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Abstract By depletion of minerals at shallow depths, there is a notable growing trend towards mining operations in deeper grounds whole the world. However, as the depth of mining and underground constructions increases, the occurrence of stress-induced failure processes, such as rockburst, both inside the rock masses, ...
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The robust ML algorithms, such as gene expression programming (GEP), GEP-based logistic regression (GEP-LR), classification and regression tree (CART) etc., were programmed and employed for the following tasks: (a) Providing a mathematical binary model to estimate the occurrence/non-occurrence of rockburst hazard; (b) ...
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with the applied stress level, representing the propensity of rocks to brittle failures like rockburst. To better replicate the rock stress conditions in deep underground mines and understand more about the evolution of some specific rock fatigue characteristics, such as strength hardening, FTS and post-peak instabilit...
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Statement of Originality I certify that this work contains no material which has been accepted for the award of any other degree or diploma in my name in any university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, exce...
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Chapter 1 Thesis Overview 1.1. Introductory Background With an increase in depth of mining and underground constructions, due to the complex stress state induced by different loading conditions (i.e. static, quasi-static and dynamic loadings), the occurrence of some destructive phenomena such as rockburst in the confin...
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many influential parameters, its mechanism is still unclear. Therefore, there exists a remarkable theoretical significance and engineering value to deeply understand the rockburst mechanism and find solutions for its prediction and treatment. 1.2. Literature Review and Research Gaps 1.2.1. Rockburst Occurrence and its ...
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such essential limitations and the complex non-linear nature of rockburst hazard, recently, the application of data-driven approaches such as machine learning (ML) algorithms have been increased in this field. The ML techniques (supervised and unsupervised algorithms) are capable of including more input parameters/pred...
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with the ordinary ones, have higher resistance against dynamic loads and are capable of absorbing energy from multiple impacts, and finally, can maintain the large deformation of rock masses; (2) Application of ground preconditioning techniques such as destressing and water infusion (hydrofracturing). Destressing can b...
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to calibrate the numerical models as well as to identify the critical stress conditions leading to dynamic failures. These experimental tests include uniaxial compression/tensile tests (Gong et al. 2019), conventional triaxial unloading tests (Huang et al. 2001), combined uniaxial and biaxial static-dynamic (cyclic) te...
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database from rockburst tests and the application of robust ML techniques. By doing so, the developed model can be used conveniently in practice to predict bursting stress when the testing apparatus is not available. 1.2.4. Seismic Events and Rock Failure Behaviour As stated earlier, rockburst can also be triggered by ...
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process as well as 𝜎 and 𝜎 can be obtained from each other. Moreover, previous studies show 𝑐 𝑡 that rocks with different 𝜎 and 𝜎 may have similar 𝐵𝐼 values representing the narrow range 𝑐 𝑡 of variation of this index (Munoz et al. 2016; Meng et al. 2020). Hence, the rock brittleness can be measured in a more...
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of the foregoing parameters with confinement level can open new insights into the failure mechanism of rocks, long-term stability of openings and reinforcement design. This task, however, requires applying a triaxial testing method, capable of recording the large lateral deformations created in the post-failure stage. ...
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The current chapter, Chapter 1, provides an introductory background regarding this research and contains topics including problem statement, literature review and research gaps, research objectives and thesis layout and conclusions and recommendations. In Chapter 2, to address objective 1, a comprehensive study is carr...
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input parameters and the corresponding output during a smart procedure, and finally, link each observation (rockburst event) to an appropriate cluster (risk level). In addition to SOM and FCM techniques, five empirical criteria are also employed to assess their capability in clustering rockburst events. Five common per...
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most probable failure type in different locations and consequently apply an appropriate controlling technique. The results of this study were prepared as a journal paper entitled “Rockburst assessment in deep geotechnical conditions using true-triaxial tests and data-driven approaches”. The details of this paper are as...
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Shirani Faradonbeh R, Taheri A, Ribeiro e Sousa L, Karakus M (2020) Rockburst assessment in deep geotechnical conditions using true-triaxial tests and data-driven approaches. International Journal of Rock Mechanics and Mining Sciences 128:104279 (IF= 7.135, Q1) In Chapter 6, by reviewing the prior rock fatigue studies,...
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uniaxial loading conditions (objective 6). This chapter also intends to examine some specific behaviours observed in the previous chapter (e.g. cyclic loading-induced strength hardening) in more depth. In this chapter, the uniformity of the testing material is initially evaluated based on the performed six 𝑈𝐶𝑆 tests...
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Prediction and control of rock burst phenomenon in deep underground mining based on rock behaviour Objective 1: A practical model for rockburst Objective 5: New testing method to capture post- occurrence prediction peak behaviour of rocks under cyclic loading Objective 2: Assessing rockburst risk levels accurately Obje...
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Cerfontaine B, Collin F (2018) Cyclic and fatigue behaviour of rock materials: review, interpretation and research perspectives. Rock Mechanics and Rock Engineering 51(2):391–414 Feng X (2017) Rockburst : mechanisms, monitoring, warning, and mitigation. Butterworth- Heinemann Gong F, Yan J, Li X, Luo S (2019) A peak-st...
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of cloud models with attribution weight. Natural Hazards 68:549–568 Meng F, Wong LNY, Zhou H (2020) Rock brittleness indices and their applications to different fields of rock engineering: A review. Journal of Rock Mechanics and Geotechnical Engineering, 68(2):549-568 Munoz H, Taheri A, Chanda EK (2016) Fracture Energy...
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Statement of Authorship Title of Paper Long-term prediction of rockburst hazard in deep underground openings using three robust data mining techniques Publication Status Published Accepted for Publication Submitted for Publication Unpublished and Unsubmitted work written in manuscript style Publication Details Shirani ...
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Chapter 2 Long-term Prediction of Rockburst Hazard in Deep Underground Openings using Three Robust Data Mining Techniques Abstract Rockburst phenomenon is the extreme release of strain energy stored in surrounding rock mass which could lead to casualties, damage to underground structures and equipment and finally endan...
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2.1. Introduction One of the most important concerns in deep underground activities such as mining and civil projects is the occurrence of rockburst phenomenon. Rockburst is an unexpected and severe failure of a large volume of over-stressed rock caused by the instantaneous release of accumulated strain energy. This ph...
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enable them to decide about the excavating and controlling methods (Adoko et al. 2013; Li et al. 2017). During the last three decades, various rockburst proneness indices have been developed based on strength parameters and rock strain energy (see Table 2.1) [15]. Table 2.1 A summary of conventional criteria for rockbu...
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increase of 𝑊 , the probability of rockburst occurrence and its intensity will increase 𝑒𝑡 (Palmstrom 1995; Jian et al. 2012; Liu et al. 2013; Li et al. 2017). Therefore, in the current study, four parameters of 𝜎 , 𝜎 , 𝜎 , and 𝑊 were adopted as the input parameters. Table 2.2 𝜃 𝑡 𝑐 𝑒𝑡 shows the descriptive...
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3(𝑄3−𝑄1),𝑄3+3(𝑄3−𝑄1)) are defined as extreme outliers and should to be omitted from the database, while those which are in the range of (𝑄1−1.5(𝑄3−𝑄1),𝑄3+1.5(𝑄3−𝑄1)) are known as suspected outliers which are common in a big database and could be considered in modelling (Middleton 2000). Fig. 2.1 shows the bo...
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Eventually, the PCs were obtained by multiplying the input parameters in related eigenvectors. Fig. 2.2 shows the scree plot of eigenvalues against the number of components. According to this figure, 92.872 % of the database variations can be explained just with three first PCs by projecting the observations on these a...
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and output layers that finally lead to high computational complexity (CC). Recently, a limbic- based emotional neural network (ENN) is developed by Lotfi and Akbarzadeh-T (2014) based on the emotional process of the brain with a single layer structure. Unlike ANNs that is formed based on a biological neuron, ENNs are b...
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where 𝑌𝑘 is the output of the winner part for 𝑘th input pattern, 𝑇𝑘 is the related target and 𝑚 is the number of training pattern targets. By minimizing the cost function, the best learning weights for WTAENN can be obtained (Lotfi et al. 2014; Lotfi and Akbarzadeh-T 2014, 2016). 2.3.1.1. Rockburst Prediction Usi...
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0.4 0.35 0.3 0.25 E S 0.2 M 0.15 0.1 0.05 0 0 50 100 150 200 250 300 Generation number and population size Figure 2.5 Variation of fitness function for different values of generation number and population size Table 2.4 Characteristics of developed GA-ENN model Parameter Value Input variables MTS, UTS, UCS, EEI Output ...
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have a vague internal computational procedure, which means the results are difficult to interpret. In the case of having a problem with many variables which act in reciprocally and non-linear ways, finding a comprehensive model may be very difficult. In these circumstances, DT can be a suitable alternative which is abl...
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pessimistic upper bound on the error rate at a leaf/node. The smaller this value, the more pessimistic the estimated error is and generally the heavier the pruning. If a CF greater than 0.5 is chosen, then the pruning will be done on the basis of unchanged classification error on the training dataset and this is equiva...
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takes advantage of basic GA and genetic programming (GP) methods. The main goal of the GEP is to find a rational mathematical relationship between the independent variables and the corresponding dependent in such a way that the defined fitness function reaches its minimal value. In GEP, possible solutions are in the fo...
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Head Tail Create initial population e.g. Q * + - a b c d a a d Express chromosomes - c Q × b + Execute each program a (𝑎+𝑏).(𝑐−𝑑) 𝑛 Evaluate fitness e.g. 𝑅𝑀𝑆𝐸= 1/𝑛 (𝑥 −𝑥 )2 𝑖𝑟𝑒𝑎𝑙 𝑖𝑝𝑟𝑒𝑑 𝑖=1 Yes Termination? Genetic operators for reprodcution: End No 1) Mutation (an element is changed to another) Q...
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where 𝑆𝐸 is the sensitivity and 𝑆𝑃 is the specificity of the chromosome 𝑖, and are given by 𝑖 𝑖 the following formulas: 𝑇𝑃 𝑆𝐸 = 𝑖 (2.13) 𝑖 𝑇𝑃 +𝐹𝑁 𝑖 𝑖 𝑇𝑁 𝑆𝑃 = 𝑖 (2.14) 𝑖 𝑇𝑁 +𝐹𝑃 𝑖 𝑖 where 𝑇𝑃, 𝑇𝑁, 𝐹𝑃, and 𝐹𝑁 represent, respectively, the number of true positives, true 𝑖 𝑖 𝑖 𝑖 nega...
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to link genes to each other. Addition (+) is a most common linking function which was used for this aim. After adjusting the GEP parameters (Table 2.5), the model was executed in training mode for 2000 generations and the results were recorded. Eq. 2.17 shows the developed rockburst index based on GEP algorithm. By fee...
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represents the instances in an actual class while each column represents the instances in a predicted class (or vice versa). Table 2.7 shows the confusion matrices of the developed models. According to Tables 2.6 and 2.7, GA-ENN and GEP models have the equal number of misclassified cases (i.e. 4 cases), while this numb...
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17 18.8 6.3 171.5 7 0 0 0 0 0 0 0 1 1 18 105.5 12.1 170 5.76 1 1 1 1 1 1 1 1 1 19 39 2.4 70.1 4.8 1 1 1 1 1 1 1 1 1 20 27.8 2.1 90 1.8 0 1 0 0 1 1 1 0 0 21 30 3.7 88.7 6.6 1 1 1 0 1 1 1 1 1 22 40.6 2.6 66.6 3.7 1 1 1 1 1 1 1 1 1 23 11 5 115 5.7 0 0 0 0 0 0 0 1 1 24 59.82 7.31 85.8 2.78 1 1 1 1 1 1 1 1 1 25 7.5 3.7 52 1...
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2.5. Sensitivity Analysis In this section a sensitivity analysis is performed to evaluate the effects of input parameters on rockburst prediction models. To this end, the relevancy factor (Kamari et al. 2015) was used which is calculated by Eq. 2.19. ∑𝑛 (𝐼 −𝐼̅ )(𝑃 −𝑃̅) 𝑟 = 𝑖=1 𝑖,𝑘 𝑘 𝑖 (2.19) √∑𝑛 𝑖=1(𝐼 𝑖,...
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geotechnical engineering applications. However, as a black-box method like ANN, GA-ENN neither can provide any equation nor a visual pattern for users. This may be considered as a disadvantage for this algorithm, but it is possible to overcome this issue by using this technique to find some optimum coefficients of the ...
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134 35 133.4 9.3 2.9 Yes References Adoko AC, Gokceoglu C, Wu L, Zuo QJ (2013) Knowledge-based and data-driven fuzzy modeling for rockburst prediction. International Journal of Rock Mechanics and Mining Sciences 61:86–95 Akdag S, Karakus M, Taheri A, et al (2018) Effects of Thermal Damage on Strain Burst Mechanism for ...
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Dong L, Shu W, Li X, et al (2017a) Three Dimensional Comprehensive Analytical Solutions for Locating Sources of Sensor Networks in Unknown Velocity Mining System. IEEE Access 5:11337–11351 Dong L, Sun D, Li X, Du K (2017b) Theoretical and Experimental Studies of Localization Methodology for AE and Microseismic Sources ...
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Underground Space Technology 68:32–37 Gong FQ, Li XB (2007) A distance discriminant analysis method for prediction of possibility and classification of rockburst and its application. Chinese Journal of Rock Mechanics and Engineering 26(5):1012-1018 (in Chinese) Güllü H (2012) Prediction of peak ground acceleration by g...
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50(4):629–644 Kamari A, Arabloo M, Shokrollahi A, et al (2015) Rapid method to estimate the minimum miscibility pressure (MMP) in live reservoir oil systems during CO2flooding. Fuel 153:310–319 Kayadelen C (2011) Soil liquefaction modeling by Genetic Expression Programming and Neuro-Fuzzy. Expert Systems with Applicati...
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The bulletin of mathematical biophysics 5(4):115–133 Middleton G V (2000) Data analysis in the earth sciences using MATLAB®. Prentice Hall, USA Mikaeil R, Haghshenas SS, Hoseinie SH (2018a) Rock Penetrability Classification Using Artificial Bee Colony (ABC) Algorithm and Self-Organizing Map. Geotechnical and Geological...
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Shi XZ, Zhou J, Dong L, et al (2010) Application of unascertained measurement model to prediction of classification of rockburst intensity. Chinese Journal of Rock Mechanics and Engineering 29(1):2720–2726 Sousa R, Einstein HH (2007) Risk analysis for tunnelling projects using bayesian networks. In: 11th Congress of th...
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Statement of Authorship Title of Paper Application of self-organising map and fuzzy c-mean techniques for rockburst clustering in deep undreground projects Publication Status Published Accepted for Publication Submitted for Publication Unpublished and Unsubmitted work written in manuscript style Publication Details Shi...
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Chapter 3 Application of Self-Organizing Map and Fuzzy c- mean Techniques for Rockburst Clustering in Deep Underground Projects Abstract One of the main concerns associated with deep underground constructions is the violent expulsion of rock induced by unexpected release of strain energy from surrounding rock masses th...
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3.1. Introduction Nowadays, there are many important mining and civil projects such as hard rock mines, hydropower stations, nuclear power plants, and water conveyance and transportation tunnels under construction in the deep ground condition all over the world. It is proved that by increasing of the depth, in-situ str...
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Strain burst Stress concentration behind the face 0 = No confinement 3 against the face s Pillar burst Changing driving shear stress t Geological Stress change acting feature upon a locking point Fault-slip burst Changing clamping normal stress s N Figure 3.1 Schematic representation of rockburst types and the effect o...
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Table 3.1 Most common strength- and energy-based criteria for the prediction of rockburst intensity Type Criterion Equation None Light Moderate Strong Strength Russenes criterion 𝜎 𝜃 <0.25 0.25 0.33−0.55 >0.55 (Russenes 1974) 𝜎 based 𝑐 −0.33 Barton et al. 𝜎 𝑐 >5 (2.5−5] − ≤2.5 (Barton et al. 1974) 𝜎 1 Hoek crite...
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using novel ML techniques (Xie and Pan 2007; Gao 2010; Shi et al. 2010; Zhou et al. 2010; Zhang et al. 2011; Li and Liu 2015). It should be mentioned that most of the used ML techniques to assess rockburst phenomenon such as ANNs have a complicated internal structure and their results are not easy to use in practice. A...
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of clustering of rockburst datasets using SOM and FCM algorithms was conducted based on the 58 data samples. Afterwards, for the sake of checking the applicability of empirical criteria, five strength-based of them were selected and finally, their accuracy in clustering the rockburst data samples was evaluated. 3.2. Me...
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𝐷 = ‖𝑋−𝑊‖ = ∑𝑛 (𝑋 −𝑊)2 (3.1) 𝑖=1 𝑖 𝑖 The so-called winner neuron (BMU) has the smallest D. In cooperation phase, the neurons which are located in the immediate vicinity of the BMU are recognized and then in the adaptation phase, these neurons are adjusted using Eq. 3.2 to shape a particular pattern on a plane ...
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logic in various sciences. Fuzzy c-mean (FCM) is one of the clustering techniques which was first proposed by Bezdek (1981) based on the iterative optimization. In fact, FCM is the advanced version of hard c-means clustering in which unlike the classic clustering, the membership degree of data in a cluster can have a v...
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3.3. Results and Discussion 3.3.1. Rockburst Data In this study, a total of 58 rockburst events were compiled from the literature belong to various underground openings all around the world (Jian et al. 2012; Dong et al. 2013; Adoko et al. 2013). Due to difficulties in recording the rockburst-related parameters and the...
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uniaxial compression (Kidybiński 1981). This parameter also can be measured directly using the double-hole method or indirectly using the rebound method. Therefore, in the current study, four parameters of maximum tangential stress, uniaxial compressive strength, tensile strength, and the elastic energy index were adop...
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Table 3.3 Descriptive statistics of collected rockburst dataset Input parameter Statistical feature 𝜎 𝜎 𝜎 𝑊 𝜃 𝑐 𝑡 𝑒𝑡 Abbreviation T UCS UTS EEI Unit MPa MPa MPa Dimensionless Minimum 2.6 20 1.3 1.1 Maximum 167.2 263 22.6 9 Mean 49.752 114.592 6.039 4.553 Variance (n) 1184.511 2673.039 18.545 4.332 Standard dev...
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3.3.2. Implementation of SOM Technique For SOM modeling, 58 datasets with the main parameters of T, UCS, UTS, EEI, and the corresponding rockburst intensities were used, and the process of modeling was conducted in MATLAB software environment. First, all the 58 datasets related to the four mentioned parameters were nor...
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Figure 3.4 Hits plot for SOM model In pursuance of more transparency, weighted distances between neighboring neurons were measured and displayed in Fig. 3.5. The axes in Fig. 3.5 show the weighted distances between neurons. The darker colors show that neurons (classes) are closer to each other and vice versa. For examp...
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FCM and examining different combinations of control parameters, the values of 100, 0.00001, and 2 were obtained for the maximum iteration, 𝜀 , and 𝑚′, respectively. Then, the algorithm 𝐿 was implemented based on the determined values and the variations of cost function was recorded that is shown in Fig. 3.7. Accordi...
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the SOM and FCM techniques along with the ones obtained from empirical criteria are given in Table 3.6. To have a quantitative insight regarding the performance of the developed models, five performance metrics i.e. accuracy rate (Grinand et al. 2008), Cohen’s Kappa coefficient (Kappa) (Cohen 1960), precision, recall, ...
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classify and predict rockburst intensity. It should be noted that the empirical methods have been developed based on specific case studies and some engineering judgments and consider few input parameters, while the datasets compiled in this study have a broad range of rock properties and locations. As mentioned in the ...
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11 N N N N L L N N 12 N N N N L L N N 13 M M L L M M M M 14 M M L L M S M M 15 S S S S S S S S 16 N N N N S N N N 17 N L N N M M M N 18 N N N N M M N N 19 S M M M S S M S 20 M S S S M M S M 21 S S S S S S S S 22 N S S S S N N N 23 N N N N M M N N 24 L M L L M S L L 25 S L N N M S L S 26 S L L L M S M S 27 N N N N M M M...
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Table 3.7 Confusion matrix for different models No. Model Confusion matrix No. Model Confusion matrix 1 Russenes Predicted 5 EEI Predicted N L M S N L M S Actual N 15 3 2 2 Actual N 11 4 6 1 L 0 0 4 0 L 0 0 1 3 M 0 0 11 8 M 0 0 9 10 S 0 4 2 7 S 0 0 3 10 2 Hoek Predicted 6 FCM Predicted N L M S N L M S Actual N 17 3 0 2...
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3.5. Summary and Conclusions Many empirical equations have been proposed by researchers to predict rockburst intensities in recent years. However, according to the literature, they are not sufficient and reliable. The maximum tangential stress, uniaxial compressive strength, uniaxial tensile strength, and elastic energ...
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References Adoko AC, Gokceoglu C, Wu L, Zuo QJ (2013) Knowledge-based and data-driven fuzzy modeling for rockburst prediction. International Journal of Rock Mechanics and Mining Sciences 61:86–95 Akdag S, Karakus M, Taheri A, et al (2018) Effects of Thermal Damage on Strain Burst Mechanism for Brittle Rocks Under True-...
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deep mining. Innovative numerical modelling in geomechanics 393–414 Chen BR, Feng XT, Li QP, et al (2013) Rock Burst Intensity Classification Based on the Radiated Energy with Damage Intensity at Jinping II Hydropower Station, China. Rock Mechanics and Rock Engineering 48(1):289–303 Chen ZY, Kuo RJ (2017) Combining SOM...
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spatial context. Geoderma 143(1-2):180–190 Hagan MT, Demuth HB, Beale MH, others (1996) Neural network design. Pws Pub. Boston He J, Dou L, Gong S, et al (2017) Rock burst assessment and prediction by dynamic and static stress analysis based on micro-seismic monitoring. International Journal of Rock Mechanics and Minin...
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approach and its application. Sci Technol Rev 33(1):57–62 Li C, Cai M, Qiao L, Wang S (1996) Rock complete stress-strain curve and its relationship to rockburst. Journal of University of Science and Technology Beijing 21(6):513-5 (in Chinese) Li N, Feng X, Jimenez R (2017) Predicting rock burst hazard with incomplete d...
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on genetic algorithm for predicting ripping production. Neural Computing and Applications 28(1):393-406 Palmstrom A (1995) Characterizing the strength of rock masses for use in design of underground structures. In: International conference in design and construction of underground structures, p 10 Rad MY, Haghshenas SS...
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Wang YH, Li WD, Lee PKK, Tham LG (1998) Method of duzzy comprehensive evaluations for rockburst prediction. Chinese Joirnal of Rock Mechanics and Engineering 17(5):493- 501 (in Chinese) Weng L, Huang L, Taheri A, Li X (2017) Rockburst characteristics and numerical simulation based on a strain energy density index: A ca...
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Statement of Authorship Title of Paper The propensity of the over-stressed rock masses to different failure mechanisms based on a hybrid probabilistic approach Publication Status Published Accepted for Publication Submitted for Publication Unpublished and Unsubmitted work written in manuscript style Publication Details...
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Chapter 4 The Propensity of the Over-Stressed Rock Masses to Different Failure Mechanisms Based on a Hybrid Probabilistic Approach Abstract The simultaneous impact of excavation-induced stress concentration and mining disturbances on deep underground mines/tunnels can result in severe and catastrophic failure like stra...
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4.1. Introduction The mechanical rock properties and their corresponding deformation failure mechanisms are dramatically different in deep underground than those in shallow conditions. This is due to the high geo-stress, ground-water pressure and high-temperature environment, which affect the rock mass for a long time....
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maximum tangential stresses by creating a local V-shaped notch on the opening boundary (Ortlepp 2001). Fig. 4.1b displays the slabbing failure in the roof of a mine drift excavated in quartzite at 1000 m depth. Strain burst is a term for the much more violent fracturing of rocks than slabbing accompanied by the high se...
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consequently have a higher potential to bursting. In addition, the strength parameters have been used extensively to assess this hazard by different researchers using supervised and unsupervised data-mining algorithms (Pu et al. 2019). On the other hand, the modulus of rigidity is an important parameter to study the st...
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mathematical models cannot be implemented to unveil the latent relationships between parameters. Hence, soft computing techniques can be assumed as alternative approaches to tackle this difficulty. These techniques learn from the experiences and recognise the patterns in the database automatically (Mitchell 1997). From...
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underground hard rock mines (mostly in Australia) with the known failure mechanism (Lee et al. 2018). Each dataset corresponds to a specific failure mechanism (i.e. strain burst, slabbing and squeezing) defined based on the in-situ observations of the fracturing process. The definition of these failure mechanisms is as...
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4.3. Methodology and Results As mentioned earlier, soft computing algorithms, e.g. artificial neural network (ANN) and support vector machine (SVM), have shown promising results in dealing with non-linear problems in different mining and geotechnical projects. However, these techniques suffer from several limitations, ...
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3 3 le b le b a l m a l m s in s in a h 2 a h 2 c c e e m m e e r r u u lia lia F 1 F 1 0 100 200 300 400 0 10 20 30 s (MPa) s (MPa) c t 3 3 le le b b a a l m l m s s in in a h 2 a h 2 c c e e m m e e r u r u lia F 1 lia F 1 0 40 80 120 160 0.0 0.1 0.2 0.3 0.4 0.5 E (GPa) n Figure 4.4 Failure mechanism with respect to ...
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determined by the user through a trial-and-error procedure. However, the length of the tail (t) is a function of head size and the maximum argument number (𝑛 ) and can be determined 𝑚𝑎𝑥 using the following equation: 𝑡 = ℎ(𝑛 −1)+1 (4.2) 𝑚𝑎𝑥 Fig. 4.5 schematically displays the foundation of the GEP algorithm. Ho...
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(i.e. recombination). Afterwards, improved solutions are transferred to the next generation (Fig. 4.5g). • The above process continues until the termination criterion is met. In this study, firstly, three separate GEP-based binary models are developed to predict the occurrence (i.e. “1”) or non-occurrence (i.e. “0”) of...
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genes for each chromosome, head size, linking function and the genetic operators, several preliminary runs are also performed to find the optimum solution with highest fitness value for each failure mechanism class. The obtained optimum values for the GEP parameters are listed in Table 4.2. By applying these settings t...
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(a) Head Tail Head Tail Create initial population - b × b a b b a b × √ b + a b b b a Gene 1 Gene 2 Linking function Root node (b) Express solutions as ETs / Root node - × b × √ b + (c) 𝑏−(𝑏×𝑎) b a Execute each program a b √𝑎+𝑏×𝑏 Gene 1 (d) Evaluate fitness Correlation coefficient (r) Gene 2 1) Mutation - b × b a...
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