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Procedia Structural Integrity 84 (2026) 409–416

© 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Conference Keywords: Artificial tunnel; 3D modelling; Soil-structure interaction; Structural integrity Abstract Three-dimensional (3D) numerical modelling is an essential tool for analyzing complex geotechnical problems involving soil structure interaction. In this study, a 3D numerical model was developed to assess the design and construction of a new artificial tunnel required for the upgrade of an existing motorway. The proposed tunnel crosses above an old underground hydraulic channel used to divert a river, creating a critical interaction between the new and existing infrastructure. The model incorporates detailed geotechnical and structural characteristics, as well as the sequential construction and operational phases. Special attention was given to reproducing the construction process realistically to evaluate its effects on the surrounding ground and structures. The results of the analysis enabled the identification of optimal technological solutions to ensure the stability of the new artificial tunnel and to safeguard the structural integrity of the underlying hydraulic channel. III Fabre Conference: Existing Bridges, Viaducts, and Tunnels: Research, Innovation, and Applications 3D modelling of a complex soil-structure interaction between a new motorway artificial tunnel and an existing underground hydraulic channel Francesco Campana b , Marco Barla a *, Santina Aiassa b , Francesco Antolini b , Luisa Alfieri c , Alessandro Piazza c a Department of Structural, Geotechnical and Building Engineering (DISEG), Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy b Geosolving Srl, Corso Orbassano 336, Torino 10137, Italy. c Alpina SpA, Via Giuseppe Ripamonti 2, Milano 20136, Italy.

* Corresponding author. E-mail address: marco.barla@polito.it

2452-3216 © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Conference 10.1016/j.prostr.2026.06.053

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1. Introduction The design of geotechnical structures invariably requires the formulation of a model of the soil-structure system, a representative framework essential for reproducing and analyzing its physical and mechanical behavior. A model represents an appropriate simplification of reality, and the skill in modelling lies in determining the level of simplification that allows distinguishing between relevant and negligible features (Wood, 2017). These principles become particularly critical in more challenging geotechnical contexts, where soil-structure interaction plays a decisive role. In such situations, traditional empirical or limit-equilibrium approaches often prove inadequate, as they are applicable only under simplified geometric, loading, and boundary conditions. Consequently, numerical modelling becomes an indispensable tool for achieving a more realistic representation of the system’s behaviour. In particular, significant spatial variability in system geometry, applied loads, or boundary conditions requires three-dimensional numerical modeling to accurately capture the overall stress-strain response and to identify and mitigate local criticalities in the engineering solution. In this context, three-dimensional numerical analyses provide substantial support in the study and design of shallow, mixed (Wang et al., 2019), and deep foundations (Jenck et al., 2009; Bagheri et al., 2019), particularly when the loading and geometric conditions of the foundation preclude the use of simpler approaches for assessing soil-structure interaction. Moreover, three dimensional numerical modelling is widely employed to investigate the interaction between tunnels and surface structures or infrastructures (Barla et al., 2012; Fargnoli et al., 2015; Yuan et al., 2019; Barla et al., 2021), as well as the interaction between infrastructures and landslides (Bru et al., 2018; Vassallo et al., 2019; Barla et al., 2024). This article presents a study of the interaction between the new Torbella artificial tunnel, part of the upgrading project for the A7-A10-A12 motorway system of Genova, the Gronda project, and the existing hydraulic channel located beneath the footprint of the planned structure (Fig. 1). The limited depth of the channel, combined with the geometric configuration of the proposed structure, constrained by the alignment of the existing highway, required the design of an articulated mixed foundation system (shallow foundations and piles) to prevent detrimental overloading of the existing hydraulic channel compromising its stability. Three-dimensional numerical modelling was employed to assess the effectiveness of the designed foundation system in limiting the interaction with the underlying channel, as well as to identify and mitigate local criticalities in order to preserve the structural integrity of the channel, which plays a significant role in ensuring the stability of the planned structure.

Fig. 1. Siting of the Torbella artificial tunnel within the infrastructural framework defined by the Gronda project.

2. The new Torbella artificial tunnel The Torbella artificial tunnel, included within the final design for the upgrading of the A7-A10-A12 motorway system of Genova (Gronda project), has been conceived to encase and protect the existing A12 motorway, enabling the construction of a platform that will serve as a strategic staging area for the development of the new A7 bypass route, through the construction of a new viaduct and a new natural tunnel. As shown in Fig. 2(a), the Torbella artificial tunnel intersects an existing hydraulic channel, which is positioned diagonally beneath the motorway alignments of the A12 motorway axis. The buried hydraulic channel was built in the second half of the 1960s as an underpass hydraulic structure for the Torbella creek to allow for the construction of the A12 motorway platform. The channel was constructed by open-cut excavation down to the foundation level, followed by casting of the foundations and base slab, erection of the concrete lining (walls and vault), and subsequent backfilling. The depth of the hydraulic channel relative to the foundation level of the artificial tunnel is

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limited to only a few meters. In particular, at the point where the two axes intersect, the depth decreases to approximately 3.4 m, as shown in Fig. 2(b). This critical condition may jeopardise the structural integrity of the hydraulic channel due to the increased loading imposed by the Torbella artificial tunnel.

(a)

(b)

Fig. 2. (a) Plan view of the designed Torbella artificial tunnel and the intersection with the hydraulic channel. (b) A-A’ cross-section of the Torbella artificial tunnel.

To mitigate the overloading of the channel, the foundation layout of the Torbella artificial tunnel has been designed to prevent direct interaction with the underlying structure by adopting pile and mixed foundation systems as illustrated in Fig. 3 a. Specifically, sidewall 1 is founded on Ø600 mm piles, 16 m in length, spaced 1.40 m apart, connected by a foundation beam 1.50 m thick and 2.40 m wide; sidewall 4 is founded on Ø600 mm piles, 18 m in length, with the same 1.40 m spacing and a foundation beam 1.50 m thick and 2.40 m wide. The two central walls (2 and 3) are founded on a footing slab with a variable width ranging from 2.92 m to 10.53 m and a thickness of 1.5 m. The structure features a transversal joint at approximately 28 m along the East tube and 31.4 m along the West tube. This divide creates two structurally independent units, both statically and seismically, which will be referred to as body 1 (easternmost) and body 2 (westernmost) (Fig. 2a). The central slab transfers the loads of Body 1 to Ø600 mm piles with a length of 18 m. For Body 2, interference with the Torbella channel necessitated the use of Ø300 mm micropiles, 20 m in length and inclined at 20° in order to prevent any interaction with the underlying channel. Furthermore, in the zone of intersection between the central foundation slab axis and the hydraulic channel axis, characterized by a limited embedment depth and the presence of a shallow connection shaft for minor streams ( Fig. 3 a and Fig. 3 b), the foundation system transitions to a direct foundation. As shown in Fig. 3 b the hydraulic channel in the area of interest has a constant cross-section, with a crown height of 5.65 m measured from the foundation level and a maximum width slightly exceeding 9 m. The unreinforced concrete lining, characterized by a variable thickness, reaches a maximum value of 2.02 m at the base of the sidewall and a minimum thickness of 65 cm at the crown.

(a)

(b)

Fig. 3. (a) Plan view of the foundation layout of the Torbella artificial tunnel; (b) Cross-section of the channel (section B-B’) and of the shaft (section C-C’).

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3. Study of the soil-structure interaction This section presents the three-dimensional numerical model developed to assess the effects of the construction of the new Torbella artificial tunnel on the existing underlying hydraulic channel. The 3D model, implemented using the finite-difference software FLAC3D 7.0 (ITASCA, 2019), was employed to identify the portions of the channel most affected by the artificial tunnel construction, verifying the preservation of its structural integrity. 3.1. The 3D numerical model The 3D model, extending 168 m in the E-W direction and approximately 135 m in the N-S direction, was sized to fully include the area where the hydraulic channel underpasses the A12 Motorway and interacts with the planned artificial tunnel, while avoiding boundary effects in the numerical solution. The model incorporates the current site topography, reconstructed from detailed surveys, the A12 motorway alignment, and the complete geometry of the hydraulic channel and the shaft, derived from as-built documents and field investigations. The geological geotechnical framework was reconstructed by spatially interpolating the two-dimensional cross-sections available in the design documentation, themselves based on extensive borehole data. From bottom to top, the subsurface consists of the Ronco Formation bedrock (ROC), its weathered mantle (ROC-Cap), the overlying alluvial deposits (Croc), and the fill materials associated with the A12 construction. An elasto-plastic constitutive law with Mohr-Coulomb failure criterion was adopted for all geotechnical units. The strength and deformability parameters of the geotechnical units used in the numerical analysis are summarized in Table 1.

Table 1. Deformability and strength parameters of the geotechnical units. Geotecnical units  [kN/m 3 ] E [MPa]  [-]  ’ [kPa] c’ [kPa] Filling soils 20 25 0.3 30 0 Alluvial deposit (Croc) 20 25 0.3 27 10 Altered bedrock (ROC-Cap) 24 150 0.25 22 30 Bedrock (ROC) 25 1500 0.20 38 75

For the structural elements of the existing hydraulic channel (bottom slab, foundations, and lining), the characteristic strength and deformability parameters of the concrete were derived from the average compressive strength obtained on cylindrical specimens retrieved through micro-coring. These elements were modelled assuming an elasto-plastic constitutive law with Mohr-Coulomb failure criterion. Conversely, the reinforced-concrete foundation beams and the central slab of the Torbella artificial tunnel were modelled as linear-elastic elements, assuming a C30/37 concrete class as specified in the design. The strength and deformability parameters adopted for all structural components are reported in Table 2.

Table 2. Deformability and strength parameters of the structural elements.

 [kN/m 3 ] E [MPa]  [-] f ck [MPa]  ’ [kPa] c’ [MPa] σ t [MPa] 24 30000 0.2 19.8 37 4.9 2.2

Structural element

Lining, bottom slab and foundations of the hydraulic channel Foundation beams and central slab of the Torbella artificial tunnel

25

33000 0.2 -

-

-

-

The structural elements of the hydraulic channel and the shallow foundations of the Torbella artificial tunnel were modeled as volume elements, while the Ø600 bored piles and micropiles were represented with “pile-type” elements, assuming soil-side failure. Without load tests, the ultimate pile-soil shear resistance was estimated from the geotechnical unit strength parameters. The tunnel superstructure was explicitly modelled using “shell-type” elements for the sidewalls and cover. The 3D model also reproduces the site topography, with the valley axis at roughly 110 m a.s.l., hosting the A12 motorway and the hydraulic channel. Boundary conditions included zero displacement normal to the lateral and bottom faces, and hinge supports at the four lower vertices. Interstitial pressure was considered via the effective stress principle, and the groundwater table, averaging 8 m below ground, was interpolated from geological sections. Fig. 4 summarizes the main construction phases reproduced in the 3D

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model. Each phase groups all the computational stages required to represent a configuration of interest of the model, each reproducing a key step in the historical and design evolution of the site.

Fig. 4. Main construction phases reproduced in the 3D numerical model.

Phase 1 involves the initialization of the stress state of the model. Starting from the initial geometry of the area, characterized by the presence of the stream incision where the Torbella creek originally flowed, and in the absence of both the A12 motorway alignment and the hydraulic channel, the stress state was assigned by bringing the system to equilibrium under gravitational loads only and by applying a lateral earth pressure coefficient at rest, k₀ = 1.0. This stage provides the initial configuration of the valley and defines the baseline stress state for all subsequent computations. Building upon this initial condition, Phase 2 reproduces the excavation of the trench down to the foundation level of the hydraulic channel, approximately 4-5 m below the ground surface and at the bedrock interface, as documented in the as-built drawings. Phase 3 then simulates the sequential construction of the foundations, the bottom slab, and the lining of the hydraulic channel, including the shaft, thereby reconstructing the channel in its original configuration. Once the channel is completed, Phase 4 introduces soil backfilling up to the final elevation of the A12 motorway. The corresponding highway load, applied along the axes of both traffic directions, as prescribed by the Italian Building Code, is subsequently imposed. This stage represents the current stress-strain condition of the hydraulic channel prior to the construction of the planned artificial tunnel. Finally, Phase 5 reproduces the design configuration by simulating the successive construction of the cast in place foundations system and the superstructure of the Torbella artificial tunnel. Initially, only the self-weight of the tunnel is considered, as the structure has not yet developed sufficient stiffness. The model then incorporates the stiffness provided by the fully cured tunnel superstructure and applies at the foundation level the total actions due to the tunnel’s self-weight and the accidental loads associated with service conditions, as evaluated through a dedicated structural model. Fig. 5a shows a detailed view of the foundations and the superstructure of the Torbella artificial tunnel, as well as its intersection with the underlying hydraulic channel, while Fig. 5b presents a detailed view of the computational mesh of the channel and the shaft, whose cover lies only 1 m below the bearing base of the central foundation slab of the artificial tunnel. Moreover, as specified in the design documents, a 0.5 m thick rigid cement treated subbase was included in the model beneath the terminal portion of the central foundation slab.

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(a)

(b)

Fig. 5. (a) Detailed view of the foundations and the superstructure of the Torbella artificial tunnel; (b) detailed view of the computational mesh of the channel and the shaft.

3.2. 3D model as a design and verification tool In the following, some of the results obtained from the proposed 3D model are presented. The model enabled a detailed study of the interaction described above, allowing the identification of design improvements to ensure the stability of the new tunnel and to safeguard the structural integrity of the underlying hydraulic channel. Fig. 6a shows, for phase 5 (completion of the artificial tunnel), the vertical displacements at the central foundation of the artificial tunnel and its interaction with the hydraulic channel. Fig. 6b, instead, presents a detailed plan view of the vertical displacements induced in the hydraulic channel and its deformed configuration resulting from the interaction (magnification factor = 2500).

(a)

(b)

Fig. 6. (a) Vertical displacements of the central foundation slab of the Torbella artificial tunnel and interaction with the hydraulic channel (stage 5); (b) Plan view of the vertical displacements of the hydraulic channel due to the interaction with the artificial tunnel (stage 5).

The construction of the artificial tunnel affects approximately 100 m of the hydraulic channel, particularly in the area intersecting the central foundation of the tunnel. The maximum vertical displacements of the artificial tunnel, about 9 mm, occur in the central portion of the foundation slab where no piles are present, and are fully consistent with the values predicted by the structural model developed for the static and seismic verifications. The vertical displacements induced in the channel, while remaining below 3 mm, exhibit a differential behavior. The analysis also allowed the identification of two transversal sections that may be critical for the stability of the channel lining (Fig. 6): Section 1-1’, located at the connection between the lining and the shaft, and Section 2-2’, corresponding to the channel portion strongly influenced by the nearby Ø600 bored piles. In Section 1-1’, the adjacent shaft, characterized by a very stiff behaviour and with its top located only 1 m below the base of the central foundation, tends to absorb a significant portion of the loads transmitted by the artificial tunnel’s direct foundation, transferring them to the closest portions of the channel lining. This condition results in high shear stresses concentrated in the right sidewall lining, potentially compromising the structural integrity of the underlying hydraulic channel. To address this issue and preserve the structural integrity of the channel lining, two design options were compared. The

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objective was to structurally isolate the shaft by reducing the load it attracts from the artificial tunnel, enhancing the “bridging effect” provided by the micropiles. This was achieved by replacing the rigid cement-treated subbase around the shaft (Design option 1) with compacted backfill material and by increasing the number of micropiles in the adjacent areas (Design option 2), as illustrated in Fig. 7.

(a)

(b)

Fig. 7. (a) Initial design of the end portion of the central foundation of the artificial tunnel and resulting vertical stress state in the shaft and channel lining. (b) Final design of the same foundation portion and corresponding vertical stress state in the shaft and channel lining. Section 1-1’ Section 2-2’

Fig. 8. Normal force (N), bending moment (M), and shear force (V) in Sections 1-1’ and 2-2’ of the channel lining at calculation stages 4 and 5.

This design local improvement was effectively achieved thanks to the ability of the 3D model to reproduce a realistic soil structure interaction. Fig. 8a also reports the distribution of normal force (N), bending moment (M), and shear force (V) for phase 4 (before the construction of the artificial tunnel) and 5 (completion of the artificial tunnel), where a reduction in the internal forces in Section 1-1’ can be observed following the Design option 2

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(Phase 5 - Design option 2). This configuration ensures the stability of the new artificial tunnel and to safeguard the structural integrity of the underlying hydraulic channel. Figure 8 also shows, as for section 1-1’, the stress distribution for calculation Stages 4 and 5 for section 2-2’. With reference to section 2-2’, the interaction with the adjacent Ø600 piles causes a downward dragging effect on the lining at the left sidewall, inducing differential settlement of the channel in that area. Despite the differential settlement of the lining (Fig. 6b) and the resulting increase in bending moment at the base of the left sidewall (Fig. 8), the lining thickness at the base, slightly over 2 m, ensures the structural integrity of the underlying hydraulic channel. Conclusions In challenging geotechnical contexts, characterized by significant spatial variability in system geometry, applied loads, or boundary conditions, soil-structure interaction plays a primary role. In such cases, the design of geotechnical structures requires detailed 3D numerical modelling to accurately capture the overall stress-strain response and to optimise the engineering solution. In the case study presented in this paper, which examines the interaction between the new Torbella artificial tunnel and the underlying hydraulic channel, the use of a 3D model made it possible not only to accurately assess the extent of the interaction between the two structures, but also to identify the sections of the channel most affected by the artificial tunnel-induced loading. It further enabled a straightforward definition of the design improvement aimed at preserving the structural integrity of the channel while ensuring the stability of the new artificial tunnel. In such complex contexts, the use of 3D models for soil-structure interaction assessment remains preferable to the adoption of simpler two-dimensional models, as it allows the actual stiffness of the engineering system to be represented and ensures an adequate evaluation of its stress-strain response during the design phase. Acknowledgments The Authors are willing to acknowledge the motorway concessionaire Autostrade per l’Italia SpA and the designer Tecne SpA for kindly providing the data used in this study. References Bagheri, M., Jamkhaneh, M. E., & Samali, B., 2018. Effect of seismic soil-pile-structure interaction on mid-and high-rise steel buildings resting on a group of pile foundations. International Journal of Geomechanics , 18 (9), 04018103. Barla, G., Barla, M., & Leuzzi, G., 2012. 3D numerical modelling and settlement monitoring during excavation of the Metro-Torino South extension. In Geotechnical Aspects of Underground Construction in Soft Ground (pp. 929-936). CRC Press. Barla, M., Insana, A., Santina, A., & Francesco, A., 2021. La modellazione numerica tridimensionale nello studio delle interferenze tra opere in sotterraneo e infrastrutture in superficie. STRADE & AUTOSTRADE , 150 . Barla, M., Insana, A., De Feudis, S., & Campana, F., 2024. Numerical modelling of existing tunnels subjected to time dependent threats. GALLERIE E GRANDI OPERE SOTTERRANEE, 150, 7-20. Bru, G., Fernández-Merodo, J., García-Davalillo, J. et al., 2018. Site scale modeling of slow-moving landslides, a 3D viscoplastic finite element modeling approach. Landslides 15, 257-272. Fargnoli, V., Gragnano, C. G., Boldini, D., & Amorosi, A., 2015. 3D numerical modelling of soil-structure interaction during EPB tunnelling. Géotechnique , 65 (1), 23-37. Jenck, O., Dias, D., & Kastner, R., 2009. Three-dimensional numerical modeling of a piled embankment. International Journal of Geomechanics , 9 (3), 102-112. ITASCA, 2019. Fast Lagrangian Analysis of Continua 3D (FLAC 3D ver. 7.0) Theory and background. Itasca Consulting Group Inc., Minneapolis, Minesota, USA. Vassallo, R., Mishra, M., Santarsiero, G., & Masi, A. 2019. Modeling of landslide-tunnel interaction: the Varco d’Izzo case study. Geotechnical and Geological Engineering, 37(6), 5507-5531. Yuan, C., Yu, H., Yuan, Z., & Wang, Y., 2019. Numerical simulation of impact caused by construction of high-rise building upon adjacent tunnels. Geotechnical and Geological Engineering , 37 (4), 3171-3181. Wang, W. D., Ng, C. W., Hong, Y., Hu, Y., & Li, Q., 2019. Forensic study on the collapse of a high-rise building in Shanghai: 3D centrifuge and

numerical modelling. Géotechnique , 69 (10), 847-862. Wood, D. M., 2017. Geotechnical modelling. CRC press.

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Procedia Structural Integrity 84 (2026) 959–966

© 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Conference Keywords: Bayesian model updating; damage assessment; model-based monitoring; bridges; surrogate models. Abstract Efficient and reliable damage detection in bridges requires models that capture complex structural behaviours while remaining computationally tractable for real-time application. Conventional finite element (FE) model updating is often infeasible due to its high computational cost and the large parameter space involved. This paper proposes a multi-surrogate framework for bridge Structural Health Monitoring (SHM) that balances model fidelity with computational efficiency. A global surrogate is first trained to emulate the bridge’s dynamic response across a broad set of potential damage parameters. From this, multiple local surrogate models are derived, each varying only a small subset of parameters corresponding to plausible damage locations, such as specific spans, girders, or supports. These surrogates provide computationally efficient approximations of structural dynamics under competing possible damage conditions. In operation, vibration sensor data are assimilated into the surrogates via Bayesian inference, and statistical metrics such as the Bayesian Information Criterion (BIC) are employed to rank scenarios while maintaining low computational cost. To ensure a realistic validation, the method is tested with real monitoring data from an instrumented bridge, where the surrogate model is trained on one FE model and damage scenarios are simulated with a separate, independently calibrated model. III Fabre Conference: Existing Bridges, Viaducts, and Tunnels: Research, Innovation, and Applications A Bayesian-based multi-surrogate framework for bridge Structural Health Monitoring Laura Ierimonti a, *, Elisa Tomassini a , Enrique García-Macías b , Filippo Ubertini a a Department of civil and Environmental Engineering, University of Perugia, Via G. Duranti, 06125, Italy b Department of Structural Mechanics and Hydraulic Engineering, University of Granada, Av. Fuentenueva sn, 18002 Granada, Spain.

* Corresponding author. E-mail address: laura.ierimonti@unipg.it

2452-3216 © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Conference 10.1016/j.prostr.2026.06.123

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1. Introduction Ensuring the safety and serviceability of bridge networks is a major challenge worldwide, as illustrated by numerous recent failures and the large proportion of aging structures in need of maintenance. Because real damage cases are rare and difficult to observe experimentally, the development of reliable SHM methods increasingly relies on techniques (e.g. vibration-based ones) that can operate under normal traffic and environmental conditions. Operational Modal Analysis (OMA) has become a cornerstone of this field (Magalhães & Cunha, 2011, Rainieri & Fabbrocino, 2014, Brincker & Ventura, 2015), enabling the continuous extraction of modal features sensitive to stiffness changes (Cabboi et al ., 2017, Quqa et al., 2021, He et al ., 2022, Tomassini et al., 2025). However, while unsupervised data-driven approaches are now routinely applied for damage detection at network scale, progressing from detection to robust damage localization and quantification remains difficult. The main limitation is the scarcity of labelled damage data and the impracticality of generating them on full-scale structures. To overcome this limitation, model-based strategies play a central role. Classical model updating, whether deterministic or Bayesian (Alkayem et al., 2018, Lam et al., 2018, García-Macías et al., 2020, Ierimonti et al., 2021, Li et al ., 2025), can provide detailed insight into the structural state, but its practical application is hindered by high computational costs when the space of the parameters is very large, causing possible ill-conditioning. Recent research has explored the use of surrogate models to approximate high-fidelity simulations with negligible evaluation time, enabling efficient probabilistic inference for SHM (Zhang et al., 2021). Yet, many existing approaches still rely on a single surrogate trained and tested on a single FE model, which may limit robustness and interpretability. In the above context, the present work introduces a multi-surrogate modelling framework designed to improve the reliability and scalability of model-based SHM in conditions where actual damage data are scarce. First, a global surrogate model is trained to reproduce the dynamic response of a bridge across a wide range of admissible damage parameters. Then, a collection of “local” surrogate models is generated, each restricted to a small subset of parameters associated with a specific damage hypothesis (e.g., a given portion, span, or support). This decomposition drastically reduces the dimensionality of the inverse problem, improving numerical conditioning and enabling efficient Bayesian inference for multiple competing scenarios. To further enhance robustness, the approach deliberately employs two independent FE models: one to generate the surrogate training data and another to produce validation damage scenarios. This avoids dependence on a single numerical formulation and provides a more realistic test of the methodology. Measured modal features from the monitored bridge are assimilated through Bayesian inference, and competing damage hypotheses are ranked using BIC (Gosh et al., 2006). 2. The proposed methodology The proposed framework consists of two major components (Fig.1): (i) a model-based component, where physics based numerical models and surrogate models are developed, and (ii) a data-driven component, where SHM data are acquired, processed, and used to update and compare damage hypotheses. Model-based component . The model-based stage begins with the development of two numerical representations of the bridge, each serving a distinct purpose in the workflow. The first, denominated as FEM A , is a computationally efficient beam-type finite element model, which is calibrated to match the global dynamic behaviour of the real structure. This simplified model is not intended to capture fine local effects; rather, it serves as a fast and flexible tool for generating a large synthetic dataset that spans a wide range of potential damage parameters across the bridge. Because surrogate models require thousands of training samples to learn the mapping between structural parameters and dynamic response, the beam model is ideal for this purpose due to its low computational cost. In parallel, a more detailed shell-element finite element model is developed and independently calibrated, denominated as FEM B . This model includes the bridge deck, girders, diaphragms, and other structural components with much higher geometric fidelity. In contrast to FEM A , FEM B is not used for surrogate training but for validating and testing the surrogate under realistic damage scenarios. By separating the model used for training from the one used to generate test scenarios, the framework avoids overfitting the surrogate to the assumptions of a single model. Once the global beam model has generated the required training data, a global surrogate model is constructed. This surrogate learns to emulate the

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dynamic response of the structure (e.g., modal frequencies, mode shapes, rotations) as a function of a wide variety of potential damage parameters. In practice, the surrogate may be implemented using neural networks or other nonlinear regression techniques. Its role is to replace the FE model in the calculation of predicted dynamics, thereby enabling fast evaluations during Bayesian updating. To further enhance efficiency and reduce ill-conditioning in the inverse problem, the global surrogate is then decomposed into a suite of local surrogate models, each associated with a particular damage hypothesis. For example, one surrogate may consider stiffness reductions only in a given span, another in a specific girder, and so on. By restricting each local surrogate to only a few parameters, the dimensionality of the inference problem becomes much smaller, leading to more stable and interpretable parameter estimation. Instead of solving one large and poorly conditioned inverse problem, the framework evaluates several smaller, targeted scenarios, each represented by its own simplified surrogate.

Fig. 1. The proposed methodology.

Data-driven component. In parallel with the model development, real SHM data are acquired from the bridge. The monitoring system typically consists of accelerometers, displacement sensors, or strain gauges installed at key structural locations. These sensors capture the dynamic response of the bridge under traffic and environmental excitation. The raw measurements undergo a rigorous data postprocessing phase, where modal properties such as natural frequencies, vibration mode shapes, or strain/displacement patterns are extracted. These processed quantities form the observational data vector are used to inform the surrogate models. Once the observational features are available, they are integrated into the surrogate-based framework through Bayesian inference. For each local surrogate model, the posterior distribution of the corresponding damage parameters is computed by comparing the surrogate predicted dynamics with the measured modal features. Because surrogate evaluations are extremely fast, this Bayesian updating can be performed for many competing damage scenarios without prohibitive computational cost. To objectively determine which damage scenario best explains the observed SHM data, the framework employs a BIC based model class selection. The BIC provides a principled balance between goodness of fit and model complexity: it penalizes models with unnecessary parameters while rewarding those that match the data accurately. Each local surrogate model receives a BIC score, and the scenario with the lowest score is identified as the most plausible representation of the current structural state. In this way, the framework does not simply estimate damage parameters but also statistically ranks the different potential damage locations. The final outcome of the process is a ranked set of damage hypotheses, together with their estimated severities and associated uncertainties. These results can be directly used by engineers to support maintenance and inspection

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planning, allowing them to focus attention on the most likely damaged regions. Because the framework combines efficient surrogate models with rigorous statistical selection criteria, it is well suited for continuous monitoring and

near real-time structural assessment. 3. BIC-based model class selection

Damage hypotheses are represented through a collection of model classes, denominated as candidates SM k . The paper employs Bayesian model class selection to identify which of these candidates is most consistent with the observed system response. Within SHM applications, candidate models frequently differ in their parameter structures, each reflecting a different type of potential deterioration. Bayesian model class selection leverages Bayesian inference (Hernández-González and García-Macías, 2024) to update belief in each model by merging prior knowledge with measurement data. For efficient comparison, the BIC is used as a practical tool for determining the model which best fits the data: BIC(SM )= − 2 ∙ log( ∗ ( ∣ ∗ (SM ))+ ∙ log , (1) where the term k corresponds to the number of the parameters within the model, n represents the number of available measurements, ∗ ( ∣ ∗ (SM )) denotes the maximized value ( ∗ are the values of updating parameters that maximize the likelihood function for model SM ) of the likelihood function ( ∣ (SM )) that quantifies how closely the model’s predictions align with the observed data . The function ( ∣ (SM )) , assuming a Gaussian distribution of the error between the model and experimental data, can be written as: ( ∣ (SM ))= ∑ ∑ √2 1 2 exp (− ( , − ˆ ( ( SM )) ) 2 2 2 ) =1 =1 , (2) where is the -th experimental frequency, ˆ ( (SM )) is the predicted frequency from the surrogate model SM , is the standard deviation associated with the -th frequency. The BIC formulation balances these elements by rewarding explanatory accuracy and penalizing unnecessary complexity. Within BMCS, the preferred model is the one yielding the smallest BIC score, as it best reconciles fidelity and parsimony. 4. The case study 4.1. Description of the real bridge The Volumni is a real bridge located in Perugia, in the Umbria region of Italy, and consists of five spans made of prestressed concrete. Overall, the structure extends for about 340 m. The deck is composed by a continuous post tensioned multi-cell box girder in prestressed concrete. The first and last spans are 42.5 m long, whereas each of the three central spans measures 85 m. Support is provided by four rectangular reinforced-concrete piers on deep foundations. Their heights vary due to the sloping ground conditions; the third pier is the tallest at approximately 12.8 m, the two adjacent piers are around 10 m, and the first pier is substantially shorter. All piers rest on deep pile foundations composed of reinforced-concrete piles. As part of the SHM programme initiated by ANAS S.p.A. (2025), the Bridge was equipped in 2023 with an extensive network of sensors consisting of a combination of one triaxial accelerometer, four biaxial accelerometers, and thirty uniaxial MEMS accelerometers, installed along the structure (Figure 2).

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Fig. 2. (a) Stabilization diagram of the Volumni Bridge (24th April, 2024, 11:00 a.m.) and first four mode shapes. (b) Sketch of the bridge and sensor deployment.

Two different FE models are built and calibrated accounting for the original design drawings: (i) FEM A and (ii) FEM B . In FEM A the deck was represented as a continuous beam with variable geometry, using 22 sections for each central span and 11 for each end span. To retrieve modal displacements at the sensor locations, rigid links and a flexible shell layer were added at deck level. The piers were modelled using prismatic beam elements with fixed bases.

Table 1. Model calibration.

Exp. FEM A ∆ FEM A − MAC FEM A FEM B ∆ FEM − MAC FEM ∆ FEM − FEM − 1 0.882 0.890 0.862 0.95 0.907 2.89 0.962 -1.97 0.99 FEM A FEM B FEM A - FEM B

No.

Type

-

1st order bending 1st order bending 1st order bending 2nd order bending 2nd order bending 2nd order bending 1st order torsional 1st order torsional 3rd order bending

2 1.342 1.285 -4.214 3 1.830 1.742 -4.818 4 3.880 3.787 -2.397 5 4.480 4.402 -1.749 6 4.823 4.730 -1.939

0.90 0.89 0.89 0.80 0.87 0.84 0.87 0.77 0.93

1.308 -2.5149

0.915 0.867 0.804 0.834 0.889 0.818 0.827 0.759 0.859 0.799 0.795

-1.74 0.14 -3.90 -2.18 -1.54 -1.66 -1.11 -1.21 0.31

0.99 0.99 0.88 0.98 0.98 0.96 0.70 0.98 0.73 0.79 0.69

1.740 3.941 4.500 4.804 5.237 5.316 6.556 9.715

-4.96 1.57 0.45 -0.39 4.93 -3.52 4.65 -0.57

7 4.991 5.150

3.194

8 5.510 5.255 -4.621

9 6.265 6.477

3.387

10 9.771 9.746 -0.259 11 11.172 11.323 1.351 12 11.768 11.631 -1.166

1st/2nd order torsional

0.73 11.507 2.30 0.78 11.689 -0.68

1.6

3rd order torsional 3rd order torsional

0.49

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Rigid links connected the pier-cap centroids to their top surfaces, where six-degree-of-freedom spring elements reproduced the sliding bearings between deck and piers; an equivalent configuration was adopted for the abutment bearings. In FEM B , the deck was modelled using shell elements with variable thickness and geometry to accurately reproduce the real bridge configuration. The piers were represented following the same modelling approach adopted in FEM A . The models were subsequently calibrated against reference modal properties extracted with the CoV-SSI algorithm implemented in the MOVA/MOSS software (García-Macías et al., 2020). The results of the calibration are summarized in Table 1. More details can be found in (Tomassini et al., 2025). 4.2. Surrogate model A surrogate model inspired by the modular feed-forward neural network (FNN) architecture proposed in Tomassini et al. , 2025 was developed to build the SM of the Volumni Bridge. The input to the FNN consisted of the non dimensional parameters , defined as functions of the stiffness multipliers of the deck with = 1,..,20, while the outputs were the corresponding normalized frequencies and mode shapes (more details can be found in Tomassini et al., 2025). The internal architecture comprises a shared block of fully connected layers for feature extraction, followed by two specialized modules: one dedicated to predicting the modal frequencies through GELU-activated layers, and a second composed of different branches devoted to mode-shape prediction using hyperbolic-tangent activations. According to this, the deck of the FEM A was discretized into 20 control regions (each span was subdivided into four equal segments, each one quarter of length of the span), and each region was associated with an independent stiffness multiplier varying within the range [0.8,1.05]. A Latin Hypercube Sampling (LHS) procedure was used for generating 1024 combinations of these parameters; for each configuration, the calibrated FEM A was used to extract the corresponding natural frequencies and mode shapes, generating the dataset used to train the surrogate model. Training was performed for 1000 epochs using a custom loss function that jointly accounts for frequency errors and MAC-based mode-shape similarity, with 15% of the samples reserved for internal validation. An independent validation set of 512 FEM A simulations confirmed the high accuracy of the surrogate model, with frequency predictions achieving 2 >0.99 and mode shapes reaching MAC values consistently above 0.98. These results demonstrate the suitability of the proposed FNN-based surrogate for efficient, stiffness-oriented damage assessment. W ith reference to Fig. 2, the spans are numbered C1 to C5 along the Florence direction, and the damage -sensitive parameters to be updated are denoted as , ( =1,…,19 -Florence direction). The selected surrogate sub-model competing candidates are defined as follows: (i) SM 1 , = θ 1 , . , θ 4 ; (ii) SM 2 , = θ 5 , . , θ 8 ; (iii) SM 3 , = θ 9 , . , θ 12 ; (iv) SM 4 , = θ 13 , . , θ 16 ; (iv) SM 5 , = θ 17 , . , θ 20 ; (v) SM 6 , = θ 1 , . , θ 20 . 5. Results and discussion Bayesian model class selection is performed to compare the six surrogate models defined in Section 4.2, with differing parameterizations of the elastic moduli. Mode correspondence between undamaged and damaged models is established using the Modal Assurance Criterion (MAC). A full MAC matrix is computed, and modal pairing is performed by maximizing MAC values, ensuring correct mode tracking. Damage is simulated by reducing the parameters θ 9 ,…, θ 12 by 20% in FEM B , corresponding to an equivalent reduction in the stiffness of the box girder. Figure 3 shows the evolution of the BIC across the iterative updating process. During the initial undamaged iterations (iterations 0-4), all surrogate models exhibit comparable BIC values, indicating limited discriminatory power due to insufficient information content in the data. Among all candidates, SM 3 consistently yields the lowest BIC values, indicating the strongest balance between goodness-of-fit and model complexity. The remaining low-dimensional models (SM 1 toSM 5 ) perform competitively but are systematically inferior to SM 3 . In contrast, SM 6 (the 20-parameter model), despite the potential flexibility of the parametrization, exhibits substantially higher BIC values throughout the iterations. This behavior reflects the strong penalization of unnecessary complexity when the additional parameters are not sufficiently supported by the data.

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Fig. 3. Bic values for the analyzed SM.

The posterior distributions of θ₉ ,.., θ₁₂ are illustrated in Figure 4 and are consistent with the simulated damage scenario while incorporating prior information. The results show that the inferred mean values slightly exceed the imposed damage level, which is attributed to the influence of the prior distributions and the uncertainty introduced by model discrepancies. Notably, SM 3 yields well-concentrated posterior distributions with relatively narrow credible intervals, indicating robust parameter identifiability and stable inference. These findings confirm that the Bayesian model class selection decisively favors reduced-order surrogate models, with SM 3 providing the optimal trade-off between model fidelity, interpretability, and statistical robustness. The inferior performance of SM 6 highlights the importance of aligning model complexity with data informativeness.

Fig. 4. Posterior distributions with the indication of mean values and standard deviation for SM 3 .

6. Conclusions This paper proposed a multi-surrogate Bayesian framework for efficient bridge damage detection that balances model fidelity and computational efficiency for SHM applications. By combining a global surrogate with multiple low-dimensional local surrogates, the approach enables rapid evaluation of competing damage scenarios.

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Bayesian inference and model class selection based on the BIC demonstrated that reduced-order surrogate models consistently outperform highly parameterized alternatives. The results indicate that the available vibration data primarily support local stiffness variations, while excessive model complexity leads to parameter non-identifiability and reduced statistical efficiency. Stable model rankings and concentrated posterior distributions confirm the robustness and interpretability of the proposed framework. It is worth noticing that the surrogate models were calibrated using one FE representation of the bridge (FEM A ), while damage scenarios were generated using a separate, independently calibrated model (FEM B ). This design choice reflects the practical absence of prior information about damaged states and mitigates potential bias arising from model self-consistency, thereby enhancing the robustness of the proposed methodology. Acknowledgements The authors acknowledge ANAS S.p.A. for access to monitoring data and technical documentation of the Volumni Bridge. This work was supported by the FABRE–ANAS 2021–2026 research program under the FABRE Research Consortium (www.consorziofabre.it/en).. The views expressed are those of the authors and not necessarily of the funding bodies. References Alkayem, N. F., Cao, M., Zhang, Y., Bayat, M., & Su, Z. (2018). Structural damage detection using finite element model updating with evolutionary algorithms: A survey. Neural Computing and Applications, 30(2), 389–411. Anas S.p.A., Monitoraggio di ponti e viadotti tramite sensori, 2025, Last accessed: 10 2025. Brincker, R., & Ventura, C. (2015). Introduction to Operational Modal Analysis. John Wiley & Sons. Cabboi, A., Magalhães, F., Gentile, C., & Cunha, Á. (2017). Automated modal identification and tracking: Application to an iron arch bridge. Structural Control and Health Monitoring, 24(1), e1854. García-Macías, E., Ubertini, F., 2020. MOVA/MOSS: Two integrated software solutions for comprehensive Structural Health Monitoring of structures. Mechanical Systems and Signal Processing 143, 106830. García-Macías, E., Venanzi, I., Ubertini, F., 2020. Metamodel-based pattern recognition approach for real-time identification of earthquake-induced damage in historic masonry structures. Automation in Construction 120. Ghosh, J.K., Delampady, M., Samanta, T., 2006. An Introduction to Bayesian Analysis: Theory and Methods. Springer-Verlag, New York. He, Z., Li, W., Salehi, H., Zhang, H., Zhou, H., & Jiao, P. (2022). Integrated structural health monitoring in bridge engineering. Automation in Construction, 136, 104168. Ierimonti, L., Cavalagli, N., Venanzi, I., García-Macías, E., Ubertini, F., 2021. A transfer Bayesian learning methodology for structural health monitoring of monumental structures. Engineering Structures 247, 113089. Lam, H.F., Yang, J.H., Au, S.K., 2018. Markov chain Monte Carlo-based Bayesian method for structural model updating and damage detection. Structural Control and Health Monitoring 25(4), e2140. Li, Q., Ni, P., Du, X., Han, Q., Xu, K., & Bai, Y. (2025). Bayesian updating using accelerated Hamiltonian Monte Carlo with gradient‑enhanced Kriging model. Computers & Structures, 307, 107598. Magalhães, F., & Cunha, Á. (2011). Explaining operational modal analysis with data from an arch bridge. Mechanical Systems and Signal Processing, 25(5), 1431–1450. Rainieri, C., & Fabbrocino, G. (2014). Operational Modal Analysis of Civil Engineering Structures (Vol. 142). Springer, New York. Tomassini, E., Centofanti, G., Chellini, G., García-Macías, E., Lepori, L., Mannella, P., Salvatore, W., Ubertini, F., 2025. Key findings from long term operational modal analysis of a landmark steel arch bridge in Italy. Structures 82, 110436.Tomassini, E., García-Macías, E., Ubertini, F., 2025. Model-based transfer learning for real-time damage assessment of bridge networks. Automation in Costruction 180, 106581. Quqa, S., Landi, L., Diotallevi, P.P., 2021. Automatic identification of dense damage-sensitive features in civil infrastructure using sparse sensor networks. Automation in Construction 128, 103740. Zhang, J., Maes, K., De Roeck, G., Lombaert, G., 2021. Model updating for a large multi-span quasi-periodic viaduct based on free wave characteristics. Journal of Sound and Vibration 506, 116161. Hernández-González, Israel Alejandro, and Enrique García-Macías. "Towards a comprehensive damage identification of structures through populations of competing models." Engineering with Computers 40.5 (2024): 3157-3174.