5.1.2. Dataset

The dataset used for this work was extracted from nine different samples of permeable pavement. The sample image was scanned using a CT machine with a voxel size of 88.194 μm. The size of one sample image after binary conversion to 8-bit resolution was 300<sup>3</sup> voxels. We resampled this image to 24,389 images with a size of 20<sup>3</sup> voxels. The size of this dataset was approximately 14.4 GB.

### *5.2. Experimental Results*

### 5.2.1. 3D Pavement Reconstruction

The reconstruction process started by defining some hyperparameters for the generator and discriminator networks. We set 10−<sup>4</sup> as the generator learning rate. Thus, it learns every 5 batches with batch normalization in all layers except the final layer. For the discriminator network, the learning rate is set to the same value as the generator network but it learns on each batch. The stochastic gradient descent using the Adam optimizer was used to perform the learning process, with momentum *β*1 = 0.5 and *β*2 = 0.9 for both networks.

We trained the network and calculated the loss for the discriminator network. The calculated loss is used to track the convergence and quality of generated objects, depicted in Figure 9. The first plot on the left is the GAN discriminator loss, the second plot in the center is the calculated loss for the original 3D-IWGAN, while the third plot is that of the 3D-IWGAN (with enhanced gradient penalty) discriminator loss. From the plots, we can see that the discriminator loss of 3D-IWGAN (enhanced GP) has a bouncing value in the beginning but it has relatively stable values after 600 iterations. Meanwhile, the discriminator loss of GAN and original GAN increase until 1000 iterations. Although our result shows that this value does not converge to zero, it is more stable in comparison to other methods. The stability in GAN's loss is also important to prevent the collapse and failure modes. To check the accuracy of our model, we added the computation of physical properties to display the similarities between our generated 3D model and the real sample. The result of this computation is presented in Permeable Pavement Analysis, Section 5.2.2.

**Figure 9.** Discriminator loss comparison. The convergence and quality of generated objects are tracked by the calculated loss.

The result of the 3D reconstructed image using GAN is displayed in Figure 10a. Figure 10b illustrates the image generated using the original 3D-IWGAN, and the image generated using 3D-IWGAN (enhanced GP) is presented in Figure 10c. The images generated using the GAN method have more pores in comparison to those generated using the

original 3D-IWGAN and our 3D-IWGAN, while the images generated by the original IW-GAN have more solid phases in comparison to other methods. Among the three methods, the 3D-IWGAN (enhanced GP) shows more realistic images of the pavement microstructure.

**Figure 10.** Comparison of voxelized 3D Images. Images are reconstructed by GAN, 3D-IWGAN, and 3D-IWGAN (enhanced GP) methods.

We reconstructed the microstructure for nine different samples, whose results are presented in Figure 11.

<sup>(</sup>**a**) 3D-GAN

 (**b**) 3D-IWGAN

**Figure 11.** Comparison of generated 3D images.

### 5.2.2. Permeable Pavement Analysis

The final part of our system is pavement analysis. After obtaining the 3D image of the pavement microstructure, we attempted to analyze the physical properties of the generated images. We attempted to evaluate five properties: porosity, permeability, hydraulic conductivity, specific surface area, and Euler characteristic.

In porous media such as permeable pavement, flow properties can be related to porosity, which is required to determine other properties such as permeability and hydraulic conductivity. Therefore, it needs to be estimated first. According to the ASTM standard, the porosity for permeable pavement is approximately 15–35% . Figure 12 shows the calculated porosity for the nine images generated using the IWGAN method. In comparison to the result of the previous GAN model, the proposed model shows better results for the values of porosity. The calculation results of the porosity from our generated 3D images

<sup>(</sup>**c**) 3D-IWGAN (enhanced GP)

shows that 66.67% of our samples are in the correct range of the standard value. Our method is better than the other methods, including none of the samples that fall within the appropriate range of standard values. The porosity values of the generated images from 3D-IWGAN (enhanced GP) illustrate a 66.67% improvement over the previous methods (3D-GAN and 3D-IWGAN).

**Figure 12.** Computed porosity of 9 different samples. Our proposed method shows the highest result for the value of porosity among other methods.

We also calculated other properties such as the specific surface area and Euler number. The specific surface area is used to define the adsorption and dissolution processes in porous media, while the Euler number is used to characterize the connectivity of porous media. This is an important factor that determines the ability of fluids to flow. A less negative Euler number indicates a reduction in pore network connectivity. The values of surface area and Euler number are presented in Table 5. According to the ASTM standard, permeable pavement has a value of surface area approximately in the range 5–15%. Our results demonstrate that all samples are in the correct range (5–15)% of the surface area.


**Table 5.** Computed surface area and Euler number of 9 samples.

After measuring the morphological values, we tackled the final part in our system: computing the permeability and hydraulic conductivity for each sample. The results of this computation can be used to determine the clogging potential of permeable pavement. The result for hydraulic conductivity is illustrated in Figure 13. It shows that the error difference in the nine different samples ranges between 1.9% and 5.6% or an average of approximately 3.54%.

**Figure 13.** Computed hydraulic conductivity. The errors range between 1.9% and 5.6% among nine different samples.

The results of pavement analysis demonstrate that the proposed 3D model yielded better values than the model generated using 3D-GAN and original 3D-IWGAN. From the nine different samples, the average error difference in hydraulic conductivity computation was found to be below 5%. Moreover, the values of physical properties extracted through the proposed 3D model using our GAN method are closer to the baseline (theory) values than other GAN methods.
