Advances in Mathematical, Numerical and Artificial Intelligence Methods in Rock Engineering Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 13164

Special Issue Editors


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Guest Editor
Department of Civil Engineering, School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China
Interests: rock mass geomechanics; hydraulic fracturing; fatigue and fracture; fracture mechanics; oil and gas development
Special Issues, Collections and Topics in MDPI journals
School of Water Conservancy Engineering, Zhengzhou University, Zhengzhou 450001, China
Interests: polymer grouting diffusion; numerical modeling; grouting reinforcement; intelligent assessment
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,   

With the rapid development of rock engineering, an increasing number of projects including mining, tunnelling, waste storage, etc., have been constructed under complex geological conditions, extreme cold or hot temperatures, high water pressure and active seismic conditions, as well as deep underground. As a heterogeneous and anisotropic material, rock contains multi-scale defects from particles, fractures, fissures, joints, stratification to fault. These defects make the rock behavior more sensitive to environmental factors, as the complicated stress–physical–chemical coupling processes easily occur in the defects and dramatically change the rock properties. These would be responsible for the more frequent occurrence of unconventional rock failure and instability, such as collapse, rockburst and large deformation in rock engineering. However, it is still very difficult to understand the rock mechanics and disaster mechanisms with complex conditions by means of traditional lab-testing. This means that the prevention and control of rock instability remains a great challenge. To address the issue, more mathematical, numerical and artificial intelligence methods should be applied in rock engineering applications.

This Special Issue aims to call for research and review articles encompassing the latest laboratory or in situ experiments, mathematical modelling, theoretical analyses, numerical simulation and artificial intelligence methods concerning rock mechanics and rock engineering.

Dr. Xin Cai
Prof. Dr. Shaofeng Wang
Prof. Dr. Yu Wang
Dr. Xueming Du
Guest Editors

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Keywords

  • constitutive model and failure criterion of rock materials
  • theoretical and analytical approaches for deformation, fracture and failure in rocks
  • numerical simulation of stress–physical–chemical coupling processes in rock
  • theoretical, analytical and numerical approaches for understanding time- or size-dependent rock failure
  • characterization of multi-scale rock damage and fracturing
  • mathematical methods for revealing mechanisms of rock disasters and establishing associated criteria
  • artificial intelligence methods in the characterization, prediction and control of unconventional rock failure

Published Papers (13 papers)

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Research

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21 pages, 10922 KiB  
Article
An Improved Rock Damage Characterization Method Based on the Shortest Travel Time Optimization with Active Acoustic Testing
by Jing Zhou, Lang Liu, Yuan Zhao, Mengbo Zhu, Ruofan Wang and Dengdeng Zhuang
Mathematics 2024, 12(1), 161; https://doi.org/10.3390/math12010161 - 04 Jan 2024
Viewed by 563
Abstract
Real-time evaluation of the damage location and level of rock mass is essential for preventing underground engineering disasters. However, the heterogeneity of rock mass, which results from the presence of layered rock media, faults, and pores, makes it difficult to characterize the damage [...] Read more.
Real-time evaluation of the damage location and level of rock mass is essential for preventing underground engineering disasters. However, the heterogeneity of rock mass, which results from the presence of layered rock media, faults, and pores, makes it difficult to characterize the damage evolution accurately in real time. To address this issue, an improved method for rock damage characterization is proposed. This method optimizes the solution of the global shortest acoustic wave propagation path in the medium and verifies it with layered and defective media models. Based on this, the relationship between the inversion results of the wave velocity field and the distribution of rock damage is established, thereby achieving quantitative characterization of rock damage distribution and degree. Thus, the improved method is more suitable for heterogeneous rock media. Finally, the proposed method was used to characterize the damage distribution evolution process of rock media during uniaxial compression experiments. The obtained results were compared and analyzed with digital speckle patterns, and the influencing factors during the use of the proposed method are discussed. Full article
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21 pages, 6826 KiB  
Article
Dynamic Evolution of Coal Pore-Fracture Structure and Its Fractal Characteristics under the Action of Salty Solution
by Min Wang, Yakun Tian, Zhijun Zhang, Qifeng Guo and Lingling Wu
Mathematics 2024, 12(1), 72; https://doi.org/10.3390/math12010072 - 25 Dec 2023
Viewed by 573
Abstract
The instability and failure of coal pillars is one of the important factors leading to the catastrophic consequences of coal mine goaf collapse. Coal mine water has the characteristics of high salinity. Long-term mine water erosion can easily deform the coal pillar structure, [...] Read more.
The instability and failure of coal pillars is one of the important factors leading to the catastrophic consequences of coal mine goaf collapse. Coal mine water has the characteristics of high salinity. Long-term mine water erosion can easily deform the coal pillar structure, eventually leading to instability and damage. This study carried out tests on coal samples soaked in salt solutions with different concentrations, and the nuclear magnetic resonance (NMR) method was used to obtain the dynamic evolution of the pore-fracture structure of coal. On the basis of fractal theory, the changes in fractal dimension of pore structure during the soaking process were discussed. The damage variable based on the pore fractal dimension was defined and the evolution relationship between the damage variable and immersion time was characterized. The findings demonstrated that the porosity change rate has an exponentially increasing relationship with the immersion time, and with the increasement of concentration of salt solution, the porosity change rate also shows increasing trends. The number of seepage pores and total pores increased with the immersion time. While, with the extension of soaking time, the number of adsorption pores first increased and then decreased. The connectivity between pores was enhanced. The relationship between the fractal dimension and the immersion time is linearly decreasing. The damage variable showed an increasing trend with the immersion time. As the concentration of salt solution increased, the damage of coal increased. The research results are of great significance for rationally evaluating the stability of coal pillars and ensuring the safe operation of underground engineering. Full article
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12 pages, 3920 KiB  
Article
Time-Frequency Response of Acoustic Emission and Its Multi-Fractal Analysis for Rocks with Different Brittleness under Uniaxial Compression
by Jianchun Ou, Enyuan Wang and Xinyu Wang
Mathematics 2023, 11(23), 4746; https://doi.org/10.3390/math11234746 - 23 Nov 2023
Viewed by 637
Abstract
The occurrence of rock burst hazards is closely related to the brittleness of rocks. Current research has paid less attention to the in-depth relationship between rock brittleness and acoustic emission (AE) signal characteristics and precursor information caused by rock fracture. Therefore, in order [...] Read more.
The occurrence of rock burst hazards is closely related to the brittleness of rocks. Current research has paid less attention to the in-depth relationship between rock brittleness and acoustic emission (AE) signal characteristics and precursor information caused by rock fracture. Therefore, in order to further improve the accuracy of the AE monitoring of rockburst hazards, uniaxial compression tests were carried out and AE were monitored for rocks with different brittleness (yellow sandstone, white sandstone, marble, and limestone) in this paper. The relationship between the mechanical properties and the time-frequency characteristics of the AE was analyzed. In addition, the multi-fractal theory was introduced to further deconstruct and mine the AE signals, and the multi-fractal characteristics of AE from rocks with different brittleness were investigated. The results show that the stronger the brittleness of the rock, the higher the main frequency and main frequency amplitude of the AE. Brittleness is positively correlated with the multi-fractal parameter Δα (uniformity of data distribution) and negatively correlated with Δf (frequency difference between large and small data). In addition, the dynamics of Δα and Δf provide new indicators for AE monitoring of rock stability, and their abrupt changes can be regarded as precursors of failure. The weaker the brittleness of the rock, the earlier the failure precursor is and the more significant it is. This has potential engineering application value, which can help identify rockburst precursors and take timely protective measures to ensure engineering safety. Full article
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16 pages, 5927 KiB  
Article
Research on Precursor Information of Brittle Rock Failure through Acoustic Emission
by Weiguang Ren, Chaosheng Wang, Yang Zhao and Dongjie Xue
Mathematics 2023, 11(19), 4210; https://doi.org/10.3390/math11194210 - 09 Oct 2023
Viewed by 683
Abstract
Dynamic failure of surrounding rock often causes many casualties and financial losses. Predicting the precursory characteristics of rock failure is of great significance in preventing and controlling the dynamic failure of surrounding rock. In this paper, a triaxial test of granite is carried [...] Read more.
Dynamic failure of surrounding rock often causes many casualties and financial losses. Predicting the precursory characteristics of rock failure is of great significance in preventing and controlling the dynamic failure of surrounding rock. In this paper, a triaxial test of granite is carried out, and the acoustic emission events are monitored during the test. The fractal characteristics of acoustic emission events’ energy distribution and time sequence are analyzed. The correlation dimension and the b value are used to study the size distribution and sequential characteristics. Furthermore, a rock failure prediction method is proposed. The correlation dimension is chosen as the main index and the b value is chosen as a secondary index for the precursor of granite failure. The study shows that: (1) The failure process can be divided into an initial stage, active stage, quiet stage, and failure stage. (2) The b value and correlation dimension both can describe the process of rock failure. There is a continuous decline before failure. Because of the complexity of the field, it is difficult to accurately estimate the stability of surrounding rock using a single index. (3) The combination of the b value and correlation dimension to establish a new method, which can accurately represent the stability of the surrounding rock. When the correlation dimension is increasing, the surrounding rock is stable with stress adjusting. When the correlation dimension is decreasing and the b value remains unchanged after briefly rising, the surrounding rock is stable, and stress is finished adjusting. When the correlation dimension and b value are both decreasing, the surrounding rock will be destroyed. Full article
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21 pages, 5729 KiB  
Article
Numerical Investigation on the Performance of Horizontal Helical-Coil-Type Backfill Heat Exchangers with Different Configurations in Mine Stopes
by Bo Zhang, Long Shi, Wenxuan Zhang, Chao Huan, Yujiao Zhao and Jingyu Wang
Mathematics 2023, 11(19), 4173; https://doi.org/10.3390/math11194173 - 05 Oct 2023
Viewed by 647
Abstract
The application of ground heat exchanger technology in backfill mines can actualize subterranean heat storage, which is one of the most effective solutions for addressing solar energy faults such as intermittence and fluctuation. This paper provides a 3D unsteady heat transfer numerical model [...] Read more.
The application of ground heat exchanger technology in backfill mines can actualize subterranean heat storage, which is one of the most effective solutions for addressing solar energy faults such as intermittence and fluctuation. This paper provides a 3D unsteady heat transfer numerical model for full-size horizontal backfill heat exchangers (BFHEs) with five configurations in a mining layer of a metal mine by using a COMSOL environment. In order to ensure the fairness of the comparative analysis, the pipes of BFHEs studied have the same heat exchange surface area. By comparing and evaluating the heat storage/release characteristics of BFHEs in continuous operation for three years, it was discovered that the helical pipe with serpentine layout may effectively enhance the performance of BFHEs. Compared with the traditional SS BFHEs, the heat storage capacity of the S-FH type is significantly increased by 21.7%, followed by the SA-FH type, which is increased by 11.1%, while the performances of U-DH and SH type are considerably lowered. Also, the impact of the critical structural factors (pitch length and pitch diameter) was further studied using the normalized parameters C1 and C2 based on the inner diameter of the pipe. It is discovered that BFHEs should be distributed in a pipe with a lower C1, and increasing C2 encourages BFHEs to increase the storaged/released heat of BFHEs. By comparatively analysing the effect of thermal conductivity, it is found that the positive effects of thermal conductivity on the performance of SH, U-DH, SA-FH, and S-FH type BFHEs are found to decrease successively. This work proposes a strategy for improving the heat storage and release potential of BFHEs in terms of optimal pipe arrangement. Full article
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25 pages, 29463 KiB  
Article
Numerical Simulation of Failure Modes in Irregular Columnar Jointed Rock Masses under Dynamic Loading
by Yingjie Xia, Bingchen Liu, Tianjiao Li, Danchen Zhao, Ning Liu, Chun’an Tang and Jun Chen
Mathematics 2023, 11(17), 3790; https://doi.org/10.3390/math11173790 - 04 Sep 2023
Cited by 1 | Viewed by 875
Abstract
The mechanical properties and failure characteristics of columnar jointed rock mass (CJRM) are significantly influenced by its irregular structure. Current research on CJRMs is mainly under static loading, which cannot meet the actual needs of engineering. This paper adopts the finite element method [...] Read more.
The mechanical properties and failure characteristics of columnar jointed rock mass (CJRM) are significantly influenced by its irregular structure. Current research on CJRMs is mainly under static loading, which cannot meet the actual needs of engineering. This paper adopts the finite element method (FEM) to carry out numerical simulation tests on irregular CJRMs with different dip angles under different dynamic stress wave loadings. The dynamic failure modes of irregular CJRMs and the influence law of related stress wave parameters are obtained. The results show that when the column dip angle α is 0°, the tensile-compressive-shear failure occurs in the CJRMs; when α is 30°, the CJRMs undergo tensile failure and a small amount of compressive shear failure, and an obvious crack-free area appears in the middle of the rock mass; when α is 60°, tensile failure is dominant and compressive shear failure is minimal and no crack area disappears; and when α is 90°, the rock mass undergoes complete tensile failure. In addition, in terms of the change law of stress wave parameters, the increase in peak amplitude will increase the number of cracks, promote the development of cracks, and increase the proportion of compression-shear failure units for low-angle rock mass. The changes in the loading and decay rate only affect the degree of crack development in the CJRMs, but do not increase the number of cracks. Meanwhile, the simulation results show that the crack expansion velocity of the CJRMs increases with the increase in dip angle, and the CJRMs with dip angle α = 60° are the most vulnerable to failure. The influence of the loading and decay rate on the rock mass failure is different with the change in dip angle. The results of the study provide references for related rock engineering. Full article
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22 pages, 1276 KiB  
Article
Prediction of Rockburst Propensity Based on Intuitionistic Fuzzy Set—Multisource Combined Weights—Improved Attribute Measurement Model
by Jianhong Chen, Yakun Zhao, Zhe Liu, Shan Yang and Zhiyong Zhou
Mathematics 2023, 11(16), 3508; https://doi.org/10.3390/math11163508 - 14 Aug 2023
Viewed by 940
Abstract
A rockburst is a geological disaster that occurs in resource development or engineering construction. In order to reduce the harm caused by rockburst, this paper proposes a prediction study of rockburst propensity based on the intuitionistic fuzzy set-multisource combined weights-improved attribute measurement model. [...] Read more.
A rockburst is a geological disaster that occurs in resource development or engineering construction. In order to reduce the harm caused by rockburst, this paper proposes a prediction study of rockburst propensity based on the intuitionistic fuzzy set-multisource combined weights-improved attribute measurement model. From the perspective of rock mechanics, the uniaxial compressive strength σc, tensile stress σt, shear stress σθ, compression/tension ratio σc/σt, shear/compression ratio σθ/σc, and elastic deformation coefficient Wet were selected as the indicators for predicting the propensity of rockburst, and the corresponding attribute classification set was established. Constructing a model framework based on an intuitionistic fuzzy set–improved attribute measurement includes transforming the vagueness of rockburst indicators with an intuitionistic fuzzy set and controlling the uncertainty in the results of the attribute measurements, as well as improving the accuracy of the model using the Euclidean distance method to improve the attribute identification method. To further transform the vagueness of rockburst indicators, the multisource system for combined weights of rockburst propensity indicators was constructed using the minimum entropy combined weighting method, the game theory combined weighting method, and the multiplicative synthetic normalization combined weighting method integrated with intuitionistic fuzzy sets, and the single-valued data of the indicators were changed into intervalized data on the basis of subjective weights based on the analytic hierarchy process and objective weights, further based on the coefficient of variation method. Choosing 30 groups of typical rockburst cases, the indicator weights and propensity prediction results were calculated and analyzed through this paper’s model. Firstly, comparing the prediction results of this paper’s model with the results of the other three single-combination weighting models for attribute measurement, the accuracy of the prediction results of this paper’s model is 86.7%, which is higher than that of the other model results that were the least in addition to the number of uncertain cases, indicating that the uncertainty of attribute measurement has been effectively dealt with; secondly, the rationality of the multiple sources system for combined weights is verified, and the vagueness of the indicators is controlled. Full article
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19 pages, 2811 KiB  
Article
Evaluation and Application of Surrounding Rock Stability Based on an Improved Fuzzy Comprehensive Evaluation Method
by Xianhui Mao, Ankui Hu, Rui Zhao, Fei Wang and Mengkun Wu
Mathematics 2023, 11(14), 3095; https://doi.org/10.3390/math11143095 - 13 Jul 2023
Cited by 1 | Viewed by 691
Abstract
Ensuring the stability of surrounding rock is crucial for the safety of underground engineering projects. In this study, an improved fuzzy comprehensive evaluation method is proposed to accurately predict the stability of surrounding rock. Five key factors, namely, rock quality designation, uniaxial compressive [...] Read more.
Ensuring the stability of surrounding rock is crucial for the safety of underground engineering projects. In this study, an improved fuzzy comprehensive evaluation method is proposed to accurately predict the stability of surrounding rock. Five key factors, namely, rock quality designation, uniaxial compressive strength, integrality coefficient of the rock mass, strength coefficient of the structural surface, and groundwater seepage, are selected as evaluation indicators, and a five-grade evaluation system is established. An improved analytic hierarchy process (IAHP) is proposed to enhance the accuracy of the evaluation. Using interval numbers rather than real numbers in constructing an interval judgment matrix can better account for the subjective fuzziness and uncertainty of expert judgment. Subjective and objective weights are obtained through IAHP and coefficient of variation, and the comprehensive weight is calculated on the basis of game theory principles. In addition, trapezoidal and triangular membership functions are employed to determine the membership degree, and an improved fuzzy comprehensive evaluation model is constructed. The model is then used to determine the stability of the surrounding rock based on the improved criterion. It is applied to six samples from an actual underground project in China to validate its effectiveness. Results show that the proposed model accurately and effectively predicts the stability of surrounding rock, which aligns with the findings from field investigations. The proposed method provides a valuable reference for evaluating surrounding rock stability and controlling construction risks. Full article
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14 pages, 8688 KiB  
Article
High Steep Rock Slope Instability Mechanism Induced by the Pillar Deterioration in the Mountain Mining Area
by Lu Chen, Xiangxi Yu, Ron Luo, Ling Zeng and Hongtao Cao
Mathematics 2023, 11(8), 1889; https://doi.org/10.3390/math11081889 - 17 Apr 2023
Viewed by 1092
Abstract
In hilly regions, landslides or slope failures are very common phenomena, when underground mineral resources are excavated. In this study, some landslide disasters in a mountain mining area were analyzed. The engineering geological and instability reason were investigated. The numerical simulation of a [...] Read more.
In hilly regions, landslides or slope failures are very common phenomena, when underground mineral resources are excavated. In this study, some landslide disasters in a mountain mining area were analyzed. The engineering geological and instability reason were investigated. The numerical simulation of a high steep rock slope disturbed by a room and pillar mine was established. The failure process of a high steep rock slope induced by the pillar deterioration was analyzed to reveal the characteristics of deformation and sliding. The results show that the pillar plays an important role in maintaining the stability of the slope, if the pillar can support the overlying rock mass, only a tiny deformation will be induced. When the pillar fails and the roof caves, the overlying rock mass above the room and pillar goaf will rapidly subside, and the crack evolution of slope is induced, forming the potential slip surface. The landslide mass gradually moves. When the rock mass at the middle and lower of the slope is squeezed out, slope sliding will be induced. The failure process can be divided into four stages as follow: tiny displacement is caused by the mining, roof collapse is caused by the pillar failure, the potential slip surface is formed from the crack evolution; the slope sliding is induced by the fracturing of rock mass at the middle and lower of the slope. Full article
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18 pages, 1529 KiB  
Article
A Novel Method for Predicting Rockburst Intensity Based on an Improved Unascertained Measurement and an Improved Game Theory
by Zhe Liu, Jianhong Chen, Yakun Zhao and Shan Yang
Mathematics 2023, 11(8), 1862; https://doi.org/10.3390/math11081862 - 14 Apr 2023
Cited by 2 | Viewed by 1092
Abstract
A rockburst is a dynamic disaster that may result in considerable damage to mines and pose a threat to personnel safety. Accurately predicting rockburst intensity is critical for ensuring mine safety and reducing economic losses. First, based on the primary parameters that impact [...] Read more.
A rockburst is a dynamic disaster that may result in considerable damage to mines and pose a threat to personnel safety. Accurately predicting rockburst intensity is critical for ensuring mine safety and reducing economic losses. First, based on the primary parameters that impact rockburst occurrence, the uniaxial compressive strength (σc), shear–compression ratio (σθ/σc), compression–tension ratio (σc/σt), elastic deformation coefficient (Wet), and integrity coefficient of the rock (KV) were selected as the evaluation indicators. Second, an improved game theory weighting method was introduced to address the problem that the combination coefficients calculated using the traditional game theory weighting method may result in negative values. The combination of indicator weights obtained using the analytic hierarchy process, the entropy method, and the coefficient of variation method were also optimized using improved game theory. Third, to address the problem of subjectivity in the traditional unascertained measurement using the confidence identification criterion, the distance discrimination idea of the Minkowski distance was used to optimize the identification criteria of the attributes in an unascertained measurement and was applied to rockburst prediction, and the obtained results were compared with the original confidence identification criterion and the original distance discrimination. The results show that the improved game theory weighting method used in this model makes the weight distribution more reasonable and reliable, which can provide a feasible reference for the weight determination method of rockburst prediction. When the Minkowski distance formula was introduced into the unascertained measurement for distance discrimination, the same rockburst predictions were obtained when the distance parameter (p) was equal to 1, 2, 3, and 4. The improved model was used to predict and analyze 40 groups of rockburst data with an accuracy of 92.5% and could determine the rockburst intensity class intuitively, providing a new way to analyze the rockburst intensity class rationally and quickly. Full article
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15 pages, 3949 KiB  
Article
Investigation of Transfer Learning for Tunnel Support Design
by Amichai Mitelman and Alon Urlainis
Mathematics 2023, 11(7), 1623; https://doi.org/10.3390/math11071623 - 27 Mar 2023
Cited by 6 | Viewed by 1238
Abstract
The potential of machine learning (ML) tools for enhancing geotechnical analysis has been recognized by several researchers. However, obtaining a sufficiently large digital dataset is a major technical challenge. This paper investigates the use of transfer learning, a powerful ML technique, used for [...] Read more.
The potential of machine learning (ML) tools for enhancing geotechnical analysis has been recognized by several researchers. However, obtaining a sufficiently large digital dataset is a major technical challenge. This paper investigates the use of transfer learning, a powerful ML technique, used for overcoming dataset size limitations. The study examines two scenarios where transfer learning is applied to tunnel support analysis. The first scenario investigates transferring knowledge between a ground formation that has been well-studied to a new formation with very limited data. The second scenario is intended to investigate whether transferring knowledge is possible from a dataset that relies on simplified tunnel support analysis to a more complex and realistic analysis. The technical process for transfer learning involves training an Artificial Neural Network (ANN) on a large dataset and adding an extra layer to the model. The added layer is then trained on smaller datasets to fine-tune the model. The study demonstrates the effectiveness of transfer learning for both scenarios. On this basis, it is argued that, with further development and refinement, transfer learning could become a valuable tool for ML-related geotechnical applications. Full article
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27 pages, 8372 KiB  
Article
Rock Thin Section Image Identification Based on Convolutional Neural Networks of Adaptive and Second-Order Pooling Methods
by Zilong Zhou, Hang Yuan and Xin Cai
Mathematics 2023, 11(5), 1245; https://doi.org/10.3390/math11051245 - 04 Mar 2023
Viewed by 1382
Abstract
In order to enhance the ability to represent rock feature information and finally improve the rock identification performance of convolution neural networks (CNN), a new pooling mode was proposed in this paper. According to whether the pooling object was the last convolution layer, [...] Read more.
In order to enhance the ability to represent rock feature information and finally improve the rock identification performance of convolution neural networks (CNN), a new pooling mode was proposed in this paper. According to whether the pooling object was the last convolution layer, it divided pooling layers into the sampling pooling layer and the classification pooling layer. The adaptive pooling method was used in the sampling pooling layer. The pooling kernels adaptively adjusted were designed for each feature map. The second-order pooling method was used by the classification pooling layer. The second-order feature information based on outer products was extracted from the feature pair. The changing process of the two methods in forward and back propagation was deduced. Then, they were embedded into CNN to build a rock thin section image identification model (ASOPCNN). The experiment was conducted on the image set containing 5998 rock thin section images of six rock types. The CNN models using max pooling, average pooling and stochastic pooling were set for comparison. In the results, the ASOPCNN has the highest identification accuracy of 89.08% on the test set. Its indexes are superior to the other three models in precision, recall, F1 score and AUC values. The results reveal that the adaptive and second-order pooling methods are more suitable for CNN model, and CNN based on them could be a reliable model for rock identification. Full article
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Review

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16 pages, 1570 KiB  
Review
The Application of Machine Learning Techniques in Geotechnical Engineering: A Review and Comparison
by Wei Shao, Wenhan Yue, Ye Zhang, Tianxing Zhou, Yutong Zhang, Yabin Dang, Haoyu Wang, Xianhui Feng and Zhiming Chao
Mathematics 2023, 11(18), 3976; https://doi.org/10.3390/math11183976 - 19 Sep 2023
Viewed by 1565
Abstract
With the development of data collection and storage capabilities in recent decades, abundant data have been accumulated in geotechnical engineering fields, providing opportunities for the usage of machine learning approaches. Thus, a rising number of scholars are adopting machine learning techniques to settle [...] Read more.
With the development of data collection and storage capabilities in recent decades, abundant data have been accumulated in geotechnical engineering fields, providing opportunities for the usage of machine learning approaches. Thus, a rising number of scholars are adopting machine learning techniques to settle geotechnical issues. In this paper, the application of three popular machine learning algorithms, support vector machine (SVM), artificial neural network (ANN), and decision tree (DT), as well as other representative algorithms in geotechnical engineering, is reviewed. Meanwhile, the applicability of diverse machine learning algorithms in settling specific geotechnical engineering issues is compared. The main findings are as follows: ANN, SVM, and DT have been widely adopted to solve a variety of geotechnical engineering issues, such as the classification of soil and rock types, predicting the properties of geotechnical materials, etc. Based on the collected relevant research, the performance of random forest (RF) in sorting soil types and assessing landslide susceptibility is satisfying; SVM has high precision in classifying rock types and forecasting rock deformation; and backpropagation ANNs and Hopfield ANNs are recommended to forecast rock compressive strength and soil settlement, respectively. Full article
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