An Integrated Resilience Assessment Framework for Riverine Bridges Based on Hydraulic Modeling and Multicriteria Analysis

Abstract

Riverine bridges are critical infrastructure that are increasingly exposed to severe hydrological hazards. This study proposes and validates a synergistic methodology for the assessment of riverine bridge resilience, integrating the conceptual 4R framework (robustness, rapidity, resourcefulness, and redundancy) with field inspections, hydrological and hydraulic modeling, including scour evaluation, within a multicriteria analysis scheme. The methodology comprises: (i) a systematic review of literature and regulations to construct a 30-parameter matrix across five dimensions (technical, economic, social, organizational, and environmental); (ii) data acquisition through field inspections, detailed topography, and technical studies; and (iii) one-dimensional hydraulic modeling in HEC-RAS under extreme scenarios (return periods of 100 to 750 years and a critical 500 m³/s scenario representing a potential overflow of the Aguada Blanca reservoir). The Bridge Resilience Index (BRI) is computed through a weighted additive model and a sensitivity analysis. Application to the San Martín Bridge (Arequipa, Peru), a structure with more than 60 years of service and recurrent preventive closures during flood events, revealed critical conditions: minimum freeboard of 0.26 m, absence of hydraulic protections, and limited institutional capacity. The resulting BRI value (1.898) indicates a low resilience level. The proposed framework provides a useful tool for risk-informed decision-making, the prioritization of interventions, and the strengthening of resilience in critical infrastructure.

1. Introduction

Riverine bridges are essential components of transportation networks, ensuring territorial connectivity and the continuous movement of people and goods across rivers. However, these infrastructure are increasingly exposed to multiple hazards, with hydrological threats being the most significant [1,2,3]. Intense rainfall, flash floods, and river overflows [4] often exceed the design capacity of hydraulic structures, generating substantial economic and social losses worldwide.

According to [5], approximately 49% of bridge failures are associated with hydrological causes, with scour induced by flood events being the primary driver of structural collapse. In the United States, between 1989 and 2000, nearly 83% of bridge collapses were attributed to external events (natural or anthropogenic), of which 53% corresponded to floods, followed by earthquakes, fires, and ice accumulation [6]. In recent years, about 60% of recorded collapses have been linked to scour processes, resulting from the progressive erosion of sediments around piers and abutments due to turbulent flow action [7]. These findings demonstrate that failures driven by hydrological factors, particularly scour, are the most critical for river bridges.

In Latin America, the exposure of infrastructure to extreme hydrological events is particularly critical due to construction limitations, inadequate maintenance, and unplanned urban expansion. These factors, compounded by the complexity of urban environments [8], have hindered the effective integration of risk management into the design and maintenance of civil works [4]. In Peru, hydrological phenomena have caused significant damage, especially to bridges, revealing high structural vulnerability. During the 2022–2023 rainy season, 118 bridges were reported destroyed and another 188 damaged [9]. Similarly, the 2016–2017 El Niño event resulted in the loss of 493 bridges and damage to an additional 943 [1,10,11].

These precedents highlight not only the magnitude of the damage but also the deficiencies in design criteria and the limited adaptive capacity of many structures located within river channels. Most existing bridges were not designed to withstand increases in design flows or the hydrological effects associated with climate change [12,13]. Therefore, analyzing the potential impacts of hydrological factors on riverine bridges is essential to ensure structural safety, regulatory compliance, and operational continuity [14,15].

From a conceptual perspective, the terms vulnerability, risk, and resilience constitute the fundamental triad of modern disaster risk management. Vulnerability is defined as the degree of susceptibility of physical and social systems to external hazards, reflecting conditions of exposure, structural limitations, and limited adaptive capacity shaped by social, economic, and cognitive factors [16,17]. Risk, in contrast, represents the probability that a hazard will cause damage to these systems based on their vulnerability, highlighting the social and territorial nature of disasters beyond their natural origin [18,19]. Resilience, for its part, is understood as the capacity of a system to absorb, adapt to, and recover its functionality after a disturbance, integrating the principles of robustness, rapidity, resourcefulness, and redundancy [20,21]. Together, these concepts provide a comprehensive understanding of infrastructure behavior under extreme hydrological events.

For bridge resilience assessment, vulnerability can represent up to 30% of the total weight within the global index, according to the guidelines proposed by [20]. The joint integration of vulnerability and resilience provides a comprehensive view of the structural and functional performance of infrastructure, as noted by [21]. Likewise, the incorporation of hydrological and hydraulic modeling results strengthens the quantitative basis of the assessment, enabling authorities to prioritize interventions and improve decision-making [1,22,23]. In this context, a literature review on resilience and vulnerability assessment in critical infrastructure was conducted, with emphasis on bridges exposed to hydrological hazards. The study location, the type of infrastructure analyzed, and the parameters used in each evaluation were identified to obtain a global understanding of the research landscape, as summarised in

Table 1. Review of Literature on Resilience and Hydrological Vulnerability Assessment.

Literature on Resilience Assessment
Author and Year	Study Location	Infrastructure	Evaluation Parameters Used
Khodadad et al. (2025) [24]	Monterrey, Mexico–Brussels, Bélgica	Cities	They used environmental variables (elevation, slope, precipitation), infrastructure-related variables (road density, public facilities), social variables (population density and vulnerability), and economic variables (poverty and economic activity).
Peng et al. (2024) [25]	Beijing, China–Munich, Germany	Cities	They analyze environmental and territorial factors linked to flood risk, such as precipitation, topography, vegetation, socioeconomic conditions, population density, and road density.
Rezvani et al. (2024) [26]	Lisboa, Portugal	Roads	They assess urban resilience using an index that integrates temporal performance, socioeconomic factors, risk exposure, and management costs.
Kenarkoohi & Hassan (2024) [27]	Washington, EE. UU.–Montreal, Canadá -	Bridges	They analyze seismic performance by considering durability, maintenance, construction complexity, embedment depth, and the use of advanced materials.
G. Zhang et al. (2024) [28]	Arizona, USA.	Bridges	They evaluate fire-exposure dimensions and structural performance, including cable deflection, deformation, strength, and rates of change in deflection.
Asghari et al. (2023) [29]	Literature review	Literature review	They incorporate holistic approaches that account for flood levels, exposed population, residential functions, exposure time, risk indicators, and performance under extreme loads, complemented by PESTEL dimensions (political, economic, social, technological, environmental, and legal) and RAF components (engagement, economic sustainability, spatial planning, service management, safety, and robustness). They also analyze technical approaches based on metrics such as flood-volume reduction, recovery times, and overall system performance.
Khan et al. (2023) [23]	British Columbia, Canadá	Bridges	They evaluate structural reliability through the analysis of foundations, abutments, bearings, piers, beams, connections, bridge age, and structural geometry; and they assess recovery capacity by considering structural health monitoring, maintenance practices, damage level, functional importance, resource availability, and accessibility.
Cao et al. (2023) [30]	Zheijiang, China	Cities	They incorporate nature-related dimensions (green coverage, topography, precipitation), economic dimensions (GDP, per capita income, public expenditure), social dimensions (population density and structure, educational level), and infrastructure dimensions (drainage network, road area, and green spaces).
Z. Zhang et al. (2023) [31]	Changchun, China	Cities	They assess environmental and infrastructure vulnerability using variables such as altitude, land use, precipitation, NDVI, slope, and road density; and they evaluate social and economic recovery capacity based on per capita GDP, investment in flood-protection measures, population density, and educational level.
Zhao et al. (2021) [32]	China	Bridges	They consider mechanical properties, durability parameters, connection systems, aerodynamic models, and the use of advanced materials.
Patel et al. (2020) [20]	Surat, India	Bridges	They evaluate resilience using the 4R framework (robustness, rapidity, resourcefulness, and redundancy) and integrate 16 TOSE factors (technical, organizational, social, and economic).
Argyroudis et al. (2020) [21]	Lisboa, Portugal	Bridges	They determine resilience through an index based on the temporal functionality curve Q(t), incorporating robustness metrics (numerical models and fragility functions) and rapidity metrics (restoration times, damage state, standard deviation, and downtime periods).
Literature on Hydrological Vulnerability Assessment
Author and Year	Study Location	Infrastructure	Evaluation Parameters Used
Avcı & Vanolya (2025) [33]	Turkey	Bridges/Culverts	They incorporate dimensions related to population and urban expansion, socioeconomic conditions, environmentally sensitive areas, and catchment-basin parameters.
Duran et al. (2025) [34]	Iowa, USA	Bridges	They evaluate structural and functional parameters related to bridge conditions, traffic volume, detour length, and flood levels.
Apollonio et al. (2025) [35]	Puglia, Italy	Rail Network	They analyze the typology of hydraulic structures, the elements exposed to traffic, critical events, and accessibility and service-disruption coefficients.
Wang et al. (2025) [36]	Kaohsiung, Taiwan	Urban Areas	They incorporate flood hazard under different return periods and the social vulnerability of sensitive groups and emergency services.
Buonora et al. (2024) [37]	Italy	Bridges	They consider foundation type, riverbed geometry, and the number of floating debris as vulnerability parameters.
Ccanccapa Puma et al. (2024) [22]	Arequipa, Peru	Bridges	They reutilize the environmental, technical, social, and economic dimensions proposed by [38].
Espinoza Vigil & Booker (2023) [1]	Arequipa, Peru	Bridges	They evaluate environmental vulnerability (flow-rate variability, water quality and composition) and physical vulnerability (bridge material and location, soil quality, geometric parameters, deck erosion, scour-protection measures, overflow and flooding risk, and regulatory compliance).
Huarca Pulcha et al. (2023) [38]	Arequipa, Peru	Bridges	They consider environmental dimensions (climate change, water quality, ecological conditions, and obstructions), technical dimensions (materials, conservation state, hydraulic protection, deck elevation, scour, and dam capacity), social dimensions (population exposure and proximity, disaster prevention, and socioeconomic conditions), and economic dimensions (road importance, traffic volume, risk-related closures, and flood history).
Martínez et al. (2023) [39]	Arequipa, Peru	Drainage water inflows to the Chili River.	They evaluate concentrations of materials and contaminants, physicochemical variables (pH, conductivity, salinity, resistivity, density, dissolved solids, turbidity, temperature), and hydrological parameters (discharge, precipitation, storm duration, and antecedent drought conditions).
Lamb et al. (2019) [40]	Great Britain	Rail Bridges	They analyze dimensions based on structural fragility, load associated with the return period, consequence/risk metrics, and the expected rate of service interruption.

:

The literature review shows that most studies address resilience and vulnerability in an isolated manner, prioritizing either technical or structural dimensions. In recent years, there has been a growing interest in integrating hydrological and hydraulic modeling with multicriteria decision methods and sustainability criteria, which has enabled a more accurate representation of scour, erosion, and flooding processes in interaction with bridge structures [37,40].

Among the available tools, HEC-RAS 1D and 2D stand out for their versatility in modeling hydraulic structures such as piers and abutments, allowing detailed assessment of flow-structure interactions and localized erosion effects [1,22,38]. However, the lack of comprehensive methodologies that combine these hydrological and hydraulic models with multicriteria analysis (including structural, social, economic, and organizational dimensions) limits the holistic assessment of hydrological resilience.

In response to this gap, the present study proposes an integrated and multidimensional methodology for assessing hydrological resilience in riverine bridges, combining hydrological and hydraulic modeling with multicriteria analysis within a clearly structured framework. The methodology is applied to the San Martín Bridge, located in the city of Arequipa in Peru, an infrastructure with more than sixty years in service and high exposure to flood events, used as a representative case study to validate the proposed resilience assessment framework, which provides a replicable, adaptable, and technically grounded tool, particularly suitable for contexts with limited data availability. Its purpose is to strengthen institutional capacities for the preventive management of bridges following extreme hydrological events, contributing to the reduction of vulnerabilities and the enhancement of territorial resilience in critical infrastructure.

2. Materials and Methods

The research methodology is developed in four main phases and is summarized in Figure 1, while the details of each phase are presented below.

2.1. Literature Review

The literature search was conducted in the Scopus and Google Scholar databases using Boolean operators to identify scientific studies related to hydrological–hydraulic resilience and vulnerability in bridges and transportation infrastructure published within the last five years. The search strategy followed common systematic review protocols for structured literature retrieval [41,42], ensuring thematic comprehensiveness. The following search formulas were applied: (i) (“hydrological vulnerability” OR “hydraulic vulnerability” OR “flood vulnerability” OR “risk assessment” OR “infrastructure resilience”) AND (“bridge” OR “bridges” OR “infrastructure” OR “transport infrastructure” OR “civil infrastructure”) AND (“hydrology” OR “hydraulics” OR “river” OR “flood” OR “scour”); and (ii) (“hydrological vulnerability” OR “hydraulic vulnerability” OR “flood vulnerability” OR “risk assessment”) AND (“bridge” OR “bridges” OR “infrastructure” OR “transport infrastructure” OR “civil infrastructure”) AND (“hydrology” OR “hydrological” OR “hydraulics” OR “flood” OR “river hazards”) AND (“vulnerability” OR “risk” OR “resilience” OR “susceptibility” OR “exposure” OR “fragility”) AND (“bridge” OR “bridges” OR “infrastructure” OR “road infrastructure”).

From the retrieved literature, a filtering process was conducted to identify studies directly aligned with the research objective. This review allowed the identification of key parameters and indicators used in previous investigations, particularly those related to channel hydrological dynamics, structural stability, and the socio-economic context, resulting in Table 1. Additionally, applicable design manuals and current Peruvian regulations (

Table 2. Design manuals and current Peruvian regulations.

Author/Year	Assessment Parameters
Ministerio de Transportes y Comunicaciones (2018) [43]	Clearance under the bridge, characteristics of the construction material, and estimated service life.
Ministerio de Transportes y Comunicaciones. (2018) [44]	Clearance under the bridge superstructure.
Centro Nacional de Estimación Prevención y Reducción del Riesgo de Desastres (2014) [45]	Service life, type of construction material, deterioration level, housing material composition, and training provided to residents.
Ministerio de Transportes y Comunicaciones (2008) [46]	Protection of structural elements such as piers, scour-control measures, and lower-bridge clearance.
Instituto Nacional de Defensa Civil (2006) [47]	Climatic conditions, water-resource quality, proximity to populated areas, and compliance with current regulatory provisions.

) related to the assessment of bridge resilience and vulnerability under hydrological events were incorporated. The findings served as the theoretical and methodological foundation for the development of the resilience evaluation matrix.

2.2. Development of the Resilience Assessment Matrix

In this work, vulnerability is conceptualized as a condition of exposure and susceptibility that amplifies the likelihood of damage under a given hazard. Resilience, by contrast, is framed as both a capacity and a process through which a system withstands disturbance, sustains service, and restores functionality, as articulated through the 4R attributes. Hazard-related information derived from hydraulic and scour analyses is employed to inform exposure levels or capacity margins; however, such evidence is not regarded as resilience in itself unless it is explicitly linked to structural capacity or protective measures.

Within this framework, parameters describing pre-existing conditions or exposure levels are treated as state variables associated with vulnerability, whereas parameters reflecting the ability to respond, adapt, or recover are treated as capacity-process variables associated with resilience. This distinction ensures that hazard-related outputs from hydraulic and scour analyses inform resilience only when explicitly linked to structural capacity, protective systems, or management processes.

A multicriteria matrix was developed to evaluate the resilience of the bridge, grounded in the four criteria of the 4R framework: Robustness, Rapidity, Resourcefulness, and Redundancy, following Patel et al. [20]. In this approach, Robustness refers to the bridge’s capacity to withstand physical damage; Rapidity concerns the time required to restore acceptable levels of functionality; Resourcefulness assesses the effective availability of technical, human, and financial resources during an emergency; and Redundancy considers the presence of structural or operational alternatives that ensure service continuity.

To structure the matrix, the 4R framework proposed by Patel et al. [20] was used as the conceptual foundation, incorporating approximately 90% of its 16 parameters due to their consistency with the fundamental attributes of infrastructure resilience. However, the present study expands and reconfigures that framework to address the specific characteristics of riverine bridges by integrating hydraulic and scour-related variables not originally included. The expansion to 30 parameters allows the incorporation of critical physical processes—freeboard, flow depths, erosive velocities, and potential scour depth—along with indicators of structural performance and institutional capacities, resulting in a methodological system that is more precise and suitable for contexts involving extreme flood events.

The outcome is an analytical structure that integrates quantitative failure metrics with operational and managerial indicators, providing a more comprehensive and rigorous assessment than previous frameworks. Based on this conceptual foundation, the matrix was organized into five dimensions, selecting parameters according to their direct influence on bridge performance under extreme hydrological events:

• Technical (10 parameters): This dimension evaluates structural and hydraulic performance through variables associated with construction materials, the conservation state of the superstructure and substructure, the effectiveness of protection systems for piers and buttons, deck clearance, scour affecting shallow foundations, inspection methods employed, and the availability of materials and equipment for emergency response.
• Economic (4 parameters): This dimension represents the financial agility and availability to execute corrective interventions, integrating variables such as the resources allocated for maintenance, the duration of procurement procedures, and the existence of funds designated for emergencies and the annual budget.
• Organizational (6 parameters): This dimension reflects the institutional capacity to anticipate, manage, and reduce risk, considering the operational level of upstream dams, the recurrence of closures due to hydrological hazards, records of previous flooding events, expected hydrological severity, implemented disaster-management actions, maturity in planning (e.g., BIM, asset management), and the availability of alternative contractors to ensure operational continuity.
• Social (8 parameters): This dimension characterizes exposure levels and the response capacity of the surrounding area, considering the predominant construction materials of nearby housing, traffic volume, proximity to populated centers and critical facilities, and the territorial extent potentially affected. It also incorporates the population’s socioeconomic level, training in risk management, the proportion of vulnerable inhabitants, the operational capacity of the emergency system, and the availability and length of alternative detour routes.
• Environmental (2 parameters): This dimension includes indicators related to climatic exposure and variability, as well as basic water-quality aspects that influence ecological conditions and the stability of the fluvial environment.

The five dimensions were organized according to the 4R criteria, enabling a functional articulation between the bridge’s physical components and risk-management processes. This approach allows the indicators to reflect not only the structural and hydrodynamic conditions but also the institutional, social, and financial capacities to anticipate, withstand, and recover from extreme events. In this way, the 4R framework operates as an integrating axis that provides a holistic perspective of asset performance under changing hydrological scenarios.

To ensure transparency and reproducibility of the proposed framework, a parameter mapping table was developed to explicitly document the conceptual role of each indicator (

Table 3. Parameter Mapping Table for Bridge Resilience Assessment.

Parameter ID	Parameter Name	Dimension	4R Assigned	Type (State/Capacity Process)	Rationale
T1	Main construction material	Technical	Robustness	Capacity-process	Structural material governs intrinsic strength and resistance to hydraulic and seismic loads.
T2	Structural conservation condition	Technical	Robustness	State (Vulnerability)	Deterioration directly affects structural reliability under extreme flows.
T3	Protection of piers and abutments	Technical	Robustness	Capacity-process	Hydraulic protections mitigate scour and reduce collapse probability during floods.
T4	Clearance under deck	Technical	Robustness	State (Vulnerability)	Insufficient freeboard increases impact risk and flow obstruction during floods.
T5	Foundation exposure to potential scour	Technical	Robustness	State (Vulnerability)	Indicates foundation exposure that reduces structural safety margins under extreme floods
T6	Age in service	Technical	Robustness	State (Vulnerability)	Older bridges often reflect outdated design standards and cumulative degradation.
E1	Preliminary restoration cost	Economic	Robustness	Capacity-process	High restoration costs limit feasible corrective actions after damage.
O1	Closures due to hydrological hazard	Organizational	Robustness	State (Vulnerability)	Recurrent closures indicate functional fragility under flood events.
O2	Historical flood events	Organizational	Robustness	State (Vulnerability)	Past flooding reflects exposure frequency and hazard recurrence.
O3	Operational capacity of upstream reservoirs	Organizational	Robustness	Capacity-process	Reservoir regulation influences downstream peak flows and flood severity.
S2	Nearby critical facilities	Social	Robustness	State (Vulnerability)	Proximity to essential services amplifies consequences of service disruption.
A1	Climate change (temperature trend)	Environmental	Robustness	State (Vulnerability)	Thermal trends affect hydrological regimes and material performance.
A2	Water quality	Environmental	Robustness	State (Vulnerability)	Poor water quality accelerates material degradation and corrosion.
T7	Estimated restoration time	Technical	Rapidity	Capacity-process	Shorter repair times enhance rapid recovery of functionality.
T8	Operational access during flooding	Technical	Rapidity	Capacity-process	Accessibility conditions determine speed of emergency and repair operations.
E2	Procurement process duration	Economic	Rapidity	Capacity-process	Faster procurement accelerates response and restoration actions.
O4	Disaster management practices	Organizational	Rapidity	Capacity-process	Preparedness programs improve coordinated and timely emergency response.
S3	Affected area or region	Social	Rapidity	State (Vulnerability)	Larger affected areas have slow recovery due to competing emergency demands.
S4	Predominant nearby housing material	Social	Rapidity	State (Vulnerability)	Fragile housing increases complexity and social disruption.
S5	Vulnerable population proportion	Social	Rapidity	State (Vulnerability)	Highly vulnerable population delays recovery and increases emergency needs.
S6	Socioeconomic level	Social	Rapidity	State (Vulnerability)	Lower socioeconomic capacity limits adaptive and recovery resources.
T9	Number of inspection techniques applied	Technical	Resourcefulness	Capacity-process	Multiple inspection methods increase diagnostic accuracy and decision quality.
O5	BIM maturity in planning	Organizational	Resourcefulness	Capacity-process	BIM enables efficient planning, scheduling, and asset management.
S7	Emergency response system capacity (ERM)	Social	Resourcefulness	Capacity-process	Strong ERM improves coordinated response and service continuity.
E3	Emergency funds allocated	Economic	Resourcefulness	Capacity-process	Financial readiness enables immediate event actions.
T10	Availability of emergency materials and equipment	Technical	Redundancy	Capacity-process	Local availability ensures backup options during infrastructure failure.
O6	Availability of backup contractors	Organizational	Redundancy	Capacity-process	Contractor redundancy increases response flexibility and speed.
S1	Traffic-based service criticality	Social	Redundancy	State (Vulnerability)	High traffic demand increases service loss and reduces operational redundancy
S8	Length of alternative detour	Social	Redundancy	State (Vulnerability)	Longer detours increase disruption and reduce network redundancy.
E4	Funds available for prevention	Economic	Redundancy	Capacity-process	Preventive funding increases adaptive capacity and reduces future losses.

). This table assigns each parameter to its corresponding dimension (technical, economic, social, organizational, or environmental), links it to one of the 4R properties, and classifies it as either a state variable (vulnerability-related) or a capacity–process variable (resilience-related), together with a concise rationale. This mapping clarifies the theoretical consistency of the matrix and supports its transferability to other riverine bridge contexts. The arrangement of the parameters follows the structure of the proposed evaluation matrix (

Table 4. Multicriteria Matrix for Resilience Assessment.

Robustness
Code	Parameter	Very Low (1)	Low (2)	Medium (3)	High (4)	Very High (5)
T1	Main construction material of the bridge	Low-strength materials (adobe, cane, wood).	Local materials of moderate strength.	Mixed or metallic structure with limited maintenance	Structural steel or reinforced concrete in good condition.	Reinforced concrete with surface protection and seismic-resistant design
T2	Structural conservation condition	Severe deterioration with high risk of collapse.	Damage compromising the structure (no immediate collapse).	Correctable deterioration; structure remains stable.	Minor structural wear.	No structural damage or deterioration.
T3	Protection of piers and abutments against flow	No protection against extraordinary flood events.	Deficient protection.	Moderate protection.	High protection.	Integral protection (riprap, wingwalls, collars; negligible vulnerability)
T4	Clearance under the deck (m)	Flow overtops the deck.	Water reaches the bridge deck.	Flow with <0.3 m clearance.	Normal flow, clearance < 2 m.	Clearance > 2 m between water surface and deck.
T5 *	Foundation exposure to potential scour *	Critical exposure: scour exceeds foundation depth.	High exposure; scour depth close to foundation level.	Moderate exposure; limited margin against estimated scour.	Minor scour exposure: adequate safety margin remains.	Foundations well embedded; negligible scour exposure.
T6	Age in service (years)	>75 years.	50–75 years.	25–50 years.	10–25 years.	<10 years.
E1	Preliminary restoration cost (from available funds)	≥25%	20–25%	15–20%	10–15%	≤10%
O1	Closures due to hydrological hazard	>2 recorded closures.	2 closures.	1 risk-related closure.	1 preventive scheduled closure.	No closures due to hazard.
O2	Historical flood events	≥4 registered events.	3 events.	2 events.	1 event.	No flood events recorded.
O3	Current operational capacity of upstream reservoirs (%)	0–20%.	21–40%.	41–60%.	61–80%.	81–100%.
S2	Nearby critical facilities (schools, shelters, hospitals)	Large facilities within <0.5 km.	Several nearby facilities.	Medium facility > 0.5–1 km.	One small facility > 0.5–1 km.	None within 1 km2.
A1	Climate change (temperature tendency)	Temperatures far above the historical average.	Temperatures clearly above the average.	Temperatures moderately above the average.	Temperatures slightly above the average.	Temperatures are stable relative to the historical average.
A2	Water quality	Very high contamination.	High contamination.	Moderate contamination.	Slight contamination.	No evidence of contamination.
Rapidity
Code	Parameter	Very Low (1)	Low (2)	Medium (3)	High (4)	Very High (5)
T7	Estimated restoration time (months)	≥12.	8–12.	4–8.	1–4.	≤1.
T8	Operational access during flooding	Critical access: isolated from both banks; prolonged total closure.	Conditional access (partial or intermittent service).	Restricted access for heavy equipment.	Partial access through one abutment.	Full access through both abutments without restrictions.
E2	Duration of the procurement process (days)	≥40.	35–40.	30–35.	25–30.	≤25.
O4 *	Disaster management practices (number of actions)	0.	≥2.	≥4.	≥5.	>6.
S3	Affected area or region (km2 or districts)	≥5 districts.	4 districts.	3 districts.	2 districts.	1 district.
S4	Predominant construction material in nearby housing	Straw mats, cardboard, or highly precarious materials.	Adobe or mud-brick.	Quincha (cane and mud).	Reinforced wood or quincha.	Masonry or reinforced concrete.
S5	Vulnerable population (≥65 years, <14 years)	>30%.	20–30%.	10–20%.	5–10%.	≤5%.
S6	Socioeconomic level (poverty)	Extreme poverty (>50%).	High poverty (30–50%)	Moderate (15–30%).	Low (5–15%).	Very Low (<5%).
Resourcefulness
Code	Parameter	Very Low (1)	Low (2)	Medium (3)	High (4)	Very High (5)
T9 *	Number of inspection techniques applied	1.	2.	3.	4.	≥5.
E3	Emergency funds allocated by the administrator (%)	0–10%	10–25%.	25–40%.	40–50%.	≥50%.
O5 *	BIM maturity level in planning	Not applicable or nonexistent	Level 0 (basic).	Level 1 (partial).	Level 2 (collaborative).	Level 3 (integrated).
S7 *	Operational capacity of the emergency response system (ERM)	None.	Limited.	Partial.	Efficient.	Comprehensive and proactive.
Redundancy
Code	Parameter	Very Low (1)	Low (2)	Medium (3)	High (4)	Very High (5)
T10 *	Availability of emergency materials and equipment (%)	≤25%.	25–50%.	50–75%.	75–100%.	>100% of the estimated requirement.
E4 *	Funds available for prevention from the annual budget (%)	0–10%.	10–30%.	30–40%.	40–50%.	≥50%.
O6	Availability of backup contractors	0.	1–10.	10–20.	20–30.	>30.
S1	Traffic-based service criticality.	Critical traffic demand: no viable alternatives, severe service disruption expected.	High traffic demand; limited alternative routes available.	Significant traffic demand; partial dependence on the bridge.	Moderate traffic with available alternative routes.	Low traffic demand: service interruption has limited impact.
S8	Length of the alternative detour (km)	>5.	3–5.	2–3.	1–2.	≤1.

Notes: * T5: This parameter is intended for the assessment of bridges without deep foundations, such as pile-supported systems. Bridges founded on deep foundations are generally associated with higher levels of structural safety against scour-related effects; therefore, they may receive a high resilience score, provided that adequate performance against scour is verified. * O4. Disaster management assesses the bridge administrator’s preparedness for acute shocks through ten practical criteria, ranging from community education, drills, and exercises to evacuation routes and safe-elevation shelters near the bridge. It includes disaster-management plans and centers, equipped first responders (inflatable boats, ropes, life vests, submersible lights), emergency-contractor contacts, local access to machinery and materials for minimum restoration works, available transport modes, and access to critical facilities (≥5 within a 5 km radius), as well as alert systems (sirens and announcements) [48,49]. * T9. The inspection technique encompasses various methods used to assess the physical condition of the bridge. A score of 1 corresponds to visual inspection; 2 to visual inspection combined with analytical techniques; 3 to visual inspection plus nondestructive testing (NDT); 4 to visual inspection, analytical techniques, and NDT; and 5 to visual inspection, analytical techniques, NDT, and underwater inspections [48]. * O5. Planning and scheduling maturity is reflected in the use of Building Information Modeling (BIM) by the bridge administrator to plan and schedule maintenance, repair, or reconstruction works on the bridge [20,50,51]. * S7. The level of emergency response management (ERM) describes the essential resources and systems required to operate the transportation network effectively, efficiently, and in a standardized manner during a crisis. This level progresses from basic manual control, such as police officers directing traffic, to the use of traffic lights or fixed illuminated signals. A subsequent stage incorporates dynamic signal timing to better adapt to traffic flow. A more advanced level includes traffic cameras and variable message signs (VMS) for active traffic management. The highest level corresponds to intelligent transportation systems (ITS) and advanced traveler information systems (ATIS) [48,52]. * T10. Resource accessibility refers to the local availability of key materials and equipment, such as steel or precast beams and piles that can be rapidly procured and mobilized to the bridge. In essence, logistical proximity and availability reduce response times and facilitate repair or reconstruction activities [20]. * E4. The availability of funds refers to the financial budget that the bridge owner has at their disposal to carry out repair and reconstruction works. Deficiencies in this budget affect redundancy because they limit the range of feasible intervention options. Therefore, when there is pressure on budget availability, the bridge’s recovery capacity is adversely affected [20].

), which is organized according to the 4R framework, rather than a sequential numerical order.

Each parameter was defined through quantifiable indicators and evaluated using a five-level ordinal resilience scale (very low, low, medium, high, and very high). The formulation of these levels was based on methodological precedents [20,38], which allowed standardizing the interpretation of results, facilitating comparison across dimensions, and ensuring the applicability of the matrix in diverse territorial contexts. Table 4 presents the developed resilience assessment matrix for bridges exposed to hydrological hazards.

Based on the literature review conducted (Table 1 and Table 2), the following vulnerability and resilience assessment matrix for bridges is proposed (Table 4).

2.3. Matrix Application

To apply the resilience assessment matrix to a bridge, the following procedure was followed:

• Bridge selection. A critical bridge within the local road network was identified, prioritizing its functional importance, its exposure to extreme events, and the existence of previous hydrological and structural impacts.
• Field surveys. Systematic inspections were conducted to document the morphology of the riverbed, identify active erosive processes, and record the elements influencing flow resistance and flow–structure interactions within the study reach.
• Topography: A detailed topographic survey of the fluvial reach was conducted, providing essential input for constructing the geometric model required for hydraulic simulation.
• Technical studies. Specialized studies were conducted, including the hydrological analysis with the estimation of extreme flows, the morphological characterization of the channel, and the geotechnical (soil mechanics) analysis, in order to generate the necessary input parameters for hydrological, hydraulic, and scour modeling.
• HEC-RAS 1D modeling. The one-dimensional model was implemented incorporating calibration and validation procedures based on available historical records, allowing simulation of flow behavior under different hydrological design scenarios. A one-dimensional (1D) hydraulic model in HEC-RAS was adopted due to its proven reliability in hydraulic simulations [53,54,55].
• Scour analysis. General and local scour were evaluated considering critical scenarios, the geotechnical properties of the riverbed, and the structural characteristics of the bridge, with the purpose of determining its vulnerability to erosive processes.
• Parameter scoring. The compilation of primary and secondary information from official local sources included social, economic, and environmental data, as well as structural, hydraulic, and operational information on the bridge. This information was complemented by field visits aimed at verifying in situ the geomorphological configuration of the channel, the condition of the approaches, and the state of the structure and its immediate surroundings, along with the results of the hydraulic modeling and scour analysis. Using all these inputs, the resilience assessment matrix was applied to assign each parameter a score between 1 and 5 (from very low to very high) according to its resilience level.
• Weighting value per criterion. The assignment of weight percentages to each parameter within each criterion was carried out considering their local relevance and the availability of information. Using these weights, the consolidated score for each criterion was determined, which subsequently allowed the calculation of its corresponding BRI (Bridge Resilience Index).

2.4. Resilience Level Assessment

2.4.1. Bridge Resilience Index (BRI)

Once the scores for each criterion and their final weights were determined, the weighted sum model (WSM) was applied. This method is recognized as conceptually clear, computationally efficient, and is widely adopted as a reference in MCDM studies [56].

BRI = ∑ Wi × RIi

(1)

where BRI = bridge resilience index; Wi = weight of each 4R; and RIi = 4Rs index (RI1, RI2, RI3 and RI4).

In this approach, each of the 4Rs is assigned a relative weight whose sum must equal one, making it particularly suitable for the integrated assessment of a single infrastructure asset while also allowing its application to a set of bridges. The procedure consists of multiplying the value obtained for each criterion by its corresponding weight and summing these results in a weighted additive structure. This enables the synthesis of a multidimensional set of attributes into a coherent global indicator of the bridge’s resilient performance.

For the weighting of these criteria, the study by Patel et al. [20] was used as a reference, which reports weighting schemes in which Robustness (R₁) receives a weight of 0.60, Rapidity (R₂) 0.19, Resourcefulness (R₃) 0.13, and Redundancy (R₄) approximately 0.08.

The final output of this process is the Bridge Resilience Index (BRI) [20], which synthesizes the asset’s ability to anticipate, withstand, respond to, and recover from extreme hydrological events. This indicator provides a quantitative, reproducible, and comparable measure of the bridge’s systemic performance and offers a robust basis for prioritizing interventions, optimizing resource allocation, and guiding the planning of mitigation measures aimed at reducing vulnerability and strengthening structural and hydraulic resilience. The resilience classification is expressed in five levels: very low, low, medium, high, and very high (

Table 5. Classification guide for the bridge resilience index (BRI).

BRI Range	Classification Resilient	General Interpretation (Resilience)
4.0–5.0	Very high	Optimal condition; fully operational and resilient.
3.0–3.9	High	Good condition; adequate resistance and partial recovery capability.
2.0–2.9	Moderate	Acceptable condition; moderate absorption and recovery capacity.
1.0–1.9	Low	Limited or partially functional condition.
<1.0	Very low	Deficient or nonexistent condition; no response capacity.

).

The global Bridge Resilience Index (BRI) is then obtained using the following equation:

$$\mathrm{B}\mathrm{R}\mathrm{I} = 0.60 {\mathrm{R}}_1 + 0.19 {\mathrm{R}}_2 +0.13 {\mathrm{R}}_3 + 0.08 {\mathrm{R}}_4$$

(2)

2.4.2. Sensitivity Analysis

Finally, a sensitivity analysis was conducted using the relative weights obtained for each parameter based on the 4Rs, in which the input factors were modified one at a time to examine the effect of each change on the outcome [57]. The weights were adjusted using predefined percentage variations (±10%, ±20%, ±30%, ±40%, and ±50%) with the aim of assessing the influence of each factor on the BRI. The analysis was performed on the parameters with the highest weighting scores, as these have a direct influence on the results [20], allowing the evaluation of the proposed weighting sensitivity and the validation of the results.

The following equation was used to quantify the sensitivity of the parameters and assess the impact of weighting changes on the remaining factors:

$$\mathrm{W}(\mathrm{F}\mathrm{i},\mathrm{C}\mathrm{P})={\displaystyle \frac{\left[\right\{1–\mathrm{W}(\mathrm{F}\mathrm{a},\mathrm{C}\mathrm{P})\}\times \mathrm{W}(\mathrm{F}\mathrm{i},0\left)\right]}{\left(\right(1–\mathrm{W}(\mathrm{F}\mathrm{a},0))}},\mathrm{i}\ne \mathrm{a}$$

(3)

where W(Fi,CP) is the weight of factor i under a percentage change CP; W(Fa,CP) is the new weight of the adjusted factor under CP; and W(Fi,0) and W(Fa,0) are the original (unchanged) weights.

3. Results

3.1. Matrix Application

3.1.1. Bridge Selection

The San Martín Bridge, located in the city of Arequipa, Peru, has been in operation since 1969 (55 years to date) and serves as a key roadway infrastructure connecting the districts of Yanahuara and Cercado, as well as other urban sectors of Arequipa. It is one of the most heavily trafficked bridges in the city. The structure spans the Chili River, whose hydrological behavior has become progressively more irregular and hazardous, exacerbated by global warming and increased surface impermeability due to urban expansion. Preventive closures during the intense rainfall events of 2012 and 2018, along with the ongoing threat of overflow and scour processes, demonstrate that the bridge is currently subjected to hydrodynamic demands for which it was not originally designed [58,59]. Figure 2 presents two essential perspectives for understanding the bridge–environment interaction: (a) a downstream view of the bridge, and (b) an upstream view.

3.1.2. Field Surveys

An on-site inspection of the San Martín Bridge was carried out to assess its geometric configuration, examine the condition of the superstructure and substructure, and verify the presence of potential scour processes at the abutments. The survey was carried out during the low-flow season (September), as illustrated in Figure 3, when the bridge was operating normally in both lanes and the reduced river flow allowed greater exposure of the structural elements.

Access to the river channel was only possible from the right bank, which allowed a detailed inspection of the right abutment, the underside of the deck, and the adjacent downstream area. The inspection revealed that the deck does not exhibit significant structural damage, although small areas of superficial erosion were identified on its lateral and bottom faces. Vegetation was also observed near the right abutment. As the inspection was conducted during the low-flow season, the reduced discharge allowed a clear assessment of the channel’s conditions. Vegetation effects on hydraulic resistance were considered in the estimation of Manning roughness coefficients using the Cowan method, following the Peruvian Hydrology, Hydraulics and Drainage Manual [46].

The right button showed stable conditions, with no signs of scour, basal erosion, or exposed foundation elements. Due to limited accessibility, a direct inspection of the left abutment was not possible; however, indirect observation from the opposite bank indicated a similar condition, with no visible evidence of erosion or scour. On the upper deck surface, the pavement exhibited moderate wear, consistent with a regular operational state.

3.1.3. Topography

The hydraulic geometry of the study reach was constructed from a high-resolution topographic survey, aimed at accurately characterizing the river channel axis and the critical upstream and downstream sections of the bridge. The survey included cross-sections spaced every 10 m and the lateral boundaries of the river. To accurately represent the bridge-channel interaction, the detailed geometry of the San Martín Bridge and its immediate surroundings was also incorporated.

The survey was conducted using a Leica TS06 total station (Leica Geosystems, Heerbrugg, Switzerland), which provided coordinates and elevations with the precision required for hydraulic modeling. The surveyed reach covered 250 m upstream and 150 m downstream of the bridge, following local regulatory guidelines [46].

The collected data were processed in Autodesk Civil 3D 2023 (Autodesk Inc., San Rafael, CA, USA), generating the geometric base on which the fundamental hydraulic parameters were incorporated: Manning roughness coefficients, contraction and expansion coefficients, integration of the bridge geometric model, and the flow rates corresponding to the defined hydrological scenarios. This structure served as the input platform for the hydraulic model developed.

3.1.4. Technical Studies

The hydrological analysis was conducted using the series of annual maximum flow rates recorded at the Charcani hydrological station for the period 1960–2024, given that the river is gauged. These data, obtained through the Integrated Hydrological Monitoring and Instrumentation System (Arequipa, Peru) [60] and administered by the Proyecto Especial Majes Siguas—Autoridad Autónoma de Majes (PEMS Autodema) (Arequipa, Peru) constitute a long-term dataset suitable for characterizing extreme events.

Based on the hydrological dataset, an outlier analysis was performed using the Water Resources Council method [61], which identified no anomalous values in the series. With the validated dataset, the Kolmogorov–Smirnov goodness-of-fit test was applied to all possible combinations of empirical and theoretical distributions (

Table 6. Kolmogorov–Smirnov goodness-of-fit.

Theoretical Delta
Distribution	California	Hazen	Weibull	Chegodayev	Blom	Tukey	Gringorten
Normal	0.1093	0.1012	0.0965	0.0980	0.0992	0.0986	0.1002
Log Normal II	0.1340	0.1259	0.1261	0.1260	0.1260	0.1260	0.1260
Log Normal III	0.0970	0.1050	0.1090	0.1066	0.1060	0.1064	0.1055
Gamma II	0.5198	0.5278	0.5254	0.5268	0.5272	0.5270	0.5275
Gamma III	0.1262	0.1181	0.1103	0.1150	0.1162	0.1155	0.1172
Log Pearson III	0.1652	0.1572	0.1573	0.1572	0.1572	0.1572	0.1572
Gumbel	0.0889	0.0820	0.0860	0.0836	0.0830	0.0833	0.0825
Log Gumbel	0.1775	0.1694	0.1695	0.1695	0.1694	0.1694	0.1694

), in accordance with Peruvian regulations [46].

The evaluation showed that the pair of distributions providing the best fit to the series of annual maximum river flows corresponds to the theoretical Gumbel distribution combined with the empirical Hazen plotting position; this combination produced the smallest theoretical delta among all alternatives analyzed.

Based on this result, the peak flows associated with the defined return periods were estimated using exclusively the parameters of the Gumbel flow-calculation function [62]. In addition, an extra scenario was incorporated, which considers the upstream reservoir design flow of 500 m³/s under the hypothesis of an overtopping event at the Aguada Blanca Reservoir, located upstream of the San Martín Bridge. These scenarios are detailed in

Table 7. Calculation of peak flows.

Scenario	T (Years)	Non-Exceedance Probability	Q Max. (m3/s)
1	100	99.000%	310.062
2	200	99.500%	349.303
3	300	99.667%	372.257
4	400	99.750%	388.543
5	500	99.800%	401.176
6	750	99.867%	424.130
7	-	-	500.000

.

The morphological characterization of the river channel was conducted through field inspections, which allowed documenting the geomorphological conditions of the bed and banks, as well as the presence of elements that influence hydraulic resistance. Based on these observations and the systematized photographic record, the Manning roughness coefficient (n) was estimated using the Cowan method [61], integrating the basic channel roughness, bed irregularities, local obstructions, and riparian vegetation.

The Manning coefficients were assigned separately for the left overbank, main channel, and right overbank, following the standard HEC-RAS parameterization approach [63].

Table 8. Manning roughness coefficients estimated using the Cowan method (downstream cross-section).

Bridge Downstream Cross-Section				0 + 150.00
UTM Coordinates (m)		East (X)	228,238
		North (Y)	8,184,353
	Left Overbank	Main channel	Right Overbank
n0	0.028	0.028	0.028
n1	0.005	0.007	0.013
n2	0.000	0.000	0.000
n3	0.000	0.000	0.000
n4	0.008	0.005	0.005
m5	1.000	1.000	1.000
n	0.041	0.04	0.046

and

Table 9. Manning roughness coefficients estimated using the Cowan method (upstream cross-section).

Bridge Upstream Cross-Section				0 + 170.00
UTM Coordinates (m)		East (X)	228,245
		North (Y)	8,184,368
	Left Overbank	Main channel	Right Overbank
n0	0.028	0.028	0.028
n1	0.010	0.010	0.010
n2	0.000	0.000	0.000
n3	0.005	0.005	0.012
n4	0.005	0.005	0.020
m5	1.000	1.000	1.000
n	0.048	0.048	0.07

present the detailed calculation of the roughness values determined for two cross-sections: one located immediately upstream and the other immediately downstream of the San Martín Bridge. According to the Cowan method [64], the roughness coefficient is expressed as the sum of components representing bed material (n₀), surface irregularities (n₁), cross-section variability (n₂), obstructions (n₃), and vegetation (n₄), multiplied by a sinuosity factor (m₅).

It is important to note that the resulting roughness coefficients are consistent with values reported in previous hydraulic studies conducted along the same river reach [65].

The information collected in the field was essential for the calibration of the hydraulic model, as it provided accurate data on channel geometry, abutment configuration, and the interaction between the flow and the bridge superstructure.

The geotechnical characterization of the site was carried out using the data obtained from the soil study, including grain-size distribution tests, moisture content, and specific weight. These parameters constitute critical inputs for the hydraulic analysis, particularly for the estimation of general and local scour, since many of the empirical and semi-theoretical formulations employed require a precise description of the physical properties of the bed material.

To complete this characterization, grain-size distribution tests were performed to determine the particle-size percentiles from the distribution curve, using sieves of 3”, 2”, 1½”, 1”, ¾”, ⅜”, and series No. 4, 10, 20, 40, 80, 100, and 200 (Figure 4). The moisture content test yielded a value of 12.62%, while the specific weight was 2.72 g/cm³. The integration of these results enabled an adequate representation of the erosive behavior of the channel and allowed a more reliable assessment of the interaction between the flow and the bridge foundation, supporting the estimation of the risk associated with scour processes.

3.1.5. HEC-RAS 1D Modeling

The hydraulic simulation of the Chili River was carried out using the HEC-RAS 6.7 software, widely recognized for its application in hydrodynamic studies that analyze flow behavior in water bodies. This program allows steady-state simulations under a one-dimensional (1D) scheme, thus facilitating the assessment of flow conditions in natural channels [66].

As an initial stage of the hydraulic modeling, the geometry of the river channel and the bridge was transferred from Autodesk Civil 3D to HEC-RAS, a procedure illustrated in Figure 5 and Figure 6.

Once the hydraulic parameters required by HEC-RAS [63], including section-specific roughness coefficients, contraction and expansion coefficients, detailed bridge geometry, and flow rates corresponding to the defined hydrological scenarios, were established, the hydraulic model was implemented.

The hydraulic model was calibrated using historical evidence from the 2012 flood event, which corresponds to the largest annual maximum discharge recorded in the analyzed hydrological series of the Chili River (236.64 m³/s). During this event, photographic records and visual documentation were available for several bridges along the study reach, including the bridge analyzed in this study. Part of this photographic evidence has been previously documented in [65,67], where the water levels reached by the river during the flood are reported. These records allowed a qualitative comparison between the observed water levels and the simulated water surface elevations obtained from the hydraulic model, using visible structural elements of the bridge, such as the deck, main girders, and abutments, as reference points.

Although direct discharge measurements were not conducted during the field campaign, the Chili River is a gauged river, and the hydrological analysis relied on long-term discharge records available at the Charcani hydrological station. The discharge observed during the 2012 event corresponds to a flow of the same order of magnitude as the design discharges estimated for the river (Table 7), confirming that it represents a hydraulically significant event for model calibration.

Due to the absence of instrumental water level records during the event and the lack of another documented extreme event within the study reach, an independent quantitative validation of the model was not possible. Nevertheless, the agreement between the simulated water surface elevations and the flood marks identified in the photographic records from the 2012 event indicates that the model adequately reproduces the observed hydraulic behavior of the river under flood conditions. Furthermore, previous studies conducted along the same river have used this event as a reference for hydraulic model calibration, obtaining results consistent with the observed flow behavior [38,68,69].

Once calibrated, the hydraulic model was used to simulate the design scenarios associated with the discharges obtained from the frequency analysis of the hydrological series (Table 7). This calibration procedure based on historical evidence and flood marks has been widely used in river hydraulic modeling studies when direct instrumental measurements are not available [70].

The simulations allowed the hydraulic flow profiles to be obtained for each analyzed scenario. Figure 7 and Figure 8 present the results corresponding to the 100-year return period discharge (Q = 310.06 m³/s), showing, respectively, the longitudinal hydraulic profile and the interaction between the river flow and the bridge structure.

The results indicate that the simulated water surface elevation (WSEL) approaches the underside of the bridge deck. The bridge deck elevation is 2297.01 m a.s.l., while the computed WSEL reaches 2296.75 m a.s.l., resulting in an available clearance of only 0.26 m.

This reduced clearance indicates a potential hydraulic insufficiency of the structure, as the available freeboard becomes minimal under the 100-year return period discharge. For higher flow scenarios, the WSEL increases further, proportionally reducing the available clearance and increasing the probability of interaction between the flow and the bridge superstructure.

3.1.6. Scour Analysis

It is important to note that significant uncertainty persists in the application of equations used to estimate scour. This uncertainty arises, on one hand, from the high complexity of the variables involved and, on the other, from the limited availability of robust theoretical models. Consequently, expressions derived from experimental studies and dimensional analysis are frequently used; however, these may produce highly conservative and sometimes divergent results. The scour analysis was conducted following the procedures established in the Peruvian national regulations [46].

Considering the above, and using the results of the soil mechanics study, the critical erosion velocity was estimated by applying the methods of Rodríguez Díaz, Melville & Coleman, and HEC-18 [62], with the purpose of identifying the type of scour induced by the flow passing through the bridge. The results obtained are summarized in

Table 10. Scour type—Rodríguez Díaz method.

Scenario	Return Period (Years)	Discharge (m3/s)	Average Flow Depth (m)	Flow Velocity (m/s)	Erosive Velocity (m/s)	Scour Type
1	100	310.06	3.39	3.29	0.816	Live-bed
2	200	349.30	3.75	3.31	0.828	Live-bed
3	300	372.26	3.91	3.37	0.833	Live-bed
4	400	388.54	4.01	3.42	0.836	Live-bed
5	500	401.18	4.10	3.44	0.838	Live-bed
6	750	424.13	4.23	3.50	0.842	Live-bed
7	-	500.00	4.38	3.52	0.868	Live-bed

and

Table 11. Scour type—Melville–Coleman and HEC-18 method.

Scenario	Discharge (m3/s)	Erosive Velocity (m/s) According to Melville–Coleman	Scour Type	Erosive Velocity (m/s) According to HEC-18	Scour Type
1	310.06	1.278	Live-bed	1.395	Live-bed
2	349.30	1.299	Live-bed	1.418	Live-bed
3	372.26	1.308	Live-bed	1.428	Live-bed
4	388.54	1.314	Live-bed	1.434	Live-bed
6	401.18	1.318	Live-bed	1.439	Live-bed
6	424.13	1.325	Live-bed	1.447	Live-bed
7	500.00	1.333	Live-bed	1.455	Live-bed

.

Once it was identified that the prevailing scour mechanism corresponds to live-bed conditions, the general scour was estimated using the Lischtvan–Levedeiev method. In accordance with Peruvian regulations [46], a return period of 500 years must be considered. The resulting maximum and minimum general scour depths were 1.505 m and 0.61 m, respectively. Figure 9 presents the graphical representation of the general scour along the bridge cross-section.

The transverse scour generated by flow contraction induced by the bridge was subsequently calculated using the Straub method [46], obtaining a value of S = 0.352 m.

Local scour is evaluated directly at the bridge support elements, in this case, the abutments. For its estimation, the procedures recommended by Ministerio de Transportes y Comunicaciones and Rodríguez Díaz [46,62] were applied. The results obtained are summarized in

Table 12. Local scour at abutments.

Method	Right Abutment (m)	Left Abutment (m)
Field	6.717	6.717
Liu y Alia	6.050	6.050
Artamonov	1.462	1.738
Froehlich	5.244	5.347

.

According to [71], local scour at abutments depends primarily on the geometry of the abutment itself, the characteristics of the sediment, and the configuration of the river channel cross-section. It is also influenced by the flow depth in both the main channel and the banks, the flow rate that directly impacts the abutment and the portion that returns to the channel, as well as river alignment and other associated hydraulic and geomorphological factors.

As shown in Table 12, the results obtained using the different methods exhibit significant variability. Consequently, and in accordance with the guidelines of the manual, the Artamonov method is adopted as the most appropriate approach for this study, given that its formulation incorporates most of the variables specified in the manual and therefore provides an estimate that is more consistent with the hydraulic and geomorphological conditions of the channel.

The potential total scour is determined as the sum of its individual components. However, the estimated value of local scour is incorporated only at the chainage corresponding to the section where the bridge abutments are located, since this phenomenon is highly localized. Figure 10 presents the result of the potential total scour estimated for the bridge, integrating the contributions of general, contraction, and local scour.

In the main structural elements of the bridge, particularly at the abutments, scour depths exceeding 1 m were estimated. However, despite efforts made, the structural drawings of the San Martín Bridge could not be obtained. Consequently, no information is available regarding the actual foundation depth that would allow a direct comparison and verification of the calculated values.

3.1.7. Parameter Scoring

Table 13. Evaluation of each parameter of the bridge under study.

Robustness
Code	Parameter	Score	Justification
T1	Main construction material	5	The field inspection confirms that the superstructure and substructure are predominantly built in reinforced concrete, consistent with the in situ observations.
T2	Structural conservation condition	3	The visual inspection identified areas with surface deterioration and exposed reinforcement corrosion, which, although not posing an immediate risk of collapse, compromises the structural integrity of the bridge.
T3	Protection of piers and abutments against flow	1	During the field visit, it was verified that the downstream abutment is in direct contact with the flow and lacks protection elements, remaining fully exposed to erosive processes.
T4	Vertical clearance under the deck (m)	1	The hydraulic modelling shows that the water surface reaches the lower part of the deck in most simulated scenarios, reducing the available hydraulic clearance (Figure 8).
T5	Foundation exposure to potential scour	1	Since the actual abutment foundation depths in the field are unknown, a conservative score of 1 is assigned. Despite extensive efforts to obtain the original structural drawings from multiple institutions, including municipal authorities and public technical archives, no records were found. Owing to the age of the bridge, the foundation embedment depth could not be verified, and this lack of information was therefore treated conservatively within the assessment.
T6	Service age (years)	2	The San Martín Bridge was inaugurated in 1959; therefore, it currently has 66 years of continuous service [72].
E1	Preliminary restoration cost (from available funds)	-	No official estimate or published study quantifying the total cost is available.
O1	Traffic closures due to hydrological risk	1	Official news reports document preventive closures of the San Martín Bridge in 2011, 2012, and 2020 due to critical rises in the Chili River flow and the associated flood risk [59,73].
O2	Flooding history	4	A significant overflow event of the Chili River was recorded, which caused impacts in areas near the San Martín Bridge, reported by national media during a channel reoccupation episode [59].
O3	Current capacity of upstream reservoirs (%)	3	Official information indicates that the Aguada Blanca reservoir shows sedimentation that has reduced its usable capacity to approximately 53%, which may increase hydrological variability downstream [74].
S2	Nearby critical facilities (schools, shelters, hospitals)	1	Based on Google Earth, two school-level educational institutions and one university were identified within a 0.5 km radius, as well as four additional schools within a 1 km radius.
A1	Climate change (temperature trend)	2	Recent studies report a sustained increase in regional temperature, associated with the progressive loss of agricultural areas and regional warming. This trend could intensify hydrological processes relevant to the bridge [75].
A2	Water quality	1	Microbiological monitoring conducted in the surroundings of the San Martín Bridge shows elevated contamination levels in the Chili River water, consistent with Vargas Maquera [76].
Rapidity
Code	Parameter	Score	Justification
T7	Estimated restoration time (months)	2	The reconstruction of the Gunther Bridge, which collapsed on February 14, 2025, was completed within approximately nine months; this project was executed by the same entity responsible for the San Martín Bridge [77].
T8	Operational access during flooding events.	4	Due to the asymmetric topographic configuration of the site, operational access would remain available only through one of the abutments, since the steep slope limits the propagation of flow toward that sector.
E2	Duration of the procurement process (days)	1	The procurement process began 151 days after the collapse of the Gunther Bridge, which occurred on February 14, 2025, according to the Municipalidad Provincial de Arequipa [78].
O4	Disaster management practices (number of actions)	4	The Prevention Plan identifies six types of actions aimed at reducing flood risk, including capacity-building activities, interventions, and implementation measures intended to strengthen disaster risk management [78]
S3	Affected area or region (km2 or districts)	2	The bridge generates direct impact on two districts (Yanahuara and Cercado) and indirect impact on two others (Sachaca and José Luis Bustamante y Rivero).
S4	Predominant construction material in nearby dwellings	5	In the immediate surroundings, dwellings are predominantly built with masonry, coexisting with a commercial area composed of buildings constructed with reinforced materials.
S5	Vulnerable population (≥65 years, <14 years)	1	According to the 2017 National Census [79], the population classified as vulnerable in the district where the bridge is located represents 31.64% of the total census count (17,541 out of 55,437 inhabitants).
S6	Socioeconomic level (poverty)	5	According to the most recent national census conducted in Peru [79], the district where the bridge is located has a poverty rate of 0.21% (118 people out of a total of 55,437 inhabitants).
Resourcefulness
Code	Parameter	Score	Justification
T9	Number of inspection techniques applied	2	Two previous studies were identified that developed hydrological and hydraulic models applied to the San Martín Bridge [38,80].
E3	Emergency funds allocated by the administrator (%)	1	According to the Public Sector Budget Expenditure Distribution [81], the Budget Program for Vulnerability Reduction and Emergency Disaster Response was allocated S/2,172,030,523. This amount represents 1.97% of the total national budget, which corresponds to S/110,524,035,517. This amount represents 1.97% of the total national budget, which corresponds to S/110,524,035,517.
O5	BIM maturity level in planning	1	According to the Municipalidad Provincial de Arequipa [79], the San Martín Bridge does not have a monitoring system based on BIM methodology.
S7	Operational capacity of the response system (ERM)	1	It was observed that traffic detours in Arequipa depend on manual traffic control performed by police officers, evidencing a complete reliance on human intervention.
Redundancy
Code	Parameter	Score	Justification
T10	Availability of emergency materials and equipment (%)	1	Although the Contingency Plan for Extreme Rainfall Events lists an inventory of operational equipment and tools distributed across four warehouses for response to critical events, the absence of structural materials or essential prefabricated elements required to ensure accelerated bridge rehabilitation is evident [82].
E4	Funds available for prevention from the annual budget (%)	5	The budget execution of the Municipalidad Provincial de Arequipa (MPA) allocated to the prevention and management of critical events reached only 9.6% of the assigned annual budget [83].
O6	Availability of backup contractors	1	The Municipalidad Provincial de Arequipa (MPA) lacks a registry of prequalified contractors for immediate emergency response. Contracting is carried out through the public bidding system [84], which introduces a dependency on procurement procedures that may compromise the promptness of the response.
S1	Traffic-based service criticality	1	Field observations indicate high vehicular flow, associated with the presence of multiple educational institutions (schools and universities) that converge in the area and use the bridge as a main connection route.
S8	Length of the alternative detour (km)	3	Geospatial simulation (Google Earth) identified that the shortest available alternative detour route has an approximate length of 2.3 km.

consolidates the values assigned to each parameter in the case study, accompanied by technical justification (field evidence, modelling results, applicable regulations, or administrative records).

3.1.8. Weighting Value per Criterion

Once the parameters were scored, relative weights were assigned to each parameter within its corresponding criterion (∑w = 1), based on dominant parameters and the specific conditions of the local context (

Table 14. Evaluation of each parameter of the bridge under study.

Robustness (R1)
Code	Parameter	Score	Weight (%)	Criterion Score
T1	Main construction material	5	0.05	0.25
T2	Structural conservation condition	3	0.10	0.30
T3	Protection of piers and abutments against flow	1	0.10	0.10
T4	Vertical clearance under the deck (m)	1	0.10	0.10
T5	Foundation exposure to potential scour	1	0.15	0.15
T6	Service age (years)	2	0.10	0.20
E1	Preliminary restoration cost (from available funds)	-	-	-
O1	Closures due to hydrological risk	1	0.15	0.15
O2	Flooding history	4	0.05	0.20
O3	Current upstream reservoir capacity (%)	3	0.05	0.15
S2	Nearby critical facilities (schools, shelters, hospitals)	1	0.10	0.10
A1	Climate change (temperature trend)	2	0.025	0.05
A2	Water quality	1	0.025	0.025
			R1=	1.775
Rapidity (R2)
Code	Parameter	Score	Weight (%)	Criterion Score
T7	Estimated restoration time (months)	2	0.25	0.50
T8	Operational access during flooding events	4	0.10	0.40
E2	Duration of the procurement process (days)	1	0.15	0.15
O4	Disaster management practices (number of actions)	4	0.10	0.40
S3	Affected area or region (km2 or districts)	2	0.10	0.20
S4	Predominant construction material in nearby dwellings	5	0.05	0.25
S5	Vulnerable population (≥65, <14)	1	0.15	0.15
S6	Socioeconomic level (poverty)	5	0.10	0.50
			R2=	2.55
Resourcefulness (R3)
Code	Parameter	Score	Weight (%)	Criterion Score
T9	Number of inspection techniques applied	2	0.25	0.50
E3	Emergency funds allocated by the administrator (%)	1	0.35	0.35
O5	BIM maturity level in planning	1	0.20	0.20
S7	Operational capacity of the response system (ERM)	1	0.20	0.20
			R3=	1.25
Redundancy (R4)
Code	Parameter	Score	Weight (%)	Criterion Score
T10	Availability of emergency materials and equipment (%)	1	0.15	0.15
E4	Funds available for prevention from the annual budget (%)	5	0.25	1.25
O6	Availability of backup contractors	1	0.20	0.20
S1	Traffic-based service criticality	1	0.20	0.20
S8	Length of the alternative detour (km)	3	0.20	0.60
			R4=	2.40

).

3.2. Resilience Level Assessment

3.2.1. Global Bridge Resilience Index (BRI)

Using Equation (1) from the Methodology section and the values of R₁–R₄ reported in Table 13, a Bridge Resilience Index (BRI) of 1.904 was obtained for the San Martín Bridge.

According to the reference scale, this value corresponds to a low resilience level, indicating a limited capacity to withstand and recover from extreme flood events. This condition is primarily influenced by deficiencies in hydraulic freeboard, scour protection, and overall structural condition. From an operational perspective, the results suggest a higher likelihood of service interruptions and an increased exposure to damage during high-energy hydrological events.

3.2.2. Sensitivity Analysis

The sensitivity analysis assessed the stability of the Bridge Resilience Index (BRI) under systematic ±50% variations in the weights assigned to each of the four resilience components (4Rs) and their associated parameters. This procedure followed the methodology of Chen et al. [57], individually adjusting the original weight of each R while proportionally redistributing the remaining weights, to identify which dimensions exert the greatest influence on BRI variation.

Table 15. Scenario 1—Change in relative weights using sensitivity analysis.

Original Weights
4Rs	−50%	−40%	−30%	−20%	−10%	0%	10%	20%	30%	40%	50%
Robustness	0.30	0.36	0.42	0.48	0.54	0.60	0.66	0.72	0.78	0.84	0.90
Rapidity	0.33	0.30	0.28	0.25	0.22	0.19	0.16	0.13	0.10	0.08	0.05
Resourcefulness	0.23	0.21	0.19	0.17	0.15	0.13	0.11	0.09	0.07	0.05	0.03
Redundancy	0.14	0.13	0.12	0.10	0.09	0.08	0.07	0.06	0.04	0.03	0.02
Robustness
Parameters	−50%	−40%	−30%	−20%	−10%	0%	10%	20%	30%	40%	50%
T1	0.05	0.05	0.05	0.05	0.05	0.05	0.05	0.05	0.05	0.05	0.05
T2	0.11	0.11	0.11	0.10	0.10	0.10	0.10	0.10	0.09	0.09	0.09
T3	0.11	0.11	0.11	0.10	0.10	0.10	0.10	0.10	0.09	0.09	0.09
T4	0.11	0.11	0.11	0.10	0.10	0.10	0.10	0.10	0.09	0.09	0.09
T5	0.08	0.09	0.11	0.12	0.14	0.15	0.17	0.18	0.20	0.21	0.23
T6	0.11	0.11	0.11	0.10	0.10	0.10	0.10	0.10	0.09	0.09	0.09
O1	0.16	0.16	0.16	0.16	0.15	0.15	0.15	0.14	0.14	0.14	0.14
O2	0.05	0.05	0.05	0.05	0.05	0.05	0.05	0.05	0.05	0.05	0.05
O3	0.05	0.05	0.05	0.05	0.05	0.05	0.05	0.05	0.05	0.05	0.05
S2	0.11	0.11	0.11	0.10	0.10	0.10	0.10	0.10	0.09	0.09	0.09
A1	0.03	0.03	0.03	0.03	0.03	0.03	0.02	0.02	0.02	0.02	0.02
A2	0.03	0.03	0.03	0.03	0.03	0.03	0.02	0.02	0.02	0.02	0.02
Rapidity
Parameters	−50%	−40%	−30%	−20%	−10%	0%	10%	20%	30%	40%	50%
T7	0.13	0.15	0.18	0.20	0.23	0.25	0.28	0.30	0.33	0.35	0.38
T8	0.12	0.11	0.11	0.11	0.10	0.10	0.10	0.09	0.09	0.09	0.08
E2	0.18	0.17	0.17	0.16	0.16	0.15	0.15	0.14	0.14	0.13	0.13
O4	0.12	0.11	0.11	0.11	0.10	0.10	0.10	0.09	0.09	0.09	0.08
S3	0.12	0.11	0.11	0.11	0.10	0.10	0.10	0.09	0.09	0.09	0.08
S4	0.06	0.06	0.06	0.05	0.05	0.05	0.05	0.05	0.05	0.04	0.04
S5	0.18	0.17	0.17	0.16	0.16	0.15	0.15	0.14	0.14	0.13	0.13
S6	0.12	0.11	0.11	0.11	0.10	0.10	0.10	0.09	0.09	0.09	0.08
Resourcefulness
Parameters	−50%	−40%	−30%	−20%	−10%	0%	10%	20%	30%	40%	50%
T9	0.32	0.30	0.29	0.28	0.26	0.25	0.24	0.22	0.21	0.20	0.18
E3	0.18	0.21	0.25	0.28	0.32	0.35	0.39	0.42	0.46	0.49	0.53
O5	0.25	0.24	0.23	0.22	0.21	0.20	0.19	0.18	0.17	0.16	0.15
S7	0.25	0.24	0.23	0.22	0.21	0.20	0.19	0.18	0.17	0.16	0.15
Redundancy
Parameters	−50%	−40%	−30%	−20%	−10%	0%	10%	20%	30%	40%	50%
T10	0.18	0.17	0.17	0.16	0.16	0.15	0.15	0.14	0.14	0.13	0.13
E4	0.13	0.15	0.18	0.20	0.23	0.25	0.28	0.30	0.33	0.35	0.38
O6	0.23	0.23	0.22	0.21	0.21	0.20	0.19	0.19	0.18	0.17	0.17
S1	0.22	0.21	0.21	0.21	0.20	0.20	0.20	0.19	0.19	0.19	0.18
S8	0.23	0.23	0.22	0.21	0.21	0.20	0.19	0.19	0.18	0.17	0.17

presents the procedure applied in the sensitivity analysis, in which each parameter is individually modified and the corresponding adjustments in the 4Rs are evaluated.

Based on these variations, new Bridge Resilience Index (BRI) values were recalculated for each range of change considered (±10%, ±20%, ±30%, ±40%, and ±50%) and for the four defined scenarios (

Table 16. Results of BRI after changes in relative weights.

Sensitivity Analysis (SA)
	−50%	−40%	−30%	−20%	−10%	0%	10%	20%	30%	40%	50%
BRI Robustness	2.004	1.989	1.971	1.951	1.928	1.904	1.877	1.848	1.817	1.784	1.748
BRI Rapidity	1.797	1.821	1.844	1.865	1.886	1.904	1.921	1.939	1.956	1.972	1.985
BRI Resourcefulness	2.014	1.990	1.967	1.945	1.924	1.904	1.885	1.867	1.850	1.834	1.820
BRI Redundancy	1.926	1.922	1.918	1.914	1.909	1.904	1.898	1.892	1.886	1.879	1.872

).

The results show that the BRI remains stable and free of discontinuities despite extreme perturbations in parameter weights. For the baseline scenario (0%), the value obtained was 1.898. When modifying the weight of Robustness, the BRI ranged from 1.714 (−50%) to 2.024 (+50%), indicating that this dimension exerts the highest influence and has the most direct effect on the hydraulic and structural response of the bridge. In contrast, variations associated with Redundancy and Resourcefulness produced smaller changes (ranges of 1.874–1.910 and 1.807–2.017, respectively), confirming that although these dimensions are relevant for emergency management, they play a lesser role in the dominant failure mechanisms of the bridge. Rapidity exhibited moderate sensitivity, with BRI values between 1.772 and 2.002, consistent with its complementary role in operational recovery.

Finally, the stability of the BRI across wide ranges of variation confirms that the applied methodology has strong internal consistency and that the weights defined for the local context are appropriate for characterizing the hydrological-hydraulic risk of the San Martín Bridge. This provides reliability for the use of the BRI as a prioritization tool in infrastructure management, ensuring that decisions are not compromised by small fluctuations in the subjective weights of the multicriteria matrix.

4. Discussion

The systematic review (Table 1) showed that most studies on flood resilience are conducted at the urban scale [25,26,30,31], incorporating socioeconomic indicators, population densities, and territorial variables. While these approaches are suitable for cities, they present a clear scale mismatch when applied to point infrastructure such as bridges. Even holistic frameworks like FRUGISP [24] or PESTEL/RAF models [29] retain a macro-level emphasis that does not capture the physical mechanisms governing hydraulic-structural performance.

In contrast, bridge-specific literature has focused almost exclusively on seismic hazards [23,27,32] or thermal effects [28]. Hydrological hazard studies remain scarce and are mainly oriented toward vulnerability analysis [1,22,37,38], without integrating a comprehensive resilience framework. This panorama confirms the absence of systematic approaches that combine measurable physical processes—freeboard, erosive velocities, and scour—with the institutional capacities that condition response and recovery.

In response, this study adopts a bridge-specific approach grounded in three pillars: (i) 1D hydraulic modeling using HEC-RAS, (ii) scour analysis, and (iii) a multicriteria matrix of 30 parameters structured under Patel et al.’s [20] 4R framework. The selected parameters focus on mechanisms governing physical failure during flood events and are complemented by organizational and economic dimensions that shape institutional response. To preserve the hydraulic–structural relevance of the index, urban indicators such as building density, employment, population composition, or urban vegetation were explicitly excluded, reducing methodological noise as noted by Asghari et al. [29].

Comparison with Table 1 shows that existing frameworks have partial scopes: Espinoza Vigil & Booker [1] (8 parameters) and Huarca Pulcha et al. [38] (16) emphasize vulnerability; Patel et al. [20] (16) introduce resilience but lack explicit hydraulic variables; and Avcı & Vanolya, Duran et al. and Buonora et al. [33,34,37] incorporate structural and environmental aspects but do not constitute a robust resilience system. Despite relying on Patel et al.’s [20] work as the conceptual baseline, the expansion to 30 parameters enabled the articulation of critical physical mechanisms (freeboard, flow depths, velocities, and scour), structural performance, and institutional capacities addressing the limitations identified by Asghari et al. [29], who highlight the need to combine quantitative failure metrics with management indicators.

Regarding the choice of a single case study, it is important to emphasize that the objective of this research is methodological validation rather than statistical generalization. The San Martín Bridge constitutes a critical and informative case, as it exhibits recurrent preventive closures, marginal freeboard under extreme flood scenarios, documented exposure to overtopping, and limited institutional response capacity. Although no piers are located within the main channel and the abutments do not protrude into the flow, the bridge remains vulnerable to hydraulic impacts through insufficient deck clearance, flow concentration at the abutments, and potential foundation exposure during extreme events. These characteristics make it a suitable testbed to evaluate the proposed resilience framework, which is not solely dependent on pier-related scour but on the interaction between hydraulic loading, structural capacity, and institutional preparedness. Single-asset case studies are widely accepted in infrastructure resilience research when the aim is to validate conceptual frameworks and analytical procedures under real-world constraints, while ensuring methodological transparency and transferability to other riverine bridges with similar configurations [21,23].

The 1D hydraulic modeling identified control thresholds consistent with the hydrological vulnerability literature [1,22,34,37,38,40]. In conclusion: bridge response during extreme events is dominated by hydrodynamics and scour processes. Additionally, the flexible weighting scheme showed stability under ±50% variations, distinguishing it from rigid methodologies such as AHP/FD [36] and confirming the consistency of the index even without formal expert panels.

Vegetation can also influence hydraulic resistance and flow structure in natural channels by modifying velocity distribution, bed shear stress variability, and sediment transport dynamics [85,86]. Although more advanced Eco hydraulic approaches based on vegetation structural parameters, such as the Leaf Area Index (LAI), have been proposed to better characterize vegetation-induced resistance [85], in the present study their influence was incorporated through the estimation of Manning roughness coefficients using the Cowan method, following the recommendations of the Peruvian Hydrology, Hydraulics and Drainage Manual [46], which remains widely applied in practical hydraulic engineering.

In addition to hydraulic resistance characterization, scour processes represent a critical mechanism controlling bridge performance during extreme flood events. The Artamonov method was adopted due to its compliance with Peruvian regulations [46] and its widespread use in regional bridge scour assessment. Despite the methodological variability shown in Table 12, the Artamonov formulation provides scour estimates that are consistent with the geomorphological and hydraulic characteristics of the study reach. It is recognized that empirical scour equations may be affected by scale effects and by the experimental datasets from which they were derived. Recent studies have proposed physically based approaches linking scour development to turbulence dynamics and near-bed flow structures [87,88]. However, the application of such approaches generally requires detailed turbulence measurements or high-resolution numerical simulations, which were beyond the scope of this study. Therefore, the use of empirical formulations consistent with national design standards remains appropriate for engineering assessment at the bridge scale. The scour depths obtained in this study should therefore be interpreted as conservative engineering estimates for the preliminary structural evaluation of the bridge foundations.

Finally, the findings show that resilience depends not only on hydraulic processes but also, and decisively, on institutional capacity to act in a timely manner. This result aligns with [20,24], demonstrating that budget availability, procurement efficiency, and operational preparedness directly influence system rapidity and redundancy. In the case of the San Martín Bridge, these institutional limitations reduced its resilience even when hazard and physical vulnerability were precisely characterized.

5. Conclusions

The literature review demonstrated that the hydrological resilience of riverine bridges depends on a multidimensional set of physical, structural, and institutional factors that have historically been analyzed in isolation. To address this gap, the present study developed a 30-parameter matrix grounded in the 4R framework, offering a bridge-specific and technically substantiated approach for resilience assessment.

The matrix was operationalized through the Bridge Resilience Index (BRI), which integrates 1D hydraulic modeling, scour analysis, and multicriteria evaluation. This combined approach enabled a quantitative representation of the main mechanisms driving resilience and vulnerability. Application to the San Martín Bridge revealed a low resilience level (BRI = 1.898), primarily due to insufficient freeboard, scour-inducing flow velocities, and limited institutional capacities for emergency response and recovery. The sensitivity analysis confirmed the stability of the BRI under ±50% variations in parameter weights, demonstrating the methodological robustness and its reduced dependence on subjective judgments, even in the absence of formal expert panels.

The findings yield four main contributions: (i) an integrated evaluation matrix specifically designed for riverine bridges; (ii) the explicit incorporation of hydraulic and scour-related processes as key determinants of bridge performance under extreme flood conditions; (iii) the contextual adaptation of the framework to real public management conditions in Peru; and (iv) empirical validation using an operational bridge, strengthening the method’s practical applicability.

Overall, the proposed methodology provides a replicable and scalable tool for the assessment and preventive management of riverine bridges. By offering an objective basis for prioritizing investments and guiding intervention strategies, it contributes to strengthening territorial resilience in the context of increasingly frequent and severe hydrological events.