Integrated Static–dynamic Assessment and Field-validated External Prestressing Strengthening of an Aging Steel Railway Bridge

This study makes the following contributions to the assessment and strengthening of existing railway bridges:

• (1)

  It proposes an integrated, full-scale assessment framework combining static load testing, dynamic vibration testing, and calibrated three-dimensional finite element modelling for aging steel railway bridges.

• (2)

  It provides empirical field evidence quantifying stiffness degradation and recovery through changes in natural frequencies, camber restoration, and member-level capacity ratios before and after external prestressing.

• (3)

  It demonstrates the effectiveness of external prestressing as a performance-based strengthening strategy by explicitly linking measured static and dynamic responses to post-strengthening structural capacity improvement.

Despite extensive research on static load testing, dynamic identification, numerical modelling and strengthening techniques for railway bridges, these components are frequently addressed as independent or sequential procedures. Comprehensive full-scale investigations that explicitly integrate static and dynamic field measurements with calibrated three-dimensional finite element modelling to support capacity-oriented decision-making remain limited. In particular, empirical evidence directly correlating changes in vibration characteristics and camber restoration with quantified improvements in member-level demand-to-capacity ratios is scarce.

The present study addresses this gap by implementing an integrated static–dynamic assessment framework in which field-measured responses are used to calibrate a numerical model and to quantitatively evaluate the effectiveness of external prestressing strengthening. By linking stiffness indicators, camber recovery, and structural capacity verification within a unified workflow, this research provides field-validated evidence supporting performance-based strengthening strategies for aging steel railway bridges.

The BH 25 railway bridge is located in Garut, West Java Province, Indonesia, and serves as part of an active railway corridor. It is a three-span steel truss bridge with a total length of 41.055 m, consisting of spans of span 1: 9.485 m, span 2: 21.930 m, and span 3: 9.635 m. Spans 1 and 3 consist of steel girder-type systems, in which the main load-bearing elements are longitudinal girders supported by transverse floor beams, forming the primary load transfer mechanism. The general geometric configuration, span arrangement, and structural layout of the bridge are summarized in Table 1. The bridge layout, elevation, and overall structural configuration are illustrated in Figure 1 – Figure 3.

Figure 1:

Cibatu - Garut Railway Map

Figure 2:

(a) Aerial view of the bridge, (b) Steel structure of the bridge

Figure 3:

Top view of the bridge

Span 2 was identified as the most critical segment due to observable camber deficiency and the presence of temporary supports. Although the bridge was originally designed with a positive camber to compensate for dead and live load effects, construction deviations resulted in a downward displacement, indicating reduced global stiffness and motivating further structural evaluation.

Static and dynamic load tests were conducted using a CC206 diesel-electric locomotive with a total weight of 90 tons and an axle load of 15 tons. The locomotive specifications, static loading configuration, and governing load combinations applied during the field test are listed in Table 2. The geometric properties and section characteristics of the bridge members, together with the adopted material properties of the existing steel components, are summarized in Table 3, respectively. The loading positions during testing are illustrated in Figure 4 and 5.

Figure 4:

CC206 locomotive used in the load testing program

Figure 5:

Static load scheme applied to Span 2 of the bridge

Static testing involved positioning the locomotive at predetermined locations along Span 2 to induce maximum deflection and internal forces. Dynamic testing was performed through controlled locomotive passage to capture vibration responses under moving loads, following Indonesian railway safety regulations and international testing guidelines. The evaluation procedures and acceptance criteria were further interpreted with reference to national structural design provisions to ensure consistency with prevailing code-based safety requirements.

The structural response of the bridge was monitored using a combination of displacement, strain and acceleration measurement systems. Linear Variable Differential Transformers (LVDTs) and strain gauge were used to measure vertical deflections at critical locations, particularly at the midspan of Span 2 as shown in Figure 6 and 7. The LVDTs had a measurement range of ±50 mm with an accuracy of ±0.01 mm. Dynamic response measurements were obtained using uniaxial accelerometers installed at selected locations along the bridge deck. The acceleration response was measured using accelerometers with a sensitivity of approximately 400 mV/g and an effective frequency range of up to 200 Hz, making them suitable for capturing the dominant vibration modes of railway bridge structures. All sensors were connected to a centralized data acquisition system with a sampling frequency of 200 Hz, ensuring sufficient resolution for both static and dynamic response measurements in accordance with the Nyquist criterion. Signal conditioning modules were employed to filter noise and stabilize the recorded signals, thereby enhancing data quality and reliability for subsequent frequency-domain analysis.

The measurement chain consisted of sensor installation, signal transmission, data acquisition, and postprocessing. Sensors were carefully calibrated prior to installation, and their placement was selected to capture both global structural response and localized behaviour. The recorded data were processed using standard signal analysis techniques, including filtering and frequency domain analysis, to extract relevant structural parameters such as deflection and natural frequencies. This instrumentation setup ensures sufficient accuracy and reliability of the measurements, allowing for a robust evaluation of the structural performance under operational loading conditions. The adopted instrumentation and measurement procedure is consistent with commonly accepted practices in full-scale bridge load testing, ensuring the reliability and reproducibility of the results.

Figure 6:

(a) Installation of the LVDT sensor on the bridge superstructure; (b) Installation of the strain gauge sensor on the bridge superstructure

Figure 7:

Installation of accelerometer sensors on the bridge structure

Sensors were installed at 1/4L, 1/2L, and 3/4L of Span 2 to capture representative global and local behaviour. This configuration ensured reliable evaluation of serviceability, stiffness, and dynamic characteristics.

A three-dimensional finite element model of the BH 25 railway bridge was developed in SAP2000 to simulate its response under static and dynamic loading. The model accurately represents the bridge geometry and structural system, with main truss members idealized as frame elements capturing axial, flexural, and shear behaviour, and the deck and secondary components modelled using equivalent beam elements. All connections were assumed rigid, and boundary conditions were defined to reflect the actual support system. Material properties were assigned based on standard steel parameters, including elastic modulus and mass density. The modelling framework, including geometry, boundary conditions, and mesh discretization, is presented in Figure 8 and 9.

Figure 8:

Three-dimensional model of bridge structure

Figure 9:

Top view of the bridge structure model

Model calibration was conducted through an iterative adjustment of the effective elastic modulus of steel members and boundary stiffness parameters to achieve agreement between measured and analytical structural responses. Two quantitative indicators were selected as calibration targets: (i) midspan deflection under static loading and (ii) dominant vertical natural frequency obtained from dynamic testing. The relative difference between numerical prediction and field measurement was evaluated as: (1) Difference(%)=|FEM−Field||Field|×100 Difference\left( \% \right) = {{\left| {FEM - Field} \right|} \over {\left| {Field} \right|}} \times 100

Convergence was considered satisfactory when the frequency deviation was below 5% and the deflection deviation remained within acceptable engineering tolerance for conservative capacity evaluation.

According to the Regulation of the Minister of Transportation of the Republic of Indonesia No. 69 of 2018, the allowable vertical deflection for railway bridges under service loading is typically limited to L/1000, where L denotes the span length. This limit is widely used as a serviceability criterion to ensure structural performance and operational safety under railway loading conditions.

The maximum measured mid-span deflection at Span 2 under static load was −11.30 mm, which is significantly lower than the allowable limit of L/1000 (21.93 mm). The measured deflection results and the corresponding allowable limits for the tested load cases are presented in Figure 10. A summary of the deflections at 1/4L, 1/2L, and 3/4L is shown in Figure 11.

Figure 10:

Deflection at midspan (1/2L) of Span 2 under service load: ‒21.88 mm

Figure 11:

Deflection of the bridge structure under locomotive static loading

It should be noted that two deflection values are discussed in this study. The value of −11.30 mm represents the maximum midspan deflection recorded during full-scale field testing under operational loading. Meanwhile, the value of −21.88 mm corresponds to the analytical prediction obtained from the finite element model under the governing load combination prior to strengthening. The difference between these values reflects the distinction between measured field response and model-based structural analysis.

The analytical prediction provides a conservative estimate relative to field measurements, supporting the reliability and safety-oriented applicability of the numerical model for subsequent structural capacity evaluation.

Although the calibrated model reproduced the dominant natural frequency within 2.25%, the predicted static midspan deflection remained larger than the field-measured value, resulting in a relative difference of approximately 48.4%. This deviation reflects a deliberate conservative modelling strategy adopted for capacity-oriented assessment. Rather than enforcing exact deflection matching, calibration prioritized accurate representation of global stiffness through dynamic response agreement, while maintaining conservative displacement predictions to avoid overestimation of structural capacity. Such an approach is considered acceptable in safety-critical infrastructure evaluation, where conservative demand estimation provides a defensible basis for strengthening decisions.

Elongation (ΔL) of the span-2 bridge girder was monitored using strain gauges installed at 1/4L, 1/2L, and 3/4L under static locomotive loading, where positive and negative values denote tension and compression, respectively. The bottom chord exhibited tensile elongation, while the top chord showed compressive elongation; strain was evaluated using ε = ΔL/L with a gauge length of 160 mm and subsequently converted to stress. The maximum tensile and compressive stresses were 111 MPa and – 124 MPa, respectively, both significantly lower than the steel yield strength (fy = 349 MPa), indicating adequate structural performance under the applied load.

Figure 12:

Measured elongation (ΔL) distribution of the Span-2 bridge girder under static locomotive loading

Figure 13:

Stress distribution of the Span-2 bridge girder derived from strain gauge measurements

The close agreement between different measurement techniques confirms the reliability of the recorded data and indicates elastic structural behaviour under service loading conditions.

Frequency-domain analysis was conducted using the Fast Fourier Transform (FFT) to transform time-domain signals into the frequency domain, from which the fundamental frequency was identified as the dominant peak corresponding to the global vibration mode, to ensure reliability, multiple measurements were analysed for consistency, and the resulting dominant vertical natural frequency of 14.65 Hz slightly lower than that predicted by the calibrated finite element model was subsequently compared with analytical results for validation, as illustrated in Figure 14 and 15.

Figure 14:

Dominant vertical (z-Direction) frequency of the bridge girders: (a) Time-domain response; (b) Frequency-domain response

Figure 15:

Dominant vertical mode (Mode 15) of the bridge structure with a frequency of 14.98 Hz

The increase in dominant natural frequency after strengthening reflects a measurable enhancement in global structural stiffness, consistent with the theoretical relationship between stiffness and natural frequency (f = √k/m). This confirms that the strengthening intervention not only improved member-level capacity but also restored system-level structural rigidity.

Although the bridge meets the serviceability requirements under static loads, the structural capacity evaluation indicates that strength-related deficiencies still exist in some critical elements of Span 2, indicating that acceptable deflection performance does not necessarily imply adequate structural safety. The calculated internal forces of the critical elements under the principal load cases provide quantitative evidence of this condition, as reflected by the demand-to-capacity ratios exceeding unity observed in some truss elements under the principal load combinations (Table 6). The overall distribution of member capacity ratios prior to strengthening further illustrates the extent of strength deficiency within the truss system (Figure 16).

Figure 16:

Capacity ratios of the bridge structure elements

It is important to note that serviceability compliance prior to strengthening did not guarantee adequate structural safety, as several members exhibited demand-to-capacity ratios exceeding unity. This finding underscores a fundamental limitation of deflection-based assessment approaches when applied to aging truss systems, where localized overstress may remain undetected despite acceptable global displacement behaviour. The integrated workflow adopted in this study demonstrates that stiffness indicators alone are insufficient without concurrent capacity verification, particularly for bridges subjected to long-term deterioration and cumulative fatigue effects.

To address the identified strength deficiencies, an external prestressing system was implemented in combination with local steel plate reinforcement. The adopted strengthening configuration, tendon profile, and anchorage system are illustrated in Figure 18 and 19. The introduction of prestressing forces modified the internal force distribution within the truss members, resulting in a systematic reduction in member utilization levels and an overall improvement in structural capacity.

Figure 17:

Side view of the external prestressing reinforcement model of the bridge structure

Figure 18:

Midspan (1/2L) deflection of the bridge structure after external prestressing under the load combination 1.0D + 1.0SD + 1.0PR

Figure 19:

Midspan (1/2L) deflection of the bridge structure after external prestressing under the load combination 1.0D + 1.0SD + 1.0LL + 1.0PR

The effectiveness of the strengthening intervention is evidenced by the post-strengthening capacity evaluation, which demonstrates a consistent decrease in demand-to-capacity ratios across critical members (Table 9). In addition to strength enhancement, the strengthening scheme also led to an improvement in global stiffness, as indicated by the increase in the dominant natural frequency to 17.07 Hz (Figure 20). Local plate reinforcement further contributed to reducing all member capacity ratios to acceptable limits, as confirmed by the final capacity assessment results (Table 9 and Figure 21).

Figure 20:

Dominant vertical (z-Direction) vibration mode (Mode 45) of the bridge structure after external prestressing and plate reinforcement, with a frequency of 17.07 Hz

Figure 21:

Capacity ratios of bridge elements after external prestressing and plate reinforcement

These results confirm that externally prestressed strengthening, when properly integrated with localized reinforcement, constitutes an effective and rational strategy for restoring both stiffness and load-carrying capacity in aging steel railway bridges. Unlike previous studies that predominantly report analytical or laboratory-scale validations, the present study provides rare full-scale field evidence from an operational bridge. The observed increase in dominant natural frequency from 14.65 Hz to 17.07 Hz corresponding to a 16.5% increase demonstrates measurable global stiffness recovery. This level of enhancement indicates substantial stiffness improvement and aligns with stiffness recovery trends reported in recent strengthening and railway bridge assessment studies.

From a theoretical perspective, the results highlight the importance of combining static and dynamic indicators to capture stiffness degradation mechanisms that cannot be identified through serviceability-based evaluation alone. The integration of field measurements with calibrated numerical modelling improves the reliability of structural diagnosis for aging steel railway bridges.

From a practical engineering perspective, the findings demonstrate that external prestressing, when properly integrated with local reinforcement, provides an effective and minimally invasive strengthening strategy for extending the service life of existing railway bridges under operational loading conditions.

While the proposed framework is demonstrated on a single steel truss railway bridge, the methodology is applicable to other existing railway bridges with similar structural typologies and loading characteristics. Nevertheless, the effectiveness of external prestressing may vary depending on bridge configuration, boundary conditions, and deterioration mechanisms. Therefore, future applications should be supported by bridge-specific assessment and model calibration.