Construction Method, Device and Application of Finite Element Model of Porous Asphalt Concrete

Abstract

The present invention provides a method, device and application for constructing a finite element model of porous asphalt concrete. The construction method includes: constructing a three-dimensional aggregate database; generating a three-dimensional discrete element model of aggregate accumulation based on the three-dimensional aggregate database, and exporting the three-dimensional discrete element model of aggregate accumulation in multiple STL files; importing the multiple STL files into MATLAB software, and using MATLAB software to convert the three-dimensional discrete element model of aggregate accumulation into a first mesoscopic model; constructing a second mesoscopic model including asphalt mortar and coarse aggregate based on the first mesoscopic model and the preset thickness of the asphalt mortar layer; writing the discrete element information of the second mesoscopic model into a.py file through MATLAB programming, and importing it into ABAQUS software for three-dimensional modeling and mesh generation, deleting the mesh corresponding to the voids, and constructing a finite element model of porous asphalt concrete. The present invention fully considers the internal inhomogeneity of materials and the characteristics of complex porous structures, and the constructed finite element model can reveal the distribution law of internal thermal stress.

Description

Technical Field

[0001] The present invention belongs to the technical field of civil engineering, and particularly relates to a method, device and application for constructing a finite element model of porous asphalt concrete. Background Art

[0002] In the field of road engineering, porous asphalt concrete has been widely used in urban roads, highways, airport runways and other fields in recent years due to its excellent water permeability, heat insulation performance and good noise absorption ability. This material can not only effectively reduce road surface water accumulation and improve driving safety, but also achieve the purpose of energy conservation and environmental protection by reducing road surface temperature and heat island effect. However, the thermal performance evaluation of porous asphalt concrete faces many technical challenges. Especially due to its complex internal porous structure and heterogeneity, traditional experimental methods are difficult to comprehensively and accurately reveal its heat conduction mechanism and thermal behavior characteristics.

[0003] Currently, for the research on the thermal conductivity of materials, indoor test methods mainly include the flat heat source method, steady state method, transient plane heat source method, etc. These methods can directly measure the thermal conductivity of materials and provide certain data support for the evaluation of material thermal performance. However, these test methods have significant limitations when applied to porous asphalt concrete. On the one hand, due to the complexity of its internal structure, the test measurement results of porous asphalt concrete often have large fluctuations, long test time and poor repeatability. On the other hand, traditional experimental methods can only provide the overall macroscopic thermal performance parameters of materials, and cannot reveal the influence of their internal porous structure on heat conduction behavior.

[0004] In addition, with the rapid development of artificial intelligence and neural network technologies, predicting the thermal conductivity of materials based on existing experimental data has become a new research direction. This method can quickly predict the thermal performance parameters of materials through learning and training of a large amount of experimental data. However, such methods usually can only provide the prediction results of macroscopic parameters and cannot deeply explore the heat conduction mechanism of porous asphalt concrete from the mesoscopic structure level. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for constructing a finite element model of porous asphalt concrete that fully considers the internal heterogeneity and complex porous structure characteristics of the material. The finite element model constructed by using this construction method is applied to thermal performance research, and can more accurately evaluate its thermal performance and reveal the internal thermal stress distribution law.

[0006] In a first aspect, the present invention provides a method for constructing a finite element model of porous asphalt concrete, where the porous asphalt concrete is composed of asphalt mortar and coarse aggregates, and the construction method includes the following steps: Step S10: Construct a three-dimensional aggregate database, where the three-dimensional aggregate database includes a plurality of coarse aggregate geometric models with different particle sizes; Step S20: Generate a virtual space, put the coarse aggregate geometric models in the three-dimensional aggregate database into the virtual space, generate an aggregate packing three-dimensional discrete element model, and export the aggregate packing three-dimensional discrete element model as a plurality of STL files, and each STL file also stores the spatial coordinate information of the coarse aggregate geometric model; Step S30: Import the plurality of STL files into MATLAB software, and use the MATLAB software to convert the aggregate packing three-dimensional discrete element model into a first mesoscopic model. The first mesoscopic model is composed of N voxels, and the voxel value of each voxel is 0 or 1. The sum of the volumes of the N voxels is the same as the volume of the virtual space. Among them, the voxels with a voxel value of 0 correspond to the coarse aggregates, and the voxels with a voxel value of 1 correspond to the voids. N is a positive integer; Step S40: Based on the first mesoscopic model and the preset thickness of the asphalt mortar layer, construct a second mesoscopic model including asphalt mortar and coarse aggregates. The target voxels in the first mesoscopic model with a voxel value of 1 and meeting the preset conditions are marked as voxel values 2 corresponding to the asphalt mortar layer in the second mesoscopic model. Among them, the preset thickness of the asphalt mortar layer is m voxels, and the condition that meets the preset conditions means that the distance between the target voxel and the adjacent voxels with a voxel value of 0 is less than or equal to m voxels. m is a positive integer; Step S50: Write the voxel information of the second mesoscopic model into a.py file through MATLAB programming, and import it into ABAQUS finite element software for three-dimensional modeling and mesh generation. Delete the meshes corresponding to the voids to construct the finite element model of the porous asphalt concrete.

[0007] In a specific implementation manner, the step S10 includes: Step 1: Obtain a plurality of coarse aggregates with different particle sizes, and obtain the two-dimensional projection images of each coarse aggregate based on the AIMS system; Step 2: Generate a plurality of three-dimensional point cloud data corresponding one-to-one to the two-dimensional projection images of each coarse aggregate based on the trained CGAN model; Step 3: Based on the plurality of three-dimensional point cloud data generated in Step 2, construct a three-dimensional aggregate database, where the three-dimensional aggregate database includes a plurality of coarse aggregate geometric models corresponding one-to-one to the plurality of three-dimensional point cloud data.

[0008] In a specific embodiment, the training method of the CGAN model includes: obtaining a plurality of aggregates for training; obtaining two-dimensional projection images of each aggregate using the AIMS system; obtaining three-dimensional aggregate contour point cloud data of each aggregate using a laser scanner; obtaining a training set, where the training set includes a plurality of data pairs, and each data pair includes a two-dimensional projection image and three-dimensional aggregate contour point cloud data of the same aggregate; training the CGAN model using the training set, and when the evaluation index is less than a preset value, the training is completed to obtain a trained CGAN model, where the evaluation index includes the FID index and the CD index.

[0009] In a specific embodiment, step S20 includes: step (1), generating a virtual space based on preset dimension data; step (2), obtaining the volume fractions of multi-level coarse aggregates based on the volume of the virtual space and the mix proportion information of the preset porous concrete, where different levels of coarse aggregates have different particle size ranges; step (3), inputting the coarse aggregate geometric models in the three-dimensional aggregate database into the virtual space according to the volume fractions of the multi-level coarse aggregates determined in step (2) based on a preset placement rule to generate an aggregate packing three-dimensional discrete element model; step (4), exporting each coarse aggregate geometric model of the aggregate packing three-dimensional discrete element model as an STL file respectively, and each STL file also stores the spatial coordinate information of the coarse aggregate geometric model.

[0010] In a specific embodiment, step S30 includes: step a, importing a plurality of STL files into the MATLAB software; step b, based on a preset grid size, dividing the virtual space of the aggregate packing three-dimensional discrete element model into N voxels through MATLAB programming and setting the voxel value of each voxel to an initial value of 1, where a voxel value of 1 represents a void; step c, determining the voxel value of each voxel based on the triangular patch information and spatial coordinate information of each coarse aggregate read from each STL file. When the number of intersection points of a ray emitted from the center point of the voxel along the positive z-axis direction with the triangular patches on the surface of the coarse aggregate is an odd number, changing the voxel value of the voxel from the initial value of 1 to 0; when the number of intersection points of a ray emitted from the center point of the voxel along the positive z-axis direction with the triangular patches on the surface of the coarse aggregate is an even number, keeping the voxel value of the voxel unchanged at 1, where the voxel with a voxel value of 0 corresponds to the coarse aggregate, and the voxel with a voxel value of 1 corresponds to the void.

[0011] In a specific embodiment, the step S40 includes: Step (1), setting the thickness of the asphalt mortar layer to m voxels; Step (2), expanding the vertex coordinates of each coarse aggregate in the first mesoscopic model outward by a distance of m voxels to obtain an intermediate mesoscopic model; Step (3), relabeling the voxel values of all candidate voxels with a voxel value of 1 in the intermediate mesoscopic model. When the number of intersection points of a ray emitted from the center point of the candidate voxel along the positive z-axis direction and the triangular patches on the surface of the coarse aggregate is odd, the candidate voxel is used as a target voxel that meets the preset conditions, and the voxel value of the target voxel is changed from 1 to 2; when the number of intersection points of a ray emitted from the center point of the candidate voxel along the positive z-axis direction and the triangular patches on the surface of the coarse aggregate is even, the voxel value of the candidate voxel remains unchanged at 1. Among them, the voxels with a voxel value of 2 correspond to the asphalt mortar layer.

[0012] In a specific embodiment, the step S40 includes: Step (1), setting the thickness of the asphalt mortar layer to m voxels; Step (2), traversing each first voxel with a voxel value of 0, and obtaining the voxel values of the second voxels whose distances from each first voxel are less than or equal to m voxels. When the voxel value of the second voxel is 1, the second voxel is used as a target voxel, and the voxel value of the target voxel is changed from 1 to 2; when the voxel value of the second voxel is 0, the voxel value of the second voxel remains unchanged at 0. Among them, the voxels with a voxel value of 2 correspond to the asphalt mortar layer.

[0013] In a second aspect, the present invention provides a device for constructing a finite element model of porous asphalt concrete, and the construction device includes:

[0014] The first construction module is used to construct a three-dimensional aggregate database, which includes a plurality of coarse aggregate geometric models with different particle sizes; a generation module is used to generate a virtual space, put the coarse aggregate geometric models in the three-dimensional aggregate database into the virtual space, generate a three-dimensional discrete element model of aggregate packing, and export the three-dimensional discrete element model of aggregate packing as a plurality of STL files, and each STL file also stores the spatial coordinate information of the coarse aggregate geometric model; a model conversion module is used to import the plurality of STL files into MATLAB software, and use the MATLAB software to convert the three-dimensional discrete element model of aggregate packing into a first mesoscopic model, which is composed of N voxels, and the voxel value of each voxel is 0 or 1, and the sum of the volumes of the N voxels is the same as the volume of the virtual space, where the voxels with voxel value 0 correspond to the coarse aggregates, and the voxels with voxel value 1 correspond to the voids, and N is a positive integer; a second construction module is used to construct a second mesoscopic model including asphalt mortar and coarse aggregates based on the first mesoscopic model and the preset thickness of the asphalt mortar layer. The target voxels with voxel value 1 and meeting the preset conditions in the first mesoscopic model are marked as voxel values 2 corresponding to the asphalt mortar layer in the second mesoscopic model, where the preset thickness of the asphalt mortar layer is m voxels, and the condition that meets the preset conditions means that the distance between the target voxel and the adjacent voxels with voxel value 0 is less than or equal to m voxels, and m is a positive integer; a third construction module is used to write the voxel information of the second mesoscopic model into a.py file through MATLAB programming, import it into ABAQUS finite element software for three-dimensional modeling and mesh generation, delete the meshes corresponding to the voids, and construct the porous asphalt concrete finite element model.

[0015] In a third aspect, the present invention provides a method for calculating the effective thermal conductivity using the porous asphalt concrete finite element model constructed by the construction method described above. The method includes the following steps: Step (1), import the porous asphalt concrete finite element model into ABAQUS analysis software, select the element type and set the material parameters and boundary conditions, and then use the software for simulation to obtain the node temperature and heat flux. Among them, the element type is selected as the heat conduction type, the material parameters include density, thermal conductivity and specific heat capacity, and the setting of the boundary conditions includes: adopting a steady-state analysis, setting different temperatures at the upper and lower boundaries of the model to form a temperature gradient, and the other boundaries are defaulted to the heat insulation condition; Step (2), calculate the equivalent thermal conductivity based on the calculation formula of the heat flux and the equivalent thermal conductivity.

[0016] Fourthly, the present invention provides a method for analyzing the pavement temperature field by using the finite element model of porous asphalt concrete constructed by the construction method described above. The method includes: importing the finite element model of porous asphalt concrete into the ABAQUS analysis software, setting material parameters and boundary conditions, and then using the software for simulation to obtain the pavement temperature field distribution and heat flux. Among them, the material parameters include density, thermal conductivity and specific heat capacity, and the setting of the boundary conditions includes: adopting transient analysis; defining the initial temperature field; setting temperature, solar radiation and wind speed on the surface of the model.

[0017] The beneficial effects of the present invention at least include:

[0018] 1. For the construction method provided by the present invention, first, a three-dimensional discrete element model of aggregate packing is constructed based on the geometric model of coarse aggregate in the aggregate database, and then the three-dimensional discrete element model of aggregate packing is exported as multiple STL files. Then, the multiple STL files are imported into the MATLAB software, and the MATLAB software is used to convert the three-dimensional discrete element model of aggregate packing into a first mesoscopic model including coarse aggregate. Then, a second mesoscopic model including coarse aggregate and asphalt mortar is constructed based on the first mesoscopic model. Each voxel in the second mesoscopic model is marked with a voxel value. When the voxel value is marked as 1, it means that the voxel corresponds to a void. When the voxel value is marked as 0, it means that the voxel corresponds to coarse aggregate. When the voxel value is marked as 2, it means that the voxel corresponds to asphalt mortar. Finally, the information of each voxel of the second mesoscopic model is written into a.py file through MATLAB programming and imported into the ABAQUS finite element software for three-dimensional modeling and mesh generation. The meshes corresponding to the voids are deleted to construct the finite element model of porous asphalt concrete. The finite element model of porous asphalt concrete can truly reproduce the three-dimensional mesoscopic characteristics of porous asphalt concrete, and can more accurately reflect the complex pore distribution and coarse aggregate arrangement characteristics inside the material. When applied to the study of thermal properties, it can more accurately evaluate its thermal properties and reveal the internal thermal stress distribution law.

[0019] 2. The present invention adopts grid discretization and grid mapping technology, which can efficiently establish the finite element model of porous asphalt concrete and perform fine mesh generation for complex three-dimensional structures. Compared with the traditional finite element modeling method, the present invention significantly improves the efficiency and accuracy of model construction and can better adapt to the complex geometric characteristics of porous materials.

[0020] In addition to the purposes, features and advantages described above, the present invention has other purposes, features and advantages. The present invention will be further described in detail below with reference to the drawings. Description of the Drawings

[0021] Figure 1Schematic diagram of the steps of a method for constructing a finite element model of porous asphalt concrete provided by an embodiment of the present invention;

[0022] Figure 2 Finite element model diagram of porous asphalt concrete constructed according to the present invention, wherein, Figure 2 (a) is a three-dimensional view of the finite element model of porous asphalt concrete, Figure 2 (b) is Figure 2 An enlarged view of part A shown in (a);

[0023] Figure 3 Internal aggregate distribution diagram of the finite element model of porous asphalt concrete constructed according to the present invention;

[0024] Figure 4 Module diagram of a device for constructing a finite element model of porous asphalt concrete provided by another embodiment of the present invention. Detailed implementation manners

[0025] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0026] The method for constructing a finite element model of porous asphalt concrete provided by the present invention fully considers the internal inhomogeneity and complex porous structure characteristics of the material. Applying this finite element model to thermal performance research can more accurately evaluate its thermal performance and reveal the distribution law of internal thermal stress, thereby providing a scientific basis for optimizing the design of pavement materials and extending the service life of roads.

[0027] According to the first aspect of the present invention, the present invention provides a method for constructing a finite element model of porous asphalt concrete, and the porous asphalt concrete is composed of asphalt mortar and coarse aggregate.

[0028] In an optional implementation manner, the asphalt mortar is a continuous and uniform mixture composed of asphalt and fine aggregate with a particle size less than 2.36 mm, and the coarse aggregate is aggregate with a particle size greater than 2.36 mm.

[0029] Please refer to Figure 1 , the construction method provided by the present invention includes the following steps:

[0030] Step S10: Construct a three-dimensional aggregate database, and the three-dimensional aggregate database includes a plurality of coarse aggregate geometric models with different particle sizes.

[0031] In the present invention, the coarse aggregates in the three-dimensional aggregate database are all convex polyhedron aggregates.

[0032] In an optional implementation manner, step S10 includes:

[0033] Step 1: Obtain a plurality of coarse aggregates, and obtain two-dimensional projection images of each of the coarse aggregates based on the AIMS system.

[0034] In the present invention, the two-dimensional projection image of the coarse aggregate is a two-dimensional projection binary image.

[0035] In the present embodiment, the coarse aggregate refers to an aggregate with an aggregate particle size ≥ 2.36 mm, and the particle size refers to the effective particle size.

[0036] In the present embodiment, the aggregate with an aggregate particle size ≥ 2.36 mm is defined as the coarse aggregate. In other embodiments, the aggregate with a particle size greater than 2.56 mm, 3 mm, or other particle size values can also be custom-defined as the coarse aggregate.

[0037] In an alternative embodiment, multiple coarse aggregates are classified into multiple levels of coarse aggregates, and different levels of coarse aggregates have different particle size ranges.

[0038] In the present embodiment, multiple coarse aggregates are classified into primary coarse aggregates, secondary coarse aggregates, tertiary coarse aggregates, and quaternary coarse aggregates. Among them, the particle size range of the primary coarse aggregates is 13.2 - 16 mm, the particle size range of the secondary coarse aggregates is 9.5 - 13.2 mm, the particle size range of the tertiary coarse aggregates is 4.75 - 9.5 mm, and the particle size range of the quaternary coarse aggregates is 2.36 - 4.75 mm.

[0039] In other embodiments, multiple coarse aggregates can also be classified into two levels of coarse aggregates, three levels of coarse aggregates, five levels of coarse aggregates, eight levels of coarse aggregates, etc. The particle size range of each level of coarse aggregates can also be adjusted. The particle size range of the same-level coarse aggregates can be self-defined, and the number of coarse aggregate levels can also be self-defined.

[0040] Specifically: First, perform a screening experiment on the crushed stones, group the crushed stones according to the preset particle size range of the multiple levels of coarse aggregates, and select a preset number of crushed stones in each group as the aggregate templates. Data of the aggregate templates are collected by the image measurement system AIMS2, two-dimensional projection images of different aggregate templates are obtained in batches, and the shape parameters of each aggregate template are analyzed and recorded. Among them, the shape parameters include the angularity and the aspect ratio, etc.

[0041] It can be understood that the aggregate templates in the same group have the same particle size range.

[0042] Step 2: Generate a plurality of three-dimensional point cloud data corresponding one-to-one to the two-dimensional projection images of each coarse aggregate based on the trained CGAN model.

[0043] In an alternative embodiment, the training method of the CGAN model includes: obtaining a plurality of aggregates for training; obtaining two-dimensional projection images of each aggregate using the AIMS system; obtaining three-dimensional aggregate contour point cloud data of each aggregate using a laser scanner; obtaining a training set, where the training set includes a plurality of data pairs, and each data pair includes a two-dimensional projection image and three-dimensional aggregate contour point cloud data of the same aggregate; training the CGAN model using the training set, and when the evaluation index is less than the preset value, the training is completed to obtain a trained CGAN model.

[0044] In the present invention, the evaluation indexes include the FID (Frechet Inception Distance) index and the CD (Chamfer Distance) index. The preset value of the FID index is 10, and the preset value of the CD index is 0.05.

[0045] In the present invention, the generator of the CGAN model receives a two-dimensional projection image as input, uses a convolutional neural network (CNN) to extract image features, and generates corresponding three-dimensional point cloud data; the discriminator compares the generated three-dimensional point cloud data (output value) with the input three-dimensional aggregate contour point cloud data (true value), and guides the generator to optimize based on the comparison result. During the training process, the FID index and the CD index are used as evaluation indexes to evaluate the generation quality and continuously adjust the learning rate, network architecture, and training strategy according to the evaluation results to improve the performance of the model and ensure a high degree of consistency between the generated three-dimensional point cloud data and the actual aggregate shape.

[0046] Step 3: Based on the plurality of three-dimensional point cloud data generated in Step 2, construct a three-dimensional aggregate database, where the three-dimensional aggregate database includes a plurality of coarse aggregate geometric models with different particle sizes corresponding one-to-one to the plurality of three-dimensional point cloud data.

[0047] It can be understood that each three-dimensional point cloud data corresponds to a coarse aggregate geometric model. If 1000 aggregates are required in the three-dimensional aggregate database, then 1000 two-dimensional projection images of coarse aggregates are obtained in Step 1, and 1000 three-dimensional point cloud data corresponding one-to-one to the 1000 two-dimensional projection images of coarse aggregates are generated in Step 2.

[0048] This step is specifically as follows: Connect the points in each three-dimensional point cloud data, and form a three-dimensional aggregate entity composed of spatial tetrahedrons according to a certain rule, and the contour surface of the three-dimensional closed aggregate can be obtained; based on all the surface triangular mesh information formed by the vertexes of the contour surface of the three-dimensional aggregate, through MATLAB code programming operation, perform conversion between text documents or other specific format files, and then import them into the discrete element software PFC to construct a plurality of aggregate geometric models, and aggregate all the aggregate geometric models to construct a three-dimensional aggregate database.

[0049] In another alternative embodiment, other existing technologies can also be used to construct a three-dimensional aggregate database.

[0050] Step S20: Generate a virtual space. According to the preset mix ratio information of the porous concrete, put the coarse aggregate geometric models in the three-dimensional aggregate database into the virtual space to generate an aggregate packing three-dimensional discrete element model, and export the aggregate packing three-dimensional discrete element model as multiple STL files, and each STL file also stores the spatial coordinate information of the coarse aggregate geometric model.

[0051] In the present invention, the PFC3D software is used to generate an aggregate packing three-dimensional discrete element model.

[0052] This step includes:

[0053] Step (1): Generate a virtual space based on the preset size data.

[0054] In the present invention, the virtual space is a cuboid or a cube, and the volume of the virtual space is V 总 .

[0055] Step (2): Based on the volume of the virtual space and the preset mix ratio information of the porous concrete, obtain the volume fractions of multi-level coarse aggregates, and different levels of coarse aggregates have different particle size ranges.

[0056] In the present invention, the preset mix ratio information of the porous concrete includes the aggregate gradation, asphalt-aggregate ratio, and target porosity.

[0057] For easy understanding, this step illustrates the calculation process of the volume of multi-level coarse aggregates by way of example. Assume that the density of asphalt is 1000 kg / m 3 , the aggregate density is 2600 kg / m 3 , the porosity is 20%, the asphalt-aggregate ratio is 4.5%, and the aggregate gradation is shown in Table 1.

[0058] Table 1 Aggregate gradation data of porous concrete

[0059]

[0060] The volume calculation process of each level of coarse aggregate is as follows: First, calculate the sum of the volumes of the aggregate and asphalt based on the porosity, then calculate the volume of asphalt based on the asphalt-aggregate ratio, then calculate the volume of the aggregate based on the volume of asphalt and the total volume, then calculate the total volume of the coarse aggregate based on the volume of the aggregate and the aggregate gradation data, and finally calculate the volume of each level of coarse aggregate based on the aggregate gradation data and the total volume of the coarse aggregate.

[0061] The specific calculation is as follows:

[0062] The calculation of the sum of the volumes of the aggregate and asphalt is: V 骨料 + V 沥青 = (1 - 20%)V 总 = 80%V 总 .

[0063] The calculation of the volume of asphalt is:

[0064] (1000×V 沥青 ) / (2600×V 骨料 ) = 4.5%; V 沥青 = (2600×4.5%)V 骨料 / 1000.

[0065] The calculation of the volume of the aggregate is: V 骨料 = 80%V 总 / [1 + (2600×4.5%) / 1000].[[]END]]

[0066] The calculation of the total volume of the coarse aggregate is: V 粗骨料 = (1 - 10.4%)V 骨料 = 89.6%×80% V 总 / [1 + (2600×4.5%) / 1000] = 64.17%V 总 .

[0067] The volumes of the coarse aggregate in each particle size range are as follows:

[0068] V 13.2~16mm = [(100 - 92.7) / 89.6]V 粗骨料 = 8.2%V 粗骨料 = 8.2%×64.17%V 总 .

[0069] V 9.5~13.2 mm = [(92.7 - 58.2) / 89.6]V 粗骨料 = 38.5%V 粗骨料 = 38.5%×64.17%V 总 .

[0070] V 4.75~9.5mm = [(58.2 - 16.7) / 89.6]V 粗骨料 = 46.3%V 粗骨料 = 46.3%×64.17% V 总 .

[0071] V 2.36~4.75mm = [(16.7 - 10.4) / 89.6]V 粗骨料 = 7.0%V 粗骨料 = 7.0%×64.17%V总 。

[0072] Taking the total volume of the virtual space as 100%, the volume fractions of each level of coarse aggregate are as follows: the volume fraction of the first-level coarse aggregate with a particle size range of 13.2 - 16 mm is 5.26%, the volume fraction of the second-level coarse aggregate with a particle size range of 9.5 - 13.2 mm is 24.7%, the volume fraction of the third-level coarse aggregate with a particle size range of 4.75 - 9.5 mm is 29.71%, and the volume fraction of the fourth-level coarse aggregate with a particle size range of 2.36 - 4.75 mm is 4.49%.

[0073] Step (3): Based on the preset placement rule, input the coarse aggregate geometric models in the three-dimensional aggregate database into the virtual space according to the volume fractions of the multi-level coarse aggregates determined in step (2) to generate an aggregate packing three-dimensional discrete element model.

[0074] In the present invention, the preset placement rule is specifically: grading and placing according to the level of the coarse aggregate, and each level of placement is based on the particle size value of the coarse aggregate, and placed in the order from large to small.

[0075] Specifically: starting from the coarse aggregate with the largest particle size, a certain number of particles are placed each time, and layered processing is carried out according to the particle size range. Through the discrete element software PFC 3D command stream, after each coarse aggregate particle is placed, the volume fraction of the coarse aggregate within the current particle size range is automatically calculated. If the volume fraction of the current coarse aggregate is less than the target volume fraction, the coarse aggregate within the current particle size range continues to be placed until the target volume fraction is reached. After the placement of the coarse aggregate within one particle size range is completed, it turns to the coarse aggregate within the next particle size range.

[0076] It can be understood that the target volume fraction is the volume fraction of the multi-level coarse aggregates determined in step (2).

[0077] For easy understanding, an example is given. First, place the first-level coarse aggregate with a particle size range of 13.2 - 16 mm. When the volume fraction of the first-level coarse aggregate reaches 5.26%, then place the second-level coarse aggregate with a particle size range of 9.5 - 13.2 mm. When the volume fraction of the second-level coarse aggregate reaches 24.7%, then place the third-level coarse aggregate with a particle size range of 4.75 - 9.5 mm. When the volume fraction of the third-level coarse aggregate reaches 29.71%, finally place the fourth-level coarse aggregate with a particle size range of 2.36 - 4.75 mm. When the volume fraction of the fourth-level coarse aggregate reaches 4.49%, the placement of all coarse aggregates is completed. When placing each level of coarse aggregate, first place the aggregate with a larger particle size range. For example, for the coarse aggregate G1 with a particle size of 14 mm and the coarse aggregate G2 with a particle size of 15 mm, when placing, first place the coarse aggregate G2.

[0078] Step (4): Export each coarse aggregate geometric model of the three-dimensional discrete element model of the aggregate accumulation as an STL file, and each STL file also stores the spatial coordinate information of the coarse aggregate geometric model.

[0079] In the present invention, the STL file is a 3D model containing the shape and geometric information of the coarse aggregate, and also stores the spatial coordinate information of the coarse aggregate.

[0080] It can be understood that if the three-dimensional discrete element model of the aggregate accumulation includes 1200 coarse aggregate geometric models, the number of exported STL files is 1200, that is, each coarse aggregate geometric model corresponds to one STL file.

[0081] Each STL file also stores the spatial coordinate information of the coarse aggregate geometric model, so that it is convenient to ensure the position of each coarse aggregate remains unchanged during subsequent format conversion.

[0082] Step S30: Import the multiple STL files into MATLAB software, and use the MATLAB software to convert the three-dimensional discrete element model of the aggregate accumulation into a first mesoscopic model. The first mesoscopic model is composed of N voxels, and the voxel value of each voxel is 0 or 1. The sum of the volumes of the N voxels is the same as the volume of the virtual space. Among them, the voxels corresponding to the coarse aggregate are marked as 0, and the voxels corresponding to the voids are marked as 1, where N is a positive integer.

[0083] This step includes:

[0084] Step a: Import multiple STL files into MATLAB software.

[0085] Step b: Based on a preset grid size, divide the virtual space of the three-dimensional discrete element model of the aggregate accumulation into N voxels through MATLAB programming, and set the voxel value of each voxel to the initial value 1. Among them, the voxel value of 1 represents a void.

[0086] In the present invention, each voxel is a regular cubic grid.

[0087] In the present invention, the preset grid size must be able to divide the length, width, and height of the model to ensure that the size of each voxel is consistent and avoid irregular or uneven division during the grid division process. For example, the length, width, and height of the model need to be divisible by the specified voxel size respectively.

[0088] Step c: Based on each of the STL files, read the triangular facet information and spatial coordinate information of each coarse aggregate, and respectively determine the voxel values of each voxel. When the number of intersection points of a ray emitted from the center point of the voxel along the positive z-axis direction and the triangular facets on the surface of the coarse aggregate is odd, change the voxel value of the voxel from the initial value of 1 to 0; when the number of intersection points of a ray emitted from the center point of the voxel along the positive z-axis direction and the triangular facets on the surface of the coarse aggregate is even, keep the voxel value of the voxel unchanged at 1. Among them, the voxels corresponding to the coarse aggregate are marked as 0, and the voxels corresponding to the voids are marked as 1.

[0089] In the present invention, the spatial coordinate information of the coarse aggregate includes the vertex coordinate information of each vertex of the coarse aggregate.

[0090] In the present invention, sequentially read the triangular facet information and spatial coordinate information of each coarse aggregate, traverse each voxel. When the voxel is inside the aggregate, the number of intersection points of a ray emitted from the center point of the voxel along the positive z-axis direction and the triangular facets on the surface of the coarse aggregate is odd; when the voxel is outside the aggregate, the number of intersection points of a ray emitted from the center point of the voxel along the positive z-axis direction and the triangular facets on the surface of the coarse aggregate is even.

[0091] Step S40: Based on the first mesoscopic model and the preset thickness of the asphalt mortar layer, construct a second mesoscopic model including asphalt mortar and coarse aggregates. The target voxels with a voxel value of 1 and meeting the preset conditions in the first mesoscopic model are marked as voxel values of 2 corresponding to the asphalt mortar layer in the second mesoscopic model. Among them, the preset thickness of the asphalt mortar layer is m voxels, and the condition that meets the preset conditions means that the distance between the target voxel and the adjacent voxels with a voxel value of 0 is less than or equal to m voxels, and m is a positive integer.

[0092] In an optional implementation manner, the step S40 includes:

[0093] Step (1): Set the thickness of the asphalt mortar layer to be m voxels.

[0094] Step (2): Expand the vertex coordinates of each coarse aggregate in the first mesoscopic model outward by a distance of m voxels to obtain an intermediate mesoscopic model.

[0095] Step (3): Relabel the voxel values of all candidate voxels with a voxel value of 1 in the intermediate mesoscopic model. When the number of intersection points of a ray emitted from the center point of a candidate voxel along the positive z-axis direction and the triangular patches on the surface of the coarse aggregate is odd, the candidate voxel is taken as a target voxel meeting the preset conditions, and the voxel value of the target voxel is changed from 1 to 2; when the number of intersection points of a ray emitted from the center point of a candidate voxel along the positive z-axis direction and the triangular patches on the surface of the coarse aggregate is even, the voxel value of the candidate voxel remains 1 unchanged. Among them, the voxels with a voxel value of 2 correspond to the asphalt mortar layer.

[0096] In another alternative embodiment, the step S40 includes:

[0097] Step (1): Set the thickness of the asphalt mortar layer to m voxels.

[0098] Step (2): Traverse each first voxel with a voxel value of 0, and obtain the voxel values of the second voxels whose distances from each first voxel are less than or equal to m voxels. When the voxel value of the second voxel is 1, the second voxel is taken as a target voxel, and the voxel value of the target voxel is changed from 1 to 2; when the voxel value of the second voxel is 0, the voxel value of the second voxel remains 0 unchanged. Among them, the voxels with a voxel value of 2 correspond to the asphalt mortar layer.

[0099] It should be noted that the distance between the first voxel and the second voxel refers to the distance between the center point of the first voxel and the center point of the second voxel.

[0100] For easy understanding, an example is given. Assume m = 2, then obtain the voxel values of the second voxels whose distances from the first voxel are 1 voxel or 2 voxels. If the voxel value of the second voxel is 1, it means that in the first mesoscopic model, this voxel represents a void, and then the voxel value is changed to 2. At this time, this voxel represents the mortar layer; if the voxel value of the second voxel is 0, it means that in the first mesoscopic model, this voxel represents the coarse aggregate, and the voxel value remains unchanged, that is, this voxel still represents the coarse aggregate.

[0101] Step S50: Write the voxel information of the second mesoscopic model into a.py file through MATLAB programming, and import it into the ABAQUS finite element software for three-dimensional modeling and mesh generation. Delete the meshes corresponding to the voids, and construct the porous asphalt concrete finite element model.

[0102] In the present invention, each voxel information includes the spatial coordinates and voxel value of the voxel.

[0103] This step includes:

[0104] Step (1): Open the ABAQUS finite element software, run the imported.py file, and obtain a finite element model with meshing completed. The finite element model includes coarse aggregates, asphalt mortar, and voids.

[0105] Specifically, start the ABAQUS / CAE interface, import the.py file through the Python script interface, run the.py file, visually check the imported model geometry in the Viewport window, confirm the correct identification of the coarse aggregate and asphalt mortar parts in the model, and check the quality of the element division. Use the Assembly module to create a model instance to ensure the correct model position.

[0106] Step (2): Convert the finite element model to mesh display and convert all meshes into isolated meshes for convenient editing.

[0107] Step (3): Retain the meshes corresponding to the coarse aggregates and asphalt mortar, and delete all other meshes corresponding to the voids to obtain the finite element model of the porous asphalt concrete.

[0108] Please refer to Figure 2 and Figure 3 , where Figure 2 is the finite element model diagram of the porous asphalt concrete constructed by the present invention, Figure 2 Figure (a) is a three-dimensional diagram of the finite element model of the porous asphalt concrete, Figure 2 Figure (b) is Figure 2 an enlarged view of part A shown in Figure (a); Figure 3 is the internal aggregate distribution diagram of the finite element model of the porous asphalt concrete, Figure 3 201 in Figure 3 represents the coarse aggregate, and 202 in

[0109] Please refer to Figure 4 , according to the second aspect of the present invention, the present invention provides a device for constructing a finite element model of porous asphalt concrete. The construction device 100 includes:

[0110] The first construction module 101 is used to construct a three-dimensional aggregate database, and the three-dimensional aggregate database includes a plurality of coarse aggregate geometric models with different particle sizes.

[0111] The generation module 102 is used to generate a virtual space, put the coarse aggregate geometric models in the three-dimensional aggregate database into the virtual space, generate an aggregate packing three-dimensional discrete element model, and export the aggregate packing three-dimensional discrete element model in multiple STL files, and each STL file also stores the spatial coordinate information of the coarse aggregate geometric model.

[0112] The model conversion module 103 is used to import the multiple STL files into MATLAB software, and convert the three-dimensional discrete element model of aggregate accumulation into a first mesoscopic model by using the MATLAB software. The first mesoscopic model is composed of N voxels, and the voxel value of each voxel is 0 or 1. The sum of the volumes of the N voxels is the same as the volume of the virtual space. Among them, the voxels corresponding to the coarse aggregate are marked as 0, and the voxels corresponding to the voids are marked as 1, where N is a positive integer.

[0113] The second construction module 104 is used to construct a second mesoscopic model including asphalt mortar and coarse aggregate based on the first mesoscopic model and the preset thickness of the asphalt mortar layer. The target voxels with a voxel value of 1 and meeting the preset conditions in the first mesoscopic model are marked as voxel values 2 corresponding to the asphalt mortar layer in the second mesoscopic model. Among them, the preset thickness of the asphalt mortar layer is m voxels, and the meeting the preset conditions means that the distance between the target voxel and the adjacent voxel with a voxel value of 0 is less than or equal to m voxels, where m is a positive integer.

[0114] The third construction module 105 is used to write the voxel information of the second mesoscopic model into a.py file through MATLAB programming, import it into ABAQUS finite element software for three-dimensional modeling and mesh generation, delete the meshes corresponding to the voids, and construct the porous asphalt concrete finite element model.

[0115] Those skilled in the art can clearly understand that for the convenience and brevity of description, the working process of the above-described construction device can refer to the content in the foregoing method embodiment and will not be elaborated herein.

[0116] According to the third aspect of the present invention, the present invention provides a method for calculating the effective thermal conductivity by using the porous asphalt concrete finite element model constructed by the above-described construction method. The method includes the following steps:

[0117] Step (1): Import the porous asphalt concrete finite element model into ABAQUS analysis software, select the element type and set the material parameters and boundary conditions, and then use the software for simulation to obtain the node temperature and heat flux.

[0118] Among them, the element type is selected as the heat conduction type, the material parameters include density, thermal conductivity and specific heat capacity, and the setting of the boundary conditions includes: adopting a steady-state analysis; setting different temperatures at the upper and lower boundaries of the model to form a temperature gradient; and defaulting other boundaries to the heat insulation condition.

[0119] In an optional implementation manner, the material parameters are data obtained based on experiments, so that the accuracy of the model calculation results can be further improved and the model error can be effectively reduced.

[0120] Step (2): Calculate the equivalent thermal conductivity based on the calculation formulas of heat flux and equivalent thermal conductivity.

[0121] In the present invention, the calculation formula of the equivalent thermal conductivity is:

[0122]

[0123] where, Q is the heat flux, L is the thickness of the specimen, A is the heat transfer area, ∆T is the temperature difference between the upper and lower ends of the model.

[0124] According to the fourth aspect of the present invention, the present invention provides a method for analyzing the pavement field temperature using the porous asphalt concrete finite element model constructed by the above-described construction method. The method includes: importing the porous asphalt concrete finite element model into the ABAQUS analysis software, setting material parameters and boundary conditions, and then performing simulation using the software to obtain the pavement field temperature field distribution and heat flux.

[0125] Among them, the material parameters include density, thermal conductivity, and specific heat capacity. The setting of the boundary conditions includes: adopting transient analysis; defining the initial temperature field; setting temperature, solar radiation, and wind speed on the surface of the model.

[0126] In an optional implementation manner, the material parameters are data obtained based on experiments, so that the accuracy of the model calculation results can be further improved, and the model error can be effectively reduced.

[0127] The present invention greatly improves the efficiency of obtaining thermal performance data and reduces the test cost and time consumption by constructing a finite element model to calculate the effective thermal conductivity and performing pavement field temperature analysis. At the same time, the present invention can generate thermal performance simulation data of porous concrete under different temperature conditions, providing efficient and accurate technical support for material design and engineering applications.

[0128] It can be understood that the porous asphalt concrete finite element model construction method and the thermal performance evaluation method provided by the present invention have strong generality and adaptability, and can also be extended to the thermal performance research of other porous composite materials.

[0129] The above content is a further detailed description of the present invention in combination with specific preferred implementation manners. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, several simple deductions and substitutions can be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A method for constructing a finite element model of porous asphalt concrete, wherein the porous asphalt concrete is composed of asphalt mortar and coarse aggregate, characterized in that: The construction method comprises the following steps: Step S10, constructing a three-dimensional aggregate database, wherein the three-dimensional aggregate database includes a plurality of coarse aggregate geometric models with different particle sizes; Step S20, generating a virtual space, putting the coarse aggregate geometric model in the three-dimensional aggregate database into the virtual space, generating a three-dimensional discrete element model of aggregate accumulation, and exporting the three-dimensional discrete element model of aggregate accumulation as a plurality of STL files, wherein each STL file also stores the spatial coordinate information of the coarse aggregate geometric model; Step S30, importing a plurality of STL files into MATLAB software, and using the MATLAB software to convert the aggregate stacking three-dimensional discrete element model into a first mesoscopic model, wherein the first mesoscopic model is composed of N voxels, and the voxel value of each voxel is 0 or 1, and the sum of the volumes of the N voxels is the same as the volume of the virtual space, wherein the voxel with a voxel value of 0 corresponds to the coarse aggregate, the voxel with a voxel value of 1 corresponds to the void, and N is a positive integer; Step S40: Based on the first mesoscopic model and the preset thickness of the asphalt mortar layer, a second mesoscopic model including asphalt mortar and coarse aggregate is constructed, and the target voxel with a voxel value of 1 in the first mesoscopic model and meeting the preset conditions is marked as a voxel value 2 corresponding to the asphalt mortar layer in the second mesoscopic model, wherein the preset thickness of the asphalt mortar layer is m voxels, and meeting the preset conditions means that the distance between the target voxel and the adjacent voxel with a voxel value of 0 is less than or equal to m voxels, and m is a positive integer; Step S50, write each voxel information of the second mesoscopic model into a .py file through MATLAB programming, and import it into ABAQUS finite element software for three-dimensional modeling and meshing, delete the meshes corresponding to the gaps, and construct the porous asphalt concrete finite element model.

2. The method for constructing a porous asphalt concrete finite element model according to claim 1, characterized in that: The step S10 comprises: Step 1, obtaining a plurality of coarse aggregates with different particle sizes, and obtaining a two-dimensional projection image of each of the coarse aggregates based on the AIMS system; Step 2: Generate multiple three-dimensional point cloud data corresponding to the two-dimensional projection image of each coarse aggregate based on the trained CGAN model; Step 3: Based on the multiple three-dimensional point cloud data generated in step 2, a three-dimensional aggregate database is constructed, wherein the three-dimensional aggregate database includes multiple coarse aggregate geometric models with different particle sizes corresponding to the multiple three-dimensional point cloud data.

3. The method for constructing a porous asphalt concrete finite element model according to claim 2, characterized in that: The training methods of the CGAN model include: Get multiple training sets; The AIMS system is used to obtain a two-dimensional projection image of each aggregate; Use a laser scanner to obtain three-dimensional aggregate contour point cloud data of each aggregate; Acquire a training set, wherein the training set includes a plurality of data pairs, each data pair including a two-dimensional projection image and three-dimensional aggregate contour point cloud data of the same aggregate; The CGAN model is trained using the training set. When the evaluation index is less than a preset value, the training is completed to obtain a trained CGAN model, wherein the evaluation index includes a FID index and a CD index.

4. The method for constructing a porous asphalt concrete finite element model according to claim 1, characterized in that: The step S20 comprises: Step (1), generating a virtual space based on preset dimension data; Step (2), based on the volume of the virtual space and the preset mix ratio information of the porous concrete, obtaining the volume fractions of multiple grades of coarse aggregate, wherein different grades of coarse aggregate have different particle size ranges; Step (3), based on a preset placement rule, according to the volume fraction of the multi-level coarse aggregate determined in step (2), the coarse aggregate geometric model in the three-dimensional aggregate database is placed into the virtual space to generate a three-dimensional discrete element model of aggregate accumulation; Step (4), exporting each coarse aggregate geometric model of the aggregate stacking three-dimensional discrete element model as an STL file, and each STL file also stores the spatial coordinate information of the coarse aggregate geometric model.

5. The method for constructing a porous asphalt concrete finite element model according to claim 1, characterized in that: The step S30 comprises: Step a, import multiple STL files into MATLAB software; Step b, based on a preset grid size, the virtual space of the three-dimensional discrete element model of aggregate accumulation is divided into N voxels through MATLAB programming, and the voxel value of each voxel is set to an initialization value of 1, wherein a voxel value of 1 represents a gap; Step c, based on each of the STL files, read the triangular face information and spatial coordinate information of each coarse aggregate, and determine the voxel value of each voxel respectively. When the number of intersections between a ray emitted by the center point of the voxel along the positive direction of the z-axis and the triangular facets on the surface of the coarse aggregate is an odd number, the voxel value of the voxel is changed from an initial value of 1 to 0; when the number of intersections between a ray emitted by the center point of the voxel along the positive direction of the z-axis and the triangular facets on the surface of the coarse aggregate is an even number, the voxel value of the voxel is kept unchanged at 1, wherein the voxel with a voxel value of 0 corresponds to the coarse aggregate, and the voxel with a voxel value of 1 corresponds to the gap.

6. The method for constructing a porous asphalt concrete finite element model according to any one of claims 1 to 5, characterized in that: The step S40 comprises: Step (1), setting the thickness of the asphalt mortar layer to m voxels; Step (2), expanding the vertex coordinates of each coarse aggregate in the first mesoscopic model outward by a distance of m voxels to obtain an intermediate mesoscopic model; Step (3), re-marking the voxel values ​​of all candidate voxels whose voxel values ​​of the intermediate mesoscopic model are 1, when the number of intersections between a ray emitted from the center point of the candidate voxel along the positive direction of the z-axis and the triangular facets on the surface of the coarse aggregate is an odd number, the candidate voxel is used as a target voxel that meets the preset conditions, and the voxel value of the target voxel is changed from 1 to 2; when the number of intersections between a ray emitted from the center point of the candidate voxel along the positive direction of the z-axis and the triangular facets on the surface of the coarse aggregate is an even number, the voxel value of the candidate voxel is kept unchanged at 1, wherein the voxel with a voxel value of 2 corresponds to the asphalt mortar layer.

7. The method for constructing a porous asphalt concrete finite element model according to any one of claims 1 to 5, characterized in that: The step S40 comprises: Step (1), setting the thickness of the asphalt mortar layer to m voxels; Step (2), traverse each first voxel whose voxel value is 0, and obtain the voxel value of the second voxel whose distance to each first voxel is less than or equal to m voxels, when the voxel value of the second voxel is 1, take the second voxel as the target voxel, and change the voxel value of the target voxel from 1 to 2; when the voxel value of the second voxel is 0, keep the voxel value of the second voxel unchanged to 0, wherein the voxel with a voxel value of 2 corresponds to the asphalt mortar layer.

8. A device for constructing a finite element model of porous asphalt concrete, characterized in that: The construction device comprises: A first construction module is used to construct a three-dimensional aggregate database, wherein the three-dimensional aggregate database includes a plurality of coarse aggregate geometric models with different particle sizes; A generation module is used to generate a virtual space, put the coarse aggregate geometric model in the three-dimensional aggregate database into the virtual space, generate a three-dimensional discrete element model of aggregate accumulation, and export the three-dimensional discrete element model of aggregate accumulation as multiple STL files, and each STL file also stores the spatial coordinate information of the coarse aggregate geometric model; A model conversion module, used to import the multiple STL files into MATLAB software, and use the MATLAB software to convert the aggregate stacking three-dimensional discrete element model into a first mesoscopic model, wherein the first mesoscopic model is composed of N voxels, and the voxel value of each voxel is 0 or 1, and the sum of the volumes of the N voxels is the same as the volume of the virtual space, wherein the voxel with a voxel value of 0 corresponds to the coarse aggregate, the voxel with a voxel value of 1 corresponds to the void, and N is a positive integer; A second construction module is used to construct a second mesoscopic model including asphalt mortar and coarse aggregate based on the first mesoscopic model and the preset thickness of the asphalt mortar layer, wherein the target voxel with a voxel value of 1 in the first mesoscopic model and meeting the preset condition is marked as a voxel value of 2 corresponding to the asphalt mortar layer in the second mesoscopic model, wherein the preset thickness of the asphalt mortar layer is m voxels, and meeting the preset condition means that the distance between the target voxel and the adjacent voxel with a voxel value of 0 is less than or equal to m voxels, where m is a positive integer; The third construction module is used to write each voxel information of the second microscopic model into a .py file through MATLAB programming, and import it into the ABAQUS finite element software for three-dimensional modeling and meshing, delete the meshes corresponding to the gaps, and construct the porous asphalt concrete finite element model.

9. A method for calculating effective thermal conductivity using a porous asphalt concrete finite element model constructed by the construction method according to any one of claims 1 to 7, characterized in that: The method comprises the following steps: Step (1), importing the porous asphalt concrete finite element model into ABAQUS analysis software, selecting the unit type and setting the material parameters and boundary conditions, and then using the software to perform simulation to obtain the node temperature and heat flux, wherein the unit type selects the heat conduction type, the material parameters include density, thermal conductivity and specific heat capacity, and the boundary conditions are set including: using steady-state analysis; setting different temperatures at the upper and lower boundaries of the model to form a temperature gradient; and other boundaries are set to insulation conditions by default; Step (2): Based on the calculation formula of heat flux and equivalent thermal conductivity, the equivalent thermal conductivity is calculated.

10. A method for analyzing the pavement field temperature using a porous asphalt concrete finite element model constructed by the construction method according to any one of claims 1 to 7, characterized in that: The method includes: importing the porous asphalt concrete finite element model into ABAQUS analysis software, setting material parameters and boundary conditions, and then using the software to perform simulation to obtain the pavement temperature field distribution and heat flux, wherein the material parameters include density, thermal conductivity and specific heat capacity, and the setting of the boundary conditions includes: using transient analysis; defining the initial temperature field; and setting the temperature, solar radiation and wind speed on the surface of the model.

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