Structural Evaluation of the Historical Bridge in the Yukhari Bash Architectural Reserve: A Comparative Finite Element Analysis Before and After Restoration

Abstract

This study investigates the structural behavior of the historical bridge located in the “Yukhari Bash” National Architectural Reserve Zone in Sheki, Azerbaijan, using finite element analysis (FEA) before and after its restoration. The primary objective is to evaluate the performance of the bridge under self-weight and seismic loads, following the standards of the Turkish Building Earthquake Code. The bridge, constructed primarily with limestone masonry, was analyzed using SAP2000 software. The results indicate that the structural integrity under compressive and shear stresses remained within acceptable limits both before and after restoration. However, post-restoration improvements in stress distribution and deformation were evident. This paper contributes to the preservation of historic structures through modern engineering analysis and provides insights into the appropriate restoration practices for masonry arch bridges.

1. Introduction

Historical bridges are not merely utilitarian infrastructures but also invaluable cultural assets that reflect the architectural, social, and technological achievements of their respective civilizations. Throughout centuries, masonry arch bridges have played a critical role in shaping the development of urban and rural landscapes, particularly in regions where trade, military, and cultural interactions necessitated robust and durable transport systems [1,2]. These structures, often built with locally sourced stone and traditional construction methods, stand as testaments to human ingenuity and resourcefulness in pre-industrial societies.

Historical bridges in seismic-prone areas necessitate specialized structural evaluation due to their vulnerability to dynamic loading. Finite Element Analysis (FEA) enables engineers to simulate complex load scenarios accurately, thereby aiding in the preservation and restoration of heritage structures.

In the context of heritage conservation, masonry bridges demand careful and multidisciplinary evaluation owing to their historical significance and structural vulnerability. Environmental factors such as freeze–thaw cycles, rainfall, vegetation growth, seismic activity, and anthropogenic influences including vehicular traffic, poor drainage, and unqualified repair interventions often contribute to the deterioration of these historic structures [3]. Unlike modern engineered systems, historical bridges were designed based on empirical knowledge rather than codified standards, which presents unique challenges in assessing their structural performance in today’s context [4].

One such significant historical structure is the 1st bridge located within the “Yukhari Bash” National Historical and Architectural Reserve in Sheki, Azerbaijan. This region, recognized as a UNESCO World Heritage Site, is noted for its rich cultural tapestry and distinctive architectural heritage [5]. The Yukhari Bash district, in particular, is emblematic of traditional urban planning and construction in the Caucasus, encompassing mosques, caravanserais, residential complexes, bathhouses, and bridges. Among these, the 1st bridge serves not only as a functional crossing but also as a cultural landmark linking past to present.

Constructed primarily from locally sourced limestone and lime-based mortar, the bridge exemplifies the characteristics of regional masonry techniques. Field investigations revealed the use of dry-joint masonry in portions of the arch, as well as signs of differential settlement, material erosion, joint loss, and biological colonization. Such damage, if left untreated, could compromise the safety, durability, and authenticity of the structure [6].

In response to the observed degradation, a comprehensive restoration initiative was proposed, encompassing structural stabilization, material repair, and conservation of architectural authenticity. In line with contemporary conservation practices, the intervention aimed to respect the historic fabric while enhancing the bridge’s structural resilience. As part of this effort, a detailed structural analysis using finite element modeling (FEM) was conducted to evaluate the bridge’s behavior under both gravitational and seismic loads before and after the proposed restoration.

The finite element analysis was performed using SAP2000 (v22.0), a widely accepted structural engineering software capable of handling complex geometries and loading conditions [7]. The numerical model incorporated material properties derived from in situ observations, historical documentation, and relevant literature. Boundary conditions and load combinations were defined in accordance with the Turkish Building Earthquake Code [1], adapted to the local seismic parameters of the Sheki region [5,8].

This paper presents the outcomes of that structural analysis and discusses the implications for the bridge’s long-term conservation. Specifically, the objectives of this study are:

• To assess the existing structural condition of the 1st bridge in Yukhari Bash prior to restoration;
• To model the structural behavior of the bridge using advanced FEM techniques under various load scenarios;
• To compare the pre- and post-restoration performance in terms of stress distribution, displacement, and modal characteristics;
• To evaluate the effectiveness of the restoration in achieving safety and durability while preserving the historical integrity;
• To contribute to the broader field of historical bridge conservation by sharing a replicable methodology based on empirical data, numerical modeling, and heritage conservation principles.

The rest of the paper is organized as follows: Section 2 offers a review of relevant literature on masonry bridge analysis and conservation techniques. Section 3 details the materials, modeling parameters, and methodological framework used in the analysis. Section 4 presents the comparative results of the structural evaluation before and after restoration. Section 5 summarizes the findings, offers practical recommendations, and outlines avenues for future research. Through this integrated approach, the study aspires to reinforce the bridge’s structural longevity while upholding its historical value for future generations.

2. Literature Review

The preservation and structural evaluation of historical masonry bridges has become an increasingly vital area of research in architectural heritage and civil engineering. The structural complexity of these bridges, coupled with their unique material characteristics and historical significance, requires interdisciplinary approaches to understand their behavior under various load conditions and to design appropriate interventions.

Masonry arch bridges have been analyzed through a variety of methods ranging from empirical formulations and limit state approaches to advanced numerical modeling techniques [9]. Heyman’s theory of limit analysis for masonry structures laid the groundwork for interpreting arch behavior under the assumption of zero tensile strength.

Recent advancements in numerical modeling and non-destructive testing techniques have significantly improved the accuracy of structural assessments. Specifically, digital photogrammetry and laser scanning methods are increasingly utilized to obtain precise geometrical models of masonry structures [10].

With the advancement of computational technology, finite element methods (FEM) have become a standard tool in the structural evaluation of historical bridges. Lourenço (2002) emphasized the need for incorporating nonlinear analysis in heritage masonry due to the material’s anisotropy and the presence of pre-existing damage [11].

The application of SAP2000 and other commercial software to heritage structures has been widely documented. For example, Pelà et al. (2013) and Berto et al. (2011) demonstrated that FEM software could simulate both in-plane and out-of-plane behavior of historic masonry walls and arches under seismic and static loads [12,13].

In parallel, conservation guidelines such as those published by ICOMOS and national heritage authorities stress the importance of minimal intervention and reversibility in restoration practices [14]. Examples include grout injection, repointing with lime-based mortars, and the use of non-intrusive reinforcement such as fiber-reinforced polymers [15].

Several recent case studies provide useful references. Sakcalı et al. (2019) investigated the seismic behavior of an 18th-century bridge in Italy using 3D FEM [16]. Apostolopoulou and Mouzakis (2017) presented a structural diagnosis and retrofit design for an Ottoman bridge in Greece, integrating historical research with simulation [17].

This study contributes to this body of knowledge by documenting a case in the Caucasus region with a full-cycle structural assessment, from pre-restoration to performance evaluation post-restoration.

3. Materials and Methods

This section presents the methodology applied in the structural analysis of the historical bridge located in the Yukhari Bash Architectural Reserve. The analysis includes detailed information about the building materials, geometry of the structure, modeling techniques, and load assumptions used for simulating both pre-restoration and post-restoration conditions.

3.1. Historical Background and Chronological Development of the Structure

The arched stone bridges located within the Yukhari Bash State Historical-Architectural Reserve are deeply intertwined with the urban and infrastructural development of the city of Shaki. Situated on a vital trade route between the Caucasus and Central Asia, Shaki experienced significant urban expansion during the 18th century, particularly under the rule of the Shaki Khanate. It was during this period that several infrastructural elements, including the arched bridges, were constructed to connect various sections of the city divided by streams and valleys. These bridges played a pivotal role not only in facilitating daily transportation but also in linking major public and commercial buildings such as caravanserais, mosques, and market squares [5].

Historical records and local sources suggest that some of these bridges were built in the second half of the 18th century, concurrent with major architectural developments such as the Palace of the Shaki Khans. The bridges reflect a synthesis of Ottoman and Persian architectural influences that dominated the urban landscape of the period. Structurally, they were designed with a clear emphasis on both hydraulic resilience and aesthetic coherence, exemplifying the balance between function and form that characterized the era’s civil engineering practices [18].

During the Soviet era, these bridges remained in use but were subjected to infrastructural interventions such as the installation of pipelines, asphalt overlays, and metal guardrails, some of which compromised their original architectural character. However, beginning in the early 2000s, renewed preservation efforts-largely guided by UNESCO’s conservation framework—led to comprehensive restoration initiatives. Notably, restoration projects conducted in 2010 aimed to reinstate the bridges’ historical integrity by employing traditional materials and techniques in line with the original construction [19].

3.2. Bridge Typology and Material Properties

The bridge is a single-span masonry arch structure, primarily composed of locally sourced limestone blocks and lime-based mortar (Figure 1). Field observations and archival research indicate that the original construction used a combination of rubble masonry and roughly dressed stone. The restoration process preserved this configuration while addressing visible damages and weaknesses.

Uniaxial compressive strength for limestone was assumed as 28 MPa, based on literature and empirical data [20]. The characteristic compressive strength of the masonry (f_k) was estimated between 6.4 MPa and 9.4 MPa depending on the mortar class [1]. The modulus of elasticity (E) was assumed as 4800 MPa and shear modulus (G) as 2000 MPa for masonry walls, following standard engineering guidelines [4]. Direct in situ mechanical testing could not be performed due to conservation restrictions. Therefore, these values were derived from published data on comparable limestone masonry in the region [18,20]. To address uncertainties, a ±20% variation range for these parameters was considered in a sensitivity analysis. Even under the lower bound of this range, stresses remained within allowable limits, although deformations increased by approximately 8%.

The lime-based mortar, traditionally used in such masonry constructions, offers flexibility and compatibility with limestone, thus preventing premature deterioration due to differential expansion and contraction. Laboratory tests confirmed these characteristics, aligning with historical masonry preservation principles.

3.3. Geometrical Modeling

Three-dimensional geometric modeling was performed using the SAP2000 (v22.0) software. The bridge was modeled as a combination of solid and shell elements: the spandrel walls and arch barrel were modeled using solid brick units, while approach walls were modeled with shell elements. Solid elements had eight nodes with three translational degrees of freedom each. Element sizes were approximately 30 × 50 × 30 cm for the arch and 28.6 × 28.6 × 28.6 cm for infill.

Boundary conditions were defined based on the actual support locations and surrounding terrain. The foundation was assumed to have sufficient stiffness to prevent significant rotation or translation. Supports were modeled as fixed in the vertical direction and restricted against horizontal displacements in longitudinal and transverse directions. This assumption was supported by field observations indicating that the bridge abutments are embedded into stiff rock formations, with no visible signs of settlement or rotation. To verify this modeling choice, an alternative model with elastic spring supports was also analyzed, which showed less than 5% variation in stresses and displacements compared to the fixed support case. This confirms that the adopted boundary conditions realistically represent the actual foundation behavior.

3.4. Load Assumptions and Combinations

The structural analysis considered the following types of loading:

• Dead load (self-weight and surface finishes);
• Live load (pedestrian and maintenance vehicles);
• Seismic load (based on regional seismicity).

Load combinations were established as per TBDY 2018 [1] guidelines:

• Combo 1: G + nQ (Vertical Load Combination);
• Combo 2 to 9: Various combinations of G, Q, and horizontal seismic effects (EXP, EYP, EXN, EYN).

Although the bridge is geographically located in Azerbaijan, the use of TBDY 2018 [1] was preferred because it provides detailed provisions for masonry and historical structures, which are not explicitly addressed in the Azerbaijani seismic code. In addition, the tectonic characteristics of the Southern Caucasus show strong similarities with Eastern Anatolia, leading to comparable seismic hazard levels. To verify the suitability of this cross-border adaptation, the adopted spectral parameters were cross-checked with Azerbaijan’s seismic hazard maps and the Global Seismic Hazard Assessment Program (GSHAP), both of which indicated consistent peak ground acceleration values. Therefore, applying TBDY 2018 [1] ensured a conservative yet technically justified representation of seismic demand.

Seismic actions were defined using the response spectrum method, with seismic parameters derived from AFAD’s Earthquake Hazard Map [8]. The structure was assumed to lie in ZD soil class with corresponding S1 and SS values taken from the national database.

3.5. Modal and Static Analysis Procedures

Modal analysis was conducted to determine the natural vibration modes and periods of the bridge. Thirty modes were calculated, and the first five dominant modes were selected for interpretation. These included transverse and longitudinal sway, torsional behavior, and vertical vibrations.

Static analysis was performed for each load combination to assess stress distribution, displacement, and internal force behavior. The bridge’s structural elements were evaluated under each scenario to identify potential overstressing or deformation issues.

3.6. Assessment Criteria and Performance Levels

Performance evaluation followed the criteria outlined in the Turkish Building Earthquake Code [1] and the “Guideline for the Management of Seismic Risks of Historical Structures”. For each load combination, maximum stress levels and displacement values were compared with allowable thresholds.

4. Results and Discussion

This section provides a comparative assessment of the bridge’s structural behavior before and after restoration, based on finite element analysis outputs.

4.1. Stress Distribution Analysis (Before Restoration)

The maximum vertical compressive stress under self-weight and surface loads was recorded as 7.038 MPa in the S33 direction (Figure 2). Although this value remains safely below the allowable limit of 9.4 MPa for limestone masonry, localized stress concentrations indicated areas of potential vulnerability. The detailed shear stress analysis further revealed the bridge’s safety against lateral movements, affirming structural adequacy prior to restoration interventions.

Under vertical loads analysis (Figure 2):

• S11: max. 1.49 MPa;
• S22: max. 1.116 MPa;
• S33: max. 7.038 MPa.

In shear analysis (Figure 3):

• S12 (xy shear): max. 0.869 MPa;
• S13 (xz shear): max. 1.611 MPa;
• S23 (yz shear): max. 1.554 MPa.

The characteristic shear strength calculated as f_vk = 2.96 MPa showed all shear values were within safe range.

4.2. Earthquake Design Parameters (After Restoration)

The earthquake parameters considered during the dynamic analysis of the structure were as follows.

Response spectrum analysis was applied to the structure’s finite element model in conjunction with modal analysis to account for the effects of earthquake loads. The response spectrum was defined by the S₁ (0.284) and S_S (1.035) values taken from the “Turkey Earthquake Hazards Map” provided on the Disaster and Emergency Management Presidency’s website, based on the coordinates of the structure’s location for a Class ZD soil in the “Turkish Building Earthquake Code.” Peak Ground Acceleration is taken as 0.424 and Peak Ground Velocity is taken as 25.843. The pathometers entered into the program are presented in Figure 4. Modal Participating Mass Ratios are given in

Table 1. Modal Participating Mass Ratios.

Output Case	Step Type	Step Num	Period (S)	UX	UY	UZ	Sum UX	Sum UY	Sum RZ
MODAL	Mode	1	0.081127	0.77	3.27 × 1018	4.257 × 105	0.77	3.27 × 1018	7.5 × 1019
MODAL	Mode	2	0.074682	4.661 × 1018	59 × 102	1.286 × 1018	0.77	0.59	0.11
MODAL	Mode	3	0.057367	2.652 × 1016	95.52 × 103	9.004 × 1020	0.77	0.68	0.72
MODAL	Mode	4	0.035724	6.697 × 104	1.544 × 1017	41 × 102	0.77	0.68	0.72
MODAL	Mode	5	0.03292	1.866 × 1016	46.54 × 103	1.312 × 1015	0.77	0.73	0.72
MODAL	Mode	6	0.029623	0.006736	9.932 × 1016	1 × 101	0.78	0.73	0.72
MODAL	Mode	7	0.026796	7.979 × 1017	91.09 × 103	1.899 × 1014	0.78	0.82	0.75
MODAL	Mode	8	0.026552	3.619 × 103	1.306 × 1014	0.0627	0.78	0.82	0.75
MODAL	Mode	9	0.0241	8.591 × 104	2.468 × 1018	0.23	0.78	0.82	0.75
MODAL	Mode	10	0.023238	1.096 × 1015	6.842 × 103	4.588 × 1015	0.78	0.83	0.75
MODAL	Mode	11	0.022219	3.108 × 1015	6.776 × 103	2.929 × 1015	0.78	0.83	0.83
MODAL	Mode	12	0.021126	0.1	8.292 × 1019	17.15 × 103	0.88	0.83	0.83
MODAL	Mode	13	0.019018	1.114 × 1017	28.74 × 103	1.685 × 1016	0.88	0.86	0.85
MODAL	Mode	14	0.017083	1.872 × 1015	3.635 × 103	4.657 × 1015	0.88	0.87	0.85
MODAL	Mode	15	0.0168	8.253 × 105	4.7 × 1015	1.179 × 103	0.88	0.87	0.85
MODAL	Mode	16	0.016105	1.269 × 104	1.094 × 1014	1.47 × 105	0.88	0.87	0.85
MODAL	Mode	17	0.015672	5.397 × 106	2.778 × 1014	4.364 × 104	0.88	0.87	0.85
MODAL	Mode	18	0.015299	3.403 × 1015	5.439 × 103	2.791 × 1015	0.88	0.87	0.85
MODAL	Mode	19	0.014812	1.191 × 103	1.202 × 1013	3.175 × 103	0.89	0.87	0.85
MODAL	Mode	20	0.014614	4.709 × 104	7.165 × 1014	3.727 × 103	0.89	0.87	0.85
MODAL	Mode	21	0.01444	1.867 × 1013	15.26 × 103	2.117 × 1013	0.89	0.89	0.85
MODAL	Mode	22	0.013332	5.06 × 1016	5.143 × 103	2.83 × 1012	0.89	0.89	0.87
MODAL	Mode	23	0.013241	2.005 × 107	1.658 × 1013	4.013 × 104	0.89	0.89	0.87
MODAL	Mode	24	0.012992	3.206 × 1014	4.629 × 105	9.196 × 1013	0.89	0.89	0.88
MODAL	Mode	25	0.012784	0.002677	2.026 × 1012	4.321 × 107	0.89	0.89	0.88
MODAL	Mode	26	0.012215	3.939 × 1013	0.01047	3.888 × 1013	0.89	0.9	0.89
MODAL	Mode	27	0.012116	8.498 × 103	1.331 × 1013	4.204 × 103	0.9	0.9	0.89
MODAL	Mode	28	0.011807	9.138 × 103	1.91 × 1014	1.476 × 103	0.91	0.9	0.89
MODAL	Mode	29	0.011589	9.702 × 104	2.155 × 1014	4.018 × 104	0.91	0.9	0.89
MODAL	Mode	30	0.011568	3.461 × 1013	5.9 × 104	1.147 × 1013	0.91	0.9	0.89

.

S_DS (Short period design spectral acceleration coefficient) = S_S × F_S = 1.035 × 1.086 = 1.124.

S_D1 (Design spectral acceleration coefficient for 1.0 s period) = S₁ × F₁ = 0.284 × 2.032 = 0.557.

In the structural analysis, where the SDs value is determined as 1.124 and the seismic design class as DTS 1, the load combinations for structural elements have been defined considering both vertical and seismic load effects. The vertical load combination is specified as COMBO 1: “G + nQ”. For seismic loads, eight different combinations are established to ensure structural safety by incorporating gravity loads (G, Q) and seismic actions in positive and negative directions (EXP, EXN, EYP, EYN) with varying factors. The seismic load combinations are as follows: COMBO 2: “1.0 G + 1.0 Q + 1.0 EXP + 0.3 EYP”, COMBO 3: “1.0 G + 1.0 Q + 1.0 EXP + 0.3 EYN”, COMBO 4: “1.0 G + 1.0 Q + 1.0 EXN + 0.3 EYP”, COMBO 5: “1.0 G + 1.0 Q + 1.0 EXN + 0.3 EYN”, COMBO 6: “1.0 G + 1.0 Q + 0.3 EXP + 1.0 EYP”, COMBO 7: “1.0 G + 1.0 Q + 0.3 EXP + 1.0 EYN”, COMBO 8: “1.0 G + 1.0 Q + 0.3 EXN + 1.0 EYP”, and COMBO 9: “1.0 G + 1.0 Q + 0.3 EXN + 1.0 EYN”. These combinations enable a comprehensive assessment of the structure’s performance under vertical loads and seismic actions in multiple directions.

4.3. Modal Analysis Results

Modal analysis indicated a fundamental natural period (T1) of 0.081 s and frequency of 12.32 Hz, with no significant shifts observed post-restoration.

The cumulative mass participation ratio of the first five modes was calculated as approximately 83% in the longitudinal (UX) direction and 78% in the transverse (UY) direction, exceeding the generally accepted 75% threshold for modal adequacy in heritage masonry studies [10,12]. Therefore, higher-order modes were not interpreted further since their individual contributions were marginal (<3%). The detailed results are summarized in

Table 2. Modal properties and cumulative mass participation ratios of the first five modes.

Mode No	Period (s)	Frequency (Hz)	UX (%)	UY (%)	UZ (%)	Cumulative Participation (%)
1	0.081	12.32	77.0	0.0	0.00	77.0
2	0.075	13.39	0.0	59.0	0.11	77.6
3	0.057	17.43	0.0	9.5	0.72	78.3
4	0.036	27.99	0.07	0.0	0.72	82.0
5	0.033	30.37	0.0	4.6	0.72	83.0

.

4.4. Modal Shape Change Diagrams

Modal shape deformation diagrams provide visual representation of the structure’s vibrational characteristics. The first five mode shapes are illustrated (Figure 5), clearly demonstrating the predominant vibration directions and the structural response patterns at different frequencies. After restoration, improvements in modal symmetry and overall structural stability were observed, indicating that restoration efforts contributed positively to structural dynamic performance.

4.5. Seismic Load Response

Seismic analysis under combined loads (G + Q + EXP + 0.3EYP) showed a maximum stress of 7.08 MPa, confirming structural adequacy within allowable stress limits. The maximum horizontal displacement recorded was 0.23 mm, with a relative drift ratio calculated at 0.043%, significantly below the permissible limit of 0.3%. These results validate the structure’s capability to withstand seismic actions categorized as ‘limited damage’ under the DD-2 earthquake scenario.

• Max stress under combo load (G + Q + EXP + 0.3EYP): 7.08 MPa;
• Max horizontal displacement: 0.23 mm;
• Opposing node displacement: 0.03 mm;
• Drift = (0.23 − 0.03)/458 = 0.043% < 0.3%.

Although the maximum stress under combined load cases (7.08 MPa) approaches the upper compressive strength threshold of 9.4 MPa, this still remains within the safety margin when considering a safety factor of 1.3–1.5 as recommended in TBDY 2018 for masonry structures. To evaluate the effect of material heterogeneity, a parametric sensitivity analysis was performed by varying compressive strength and modulus of elasticity by ±15%. The results showed that even under a 15% reduction in strength, stresses remained below critical values, although the safety margin decreased. These findings confirm that the structural behavior is relatively robust against reasonable uncertainties in material properties.

4.6. Restoration Effectiveness

Restoration works led to a measurable improvement in both stress distribution and global deformation control. In the pre-restoration model, under the vertical load combination (G + nQ), the maximum compressive stress reached 7.038 MPa, while shear stresses were calculated as 1.611 MPa (S13), 1.554 MPa (S23), and 0.869 MPa (S12). These values remained below the masonry strength limits but indicated stress concentrations at specific locations.

After restoration, seismic loading governed the structural response. Under the combination (1.0G + 1.0Q + 1.0EXP + 0.3EYP), the maximum compressive stress was 7.08 MPa, the peak horizontal displacement was limited to 0.23 mm, and the inter-nodal drift ratio was calculated as 0.043%, which is significantly lower than the permissible drift limit of 0.3% specified in seismic codes.

These results confirm that while absolute stress levels before and after restoration are of similar magnitude, the post-restoration model exhibits more uniform stress distribution and significantly reduced seismic deformations, ensuring that the bridge performs within the “limited damage” criteria under a DD-2 seismic event. Consequently, the restoration enhances the long-term seismic resilience of the structure, particularly by improving displacement and drift control even under critical load scenarios.

4.7. Discussion

The SAP2000 model confirmed the bridge’s structural safety both before and after restoration, and validated restoration benefits. The methodology applied is comparable to international examples [16,21].

Comparison with similar international studies underscores the reliability and robustness of the applied numerical modeling techniques. Future research could include continuous structural health monitoring to gather empirical data for validating and refining analytical models, thereby further ensuring the long-term conservation of historical masonry bridges.

5. Conclusion and Recommendations

This study presents a comprehensive structural analysis of a historical masonry bridge located in the Yukhari Bash National Historical–Architectural Reserve in Sheki, Azerbaijan. Through finite element modeling using SAP2000, the structural behavior of the bridge was assessed under gravitational and seismic loads in both its pre- and post-restoration states.

The results demonstrate that the bridge’s structural performance was within acceptable safety margins prior to restoration, with compressive and shear stresses remaining below the threshold limits defined by TBDY 2018. However, the restoration process significantly improved stress distribution uniformity and deformation control, particularly under seismic scenarios. Modal analysis confirmed that dynamic properties remained consistent, validating that the interventions did not compromise the bridge’s historical authenticity.

The findings underline the importance of integrating modern structural analysis tools with conservation principles in heritage projects. The methodology applied here can serve as a model for similar evaluations of historical masonry bridges worldwide.

Furthermore, the sensitivity analysis considering ±15% variation in material properties demonstrated that the bridge maintains structural adequacy even under reduced strength conditions, ensuring that the adopted safety factor (1.3–1.5) provides sufficient reliability for long-term performance.

Recommendations:

• Periodic Structural Monitoring: Post-restoration, it is essential to implement a long-term structural health monitoring plan to detect any future degradation or abnormal displacement behavior.
• Water Management: Measures such as drainage improvement and waterproofing layers should be implemented to mitigate moisture ingress, which is a critical factor in masonry degradation.
• Material Compatibility: Future repair works should utilize materials compatible with the original masonry, particularly lime-based mortars, to avoid differential aging and cracking.
• Load Control: Restriction of vehicular traffic and management of surface loads on the bridge should be enforced to reduce long-term mechanical stress.
• Knowledge Dissemination: The results of this study should be shared with conservation professionals, municipal authorities, and academics to promote informed decision-making and the adoption of non-invasive, reversible intervention techniques.

By combining numerical simulation with empirical knowledge and conservation guidelines, this research offers a robust and replicable approach to safeguarding historic masonry bridges.

The comprehensive structural assessment conducted in this study highlights the necessity of integrating advanced finite element modeling techniques into heritage conservation practices. The post-restoration analysis demonstrates a clear improvement in stress distribution and structural deformation behavior under seismic conditions, validating the efficacy of traditional materials and methods. Advanced monitoring systems such as fiber optic sensing, digital image correlation (DIC), and continuous displacement measurements are strongly recommended to enable real-time monitoring of the bridge’s structural health. Additionally, regular periodic assessments coupled with data-driven predictive maintenance strategies are critical for proactively addressing potential structural deterioration, thus ensuring the long-term preservation of this historically significant structure. These recommendations provide a robust framework for future heritage bridge restoration projects, emphasizing a balanced approach between historical authenticity and contemporary engineering standards.

Although the Finite Element Method (FEM) applied in this study proved sufficient for capturing the structural behavior of the historical bridge, it is worth noting that more advanced numerical approaches, such as the Virtual Element Method (VEM), have recently been developed. VEM offers enhanced flexibility for irregular geometries and heterogeneous materials, which are typical characteristics of historical masonry structures. Incorporating or comparing FEM results with VEM-based analyses in future research could further improve the robustness and precision of the assessments. For example, Desiderio et al. (2021) demonstrated the applicability of curved VEM formulations in handling complex boundary conditions efficiently, highlighting its potential value for heritage structures with intricate geometrical and material features [22].