Advances in Computational Intelligence in Geotechnical and Geological Engineering

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

Deadline for manuscript submissions: closed (1 February 2024) | Viewed by 21204

Special Issue Editors


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Guest Editor
School of Civil and Environmental Engineering, University of Technology Sydney, Ultimo, NSW 2007, Australia
Interests: rock mechanics; tunneling; artificial intelligence and optimization algorithms; geotechnical engineering
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Guest Editor
School of Civil and Environmental Engineering, University of Technology Sydney, Ultimo 2007, Australia
Interests: ground improvement techniques; development of smart tools using MATLAB

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Guest Editor
Institute of Innovation, Science and Sustainability, Federation University Australia, Ballarat, VIC 3350, Australia
Interests: rock mechanics; rock blasting; geomechanics; soft computing
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
School of Mines, China University of Mining and Technology, Xuzhou 221116, China
Interests: intelligent mining and rock control; artificial intelligence and optimization algorithms

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Guest Editor
Centre of Tropical Geoengineering (GEOTROPIK), School of Civil Engineering, Faculty of Engineering, Universiti Teknologi Malaysia, Johor Bahru 81310, Malaysia
Interests: rock mechanics; geotechnical and mining engineering; artificial intelligence and machine learning; innovative construction; aggregates

Special Issue Information

Dear Colleagues,

The theory, design, implementation and evolution of motivated computational paradigms are the focus of the field known as computational intelligence (CI). CI utilizes algorithms/approaches such as artificial neural networks, fuzzy logic, evolutionary theory, learning theory and probabilistic theory, making it a good and useful fit for real-life complex problems. Due to the complicated interactions created between dependent and independent variables, these techniques can be successfully implemented in different fields of science and engineering.

The Special Issue entitled "Advances in Computational Intelligence in Geotechnical and Geological Engineering" is devoted to the publication of the latest research, design and development of CI solutions (i.e., classification, regression and time series) in the areas of geotechnical, geomechanical and geological engineering. We invite researchers to contribute original research and review articles stimulating the continuing research efforts contributed to applications of recent CI and soft computing methods for solving relevant problems. In addition, research articles in-line with the scientific combination of CI-based, risk-based and reliability-based techniques with basic theories and concepts in geotechnics and geomechanics are highly welcomed.

Dr. Danial Jahed Armaghani
Prof. Dr. Hadi Khabbaz
Dr. Manoj Khandelwal
Dr. Niaz Muhammad Shahani
Dr. Ramesh Murlidhar Bhatawdekar
Guest Editors

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • novel geotechnical construction and material techniques
  • metaheuristic techniques
  • advances in soil and rock mechanics
  • geomechanical engineering
  • geology and geophysics
  • advanced statistical techniques
  • hybrid-based intelligence techniques
  • optimized machine learning techniques
  • tunneling and underground space technology
  • foundation engineering
  • surface and deep excavation
  • smart infrastructure construction
  • theory-guided machine learning techniques
  • probabilistic and reliability methods
  • risk-based approach in design and construction

Published Papers (12 papers)

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Research

31 pages, 7397 KiB  
Article
Slope Stability Prediction Using k-NN-Based Optimum-Path Forest Approach
by Leilei Liu, Guoyan Zhao and Weizhang Liang
Mathematics 2023, 11(14), 3071; https://doi.org/10.3390/math11143071 - 12 Jul 2023
Cited by 3 | Viewed by 1079
Abstract
Slope instability can lead to catastrophic consequences. However, predicting slope stability effectively is still challenging because of the complex mechanisms and multiple influencing factors. In recent years, machine learning (ML) has received great attention in slope stability prediction due to its strong nonlinear [...] Read more.
Slope instability can lead to catastrophic consequences. However, predicting slope stability effectively is still challenging because of the complex mechanisms and multiple influencing factors. In recent years, machine learning (ML) has received great attention in slope stability prediction due to its strong nonlinear prediction ability. In this study, an optimum-path forest algorithm based on k-nearest neighbor (OPFk-NN) was used to predict the stability of slopes. First, 404 historical slopes with failure risk were collected. Subsequently, the dataset was used to train and test the algorithm based on randomly divided training and test sets, respectively. The hyperparameter values were tuned by combining ten-fold cross-validation and grid search methods. Finally, the performance of the proposed approach was evaluated based on accuracy, F1-score, area under the curve (AUC), and computational burden. In addition, the prediction results were compared with the other six ML algorithms. The results showed that the OPFk-NN algorithm had a better performance, and the values of accuracy, F1-score, AUC, and computational burden were 0.901, 0.902, 0.901, and 0.957 s, respectively. Moreover, the failed slope cases can be accurately identified, which is highly critical in slope stability prediction. The slope angle had the most important influence on prediction results. Furthermore, the engineering application results showed that the overall predictive performance of the OPFk-NN model was consistent with the factor of safety value of engineering slopes. This study can provide valuable guidance for slope stability analysis and risk management. Full article
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23 pages, 4956 KiB  
Article
Modelling Soil Compaction Parameters Using an Enhanced Hybrid Intelligence Paradigm of ANFIS and Improved Grey Wolf Optimiser
by Abidhan Bardhan, Raushan Kumar Singh, Sufyan Ghani, Gerasimos Konstantakatos and Panagiotis G. Asteris
Mathematics 2023, 11(14), 3064; https://doi.org/10.3390/math11143064 - 11 Jul 2023
Cited by 6 | Viewed by 1745
Abstract
The criteria for measuring soil compaction parameters, such as optimum moisture content and maximum dry density, play an important role in construction projects. On construction sites, base/sub-base soils are compacted at the optimal moisture content to achieve the desirable level of compaction, generally [...] Read more.
The criteria for measuring soil compaction parameters, such as optimum moisture content and maximum dry density, play an important role in construction projects. On construction sites, base/sub-base soils are compacted at the optimal moisture content to achieve the desirable level of compaction, generally between 95% and 98% of the maximum dry density. The present technique of determining compaction parameters in the laboratory is a time-consuming task. This study proposes an improved hybrid intelligence paradigm as an alternative tool to the laboratory method for estimating the optimum moisture content and maximum dry density of soils. For this purpose, an advanced version of the grey wolf optimiser (GWO) called improved GWO (IGWO) was integrated with an adaptive neuro-fuzzy inference system (ANFIS), which resulted in a high-performance hybrid model named ANFIS-IGWO. Overall, the results indicate that the proposed ANFIS-IGWO model achieved the most precise prediction of the optimum moisture content (degree of correlation = 0.9203 and root mean square error = 0.0635) and maximum dry density (degree of correlation = 0.9050 and root mean square error = 0.0709) of soils. The outcomes of the suggested model are noticeably superior to those attained by other hybrid ANFIS models, which are built with standard GWO, Moth-flame optimisation, slime mould algorithm, and marine predators algorithm. The results indicate that geotechnical engineers can benefit from the newly developed ANFIS-IGWO model during the design stage of civil engineering projects. The developed MATLAB models are also included for determining soil compaction parameters. Full article
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22 pages, 9322 KiB  
Article
Data-Driven Optimized Artificial Neural Network Technique for Prediction of Flyrock Induced by Boulder Blasting
by Xianan Wang, Shahab Hosseini, Danial Jahed Armaghani and Edy Tonnizam Mohamad
Mathematics 2023, 11(10), 2358; https://doi.org/10.3390/math11102358 - 18 May 2023
Cited by 12 | Viewed by 1357
Abstract
One of the most undesirable consequences induced by blasting in open-pit mines and civil activities is flyrock. Furthermore, the production of oversize boulders creates many problems for the continuation of the work and usually imposes additional costs on the project. In this way, [...] Read more.
One of the most undesirable consequences induced by blasting in open-pit mines and civil activities is flyrock. Furthermore, the production of oversize boulders creates many problems for the continuation of the work and usually imposes additional costs on the project. In this way, the breakage of oversize boulders is associated with throwing small fragments particles at high speed, which can lead to serious risks to human resources and infrastructures. Hence, the accurate prediction of flyrock induced by boulder blasting is crucial to avoid possible consequences and its’ environmental side effects. This study attempts to develop an optimized artificial neural network (ANN) by particle swarm optimization (PSO) and jellyfish search algorithm (JSA) to construct the hybrid models for anticipating flyrock distance resulting in boulder blasting in a quarry mine. The PSO and JSA algorithms were used to determine the optimum values of neurons’ weight and biases connected to neurons. In this regard, a database involving 65 monitored boulders blasting for recording flyrock distance was collected that comprises six influential parameters on flyrock distance, i.e., hole depth, burden, hole angle, charge weight, stemming, and powder factor and one target parameter, i.e., flyrock distance. The ten various models of ANN, PSO–ANN, and JSA–ANN were established for estimating flyrock distance, and their results were investigated by applying three evaluation indices of coefficient of determination (R2), root mean square error (RMSE) and value accounted for (VAF). The results of the calculation of evaluation indicators revealed that R2, values of (0.957, 0.972 and 0.995) and (0.945, 0.954 and 0.989) were determined to train and test of proposed predictive models, respectively. The yielded results denoted that although ANN model is capable of anticipating flyrock distance, the hybrid PSO–ANN and JSA–ANN models can anticipate flyrock distance with more accuracy. Furthermore, the performance and accuracy level of the JSA–ANN predictive model can estimate better compared to ANN and PSO–ANN models. Therefore, the JSA–ANN model is identified as the superior predictive model in estimating flyrock distance induced from boulder blasting. In the final, a sensitivity analysis was conducted to determine the most influential parameters in flyrock distance, and the results showed that charge weight, powder factor, and hole angle have a high impact on flyrock changes. Full article
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17 pages, 7753 KiB  
Article
Predictive Modeling of the Uniaxial Compressive Strength of Rocks Using an Artificial Neural Network Approach
by Xin Wei, Niaz Muhammad Shahani and Xigui Zheng
Mathematics 2023, 11(7), 1650; https://doi.org/10.3390/math11071650 - 29 Mar 2023
Cited by 8 | Viewed by 1743
Abstract
Sedimentary rocks provide information on previous environments on the surface of the Earth. As a result, they are the principal narrators of the former climate, life, and important events on the surface of the Earth. The complexity and cost of direct destructive laboratory [...] Read more.
Sedimentary rocks provide information on previous environments on the surface of the Earth. As a result, they are the principal narrators of the former climate, life, and important events on the surface of the Earth. The complexity and cost of direct destructive laboratory tests adversely affect the data scarcity problem, making the development of intelligent indirect methods an integral step in attempts to address the problem faced by rock engineering projects. This study established an artificial neural network (ANN) approach to predict the uniaxial compressive strength (UCS) in MPa of sedimentary rocks using different input parameters; i.e., dry density (ρd) in g/cm3, Brazilian tensile strength (BTS) in MPa, and wet density (ρwet) in g/cm3. The developed ANN models, M1, M2, and M3, were divided as follows: the overall dataset, 70% training dataset and 30% testing dataset, and 60% training dataset and 40% testing dataset, respectively. In addition, multiple linear regression (MLR) was performed for comparison to the proposed ANN models to verify the accuracy of the predicted values. The performance indices were also calculated by estimating the established models. The predictive performance of the M2 ANN model in terms of the coefficient of determination (R2), root mean squared error (RMSE), variance accounts for (VAF), and a20-index was 0.831, 0.27672, 0.92, and 0.80, respectively, in the testing dataset, revealing ideal results, thus it was proposed as the best-fit prediction model for UCS of sedimentary rocks at the Thar coalfield, Pakistan, among the models developed in this study. Moreover, by performing a sensitivity analysis, it was determined that BTS was the most influential parameter in predicting UCS. Full article
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18 pages, 5835 KiB  
Article
Refined Design and Optimization of Underground Medium and Long Hole Blasting Parameters—A Case Study of the Gaofeng Mine
by Feng Gao, Xin Li, Xin Xiong, Haichuan Lu and Zengwu Luo
Mathematics 2023, 11(7), 1612; https://doi.org/10.3390/math11071612 - 27 Mar 2023
Cited by 1 | Viewed by 1469
Abstract
Previously conducted studies have established that the rationality of the parameters of medium-deep hole blasting is one of the main factors affecting the blasting effect. To solve the problem of the parameter design and optimization design of medium-deep hole blasting in underground mines, [...] Read more.
Previously conducted studies have established that the rationality of the parameters of medium-deep hole blasting is one of the main factors affecting the blasting effect. To solve the problem of the parameter design and optimization design of medium-deep hole blasting in underground mines, a method of parameter design and the optimization of medium-deep hole blasting based on the blasting crater tests and numerical simulation analyses has been proposed in this study. Based on the background of deep underground mining in Gaofeng Mine, a two-hole blasting model has been established, and the blasting parameters are simulated and analyzed by the damage stress variation of the two-hole model. During the study, the initial values of blasting parameters were first obtained from the field blasting crater test, then the blasting parameters were optimized and analyzed by LS-DYNA software, and finally, the optimization scheme was demonstrated by the corresponding blasting test. The results of the field test showed that the design method of integrated blast crater test and numerical simulation analysis can effectively optimize the design of medium-deep hole blasting parameters and improve the blasting effect to a large extent. This study also provides an effective design system for the design of deep hole blasting parameters in similar mines. Full article
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17 pages, 10231 KiB  
Article
Analysis of Microscopic Pore Characteristics and Macroscopic Energy Evolution of Rock Materials under Freeze-Thaw Cycle Conditions
by Yigai Xiao, Hongwei Deng, Guanglin Tian and Songtao Yu
Mathematics 2023, 11(3), 710; https://doi.org/10.3390/math11030710 - 31 Jan 2023
Cited by 1 | Viewed by 1342
Abstract
The repeated cyclic freeze-thaw effect in low-temperature environments causes irreversible damage and deterioration to the microscopic pore structure and macroscopic mechanical properties of a rock. To study the effects of the freeze-thaw cycle on the porosity and mechanical properties, the indoor freeze-thaw cycle [...] Read more.
The repeated cyclic freeze-thaw effect in low-temperature environments causes irreversible damage and deterioration to the microscopic pore structure and macroscopic mechanical properties of a rock. To study the effects of the freeze-thaw cycle on the porosity and mechanical properties, the indoor freeze-thaw cycle test and mechanical tests of sandstone-like materials were conducted. Based on nuclear magnetic resonance, the influence of the freeze-thaw cycle on microscopic pores was analyzed, and the intrinsic relationship between porosity and mechanical strength was discussed. Meanwhile, the energy change in the uniaxial compression test was recorded using the discrete element software (PFC2D). The influence of freeze-thaw cycles on different types of energy was analyzed, and the internal relationship between different energies and freeze-thaw cycles was discussed. The results showed that the microscopic pore structure is dominated by micropores, followed by mesopores and the smallest macropores. With an increase in the freeze-thaw cycle, both micropores and mesopores showed an increasing trend. The porosity showed an exponentially increasing trend with the increase in freeze-thaw cycles. The peak strength and elastic modulus decreased exponentially with the increase in freeze-thaw times, while the peak strain showed an exponentially increasing trend. The strain energy and bond strain energy showed a trend of increasing and decreasing in the front and back stages of the peak strength, respectively. However, the frictional energy always showed an increasing trend. The total energy, strain energy, bond strain energy, and friction energy all showed exponential increases with the increase in the number of freeze-thaw cycles. Full article
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14 pages, 4562 KiB  
Article
Tailings Pond Classification Based on Satellite Images and Machine Learning: An Exploration of Microsoft ML.Net
by Haoxuan Yu and Izni Zahidi
Mathematics 2023, 11(3), 517; https://doi.org/10.3390/math11030517 - 18 Jan 2023
Cited by 2 | Viewed by 2019
Abstract
Mine pollution from mining activities is often widely recognised as a serious threat to public health, with mine solid waste causing problems such as tailings pond accumulation, which is considered the biggest hidden danger. The construction of tailings ponds not only causes land [...] Read more.
Mine pollution from mining activities is often widely recognised as a serious threat to public health, with mine solid waste causing problems such as tailings pond accumulation, which is considered the biggest hidden danger. The construction of tailings ponds not only causes land occupation and vegetation damage but also brings about potential environmental pollution, such as water and dust pollution, posing a health risk to nearby residents. If remote sensing images and machine learning techniques could be used to determine whether a tailings pond might have potential pollution and safety hazards, mainly monitoring tailings ponds that may have potential hazards, it would save a lot of effort in tailings ponds monitoring. Therefore, based on this background, this paper proposes to classify tailings ponds into two categories according to whether they are potentially risky or generally safe and to classify tailings ponds with remote sensing satellite images of tailings ponds using the DDN + ResNet-50 machine learning model based on ML.Net developed by Microsoft. In the discussion section, the paper introduces the environmental hazards of mine pollution and proposes the concept of “Healthy Mine” to provide development directions for mining companies and solutions to mine pollution and public health crises. Finally, we claim this paper serves as a guide to begin a conversation and to encourage experts, researchers and scholars to engage in the research field of mine solid waste pollution monitoring, assessment and treatment. Full article
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17 pages, 4462 KiB  
Article
Applications of Two Neuro-Based Metaheuristic Techniques in Evaluating Ground Vibration Resulting from Tunnel Blasting
by Danial Jahed Armaghani, Biao He, Edy Tonnizam Mohamad, Y.X Zhang, Sai Hin Lai and Fei Ye
Mathematics 2023, 11(1), 106; https://doi.org/10.3390/math11010106 - 26 Dec 2022
Cited by 3 | Viewed by 1491
Abstract
Peak particle velocity (PPV) caused by blasting is an unfavorable environmental issue that can damage neighboring structures or equipment. Hence, a reliable prediction and minimization of PPV are essential for a blasting site. To estimate PPV caused by tunnel blasting, this paper proposes [...] Read more.
Peak particle velocity (PPV) caused by blasting is an unfavorable environmental issue that can damage neighboring structures or equipment. Hence, a reliable prediction and minimization of PPV are essential for a blasting site. To estimate PPV caused by tunnel blasting, this paper proposes two neuro-based metaheuristic models: neuro-imperialism and neuro-swarm. The prediction was made based on extensive observation and data collecting from a tunnelling project that was concerned about the presence of a temple near the blasting operations and tunnel site. A detailed modeling procedure was conducted to estimate PPV values using both empirical methods and intelligence techniques. As a fair comparison, a base model considered a benchmark in intelligent modeling, artificial neural network (ANN), was also built to predict the same output. The developed models were evaluated using several calculated statistical indices, such as variance account for (VAF) and a-20 index. The empirical equation findings revealed that there is still room for improvement by implementing other techniques. This paper demonstrated this improvement by proposing the neuro-swarm, neuro-imperialism, and ANN models. The neuro-swarm model outperforms the others in terms of accuracy. VAF values of 90.318% and 90.606% and a-20 index values of 0.374 and 0.355 for training and testing sets, respectively, were obtained for the neuro-swarm model to predict PPV induced by blasting. The proposed neuro-based metaheuristic models in this investigation can be utilized to predict PPV values with an acceptable level of accuracy within the site conditions and input ranges used in this study. Full article
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25 pages, 6418 KiB  
Article
Intelligent Prediction of Maximum Ground Settlement Induced by EPB Shield Tunneling Using Automated Machine Learning Techniques
by Syed Mujtaba Hussaine and Linlong Mu
Mathematics 2022, 10(24), 4637; https://doi.org/10.3390/math10244637 - 07 Dec 2022
Cited by 6 | Viewed by 2023 | Correction
Abstract
Predicting the maximum ground subsidence (Smax) in the construction of soil pressure balanced shield tunnel, particularly on soft foundation soils, is essential for safe operation and to minimize the possible risk of damage in urban areas. Although some research has been done, this [...] Read more.
Predicting the maximum ground subsidence (Smax) in the construction of soil pressure balanced shield tunnel, particularly on soft foundation soils, is essential for safe operation and to minimize the possible risk of damage in urban areas. Although some research has been done, this issue has not been solved because of its complexity and many other influencing factors. Due to the increasing accuracy of machine learning (ML) in predicting surface deformation of shield tunneling and the development of automated machine learning (AutoML) technology. In the study, different ML prediction models were constructed using an open source AutoML framework. The prediction model was trained by the dataset, which contains 14 input parameters and an output (i.e., Smax). Different AutoML frameworks were employed to compare their validities and efficiencies. The performance of the model is estimated by contrasting the prediction accuracy parameters, including root mean square error (RMSE), mean absolute error (MAE) and determinant coefficient (R2).With a coefficient of determination (R2) of 0.808, MAE of 3.7, and RMSE of 5.2 on the testing dataset, the best prediction model i.e., extra tree regressor showed better performance, proving that our model has advantages in predicting Smax. Furthermore, the SHAP analysis reveal that the soil type (ST), torque (To), cover depth (H), groundwater level (GW), and tunneling deviation have a significant effect on Smax compared to other model inputs. Full article
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21 pages, 4858 KiB  
Article
Prediction of Strength Parameters of Thermally Treated Egyptian Granodiorite Using Multivariate Statistics and Machine Learning Techniques
by Mohamed Elgharib Gomah, Guichen Li, Naseer Muhammad Khan, Changlun Sun, Jiahui Xu, Ahmed A. Omar, B. G. Mousa, Marzouk Mohamed Aly Abdelhamid and M. M. Zaki
Mathematics 2022, 10(23), 4523; https://doi.org/10.3390/math10234523 - 30 Nov 2022
Cited by 4 | Viewed by 1364
Abstract
The mechanical properties of rocks, such as uniaxial compressive strength and elastic modulus of intact rock, must be determined before any engineering project by employing lab or in situ tests. However, there are some circumstances where it is impossible to prepare the necessary [...] Read more.
The mechanical properties of rocks, such as uniaxial compressive strength and elastic modulus of intact rock, must be determined before any engineering project by employing lab or in situ tests. However, there are some circumstances where it is impossible to prepare the necessary specimens after exposure to high temperatures. Therefore, the propensity to estimate the destructive parameters of thermally heated rocks based on non-destructive factors is a helpful research field. Egyptian granodiorite samples were heated to temperatures of up to 800 °C before being treated to two different cooling methods: via the oven (slow-cooling) and using water (rapid cooling). The cooling condition, temperature, mass, porosity, absorption, dry density (D), and P-waves were used as input parameters in the predictive models for the UCS and E of thermally treated Egyptian granodiorite. Multi-linear regression (MLR), random forest (RF), k-nearest neighbor (KNN), and artificial neural networks (ANNs) were used to create predictive models. The performance of each prediction model was also evaluated using the (R2), (RMSE), (MAPE), and (VAF). The findings revealed that cooling methods and mass as input parameters to predict UCS and E have a minor impact on prediction models. In contrast, the other parameters had a good relationship with UCS and E. Due to severe damage to granodiorite samples, many input and output parameters were impossible to measure after 600 °C. The prediction models were thus developed up to this threshold temperature. Furthermore, the comparative analysis of predictive models demonstrated that the ANN pattern for predicting the UCS and E is the most accurate model, with R2 of 0.99, MAPE of 0.25%, VAF of 97.22%, and RMSE of 2.04. Full article
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26 pages, 11808 KiB  
Article
Rainfall-Induced Landslides from Initialization to Post-Failure Flows: Stochastic Analysis with Machine Learning
by Haoding Xu, Xuzhen He and Daichao Sheng
Mathematics 2022, 10(23), 4426; https://doi.org/10.3390/math10234426 - 24 Nov 2022
Cited by 5 | Viewed by 1249
Abstract
Rainfall-induced landslides represent a severe hazard around the world due to their sudden occurrence, as well as their widespread influence and runout distance. Considering the spatial variability of soil, stochastic analysis is often conducted to give a probability description of the runout. However, [...] Read more.
Rainfall-induced landslides represent a severe hazard around the world due to their sudden occurrence, as well as their widespread influence and runout distance. Considering the spatial variability of soil, stochastic analysis is often conducted to give a probability description of the runout. However, rainfall-induced landslides are complex and time-consuming for brute-force Monte Carlo analyses. Therefore, new methods are required to improve the efficiency of stochastic analysis. This paper presents a framework to investigate the influence and runout distance of rainfall-induced landslides with a two-step simulation approach. The complete process, from the initialization of instability to the post-failure flow, is simulated. The rainfall infiltration process and initialization of instability are first solved with a coupled hydro-mechanical finite element model. The post-failure flow is simulated using the coupled Eulerian–Lagrangian method, wherein the soil can flow freely in fixed Eulerian meshes. An equivalent-strength method is used to connect two steps by considering the effective stress of unsaturated soil. A rigorous method has been developed to accurately quantify the influence and runout distance via Eulerian analyses. Several simulations have been produced, using three-dimensional analyses to study the shapes of slopes and using stochastic analysis to consider uncertainty and the spatial variability of soils. It was found that a two-dimensional analysis assuming plain strain is generally conservative and safe in design, but care must be taken to interpret 2D results when the slope is convex in the longitudinal direction. The uncertainty and spatial variability of soils can lead to the statistic of influence and runout distance. The framework of using machine-learning models as surrogate models is effective in stochastic analysis of this problem and can greatly reduce computational effort. Full article
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30 pages, 18327 KiB  
Article
Progressive Fracture Behavior and Acoustic Emission Release of CJBs Affected by Joint Distance Ratio
by Yongyi Wang, Bin Gong, Yongjun Zhang, Xiaoyu Yang and Chun’an Tang
Mathematics 2022, 10(21), 4149; https://doi.org/10.3390/math10214149 - 06 Nov 2022
Cited by 14 | Viewed by 1315
Abstract
The progressive collapse behavior and energy release of columnar jointed basalts (CJBs) can be greatly influenced by different joint distance ratios. By adopting the digital image correlation, a series of heterogeneous CJB models are established. The continuous fracture process and acoustic emissions (AEs) [...] Read more.
The progressive collapse behavior and energy release of columnar jointed basalts (CJBs) can be greatly influenced by different joint distance ratios. By adopting the digital image correlation, a series of heterogeneous CJB models are established. The continuous fracture process and acoustic emissions (AEs) are captured numerically under varying lateral pressures. The load curves under different joint distance ratios and model boundaries are analyzed. Meanwhile, the strength, deformation modulus and AE rule are discussed. The data indicate that under plane strain, the troughs of compression strength appear at the column dip angle β = 30°, 150°, 210° or 330°; the equivalent deformation modulus changes in an elliptical way with β increasing; the compression strength and equivalent deformation modulus are higher than the case between plane stress and plane strain under different joint distance ratios. When β = 30°, the accumulation of AE energy corresponding to the stress peak under plane strain are higher than the case between plane stress and plane strain but becomes lower when β increases to 60°, which implies the critical transformation of the AE energy-related failure precursor affected by column dip angle. These achievements will contribute to the design, construction and support of slopes and tunnels encountering CJBs. Full article
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