Finite Element Modelling Approaches for Assessing Column Stability in Heritage Structures: A Case Study of the Mosque–Cathedral of Córdoba

Abstract

This study has investigated the structural and seismic performance of monolithic stone columns in the historical Mosque–Cathedral of Córdoba, with a focus on the earliest section constructed during the reign of Abd al-Rahman I (VIII century). An advanced 3D finite element (FE) model has been developed to assess the effects of geometric imperfections and component interactions on the stability of columns under both vertical and horizontal static loading. Three distinct modelling strategies have been employed in OpenSees 3.7.1, incorporating column inclination and contact elements to simulate mortar interfaces. Material properties have been calibrated using experimental data and in situ observations. The gravitational analysis has shown no significant damage in any of the configurations, aligning with the observed undamaged state of the structure. Conversely, horizontal analyses have revealed that tensile damage has predominantly occurred at the lower shaft. The inclusion of contact elements has led to a significant reduction in lateral resistance, highlighting the importance of accounting for friction and interface behaviour. Column inclination has been found to have a significant influence on failure patterns. These findings have highlighted the critical role of detailed modelling in evaluating structural vulnerabilities. Such features are generally included in the numerical modelling and evaluation of heritage buildings. Consequently, they can contribute to a better understanding of the seismic behaviour of historic masonry structures.

1. Introduction

1.1. Challenges in Modelling Stacked Stone Columns in Heritage Structures

Historical structures have been highly vulnerable to natural hazards, particularly earthquakes. Over the centuries, these events have caused severe damage to monumental buildings such as churches, mosques and minarets [1,2,3,4]. Since heritage buildings were built without seismic design principles, they often present structural and seismic weaknesses such as poor horizontal connections, irregular construction or heterogeneous materials [5]. The vulnerability of these monuments can be further aggravated by the gradual degradation of materials caused by environmental conditions and prolonged structural stresses [6]. Consequently, assessing the seismic vulnerability of these structures has been essential both for their preservation and for developing risk-reduction strategies [7,8,9,10].

In many heritage sites, including mosques, churches and classical temples, the vertical load-bearing system relies on stone columns made of marble, granite or limestone. These columns were often reused from earlier constructions. In some cases, they were assembled from multiple segments with little or no mortar. Traditionally, columns typically rested directly on stone bases without any physical connection, which makes them highly vulnerable to lateral loading [11]. Over time, geometric irregularities and accumulated deformations have made the columns increasingly prone to rocking, sliding, or localised cracking under seismic loads [10].

Long-term damage processes such as creep and accumulated deformation had been identified as crucial features that should be explicitly included when modelling heritage buildings [12]. In fact, idealised representations risk underestimating their actual behaviour. As highlighted by several authors, the structural assessment of heritage columns should not only consider the mechanical modelling but also integrate the history of the building, its actual geometry, existing alterations and accumulated damage [13].

Previous works also showed that the choice of the geometric model strongly influenced the outcomes from structural analyses of heritage buildings: overly simplified geometries could alter stress values and failure mechanisms [14]. Despite this, studies on the structural stability of heritage buildings are usually carried out on a global scale, often neglecting the specific behaviour of column elements [10,15]. This gap is especially significant for multi-drum and freestanding columns, which are among the most sensitive components to lateral forces and represent a major challenge in structural heritage engineering [16,17,18].

1.2. Numerical Modelling Approaches of Stacked Heritage Columns

Advanced numerical modelling has become essential for analysing the behaviour of heritage structures. The finite element (FEM) and the discrete element (DEM) methods have been the most widely used approaches to study the response of heritage buildings [19]. FEM enables the detailed representation of geometry, nonlinear constitutive behaviour and contact interactions. Also, it has been proven particularly effective for simulating cracking and crushing under static and dynamic loading. It can also reproduce frictional sliding at interfaces by introducing zero-length contact elements.

DEM, in contrast, represents the structural configuration as a system of rigid or deformable blocks that interact through contact laws. This approach has been especially useful for capturing rocking, sliding and separation phenomena in dry-jointed systems [19]. More recently, hybrid FEM–DEM strategies were developed to combine the strengths of both methods, improving the simulation of discontinuous behaviour while retaining material reliability [20,21].

Although hybrid methods offer promising results, FEM remains the most frequently adopted in engineering practice due to its versatility and its integration into widely used platforms such as OpenSees [22]. Its ability to simulate both global response and localised damage has made it one of the most reliable tools for heritage assessment. At the same time, new advances such as 3D laser scanning have allowed researchers to capture highly detailed geometries of heritage buildings [23]. However, translating these into FEM meshes remains a challenge due to the complexity when meshing the geometry, among other issues.

1.3. Previous Studies on the Structural Assessment of Stacked Heritage Columns

The structural and seismic response of freestanding and stacked stone columns has been widely studied. Earlier works showed that horizontal excitations can produce significant sliding and energy dissipation in freestanding heritage columns [18]. Also, geometric irregularities and load direction were found to be decisive in rocking behaviour and cracking patterns in old buildings [20,21]. Other works introduced specific modelling strategies to reproduce rocking behaviour and interface contact through distributed springs. These approaches were validated with FEM on commercial software and experimental data [24]. Numerical analyses using ABAQUS, validated with shaking-table tests on scaled multi-drum columns, confirmed the critical role of interface slip and energy dissipation under horizontal excitation [18].

DEM-based studies provided further insights. Simulations demonstrated that vertical accelerations worsen overturning in dry-jointed systems [16,25]. Analyses of multi-drum columns showed that drum joints can act as dissipation devices, altering stability mechanisms [25]. Other research focused on the parametric analysis of the seismic response of isolated columns, incorporating contact elements to simulate the interaction between individual components [18,26].

Combined FEM–DEM models were also developed to capture both material reliability and discontinuous behaviour. This approach was proven particularly valuable for seismic sensitivity analysis of classical columns [20]. Also, the FEM-DEM method was used to enhance the understanding of classical masonry columns, including their sensitivity to seismic excitations [21,27]. Mesh discretisation and interface modelling were also highlighted as critical factors for reliable dry-stone masonry simulations [28,29].

Experimental campaigns were essential in validating these models under static and dynamic conditions [30]. These campaigns were based on either non-destructive characterisation using the hammer impact test [31] or shaking-table tests. In [20,32], shaking-table tests on scaled marble columns confirmed numerical predictions of rocking behaviour and collapse. Additional experiments demonstrated how reducing the number of column drums increases the bearing capacity under static and dynamic loads [17]. In general, studies on scaled stone columns consistently provided insights into failure mechanisms and improved conservation strategies [9,21].

Other investigations examined the influence of geometric features, material properties and reinforcement techniques [33,34]. Solutions such as titanium or metallic connectors were sometimes proposed to improve seismic resistance [29]. However, their effectiveness remained highly dependent on the configuration of columns.

Still, most of these works relied on idealised or simplified geometries, often ignoring the material variability, accumulated deformations and irregularities characteristic of real heritage columns. For example, FEM evaluations of mosques and churches often relied on idealised geometries, neglecting deformations and pre-existing cracks [8,35].

1.4. Scope and Novelty of the Work

The Mosque–Cathedral of Córdoba (Spain) provides an ideal case for addressing these gaps. Its hypostyle hall contains more than 1300 stone columns supporting arches and timber roofing. Field surveys revealed inclinations of up to 3.5° (up to 12 cm) from the vertical axis [36], raising concerns about their stability under gravitational and seismic actions. Previous studies generally adopted idealised geometries, overlooking these imperfections, even though they represent a major detrimental factor for stability [10,37]. As emphasised by several authors, modelling existing damage and deformation is critical to ensure realistic predictions of the structural performance [12].

In a recent study conducted by the authors [37], the geometric and material calibration of part of the monument was obtained using non-destructive tests, improving knowledge of its global behaviour. However, a detailed analysis of individual columns, explicitly accounting for measured inclination and contact behaviour, has not been carried out.

This paper addresses these gaps by presenting a numerical study of the stone columns in the oldest part of the Mosque–Cathedral, dating from the period of Abd al-Rahman I (VIII century). The research develops full-scale three-dimensional FEM models of the columns, integrating three key aspects that are often ignored: (i) realistic geometric imperfections, (ii) nonlinear material models calibrated with experimental data and (iii) contact elements simulating mortar-like behaviour. Unlike previous studies, these features have been combined in full-scale models based directly on survey data.

The novelty of this work lies in demonstrating how column inclination and contact interactions, when modelled together, significantly modify the seismic response, changing both capacity and failure mechanisms. This finding has direct implications for the conservation of hypostyle mosques and similar heritage buildings. By moving beyond global analyses, this study provides a detailed understanding of how local imperfections affect overall vulnerability, offering new guidance for preservation strategies.

The structure of the rest of this paper is as follows. Section 2 presents the case study, describing the architectural features of the Mosque–Cathedral, the seismic hazard of the region and the current state of the columns. Section 3 explains the modelling strategy, including geometry, materials, contact formulation and loading conditions. Section 4 presents the results of gravitational and lateral analyses, followed by a discussion in Section 5. Section 6 concludes with the main findings and perspectives for future work.

2. Case Study: The Mosque–Cathedral of Córdoba

2.1. Historical and Architectural Context

The Mosque–Cathedral of Córdoba is an emblematic monument that represents centuries of cultural and architectural evolution. It is a UNESCO World Heritage Site. It was originally constructed as a mosque between the VIII and X centuries and, later, expanded with Christian architectural elements until the XV century in Figure 1a.

The Mosque–Cathedral follows a hypostyle layout characterised by a large hall with repeating rows of stone columns arranged in parallel naves. Each column supports the iconic system of double arches [38]: a lower horseshoe-shaped arch, which provides lateral stiffness and distributes loads, and an upper semicircular arch, which transfers loads from the timber roof in Figure 1b. This arrangement not only allowed greater interior height but also created the distinctive visual rhythm of the monument. The columns are highly heterogeneous in origin and material, including marble, granite and limestone, many of which were spolia reused from earlier Roman and Visigothic buildings.

The bases are generally composed of simple stone bases with no mechanical connectors. The capitals vary from Corinthian to Visigothic typologies depending on their origin. Representative measurements indicate column heights of approximately 4.5–5.0 m and diameters ranging between 0.35 m and 0.45 m, while capital heights average 0.6 m. Foundations consist of stone platforms integrated into the floor without mortar connections, which highlights the structural sensitivity of the system to lateral actions. More detailed discussions of the historical and architectural features of the building can be found in [37,39].

The monument is located in southern Spain in the city of Córdoba, a region of moderate seismicity associated with the intraplate seismicity caused by the convergence of the Eurasian and African plates. Although Córdoba is not among the most seismically active areas of the Iberian Peninsula, historic earthquakes such as the 1755 Lisbon and the 1504 Carmona events affected the region. Even moderate ground motions may entail a risk for slender masonry columns with no physical connections. For this reason, a seismic assessment is necessary to ensure the long-term preservation of the monument.

The specific sector analysed in this study belongs to the original mosque commissioned by Abd al-Rahman I in the VIII century. Located in the northwestern portion of the present-day prayer hall in Figure 1a, this area is approximately 90 m wide and 20 m long and consists of 11 longitudinal naves in Figure 2. There are a total of 130 columns of marble, jasper and limestone, which support the characteristic horseshoe arches of this early construction phase.

2.2. Current State of the Columns Under Study

The geometric properties of the columns analysed here have been derived from previous research [40]. According to both the literature and information provided by the building’s conservation team, no severe damage has been observed in any section of the structure. The Mosque–Cathedral follows a continuous maintenance and rigorous conservation programme.

In Figure 3a, the connection between the shaft and the capital of one of the most demanded columns is presented. In Figure 3b, the base–shaft connection can be seen while an in situ test is being carried out. For additional information on the experimental campaign carried out, the authors are referred to the previous work of the authors [37,39]. As can be seen, the inspections confirmed the absence of visible tensile cracks or detachment in the structural elements. This will be consistent with the negligible tensile damage predicted by the numerical analyses under gravitational loading.

Nevertheless, geometric surveys have revealed deviations of several columns from an ideal vertical alignment in the sector studied [36]. These inclinations represent a key parameter for the structural assessment. The maximum recorded deviation was 3.5° in both directions relative to the horizontal load axis. This has been used in this study as a worst-case scenario to simulate the boundary conditions (

Table 1. Deflection of the columns in the Abd al-Rahman I sector, adapted from [28]. (Number of columns: 130).

Values/Direction	North (+)–South (−)	East (+)–West (−)
Average	0.91°	0.18°
Maximum	3.44°	1.59°
Minimum	−1°	−2.28°
Standard deviation	0.80	0.84

).

Table 2. Mechanical properties of the materials used in the numerical models.

Material	Colour Legend	ρ (T/m3)	E (GPa)	G (GPa)	v	ƒc (MPa)	ƒt (MPa)
Marble	Purple	2.8	16	6	0.25	67	3.50
Granite	Blue	2.8	42	14	0.25	63	3.45
Brick masonry	Brown	1.8	1.7	0.55	0.2	3.57	0.12

shows the values of the elastic modulus, compressive strength and tensile strength used in this study and adopted from previous research by the author [37,39]. It should be noted that values reported in [37,39] were derived from a combination of sources. This involved non-destructive in situ tests such as rebound hammer and ultrasonic pulse velocity, complemented by published values for similar stone types [41]. These parameters reflect typical ranges for heritage marble, granite and brick masonry. However, natural stone exhibits significant variability due to heterogeneity in grain size, presence of micro-cracks, mineralogical composition and provenance. For example, some granite columns show quartz inclusions, while certain limestone elements exhibit variable porosity related to their historical quarry origin. The age of the reused Roman and Visigothic columns also contributes to differences in mechanical response. Therefore, the values adopted represent averaged properties, which allow for numerical feasibility but may not capture the full variability of the actual material.

3. Numerical Modelling Strategies

3.1. FEM Model

The numerical analyses have been performed in the OpenSees framework [22], using the STKO 4.1.0 software interface [42]. A macro-mechanical strategy has been adopted, as it allows the simulation of full-scale elements while still capturing localised damage. Solid elements have been used over shell or beam formulations to achieve a more realistic stress–strain response. This choice follows earlier studies that demonstrated the advantages of solid discretisation in heritage structures, particularly for representing cracking and stress concentrations in irregular geometries [43,44,45].

In Figure 4, the 2D schematic drawings illustrate the main geometric parameters of representative columns, including height, diameter and the location of the centre of mass.

For the FEM analysis, three different modelling strategies have been implemented:

• CONT model—a perfectly vertical column, represented as a single continuous solid element with no contact interfaces;
• DIV_ZL model—a column divided into four blocks (base, second base, shaft and capital), connected through zero-length contact (ZL) elements to reproduce interface behaviour;
• Inclined models—columns with a maximum tilt of ±3.5° (from Table 1), applied to both the CONT and DIV_ZL configurations. These models are denoted by adding the inclination to their nomenclature (e.g., CONT+3.5, DIV_ZL−3.5).

A refined meshing strategy has been used to ensure both architectural reliability and numerical stability in Figure 5. In Figure 5a, the materials implemented in the FEM can be observed, considering the colour legend presented in Table 2. In Figure 5b, the divisions created to normalise the mesh are shown. In Figure 5c, the FEM mesh of the base is shown in detail. Figure 5d presents the arcade modelling, including pointing out the brick masonry material. Figure 5e shows the distribution of the reaction force in the Z direction under vertical loading conditions.

Following the recommendations of [46,47], a mesh size of 0.05 m has been selected as a compromise between accuracy and computational cost after a sensitivity analysis of the size. The irregular geometry of the columns has been discretised with tetrahedral solid elements, each with four integration points. The resulting FEM model contains 20,110 solid elements and 3722 nodes.

3.2. Nonlinear Material Behaviour

The nonlinear behaviour of the materials has been simulated using a damage–plasticity model [48], which is suitable for brittle materials such as stone. Separate constitutive laws have been defined for compression and tension in Figure 6. For the compression, gradual stiffness degradation has been implemented, capturing the combined effects of plastic flow and crushing. The compressive law is defined by the elastic limit (f_c0), peak strength (f_cp) and residual capacity (f_cr), with ε_cp representing the strain at peak stress. For the tension, a brittle response has been considered, characterised by sudden stiffness loss and crack propagation. Fracture energies (G_c and G_t) have been calculated following the procedure in [49]. To ensure mesh-size independence, the input values have been scaled by the characteristic element length (l_ch). The constitutive parameters have been calibrated against the mechanical properties in Table 2, derived from experimental tests and visual inspections of the actual columns.

3.3. Damage Assessment

To evaluate the state of the columns under different loading conditions, the numerical analyses have employed a damage–plasticity constitutive model that defines independent indices for tensile and compressive degradation. These indices provide a scalar measure of material deterioration, with values ranging from 0 (undamaged) to 1 (complete loss of capacity). This approach allows for the identification of localised vulnerabilities, such as zones prone to tensile cracking near the shaft base or sliding along block interfaces, even in scenarios where the global structure remains stable.

The tensile damage index (d⁺) represents crack initiation and propagation. Values close to 1 indicate near-complete tensile failure and loss of tensile stiffness. For instance, results reported as high as d^+/− = 0.85~0.90 correspond to situations where the material has almost fully exhausted its tensile strength and stiffness, signifying imminent cracking at that location. The compressive damage index (d⁻) reproduces progressive crushing under compressive stresses.

3.4. Contact Formulation and Boundary Conditions

For models including segmentation, the interaction between blocks has been simulated through the zeroLengthContactASDimplex element in OpenSees. This formulation uses a penalty-based friction law governed by the Mohr–Coulomb criterion, as shown in Equation (1):

$$T=\mu N+c$$

(1)

where T is the tangential force, N is the normal force, μ is the friction coefficient, and c is the cohesion (summed over the effective contact area).

The parameters have been chosen based on experimental references and the literature: μ has been set to 0.4, which is within the typical range of 0.3–0.5 [41]. c has been equal to 0.1 MPa, consistent with well-preserved stone interfaces [50]. The normal and tangential stiffnesses (K_n, K_t) have been set as 2 × 10⁹ kPa/m and 6 × 10⁸ kPa/m, respectively, according to [41]. Contact elements have been defined between master–slave node pairs aligned with the global Z-axis. The IMPL-EX integration scheme has been employed to improve convergence in highly nonlinear steps.

The vertical loads transmitted by the arches and timber roof have been applied as uniform pressures on the column capitals. However, the superstructure was not modelled as deformable elements, and no contact elements were introduced at the top interface. This simplification isolates the column behaviour but neglects the stiffening role of the upper arches and roof, which is recognised as a stabilising mechanism in the actual structure.

The boundary conditions reproduce the combined effects of gravitational and lateral loading, together with measured geometric imperfections.

• Vertical loads: applied incrementally using the load-control method. First, the self-weight was considered as a volumetric force based on material densities. Then, additional loads from the superstructure were incorporated. A preliminary FE analysis of the arcade in Figure 5e yielded a maximum column force of 11.93 kN/m², which has been applied as a uniform pressure on the capitals;
• Horizontal loads: three patterns have been tested: (i) discrete nodal forces along the height, (ii) uniformly distributed loads and (iii) triangular loads proportional to height. For consistency, load magnitudes were normalised across all the simulations. The displacement-control method has been used to drive the nonlinear analyses;
• Geometric imperfections: column inclinations of ±3.5° have been explicitly introduced as rotations about the Y-axis (green). This allows the evaluation of how realistic deviations influence seismic behaviour.

4. Analysis of the Results

4.1. Nonlinear Static Gravitational Analysis

The first set of simulations has focused on the gravitational response of the columns. Figure 7 illustrates the damage patterns in compression (d⁻) and tension (d⁺) after applying the self-weight and the additional loads from the arcades. Damage values range from 0 (undamaged) to 1 (fully damaged).

For the perfectly vertical continuous model (CONT) (Figure 7a), no significant tensile or compressive damage has been observed. This is consistent with in situ inspections, where no deterioration is visible in the columns. Introducing the segmentation with contact interfaces (DIV_ZL model) has not substantially altered the response: the stress distribution remained nearly identical, with negligible damage in both tension and compression in Figure 7d,e. These results confirm that, under gravitational loading alone, neither interfaces nor segmentation play a decisive role in the behaviour of the columns.

Inclination, however, has introduced notable changes. When the column has been tilted by +3.5° about the Y-axis, tensile damage concentrated in the lower shaft has reached approximately 30% of the tensile capacity in Figure 7b. For the −3.5° inclination, values have been slightly lower, around 26%. In both cases, compressive damage has remained negligible in Figure 7c, showing that bending primarily has affected the tensile response.

When combining inclination with segmentation (DIV_ZL), tensile damage has risen significantly: nearly 70% for the +3.5° case (Figure 7d) and over 80% for the −3.5° case. Compressive damage has also increased, reaching 18% and 26%, respectively, in Figure 7e. Nevertheless, tensile values have remained just below the typical cracking threshold (85–90% of ultimate tensile strength). Hence, this means that the indicated values represent moderate stiffness degradation without surpassing the peak compressive strength f_cp. Therefore, the material response remained within the nonlinear pre-peak regime and did not reach crushing failure.

These findings indicate that column inclination triggers tensile stress concentration under vertical loads and that segmentation has an additional detrimental effect on tensile distribution. Including contact surfaces/considering segmentation in the model alone under vertical loads does not significantly affect the outcome.

4.2. Nonlinear Static Horizontal Analysis

The second phase of this study has analysed the response under horizontal loading. Capacity curves have been obtained for three load distribution patterns: nodal proportional, uniform and triangular. As shown in Figure 8, the triangular pattern has consistently produced the most unfavourable response, leading to lower peak resistance and earlier transition into the nonlinear regime.

It should be noted that the continuation of pushover curves beyond the plotted displacement range arises from the use of displacement-controlled analyses. In physical terms, this means that global collapse had not yet occurred within the considered range. However, localised damage such as tensile cracking or sliding has already been significant. In practice, the functional limit state of the structure would be reached well before the maximum displacements observed in the numerical curves.

Damage maps in Figure 9 confirm that the tensile stresses are concentrated near the lower shaft for all the cases. Even in the perfectly vertical continuous column in Figure 9a, tensile damage has reached d+ = 0.98. This indicates a high likelihood of cracking, while compressive damage has remained moderate (d− ≈ 0.6).

When contact interactions have been introduced in Figure 9b, the columns have exhibited a more compliant response. Unlike the continuous model, the DIV_ZL column lacked a distinct peak resistance in the capacity curve in Figure 8b. In fact, in the discontinuous (DIV-ZL) configurations, governed by the Mohr–Coulomb interface criterion, the failure mechanism was dominated by sliding at the interfaces rather than by column overturning. The adopted values of friction coefficient and cohesion resulted in progressive shear slip under horizontal actions, delaying uplift and preventing overturning within the analysed displacement ranges. Instead, gradual energy dissipation through interface sliding has dominated the behaviour. This mechanism has reduced the peak resistance by about 50%, from 66 kN (continuous) to 36 kN (segmented). Figure 10 illustrates how tensile damage has been concentrated along the interfaces, reinforcing the importance of contact modelling.

Inclination has further amplified these effects. In the CONT model with +3.5° inclination in Figure 9c, the peak tensile damage has reached d+ = 1.0, corresponding to crack formation, with a diagonal fracture spanning the lower shaft. The −3.5° case, however, has shown an 80% higher peak resistance compared to the +3.5° case. This highlights the strong directional dependence of inclination relative to load. Despite this, the tensile damage again has reached 1.0, accompanied by compressive damage of up to 0.86.

For segmented models with inclination in Figure 9d,e, the combination of contact interactions and geometric imperfections has proved especially detrimental. In the +3.5° case, lateral resistance has been minimal, with peak loads barely exceeding 1.8 kN. This suggests that rocking and sliding at the interfaces have completely dominated the response. Conversely, the −3.5° case has displayed a delayed but much stronger resistance. After an initial phase of sliding with negligible capacity, the column has mobilised a peak resistance of about 68 kN, significantly higher than in other inclined cases. Here, the tensile damage has stabilised at 0.83, while compressive damage peaked at 0.64. This confirms that energy dissipation through sliding became the governing mechanism.

5. Discussion

The results obtained in this work have confirmed and extended findings from previous research on the behaviour of heritage stone columns. Earlier studies already highlighted that freestanding and multi-drum columns are particularly sensitive to horizontal actions, with rocking and sliding dominating their response [16,18,20]. The analyses of this work have reproduced these mechanisms. Also, it has been observed that the tensile cracking develops at the lower shaft, while contact sliding governs the overall lateral resistance in segmented columns.

The reliability of the modelling approach is reinforced by comparison with published experimental data and observations from other heritage contexts. Shaking-table tests on scaled marble columns [20,33] have demonstrated failure mechanisms dominated by rocking, sliding and tensile cracking at the base, which are consistent with the patterns obtained in this study. Similarly, DEM-based analyses of multi-drum columns [25,26] reported significant reductions in lateral capacity due to interface sliding, in agreement with the results of the DIV-ZL models. In line with those works, it has been found that the energy dissipation occurs primarily through interface sliding, which delays or modifies the failure mode compared to monolithic systems. The approximate 50% drop in the resistance observed here is consistent with the tendency reported in [18,29].

Field reports of earthquake damage in heritage mosques and colonnades [2,16,35] also confirm that sliding and rocking are predominant, often accompanied by cracking at the column base. The agreement between numerical findings and both experimental and observational evidence provides confidence in the predictive capacity of the adopted finite element approach, despite the inherent simplifications.

Geometric imperfections have been identified in other studies as a key factor in altering the response of heritage columns [12,21]. The results obtained in this study confirm this influence, adding further evidence that the orientation of inclination relative to the applied load can either reduce or enhance resistance. This directional dependence has rarely been emphasised in previous works and represents a key novelty of the present study.

The role of the upper arches and timber roof should be highlighted as a stabilising component. Their presence is expected to provide additional restraint against lateral displacements and rocking, which was not explicitly reproduced in the current models. The analyses of isolated columns should therefore be regarded as conservative, focusing on local vulnerabilities.

From a conservation perspective, the results highlight the importance of minimising tensile stresses and sliding at the base–shaft interface. Strategies that may be considered include the use of compatible lime-based grouts or micro-injection techniques to improve contact surfaces, the installation of discreet reinforcement such as titanium dowels or stainless-steel connectors to provide additional shear transfer, and the implementation of non-invasive monitoring systems (e.g., inclinometers, 3D laser scanning) to track long-term deformations. Although invasive interventions should be avoided to preserve authenticity, parametric studies in the literature have demonstrated that subtle improvements in base anchorage or interface friction can significantly enhance seismic performance without altering visual integrity.

Finally, the gravitational analyses have confirmed that current inclinations in the Mosque–Cathedral columns remain below critical thresholds, which aligns with in situ observations of their good preservation state. This supports the idea that vulnerability becomes most relevant under horizontal loading scenarios, rather than under vertical stresses.

While the present study has focused on the behaviour of isolated columns, the actual stability of the Mosque–Cathedral depends on the interaction of almost a thousand columns, the double arches and the timber roof. The global system benefits from additional restraint provided by the arches, as well as mutual confinement effects among adjacent columns and walls. Consequently, the numerical results reported here should be interpreted as conservative indicators of local vulnerabilities, particularly with respect to tensile cracking and sliding at the base–shaft interface. These local mechanisms represent the first stages of damage and, when considered across the entire hypostyle hall, may accumulate into system-wide vulnerabilities. Therefore, the single-column assessment can be regarded as the first step in a hierarchical evaluation framework: (i) local element stability, (ii) interaction at the arcade level and (iii) global performance of the monument. This approach ensures that the intrinsic weaknesses of individual columns are not overlooked, while recognising the stabilising role of the superstructure.

6. Conclusions

This study has presented a numerical investigation into the structural behaviour of stone columns in the Mosque–Cathedral of Córdoba, focusing on the oldest sector dating from the VIII century. Using the FEM within OpenSees, nonlinear static analyses under both gravitational and horizontal loading have been performed. To do so, models have explicitly included the measured column inclinations and contact interactions between components. The main conclusions can be summarised as follows:

• Under gravitational loads, both continuous and segmented models without inclination have shown negligible damage, consistent with the undamaged condition observed in situ. Inclination introduced minor tensile stresses at the lower shaft, but these remained below the typical threshold for crack formation. This confirms that current deformations do not pose an immediate risk to the monument’s stability;
• Under horizontal loading, tensile damage has been concentrated at the lower shaft, leading to significant reductions in lateral resistance. Among the loading patterns tested, triangular distributions consistently produced the most unfavourable response;
• Contact interfaces between column segments reduced peak lateral resistance by about 50% while also changing the failure mechanism from monolithic cracking to sliding-dominated behaviour. This finding highlights the importance of accounting for mortar joints and frictional interfaces in realistic models;
• Column inclination has been shown to strongly affect performance. Resistance decreased significantly when horizontal forces were applied in the same direction as the inclination, but increased when applied in the opposite direction. This directional effect underscores the need to incorporate measured geometric irregularities in structural assessments.

Overall, this study has provided new insights into how imperfections and contact behaviour combine to influence the seismic vulnerability of heritage stone columns. The results reinforce the importance of moving beyond idealised global models, adopting detailed approaches that capture local damage mechanisms. These findings can inform conservation strategies not only for the Mosque–Cathedral of Córdoba but also for similar hypostyle monuments worldwide. The modelling outcomes suggest that preventive conservation strategies should prioritise the improvement of base–shaft interfaces and the monitoring of inclined columns. Potential reinforcement solutions, provided they remain minimally invasive, could enhance seismic safety while respecting the authenticity of the monument.

Nevertheless, beyond these specific results, some limitations should be pointed out. First, it should be noted that the adopted parameters correspond to average values and do not fully represent the heterogeneity of natural stone. Consequently, the results of the simulations should be interpreted as indicative of general trends rather than exact predictions of localised behaviour. This limitation is consistent with the approach adopted in other studies on heritage structures, where simplification is necessary to ensure model tractability. Second, the influence of soil–structure interaction has not been considered in this work. Since foundation conditions may modify both global stability and local damage mechanisms, this factor should be addressed in future studies.

Future work should extend this research by conducting dynamic time-history analyses, exploring seismic response under realistic ground motions and evaluating possible reinforcement strategies to enhance resilience while respecting the authenticity of the monument.