Abstract
Fine calculation of bridge temperature fields is significant for accurately evaluating thermal actions in bridge structures. Determining thermal loads on bridge surfaces caused by solar radiation is the most challenging part of the numerical thermal analysis because the sunlit and shaded areas on bridge surfaces change continuously with the sun’s rotation. Existing methods have low accuracy in determining thermal loads and cannot be applied to complex bridges. This study presents a new method for calculating temperature fields based on the advantages of building information modeling (BIM) technology in solar radiation analysis (SRA) and information sharing. This method starts with obtaining an accurate hourly insolation distribution on bridge surfaces through SRA implemented in a BIM system. Then, a Python script seamlessly maps the insolation information to finite element surfaces as thermal loads. This paper details the new method’s implementation steps and technical details, and a practical application on a concrete box girder demonstrates its applicability and effectiveness. Compared with previous methods, the proposed method has significant advantages, such as a more accurate calculation for solar radiation, a lower technical threshold, a higher degree of automation, less computational time, and easier finite element modeling.
1. Introduction
As an essential component of outdoor traffic lines, bridges are inevitably affected by the surrounding environment during their whole service lifecycle. Among the various environmental actions, the structural nonuniform temperature distribution caused by solar radiation, also known as the temperature gradient, forms one of the important considerations for concrete box girder bridges. Some studies showed that the nonuniform temperature-induced stress could reach or even exceed the stress caused by vehicular live load [1].
The evaluation of accurate values for thermal actions is vital for structural engineers during bridges’ design and construction phases [2]. The possible thermal effects during a bridge service lifecycle should be roundly considered in the design process because they have often been associated with concrete bridge damage [3]. The cumulative effects of temperature gradients and other long-term loads may well exceed the tensile strength of concrete and cause cracking [4]. In some cases, thermal effects should be taken as the leading variable action in characteristic combinations for serviceability limit states [5]. During the construction period, because solar radiation strongly influences the bare concrete box girders without deck pavement, the structural temperature gradient effects are more serious than when a bridge is in service [6]. The structural deformations caused by daily thermal actions are essential for the bridge survey, the design of the falsework, and the determination of the formwork elevation.
Although engineers and scholars have generally accepted the importance of nonuniform temperature fields, there is still a lack of model that can accurately and comprehensively describe the structural temperature gradient due to its highly complex influence factors. For example, the current AASTO design specification [7] only provides engineers with a representative profile of the nonlinear vertical temperature gradient to predict the vertical thermal behavior of a bridge. This simplification leads to the long-term neglect of the structural lateral behavior and may endanger structural safety. An experimental study on I-shaped girders showed that the current specification is inaccurate in predicting the shape and magnitude of temperature gradients [8]. Another long-term monitoring experiment on a box-girder bridge indicated that the tensile stress caused by transverse temperature gradients is so significant that it cannot be ignored in structural design [9]. Therefore, it is necessary to carry out a refined temperature field analysis for some unique bridges.
However, the calculation of nonuniform temperature fields is very complicated. It is generally believed that temperature fields are related to many factors, such as climatic conditions, geographic location, bridge orientation, and geometric and material properties [2, 10]. Using finite element (FE) thermal analysis to solve temperature fields is a commonly used and proven method. The most complex and challenging part of the thermal analysis lies in applying the real solar radiation intensity to the FE model because the structure consists of many elements, and their sunlit and shaded faces change continuously with the sun’s rotation [11]. Although there have been many publications about bridge temperature fields in recent decades, few of them are innovative in methods for temperature field simulation. The existing methods, which will be detailed in Section 2, still have some shortcomings regarding calculation time, calculation accuracy, and applicability to complex bridges. Benefiting from the promotion and application of building information modeling (BIM) technology in the architecture, engineering, and construction (AEC) industry in the past decade, the authors drew inspiration from the solar analysis of BIM (Figure 1) and developed an innovative method for finely calculating bridge temperature fields. This method starts with obtaining an accurate hourly insolation distribution on bridge surfaces through solar radiation analysis (SRA) implemented in a BIM system. The insolation results are then mapped to a finite element analysis (FEA) system and applied to bridge surfaces as heat flux. Although this paper describes concrete box girders, this method can be applied to any type of bridge structure, especially those with complex shading relationships that existing techniques cannot solve.
The remainder of this paper is organized as follows: Section 2 reviews several existing methods for temperature field calculation and compares their merits and demerits; Section 3 proposes a novel method for the fine calculation of temperature fields and introduces its implementation path and critical components in detail; Section 4 demonstrates a specific application of the proposed method with a real example; finally, Section 5 summarizes the advantages of the method and discusses several future application fields.
2. State-of-the-Art
Accurate calculation of the temperature fields of a bridge requires three primary conditions: actual weather data, dynamic thermal loads, and appropriate thermal boundary models. Thermal loads on bridge surfaces are mainly caused by solar radiation. Moreover, its calculation is the most challenging work of the three for the following reasons: (1) surfaces with different inclination angles and orientations receive different solar radiation intensities, which vary in a day with the change of solar altitude; (2) the shading between structural surfaces under direct sunlight is a factor that must be considered. In the existing literature, there are three methods for calculating thermal loads.
2.1. Trigonometric Formula Method
The rotation and revolution of the earth follow specific laws. As seen from the earth, the sun’s position changes periodically every year, so the relative position between the sun and a given point on the earth at any moment can be calculated using geometric approaches. The position of a point on the earth is usually expressed by longitude and latitude, while the sun’s position is usually characterized by its altitude and azimuth angles. There is a set of mature formulas to calculate the sun’s position [12, 13].
The shaded area on the webs of a bridge at any time can be determined with the help of trigonometric functions (see more details in [14, 15]), which consider parameters such as web inclination and overhang length (Figure 2). Thermal loads on exterior surfaces of the bridge can be determined by calculating the solar radiation intensities for the sunlit and shaded areas, respectively. By repeating this calculation in increments of 1 hour, the dynamic thermal loads in a day can be ultimately determined. In addition to the shadow recognition on the webs of a box girder, Zhang et al. [15] developed a formula to calculate the shadow width on the bottom flange of an I-shaped steel beam for steel-concrete composite girders.
2.2. Hemicube Method
In some FE systems, the sunlit and shaded elements can be determined using a so-called hemicube method, which is initially used to calculate angle coefficients (or view factors) between surfaces, namely a radiation energy percentage emitted from one surface to another. Abid et al. [16, 17] applied this method offered by COMSOL to estimate the surface-to-surface radiation of a box girder. When the hemicube method is used for solar radiation modeling, in addition to structural elements, an additional radiation element is required to be established to calculate the angle coefficients between it and structural elements. If the angle coefficient does not equal zero, the radiation element can “see” the structural element, so this element is defined as the sunlit element. Otherwise, the structural element that the radiation element cannot “see” is the shaded element [11]. Xu [18] established a virtual sun element on the ANSYS platform to determine the bridge FE model’s sunlit and shaded elements using the built-in radiation matrix generator AUX12 to calculate the angle coefficients, where the position of the virtual sun was determined by a new radiation calendar timing system. By this approach, the solar radiation intensity on the surfaces of all elements at any given time could be calculated. Gao et al. [11] applied the same approach to the calculation of temperature action on a supertall structure (Figure 3). The calculated temperature distribution and temperature-induced stress of the structure agreed with the field monitoring data.
2.3. Ray Tracing Algorithm
The sunlit or shaded effect is often achieved in computer graphics using the ray tracing algorithm [19]. Rays are first created by taking points on the surfaces of a bridge as stars and pointing to the sun. Then, the sunlit or shaded state of a point on the bridge is determined by checking whether the corresponding ray intersects the wireframe of the bridge: if it does, this point is shaded; if it does not, this point is sunlit [13]. The ray tracing algorithm requires that each ray must be checked against each object in the scene. For a complex long-span bridge structure, the number of surfaces and elements in the three-dimensional (3D) FE model is so large that the intersection calculations may consume many computing resources and time. To reduce the blindness of intersection calculations and improve computational efficiency, an accelerated algorithm called space subdivision technology is usually used in combination with the ray tracing algorithm [19].
The ray tracing algorithm can be implemented by secondary development based on a FE platform, such as subroutine programming in Abaqus and APDL programming in ANSYS. Zhu and Meng [20] developed a 3D sunlight-sheltering algorithm based on ray tracing technology to predict the temperature field of a cable-stayed bridge precisely. Gu et al. [21] proposed a quick identification method for the shadow based on ray tracing technology and space subdivision technology in calculating the 3D sunshine temperature field of a long-span bridge structure. Sheng et al. [13] studied the time-varying temperature field of a small radius curved concrete box girder bridge using the ray tracing algorithm to determine the shadow surface.
2.4. Comments on Existing Methods
Among the abovementioned three methods, the trigonometric formula method is the simplest, but it is not suitable for complex shading relationships, so its application conditions are limited. Regarding the hemicube method, the virtual sun element size and virtual sun-structure distance significantly affect the number of the determined irradiation elements [11], which may affect the calculation accuracy. Specifically, when the size of the virtual sun element is considerably large, the virtual sun-structure radiation pairs cannot fulfill the requirements of parallel light, thereby resulting in an inaccurate determination of the irradiation elements. Oppositely, when the size of the virtual sun element is considerably small, the angle coefficients between the virtual sun and the structural elements are nearly equal to zero, which results in a relatively small number of irradiation elements. The ray-tracing algorithm has good applicability and calculation accuracy in shadow recognition, yet it consumes a lot of computing time, and the finer the mesh, the longer the calculation time. Regarding the calculation of solar radiation intensity, the abovementioned three methods can only accurately consider the direct component of solar radiation, but not the diffuse component for its anisotropic nature [22].
Furthermore, both the hemicube method and the ray-tracing algorithm require 3D FE modeling to identify shaded elements on surfaces, which means that all problems related to temperature fields must be solved in 3D space. However, 3D temperature fields, in many cases, are not necessary at all. For example, when a 2D beam element is used in FE modeling to calculate thermal effects, a 2D temperature gradient profile is more valuable than the 3D temperature distribution.
3. Methodology
3.1. Background
The rise of BIM technology is regarded as an information revolution in the AEC industry. BIM is described as a modeling technology and associated set of processes to produce, communicate, and analyze building models [23]. The most significant value of a BIM model is that its integrated information can be shared and communicated by stakeholders throughout the project lifecycle. BIM has the feature of 3D visualization, which makes it advantageous in energy analysis and sunlight simulation because those analyses need 3D external shells for solar radiation. Several examples showed the applications of BIM in these respects. Aranda et al. [24] defined a method for using BIM lighting simulation in the design process of new roads to analyze the possibility of icing on mountain roads due to lack of sunlight. Salimzadeh et al. [25] developed a parametric modeling platform for the design of surface-specific photovoltaic module layouts on the entire skin of buildings using BIM solar analysis tools. Similarly, the temperature distribution of a bridge is also closely related to solar radiation, and the advantages of BIM in these respects show its great potential in the solution of temperature fields.
3.2. Implementation Framework
This study aims to develop a new method of “BIM + FEA” for the fine calculation of bridge temperature fields. The implementation framework of this method is shown in Figure 4. Revit and Abaqus are used as the BIM and FEA platforms, respectively. First, the bridge BIM model is created in Revit. Then, SRA is performed in Dynamo, a graphical programming plugin for Revit. In this step, a specialized solar analysis tool reads real weather data and model information, such as geometry, location, and orientation, to generate the 3D hourly insolation distributions (or called insolation fields) on bridge surfaces. If a 3D temperature field is to be calculated, the 3D insolation fields and weather data are integrated and exported as a data file for the subsequent FE thermal analysis; if a 2D temperature field is to be calculated, the cross-sectional information and its corresponding insolation values are first extracted and then exported together with the weather data. The final step is to establish the FE model in Abaqus using the data derived from the previous step and to perform heat transfer analysis to generate the 2D or 3D temperature field. In this step, the 2D geometrical information derives from the data file, and the 3D geometrical information is transferred from BIM geometry.
3.3. BIM Model Creation
Strictly speaking, the creation of BIM models needs to meet specific standards, namely the BIM level of development (LOD) specification, which is a reference that enables practitioners in the AEC industry to specify and articulate with a high level of clarity, the content, and reliability of building information models at various stages in the design and construction process [26]. For example, LOD 200 of a highway bridge precast concrete I-shaped girder includes the type of structural concrete system and the approximate geometry (e.g., depth) of structural elements, while LOD 300 includes specific sizes, locations, and orientations of main concrete structural members [26]. Real geometric information is undoubtedly required for the fine calculation of temperature fields. Other nongeometric information, such as location and orientation, must be veritably defined because they, together with geometry, are the primary data for SRA. As for elevation information, although solar radiation is not correlated to building height [11], the air temperature and wind speed at the bridge need to be corrected along the height in some cases, such as high-rise structures and bridge towers, according to the elevation difference between the structure and the weather station. Therefore, when the influence of this elevation difference cannot be negligible, the elevation information needs to be defined in BIM. The above discussion shows that the BIM model for bridge temperature field analysis is recommended to meet the requirements of LOD 300.
BIM modeling is not a burden for the calculation of temperature fields due to its significant advantages in parametric modeling, let alone the geometry created in BIM will be shared with FEA (Figure 4). In practical applications, differentiated modeling can be adopted to reduce the workload according to specific analysis objects. Specifically, those objects to be accurately simulated in FEA need to meet the requirements of LOD 300, whereas other objects with shading effects on simulated objects only need real 3D external shells. This is one of the advantages of the proposed method. It means those elements that are irrelevant to temperature field analysis but affect insolation only need to be established in BIM rather than in FE systems. Imagine a situation where the temperature field of an urban bridge surrounded by high-rise buildings needs to be finely analyzed. Establishing the surrounding building models in FE systems for determining the sunlit and shaded surfaces of the bridge is impractical. However, even such an extreme case can be easily solved by BIM. The process of 3D modeling in Revit is not the focus of this paper. The following content will start with an available bridge Revit model.
3.4. Weather Data Processing
Bridge temperature fields are extremely dependent on weather conditions, so real weather data are the premise for accurately predicting bridge temperature fields. The most reliable weather data source is field measurements at the bridge, followed by data from the nearest weather station.
Generally speaking, the calculation of temperature fields requires hourly weather data. A specific weather file format, WEA, is required to utilize off-the-shelf solar analysis tools in Revit. WEA is generally associated with Autodesk Ecotect, a program for designing energy-efficient buildings. WEA files can be created by Weather Tool or converted from EPW files using the EnergyPlus Weather Converter application [27]. A complete WEA file consists of 8760 hours (365 days × 24 hours/day) of weather data for a full year, and its original use is to simulate the annual energy consumption of a building. However, bridge temperature fields only need weather data for a given period. Therefore, all we need to do is to replace the corresponding fields in the WEA file with real weather data. Among all the weather elements in a WEA file, solar direct normal radiation, diffuse horizontal radiation, air temperature, and wind speed are necessary to implement the proposed framework. However, some radiation-related data sources have only global horizontal radiation. In this case, using a separation model, e.g., Perez model [28] or BRL model [29, 30], in advance to split the global into direct and diffuse horizontal values is an indispensable step.
3.5. Solar Radiation Analysis in BIM
Before starting the following discussion, it is necessary to elaborate on the definition of insolation because it is sometimes confused with irradiance. Irradiance is an instantaneous measurement of solar power over some area, and its unit is W/m2, while insolation is a measurement of the cumulative solar energy measured over some area for a defined period (e.g., annual, monthly, and daily) and its common unit is kWh/m2 [31]. When a time interval of 1 hour is stated, the unit of insolation can be converted into W/m2, representing the total solar energy hitting an area over an hour.
The primary purpose of this step is to calculate hourly insolation fields, which reflect the hourly spatial distribution of heat flux on bridge surfaces. Solar radiation plays a vital role in affecting the temperature distribution in a bridge [9], so the correctness of solar radiation calculation directly affects the prediction accuracy of temperature fields. Autodesk Revit provides users with two tools for solar insolation analysis: one is the Insight plugin, as shown in Figure 1; the other is a package called Solar Analysis, which relies on the Dynamo programming environment to run [32]. Comparatively speaking, the former is not flexible enough in application, while the latter can achieve diversified functions through programming; thus, in the proposed framework, SRA is implemented in Dynamo. Dynamo is a graphical programming interface that permits users to type lines of codes and scripts or to develop an algorithm that consists of nodes, and it provides seamless integration between Revit models and various simulation tools. The node package Solar Analysis can parse WEA files and calculate insolation values considering the effect of shading. In terms of calculation accuracy, given solar direct normal and diffuse horizontal radiation, this package uses Perez solar model [22], an anisotropic diffuse model, to calculate the incident solar radiation on inclined surfaces such as webs of box girders. It is worth mentioning that Perez solar model is also used by the U.S. National Renewable Energy Lab (NREL) and their PVWatts® tool. Results from Solar Analysis have been validated directly by NREL, and findings conclude that differences between the results were less than 1% [33]. Therefore, the proposed framework has obvious advantages in calculating surface incident radiation.
Two programming languages, Python and DesignScipt, are used in Dynamo to implement this work. As shown in Figure 5, on the premise that a Revit model is available, SRA can be performed as follows:(1)Select surfaces for SRA from the Revit model, where the analysis surfaces and shading surfaces are grouped separately.(2)Configure the analysis settings, including specifying the weather file path, setting the time study range, and setting the spacing between calculation points (see Figure 5(c)), where the spacing only represents the fineness of SRA in Revit but is irrelevant to FE mesh density.(3)Conduct SRA with an increment step of 1 hour. Taking three analysis steps as an example, Figure 5(d) shows the output structure of SRA. The outputs include (1) analysis step name, named in an apprehensible form; (2) air temperature, namely the ambient temperature in subsequent FE boundary condition modeling; (3) wind speed, also used in FE boundary condition modeling; (4) hourly insolation (in unit W/m2), where each insolation value corresponds to the heat flux at its calculation point; and (5) coordinates of calculation points, used for mapping insolation to the same position in the FE model.
Thus far, all outputs already meet the needs of a 3D temperature field calculation. They are formatted in Dynamo by programming and then exported in CSV format for subsequent 3D FE thermal analysis. For a 2D temperature field calculation, however, some extra steps need to be performed, such as selecting the desired cross section, extracting the 2D section information, and projecting the nearest calculation points and their insolation values on the selected section. Eventually, the data file that includes 2D insolation fields, cross-sectional information, and weather data are also exported in CSV format.
In Dynamo, the correctness of SRA can be visually verified by visualizing the analysis results. For example, Figure 5(e) shows the average insolation distribution on the surfaces of a box girder during 9:00-10:00 am. In the morning, owing to the lower solar altitude, the sunlit area on the web receives the maximum insolation, followed by the top surface, while the shaded area on the web receives the minimum value. Compared with Figure 5(b), which shows the sunlight state at 9:30 am in ray tracing mode in Revit, Figure 5(e) has a similar shaded shape and visually reflects the insolation distribution in that particular period. It should be noted that the shadow in Figure 5(b) is an instantaneous state, while Figure 5(e) is an average state over 1 hour.
Tips in SRA are as follows: (1) the spacing between calculation points affects the accuracy of insolation distribution on surfaces that contain shaded areas but not on fully exposed surfaces; thus, it is recommended to set the spacing differently to save calculation time. (2) Analysis step naming is suggested to be similar to Figure 5(d) because it clearly shows the period corresponding to the analysis step—for example, “step2-D1-10to11” represents the analysis step No. 2, and its time study range is from 10:00 am to 11:00 am on the first day—which is helpful for users quickly identifying the moment that a temperature field corresponds to when reading the results of FE analysis.
3.6. Information Transfer from BIM to FEA
The results of SRA can be used for manual or automatic FE modeling. The latter needs to write data interface scripts for automatically reading the CSV data file, generating meshes, creating boundary conditions, and solving. In Abaqus, Python scripts let users accomplish tasks that would be time-consuming or practically impossible in the GUI (Abaqus/CAE). Using a script, users can automate a repetitive task, vary simulation parameters as part of an optimization study, extract information from large output databases, and even create user interfaces that customize the look and feel of Abaqus. Therefore, the information transfer from BIM to FEA and FE modeling can be implemented by writing a Python script in Abaqus. Unlike FE modeling in previous research, the proposed framework imposes solar radiation loads by mapping. As shown in Figure 4, a complete 2D FE model can be established through a Python script because the CSV file already contains the 2D section data of a bridge. However, 3D FE modeling requires importing the 3D geometry (SAT format) from Revit to Abaqus in addition to the CSV file. Note that the coordinates of the 3D geometry in both systems must be consistent to ensure correct insolation mapping (Figure 6).
3.7. Boundary Condition
FE heat transfer analysis is widely used in the calculation of temperate fields. Although the application of this method has been decades of history, it is still necessary to discuss the boundary conditions under the novel framework proposed in this paper. The three main heat exchange processes are radiation, convection, and conduction. The heat exchange between a bridge and its surrounding environment is shown in Figure 7.
3.7.1. Solar Radiation
The factors that cause heat gain on bridge surfaces are solar direct (beam) radiation , diffuse radiation , and reflected radiation . They are all absorbed by bridge surfaces in the form of short-wave radiation. The heat gain on bridge surfaces, , can be expressed as follows:where is the absorptivity of the surface material for short-wave radiation, and is the total solar radiation that strikes the surface. Among the three components of solar radiation, and are the main influence factors and they have been included in the results of SRA (more specifically, the package Solar Analysis), while needs an additional calculation by the following equation.where is the ground reflection coefficient (albedo), is the global horizontal (sometimes called total) radiation, and is the surface inclination angle. The value of is relatively small compared to and , so some early studies ignored it in calculating solar radiation [2]. However, another view believes that will affect the structural temperature of the web and the bottom slab of a bridge, so it was considered in recent publications [16, 34]. In the proposed framework, can be figured out and added into equation (1) by programming in Dynamo or Abaqus Python.
3.7.2. Heat Convection
Heat convection, as the heat transfer mechanism between surfaces and surrounding air, is correlated with air movement at the outer surfaces and the temperature difference between the surface temperature Ts and ambient temperature Ta. The heat flux of convective heat transfer is expressed by the classical formula:where is the surface convection coefficient (W/m2·°C).
Substantial research has been done on the formulation of models for estimating the convection coefficient. In the existing literature, the most commonly used is the linear convection model, which is expressed as follows [35]:where is the wind speed, which originally refers to the free flow wind speed in the wind tunnel, but in practical applications, it seems to have been replaced by the local wind speed near the building surface [35] or the wind speed observed at weather stations.
In addition to the linear model, a convection model that considers the temperature difference between surfaces and zone air was used in previous publications [36], which is expressed as follows:
Although the convection coefficients calculated by different models differ, even if the deviation between them is within 20%, the resulting deviation of surface temperatures does not exceed 6% [14]. Thus, different convective models have little influence on the calculation results in calculating temperature fields.
3.7.3. Heat Radiation
All objects with a temperature greater than absolute zero will emit thermal radiation into their surroundings. In natural environments, radiative heat transfer is the heat emitted from the heated surface to the ambient atmosphere by long-wave radiation. Radiative heat transfer flux, , between exposed surfaces and surrounding air can be expressed as follows:where is long-wave radiation emissivity of girder surfaces, is the Stefan–Boltzman constant, which equals 5.67 × 10−8 W/m2K4.
4. Practical Application
4.1. Bridge Description
The measured data of this actual case is from [37]. Nenjiang Bridge (47.27°N, 123.87°E) is located in Qiqihar, a city in the west of Heilongjiang Province, China. The bridge has a total width of 24.5 m and consists of two separate single-cell box girders. The superstructure of the main bridge adopts a variable cross-sectional prestressed concrete continuous box girder with a span arrangement of (41 + 6 × 65 + 41) m (Figure 8). The root and midspan heights of the girder are 4.0 m and 2.0 m, respectively, and the height of the girder changes twice parabolically. The bridge generally runs east-west, and the angle between the bridge axis and the true north direction is about 107°. Construction on the bridge began in October 2009 and was completed in October 2011. Temperature sensors were installed on the section between Pier 12 and Pier 13, and 12 m away from Pier 13 (Figure 8(b)), where the section height is 2.9 m (Figure 8(c)). The time range of field data collection was from the 4th to the 6th of June in 2011, when the bridge deck pavement had not been constructed.
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4.2. Calculation of Temperature Field
The calculation of 2D temperature fields on the measured section of Nenjiang Bridge was performed to demonstrate the practical application of the proposed framework. In this study, the BIM model of the bridge was quickly created in Revit through parametric modeling. The weather data were derived from the historical reanalysis dataset of the European Center for Medium-Range Weather Forecasts (ECMWF) and provided by Xihe Energy Big Data Platform [38]. A total of 120 hourly weather records from the 2nd to the 6th of June in 2011 were obtained at Qiqihar weather station (about 13 km away from the bridge).
By viewing the sun’s trajectory (see Figure 9(a)) over the time study range in Revit, the areas that affect the insolation of the measured section could be determined. As shown in Figure 9(b), they were selected as shading surfaces in SRA, while those local areas that contain the measured section were selected as analysis surfaces. The reason for selecting the limited surfaces for SRA is to save analytical time. The calculation point spacing was set to 0.5 m, and the data of 118 analysis steps were eventually generated. These data, including analysis step names, insolation values, air temperatures, wind speeds, and coordinates of analysis points, were exported in CSV format and read in Abaqus through a Python script for automatic FE modeling and analysis. As shown in Figure 9(c), the insolation was perfectly mapped onto the edges of the 2D section in Abaqus, where the heat flux was equal to insolation times the surface absorption coefficient. Several details of the insolation results indicated the correctness of SRA. For example, at about 5:00 am, when the solar altitude was low, the vertical surface of the interior overhang received the maximum incident solar radiation (the guardrails were not considered in the model), followed by the top surface, while the incident radiation on the surface of the interior web was almost 0 due to the shading of the right bridge. In addition, although the exterior web of the girder was always in shaded areas for a whole day due to the shading of the longer overhang, it could receive diffuse radiation. Accurate calculation of diffuse radiation on bridge surfaces is one of the strengths of the proposed framework.
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Abaqus/CAE 2020 was used to conduct the 2D transient heat transfer analysis of the bridge. The cross section was modeled using a 4-node linear heat-transfer quadrilateral element DC2D4, and the mesh size was set to 0.05 m. Thermodynamic parameters in the calculation are shown in Table 1, in which the conductivity was inversely deduced according to the law of one-dimensional heat conduction (e.g., the vertical heat transfer at the three points in the middle of the bottom flange) under the known data such as measurement point spacing, interval time, and measured temperature. Boundary conditions considered in FE modeling were as follows: (1) exterior surface heat flux caused by solar short-wave radiation, where the ground albedo was taken as 0.2 in the calculation of solar-reflected radiation; (2) surface heat convection, where the wind speed inside the box girder was 0 m/s; (3) long-wave radiation, including the radiation from exterior surfaces to the surrounding environment and the cavity radiation inside the box girder. The initial structural temperature of the box girder was set to 20°C, and eventually, 119 analysis steps (one more initial step than SRA) were calculated in FEA.
4.3. Comparison of FEA and Measured Results
The results of the first two days were used to eliminate the effect of the initial concrete temperature, so the comparison started on June 4th. Figure 10 shows the comparisons of several items, such as the bridge deck surface (measuring point No. 15), web surface (measuring point No. 21), and vertical and lateral temperature gradients corresponding to the maximum temperature on the bridge deck. It can be observed that the variation trends were similar for the measured and calculated values, especially at the bridge deck surface, where the calculated temperatures were almost the same as the measured temperatures (Figure 10(a)). The maximum temperature difference between the calculated and measured values on the surface of the outer web was within 3°C (Figure 10(b)). There were two reasons for this: (1) the local air temperature and wind speed around the web were the main factors affecting its temperature distribution because the web was always in a shaded area during that time range, whereas the local weather data around the web were replaced by the data from weather station; (2) the weather data were derived from the historical reanalysis dataset rather than first-hand measurement.
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5. Conclusions and Prospects
The main contribution of this paper is the proposal of a new calculation method for bridge temperature fields based on BIM technology. Compared with the existing methods, the proposed method has significant advantages.(1)A More Accurate Calculation for Solar Radiation. On the one hand, the specialized solar analysis tool is used to calculate the solar radiation (especially the diffuse radiation component) reaching bridge surfaces, ensuring thermal load calculations’ accuracy. On the other hand, the new method can consider more complex shading effects, especially those from objects around the bridge but unrelated to the FE calculation.(2)A Lower Technical Threshold. Shadow recognition and solar radiation calculation are automatically completed in BIM, avoiding complex subroutine or APDL programming in FE systems. Users do not need to master the specific ray tracing algorithm and the interdisciplinary solar radiation model to calculate temperature fields. All they need to do is merely to “carry” the data generated in BIM to the FE model.(3)A Higher Degree of Automation. Insolation and weather data generated in BIM can be output in user-desired format through Dynamo programming, which is convenient for users to write the calculation script to read these data for automatic FE modeling. Taking the case study in this paper as an example, although there were more than 100 analysis steps with more than 10,000 pieces of data, the whole process, from modeling to calculation, was automatically completed in a few minutes through a Python script.(4)Less Computational Time. Unlike existing methods that require 3D FE modeling for shadow recognition, the new method separates SRA from FEA, which means that the SRA is performed in a BIM 3D environment, while the FEA can optionally adopt 3D or 2D. The calculation of 2D temperature gradient profiles requires fewer resources and less time.(5)Easier FE Modeling. Since 3D geometry is created in BIM rather than in FE systems, the parametric modeling tool of BIM makes geometric modeling easier. In addition to being used for solar radiation analysis, the geometric model created in BIM can also be shared with FE modeling.
The subsequent research regarding the proposed method can be considered from two aspects. One is the development of refined boundary condition models with more influence factors considered. In the future, a multifactorial boundary condition model considering the wind speed, wind direction, and the correction of windward and leeward is expected to be established through experimental and numerical methods. The other is the further applications based on the proposed method. As an innovative use of information technology in solving the issues related to bridge temperature fields, the proposed method has a broad application prospect. In the design stage, given historical weather data, this method can be used to predict the representative value of the temperature gradient action during the design reference period of the bridge. In the construction stage, using the field-monitored weather data, this method can be used to calculate the thermal deformation caused by solar radiation to correct the formwork elevation in a segmental cantilever construction process. In the service stage, using weather records in the health monitoring, this method can precisely separate thermal effects from bridge health monitoring stress data to evaluate the bridge’s service condition more reliably.
Data Availability
The data used to support the findings of the study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest regarding the publication of this paper.
Acknowledgments
This research was supported by the Science and Technology Research Project of Department of Education of Hubei Province (Grant no. D20213001) and Science and Technology Project of Department of Transportation of Hubei Province (Grant no. 2022-11-2-8).