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Automatic crack detection is always a challenging task due to the influence of stains, shadows, complex texture, uneven illumination, blurring, and multiple scenes [2]. In the past decades, scholars have proposed a variety of image-based algorithms to automatically detect cracks on concrete surfaces and pavement. In the early studies, most of the methods are based on the combination or improvement of traditional digital image processing techniques (IPTs) [3], such as thresholding [4,5,6] and edge detection [7,8,9,10]. However, these methods are generally based on the significant assumption that the intensities of crack pixels are darker than the background and usually continuous, which makes these methods difficult to use effectively in the environment of complex background noise [11,12]. In order to improve the accuracy and integrity of crack detection, the methods based on wavelet transform [13,14] are proposed to lift the crack regions. However, due to the anisotropic characteristics of wavelets, they may not deal well with cracks with large curvatures or poor continuities [2].

In recent studies, several minimal path methods [15,16] have also been used for crack detection. Although these methods make use of crack features in a global view [3] and achieve good performance, their main limitation is that seed points for path tracking need to be set in advance [17], and the calculation cost is too high for practical application.

Unet [32], as a typical representative of semantic segmentation algorithm, has achieved great success in medical image segmentation. There are many similarities between pavement crack detection and medical image segmentation, so it is natural to apply Unet to pavement crack segmentation.

The patchwise detection method, which divides the original pavement images into many small patches, is adopted by more researchers due to its two advantages. First, more data can be generated, and second, the localization information of cracks can be obtained. Zhang et al. [39] proposed a six-layer CNN network with four convolutional layers and two fully connected layers and used their convolutional neural network to train 99 99 3 small patches, which were split from 3264 2248 road images collected by low-cost smartphones. The output of the network was the probability of whether a small patch was a crack or not. Their study shows that deep CNNs are superior to traditional machine learning techniques, such as SVM and boosting methods, in detecting pavement cracks. Pauly et al. [40] used a self-designed CNN model to study the relationship between network depth and network accuracy and proved the effectiveness of using a deeper network to improve detection accuracy in pavement crack detection based on computer vision. In contrast with [39], which used the same number of convolution kernels in all convolution layers, Nguyen et al. [41] used a convolution neural network with an increased number of convolution kernels in each layer because the features were more generic in the early layers and more original dataset specific in later layers [42]. Eisenbach et al. [43] presented the GAPs dataset, constructed a CNN network with eight convolution layers and three full connection layers, and analyzed the effectiveness of the state-of-the-art regularization techniques. However, its network input size was 64 64 pixels, which was too small to provide enough context information. The same problem also existed in [44,45,46].

Zhang et al. put forward CrackNet [52], which is an earlier study on pixel-level crack detection based on CNN. The prominent feature of CrackNet is using a CNN model without a pooling layer to retain the spatial resolution. Fei et al. have upgraded it to Cracknet-V [53]. While CrackNet and its series versions perform well, they are primarily used for 3D road crack images, and their performances on two-dimensional (2D) road crack images have not been validated. Fan et al. [3] proposed a pixel-level structured prediction method using CNN with full connections (FC) layers, but it has the disadvantage that it requires a long inference time for testing.

The CFD dataset, published in [23], consists of 118 RGB images with a resolution of 480 320 pixels. All of the images were taken using an iPhone5 smartphone on the road in Beijing, China, and can roughly reflect the existing urban road conditions in Beijing. These crack images have uneven illumination and contain noise such as shadows, oil spots, and lane lines, and most cracks in these images are thin cracks, which make crack detection difficult. We randomly divided 70% of the dataset (82 images) for training and 30% of the dataset (36 images) for testing.

The Crack500 dataset, shared by Yang et al. in the literature [60], contains 500 original images with a resolution of 2560 1440 collected at the main campus of Temple University. Each original image was cropped into a non-overlapping image area of 640 360, resulting in 1896 training images, 348 validation images, and 1123 test images. These images are characterized by low contrast between cracks and background, as well as noise such as oil pollution and occlusions, which increase the difficulty of detection.

The DeepCrack dataset [2] contains 537 crack images, including both concrete pavement and asphalt pavement, with complex background and various crack widths, ranging from 1 pixel to 180 pixels. We kept the same data split as the original paper, with 300 images for training and 237 images for testing.

Figure 3 shows the crack detection results of six typical input images of our method and the three methods to be compared. The first column is the original input crack image, the second column is the label image corresponding to the first column image, and the next four columns are the predicted output images of the four comparison algorithms. As can be seen from Figure 3, all these algorithms could detect the rough crack profile. However, in terms of details, all three algorithms, FCN, Unet, and SegNet, had false detection and missing cracks resulting in discontinuity of cracks to a varying degree. Our algorithm was obviously better than the three algorithms, with the least false detection and missing cracks, and the closest to the ground truth.

The work address the calculation of head loss of Non-Darcian flow in flexural cracks with different shapes to predict the energy loss. Laboratory set-up is established to do the experiment and authors indicate that these results are validated using CFD. The topic and the methodology could be interesting for the reader, but several aspects must be clarified and improved. The paper has very important scientific and methodological shortcomings and it must be rewritten.

The local head loss was closely related to flow velocity and fracture shape and can be represented as. The relationship between the local head loss coefficient ζ (θ) and the crack shape θ can be effectively summarized with the logistic function, shown in equation (13).

The friction resistance loss from the local resistance loss could be separated by the head loss calculation of network cracks. The calculation process of local head loss can be optimized by the fast calculation model composed of logistic function.

CFD models of flexural crack with different angles to compute the energy loss as well as comparison was presented. Overall the manuscript contains a well thought out. The conclusion is well explained by the presented results. I have comments below that should be addressed:

This study proposed a fast calculation model that the aperture and the shape of flexural crack are considered to predict local head loss directly. The fracture fluid represented characteristics of non-Darcian flow that could be depicted by the Forchheimer equation when the flow velocity was sufficiently large in a physical experiment on the single fracture using fracture apertures e of 0.77, 1.18, 1.97, and 2.73 mm (R2 > 0.99). Following the formulation of a numerical model from computational fluid dynamics (CFD) which is to verify the calculation of single fractures, a CFD model of flexural crack with different angles were built to compute the energy loss of each, which can verify the physical experiment results very well (Pearson correlation coefficient >0.99). After eliminating the influence of crack width, it is found that the local head loss of the flexural crack varied with the bending angle, and its coefficient was expressed by the deformation of the logistic equation. Therefore, we established a fast calculation model with fracture angle and velocity as variables. By using this model, as well as a frictional head loss equation fitted by the Forchheimer equation (R2 > 0.99), the head loss of crossed fissures with fixed fracture aperture could be easily calculated. 2ff7e9595c