Deep learning-based key-block classification framework for discontinuous rock slopes

Honghu Zhu, Mohammad Azarafza, Haluk Akgün

a School of Earth Sciences and Engineering, Nanjing University, Nanjing, 210023, China

b Department of Civil Engineering, Tabriz University, Tabriz, 5166616471, Iran

c Department of Geological Engineering, Middle East Technical University, Ankara, 06800, Turkey

Keywords:Block theory Discontinuous rock slope Deep learning Convolutional neural network Image-based classification

ABSTRACT The key-blocks are the main reason accounting for structural failure in discontinuous rock slopes, and automated identification of these block types is critical for evaluating the stability conditions.This paper presents a classification framework to categorize rock blocks based on the principles of block theory.The deep convolutional neural network (CNN) procedure was utilized to analyze a total of 1240 highresolution images from 130 slope masses at the South Pars Special Zone, Assalouyeh, Southwest Iran.Based on Goodman’s theory, a recognition system has been implemented to classify three types of rock blocks, namely, key blocks, trapped blocks, and stable blocks. The proposed prediction model has been validated with the loss function, root mean square error (RMSE), and mean square error (MSE). As a justification of the model, the support vector machine (SVM), random forest (RF), Gaussian na?ve Bayes(GNB), multilayer perceptron (MLP), Bernoulli na?ve Bayes (BNB), and decision tree (DT) classifiers have been used to evaluate the accuracy, precision, recall, F1-score, and confusion matrix. Accuracy and precision of the proposed model are 0.95 and 0.93, respectively, in comparison with SVM(accuracy = 0.85, precision = 0.85), RF (accuracy = 0.71, precision = 0.71), GNB (accuracy = 0.75,precision=0.65),MLP(accuracy=0.88,precision=0.9),BNB(accuracy=0.75,precision=0.69),and DT(accuracy = 0.85, precision = 0.76). In addition, the proposed model reduced the loss function to less than 0.3 and the RMSE and MSE to less than 0.2,which demonstrated a low error rate during processing.

1. Introduction

A rock slope with a discontinuity network is different from intact rock in that it significantly affects the slope stability condition(Hungr et al.,2014;Azarafza et al.,2017a;Wang et al.,2020a,b,c; Huang et al., 2021). According to Goodman (1989), the discontinuity network imposes several features on rock masses, such as nonlinear behaviors at low stresses, reduction of the tensile strength,anisotropy effects,increase in permeability,and limitation of the shear strength on the boundary between discontinuity faces and rock blocks.These features provide a specific condition on the mechanical behaviors of the rock masses and failure regarding various mechanisms (Wang et al., 2020a, b, c; Chen et al., 2020).Hudson and Harrison (1997) pointed out that the discontinuity network is mainly responsible for structural instabilities in rock masses and affects the engineering properties of rocks. Hence,understanding the geometric properties of discontinuities and their effects on rock blocks is essential for stability analyses of rock masses (Jing, 2000). In general, the discontinuities in the rock masses reduce the strength and stiffness, which are considered as non-ideal conditions. Uniaxial compressive tests of the intact rock may give an indicator of its mechanical parameters, such as strength and stiffness;however,it is not valid for the case of a rock mass in presence of discontinuities.Herein,the rock masses lead to critical conditions regarding the failure mode of rock slopes.Therefore,understanding the discontinuity network of rock slopes is key to stability assessments (Vutukuri and Katsuyama,1994).

Goodman and Shi (1985) presented a quantified methodology based on geometric properties of a discontinuity network in rock masses to characterize rock masses and estimate the stability of rock masses, named “block theory” (referred to as Goodman’s theory or the key-block analysis method). The process traces the discontinuity properties and rock block durability to assess stability conditions at the surface or in underground geotechnical structures(Wang et al., 2018). Goodman and his colleagues utilized the limit equilibrium method to investigate rock block instability by graphical (i.e.based on stereographic projection) as well as analytical approaches (i.e.based on the vector method) (Azarafza et al.,2017b). In the block theory, the rock blocks generated by discontinuity intersections in the rock body may be categorized as finite and infinite blocks. Fig. 1 presents block classification in rock masses. The finite blocks, which can be classified as key-blocks,potential key-blocks, trapped blocks, or stable blocks, are responsible for structural failures in the rock masses triggered by critical rock blocks,known as key-blocks(Azarafza et al.,2020a).Over the past few decades,the applications of block theory have significantly increased in rock engineering (Turanboy, 2010; Kulatilake et al.,2011; Wang and Ni, 2014; Wang et al., 2018; Zhang et al., 2020;Azarafza et al., 2020b).

Applications of the key-block theory to slope stability analysis have advanced more rapidly than that applied to underground studies due to the flexibility of the method for various modes of kinematic slope failure (Wang et al., 2017). The main aim of block theory is to geometrically analyze different rock block types generated by the discontinuity network in discontinuous rock slopes under the assumption that the key-blocks are subjected to gravitational loads. The loads are primarily the result of the selfweight of each key-block along with support forces, water pressures,seismic forces,etc.(Jiang and Zhou,2017;Fu et al.,2019).The block theory identifies key blocks by considering the sliding and falling direction and the direction of the resultant driving force.The limit equilibrium approach allows a stability assessment of those results in the key blocks (Goodman,1995).

Fig. 1. Block classification in a rock slope based on the block theory (adapted from Kulatilake et al., 2011).

It is well known that discontinuous rock slopes generally involve three-dimensional (3D) failures. The spatial emplacement of rock blocks and their shapes,orientation,and types are dictated by discontinuity networks that specify the blocks’ geometric positions in slope masses. Goodman (1995) stated that the movement of blocks along the gapping geometric direction is based on the resisting and driving forces on the discontinuity surface.The block theory uses the ‘finiteness’ and ‘removability’ theorems to analyze spatial geometry and defines line and plane equations/inequalities in space (discontinuities), which can easily convert the recorded information from polar coordinates (dip/dip direction of discontinuities) to Cartesian coordinates. The block removability(described as failure) is defined based on the convex polyhedral geometry convergence in slope masses. The finiteness theorem used to calculate the joint pyramid, JP (the common spaces between half-spaces of discontinuity planes that form part of the block pyramid), the excavation pyramid, EP (a group of extraction half-spaces that are displaced to form a block pyramid), the space pyramid, SP (complementary half-space of excavation pyramid)and the block pyramid,BP(the factor for determining the convexity and concavity of blocks), which is utilized for the mathematical definition for block geometry and stability analyses (Azarafza and Zhu, 2022). Applications of these parameters lead to quantifying the discontinuity network and rock block geometry in space and are used for slope stability analysis (Goodman and Shi,1985).

There has been a rapid development in applications of artificial intelligence and machine learning technologies to rock engineering and slope stability problems (Chen et al., 2021). In addition, applications of deep-learning techniques, such as deep neural networks, to extract rock structure information and categorize relevant data with high accuracy have received vast attentions(Wang et al., 2020a, b, c; Robson et al., 2020). Using such procedures to identify the failure mechanism, characteristics of slope masses, and discontinuity network properties has improved the efficiency, accuracy, and consistency of geoengineering analyses(Chen et al.,2021).This study used the deep learning technique to explore the structural mechanisms in discontinuous rock slopes to identify the key blocks that trigger slope failures. In this regard,deep neural networks have been used to classify rock blocks and extract the key blocks based on the principles of Goodman’s block theory.

2. Background

Deep learning is a sub-branch of machine learning that utilizes structured artificial neural networks (ANNs) with representative learning (i.e.supervised, semi-supervised or unsupervised) for extraction of the relevant features (LeCun et al., 2015). These extracted features can be used for classification or prediction with high accuracy. Deep learning architectures are categorized as several deep neural networks which are applied based on the aim and scales of the tasks, such as computer vision, pattern recognition, and deep classification (Hearty, 2016). The adjective‘deep’ in‘deep learning’ refers to as multiple layers in the ANN network(Aggarwal,2018).Convolutional neural networks(CNNs)are a class of deep neural networks that are commonly applied to analyze visual imagery (He et al., 2016; Gu et al., 2018). A CNN network consists of an input, hidden, output, and other deep neural networks where CNN’s hidden layers include layers that perform convolutions. In the CNN, the input data are evaluated by convolution, pooling, batch normalization, dense, dropout, and fully connected layers to predict the outputs. These layers can be increased based on learning depth to achieve high accuracy in assessments (Aggarwal, 2018). The input data provide the first layer of evaluation as a data matrix in which each element has a specific feature value. Hence, the input layer is the primary feature map modified and organized by each convolutional layer and unit.These units extract different features from the input data. The first convolutional layer extracts some low-level features (e.g. lines, edges and corners).

Further convolutional layers iteratively learn more intricate representations or features. Pooling is a critical manipulation in CNNs,and max-pooling is the most common manipulation among different pooling approaches. Max-pooling aims to divide feature maps into several rectangular zones and provide the maximum value for each zone(Wang et al.,2019).Batch normalization,which seeks to increase the network’s speed,performance,and stability,is used to normalize the input layer by re-centering and re-scaling.The dense or regular densely connected layer is commonly used as a linear/nonlinear layer applied to the input and returned to the output.Fully connected layers connect every neuron in a preceding layer to every neuron in a subsequent layer (Aggarwal, 2018).Combining these layers in a sequence can extract the desired features and thereby classify the input data into the selected classes(Hearty, 2016).

In the block theory, key blocks are responsible for progressive slope failures regardless of the type of failure mechanism(Liu et al.,2017). Identification of these blocks can help provide efficient and accurate stability assessment and conduct rapid stabilization measures (Zhang et al., 2020). In addition, the key-block stabilization could deactivate progressive failures in discontinuous rock slopes, resulting in fewer support requirements. The study presented herein attempts to provide automated procedures to identify and classify rock blocks and extract key-block emplacement in multiple rock slope structures with high accuracy. In this regard,the deep learning model adopts deep-feature extraction of rock mass characteristics such as discontinuity network, rock block geometry and movable key-blocks based on Goodman’s assumptions(Goodman and Shi,1985).In accordance with these parameters,the proposed method can be used as an operational or complementary procedure for geoengineering surveys in slope stability analysis.

3. Material and methods

3.1. Data collection

The CNN-based algorithm herein utilized a comprehensive dataset based on 130 different slope cases.The primary dataset was the image database of the discontinuous rock slope surfaces based on images taken by a high-resolution digital camera (Sony Cybershot DSCS730) in the afternoon in natural sunlight. Details of the digital camera are presented in Table 1.A base plate fixed the device slip,and the photographer attempted to obtain the lowest shadow from the outcrop surface. After several shots, the best image was taken and then prepared as an original image during the processing operation. To provide a suitable picture, the image considered the direct surface of the slope outcrops without vegetation. These images were used to extract the geometrical properties of rock masses and perform a classification using the CNN model.

Furthermore,the images in the outcrops of different slopes were taken at a specific distance of 1-1.5 m from the camera to enrich the compiled dataset. As a result, 1240 images from 130 discontinuous rock slope faces without shading and vegetation were taken at the South Pars Special Zone(SPSZ),Assalouyeh,southwest Iran. The locations of the slopes under investigation are shown in Fig. 2. The slopes originate from sedimentary rocks related to the Aghajari and Mishan formations in the SPSZ region. Although theblock theory focuses on stress dimensions and the geometrical conditions of rock masses regardless of the geological context of the rock structures to conduct stability assessments,the description of the geological units for slopes can be considered a side-work to understand the stability status of the slope. As mentioned previously, the studied slopes entail sedimentary units related to the Aghajari and Mishan formations. These formations generally consist of limestone, argillaceous lime, calcareous marl, marlstone and sandstone (Geological Survey of Iran, 2009). Since the slopes are jointed and exposed to the atmosphere without considerable vegetation, from a geological point of view, they are exposed to a lower degree of weathering,which has not affected their structural durability in most cases.

Table 1 Details of the digital camera used in this study.

Fig. 2. Location of the slopes in the South Pars region, Iran.

Table 2 Labeled images based on rock block types.

3.2. Data processing

The images need to promote the quality and label based on block class to estimate rock block conditions based on block theory classification. According to Goodman’s block classification, these labels could represent a finite group and discretion,as illustrated in Fig.1.The number of images in each label is listed in Table 2.Several samples of the primary dataset are shown in Fig. 3. The figure provides a view of the studied slopes that form the primary database playing an important role in the classifications. It should be noted that providing an appropriate image dataset with the correct position is essential for efficient classification. Avoiding shadows,noises, and erroneous orientations could reduce errors during the main processing stage. Therefore, the fast capture of the vital position for proper imaging could provide accurate results,which are a significant challenge for the massive dataset produced for rock block classification.The dataset was repeatedly used in CNN-based modeling and image processing procedures.First,the images were taken and filtered by image pre-processing(reducing the noise and shadows). The CNN algorithm was used to supervise the classification by using labels to classify the blocks. The algorithm only works on the outcropping of rocks with sharp (clear) discontinuities detected.The model can provide accurate results if images are not clear or are associated with noises and shadows. If the images are not analyzed using the mentioned regulations, it can significantly affect the performance of the model.

Fig. 3. A perspective view of the samples in the primary database.

In the interim, since the deep-learning models have been portrayed by obtaining the limit of deep features for the categories,it is consequently desired to utilize the deep-learning prediction models for pre-training procedures. Fig. 4 provides a prediction model to classify the types of rock blocks regarding block theory classification defined by Fig.1.In Fig.4,each number represents the specific class of the blocks based on Goodman’s theory. For example, 1 is a key-block, 2 is a trapped block, and 3 is a stable block.

In general, by considering the model implementation, the CNN is used to extract the relevant features of images. Rock block classification is considered the main feature,as described by Goodman and Shi (1985). Fig. 5 provides information on the rock block classification of rock slopes regarding the block theory as described by Kulatilake et al.(2011)in Fig.1.Based on Fig.5,it may be observed that the main activation key for instability and failure in rock slopes is the key blocks. Hence, the first feature must be identification of the key blocks. Subsequent to the first feature, the trapped blocks may trigger sliding in the rock slopes, leading to progressive failures in the slopes(Azarafza et al.,2021).Since consideration of such classification procedures could aid in stabilizing these slopes, a method that could accurately classify the rock blocks and extract the potentially unstable blocks may be considered as an asset for rapid stabilization measures. The CNN model is capable of classifying such groups with respect to the images and learning stages.However,since it requires preparation of a comprehensive database of high-resolution images, the images were provided and labeled according to the block class, and then categorized into different groups and gathered in a primary database for the CNN model. A strong primary database provides appropriate learning and test sets, aided the learning model with a lower error rate.

Fig. 4. A sample illustration for detection and classification by the CNN-based model.

3.3. Proposed model

The proposed model was implemented using Python and established for a 21-layered deep CNN, which contained pooling,dense, dropout, softmax, convolutional layers, and activations.Convolutional or Convs layers are widely used as feature generators from basic images in the primary dataset. The pooling layers generate outputs similar to the Convs layers and reduce the dimensions of the features during processing. The two primary pooling layers used in CNNs were calculated by the max or mean operators referred to as max-pooling or mean-pooling. This study used a max-pooling operator for evaluations and kept the framework invariant.The dropout layers are mainly used to process and reduce over-fitting during the processing stage by preventing complex co-adaptations to the training data. The proposed model represents a fairly efficient path through averaging with CNNs to randomly drop out units of a neural network during the training process, which helped to improve the CNN structure. The dense layers (also called fully connected layers) refer to as the layers whose internal neurons connect to every neuron in the CNNs.These layers provide the path for the connection between the layers for which the flattened matrix goes through a fully connected layer to classify the images. Softmax layers help to normalize the weighted vectors in the multi-classification process. Finally, the activations were used to modify the nonlinearity in the Convs outputs. The rectified linear unit (ReLU) is the standard activation function (rectifier) used to calculate a reasonable gradient. The ReLU function avoids gradient dispersion and visual feature extraction in logistic sigmoid in deep neural networks. It has become popular due to its capabilities (Aggarwal, 2018). The ReLU function was also used as an activation operator.

The proposed model has been applied to the primary dataset to estimate the rock block class concerning categorization of the block theory. The primary dataset was randomly divided into training(70%) and testing (30%) sets. Table 3 provides the proportions of testing and training sets with the number of images involved in each group. The results were verified by using evaluation criteria and justified by standard machine learning classifiers. The CNNbased model procedure flowchart is presented in Fig. 6.

Fig. 5. Rock block types regarding block theory (adapted from Goodman and Shi,1985).

3.4. Evaluation criteria and verification

To rigorously assess the proposed methodology,its accuracy was evaluated using statistics from the overall accuracy by a confusion matrix and was compared with the accuracies of commonly used machine learning methods for verification and justifications. The confusion matrix or error matrix is a well-known matrix that estimates evaluation criteria or metrics layout, allowing visualized and structured learning algorithms, typically supervised learning(Aggarwal, 2018). Each table row represents the instances in an actual class, while each column represents the instances in a predicted class, or vice versa(Chollet, 2017). The matrix contains two rows and two columns that report the number of true positives(TP), false positives (FP), true negatives (TN), and false negatives(FN), which allows detailed analysis of correct classifications named accuracy (Aggarwal, 2018). The precision (positive predictive value) and recall (sensitivity) are the fractions of retrieved relevant instances, which are used to demonstrate the algorithm’s capabilities.In the classification tasks,the precision for a class is the number of true positives divided by the total number of elements labeled as belonging to the positive class. Recall in this context is defined as the number of true positives divided by the total number of features that belong to the positive class (Goodfellow et al.,2016).

On the other hand, the combination measures of precision and recall is a harmonic mean that is known as the F1-score or Fmeasure value(Aggarwal,2018).The accuracy,precision,recall,and F-measure are evaluation criteria in a confusion matrix representing the learning-based algorithm performance. Increased evaluation criteria values imply that the model performance is significantly improved(Chollet,2017).Table 4 and Fig.7 display the components of the confusion matrix. From the confusion matrix,the mean square error (MSE) and root mean square error (RMSE)were used to evaluate the error rate of this model. As a model implementation, the CNN-based prediction model was run for 5000 iterations (epochs) to learn based on the training and test datasets. The covariates are classified into three groups, including key-blocks,trapped blocks,and stable blocks,as described in Fig.5.Table 5 provides the hyperparameters used in the study. Hyperparameters are mainly used to optimize the fitting process, which can increase the prediction accuracy of the applied machine learning models (Adnan et al., 2020). In fact, the objective of hyperparameters is to optimize the evaluation values classified into different optimizers. The study used the grid search technique for assessments.

Table 3 Proportion of training and testing sets provided from the primary set.

Fig. 6. Flowchart of the CNN-based model.

Table 4 Basics of the confusion matrix in machine learning (Müller and Guido, 2016).

Fig. 7. Confusion matrix estimated for the prediction models (verifications and justifications): (a) Accuracy, and (b) Precision, recall and F1-score.

Table 5 Hyperparameters for evaluation values in utilized machine learning-based models.

3.5. Justification

Justification plays a vital role in estimating the capability and model performance during specific procedures. In this regard,typical machine learning procedures such as support vector machine (SVM), random forest (RF), Gaussian na?ve Bayes (GNB),multilayer perceptron (MLP), Bernoulli na?ve Bayes (BNB), and decision tree(DT)classifiers were used to justify the deep-learning model established by CNN.

4. Results and discussion

The proposed model was performed with Python and trained in TensorFlow core by Google Colaboratory(Google-Colab),a product of Google research. The model was run using the training set and tested set with the aid of the primary dataset containing 1240 images from 130 discontinuous rock slope faces with no shading and vegetation. The model was verified by the confusion matrix and benchmark classifiers to evaluate the proposed model’s performance and capability for identifying the key blocks.The training process was controlled and validated by the loss function, RMSE and MSE.Fig.8 illustrates the validation of the CNN-based training process.In Fig.8a,the loss value decreases to 0.2,representing the model’s capability and robustness. A lower loss function provides better performance that indicates the accuracy of the model. The MSE and RMSE provide the error between the measured and predicted values of the model,demonstrating the algorithm’s accuracy(Table 4). Fig. 8b-c shows that the estimated error rates of the prediction model are less than 0.3.Similar to the loss function,the MSE and RMSE indicate that the model’s performance has reached an acceptable level. In addition, Fig. 8d presents the accuracy variation during the training process, which is estimated to be approximately 95%. Table 5 presents the obtained evaluation criteria compared with benchmark classifiers. In this table, the proposed model achieves the highest accuracy and precision values.Based on the obtained results,the proposed model resulted in a 0.95 accuracy and 0.93 precision, and other classifiers had the following values: SVM (accuracy = 0.85, precision = 0.85), RF(accuracy = 0.71, precision = 0.71), GNB (accuracy = 0.75,precision = 0.65), MLP (accuracy = 0.88, precision = 0.9), BNB(accuracy = 0.75, precision = 0.69), and DT (accuracy = 0.85,precision=0.76).In addition,the estimated error rate with the loss function was reduced to less than 0.3,and the RMSE and MSE were reduced to lesss than 0.2, which indicated a low error rate during processing.

To further explore the rock block classification algorithm, an evaluation of the recognition patterns for the block status based on the block theory is presented in Table 6. The results show that the percentage of block class recognition with the CNN-based algorithm results in three rock block types:key-blocks,trapped blocks,and stable blocks,where the potential key-blocks are considered a key-block group.Several images were selected and tested with the proposed algorithm to prepare the visualization and to test the rock block classification. Fig. 9 presents image recognition of the rock block class. This figure shows that the four classes represent Goodman’s four rock block types as predicted by the model,which provides acceptable identification results(see Table 7).

Although machine learning models, such as CNNs, can extract various features from images,high-resolution images are a priority in feature extraction. In this regard,the CNN model must consider the limitations and requirements in the analysis before preparing images similar to this work. The primary limitations associated with the implementation of the procedure are as follows:

(1) Decreased image quality reduces the accuracy of feature extraction;

(2) Models for small scales provide satisfactory results, and those for large scales are associated with reduced identification accuracy;and

Fig.8. Validation results for the proposed model:(a)Loss function,(b)MSE,(c)RMSE,and (d) Accuracy.

(3) Noise, such as vegetation, shadow, and lack of sufficient direct light, also reduces the accuracy of the model and significantly prolongs the pre-processing process.

In general, intelligent technologies (regardless of their limitations) have always been considered a complementary and alternative approach to traditional methods. For example, using the results in engineering practice of the presented method can accelerate the stability analysis process and applications of proper stabilizations in different regions. The future applications of the proposed prediction model in a slope survey can be categorized into the following aspects:

(1) Apply to quantify the slope’s critical blocks;

(2) Provide an appropriate way to achieve the general conditions in rock slopes;

(3) Estimate sliding sensitive areas with low information;

(4) Reduce dependence on costly and extensive field information and field surveys;

Table 6 Controlled learning model results for different algorithms.

Table 7 Rock structure classification results based on the block theory.

(5) Identify key-blocks in different ranges without the need to extract a discontinuity network and perform stereonet projection;and

(6) Provide an appropriate stabilization based on key-block emplacements in rock slopes.

5. Conclusions

An in-depth understanding of the rock block condition in discontinuous rock slopes is critical for a rapid, efficient, and successful stabilization procedure. The block theory provides an effective method to identify the right rock blocks for stabilization,which significantly affects progressive failures in the slope masses.The current study uses the block theory principles to classify rock blocks,especially the identification of key blocks.In this regard,the deep learning procedure and CNN were used to identify,recognize and rank the rock block and extract the key-blocks from the rock slope masses. The applications of deep learning techniques to classification and prediction of rock structures have received considerable attentions due to their accuracy in providing prediction models with appropriate precision. Utilization of the CNN technique helps to prepare a database of rock slopes based on images.By training the model to gather information on rock block conditions and categorizing the blocks in the slopes,it can be used to stabilize the slopes before failures. In this regard,1240 images were recovered from 130 rock slope faces without shading and vegetation in southwest Iran to form the primary database. The preparation of a comprehensive database is considered an important stage in learning the CNN model.The images have to be taken with less noise and high resolution. After the images were taken under specific daylight conditions, the primary CNN modeling database was prepared. As a methodology, the CNN-based prediction model was trained and tested by individual sets extracted from the primary database (30%-70%). The model was controlled with loss, RMSE, and MSE error functions, and verified by evaluation criteria(confusion matrix).In addition,the SVM,RF,GNB,MLP,BNB and DT classifiers were used as comparative justifications for the model.The results of the model can be useful for the identification of key-blocks.Locating the critical blocks(key and trapped blocks)that have the potential to trigger sliding regardless of the failure mechanism can be considered first-aid stabilization and control of the main failures.On the other hand,information on the location of the critical blocks leads to the safe and reliable design of support systems for slopes.

Fig. 9. Image recognition of the rock block class by the proposed algorithm (numbers indicated the percentage of block type intensity).

According to the analysis results, the proposed model had the highest accuracy and precision values (accuracy = 0.95,precision = 0.93) compared with other classifiers. In addition, the loss function, RMSE, and MSE indicated that the proposed model with 5000 iterations achieved error rates of less than 0.2 and 0.3,respectively. Furthermore, it was determined that the CNN-based model trained by an extensive database (1240 images) can obtain rock block features more comprehensively with high accuracy. A comparison of the accuracy of the proposed model with the benchmark classifiers, including SVM, RF, GNB, MLP, BNB and DT,indicated the superiority of the CNN model for rock block recognition and classification.The CNN model is capable of investigating and classifying key blocks as well as trapped blocks to categorize the critical blocks in different rock slopes.The model identified and classified potentially unstable blocks with the highest accuracy and precision compared with the other machine learning procedures.This approach enables the acquisition of detailed information on rock mass blocky structures.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grant No. 42077235) and the National Key Research and Development Program of China (Grant No.2018YFC1505104).