Introduction

Chinese traditional timber lounge bridges embody the craftsmanship of traditional Chinese timber architecture, with their structural forms reflecting the essence of refined traditional culture and profound historical heritage. These bridges have become an important bond sustaining cultural identity and collective memory. In recent years, fire-induced damage to traditional timber lounge bridges has become increasingly frequent and sudden, owing to the deterioration of their structural performance, coupled with frequent extreme events and intensified human activities. Therefore, investigation of the fire risk of traditional timber lounge bridges under realistic fire scenarios is essential for their effective protection.

Research has been conducted on the fire performance of traditional timber lounge bridges. Kodur and Naser [1] investigated the importance factor in bridge design against fire hazards and reported that geometrical characteristics and material properties are key considerations. The distinctive configuration and exposed timber members of lounge bridges increase their susceptibility to fire. Cui and Chun [2] conducted fire dynamics analysis on a typical timber lounge bridge with cantilever beams and found that when the fire exposure time reached 1084 s, the fire risk index increased rapidly, with a peak value approximately 1.7 times that at the flashover point (847 s). Cui et al. [3] further investigated the influence of weatherboard height on the fire dynamic characteristics of a traditional timber lounge bridge and reported that, with increasing weatherboard coverage, most fire-related parameters deteriorated and fire risk increased. Therefore, a fully enclosed configuration was highly detrimental to fire resistance. However, the above studies primarily focused on re dynamics and did not consider the effects of fire spread on timber member damage, including charring and the degradation of mechanical properties at elevated temperatures. The fire-induced deterioration of timber members under realistic fire conditions is critical for evaluating the fire safety of such bridges.

Charring behavior and fire damage of traditional timber members under the ISO 834 standard fire condition [4] have also been investigated. Xu et al. [5] studied the combustion and charring characteristics of five common structural timber species using cone calorimeter tests and reported that the charring rate increased rapidly during the initial stage of fire exposure. Song et al. [6] reported that the fire resistance of traditional timber mortise–tenon joints was less than one hour, and that fire damage, including charring of beams and columns and degradation of mechanical properties, was highly detrimental to the integrity of frame structures. Zhang et al. [7] investigated the fire resistance of a historic timber building under multiple fire scenarios and reported that the fire resistance of the entire timber frame ranged from 460 to 519 s, highlighting the necessity of implementing fire protection measures for traditional timber frames. Xu et al. [8] reported that after 60 min of fire exposure, the compressive capacity of unprotected round timber columns decreased by up to 80.2%. Xu et al. [9] reported that after 40 min of fire exposure, the bending capacity of unprotected timber beams decreased by up to 62.0%. These findings demonstrate that fire-induced damage to timber columns and beam-column frames is severe and can significantly increase the risk of collapse in traditional timber bridges. Therefore, evaluation of the fire safety of traditional timber bridges under realistic fire conditions is of paramount importance.

To enhance understanding of the fire hazard and fire resistance of traditional timber lounge bridges under realistic fire conditions, Dengyun Bridge—a representative traditional timber lounge bridge—was selected as a case study for fire dynamics analysis and structural–thermal coupling analysis. Fire dynamics analysis was first conducted to obtain temperature–time curves and to investigate the evolution of fire spread. Subsequently, structural–thermal coupling analysis was performed to determine the charring depth of the primary timber members. Finally, structural safety was evaluated using the effective cross-sectional method, taking into account the calculated charring depths. This research provides guidance for the fire protection of traditional timber lounge bridges.

Introduction to the Dengyun bridge

Dengyun Bridge, a traditional Chinese timber lounge bridge located in Zhejiang Province, China, was selected for fire dynamics analysis due to its distinctive structural configuration based on cantilevered timber beams as shown in Fig. 1. The bridge comprises two spans with a total length of 20 m. Stone masonry was used to construct the central pier and side abutments. Logs of varying lengths were arranged orthogonally on the central pier to form cantilever beams. Traditional Chinese timber frames with mortise-and-tenon joints, enclosed by timber walls, were installed on the upper surface of the cantilever beams, as illustrated in Fig. 1a.

Fig. 1
Fig. 1Fig. 1
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Detailed geometry of Dengyun Bridge (units: mm)

The detailed geometry of Dengyun Bridge is illustrated in Fig. 1b. The timber frame comprises columns, beams, rafters, purlins, and timber boards as shown in Fig. 1c. The total height of the timber frame is 5.1 m. The frame consists of a central bay measuring 3370 mm in length and two side bays, each 970 mm long. All columns have a diameter of 180 mm. The beams in the central bay have a cross section of 110 mm × 320 mm, while those in the side bays have cross sections of 110 mm × 140 mm and 110 mm × 180 mm. Most purlins have a diameter of 140 mm. The timber boards have a thickness of 50 mm. The diameters of the cantilever timber beams gradually increase from 150 mm at the soffit to 300 mm at the top. A fully covered weatherboard configuration was adopted in accordance with the recommendation of Cui et al. [3].

Fire dynamics analysis

Model development

A fire dynamics analysis model of Dengyun Bridge was developed using fire dynamics simulator (FDS), as shown in Fig. 2. The density of the timber members was taken as 424.17 kg/m3, based on recommendations from similar research on FDS simulation of Dengyun Bridge conducted by Cui and Chun [2]. And such value was very close to the density of commonly used timber in China.

Fig. 2
Fig. 2
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Fire dynamics analysis model of the Dengyun Bridge

Mesh sensitivity analysis indicated that the appropriate mesh size should range from 1/4 to 1/16 of the characteristic flame diameter, D*, which can be expressed as follows [10]:

$$D^{*} = \left( {\frac{Q}{{\rho_{0} c_{{\text{p}}} T_{0} \sqrt g }}} \right)^{0.4}$$
(1)

where Q denotes the heat release rate of the fire source, ρ0 denotes the density of ambient air, cp is the specific heat capacity of ambient air, T0 denotes the initial ambient temperature, and g is the acceleration due to gravity. Table 1 summarizes the key parameters of the fire source. To ensure computational efficiency while maintaining accuracy, a refined mesh size of 0.2 m was adopted in the vicinity of the fire source, whereas a mesh size of 0.4 m was used in the remaining regions.

Table 1 Key parameters of the fire source [10]
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Details of the fire source are shown in Fig. 3. Due to the presence of candle boxes placed at the mid-span of the bridge, the fire was most likely to initiate at this location. Therefore, a scenario involving a candle box igniting at the center of the span was adopted for simulation. Considering a real simulation of the candle box geometry, an ignition source with a side length of 0.6 m was positioned at the mid-span of Dengyun Bridge, at a height of 1.7 m above the bridge floor, as illustrated in Fig. 3a.

Fig. 3
Fig. 3
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Details of the fire source

The upper surface of the ignition source was defined as a custom burner surface (i.e., the burning surface with brown symbol, a square with a side length of 0.6 m, as shown in Fig. 3b), while the remaining surfaces were assigned the default inert surface (i.e., non-burning surfaces with yellow symbol, as shown in Fig. 3b). Power law design fire curve was determined according to ISO/TS 16733-2: 2026 [10]. For design purposes, an exponential or power law rate of energy release is generally used. The most commonly used relationship of heat release rate and time is “t2 fire”. In such conditions, the heat release rate can be expressed as:

$$\dot{Q}\left( t \right) = \alpha t^{2}$$
(2)

where α is the fire growth coefficient, t is the time, and \(\dot{Q}\) is the heat release rate. The fire growth coefficient for an ultra-fast fire was taken as 0.1778, and the heat release rate per unit area of the burner surface was specified as 1000 kW/m2 according to ISO/TS 16733-2: 2026 [10]. The total heat release of all the combustibles was determined to be 1065 MJ, considering the total quantity of combustibles provided (paraffin, timber, incense, etc.). After reaching its peak value, the heat release rate was assumed to remain constant until all combustibles were completely consumed.

A pyrolysis model was adopted in the FDS fire model to consider the combustion of timber. Parameters of the pyrolysis model were determined following the suggestion of a similar study on fire hazard analysis of a traditional timber structure presented by Zhang et al. [11]. The reference temperature of timber was 150 ℃, the heat release from timber combustion was 20,000 kJ/kg, and the reaction heat was 5000 kJ/kg.

The exterior of Dengyun Bridge was modeled as an open atmospheric environment with an initial ambient temperature of 20 ℃ and an air pressure of one standard atmosphere. Owing to the symmetry of the temperature distribution within the model, thermocouples were arranged on one side of the bridge only as shown in Fig. 4 and Table 2. To effectively capture the temperature evolution in the vicinity of the fire source, 14 thermocouples were installed within a radius of 3 m from the fire source as illustrated in Fig. 4b. In the remaining compartments, two thermocouples at different heights were positioned to monitor the temperature development.

Fig. 4
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Temperature measurement scheme of Dengyun Bridge

Table 2 Labels and location of the thermocouples near the fire source
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The FDS simulation time was set to 2 h, which was sufficient to allow the flames to spread throughout the entire bridge. Considering the relatively low probability of strong wind occurring simultaneously with a fire, the effect of wind speed was not taken into account.

Results and discussion

The temperature–time curves near the fire source (see Fig. 4b and Table 2) are presented in Fig. 5. The results indicate that the temperatures directly above the fire source increased rapidly during the initial stage, and the rate of increase was higher than that of the commonly used ISO 834 temperature–time curve [2]. After the combustibles were completely consumed (15 min after ignition), these temperatures decreased rapidly to approximately 300 ℃.

Fig. 5
Fig. 5
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Temperature–time curves near the fire source

In the x direction, temperatures measured at a height of 0.4 m above the fire source exhibited a similar development trend, as no significant timber components were present at this level. When the vertical distance increased to 1.4 m, the measurement points were closer to the timber roof members. Consequently, these temperatures were higher than those recorded at 0.4 m above the fire source.

In the y direction, temperatures at a height of 0.4 m above the fire source also showed a similar development trend. However, when the height increased to 1.4 m, the temperatures varied significantly depending on the horizontal distance from the fire source. Measurement points located farther from the fire source were closer to the burning sloping roof; therefore, the temperatures at these locations increased more rapidly and reached a higher peak value.

The evolution of fire spread is illustrated in Fig. 6. Five minutes after ignition, smoke had spread throughout the entire bridge structure. After 10 min, flames propagated from the center toward both ends of the bridge along the upper timber roof. By 20 min after ignition, the whole bridge structure had entered a state of full combustion. After 60 min, most of the flames had extinguished, as the timber components had been largely consumed by the fire.

Fig. 6
Fig. 6
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Evolution of fire spread

Charring depth of timber members

The zero strength layer method was used to consider the fire damage on the whole structure. The zero strength layer of each timber member was estimated as a sum of the charring depth and additional 7 mm to account for the reduction in elastic modulus and strength of timber below 288 ℃ according to EN 1995-1-2 [12]. The temperature–time curves obtained for each compartment from the fire dynamics analysis were used to determine the temperature distribution within each timber component. The locations of the thermocouples in each compartment are shown in Fig. 4a and Table 3. The charring depth of the timber components was evaluated based on the simulated temperature distributions. A 288 ℃ isothermal line was adopted to define the charring depth, in accordance with EN 1995-1-2 [12]. Finite element method (FEM)-based models for temperature analysis were developed using the commercially available FEM software ABAQUS [13] as illustrated in Fig. 7. Thermal parameters of timber presented by EN 1995-1-2 [12] were adopted in the simulation. The thermal properties of timber are summarized in Table 4.

Table 3 Labels and locations of the thermocouples in each compartment
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Fig. 7
Fig. 7
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FEM model for thermal analysis

Table 4 Thermal properties of timber
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The relationships between charring depth and fire exposure time for the thermocouple locations are presented in Fig. 8. The original results obtained from the thermal analysis were adjusted by adding an initial allowance of 7 mm to determine the zero strength layer (Fig. 8b), in accordance with EN 1995-1-2 [12]. For certain thermocouple locations, negligible charring was observed and therefore is not shown in Fig. 8. As illustrated in Fig. 8c, the charring depth above the fire source was significantly greater than that below it. This can be attributed to the rapid fire spread along the timber roof as shown in Fig. 6.

Fig. 8
Fig. 8
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Charring depth and zero strength layer-fire exposure time curves for the thermocouple locations

Structural safety evaluation

Model development

A finite element model for structural analysis was developed using the commercially available FEM software ABAQUS [13], as shown in Fig. 9. Beam elements with timber longitudinal mechanical performance were employed to simulate the mechanical behavior of the timber members. The density and elastic modulus of the timber were taken as 416 kg/m3 and 9600 MPa, respectively, in accordance with a previous study on Dengyun Bridge [2]. Pinned boundary conditions were assigned at both ends of Dengyun Bridge. The remaining connections were assumed to be rigid, considering the integrity of the timber joints. A uniformly distributed live load of 2 kN/m2 (design load) was applied to the bridge. Roof members can increase the gravity of the bridge. Therefore, these members were considered for structural analysis. A fixed boundary between the deck and the beams was assumed.

Fig. 9
Fig. 9
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FEM model for structural analysis

The FEM analysis procedure was as follows: (1) the fire exposure time was determined; (2) charring depth and zero strength layer of each member were calculated according to Fig. 8b; (3) the residual effective cross section of each member was determined; (4) the FEM model with the residual effective cross section was developed and analyzed.

Results and discussion

The deflections of Dengyun Bridge at different fire exposure times are presented in Fig. 10. The maximum deflection under ambient conditions (without fire, the bridge in normal condition) was 27.40 mm (D/L = 1/364), which was very close to the measured value. This indicates that the developed FEM model can reasonably represent the mechanical behavior of Dengyun Bridge under dead and live loads. Large vertical deformation occurred at the bottom of the bridge due to the application of both live and dead loads, as shown in Fig. 10a. After 10 min of fire exposure, the maximum deflection increased rapidly. When the fire exposure time reached 20 min, the maximum deflection reached 39.69 mm (D/L = 1/250), which was very close to the limit specified in the current design code [14]. At this stage, Dengyun Bridge was considered to have reached failure under fire conditions. Therefore, it is essential to implement effective fire detection and protection measures for Dengyun Bridge given the short failure time under realistic fire scenarios. With further increase in fire exposure time, the maximum deflection did not increase significantly as the combustibles had already been completely consumed. In addition, the nearby cantilever beams did not deform due to the strong constraints provided by the bottom stone pier at the middle of the bridge.

Fig. 10
Fig. 10Fig. 10
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Deflections of the Dengyun Bridge at different fire exposure times

Conclusions

A numerical simulation of fire hazard analysis and fire resistance evaluation for a traditional timber lounge bridge was conducted based on fire dynamics analysis and structural–thermal coupling analysis. The following conclusions can be drawn:

  1. 1)

    The temperatures directly above the fire source increased rapidly during the initial stage, and the rate of increase was higher than that of the commonly used ISO 834 temperature–time curve. After the combustibles were completely consumed (15 min after ignition), these temperatures decreased rapidly to approximately 300 ℃.

  2. 2)

    Five minutes after ignition, smoke had spread throughout the entire bridge structure. After 10 min, flames propagated from the center toward both ends of the bridge along the upper timber roof. By 20 min after ignition, the whole bridge structure had entered a state of full combustion. After 60 min, most of the flames had been extinguished.

  3. 3)

    Thermal analysis indicated that the charring depth above the fire source was significantly greater than that below it.

  4. 4)

    When the fire exposure time reached 20 min, the maximum deflection reached 39.69 mm (D/L = 1/250), which was very close to the limit specified in the current design code. Therefore, it is essential to implement effective fire detection and protection measures for Dengyun Bridge given the short failure time under realistic fire conditions.