**6. Conclusions**

Although permeable pavement has been extensively used to allow rainwater to pass through the pores into the ground, to control water quality, and to reduce the surface temperature, it has some obstacles during utilization: obtaining samples, maintenance cost, and clogging issues.

To overcome above-mentioned problems, in this paper, we proposed a three-dimensional microstructure reconstruction framework for permeable pavement analysis as one of the virtual experiment solutions. Since we utilized the generative model of 3D-IWGAN with an enhanced gradient penalty, our framework can effectively generate 3D microstructure reconstruction from a single 2D image of permeable pavement. To the best of our knowledge,

3D-IWGAN has not been used for the 3D model reconstruction of permeable pavement materials. From the visualization of the generated 3D microstructure images from nine samples, we have observed that our framework generates realistic 3D images.

When analyzing the flow in porous media, it is crucial to improve the values of porosity. Incorrect values of porosity will affect the other physical properties of permeable pavements such as permeability and hydraulic conductivity. These two properties are also important to assess the quality of generated images that are later used for pore network analysis. We have demonstrated that our framework generates more realistic 3D microstructure images, maintaining the values of these physical properties within the range of the standard values. In particular, the porosity values of the generated 3D images from 3D-IWGAN with enhanced GP were improved by 66.67% compared to the previous methods (3D-GAN and 3D-IWGAN).

Our proposed 3D microstructure reconstruction framework can be extended in two directions. First, we can add an additional module that generates and analyzes the pore network to conduct comprehensive virtual experiments. Second, we can combine some empirical methods with our framework to increase the quality of the generative model and avoid random errors.

**Author Contributions:** L.E.F. wrote the original version of the paper and the study, collected datasets, and conducted the experiments. J.A. provided the datasets, analyzed the data, and wrote the paper. S.L. contributed to revising the paper. J.K. supervised the work, and wrote and revised the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was partly supported by an Institute of Information & communications Technology Planning & Evaluation (IITP) gran<sup>t</sup> funded by the Korean governmen<sup>t</sup> (MSIT) (No. 2020-0-00121, Development of data improvement and dataset correction technology based on data quality assessment), by the Institute of Information & Communications Technology Planning & Evaluation (IITP) gran<sup>t</sup> funded by the Korean governmen<sup>t</sup> (MSIT) (No.2019-0-01343, Regional strategic industry convergence security core talent training business) and by the Korea Agency for Infrastructure Technology Advancement (KAIA) gran<sup>t</sup> funded by the Ministry of Land, Infrastructure, and Transport (Grant 21CTAP-C152124-03).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** This work was partly supported by the Capacity Enhancement Program for Scientific and Cultural Exhibition Services through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2018X1A3A1069642) and by the National Research Foundation of Korea (NRF) gran<sup>t</sup> funded by the Korean governmen<sup>t</sup> (MSIT) (No. 2018R1A5A7059549).

**Conflicts of Interest:** The authors declare no conflict of interest.
