Editorial

5 pages, 175 KiB

Open AccessEditorial

Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics

by Shaofeng Wang, Xin Cai, Jian Zhou, Zhengyang Song and Xiaofeng Li

Mathematics 2022, 10(18), 3403; https://doi.org/10.3390/math10183403 - 19 Sep 2022

Cited by 2 | Viewed by 1319

With the increasing requirements for energy, resources and space, numerous rock engineering projects (e [...] Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

Research

Jump to: Editorial

11 pages, 950 KiB

Open AccessArticle

Closed-Form Solutions for Locating Heat-Concentrated Sources Using Temperature Difference

by Daoyuan Sun, Yifan Wu, Longjun Dong and Qiaomu Luo

Mathematics 2022, 10(16), 2843; https://doi.org/10.3390/math10162843 - 10 Aug 2022

Cited by 3 | Viewed by 1159

Abstract

The closed-form solution, one of the effective and sufficient optimization methods, is usually less computationally burdensome than iterative and nonlinear minimization in optimization problems of heat source localization. This work presents two-dimensional, closed-form solutions for locating heat-concentrated sources using temperature differences for known [...] Read more.

The closed-form solution, one of the effective and sufficient optimization methods, is usually less computationally burdensome than iterative and nonlinear minimization in optimization problems of heat source localization. This work presents two-dimensional, closed-form solutions for locating heat-concentrated sources using temperature differences for known and unknown temperature gradient systems. The nonlinear location equations for heat-concentrated source location are simplified to linear equations, and they are solved directly to obtain the analytical solution. To validate the accuracy of the proposed analytical solutions, three numerical examples of heat source localization were conducted. Results show that the proposed analytical solutions have a higher accuracy than iterative results by Levenberg–Marquardt. The locating accuracy for the three sources using AS-KTG improved by 94.82%, 90.40%, and 92.77%, while the locating accuracy for the three sources using AS-UTG improved by 68.94%, 16.72%, and 46.86%, respectively. It is concluded that the proposed method can locate the heat sources using temperatures and coordinates of sensors without the need for a heat transfer coefficient, a heat transfer rate, and thermal conductivity. These proposed analytical solutions can provide a new approach to locating heat sources for more complicated conditions using temperature differences, such as the localization of geothermal sources and nuclear waste leak points. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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16 pages, 7711 KiB

Open AccessArticle

Back Analysis of Surrounding Rock Parameters in Pingdingshan Mine Based on BP Neural Network Integrated Mind Evolutionary Algorithm

by Jianguo Zhang, Peitao Li, Xin Yin, Sheng Wang and Yuanguang Zhu

Mathematics 2022, 10(10), 1746; https://doi.org/10.3390/math10101746 - 20 May 2022

Cited by 14 | Viewed by 1213

Abstract

The mechanical parameters of surrounding rock are an essential basis for roadway excavation and support design. Aiming at the difficulty in obtaining the mechanical parameters of surrounding rock and large experimental errors, the optimized BP neural network model is proposed in this paper. [...] Read more.

The mechanical parameters of surrounding rock are an essential basis for roadway excavation and support design. Aiming at the difficulty in obtaining the mechanical parameters of surrounding rock and large experimental errors, the optimized BP neural network model is proposed in this paper. The mind evolutionary algorithm can adequately search the optimal initial weights and thresholds, while the neural network has the advantage of strong nonlinear prediction ability. So, the optimized BP neural network model (MEA-BP model) takes advantage of the two models. It can not only avoid the local extreme value problem but also improve the accuracy and reliability of the prediction results. Based on the orthogonal test method and finite element analysis method, training samples and test samples are established. The nonlinear relationship between rock mechanical parameters and roadway deformation is established by the BP model and MEA-BP model, respectively. The importance analysis of the three input variables shows that the ∆D is the most important input variable, while ∆BC has the smallest impact. The comparison of prediction performance between the MEA-BP model and BP model demonstrates that the optimized initial weights and thresholds can improve the accuracy of prediction value. Finally, the MEA-BP model has been well applied to predicting the mechanical parameter for the surrounding rock in the Pingdingshan mine area, which proves the accuracy and reliability of the optimized model. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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12 pages, 7690 KiB

Open AccessArticle

Numerical Modeling and Investigation of Fault-Induced Water Inrush Hazard under Different Mining Advancing Directions

by Chong Li and Zhijun Xu

Mathematics 2022, 10(9), 1561; https://doi.org/10.3390/math10091561 - 05 May 2022

Cited by 4 | Viewed by 1337

Abstract

Evaluations of the risk of fault-induced water inrush hazard is an important issue for mining engineering applications. According to the characteristics of the seam floor during mining advancing, a mechanical model of fault activation is built to obtain the equations of normal stress [...] Read more.

Evaluations of the risk of fault-induced water inrush hazard is an important issue for mining engineering applications. According to the characteristics of the seam floor during mining advancing, a mechanical model of fault activation is built to obtain the equations of normal stress and shear stress on the surface of fault, as well as the mechanics criterion of fault activation. Furthermore, using FLAC^3D numerical software, the stress variation on the surface of fault under two different mining advancing directions are numerically simulated, and the distribution characteristics of the plastic failure zone of the roof and floor near the fault are obtained. The results show that: (1) When mining advances from the hanging wall, the normal stress increases more greatly than that from the foot wall, the shear stress distribution changes drastically with a large peak, and it is more likely to cause fault activation. (2) When mining advances from the hanging wall and approaches the fault, the normal stress and shear stress within the fault first increases, and then decreases suddenly. When mining advances from the foot wall, the normal stress and shear stress increases constantly, and the fault zone stays in the compaction state where the hanging wall and foot wall are squeezed together, which is unfavorable for water inrush hazard. (3) When mining advances from the hanging wall, the deep-seated fault under the floor is damaged first, and the plastic failure zone of the floor increases obviously. When mining advances from the foot wall, the shallow fault under the floor is damaged first, and the plastic failure zone of roof increases obviously. (4) For a water-conducting fault, the waterproof coal pillar size of the mining advancing from the hanging wall should be larger than that from the foot wall. (5) The in-situ monitoring results are in agreement with the simulation results, which proves the effectiveness of the simulation. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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20 pages, 7760 KiB

Open AccessArticle

Effects of Strain Rate and Temperature on Physical Mechanical Properties and Energy Dissipation Features of Granite

by Yangchun Wu, Linqi Huang, Xibing Li, Yide Guo, Huilin Liu and Jiajun Wang

Mathematics 2022, 10(9), 1521; https://doi.org/10.3390/math10091521 - 02 May 2022

Cited by 9 | Viewed by 1732

Abstract

Dynamic compression tests of granite after thermal shock were performed using the split Hopkinson pressure bar system, to determine the effects of strain rate and temperature on the dynamic mechanical parameters, energy dissipation features and failure modes of granite. The results indicate that [...] Read more.

Dynamic compression tests of granite after thermal shock were performed using the split Hopkinson pressure bar system, to determine the effects of strain rate and temperature on the dynamic mechanical parameters, energy dissipation features and failure modes of granite. The results indicate that the dynamic compressive strength increased exponentially with strain rate and decreased with increasing temperature. Temperature and incident energy can equivalently transform for the same dynamic compressive strength. Dynamic elastic modulus of granite decreased obviously with increasing temperature but did not have a clear correlation with strain rate. As the impact gas pressure increased, the stress-strain curves changed from Class II to Class I behavior, and the failure modes of specimens transformed from slightly split to completely pulverized. The critical temperature at which the stress-strain curves changed from Class II to Class I was determined to be 300 °C, when the impact gas pressure is 0.6 MPa. As the applied temperature increased, density, wave velocity and wave impedance all decreased, meanwhile, the degree of granite specimen crushing was aggravated. Under the same incident energy, as the temperature increased, the reflected energy increased notably and the absorbed energy increased slightly, but the transmitted energy decreased. For the same temperature, the reflected and absorbed energies increased linearly as the incident energy increased, whereas the transmitted energy increased logarithmically. The SEM images of the thermal crack distribution on the granite specimen surface at different temperatures can well explain the essence of mechanical parameters deterioration of granite after thermal shock. This work can provide guidance for impact crushing design of high temperature rocks during excavations. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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25 pages, 8755 KiB

Open AccessArticle

Reliability Modelling of Pipeline Failure under the Impact of Submarine Slides-Copula Method

by Laifu Song, Hao Ying, Wei Wang, Ning Fan and Xueming Du

Mathematics 2022, 10(9), 1382; https://doi.org/10.3390/math10091382 - 20 Apr 2022

Cited by 6 | Viewed by 1778

Abstract

The instability of seabed slope sediments is the main factor influencing the safety of marine resource development. Therefore, to ensure the safe operation of submarine pipelines under complex and uncertain seabed rock and soil conditions, a reliability model was developed to elucidate the [...] Read more.

The instability of seabed slope sediments is the main factor influencing the safety of marine resource development. Therefore, to ensure the safe operation of submarine pipelines under complex and uncertain seabed rock and soil conditions, a reliability model was developed to elucidate the trend of impact-related pipeline damage due to submarine slides. Then, a risk assessment of the damage process of submarine slides impacting pipelines was conducted, which is of great significance for the in-depth safety assessment of pipelines impacted by submarine slides. Based on the copula function, a joint probability distribution model considering the correlation among risk variables was established for rational correlation characterization. A probability analysis method of impact-related pipeline damage attributed to submarine slides based on the copula function was proposed. The Monte Carlo simulation (MCS) method was employed to simulate the random uncertainty in limited observation values and accurately determine the reliability of safe pipeline operation under the action of submarine slides. The conclusions were as follows: (1) Based on the copula function, a joint probability distribution model of risk variables with any marginal distribution function and related structure could be developed. (2) The copula function could reasonably characterize relevant nonnormal distribution characteristics of risk variables and could simulate samples conforming to the distribution pattern of the risk variables. (3) The failure probability calculated with the traditional independent normal distribution model was very low, which could result in a notable overestimation of the reliability of submarine pipelines. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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13 pages, 2545 KiB

Open AccessArticle

Diffusion Mechanism of Slurry during Grouting in a Fractured Aquifer: A Case Study in Chensilou Coal Mine, China

by Minglei Zhai, Dan Ma and Haibo Bai

Mathematics 2022, 10(8), 1345; https://doi.org/10.3390/math10081345 - 18 Apr 2022

Cited by 5 | Viewed by 1589

Abstract

Grouting is one of the main technical means to prevent water inrush hazards in coal seam floor aquifers. It is of great significance to elucidate the diffusion law of slurry in the process of grouting in fractured aquifers for safe mining in coal [...] Read more.

Grouting is one of the main technical means to prevent water inrush hazards in coal seam floor aquifers. It is of great significance to elucidate the diffusion law of slurry in the process of grouting in fractured aquifers for safe mining in coal mines. In this paper, the mechanism of slurry diffusion in horizontal fractures of fractured aquifers was studied based on the Bingham slurry with time-varying characteristics; additionally, a one-dimensional seepage grouting theoretical model considering the temporal and spatial variation of slurry viscosity under constant grouting rate was established. In this model, the grouting pressure required by the predetermined slurry diffusion radius can be obtained by knowing the grouting hole pressure and injection flow. Slurry properties, fracture parameters, grouting parameters, and water pressure were the parameters affecting the slurry diffusion process. Looking at the problem of water disaster prevention of coal seam floor in the Working Face 2509 of the Chensilou Coal Mine, according to the aquifer parameters and model calculation results, a grouting scheme with a slurry diffusion radius of 20 m and grouting pressure of 12 MPa was proposed. Finally, with the comparative analysis of the transient electromagnetic method (TEM) and water inflow before and after grouting, it was verified that the design grouting pressure and the spacing of grouting holes were reasonable and the grouting effect was good. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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22 pages, 10685 KiB

Open AccessArticle

Mining Stress Evolution Law of Inclined Backfilled Stopes Considering the Brittle-Ductile Transition in Deep Mining

by Yuan Zhao, Guoyan Zhao, Jing Zhou, Xin Cai and Ju Ma

Mathematics 2022, 10(8), 1308; https://doi.org/10.3390/math10081308 - 14 Apr 2022

Cited by 4 | Viewed by 1334

Abstract

To study the mining stress evolution law of inclined backfilled stope in deep mining, this paper first proposes a method for determining the parameters of the brittle-ductile transition model corresponding to the Hoek–Brown criterion and Mohr-Coulomb criterion under high geostress. Then, a model [...] Read more.

To study the mining stress evolution law of inclined backfilled stope in deep mining, this paper first proposes a method for determining the parameters of the brittle-ductile transition model corresponding to the Hoek–Brown criterion and Mohr-Coulomb criterion under high geostress. Then, a model composed of inclined backfilled stopes with different depths is established to simulate the sequential mining process of ore bodies with varying depths from shallow to deep. The numerical model’s stratum displacement, rock mass stress distribution, and risk factors show that the mining-induced stress will move to the upper stopes and the stratum below the deepest stope. The transfer range and influence degree of mining-induced stress will increase with the increase of the deep mining, resulting in the most dangerous backfilled stope occurring one to two layers above the deepest stope and the apparent stress concentration area occurring below the deepest stope. To prevent disasters caused by mining stress, pillars in inclined deep stopes should have large safety factors. Replacing low-strength backfills with high-strength backfills can reduce the stress concentration in the stratum below the deepest stope. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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21 pages, 7041 KiB

Open AccessArticle

Optimization of Genetic Algorithm through Use of Back Propagation Neural Network in Forecasting Smooth Wall Blasting Parameters

by Ying Chen, Shirui Chen, Zhengyu Wu, Bing Dai, Longhua Xv and Guicai Wu

Mathematics 2022, 10(8), 1271; https://doi.org/10.3390/math10081271 - 11 Apr 2022

Cited by 9 | Viewed by 1497

Abstract

With the continuous development in drilling and blasting technology, smooth wall blasting (SWB) has been widely applied in tunnel construction to ensure the smoothness of tunnel profile, diminish overbreak and underbreak, and preserve the tunnel’s interior design shape. However, the complexity of the [...] Read more.

With the continuous development in drilling and blasting technology, smooth wall blasting (SWB) has been widely applied in tunnel construction to ensure the smoothness of tunnel profile, diminish overbreak and underbreak, and preserve the tunnel’s interior design shape. However, the complexity of the actual engineering environment and the deficiency of current optimization theories have posed certain challenges to the optimization of SWB parameters under arbitrary geological conditions, on the premise that certain control targets are satisfied. Against the above issue, a genetic algorithm (GA) and back propagation (BP) neural network-based computational model for SWB design parameter optimization is proposed. This computational model can comprehensively reflect the relation among geological conditions, design parameters, and results by training and testing the 285 collected sets of test data samples at different conditions. Moreover, it automatically searches optimal blasting design parameters through the control of SWB targets to acquire the optimal design parameters based on specific geological conditions of surrounding rocks and under the specified control targets. When the optimization algorithm is compared with other current optimization algorithms, it is shown that this algorithm has certain computational superiority over the existing models. When the optimized results are applied in practical engineering, it is shown that in overall consideration of the geological conditions, control targets, and other influencing factors, the proposed GA_BP-based model for SWB parameter optimization has high feasibility and reliability, and that its usage can be generalized to analogous tunneling works. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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20 pages, 9552 KiB

Open AccessArticle

Research on Zonal Disintegration Characteristics and Failure Mechanisms of Deep Tunnel in Jointed Rock Mass with Strength Reduction Method

by Baoping Chen, Bin Gong, Shanyong Wang and Chun’an Tang

Mathematics 2022, 10(6), 922; https://doi.org/10.3390/math10060922 - 14 Mar 2022

Cited by 21 | Viewed by 1840

Abstract

To understand the fracture features of zonal disintegration and reveal the failure mechanisms of circle tunnels excavated in deep jointed rock masses, a series of three-dimensional heterogeneous models considering varying joint dip angles are established. The strength reduction method is embedded in the [...] Read more.

To understand the fracture features of zonal disintegration and reveal the failure mechanisms of circle tunnels excavated in deep jointed rock masses, a series of three-dimensional heterogeneous models considering varying joint dip angles are established. The strength reduction method is embedded in the RFPA method to achieve the gradual fracture process, macro failure mode and safety factor, and to reproduce the characteristic fracture phenomenon of deep rock masses, i.e., zonal disintegration. The mechanical mechanisms and acoustic emission energy of surrounding rocks during the different stages of the whole formation process of zonal disintegration affected by different-dip-angle joints and randomly distributed joints are further discussed. The results demonstrate that the zonal disintegration process is induced by the stress redistribution, which is significantly different from the formation mechanism of traditional surrounding rock loose zone; the dip angle of joint set has a great influence on the stress buildup, stress shadow and stress transfer as well as the failure mode of surrounding rock mass; the existence of parallel and random joints lead the newly formed cracks near the tunnel surface to developing along their strikes; the random joints make the zonal disintegration pattern much more complex and affected by the regional joint composition. These will greatly improve our understanding of the zonal disintegration in deep engineering. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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23 pages, 11132 KiB

Open AccessArticle

Novel Ensemble Tree Solution for Rockburst Prediction Using Deep Forest

by Diyuan Li, Zida Liu, Danial Jahed Armaghani, Peng Xiao and Jian Zhou

Mathematics 2022, 10(5), 787; https://doi.org/10.3390/math10050787 - 01 Mar 2022

Cited by 30 | Viewed by 2551

Abstract

The occurrence of rockburst can cause significant disasters in underground rock engineering. It is crucial to predict and prevent rockburst in deep tunnels and mines. In this paper, the deficiencies of ensemble learning algorithms in rockburst prediction were investigated. Aiming at these shortages, [...] Read more.

The occurrence of rockburst can cause significant disasters in underground rock engineering. It is crucial to predict and prevent rockburst in deep tunnels and mines. In this paper, the deficiencies of ensemble learning algorithms in rockburst prediction were investigated. Aiming at these shortages, a novel machine learning model, deep forest, was proposed to predict rockburst risk. The deep forest combines the characteristics of deep learning and ensemble models, which can solve complex problems. To develop the deep forest model for rockburst prediction, 329 real rockburst cases were collected to build a comprehensive database for intelligent analysis. Bayesian optimization was proposed to tune the hyperparameters of the deep forest. As a result, the deep forest model achieved 100% training accuracy and 92.4% testing accuracy, and it has more outstanding capability to forecast rockburst disasters compared to other widely used models (i.e., random forest, boosting tree models, neural network, support vector machine, etc.). The results of sensitivity analysis revealed the impact of variables on rockburst levels and the applicability of deep forest with a few input parameters. Eventually, real cases of rockburst in two gold mines, China, were used for validation purposes while the needed data sets were prepared by field observations and laboratory tests. The promoting results of the developed model during the validation phase confirm that it can be used with a high level of accuracy by practicing engineers for predicting rockburst occurrences. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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17 pages, 6201 KiB

Open AccessArticle

Effect of Lithology on Mechanical and Damage Behaviors of Concrete in Concrete-Rock Combined Specimen

by Kewei Liu, Shaobo Jin, Yichao Rui, Jin Huang and Zhanxing Zhou

Mathematics 2022, 10(5), 727; https://doi.org/10.3390/math10050727 - 25 Feb 2022

Cited by 12 | Viewed by 1634

Abstract

A concrete structure built on rock foundation works together with the connected rock mass, which has a significant effect on the mechanical behaviors of the concrete structure. To study the effect of lithology on the mechanical and damage behaviors of concrete in a [...] Read more.

A concrete structure built on rock foundation works together with the connected rock mass, which has a significant effect on the mechanical behaviors of the concrete structure. To study the effect of lithology on the mechanical and damage behaviors of concrete in a concrete-rock combined specimen (CRCS), first, a test method for measuring the concrete part (concrete in CRCS) is adopted, then, uniaxial compression tests on seven types of specimens are performed and acoustic emission (AE) events are simultaneously monitored. Test results show that the low-strength concrete part plays a major role in the fracture behavior of CRCS. When the CRCS is failed, a sudden stress drop happens in CRCS, and the rock part (rock in CRCS) experiences a rapid axial strain recovery and intensifies the failure of the concrete part. The load-bearing and deformation capacities of the concrete part increase with the strength of the rock part, but the rock part shows the opposite behaviors under the influence of the concrete part. Furthermore, the damage of CRCS is mainly formed in the concrete part, and the damage extent of the concrete part is positively correlated with the strength of the rock part. Finally, a damage constitutive model of the concrete part is established and validated. This model can be used to accurately describe the effect of lithology on the mechanical response of the concrete part under uniaxial compression loading. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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21 pages, 11242 KiB

Open AccessArticle

Modeling Uranium Transport in Rough-Walled Fractures with Stress-Dependent Non-Darcy Fluid Flow

by Tong Zhang, Xiaodong Nie, Shuaibing Song, Xianjie Hao and Xin Yang

Mathematics 2022, 10(5), 702; https://doi.org/10.3390/math10050702 - 23 Feb 2022

Cited by 2 | Viewed by 1360

Abstract

The reactive-transportation of radioactive elements in fractured rock mass is critical to the storage of radioactive elements. To describe the reactive-transportation and distribution morphology of a uranium-containing solution, a stress-dependent reactive transport model was developed, and the simulator of FLAC3D-CFD was employed. The [...] Read more.

The reactive-transportation of radioactive elements in fractured rock mass is critical to the storage of radioactive elements. To describe the reactive-transportation and distribution morphology of a uranium-containing solution, a stress-dependent reactive transport model was developed, and the simulator of FLAC3D-CFD was employed. The uranium transport experiment subjected to the variation of confining stress of 5–19 MPa and hydraulic pressure of 0.5–3.5 MPa was conducted in fractured rock mass. The results show that the uranium-containing solution transport and distribution is significantly dependent on the evolution of the connected channel in rough-walled fracture, which is significantly influenced by the confining stress and hydraulic pressure. In more detail, the increase of confining stress resulted in the anisotropic of seepage channel in aperture, and corresponding turbulence flow and uranium retention were presented at the fracture aperture of 2–5 μm. As the increase of hydraulic pressure, flow regime evolved from the inertial flow to vortex flow, and the transformation region is 16 MPa confining stress and 1.5 MPa hydraulic pressure. The evolution of loading paths also dominates the flow and solute transport, and high seepage speed and strong solute transport were presented at the k = 1 (ratio of vertical stress loading to horizontal stress unloading), and a laminar flow and weak solute transport were presented at k = 0. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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19 pages, 7558 KiB

Open AccessArticle

Regressive and Big-Data-Based Analyses of Rock Drillability Based on Drilling Process Monitoring (DPM) Parameters

by Shaofeng Wang, Yu Tang, Ruilang Cao, Zilong Zhou and Xin Cai

Mathematics 2022, 10(4), 628; https://doi.org/10.3390/math10040628 - 17 Feb 2022

Cited by 6 | Viewed by 1761

Abstract

Accurate, rapid and effective analysis of rock drillability is very important for mining, civil and petroleum engineering. In this study, a method of rock drillability evaluation based on drilling process monitoring (DPM) parameters is proposed by using the field drilling test data. [...] Read more.

Accurate, rapid and effective analysis of rock drillability is very important for mining, civil and petroleum engineering. In this study, a method of rock drillability evaluation based on drilling process monitoring (DPM) parameters is proposed by using the field drilling test data. The revolutions per minute (N), thrust, torque and rate of penetration (ROP) were recorded in real time. Then, the two-dimensional regression analysis was utilized to investigate the relationships between the drilling parameters, and the three-dimensional regression analysis was used to establish models of ROP and specific energy (SE), in which the N-F-ROP, N-T-ROP and the improved SE model were obtained. In addition, the random forest (RF) and support vector machine combined with genetic algorithm (GA-SVM) were applied to predict rock drillability. Finally, a prediction model of uniaxial compressive strength (UCS) was established based on the SE and drillability index, I_d. The results show that both regression models and prediction models have good performance, which can provide important guidance and a data source for field drilling and excavation processes. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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16 pages, 4868 KiB

Open AccessArticle

Acoustic Emission b Value Characteristics of Granite under True Triaxial Stress

by Longjun Dong, Lingyun Zhang, Huini Liu, Kun Du and Xiling Liu

Mathematics 2022, 10(3), 451; https://doi.org/10.3390/math10030451 - 30 Jan 2022

Cited by 30 | Viewed by 2629

Abstract

The acoustic emission b value is an important and widely used parameter for the early prediction of rock fractures. In this study, five groups of true triaxial compression tests were conducted on granite specimens to analyze changes in b value during the process [...] Read more.

The acoustic emission b value is an important and widely used parameter for the early prediction of rock fractures. In this study, five groups of true triaxial compression tests were conducted on granite specimens to analyze changes in b value during the process of rock failure, and to investigate the b value characteristics of acoustic emission events. First, the acoustic emission events that simultaneously triggered at least four sensors were located using P-wave arrivals and sensor coordinates. Then, considering various intervals of acoustic emission event counts, stress magnitude, and stress proportion, b values were calculated using the values of the maximum amplitude, average amplitude, maximum absolute energy, and average absolute energy of the acoustic emission events. In addition, the goodness of the fitting curves was used to evaluate the fitting reliability of the b values. The results indicated higher accuracy of b value when calculated using the average amplitude setting for intervals of acoustic emission event counts of 200 or greater, stress magnitude of 20 MPa or greater, and stress proportion of 10% or greater. Moreover, the interval of event counts of 200 is suggested as a window parameter for b value calculations, and the b values are observed to exhibit a decreasing trend before fracture for more than 80% of the specimens. Furthermore, the b value tends to decrease with an increase in confining pressure. Thus, the b value can be used as an indicator for validating the stress concentration area, including magnitudes and accumulative probability density distribution of events, which is a beneficial complement to clarifying precursor information of rock mass instability. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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20 pages, 3626 KiB

Open AccessArticle

Predictive Modeling of Short-Term Rockburst for the Stability of Subsurface Structures Using Machine Learning Approaches: t-SNE, K-Means Clustering and XGBoost

by Barkat Ullah, Muhammad Kamran and Yichao Rui

Mathematics 2022, 10(3), 449; https://doi.org/10.3390/math10030449 - 30 Jan 2022

Cited by 41 | Viewed by 3453

Abstract

Accurate prediction of short-term rockburst has a significant role in improving the safety of workers in mining and geotechnical projects. The rockburst occurrence is nonlinearly correlated with its influencing factors that guarantee imprecise predicting results by employing the traditional methods. In this study, [...] Read more.

Accurate prediction of short-term rockburst has a significant role in improving the safety of workers in mining and geotechnical projects. The rockburst occurrence is nonlinearly correlated with its influencing factors that guarantee imprecise predicting results by employing the traditional methods. In this study, three approaches including including t-distributed stochastic neighbor embedding (t-SNE), K-means clustering, and extreme gradient boosting (XGBoost) were employed to predict the short-term rockburst risk. A total of 93 rockburst patterns with six influential features from micro seismic monitoring events of the Jinping-II hydropower project in China were used to create the database. The original data were randomly split into training and testing sets with a 70/30 splitting ratio. The prediction practice was followed in three steps. Firstly, a state-of-the-art data reduction mechanism t-SNE was employed to reduce the exaggeration of the rockburst database. Secondly, an unsupervised machine learning, i.e., K-means clustering, was adopted to categorize the t-SNE dataset into various clusters. Thirdly, a supervised gradient boosting machine learning method i.e., XGBoost was utilized to predict various levels of short-term rockburst database. The classification accuracy of XGBoost was checked using several performance indices. The results of the proposed model serve as a great benchmark for future short-term rockburst levels prediction with high accuracy. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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19 pages, 5577 KiB

Open AccessArticle

Physical and Mechanical Properties Evolution of Coal Subjected to Salty Solution and a Damage Constitutive Model under Uniaxial Compression

by Min Wang, Qifeng Guo, Yakun Tian and Bing Dai

Mathematics 2021, 9(24), 3264; https://doi.org/10.3390/math9243264 - 16 Dec 2021

Cited by 3 | Viewed by 2124

Abstract

Many underground reservoirs for storing water have been constructed in China’s western coal mines to protect water resources. Coal pillars which work as dams are subjected to a long-term soaking environment of concentrated salty water. Deterioration of the coal dam under the attack [...] Read more.

Many underground reservoirs for storing water have been constructed in China’s western coal mines to protect water resources. Coal pillars which work as dams are subjected to a long-term soaking environment of concentrated salty water. Deterioration of the coal dam under the attack of the salty solution poses challenges for the long-term stability and serviceability of underground reservoirs. The evolution of the physical and mechanical properties of coal subjected to salty solutions are investigated in this paper. Coal from a western China mine is made to standard cylinder samples. The salty solution is prepared according to chemical tests of water in the mine. The coal samples soaked in the salty solution for different periods are tested by scanning electron microscope, nuclear magnetic resonance, and ultrasonic detector techniques. Further, uniaxial compression tests are carried out on the coal specimens. The evolutions of porosity, mass, microstructures of coal, solution pH values, and stress–strain curves are obtained for different soaking times. Moreover, a damage constitutive model for the coal samples is developed by introducing a chemical-stress coupling damage variable. The result shows that the corrosion effect of salty solution on coal samples becomes stronger with increasing immersion time. The degree of deterioration of the longitudinal wave velocity (v_p) is positively correlated with the immersion time. With the increase in soaking times, the porosity of coal gradually increases. The relative mass firstly displays an increasing trend and then decreases with time. The peak strength and elastic modulus of coal decreases exponentially with soaking times. The developed damage constitutive model can well describe the stress–strain behavior of coal subjected to salty solution under the uniaxial compression. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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16 pages, 4316 KiB

Open AccessArticle

Research on Deep-Hole Cutting Blasting Efficiency in Blind Shafting with High In-Situ Stress Environment Using the Method of SPH

by Bo Sun, Zhiyu Zhang, Jiale Meng, Yonghui Huang, Hongchao Li and Jun Wang

Mathematics 2021, 9(24), 3242; https://doi.org/10.3390/math9243242 - 14 Dec 2021

Cited by 4 | Viewed by 1910

Abstract

This article aiming at the lack of research on the influence of rock clamp production on cutting blasting under high in-situ stress conditions and the lack of rock damage criteria for RHT constitution in numerical simulation. Combined with the critical rock damage criterion [...] Read more.

This article aiming at the lack of research on the influence of rock clamp production on cutting blasting under high in-situ stress conditions and the lack of rock damage criteria for RHT constitution in numerical simulation. Combined with the critical rock damage criterion and the embedded function of RHT constitution, the criterion for determining the critical damage of rock in RHT constitutive was studied, and the mechanical parameters of Metamorphic sodium lava were substituted to obtain the critical damage threshold of rock in numerical simulation. The smooth particle hydrodynamics (SPH) method was used to numerically simulate and analyze the influence of different rock clamping coefficients on the rock damage range and the cavity area in the cutting blasting. The stress state applied by the numerical simulation was inversely deduced by the field test scanning results to simulate the rock clamping coefficient K_r at the corresponding depth. The relationship between the cavity area S_c and the free surface distance D_f is analyzed and established. The results show that the rock clip production has an inhibitory effect on the development and propagation of blast-induced cracks. The stress applied in the numerical simulation affects the range and development degree of cracks, and the cracks generated by the explosion are mainly circumferential cracks. The larger coefficient of rock clip production, the more obvious the inhibitory effect on cut blasting, the less the blast-induced cracks and the smaller the rock damage circle. The fitting results show that the curve fitting degree is about 0.94, which proves the accuracy of S_c-D_f curve, and provides important reference value for the design of one-time completion blasting of upward blind shaft. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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17 pages, 3919 KiB

Open AccessArticle

Reliability Analysis of High Concrete-Face Rockfill Dams and Study of Seismic Performance of Earthquake-Resistant Measures Based on Stochastic Dynamic Analysis

by Zhuo Rong, Xiang Yu, Bin Xu and Xueming Du

Mathematics 2021, 9(23), 3124; https://doi.org/10.3390/math9233124 - 04 Dec 2021

Cited by 3 | Viewed by 1928

Abstract

The randomness of earthquake excitation has a significant impact on the seismic performance of high earth-rock dams. In this paper, the seismic performance of geosynthetic-reinforced soil structures (GRSS) of high concrete face rockfill dams (CFRDs) is evaluated from the stochastic perspective. Multiple groups [...] Read more.

The randomness of earthquake excitation has a significant impact on the seismic performance of high earth-rock dams. In this paper, the seismic performance of geosynthetic-reinforced soil structures (GRSS) of high concrete face rockfill dams (CFRDs) is evaluated from the stochastic perspective. Multiple groups of seismic ground motions are generated based on spectral expression-random function non-stationary model. Taking Gushui CFRD as an example, this study calculates the failure probability of each damage level of non-reinforce slopes and reinforce slopes based on generalized probability density evolution method (GPDEM) and reliability analysis is presented though multiple evaluation indicators. The result shows that GRSS can reduce the mild damage of CFRDs during earthquake and restrain the moderate and severe damage. The influence of vertical spacing and length of GRSS on the seismic performance is obtained, which provides a reference for the seismic design and risk analysis of CFRDs. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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13 pages, 2368 KiB

Open AccessArticle

Rockburst Interpretation by a Data-Driven Approach: A Comparative Study

by Yuantian Sun, Guichen Li and Sen Yang

Mathematics 2021, 9(22), 2965; https://doi.org/10.3390/math9222965 - 20 Nov 2021

Cited by 7 | Viewed by 1527

Abstract

Accurately evaluating rockburst intensity has attracted much attention in these recent years, as it can guide the design of engineering in deep underground conditions and avoid injury to people. In this study, a new ensemble classifier combining a random forest classifier (RF) and [...] Read more.

Accurately evaluating rockburst intensity has attracted much attention in these recent years, as it can guide the design of engineering in deep underground conditions and avoid injury to people. In this study, a new ensemble classifier combining a random forest classifier (RF) and beetle antennae search algorithm (BAS) has been designed and applied to improve the accuracy of rockburst classification. A large dataset was collected from across the world to achieve a comprehensive representation, in which five key influencing factors were selected as the input variables, and the rockburst intensity was selected as the output. The proposed model BAS-RF was then validated by the dataset. The results show that BAS could tune the hyperparameters of RF efficiently, and the optimum model exhibited a high performance on an independent test set of rockburst data and new engineering projects. According to the ensemble RF-BAS model, the feature importance was calculated. Furthermore, the accuracy of the proposed model on rockburst prediction was higher than the conventional machine learning models and empirical models, which means that the proposed model is efficient and accurate. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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18 pages, 4767 KiB

Open AccessArticle

Diffusion Model of Parallel Plate Crack Grouting Based on Foaming Expansion Characteristics of Polymer Slurry

by Jiasen Liang, Shaokun Ma and Xueming Du

Mathematics 2021, 9(22), 2907; https://doi.org/10.3390/math9222907 - 15 Nov 2021

Cited by 8 | Viewed by 1488

Abstract

Polymers as a new chemical grouting material have been widely used in fractured rock mass; however, the understanding of polymer diffusion characteristics still needs to be further improved. In order to study the diffusion mechanism of foamed polymer slurry in rock fissures, the [...] Read more.

Polymers as a new chemical grouting material have been widely used in fractured rock mass; however, the understanding of polymer diffusion characteristics still needs to be further improved. In order to study the diffusion mechanism of foamed polymer slurry in rock fissures, the radial diffusion model of polymer single crack grouting is derived in consideration of the factors such as grouting volume, crack width and expansion rate. The influence of different factors on slurry diffusion radius, diffusion pressure and flow rate is analyzed, The diffusion model is verified by finite element numerical simulation. The findings show that (1) The results of slurry diffusion radius, pressure and velocity distribution at different times under different working conditions in the present model are in good agreement with the analytical solution; (2) The diffusion pressure is directly proportional to the grouting volume and expansion multiple, and inversely proportional to the crack width. In addition, diffusion pressure decreases with the increase of diffusion distance, and the pressure at the corresponding distance increases slowly with time, and finally tends to be stable; (3) For the same section, the radial velocity decreases slowly with the increase of time; for different sections, the flow velocity increases sharply with the increase of the distance between the section and the central axis of the grouting hole. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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13 pages, 3296 KiB

Open AccessArticle

Variable Weight Matter–Element Extension Model for the Stability Classification of Slope Rock Mass

by Shan Yang, Zitong Xu and Kaijun Su

Mathematics 2021, 9(21), 2807; https://doi.org/10.3390/math9212807 - 04 Nov 2021

Cited by 4 | Viewed by 1808

Abstract

The slope stability in an open-pit mine is closely related to the production safety and economic benefit of the mine. As a result of the increase in the number and scale of mine slopes, slope instability is frequently encountered in mines. Therefore, it [...] Read more.

The slope stability in an open-pit mine is closely related to the production safety and economic benefit of the mine. As a result of the increase in the number and scale of mine slopes, slope instability is frequently encountered in mines. Therefore, it is of scientific and social significance to strengthen the study of the stability of the slope rock mass. To accurately classify the stability of the slope rock mass in an open-pit mine, a new stability evaluation model of the slope rock mass was established based on variable weight and matter–element extension theory. First, based on the main evaluation indexes of geology, the environment, and engineering, the stability evaluation index system of the slope rock mass was constructed using the corresponding classification criteria of the evaluation index. Second, the constant weight of the evaluation index value was calculated using extremum entropy theory, and variable weight theory was used to optimize the constant weight to obtain the variable weight of the evaluation index value. Based on matter–element extension theory, the comprehensive correlation between the upper and lower limit indexes in the classification criteria and each classification was calculated, in addition to the comprehensive correlation between the rock mass indexes and the stability grade of each slope. Finally, the grade variable method was used to calculate the grade variable interval corresponding to the classification criteria of the evaluation index and the grade variable value of each slope rock mass, so as to determine the stability grade of the slope rock. The comparison results showed that the classification results of the proposed model are in line with engineering practice, and more accurate than those of the hierarchical-extension model and the multi-level unascertained measure-set pair analysis model. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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13 pages, 8778 KiB

Open AccessArticle

A Numerical Investigation to Determine the p–y Curves of Laterally Loaded Piles

by Kexin Yin, Lianghui Li and Eugenia Di Filippo

Mathematics 2021, 9(21), 2783; https://doi.org/10.3390/math9212783 - 02 Nov 2021

Cited by 2 | Viewed by 1775

Abstract

This paper focuses on a numerical approach to finding the p–y curves for laterally loaded piles. The Drucker–Prager plastic model is employed and implemented within a finite element MATLAB code. The pre- and post-processing code for Gmsh and related numerical tools are established [...] Read more.

This paper focuses on a numerical approach to finding the p–y curves for laterally loaded piles. The Drucker–Prager plastic model is employed and implemented within a finite element MATLAB code. The pre- and post-processing code for Gmsh and related numerical tools are established as well. The p–y curve results from this new approach have been validated and compared to the typical design equations of API (American Petroleum Institute) and Matlock. The validation reveals that the code leads to lower p–y curves than the API and Matlock equations when the horizontal displacement is less than 0.35 times the diameter of the pile (B). A sensitivity analysis of the number of elements and the interface thickness is presented. The results indicate that the obtained p–y curves are independent of the two factors. Finally, the influence of clay content on the p–y behavior is investigated by the implemented MATLAB code. When y < 0.15B, the same lateral capacity values are resulted at clay contents of 27.5% and 55%, and they are higher than the ones for 0% clay content. The p–y curves show a decreasing trend with increasing clay content after y > 0.15B. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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18 pages, 8750 KiB

Open AccessArticle

Analytical Stress Solution and Numerical Mechanical Behavior of Rock Mass Containing an Opening under Different Confining Stress Conditions

by Lihai Tan, Ting Ren, Linming Dou, Xiaohan Yang, Gaofeng Wang and Huaide Peng

Mathematics 2021, 9(19), 2462; https://doi.org/10.3390/math9192462 - 02 Oct 2021

Cited by 6 | Viewed by 1724

Abstract

In this study, the triangle interpolation method for the calculation of mapping functions of plates containing an opening with arbitrary shapes is investigated with an improved method for point adjudgment during iterations. Afterwards, four kinds of openings with typical shapes are considered and [...] Read more.

In this study, the triangle interpolation method for the calculation of mapping functions of plates containing an opening with arbitrary shapes is investigated with an improved method for point adjudgment during iterations. Afterwards, four kinds of openings with typical shapes are considered and the mapping functions for them are calculated, based on which the influence of calculation parameters such as iteration time and the number of terms on the accuracy of mapping function is discussed. Finally, the stress around an inverted U-shaped opening and around an arched opening under different far-field stress conditions is calculated and the effect of opening shape and lateral pressure coefficient on stress distribution and rock mechanical behaviors is further analyzed combined with the discrete element method (DEM) numerical simulation. The result shows that the stability and failure pattern of the rock mass is correlated with the stress around the opening, which is affected by the opening shape. The existence of opening also greatly reduces the enhancing influence of confining stress on rock specimen. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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