In order to accurately identify and quantitatively calculate the surface cracks of rock mass under SHPB impact loading, an automatic crack detection algorithm was proposed and evaluated by the experiment. In SHPB experiment, cracks on the rock surface can effectively reflect its current state and better analyze the damage process. Firstly, the SHPB system was used to impact 12 groups of rock specimens under different impact velocities. A high-frame camera with 50,000 FPS was used to capture the damage process of the rock mass; using the manual annotation method, we got a dataset of SHPB damage images including a total of 310 original images and 310 corresponding cracked annotations. Secondly, a deep convolution network model named CrackSHPB was designed based on a deep learning algorithm. The algorithm can automatically identify the crack on the rock surface during impact damage process and further provide a quantitative result of cracks, crack area. Finally, after the crack on the rock surface in each frame image was identified automatically through the model, cracks were quantitatively analyzed by the proposed algorithm, the growth rate of cracks was calculated, and their evolution law was concluded. The crack identification algorithm proposed in this paper can provide a more accurate quantitative method for rock damage by cracks on the rock surface, and evolution law can further explain the failure process of rock at high strain rate.
Split-Hopkinson pressure bar (SHPB), developed by Kolsky in 1950, is an experimental device that can effectively study the constitutive relations of materials and effectively analyze the dynamic mechanical properties of rock materials [
In recent years, with the development of microelectronics technology, high-frame camera technology has become popularized, and more and more researchers have adopted high-speed camera to record the entire process of rock failure. They studied the fracture characteristics of rock mass by the law of surface crack propagation. Zhao et al. [
However, the identification of surface cracks in rock mass is very challenging: (1) the gray value of a crack is very close to the gray value of the surface of the rock mass, which makes it very difficult for us to use the traditional method, which is based on threshold segmentation in traditional image processing algorithms for crack identification; (2) the surface of rock mass often contains a large amount of background noise, making the texture structure very complicated to analyze; (3) when the rock mass is damaged by impact, the crack morphology that is produced varies in topological structure, and it is very difficult to provide an exact definition of a crack.
In recent years, deep learning technology has made breakthrough progress in many fields [
The experimental system used the
Schematic diagram of the SHPB experimental system.
A picture of the test specimens is shown in Figure
Diagram of the rock specimens.
Destruction process images for rock specimen under SHPB impact damage.
As illustrated in Figure
In the study, RatSnake software was used to mark the cracks in the image at the pixel level, which was an efficient software for image annotation [
Labeling result for rock surface.
After labeling the image for the impact damage of each specimen, the recorded data need to be divided. In the experiment, 12 impact fracture experiments were performed on the same kind of rock samples, and 11 were successfully completed. In a traditional machine learning or deep learning application, the dataset usually splits into training dataset and testing dataset [
Dataset creation process.
Loss curve in training process for CrackSHPB model.
The detailed experimental steps are as follows. (1) Cut, polish, and process the collected test pieces into standard patterns. (2) Affix the strain gauges on the input and output rods and connect the highly dynamic strain gauges to the waveform recorders. (3) Fix the position of the rock specimens. Because the rock specimens are susceptible to slipping when subjected to an SHPB impact; it is necessary to evenly apply Vaseline to the contact portion of the SHBP rod and the rock specimens before the experiment. (4) Connect the trigger to the speed test system and the video acquisition system. (5) Adjust the power system and perform the first impact damage. When the destruction is complete, check the data in the waveform recorder and video acquisition system. (6) According to the previous steps, the impact destruction experiment is performed in sequence and the impact velocity of the bullet changes with the different impact volume of the bullet. The experimental process was repeated several times.
As shown in Figure
Incident, transmitted, and reflected wave signals of bxy1 to bxy6.
As illustrated in the Figure
Image result after nonlocal mean filtering.
The overall structure of CrackSHPB designed in this paper is shown in Figure
CrackSHPB model and crack identification flow chart.
The largest part of CrackSHPB is the convolution kernel. The convolution operation is a kind of local operation, which can effectively extract various local information of a two-dimensional image [
The activation function is mainly used to increase the nonlinear expression capability of CrackSHPB. Since the linear layer is added after the linear mapping, it cannot be fitted to a higher-order function. Therefore, the activation function layer is sometimes referred to as a nonlinear mapping layer. The traditional activation function uses
The main role of the loss function is to address the case in which the forecast output of the sample training output deviates from the actual result [
In the design of the CrackSHPB model, the cross-entropy loss function is chosen (cross-entropy) [
After the objective function has been designed, the optimization method must be chosen for solving the above equations. Because the definition of the damage function in the deep learning network is very complicated and there is no analytical solution to the optimization problem, we must find the optimal solution using numerical analysis methods. The stochastic gradient descent (SGD) is a simple but very effective method. For a traditional optimization problem, it can quickly find the minimum value of the function. In addition, SGD has been successfully applied to large-scale and sparse machine learning problems often encountered in text categorization and image classification [
After designing the structure of the model, the training data that were prepared in the first step are input into the model for training. When evaluating the CrackSHPB model, the value of
From Figure
As shown in Figure
Parameter visualization results.
In the field of artificial intelligence or machine learning, the confusion matrix [
Confusion matrix for crack identification.
Actual crack | Actual noncrack | |
---|---|---|
Predicted crack | TP | FP |
Predicted noncrack | FN | TN |
We can think of the identification of surface cracks in rock as the two-category problem of judging each pixel in the image, whether the current pixel belongs to a crack or not. Therefore, there are 4 different cases for each pixel: (1) this pixel belongs to a crack, and the test result is also a crack. The judgment result is true positive (TP); (2) this pixel belongs to a crack, but the detection result is noncrack. The judgment result is false negative (FN); (3) this pixel belongs to noncrack, and the detection result is also noncrack. The judgment result is true negative (TN); (4) this pixel belongs to noncrack, but the detection result is a crack. The judgment result is false positive (FP)
Among them,
In the experiment, there were 11 groups of sandstone specimens obtained for impact destruction video, and 3 sets (bxy1, bxy3, and bxy5) were used as training data to obtain the CrackSHPB model. Therefore, the remaining 8 sets of video images are used as test sets to verify the recognition effect of the CrackSHPB model. The detection results are shown in Table
The crack detection result of CrackSHPB model.
Number |
|
|
|
---|---|---|---|
bxy2 | 0.872 | 0.902 | 0.884 |
bxy4 | 0.966 | 0.845 | 0.900 |
bxy6 | 0.821 | 0.853 | 0.834 |
bxy7 | 0.907 | 0.872 | 0.888 |
bxy8 | 0.936 | 0.878 | 0.905 |
bxy9 | 0.912 | 0.863 | 0.887 |
bxy10 | 0.940 | 0.864 | 0.899 |
bxy11 | 0.808 | 0.913 | 0.853 |
AVG | 0.895 | 0.874 | 0.881 |
Due to space limitations, a set of SHPB impact video recognition results at different stages are given. As shown in Figure
Example of crack identification results.
To visually demonstrate the effect of identifying cracks by CrackSHPB, some identification images with the quantized result in pixel-level are presented in Figure
Besides the above evaluation index, we also compute the area under the receiver operating characteristic curve (ROC AUC). ROC curve is a commonly used graph that summarizes the performance of a classifier overall possible thresholds. For a ROC curve, the closer it is to the upper left corner, that is, the closer the AUC value is to 1, the better the classifier is [
As shown in Figure
ROC curves of BCM crack detection results.
After cracks are identified and quantified, and it is possible to accurately analyze the rate of increase of cracks in rock specimens when subjected to impact damage. Figure
Crack quantitative results for BCM5.
From Figure
Crack quantitative results.
Number | Impact velocity (m/s) | Captured frames (frame) | Started crack frame (frame) | Crack propagation rate (pixels/frame) |
|
---|---|---|---|---|---|
bxy1 | 4.687 | 26 | 6 | 299.50 | 0.98 |
bxy2 | 5.150 | 26 | 11 | 332.30 | 0.99 |
bxy3 | 4.443 | 23 | 11 | 417.29 | 0.96 |
bxy4 | 4.385 | 23 | 10 | 348.49 | 0.99 |
bxy5 | 3.377 | 27 | 15 | 209.85 | 0.99 |
bxy6 | 3.167 | 82 | 47 | 59.75 | 0.94 |
bxy7 | 3.511 | 19 | 6 | 295.40 | 0.99 |
bxy8 | 3.246 | 32 | 21 | 370.22 | 0.99 |
bxy9 | 3.869 | 20 | 8 | 423.64 | 0.99 |
bxy10 | 4.307 | 16 | 6 | 371.42 | 0.98 |
bxy11 | 5.502 | 16 | 11 | 676.14 | 0.99 |
In the process of impact failure, with the increase of strain, cracks appear at the center of the disc when its maximum stress value reaches the tensile strength of the rock mass. As the strain of the test piece continues to increase, the crack in the center of the test piece continues to expand in the axial direction and the main crack develops. Before the main crack penetrated, secondary cracks began to appear at both ends of the test piece due to the compressive and shear stresses acting on the contact part between the test piece and the rod. The secondary crack propagates along the two ends of the test piece to the inside, and finally breaks through with the main crack to form a broken surface, leading to complete destruction of the test piece. And the image of the crack penetrating and the image after impact damage are shown in the Figures
Images of the crack penetrating.
Image after impact damage.
In this paper, we set a SHPB experiment test system with high-frame-rate camera, and 12 groups of rock specimens was damaged under different impact velocities and the damage process video of the rock mass was captured by the camera. Then, we proposed a CrackSHPB model to detect cracks on rock surface based on deep learning. Finally, we analyze the evolution law and damage process of rock at high strain rate. The following conclusions can be made through our experimental study: The CrackSHPB model, established based on the deep learning method, can effectively identify cracks on the surface of sandstone. Accuracies of 89.5%, 87.4%, and 88.1% were obtained in terms of Through the CrackSHPB model, the cracks on the surface of rock can be identified at the pixel level, and the accurate crack quantification result can be obtained by counting the pixels. When the sandstone specimen is damaged by impact, the crack growth rate of the sandstone specimen after crack initiation accords with the linear model. In the impact damage process, the main crack first appeared in the center of rock specimen and then expanded to the two ends with secondary cracks which randomly distributed.
Data used in this article are available through email from the corresponding author.
The authors declare that they have no conflicts of interest.
This research was supported by the National Natural Science Foundation of China (51404277 and 51274206). This support is greatly acknowledged and appreciated.