¹⁷. In this regard, Lancellotta et al.¹⁸ have noted that ancient walls and structural elements lacking strong foundations are particularly vulnerable to such pressure, and the structures partially submerged in water are susceptible to additional forces, which can induce lateral movement or differential settlement. In addition, water saturation resulting from flooding can severely accelerate the decay of columns and ancient structural materials¹⁹. For instance, sandstone and limestone, materials commonly used in ancient columns, are porous and highly absorbent, allowing water to penetrate the structure. Consequently, a research by Hatır²⁰ shows that prolonged water exposure leads to salt crystallization and temperature variations cycles that can cause spalling, scaling and micro fracturing²¹. Additionally, water ingress into microcracks and fissures weakens the column’s structural continuity, making it more vulnerable to future environmental factors, including seismic activity. Furthermore, flooding can also erode soil and sediment around the base of columns, potentially undermining their stability²². In this regard, columns with eroded foundations are especially susceptible to seismic forces because the lack of stable support increases the likelihood of toppling²³. In this way, flooding not only directly damages archeological columns but also creates conditions that increase their vulnerability to future seismic impacts²⁴. The combined effects of flooding and earthquakes on archeological columns or modern structures present compounding challenges for structural stability²⁵. Flooding-induced erosion and material degradation often reduce a column’s natural frequencies, leading to increased resonance with seismic forces²⁶. Moreover, the added weight of water-saturated materials increases the seismic mass of a column, thereby intensifying the forces it experiences during an earthquake. This cumulative effect emphasizes the importance of understanding both hazards for accurate risk assessments and conservation efforts²⁷.

The combined effects of earthquakes and flooding present complex challenges for the preservation of Egypt’s archeological structures, particularly monolithic stone columns that have suffered centuries of environmental exposure and gradual material degradation. Developing effective strategies is essential to protect these ancient structures for future generations. To address this need, a comprehensive analysis was conducted on the monolithic stone columns at the El-Ashmonein archeological site, which included both seismic and flooding scenarios. This dual approach aimed to accurately assess the structural impacts of these natural forces on the stability and durability of the stone columns. In this paper, various in situ methodologies were employed, including high-resolution photographic documentation, precision measurements, detailed engineering surveys, and structural assessments to record visible deformations, damage and decay patterns. These assessments were specifically focused on the Basilica church columns and its surrounds at the El-Ashmonein site, Minia, Egypt, where the columns are particularly vulnerable to environmental forces due to their age, material composition and previous exposure to damaging events and loads.

Furthermore, a Finite Element Method (FEM) analysis was performed to simulate and evaluate the effects of flooding and seismic loads on the stone columns. For flooding, multiple impact scenarios were created to understand how varying water levels, hydrostatic pressures, and soil saturation levels influence the foundational stability and potential for structural displacement in the columns. This flooding analysis was particularly important for predicting the effects of periodic water exposure, which can cause moisture absorption, capillary rise and salt crystallization that leads to material weakening. The seismic analysis utilized FEM to simulate earthquake forces, incorporating data on probable seismic intensity for the region and testing the columns’ response to lateral and vertical vibrations. Different seismic loading conditions were analyzed to determine the resulting stress distributions, modal frequencies, and deformation patterns. This approach allowed for a clear understanding of the potential risks subjected by seismic activity, including identifying areas of stress concentration that could lead to cracking or even collapse in vulnerable sections of the columns.

Egypt lies on the northeastern edge of the African Plate, making its seismic risk profile closely tied to regional tectonic dynamics. In this sense, major sources of seismicity include the Eastern Mediterranean Subduction Zone, the Red Sea Rift, and the tectonically active Gulf of Aqaba and Gulf of Suez²⁸. The Red Sea Rift, a divergent boundary between the African and Arabian plates, has been active for approximately 30 million years and extends into both gulfs, contributing significantly to Egypt’s seismicity²⁹. Among these, the Gulf of Aqaba stands out for its potential to generate large-magnitude earthquakes, such as the notable 7.3 magnitude event on November 22, 1995, which was widely felt across Egypt, including in Cairo and Alexandria³⁰. While the Gulf of Suez is comparatively less seismically active, both regions have historically exposed a high seismic risk³¹.

Historical records further demonstrate Egypt’s vulnerability to seismic events, especially in densely populated areas like Cairo and the Nile Delta (Table 1). One of the most destructive earthquakes in recent history was the 1992 Cairo earthquake, which reached a magnitude of 5.8. It caused extensive structural damage, over 500 fatalities, more than 6000 injuries, and widespread building collapses, particularly where construction had not followed modern seismic standards^32,33,34. A historical compilation by Badawy documented around 83 significant earthquakes in Egypt between 2200 BC and 1899 AD, based on Arabic sources and earlier seismic catalogs³⁵. Current seismic hazard assessments divide Egypt into zones of varying risk, with the highest seismicity observed in the Sinai Peninsula and along the Red Sea coast due to proximity to active fault systems. Meanwhile, although the Nile Valley and Delta regions are less tectonically active, the high population density and vulnerable infrastructure increase the potential damage from any significant earthquake³⁶.

Table 1 Some recorded historical earthquakes in Egypt and their impact

Flooding happens often in Egypt and has a big impact on the environment, economy, and daily life. Since Egypt is mostly hot and dry, water is very important. The Nile River has always been the main source of water and support for the people of Egypt³⁷. Understanding the causes and impacts of flooding in Egypt, along with the strategies employed for mitigation, is essential for effective water management and disaster preparedness. Egypt has experienced various forms of flooding throughout its history (Table 2), largely linked to the Nile River’s annual inundation cycle³⁸. For centuries, this seasonal flooding deposited nutrient-rich silt onto the surrounding agricultural lands, enabling the growth of crops and sustaining the ancient civilization³⁹. However, the construction of the Aswan High Dam in 1970 fundamentally changed the dynamics of the Nile’s flooding patterns. While the dam has provided benefits such as hydroelectric power and irrigation, it has also disrupted the natural flooding cycle, leading to a range of environmental issues, including soil salinization and reduced sediment flow^40,41.

Table 2 Some recorded historical flooding In Egypt and their impact

Flooding in Egypt can be attributed to several factors, including climate change, heavy rainfall, and the management of water resources⁴². Climate change has led to increased variability in weather patterns, resulting in more frequent and intense rainfall events in some regions. For instance, the winter months often see substantial rainfall, particularly in the northern coastal areas⁴³. These sudden downpours can overwhelm drainage systems, leading to flash floods in urban areas. Moreover, the management of the Nile River and its tributaries plays an important role in flooding. The Aswan High Dam, while controlling floods, has also contributed to altered sediment transport and reduced floodplain dynamics⁴⁴. Additionally, urbanization has exacerbated flooding risks, as impervious surfaces prevent water infiltration and increase runoff. In cities like Cairo, inadequate drainage infrastructure often fails to cope with heavy rainfall, resulting in urban flooding⁴⁵.

Methods

In situ surveying and monitoring of the archeological columns involved a thorough recording and documentation of structural issues using detailed photographs to capture and track areas of deterioration and damage. This photographic documentation enabled visual assessments and served as a valuable reference for analyzing the progression of any structural problems. Additionally, laser measurements provided precise engineering dimensions, ensuring an accurate record of the columns’ physical characteristics and aiding in any necessary restoration or stabilization planning. In addition, for a more precise analysis of structural stability, a total station was employed to monitor specific columns, focusing on inclination angles and displacements. This instrument allowed for accurate measurements of shifts or tilts in the columns, which may be due to dynamic or environmental forces. Monitoring these inclination angles and displacements is important, as even slight deviations can indicate potential instability or structural weaknesses that may worsen under continued exposure to environmental factors, such as seismic activity or changes in soil conditions.

Moreover, the analysis of the archeological column involved creating a finite element model using SAP2000, where both seismic and flood loads were calculated and applied to evaluate the column’s structural behavior under these forces. This model allowed for a detailed examination of the column’s response to each load type, considering the unique characteristics of the column’s material and geometry. By simulating these load conditions, the study aimed to assess how seismic vibrations and flood forces contribute to potential instabilities or stress concentrations that may lead to damage or structural compromise over time.

The column was represented as a 3D solid element with its shaft modeled in granite and base in limestone, incorporating material properties derived from previously published laboratory tests on El-Ashmonein samples. Young’s modulus values were assigned as 5425 MPa for sound granite, 2950 MPa for weathered granite, and 2030 MPa for limestone, assuming linear elastic, homogeneous, and isotropic behavior for all materials. Fixed-base boundary conditions were applied, and dead load, seismic, and flood scenarios were simulated. Seismic loads were calculated using the Egyptian Code of Practice (Zone 1, soil type E), while flood loading followed the ASCE/SEI 7-10 guidelines for breaking wave forces on vertical columns, applying lateral pressures corresponding to water depths of 1, 2.2, and 3 m. The model evaluated modal frequencies, displacement responses, and stress distributions in both sound and decayed column conditions. Although destructive testing was not feasible, the model’s outputs were validated qualitatively by comparing simulated deformations and stress zones with in situ observations, including column inclinations, visible cracking, and measured top displacements.

The monolithic stone column under analysis, as shown in Fig. 5, has dimensions of 800 mm in diameter and a height of 8.6 m. This structural element was evaluated under seismic and flood load scenarios to gauge both its localized and overall stability under demanding environmental conditions. The Egyptian Code of Loads⁴⁶ was used to define seismic loads, while the American Standard Code of Loads⁴⁷ was applied for flood loads, given that the Egyptian code lacks specific flood load provisions. Utilizing these standards provides a comprehensive framework for assessing the column’s resilience, ensuring that both seismic and flood risks, relevant to the conditions of the Minia region are considered.

The load calculation parameters align closely with the geological and seismic profile of the Minia region. Seismic parameters place the column in Earthquake Zone 1, with a subsoil classification of “E” according to geotechnical reports, indicating the presence of relatively soft or less stable ground. The seismic response spectrum applied is Type 1, as suitable for non-coastal areas, and a behavior factor of 1 was chosen to streamline the seismic assessment, maintaining conservative force levels without ductility reductions.

To calculate flood loads on the critical column, the ASCE/SEI 7-10 code section on “Breaking Wave Loads on Vertical Pilings and Columns” was used. This code allows us to estimate the net force exerted by a breaking wave on a rigid vertical column. The force F_D, acting at the still water elevation, is calculated using⁴⁸:

$${{\rm{F}}}_{{\rm{D}}}=0.5{{\rm{\gamma }}}_{{\rm{w}}}{{\rm{C}}}_{{\rm{D}}}{\rm{D}}{{{\rm{H}}}_{{\rm{b}}}}^{2}$$

where F_D = net wave force, in lb (kN); γ_w = unit weight of water, in lb per cubic ft (kN/m³), = 62.4 pcf (9.80 kN/m³) for fresh water and 64.0 pcf (10.05 kN/m³) for salt water; C_D = coefficient of drag for breaking waves, = 1.75 for round columns and = 2.25 for square columns; D = column diameter, in ft (m) for circular sections, or for a square pile or column, 1.4 times the width of column in ft (m); H_b = breaking wave height, in ft (m).

To determine the breaking wave height H_b, the formula used is H_b = 0.78d_s, where d_s represent the local still water depth. This depth, in turn, is calculated by:

$${{\rm{d}}}_{{\rm{s}}}=0.65(\mathrm{BFE}-G)$$

with BFE as the base flood elevation and G as the ground elevation. For this analysis an incremental study with BFE-G values set at 2, 4, and 6 m to represent varying flood depths, was conducted. Consequently, these flood load parameters were given:

(BFE-G) is assumed based on incremental study (2, 4 and 6 m)

ɤ_w = 9.8 kN/m³

C_D = 1.75

D = 0.8 m

H_b = 1, 2.2 and 3 m as per the incremental study

F_D = 0.7, 2.8 and 6.3 tons respectively, as per the incremental study

Laboratory tests related to the physical and mechanical properties of the building materials used in this study particularly for granite and limestone were based on previously published results, which analyzed samples from the same archeological context at the El-Ashmonein site⁴⁹.

Results

Significance of the case study

This paper centers on the structural challenges and assessment of the ancient monolithic granite columns at the El-Ashmonein archeological site, positioned at 27°46′55"N, 30°48′11"E in the Mellawy center of Minia Governorate, Egypt (Fig. 1A, B)^49,50. Known in antiquity as Hermopolis Magna, El-Ashmonein is one of Egypt’s prominent archeological sites, historically renowned as a vital cultural and religious center. It was primarily dedicated to Thoth, the ancient Egyptian god of wisdom, writing and knowledge, often depicted as an ibis or baboon. This city served as a major spiritual and intellectual hub where worship and scholarly activity flourished. As an important center of the Thoth cult, Hermopolis Magna facilitated the exchange of ideas between Upper and Lower Egypt and became a prominent crossroads of Egyptian and foreign influence, particularly Greek and Roman. Architectural remains, including grand temples, colossal statues and towering granite columns, testify to the city’s high craftsmanship, religious importance and cultural wealth. Alongside these structures, the site houses numerous artifacts, such as inscriptions and reliefs, that offer valuable information about the religious practices, social customs and everyday lives of the ancient inhabitants^49,51.

Fig. 1: Overview of the El-Ashmonein Archaeological Site and Study Area.

A Google Earth map providing an overview of the El Ashmonein archeological site, situated between the villages of El-Idara and El-Ashmonein, Mellawy city, Minia. B Map of the case study area, marking the archeological remains. C General view of the area under study for analysis.

El-Ashmonein’s layered history reflects a blend of Egyptian and Greco-Roman influences, with remnants from the Pharaonic, Greek and Roman eras revealing its historical significance. However, despite its rich history, no remains from the earliest periods have been found, likely due to the destruction that impacted the city over time. Presently, the site is largely ruined, with only small fragments of temples still standing amidst general rubble. One of the best-preserved areas is the Roman-period agora, which includes an early Christian Basilica from the early fourth century AD (Fig. 1C), providing evidence of the town’s prosperity in late antiquity and bearing testimony to its transformation over centuries⁵². The current state of El-Ashmonein and its basilica highlights the vast, fertile region of the Nile Valley in which it is situated, underscoring the cultural and economic significance it once held. In this context, research and excavation efforts at the site continue to enhance our understanding of Egypt’s complex history, religious practices and the dynamics of its interactions with other ancient civilizations, positioning El-Ashmonein as an essential location for the study of ancient Mediterranean cultures.

Destruction of monolithic granite columns under dynamic loads

The vulnerability of ancient monolithic granite columns to dynamic loads, especially seismic events and flooding, is evident in both theoretical analysis and field observations from our case study. These columns carved from a single stone block and originally designed to support vertical static loads from roofing and architectural beams, show significant susceptibility when subjected to lateral forces generated by earthquakes and environmental stressors like flooding.

During seismic events, lateral ground motions introduce bending and shear stresses along the column’s shaft, with critical concentrations typically found at the base and midsections. Despite granite’s high compressive strength, it remains brittle and lacks ductility, making it susceptible to tensile cracking and shear failure under dynamic loading. In situ analysis of our study area reveals fractures and shear lines that align with these high-stress zones, as documented in Fig. 2. This damage corresponds with typical seismic response patterns of freestanding monolithic columns, including rocking, displacement and even overturning, especially in the absence of internal reinforcement. In this regard, one major contributing factor to seismic vulnerability is resonance. In this way, each column possesses a distinct set of natural frequencies based on its geometry, material density and boundary conditions. When seismic waves approach these frequencies, resonant amplification occurs, intensifying vibrations and generating substantial internal stresses. Field observations confirm this, as evidenced by visible displacement, horizontal cracking, and partial tilting at the bases of several columns (Fig. 2A–H).

Fig. 2: Structural failures (fracturing, cracking, and scattering) in the granite columns at the El-Ashmunein archeological site.

A, B Numerous columns with missing segments due to fractures propagating over time and causing complete separation. The scattered column drums lying on the ground are a clear indication of past structural failure. C, D Fractured columns with large cracks running through their shafts. E–G Additional column segments lying detached and scattered, with some pieces partially buried in the soil. H Visible remnants of a column partly embedded in the ground indicate that the site has undergone considerable damage and degradation.

In addition to seismic forces, the effects of flooding compound the structural deterioration of these ancient elements. Granite itself is relatively less porous than limestone, but in our case study, the columns rest on limestone bases or are integrated with limestone architectural elements. In this context, limestone’s high porosity allows significant water infiltration during flooding, which alters its mechanical properties, increasing its weight and reducing internal cohesion. Prolonged and repeated saturation events weakened the stone matrix, leading to surface erosion, internal dissolution of calcium carbonate and increased susceptibility to biological colonization. Figure 2E, H shows partially submerged or soil-embedded column fragments, illustrating the interaction between stone degradation and environmental exposure.

Moreover, flooding undermines the ground bearing capacity around column foundations. Saturated soils often undergo differential settlement, especially beneath heavier or already stressed columns. This uneven support introduces tilting and bending moments that further propagate cracks in both the shaft and the base. The cumulative effects of saturation, material weakening, and structural misalignment diminish the columns’ ability to withstand future seismic shocks.

Field observation also indicate that limestone bases under granite columns, like those in the documented area, are especially exposed to failure during dynamic interactions. The base not only absorbs some of the earthquake energy but may also serve as a weak point when its tensile capacity is exceeded. Several fractured columns from the site exhibit shear patterns at the limestone-granite interface, confirming the critical role of base behavior in overall stability. In this sense, Fig. 2 presents a visual summary of these degradation processes and Fig. 2A, B shows standing columns with visible cracks and weathering; Fig. 2C–G illustrates horizontally displaced, broken, or abandoned segments, many with jagged fracture edges or signs of mechanical impact. The location and orientation of fragments reflects both seismic displacement and long-term environmental exposure. In Fig. 2H, a fragment partially embedded in soil near vegetation highlights the neglect and continuing deterioration due to natural encroachment.

Figure 3 presents various forms of decay and deterioration on granite columns, which significantly impact their structural stability. In Fig. 3A, we see a group of columns that showcase widespread surface weathering. This type of degradation is caused by prolonged exposure to environmental factors, including moisture, temperature fluctuations and possibly pollution. Such wear can compromise the column’s load-bearing capacity over time by eroding its outer layers, reducing the structural residence and making it more susceptible to cracks and fractures. Figure 3B highlights a localized crack on the column’s surface, possibly due to the accumulation of stresses from environmental cycles and the inherent weaknesses in the granite material. Weaknesses such as micro-cracks and porous areas allow for water infiltration, which accelerates deterioration through processes like freeze-thaw cycles, further undermining the stability of the structure.

Fig. 3: The figure illustrates various types of deterioration affecting the granite columns.

A shows a group of columns exhibiting extensive surface erosion. B highlights a small isolated crack on the column’s exterior. C shows rounded edges and surface pits, signs of granular breakdown. D presents a larger crack running through a major portion of the column, indicative of structural weakness. E, F display advanced degradation, with noticeable chipping and breakage, evidence of material loss. G, H focus on damage at the columns’ bases, where erosion and encroaching vegetation are visibly contributing to decay.

In Fig. 3C, a rounding of the column edges and surface pitting are observed, indicating ongoing granular disintegration. This type of damage typically stems from the natural mineral composition of granite, where weaker minerals erode faster under environmental exposure, leaving the surface rough and uneven. In addition, Fig. 3D shows a larger crack extending through a significant portion of the column indicating that the column’s internal structure may be compromised. When such cracks appear, they can propagate under the load, leading to a higher risk of structural failure, especially during seismic or flood events. Furthermore, Fig. 3E, F shows more advanced deterioration, with parts of the columns visibly chipped or broken off. These fractures are direct evidence of material loss, further lowering the column’s capacity to bear loads and increasing its vulnerability to external forces. Figure 3G, H displays damage at the base of the limestone columns, where erosion and vegetation growth are apparent. These conditions suggest that the foundations are weakened, possibly by soil movement or the growth of roots, which can destabilize the columns from below. The weakened base reduces the frictional resistance needed to counteract sliding forces, increasing the risk of displacement during lateral loads.

In situ instability monitoring for the tetrastyle columns

The structural instability of the tetrastyle stone columns at El-Ashmonein site is a major concern (Fig. 4), as inclination and horizontal displacement measurements show an observed deviation from the original vertical alignment. For this, the structural instability in ancient columns can result from several factors, such as natural weathering, seismic activity, flooding load, foundational settling and environmental effects. Inclination angles and displacement measurements provide important vision into each column’s current stability and potential vulnerabilities. Columns 3 and 4, with inclination angles of 1.712° and 2.719° (Fig. 4A, B), respectively, show considerable tilting, with Column 4 exhibiting the largest horizontal displacement at 46 cm (Fig. 4A, B). These measurements indicate substantial leaning and present a risk to the columns’ structural durability. In this context, a tilt greater than 2° is generally regarded as critical⁵³, signaling dangerous instability and the potential for partial or complete collapse⁵⁴. In addition, horizontal displacement, the top shift distance from the original position, further illustrates this risk. With recorded displacements of 21 cm, 29 cm (Fig. 4A, B), and especially 46 cm, the columns are evidently shifting out of alignment, which can lead to increased stress on the lower portions and uneven load distribution across each structure. Such a shift escalates the potential for collapse, emphasizing the need for immediate and thorough assessment.

Fig. 4: Stability monitoring of freestanding tetrastyle stone columns using total station.

A–C Detailed measurements for each column; Column (1) has a height of 8.75 m, an inclination angle of 1.38°, and a displacement of 21 cm; Column (2) also stands at 8.75 m with an inclination angle of 0.46° and a displacement of 7 cm; Column (3) measures 9.70 m in height with an inclination angle of 1.712° and a displacement of 29 cm; Column (4) is 9.70 m tall with an inclination angle of 2.719° and a displacement of 46 cm.

The observed instability could be caused by a combination of foundational weakening and seismic impact (Fig. 4C), environmental erosion, and vegetation growth, each contributing to progressive tilting over time. Foundational settling may be due to centuries of erosion and compaction in the soil and materials beneath the columns, while seismic activity in Egypt may have exacerbated shifts and stress within the structures. Environmental erosion from wind, rain and temperature fluctuations weakens the stone surfaces, especially at the base, and fosters vegetation growth, which can further destabilize the columns through physical pressure or moisture retention in cracks. Addressing this instability is essential for conservation. Recommended measures include foundation reinforcement to counter erosion, temporary supports to stabilize columns with severe displacement, and ongoing tilt monitoring using total stations or laser scanners to track minor shifts over time. Without intervention, these inclinations and displacements will worsen, threatening not only the preservation of these historically structures but also the safety of visitors to the site.

Structural analysis and seismic validation on granite columns

The preservation of ancient monolithic stone columns requires an in-depth understanding of both the immediate and long-term impacts of environmental and structural forces. Modern conservation efforts advantage advanced engineering techniques, such as finite element modeling, to assess and monitor the structural health of these columns. By creating virtual models, we can simulate seismic and hydrostatic forces to identify potential failure points and analyze how vibrational modes might affect the column’s stability. This approach helps conservators and engineers predict areas most susceptible to damage and develop tailored strategies to reinforce or protect the columns against deterioration over time.

In this study, the column was modeled using SAP2000 software, with a solid element to accurately represent its structure, as illustrated in Fig. 5. Two distinct models were created; (1) one representing the granite column in its original/Sound state, and (2) another showing it after weathering effects. The material properties of the column’s granite and the limestone footing were defined in the software (Fig. 5A, B), with specific attention to each material’s elastic modulus (E). The elastic modulus values are 2030 MPa for limestone, 5425 MPa for unweathered granite, and 2950 MPa for weathered granite, reflect how the materials respond to stress. The program automatically calculated the column’s weight, while additional lateral load cases were manually defined and applied. These detailed parameters allow for a realistic simulation, enabling a better understanding of how different forces interact with the column and affect its structural integrity over time.

Fig. 5: Structural analysis and material composition of a monolithic freestanding column.

A simulated three-dimensional view of the finite element model developed for analyzing the structural behavior of the monolithic column. B Photograph of the actual monolithic freestanding column in greater detail, highlighting the distinct materials used for different parts of the structure: the shaft, carved from granite, and the base, made from limestone. After Fahmy⁴⁸.

Vibrational modes and shapes of the sound and decayed columns

The dynamic behavior of columns under seismic or other dynamic loads is governed by their modal frequencies and the corresponding vibration modes. The results from the modal analysis of both the sound (original) and decayed (weathered) states of the column provide analysis on how the column will respond to dynamic forces. The modal analysis reveals a spectrum of vibration modes ranging from low frequencies (associated with longer periods and slower vibrations) to high frequencies (with shorter periods and more rapid oscillations). These different modes offer a detailed understanding of how the column might deform and react under varying dynamic conditions.

For the sound column, the modal analysis indicates that the fundamental periods in the first modes are relatively long, which corresponds to lower frequencies. For example, both Mode 1 and Mode 2 (Fig. 6) have a period of 0.42 s and a frequency of 2.37 Hz, meaning that the initial vibrations of the column are slow and the column oscillates fewer times per second. These modes represent the overall structural behavior of the column, where the entire column deforms as a single, coherent unit under seismic or dynamic forces. As we move to the higher modes, the periods shorten and the frequencies increase. In Mode 12 (Fig. 6), the period drops dramatically to 0.01 s, resulting in a frequency of 111.47 Hz. These higher modes involve faster, more localized oscillations within the material of the column. They correspond to finer deformations, such as slight movements or vibrations in localized regions of the stone, rather than large-scale structural shifts. The higher modes are often associated with higher-order resonances that involve vibrations within specific regions of the column, such as at the edges or near imperfections in the material. In this sense, the overall implication for the sound column is that its structural integrity is maintained, with the column able to resist seismic forces effectively. Lower-frequency modes dominate its dynamic behavior, and the column exhibits relatively low deformation under seismic loading.

Fig. 6: Twelve mode shapes of a vertical column structure under fixed base boundary conditions.

The modes illustrate the characteristic deformation patterns due to either buckling (for stability analysis) or free vibration (for dynamic analysis). After Fahmy⁴⁸.

In the decayed (weathered) column, the modal analysis reveals significant changes in its dynamic behavior. The most notable difference is an increase in the fundamental period, from 0.42 s in the sound column to 0.58 s in the decayed column, resulting in a lower frequency of 1.73 Hz in Mode 1 and Mode 2 (Fig. 6). This increase in the period reflects a loss of stiffness in the column due to the weathering process, which makes the material more flexible and less able to resist dynamic forces. Consequently, the decayed column vibrates more slowly under the same seismic or dynamic loads, leading to larger deformations compared to the sound column. The lower frequency of the decayed column means that it will exhibit more significant displacement when subjected to low-frequency seismic events, as the structure becomes more compliant and less rigid. The longer periods and lower frequencies in the decayed column suggest that it will experience greater deformation in response to seismic loads, particularly in the lower-frequency modes. The increased displacement can lead to structural instability over time, especially if the decay continues without proper reinforcement or restoration. This makes the decayed column more vulnerable to further damage under dynamic loading conditions, and if the deterioration progresses, it could eventually lead to the failure or collapse of the column.

For higher modes (Modes 9 to 12) (Fig. 6), both the sound and decayed columns exhibit faster oscillations, but the frequencies for the decayed column are slightly lower compared to the sound column. For example, in Mode 12, the decayed column has a period of 0.01 s and a frequency of 81.56 Hz, compared to the sound column’s frequency of 111.47 Hz. This reduction in frequency reflects the increased compliance of the decayed column, which is less stiff and more prone to localized deformations.

Higher-frequency modes typically correspond to smaller, more localized vibrations within the material. In the decayed column, these localized vibrations are more pronounced due to the material’s increased flexibility. This may lead to more concentrated damage in areas where the column is weakest, such as at cracks or where weathering has caused a degradation of the stone’s internal structure. Over time, such localized damage can propagate, potentially leading to cracks or even partial collapse in specific areas of the column. These higher modes suggest that the decayed column’s ability to resist rapid or high-frequency dynamic forces is compromised, and it may be more vulnerable to such forces than the sound column. The dynamic response of the decayed column indicates a significant loss of structural stability compared to the sound column. The fundamental increase in the period (and corresponding decrease in frequency) of the decayed column means that it becomes more flexible and deformable under seismic loading. This increased flexibility makes the column less capable of resisting lateral forces, which can lead to excessive displacement and potentially progressive damage over time. The ability of the column to handle dynamic loading is particularly affected in the lower-frequency modes, where the largest deformations occur. In contrast, the sound column remains relatively rigid and stable under seismic loads, with lower-frequency modes governing its overall structural behavior. Its ability to resist seismic forces and maintain structural stability is far superior to that of the decayed column, which is more susceptible to deformation, cracking, and failure.

The implications of these modal analysis results are profound when considering the fundamental concepts of seismic demand, capacity, and local failure mechanisms, which are central to earthquake engineering and extensively discussed in scientific literature and seismic design codes. In this context, seismic demand quantifies the intensity of ground motion a structure is subjected to during an earthquake, characterized by ground acceleration, velocity, and displacement time histories, and represented through response spectra^55,56. The frequency content of seismic demand is particularly critical; structures with natural frequencies close to the dominant frequencies of ground motion can experience resonance, leading to amplified responses^57,58. Modern seismic design often employs Non-linear Time History Analysis (NLTHA) to capture the realistic dynamic response of structures to actual or simulated ground motions, providing a more accurate assessment of displacement and force demands⁵⁹. The current results for the decayed column, specifically the shift to longer periods (lower frequencies), directly imply a heightened susceptibility to larger deformations when subjected to low-frequency seismic demands. Such demands, typically associated with large displacements, will find the decayed column more compliant and therefore more vulnerable to resonance and amplified responses, exacerbating its structural distress.

Structural capacity refers to a structure’s ability to resist the imposed seismic demands without exceeding predefined performance objectives. This involves evaluating both strength capacity (the maximum force a component can withstand) and deformation capacity (the maximum deformation a component can undergo before significant strength degradation). For masonry and reinforced concrete structures, capacity is profoundly influenced by material properties, geometric configurations and the detailing of reinforcement or interlocking elements^60,61. Performance-Based seismic design explicitly links different performance levels to varying levels of damage and corresponding structural capacities⁶². The observed increase in the fundamental period and decrease in frequency of the decayed column are direct manifestations of a significant reduction in its stiffness and, consequently, its capacity to resist lateral seismic forces without experiencing excessive deformation. This reduced capacity means that the decayed column will reach its limit states, including various local failure mechanisms, at significantly lower seismic demands compared to the sound column. These local failure mechanisms are specific modes of failure that occur at a localized part of a structural element and can ultimately lead to global structural distress or collapse if not properly addressed in design. For columns, common local failure mechanisms under seismic loading include flexural yielding and crushing (especially if transverse confinement is inadequate), brittle shear failure, buckling of longitudinal reinforcement, and bar slippage or bond failure⁶³. The larger deformations predicted by our modal analysis for the decayed column, particularly in the lower modes, directly increase the likelihood of secondary effects such as P-Delta effects, which can further exacerbate demands and accelerate local buckling or instability, as depicted in the buckling modes of Fig. 6 Furthermore, the slightly lower frequencies in the higher modes of the decayed column reflects increased compliance, leading to more pronounced localized vibrations and potentially concentrated damage in weakened areas, such as pre-existing cracks or regions of advanced material degradation. Understanding these local mechanisms is critical in seismic design, as codes like Eurocode 8 (EN 1998) and ASCE 7 incorporate “capacity design” principles, aiming to ensure that ductile failure mechanisms are prioritized, while brittle local failure mechanisms are prevented by providing sufficient overstrength in those elements⁶⁴. In this regard, the current results unequivocally demonstrate that the decayed column’s dynamic response makes it highly vulnerable to these local failure mechanisms. Its significantly compromised ability to handle dynamic loading, particularly in the lower-frequency modes, means it is far more susceptible to the progressive deformation, cracking, and eventual failure that these mechanisms entail under seismic demand than the sound column.

Base reactions for structural analysis

The base reactions in structural engineering refer to the forces exerted at the base of a structure due to various load cases. These forces, acting in the x, y, and z directions (representing horizontal, lateral, and vertical forces), reveal how different external loads impact the stability and integrity of the structure. Understanding these base reactions is essential in evaluating the stresses that the base of the structure must withstand to remain stable and secure. The data for base reactions across several load scenarios, including dead load, earthquake (EQ) forces, and different flood load cases was calculated. The units for these reactions are given in ton-force (Tonf), which measures the intensity of the force applied in each direction.

The dead load (DL) represents the static weight of the structure itself, which includes materials, fixtures, and other permanent elements. This load applies a constant vertical force (FZ) of 11.40 Tonf, which is the weight that the base must support under normal conditions without any external disturbances. There is no force in the x or y directions (FX and FY), indicating that the dead load acts purely vertically downward.

The EQ-X and EQ-Y cases (Earthquake Load Cases) simulate the horizontal forces caused by seismic activity in two orthogonal directions. In the EQ-X case, there is a horizontal force of −2.55 Tonf in the x direction (FX), representing a lateral load from an earthquake along the x-axis. Similarly, the EQ-Y case shows a −2.55 Tonf force in the y direction (FY), indicating lateral seismic force along the y-axis. Both cases have zero force in the vertical direction (FZ), as earthquake loads typically affect the horizontal stability rather than applying vertical pressure. These earthquake forces test the structure’s resilience to lateral movement and are critical in ensuring it can withstand seismic events. On the other hand, the flood load cases (Flood-1, Flood-2, and Flood-3) represent scenarios where the structure is subjected to lateral forces from water pressure during flood events. Each case varies in intensity, likely representing different levels or conditions of flooding. Flood −1 applies a relatively low horizontal force of −0.70 Tonf in the x direction, simulating a minor flood impact. Flood −2 increases this force to −2.80 Tonf, indicating a moderate flood condition with a stronger lateral push. Flood −3 has the highest horizontal force, −6.30 Tonf in the x direction, simulating a severe flood scenario with significant lateral force against the structure. Like the earthquake cases, these flood loads do not have any vertical component (FZ = 0), as they mainly exert pressure from the side rather than adding weight vertically.

Each load case highlights different stressors that the structure’s base must withstand. The dead load provides a baseline of constant vertical pressure, while the earthquake and flood loads introduce additional horizontal forces that test the structure’s lateral stability. These base reactions were analyzed to ensure the foundation and base can handle these forces without failure, especially under severe conditions such as major earthquakes or floods. Proper reinforcement, material choice, and design adjustments are often required based on these calculations to maintain the structure’s overall stability and safety.

Global behavior of column under seismic and flood lateral loads

The analysis of seismic and flood lateral loads on the columns demonstrated important look into its stability against sliding forces. The resistance to sliding forces depends on the friction between the columns bases and their foundations, calculated as R = μ × W, where R is the sliding resisting force, μ is the friction coefficient (0.3), and W is the column’s total weight (11.40 tons). Applying these values, we find that R = 0.3 × 11.4 = 3.42 tons. In the case of seismic lateral load, the base shear amounts to 2.55 tons, which is lower than the sliding resisting force of 3.42 tons. This indicates that the column has adequate stability against sliding under seismic conditions, confirming that it is safe against lateral forces generated by seismic activity.

When considering the impact of flood loads, however, the column’s behavior changes based on the height of breaking waves impacting it. The results for three distinct flood load cases presented each representing different breaking wave heights (H_b (m)) and their corresponding sliding flood loads. In the first flood load case, with a wave height of 1 m, the sliding flood load is 0.7 tons, which is significantly less than the sliding resisting force of 3.42 tons, indicating that the column is safe against sliding with a considerable factor of safety. For the second flood load case, with a wave height of 2.2 m, the sliding flood load increases to 2.80 tons, which is still below the sliding resisting force, though the margin of safety is reduced.

In the third flood load case, the wave height reaches 3 m, resulting in a sliding flood load of 6.30 tons. This load exceeds the sliding resisting force of 3.42 tons, rendering the column unsafe against sliding under this scenario. As the resisting force is insufficient to counter the lateral forces from such a significant flood load, the column is likely to experience drifting during flooding conditions of this magnitude. For this, the column remains stable against sliding forces in the first two flood cases but becomes vulnerable in the third case, underscoring the importance of additional measures or reinforcements to prevent drifting under severe flooding conditions.

Sound and decayed column deformations under seismic and flood lateral loads locally

The deformation behavior of ancient stone columns under seismic and flood lateral loads is highly dependent on the structural integrity of the column, which can be significantly influenced by weathering and decay over time. This comparison between a sound column and a decayed column reveals the critical role that material preservation plays in the column’s ability to withstand dynamic loading conditions. For the sound column (Fig. 7), the structural stability is maintained, with minimal deformation observed at the top under earthquake loading, measuring only 2.44 cm. This relatively small deformation indicates that the column retains its original stiffness and stability, allowing it to efficiently distribute the seismic forces. The lower portion of the column experiences even less deformation, which suggests a high resistance to the applied lateral loads and a stable structural response. This uniform deformation pattern in the sound column reflects its intact material and cohesive joints, which prevent excessive displacement and maintain the column’s stability during dynamic events like earthquakes. In essence, the sound column is structurally resilient, capable of withstanding both static and dynamic loads without significant damage or failure.

Fig. 7: Deformation modes under earthquake load.

(1) Load for sound columns and the deformation at top is 2.44 cm. (2) Load for decayed stone column and the deformation at the top is 3.34 cm. After Fahmy⁴⁸.

In contrast, the decayed column (Fig. 7) shows a marked increase in deformation, particularly at the top, where the displacement increases to 3.34 cm under similar seismic loading. This greater deformation indicates a loss of structural stiffness and stability, which is directly attributable to the weathering and decay of the stone. As the material deteriorates, it becomes more prone to cracking, erosion, and internal degradation, weakening the column’s overall ability to resist lateral forces. The increased top deformation suggests that the column’s ability to distribute seismic forces has been compromised, and its weakened structure leads to greater displacement under the same seismic loads. Over time, such increased deformation can exacerbate the damage, potentially leading to progressive structural instability or even collapse if the decay continues without intervention. The weakened dynamic response of the decayed column results in its reduced capacity to absorb and resist seismic forces, making it more vulnerable to failure. Additionally, the loss of stiffness may alter the column’s natural frequency and damping properties, increasing the likelihood of resonance effects during earthquakes and further accelerating the deformation. Therefore, the structural decay of ancient columns significantly impacts their dynamic behavior, highlighting the critical need for preservation and restoration measures to prevent catastrophic failure. Without timely reinforcement or conservation, the continued degradation of the column will likely lead to irreparable damage, posing risks to the structural integrity of the entire archeological site and necessitating immediate conservation efforts to safeguard these valuable heritage structures.

When assessing the deformation modes of ancient stone columns under flooding conditions, the analysis is conducted for both sound and decayed columns, considering various flooding scenarios with different water depths of 1 m, 2 m, and 3 m. These cases explore how flooding influences the deformation of columns, comparing the structural behavior of sound and decayed columns under rising water levels. The deformation is observed primarily at the top of the column structurally, which reflects the column’s vulnerability to lateral forces exerted by water pressure during flooding.

For the sound column under 1 m of flooding (Fig. 8), the deformation at the top is observed to be 1.23 cm. This relatively small displacement indicates that the column retains its structural stability and stiffness despite the applied hydrostatic pressure from the water. The flooding causes some lateral force at the base, but the column, being sound, can still distribute this pressure effectively, preventing significant displacement. The column remains stable, showing only slight deformation at the top, which is a typical response for sound stone columns under mild flooding conditions. The material’s strength, along with its solid structural connections, allows it to resist the applied forces without substantial distortion or failure.

Fig. 8: Deformation modes under flooding cases 1 m, 2 m and 3 m for the sound column and decayed column.

(1) The deformation at top is 1.23 cm for the sound column under 1 m flooding. (2) The deformation at top is 4.93 cm for sound column under 2 m flooding. (3) The deformation at top is 11.08 cm for sound column under 3 m flooding. (4) The deformation at top is 2.3 cm for decayed column under 1 m flooding. (5) The deformation at top is 9.2 cm for decayed column under 2 m flooding. (6) The deformation at top is 20.07 cm for sound column under 3 m flooding. After Fahmy⁴⁸.

For the decayed column under 1 m of flooding (Fig. 8), the deformation at the top increases to 2.3 cm. This larger deformation indicates that decay has weakened the column’s material properties, making it more susceptible to the pressure exerted by the flooding water. The decay process causes a reduction in the stiffness of the column, which results in a greater displacement at the top. As water levels rise, the weakened column is less able to resist lateral forces, causing the column to bend and deform more significantly than its sound counterpart. This highlights how decay compromises the structural stability of the column, making it more vulnerable to external loads such as those exerted by floodwaters.

When the flooding increases to 2 m (Fig. 8), the deformation at the top of the sound column rises to 4.93 cm. The increase in deformation indicates that the column’s resistance to the applied lateral forces is beginning to diminish, but it remains structurally sound. The higher water level exerts more pressure on the column, and while it still distributes the forces adequately, the displacement increases as a result of the greater hydrostatic load. The column’s material and structural cohesion are still sufficient to resist failure, but the deformation is more pronounced due to the increased pressure from the rising water.

In the decayed column, the deformation under 2 m of flooding increases significantly to 9.2 cm. The greater displacement is indicative of the further deterioration of the column’s material, which no longer has the same capacity to resist the increased pressure from the higher water level. As the flooding intensifies, the column’s weakened state becomes more apparent, as it bends more significantly under the pressure. The higher deformation observed in the decayed column under these conditions underscores the impact of decay on the column’s ability to withstand not only seismic but also flooding loads. The increased displacement may lead to further structural instability and potential failure if the decay continues without intervention.

Under 3 m of flooding (Fig. 8), the sound column experiences a deformation of 11.8 cm at the top. The deformation increases as the water level reaches its maximum height, exerting even more pressure on the column. Despite the increased pressure, the sound column still maintains its overall structural stability, and the deformation remains manageable. The column’s material strength and stiffness allow it to continue resisting the flooding forces without catastrophic failure. However, the deformation is now more pronounced due to the extreme conditions, indicating that the column’s capacity to resist lateral forces is being tested but is not yet compromised.

For the decayed column under 3 m of flooding, the deformation at the top increases to 20.7 cm. This significant increase highlights the vulnerability of the decayed column under extreme flooding conditions. As the flooding deepens, the weakened stone material and the loss of structural cohesion in the column result in greater lateral displacement. The increased deformation refers to that the column is at a higher risk of further damage or collapse due to the combined effects of decay and the extreme water pressure. The decayed column’s inability to resist the lateral forces as effectively as the sound column makes it far more susceptible to failure under these conditions.

In this regard, the deformation modes of the sound and decayed columns under flooding conditions reveal a clear contrast in their structural responses. As the flooding depth increases from 1 m to 3 m, the deformation in both columns increases, but the sound column consistently shows smaller deformations compared to the decayed column. The sound column remains relatively stable and can resist the applied forces without excessive deformation. In contrast, the decayed column, with its reduced material strength and structural cohesion, experiences larger deformations and becomes more vulnerable to failure as the water levels rise. The increased deformation in the decayed column at higher flooding depths demonstrates the significant impact of weathering and decay on the column’s ability to withstand lateral forces.

The comparison between in situ displacement measurements obtained using a total station and the numerical results from the FEM simulation provides a meaningful validation of the modeling approach. Field measurements revealed horizontal displacements ranging from 7 cm to 46 cm at the top of the columns, with inclination angles reaching up to 2.719°. These values indicate significant structural instability, exceeding the generally accepted threshold of 2° for critical tilt. In contrast, the FEM simulations under seismic loading predicted top displacements of 2.44 cm for the sound column and 3.34 cm for the decayed column. Under flooding conditions, simulated displacements reached 11.8 cm and 20.7 cm for sound and decayed columns respectively, at a flood depth of 3 m. While these numerical results are lower than the maximum values recorded on-site, they are consistent in trend and magnitude when considering that the FEM model simulated single load cases, whereas the in-situ measurements reflect cumulative effects over decades or centuries, including seismic events, repeated flooding, soil erosion, and ongoing material decay. The close correlation underlines the FEM model’s capability to approximate structural behavior under specific loading scenarios, but also emphasizes that actual long-term displacements are influenced by multiple interacting factors. These results confirm that while the model is suitable for scenario-based risk assessment, it should be complemented with continuous field monitoring to capture real-time deterioration dynamics and inform timely conservation actions.

The stress analysis of the columns, as shown in Fig. 9, offers critical information into the structural behavior of both sound (original) and decayed (weathered) material under various load conditions. Figure 9(1) and (2) depicts the maximum and minimum stresses within the sound column, while Fig. 9(3) and (4) represents similar data for the decayed column. The results indicate that in both cases, the columns are subjected to compressive and tensile stresses that exceed standard allowable limits. However, despite this overstress, the columns are not anticipated to experience local failure immediately. This refers to that the stress distribution across the columns remains relatively balanced, preventing any singular, highly stressed area from collapsing under load. Nonetheless, these findings raise concerns about long-term structural stability, especially in the decayed column, where material degradation could lead to future vulnerabilities.

Fig. 9: The maximum and minimum stresses within the columns under the envelope of the several load cases.

(1) The maximum stresses within the sound column. (2) The minimum stresses within the sound column. (3) The maximum stresses within the decayed column. (4) The minimum stresses within the decayed column. This color-coded stress analysis provides a clear visual understanding of how both sound and decayed columns manage loads, illustrating the importance of material cohesion in maintaining balanced stress distribution and overall stability. After Fahmy⁴⁸.

In the Fig. 9(1), the sound column is subjected to maximum stress. Here, we see a strong presence of red and pink tones at the base, indicating areas experiencing the highest levels of compressive and tensile stress. This is typical for a column under axial load, as the base tends to bear the most weight and therefore endures greater stress. As we move upward, the colors shift towards yellow and green, signifying a gradual decrease in stress levels. The upper portion of the column, which shows green and possibly light blue shades, indicates zones where the stress is minimal due to the lower load being carried. While in the Fig. 9(2) represents the minimum stress distribution in the sound column. In this case, we notice that the colors are generally cooler (yellow to green) with few instances of red at the base. This pattern suggests that even under lower stress conditions, the column’s base is still the most stressed region, while the middle and upper sections experience much less strain. The yellow and green colors at the top reflect zones of structural stability, where the material isn’t under significant stress, indicating that the sound column is effectively managing its load distribution.

Figure 9(3) displays maximum stress levels in the decayed column. Here, the stress profile appears similar in terms of color distribution, but the decay introduces variations in material strength, making the red and pink areas potentially more susceptible to failure. The red zone at the base, which is extensive, signifies that this part of the decayed column is enduring high stress but may be less capable of withstanding it due to weakened material. The shift to orange, yellow, and green colors as we move upward shows that stress levels decrease along the length of the column, but the decayed material at the base remains vulnerable. Figure 9(4) represents minimum stress distribution in the decayed column. The colors are generally warmer (mostly orange and yellow) than those in the sound column’s minimum stress image, indicating an overall higher level of stress even at minimum load. This difference highlights that the decayed column, even under minimal stress conditions, has a limited ability to bear loads effectively, especially at the base. The areas of orange and yellow tones suggest a less efficient distribution of load due to material degradation, increasing the likelihood of stress concentration and, potentially, future material failure if further exposed to environmental stressors.

To mitigate potential risks, conservation and reinforcement measures are recommended, especially for the decayed column. Structural reinforcement at the base and in areas of significant material loss could improve load distribution and reduce excessive stress on weakened zones. Additionally, implementing preventive conservation techniques, such as protection against moisture and temperature fluctuations, will help slow further decay. Regular structural health monitoring is also advisable to detect any progressive changes in stress distribution over time. By actively managing these vulnerabilities, the structural stability and longevity of these historic columns can be significantly enhanced, preserving their structural stability for future generations.

While the presented FEM analysis provides valuable analysis into the behavior of monolithic granite columns under seismic and flooding conditions, several methodological limitations and modeling uncertainties must be acknowledged. The model assumes linear elastic behavior for both granite and limestone, with assigned Young’s modulus values of 5425 MPa for sound granite, 2950 MPa for weathered granite, and 2030 MPa for limestone. These values were sourced from previous studies, where local micro-cracking and mineral loss can significantly reduce stiffness and strength. The boundary conditions used, a fixed base, do not consider soil-structure interaction or foundation settlement, which could alter displacement responses, particularly under flooding scenarios. For example, the simulation predicted a top displacement of 3.34 cm for the decayed column under seismic loading, yet actual displacement could be higher or lower depending on subsoil behavior. Furthermore, flood-induced lateral loads reaching 6.3 tons at 3 m water depth exceeded the modeled sliding resistance of 3.42 tons, suggesting potential instability; however, real flood dynamics may involve additional factors such as debris impact or uneven saturation, which are not accounted for in the current model. Validation was limited to qualitative comparison with field measurements, such as inclination angles up to 2.719° and horizontal displacements up to 46 cm, rather than experimental calibration. Despite these constraints, the approach remains broadly applicable for assessing the vulnerability of similar freestanding heritage structures, provided that local adjustments are made for material properties, soil behavior, and environmental conditions.

Conservation guidelines for the preservation of monolithic stone columns at El-Ashmonein

The monolithic granite columns at El-Ashmonein are invaluable components of Egypt’s cultural heritage, embodying centuries of religious and architectural significance. To protect these columns from seismic and flooding threats, as well as from progressive material decay, a comprehensive conservation strategy must address both structural stabilization and environmental protection. Below are detailed conservation guidelines to ensure these ancient structures are preserved for future generations.

Structural and materials reinforcement and stabilization

Strengthening the foundation is essential to support the columns against lateral loads from seismic and flood forces. For columns showing significant tilting (inclination angles over 2°), reinforce the base with injected grout or reinforced concrete pads beneath the existing foundation. This will create a stable load distribution and reduce tilting risks. It’s recommended to work with conservation-compatible materials to ensure any additions blend seamlessly with the original structure. To counteract internal fractures and surface cracks, inject compatible, non-invasive resin consolidants or mortars within cracks and porous areas. This internal consolidation will help resist further cracking during seismic events. For severe fractures, micro-bolting or the use of fiber-reinforced polymer (FRP) wraps around critical areas can provide added tensile strength without altering the column’s exterior appearance. Moreover, apply lime-based or mineral-based mortars to areas where material has decayed or eroded. This will protect vulnerable areas from water intrusion and further degradation. The surface repair should be minimally invasive, respecting the column’s original esthetics and geometry.

To mitigate water absorption, especially in decayed columns, apply a breathable water-repellent coating. Ensure these coatings allow vapor permeability to prevent internal moisture accumulation, which could worsen cracking or salt crystallization over time. Silane- and siloxane-based products are often suitable for porous stones, as they provide a barrier against moisture without sealing the material entirely. In addition, vegetation surrounding the columns can lead to root infiltration and soil destabilization, which can compromise the foundation. Remove vegetation around the base of each column and apply a shallow layer of gravel to discourage future growth. For broader landscape conservation, implement controlled planting of non-invasive, shallow-rooted species away from the column bases to maintain the area’s esthetic while protecting structural durability. Furthermore, soil erosion around the base of the columns can destabilize their foundations, especially in flood or heavy rains-prone periods. Use geotextiles, stone-filled trenches, or low-retaining walls around the columns to manage soil movement and maintain a stable environment. An additional benefit is that these measures will prevent the soil from absorbing excessive moisture, thereby reducing subsidence risks.

Seismic and flood load resistance

Given the calculated sliding resisting force of 3.42 tons for these columns, increase the base’s resistance to sliding under high flood loads by roughening the foundation surface or applying natural aggregate beneath the columns. Additionally, increasing the friction coefficient by embedding natural stone fragments around the base will help the columns resist lateral flood forces. In addition, installing low stone or brick flood barriers around vulnerable columns, particularly those located in low-lying areas. These barriers can deflect or slow down water flow during heavy rains, reducing the direct impact of floodwater. In areas with high flood risk, consider temporary sandbagging during peak rainfall seasons, with drainage systems installed to redirect water flow safely away from the site. If feasible, consider installing base isolators or specialized seismic shock-absorbing pads beneath selected columns with severe tilting or decay. This approach, although innovative, would help minimize vibration transfer to the columns during earthquakes, protecting them from direct seismic forces. Simulation model was designed to mitigate the seismic and flooding risks for the freestanding stone columns as shown in Fig. 10. This proposed model incorporates a layered foundation system, starting with a concrete base that ensures overall stability and load distribution. Above this, a compacted fine sand layer is introduced to accommodate differential settlement and provide cushioning against dynamic loading⁶⁵. The main seismic mitigation element is a high-damping lead-rubber bearing system, which functions as a base isolator, significantly reducing the transmission of ground vibrations to the overlying stone column during seismic events^66,67. This mechanism absorbs and dissipates seismic energy, lowering lateral displacement and stress concentrations in the column shaft. The entire system is enclosed with lateral soil confinement, enhancing its resistance to horizontal flooding forces and erosion. Such an integrated structural base design represents a conservative and reversible intervention approach suitable for heritage conservation, aiming to protect freestanding columns from the dual threats of earthquakes and high-water pressures without altering the original monument materials.

Fig. 10

The figure illustrates a proposed simulation model designed to mitigate both seismic and flooding risks for freestanding stone columns in archeological settings.

Regular monitoring and assessment

Utilizing advanced measurement tools such as total stations, laser scanners, or photogrammetry to monitor column inclination and displacement periodically. Any detected shift beyond the critical 2° inclination threshold should prompt immediate intervention to prevent further destabilization. Install vibration sensors to record seismic responses, enabling the assessment of how each column reacts to minor tremors over time. This data will support proactive conservation planning by identifying early signs of resonant behavior or stress that could lead to future damage. In addition, conducting an annual in-depth structural analysis, including ultrasonic testing, glossometry, colorimetry and microscopic analysis to detect micro-cracks, material discoloration, or loss of structural stiffness. These non-invasive tests can identify areas at risk for fractures or degradation and allow for timely interventions.

Discussion

This study provides a detailed dual analysis of seismic and flooding vulnerabilities for the ancient monolithic granite columns at the El-Ashmonein archeological site in Minia, Egypt, underscoring both structural and conservation challenges induced by these natural forces. Seismic and flooding risks are particularly significant for ancient columns, given their age, material composition, and exposure to environmental stressors. Using finite element modeling (FEM), we determined that seismic loads create substantial lateral displacement in the columns, especially in decayed structures. Sound columns maintained lateral displacements of 2.44 cm under typical seismic loads, a figure that remained within safe structural limits. However, decayed columns exhibited displacements of up to 3.34 cm, or about 37% greater movement, highlighting the amplified risk in weakened materials. The modal analysis demonstrated that decayed columns have longer fundamental periods of 0.58 seconds and lower frequencies of 1.73 Hz, compared to 0.42 s and 2.37 Hz in sound columns. This increased flexibility in decayed columns raises the risk of resonance under seismic forces, making them especially vulnerable to compounding damage from successive events.

Flooding impacts present a different yet equally complex threat to the columns’ structural integrity, as increased hydrostatic pressure and soil saturation lead to potential deformation and settlement. In flooding simulations, the decayed columns displayed significant vulnerability, with lateral displacements reaching 20.7 cm under extreme flood conditions (3 m of water depth), compared to 11.8 cm in sound columns, a near-doubling of deformation. This difference indicates that decayed material, with its reduced load-bearing capacity and increased porosity, is far more susceptible to lateral forces in high water scenarios. At lower flooding levels of 1-m, sound columns exhibited only 1.23 cm of displacement, while decayed columns showed 2.3 cm, demonstrating the progressive impact of decay even at minimal water levels. As flooding continues to exert lateral pressure, columns with degraded materials could face tilting, sliding, or even partial collapse, especially if compounded by recurrent flooding or seismic shocks.

The results emphasize the critical need for comprehensive conservation strategies that consider both seismic and flooding risks, particularly for historical structures with compromised materials. Structural reinforcement measures, such as grout injection in foundational cracks, installation of reinforced concrete pads, and application of water-resistant coatings that are recommended to enhance stability and reduce moisture infiltration. Additionally, creating environmental controls around the columns, such as low-lying barriers to deflect floodwater and controlled vegetation removal, would help mitigate further material decay and foundational erosion. For seismic protection, introducing base isolators or installing shock-absorbing pads beneath the most vulnerable columns could minimize the transfer of ground vibrations, reducing lateral stress and potential rocking. These conservation methods align with the values of preservation and safety, aiming to secure the structural and cultural integrity of El-Ashmonein’s heritage assets.

Beyond its local context, the implications of this study are globally relevant. Many heritage sites across the Mediterranean, South Asia, and Latin America contain freestanding monolithic or masonry columns exposed to similar dynamic and environmental threats. The methodology applied here, integrating structural monitoring with FEM simulations, offers a scalable, non-invasive framework for evaluating the stability of heritage structures under multi-hazard conditions. The results also highlight the importance of integrating environmental change modeling (e.g., flood level rise and seismicity) into conservation planning. This approach aligns with international conservation goals under UNESCO and ICOMOS, promoting proactive, data-driven risk management strategies.

However, several limitations must be acknowledged. The FEM models assumed linear elastic behavior and used idealized boundary conditions (e.g., fixed bases), omitting critical factors such as soil-structure interaction, nonlinear fracture propagation, cumulative weathering, and dynamic debris impact during floods. Material properties were estimated based on literature values rather than site-specific destructive or micro-mechanical testing. Furthermore, validation was limited to qualitative comparison with field observations, without extensive sensor-based real-time monitoring.

Despite these constraints, the research provides a basic foundation for prioritizing conservation interventions, recommending the integration of seismic base isolators, enhanced foundations, and hydrological defenses. Future work should incorporate probabilistic hazard analysis, nonlinear time-history simulations, and long-term displacement monitoring to further refine structural vulnerability assessments. In sum, this paper contributes a replicable, interdisciplinary model for safeguarding stone column heritage against the increasing threats of seismic and hydrological extremes worldwide.