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Mechanical Properties of Rocks under Complex Stress Conditions

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Civil Engineering".

Deadline for manuscript submissions: closed (20 March 2023) | Viewed by 26300

Special Issue Editors


E-Mail Website
Guest Editor
School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
Interests: rock mechanics; reservoir geomechanics; energy evolution; rockburst; underground engineering
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China
Interests: rock mechanics; tunnel engineering; rock dynamics
State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China
Interests: underground engineering; rock failure; rock mechanics; numerical method
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
1. School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China
2. School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
Interests: rock mechanics; damage evolution; high temperature; strength criterion; constitutive theory

Special Issue Information

Dear Colleagues,

Around the world, rock projects such as traffic tunnels, water conservancy dams, civil air defense construction, and deep mineral mining, are becoming widespread. Due to the current demand for new energy and environmental protection, projects such as CO2 geological storage, nuclear waste storage, geothermal development, and underground energy storage have also experienced rapid development. In the future, humans may conduct lunar mining and construct Mars bases; for such rock engineering constructions, rocks would be hosted in a complex thermal–hydro–mechanical–chemical (THMC) geological environment while being simultaneously subjected to excavation, drilling, support, hydraulic fracturing, liquid nitrogen freezing, blasting, etc. In addition, these systems experience a strong time effect. Under such complex conditions and multifactor mechanisms, the mineral composition, pore and fissure structure, deformation, strength, brittleness, fluid migration, and stability of rocks may undergo fundamental changes.

Though challenging, it is essential to characterize the mineralogical, physical, and mechanical behaviors of rocks under complex conditions and take these behaviors into account with engineering modeling and design. This knowledge can advance our understanding of rock materials and promote the safety and efficiency of rock engineering construction and operations.

This Special Issue aims to collect new findings on the mechanical properties of rock materials under complex stress conditions, new methods for their characterization and prediction, and new applications in related rock engineering. Potential topics of interest include, but are not limited to, the following:

  • Mineral composition and grain/pore-scale texture;
  • Physical properties (wave velocity, acoustic emission, electrical conductivity, etc.);
  • Mechanical properties (strength, brittleness, energy evolution, permeability, etc.);
  • Damage and fracture behavior (fracture toughness, fragmentation, etc.);
  • Constitutive model and strength criterion;
  • Artificial intelligence and big data methods for rock mechanical properties prediction;
  • Coupled thermal–hydrological–mechanical–chemical (THMC) modeling;
  • Numerical modeling and calculation methods;
  • Laboratory tests and physical simulations;
  • Field practice (coal mining, unconventional oil and gas extraction, geothermal development, CO2 geological storage, etc.).

Prof. Dr. Zhizhen Zhang
Dr. Xiaomeng Shi
Prof. Dr. Xuewei Liu
Prof. Dr. Xiaoli Xu
Guest Editors

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Keywords

  • rock mechanics and physics
  • rock deformation and strength
  • rock damage and fracture
  • rock creep and relaxation
  • rock energy evolution
  • theoretical analysis
  • numerical simulation
  • laboratory test
  • rock engineering

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Published Papers (15 papers)

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Editorial

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3 pages, 166 KiB  
Editorial
Mechanical Properties of Rocks under Complex Stress Conditions: Investigations Using Experimental and Numerical Methods
by Xuewei Liu, Zhizhen Zhang, Xiaomeng Shi and Xiaoli Xu
Appl. Sci. 2023, 13(9), 5753; https://doi.org/10.3390/app13095753 - 6 May 2023
Viewed by 1325
Abstract
Rock engineering constructions are widely attested in energy mining, geothermal development, and underground energy storage projects [...] Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)

Research

Jump to: Editorial, Review

14 pages, 5171 KiB  
Article
Study on Stiffness Parameters of the Hardening Soil Model in Sandy Gravel Stratum
by Xiaomeng Shi, Jinglai Sun, Yi Qi, Xiangyang Zhu, Xueming Zhang, Ruisong Liang and Hongjiang Chen
Appl. Sci. 2023, 13(4), 2710; https://doi.org/10.3390/app13042710 - 20 Feb 2023
Cited by 2 | Viewed by 2981
Abstract
Sandy gravel stratum is very common in tunnels and underground engineering projects. The accurate determination of mechanical parameters is crucial for engineering design and construction. The Hardening Soil (HS) Model, which accounts for both shear hardening and compression hardening, has demonstrated advantages in [...] Read more.
Sandy gravel stratum is very common in tunnels and underground engineering projects. The accurate determination of mechanical parameters is crucial for engineering design and construction. The Hardening Soil (HS) Model, which accounts for both shear hardening and compression hardening, has demonstrated advantages in numerical simulations. This study conducts large-scale mechanical experiments, including triaxial drained shear tests, loading-unloading tests, and standard consolidation tests, on sandy gravel specimens. The results reveal that the ratio of the three stiffness parameters in the HS Model, namely Young’s modulus under triaxial loading (E50), oedometric loading (Eoed), and unloading-reloading (Eur) is 1:1:4.3. The validity of the established stiffness ratio relationship is verified through numerical simulations of a foundation pit project and comparison with field monitoring data, demonstrating a consistent agreement between the simulation results and actual monitoring values. Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
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<p>Undisturbed sandy gravel gradation curve.</p>
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<p>Stress–strain curve of <span class="html-italic">E</span><sub>50</sub> and <span class="html-italic">E</span><sub>ur</sub>.</p>
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<p>Large-scale triaxial compression testing machine.</p>
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<p>Triaxial compression test process (<b>a</b>) specimen fabrication (<b>b</b>) specimen before test (<b>c</b>) specimen after test.</p>
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<p>100 kPa undisturbed stress–strain curve.</p>
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<p>Loading-unloading-reloading experimental curve of sandy gravel.</p>
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<p>Large-scaled consolidator.</p>
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<p>Curve of standard consolidation test of sandy gravel soil sample.</p>
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<p>The finite element model of the foundation pit.</p>
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<p>Comparison of surface settlement value under various excavation conditions. (<b>a</b>) step 1; (<b>b</b>) step 2; (<b>c</b>) step 3; (<b>d</b>) step 4; (<b>e</b>) step 5; (<b>f</b>) step 6.</p>
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<p>Comparison of surface settlement values of key monitoring points. (<b>a</b>) key point 1; (<b>b</b>) key point 2.</p>
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<p>Comparison of horizontal deformation of retaining piles in different steps. (<b>a</b>) step 1; (<b>b</b>) step 2; (<b>c</b>) step 3; (<b>d</b>) step 4; (<b>e</b>) step 5; (<b>f</b>) step 6.</p>
Full article ">Figure 12 Cont.
<p>Comparison of horizontal deformation of retaining piles in different steps. (<b>a</b>) step 1; (<b>b</b>) step 2; (<b>c</b>) step 3; (<b>d</b>) step 4; (<b>e</b>) step 5; (<b>f</b>) step 6.</p>
Full article ">
14 pages, 3092 KiB  
Article
Analysis of Crack-Characteristic Stress and Energy Characteristics of Sandstone under Triaxial Unloading Confining Pressure
by Yanwei Duan, Guohua Zhang and Tao Qin
Appl. Sci. 2023, 13(4), 2671; https://doi.org/10.3390/app13042671 - 19 Feb 2023
Cited by 4 | Viewed by 1213
Abstract
The deformation and failure of underground engineering are usually caused by unloading. In this work, triaxial unloading confining pressure tests are carried out to simulate the failure process of rock mass caused by unloading, analyze the crack-characteristic stress, and study the energy evolution [...] Read more.
The deformation and failure of underground engineering are usually caused by unloading. In this work, triaxial unloading confining pressure tests are carried out to simulate the failure process of rock mass caused by unloading, analyze the crack-characteristic stress, and study the energy evolution of rock under unloading and the pre-peak and post-peak energy characteristics combined with the energy theory. The results show that, when the confining pressure increases from 5 MPa to 20 MPa, crack closure stress σcc, crack initiation stress σci, dilatancy stress σcd, and peak stress σp are 6.34 times, 2.75 times, 1.93 times, and 1.66 times higher than the original, respectively. By comparing the increase in crack-characteristic stress, it can be found that the confining pressure has a large effect on the crack closure stress and crack initiation stress, while the dilatation stress and peak stress have relatively little influence. From the perspective of energy evolution, the pre-peak axial absorption energy U1 increases exponentially, the elastic energy Ue is similar to U1, and the circumferential consumption energy U3 and dissipation energy Ud are small. After reaching the peak stress, the growth rate of U1 decreases slightly, Ue decreases rapidly, and U3 increases rapidly but only as a small fraction of the total energy, while Ud grows almost exponentially and rapidly becomes the main part of the energy. Under each crack-characteristic stress state, the energy characteristic parameters gradually increase with the increase in confining pressure, which is manifested by the increase in slope in the linear fitting formula of energy characteristic parameters. The release process of the releasable elastic energy after the peak stress can be divided into three stages of “slow–fast–slow”, and the energy release process shows an obvious confining pressure effect. Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
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Figure 1

Figure 1
<p>TOP INDUSTRIE Rock 600-50 Rock automatic servo rheometer.</p>
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<p>Stress–strain curves of sandstone (<span class="html-italic">σ</span><sub>3</sub> = 10 MPa).</p>
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<p>Crack-characteristic stresses of sandstone under different confining pressure.</p>
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<p>The ratio of crack-characteristic stresses of sandstone under different confining pressure.</p>
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<p>Calculation principle of energy.</p>
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<p>Energy evolution curve of sandstone under unloading confining pressure: (<b>a</b>) <span class="html-italic">σ</span><sub>3</sub> = 5 MPa, (<b>b</b>) <span class="html-italic">σ</span><sub>3</sub> = 10 MPa, (<b>c</b>) <span class="html-italic">σ</span><sub>3</sub> = 15 MPa, and (<b>d</b>) <span class="html-italic">σ</span><sub>3</sub> = 20 MPa.</p>
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<p>Energy eigenvalue curves under different confining pressure: (<b>a</b>) <span class="html-italic">σ<sub>cc</sub></span>, (<b>b</b>) <span class="html-italic">σ<sub>ci</sub></span>, (<b>c</b>) <span class="html-italic">σ<sub>cd</sub></span>, and (<b>d</b>) <span class="html-italic">σ<sub>p</sub></span>.</p>
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<p>Variation curves of reliable elastic energy under different confining pressures.</p>
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15 pages, 9891 KiB  
Article
Influence of Stress Anisotropy on Petrophysical Parameters of Deep and Ultradeep Tight Sandstone
by Hui Zhang, Ke Xu, Binxin Zhang, Guoqing Yin, Haiying Wang, Zhimin Wang, Chao Li, Shujun Lai and Ziwei Qian
Appl. Sci. 2022, 12(22), 11543; https://doi.org/10.3390/app122211543 - 14 Nov 2022
Cited by 2 | Viewed by 1288
Abstract
Rock mechanics parameters control the distribution of in situ stress and natural fractures, which is the key to sweet spot evaluation in reservoir engineering. Combined with the distribution of in situ stress, an experimental scheme of stress on rock physical parameters was designed. [...] Read more.
Rock mechanics parameters control the distribution of in situ stress and natural fractures, which is the key to sweet spot evaluation in reservoir engineering. Combined with the distribution of in situ stress, an experimental scheme of stress on rock physical parameters was designed. The results show that rock sonic velocity is extremely sensitive to water saturation under overburden pressure. At ultrasonic frequencies, when the water saturation increases from 0% to 80%, the P-wave velocity increases first and then decreases. When the water saturation continues to increase to 100%, the P-wave velocity increases. This is due to the effect of water saturation on the shear modulus. Saturation is negatively correlated with shear wave velocity and resistivity. Different minerals have different control effects on the rock P-S wave velocity ratio. Quartz content plays a dominant role, and the two are negatively correlated, followed by feldspar and clay, and the two are positively correlated with the P-S wave ratio. The confining pressure, axial compression, stress ratio and burial depth are positively correlated with the P-S wave and negatively correlated with the P-S wave ratio; in descending order, the influencing factors of stress on the petrophysical parameters are maximum stress ratio > confining pressure > axial pressure. Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
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Figure 1
<p>Fault Outline Map of Kelasu Structural Belt.</p>
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<p>Working principle of the SCMS-SD, a high-temperature and high-pressure rock sonic electrical measuring instrument.</p>
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<p>The stress ratio distribution frequency.</p>
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<p>The core before and after the experiment.</p>
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<p>Waveform diagrams of P-wave (<b>a</b>) and S-wave (<b>b</b>) signal variation.</p>
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<p>Relationship curves between P-wave velocity, S-wave velocity, resistivity and water saturation.</p>
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<p>Relationship curves between feldspar content, quartz content, clay content and aspect ratio.</p>
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<p>Relationship curve between resistivity and stress ratio.</p>
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<p>Relationship curves between the P-wave velocity, S-wave velocity, S-wave ratio and stress ratio.</p>
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<p>Curves of P-wave velocity, S-wave velocity and confining pressure.</p>
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<p>Curves of P-S wave ratio, resistivity and confining pressure.</p>
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<p>Relationship curves between P-S wave ratio, resistivity and confining pressure.</p>
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<p>Correlation curves between P-S wave ratio, resistivity and axial pressure.</p>
Full article ">
20 pages, 10604 KiB  
Article
Prediction Method for Mine Earthquake in Time Sequence Based on Clustering Analysis
by Peng Zhang, Xiaolin Li and Junli Chen
Appl. Sci. 2022, 12(21), 11101; https://doi.org/10.3390/app122111101 - 2 Nov 2022
Cited by 6 | Viewed by 1540
Abstract
Under the background of the intelligent construction of a coal mine, how to efficiently extract effective information from the massive monitoring data of mine earthquakes, and improve prediction accuracy, is a research hotspot in the field of coal mine safety production. In view [...] Read more.
Under the background of the intelligent construction of a coal mine, how to efficiently extract effective information from the massive monitoring data of mine earthquakes, and improve prediction accuracy, is a research hotspot in the field of coal mine safety production. In view of this problem, more and more machine learning methods are being applied to the prediction on mine earthquakes. Considering that clustering analysis can enhance the correlation between microseism data, we propose a method whose main idea is to cluster microseism data before establishing the prediction model, and then train the model, so as to improve prediction accuracy. Specifically, microseism events on a working face are divided into clusters in advance by the Spatial Temporal-DBSCAN(ST-DBSCAN) algorithm, then a prediction model is established with Support Vector Regression (SVR) to predict the occurrence location and daily frequency of high-energy mine earthquake events. A set of engineering experiments were conducted in H Coal Mine, and the results show that the spatial-temporal clustering analysis of microseism events can indeed improve the prediction accuracy of machine learning methods on mine earthquakes. Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
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Figure 1
<p>Schematic representation of the spatial-temporal neighborhood.</p>
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<p>Schematic diagram of SVM structure.</p>
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<p>Basic concept diagram of SVR.</p>
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<p>Schematic diagram of LSTM structure.</p>
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<p>The workflow of mine earthquake prediction in time sequence.</p>
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<p>Distribution of microseisms on working face.</p>
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<p>Distribution of microseisms in three-dimensional space.</p>
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<p>9-Dist graph. (<b>a</b>) Spatial distance. (<b>b</b>) Temporal distance.</p>
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<p>Histogram of SC and noise rate of clustering results of parameter combinations.</p>
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<p>Three-dimensional scatter plot of clustering results.</p>
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<p>Distribution of microseism clusters on working face.</p>
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<p>The workflow of microseism location data processing.</p>
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<p>Prediction of SVR with different kernel functions on X coordinate. (<b>a</b>) Linear kernel. (<b>b</b>) Sigmoid kernel. (<b>c</b>) Polynomial kernel. (<b>d</b>) RBF kernel.</p>
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<p>The workflow of microseism energy data processing.</p>
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<p>Prediction of SVR with different kernel functions on daily frequency of <math display="inline"><semantics> <mrow> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mn>4</mn> <mo> </mo> </mrow> </msup> <mi mathvariant="normal">J</mi> </mrow> </semantics></math> level. (<b>a</b>) Linear kernel. (<b>b</b>) Sigmoid kernel. (<b>c</b>) Polynomial kernel. (<b>d</b>) RBF kernel.</p>
Full article ">Figure 16
<p>Prediction of LSTM model. (<b>a</b>) X coordinates of high-energy events. (<b>b</b>) Daily frequency corresponding to <math display="inline"><semantics> <mrow> <msup> <mrow> <mn>10</mn> </mrow> <mn>4</mn> </msup> <mi mathvariant="normal">J</mi> </mrow> </semantics></math> energy level events.</p>
Full article ">
16 pages, 15809 KiB  
Article
Motion Characteristics of Collapse Body during the Process of Expanding a Rescue Channel
by Yanlong Fu, Kai Xie, Fukun Xiao, Gang Liu, Zhiyuan Hou and Rui Zhang
Appl. Sci. 2022, 12(21), 11034; https://doi.org/10.3390/app122111034 - 31 Oct 2022
Cited by 1 | Viewed by 1152
Abstract
For the rapid construction of a rescue channel in the process of underground emergency rescue, a method for the expanded rescue channel in the collapse body is proposed and verified by a model test and a numerical simulation experiment. The motion characteristics and [...] Read more.
For the rapid construction of a rescue channel in the process of underground emergency rescue, a method for the expanded rescue channel in the collapse body is proposed and verified by a model test and a numerical simulation experiment. The motion characteristics and motion law of the expanded collapse body are analyzed on the basis of the mechanics of granular media, and a comparative simulation study on the main influencing factors of the collapse body motion is carried out. The results show that: (1) When the collapse body is expanded for a rescue channel, it will form three types of six relative slip planes. According to the position of the slip plane and the distribution of displacement, the collapse body can be divided into a direct displacement region, a stable region, and an indirect displacement region. (2) The expansion process can be divided into the initial start-up stage, the uplift stage, and the collapse stage, according to the formation time of the slip plane and the displacement law of the collapse body. (3) The results of the numerical simulation and the theoretical analysis of the granular media show that the dip angle of the slip plane is determined by the internal friction angle of the collapse particles, and the dip angles of the three slip planes are below θ1=90°φ, θ2=45°+φ/2, and θ3=90°+φ/2. (4) The transverse scope and longitudinal distance is brought by the expansion increase with the increase in the expansion size, and the simulated dip angles of the slip plane are larger than the theoretical values due to the size effect. (5) In the expansion process, the strong force chain in the collapse body is concentrated in the stress arch above the expander device, and the failure and reconstruction laws of the stress arch at each stage are consistent with the formation of the slip plane and the uplift and instability law of the collapse body. Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
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Figure 1

Figure 1
<p>Schematic diagram of rescue channel expansion in collapse body.</p>
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<p>Similar simulation device and collapse body sample.</p>
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<p>Particle expansion process.</p>
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<p>Numerical model of expansion test.</p>
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<p>Displacement of collapse body under different expansion sizes: (<b>a</b>) the position of the mark particles when the expansion size is 80 mm; (<b>b</b>) the position of the mark particles when the expansion size is 100 mm; (<b>c</b>) the position of the mark particles when the expansion size is 120 mm; (<b>d</b>) the particles displacement when the expansion size is 0.8 m; (<b>e</b>) the particles displacement when the expansion size is 1.0 m; (<b>f</b>) the particles displacement when the expansion size is 1.2 m.</p>
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<p>Displacement change in expansion process under different working conditions: (<b>a</b>) the expansion process of the collapse body with different internal friction angles when the expansion size is 1.2 m; (<b>b</b>) the expansion process of the collapse body with different expansion sizes when the internal friction angle is 37.5°.</p>
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<p>Schematic diagram of the displacement of the collapse body in the channel expansion process: (<b>a</b>) the initial start-up stage; (<b>b</b>) the uplift stage; (<b>c</b>) the collapse stage.</p>
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<p>Variation curve of dip angle for the slip plane: (<b>a</b>) the dip angle of the slip plane with different expansion sizes when the internal friction angle is 37.5°; (<b>b</b>) the dip angle of the slip plane with different internal friction angles when the expansion size is 1.2 m.</p>
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<p>Variation curve of maximum width of displacement region.</p>
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<p>Boundary stress curve.</p>
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<p>Force analysis of slip plane 2.</p>
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<p>Force analysis of slip plane 1.</p>
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<p>Evolution of force chain grid.</p>
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<p>Characteristic evolution curve of contact force chain: (<b>a</b>) the proportion of strong chains at different internal friction angles; (<b>b</b>) the coordination number proportion at different internal friction angles.</p>
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<p>Variation curve of potential energy–kinetic energy.</p>
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17 pages, 10992 KiB  
Article
Mechanism of Coal Burst Triggered by Disturbing Mining-Induced Stress: An Experimental Investigation
by Jinzheng Bai, Linming Dou, Xuwei Li, Jinrong Cao, Kangkang Wang, Yanjiang Chai and Jiliang Kan
Appl. Sci. 2022, 12(21), 10993; https://doi.org/10.3390/app122110993 - 30 Oct 2022
Cited by 1 | Viewed by 1576
Abstract
The true triaxial test can accurately simulate the dynamic and static load superposition environment of deep mining and then reproduce the spatial and temporal evolution process of coal-rock dynamic disasters. This study used a self-developed true triaxial coal-rock dynamic behavior test system to [...] Read more.
The true triaxial test can accurately simulate the dynamic and static load superposition environment of deep mining and then reproduce the spatial and temporal evolution process of coal-rock dynamic disasters. This study used a self-developed true triaxial coal-rock dynamic behavior test system to investigate the dynamic failure characteristics and mechanism of coal bursts under different mining-induced stress disturbances. The results show that the perturbation duration of the coal samples under quasi-static load decreases with the increase of the disturbance rate, and the perturbation stress level increases first and then decreases. The coal samples can accumulate higher strain energy and show progressive and dynamic failure. The perturbation duration and stress peak of the coal sample under the cycle load decreased with the increase of the cycle amplitude and frequency, and the coal sample first spalled off on the free surface. The damage then developed internally until the coal burst. The perturbation duration and stress peak of coal samples decrease with the increase of transient stress and the perturbation stress levels. The dynamic failure process of coal samples is straightforward, and the strength of coal burst is violent and is more difficult to predict. The conclusions obtained help to deepen the understanding of the triggering mechanism of coal bursts. Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
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Figure 1

Figure 1
<p>True triaxial coal-rock dynamic behavior testing system: (<b>a</b>) schematic diagram of equipment; (<b>b</b>) single face unloading part with a droppable loading bar.</p>
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<p>Coal samples used in the experiment.</p>
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<p>Coal burst characteristics.</p>
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<p>Different types of load disturbance.</p>
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<p>Stress path of different disturbance stress: (<b>a</b>) static load; (<b>b</b>) cyclic load; (<b>c</b>) transient load.</p>
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<p>Relationship of control variables and quasi-static stress parameters: (<b>a</b>) disturbance rate; (<b>b</b>) stress level.</p>
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<p>Relationship of control variables and cyclic stress parameters: (<b>a</b>) cyclic amplitude; (<b>b</b>) cyclic frequency.</p>
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<p>Relationship of control variables and transient stress parameters: (<b>a</b>) transient increment; (<b>b</b>) stress level.</p>
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<p>Relationship of static stress control variables and peak strain: (<b>a</b>) disturbance rate; (<b>b</b>) stress level.</p>
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<p>Relationship of cyclic stress control variables and peak strain: (<b>a</b>) cyclic amplitude; (<b>b</b>) cyclic frequency.</p>
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<p>Relationship of transient stress control variables and peak strain: (<b>a</b>) transient increment; (<b>b</b>) stress level.</p>
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<p>Typical impact failure characteristics of different mining disturbances: (<b>a</b>) static load; (<b>b</b>) cyclic load; (<b>c</b>) transient load.</p>
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<p>Typical impact failure characteristics of different mining disturbances: (<b>a</b>) static load; (<b>b</b>) cyclic load; (<b>c</b>) transient load.</p>
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<p>Typical impact failure characteristics of different mining disturbances: (<b>a</b>) static load; (<b>b</b>) cyclic load; (<b>c</b>) transient load.</p>
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<p>Typical impact failure characteristics of different mining disturbances: (<b>a</b>) static load; (<b>b</b>) cyclic load; (<b>c</b>) transient load.</p>
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<p>Characteristics of coal burst pit: (<b>a</b>) static load; (<b>b</b>) cyclic load; (<b>c</b>) transient load.</p>
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<p>Characteristics of coal burst pit: (<b>a</b>) static load; (<b>b</b>) cyclic load; (<b>c</b>) transient load.</p>
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<p>Triggering mechanism of coal burst under different disturbing mining-induced stress.</p>
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17 pages, 6727 KiB  
Article
Experimental Investigation on Compressive Strength, Ultrasonic Characteristic and Cracks Distribution of Granite Rock Irradiated by a Moving Laser Beam
by Lianfei Kuang, Lipeng Sun, Dongxu Yu, Yijiang Wang, Zhaoxiang Chu and Jo Darkwa
Appl. Sci. 2022, 12(20), 10681; https://doi.org/10.3390/app122010681 - 21 Oct 2022
Cited by 5 | Viewed by 3105
Abstract
Efficient fracturing is the key issue for the exploitation of geothermal energy in a Hot Dry Rock reservoir. By using the laser irradiation cracking method, this study investigates the changes in uniaxial compressive strength, ultrasonic characteristics and crack distributions of granite specimens by [...] Read more.
Efficient fracturing is the key issue for the exploitation of geothermal energy in a Hot Dry Rock reservoir. By using the laser irradiation cracking method, this study investigates the changes in uniaxial compressive strength, ultrasonic characteristics and crack distributions of granite specimens by applying a laser beam under various irradiation conditions, including different powers, diameters and moving speeds of the laser beam. The results indicate that the uniaxial compressive strength is considerably dependent on the power, diameter and moving speed of the laser beam. The ultrasonic-wave velocity and amplitude of the first wave both increase with a decreased laser power, increased diameter or moving speed of the laser beam. The wave form of irradiated graphite is flattened by laser irradiation comparing with that of the original specimen without laser irradiation. The crack angle and the ratio of the cracked area at both ends are also related to the irradiation parameters. The interior cracks are observed to be well-developed around the bottom of the grooving kerf generated by the laser beam. The results indicate that laser irradiation is a new economical and practical method that can efficiently fracture graphite. Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
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<p>Devices used in experiments: (<b>a</b>) laser system, (<b>b</b>) electro-hydraulic testing servo machine, (<b>c</b>) ultrasonic tester, (<b>d</b>) X-ray micro-imaging system.</p>
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<p>Schematic of moving laser irradiation.</p>
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<p>Uniaxial compressive strength versus (<b>a</b>) laser power, (<b>b</b>) laser-beam diameter, (<b>c</b>) moving speed of laser beam, (<b>d</b>) uniaxial compressive strength–strain curve.</p>
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<p>Images of granite with different irradiation parameters under uniaxial compression.</p>
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<p>XRD curve of (<b>a</b>) original specimen and (<b>b</b>) molten graphite.</p>
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<p>The influence of (<b>a</b>) laser-power output, (<b>b</b>) beam diameter, (<b>c</b>) moving speed on wave velocity and first-wave amplitude.</p>
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<p>Wave form versus (<b>a</b>) original specimen, laser powers of (<b>b</b>) 600 W and (<b>c</b>) 1000 W, beam diameters of (<b>d</b>) 8 mm and (<b>e</b>) 12 mm and moving speeds of (<b>f</b>) 1 mm/s and (<b>g</b>) 4 mm/s.</p>
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<p>Wave form versus (<b>a</b>) original specimen, laser powers of (<b>b</b>) 600 W and (<b>c</b>) 1000 W, beam diameters of (<b>d</b>) 8 mm and (<b>e</b>) 12 mm and moving speeds of (<b>f</b>) 1 mm/s and (<b>g</b>) 4 mm/s.</p>
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<p>Cracks of irradiated granite on the lateral surface.</p>
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<p>Cracks of irradiated granite on the bottom surface.</p>
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<p>The influence of (<b>a</b>) laser power, (<b>b</b>) beam diameter, (<b>c</b>) moving speed of laser beam on crack angles and ratio of cracked area.</p>
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<p>Rendered images of irradiated specimens from (<b>a</b>) front, (<b>b</b>) top and (<b>c</b>) right views.</p>
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<p>Interior-crack images of vertical section at (<b>a</b>) axis and (<b>b</b>) 3/4 diameter plane.</p>
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<p>Interior-crack length and width at (<b>a</b>) starting point and (<b>b</b>) axial plane.</p>
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17 pages, 4901 KiB  
Article
Mechanical Properties and Damage Evolution of Heated Granite Subjected to Liquid Nitrogen Cooling
by Chunbo Zhou, Feng Gao, Chengzheng Cai, Wenqi Zheng and Liupeng Huo
Appl. Sci. 2022, 12(20), 10615; https://doi.org/10.3390/app122010615 - 20 Oct 2022
Cited by 4 | Viewed by 1405
Abstract
To investigate the effect of liquid nitrogen on the granite failure process, the deterioration effect of liquid nitrogen on heated granite was investigated from experimental and theoretical perspectives. The mechanical properties of heated granite (25, 100, 200, 300, and 400 °C) after different [...] Read more.
To investigate the effect of liquid nitrogen on the granite failure process, the deterioration effect of liquid nitrogen on heated granite was investigated from experimental and theoretical perspectives. The mechanical properties of heated granite (25, 100, 200, 300, and 400 °C) after different cooling treatments (air cooling and liquid nitrogen cooling) were investigated by uniaxial compression tests. The damage evolution analysis was performed by a statistical damage constitutive model and the dissipation energy ratio was newly defined. The results show that there is an increase in the uniaxial compressive strength of heated granite before 200 °C, which is due to the competitive relationship between the thermal cracking and crack closure. Liquid nitrogen cooling can deteriorate the mechanical properties of heated granite in terms of strength and deformability. At 400 °C, the reduction rates of compressive strength and stiffness between air cooling and liquid nitrogen cooling reached 32.36% and 47.72%, respectively. Liquid nitrogen cooling induces greater initial thermal damage and, consequently, leads to a greater degree of total damage before the peak stress and makes rock easier to be damaged. At 400 °C, the total damage at the peak stress increased from 0.179 to 0.587 after the liquid nitrogen cooling. The difficulty of damage can be quantified by the dissipation energy ratio. In addition, the deterioration of liquid nitrogen on granite is positively related to temperature. This study confirmed the deterioration effect of liquid nitrogen and promoting effect of temperature, providing a theoretical approach to the degradation mechanism of liquid nitrogen. Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
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<p>Experimental procedure.</p>
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<p>Thermal treatment schedule.</p>
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<p>Stress–strain curves in uniaxial compression of specimens under: (<b>a</b>) air cooling and (<b>b</b>) liquid nitrogen cooling (<b>c</b>) at 300 °C and (<b>d</b>) at 400 °C.</p>
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<p>Effect of liquid nitrogen cooling on uniaxial compressive properties: (<b>a</b>) uniaxial compressive strength and (<b>b</b>) reduction rate of compressive strength between air and liquid nitrogen cooling.</p>
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<p>Effect of liquid nitrogen cooling on deformability: (<b>a</b>) Young’s modulus, (<b>b</b>) reduction rate of Young’s modulus between air and liquid nitrogen cooling, (<b>c</b>) Poisson’s ratio, and (<b>d</b>) increase rate of Poisson’s ratio between air and liquid nitrogen cooling.</p>
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<p>Experimental and theoretical stress–strain curves for heated granite after different cooling treatments.</p>
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<p>Experimental and theoretical stress–strain curves for heated granite after different cooling treatments.</p>
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<p>Theoretical stress–strain curves of heated granite after different cooling treatments (calculated by average value).</p>
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<p>Total damage variables of heated granite after different cooling treatments.</p>
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<p>Total damage variables versus standardized strain.</p>
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<p>Damage evolution rate versus standardized strain.</p>
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<p>Damage evolution rate versus standardized strain.</p>
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<p>Effect of liquid nitrogen cooling on energy dissipation ratio.</p>
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17 pages, 4587 KiB  
Article
Research on Rock Strength Test Based on Electro-Hydraulic Servo Point Load Instrument
by Xiaoxia Zhou, Lei Qiao, Faquan Wu, Zhaoyuan Wang, Yinhong Chen and Jie Wu
Appl. Sci. 2022, 12(19), 9763; https://doi.org/10.3390/app12199763 - 28 Sep 2022
Cited by 6 | Viewed by 1430
Abstract
A new electro-hydraulic servo point load instrument was designed to address the problem that the existing point load instrument cannot be loaded continuously and uniformly; different loading rates (using three loading rates: 0.1, 0.5, 1.0 kN/s) were conducted on fine-crystalline granite, coarse-crystalline granite, [...] Read more.
A new electro-hydraulic servo point load instrument was designed to address the problem that the existing point load instrument cannot be loaded continuously and uniformly; different loading rates (using three loading rates: 0.1, 0.5, 1.0 kN/s) were conducted on fine-crystalline granite, coarse-crystalline granite, and siltstone (each rock sample contains four sizes: 203, 303, 403, 503 mm3) for point load tests. Firstly, the influence of loading rate on the axial stress distribution of rock sample loading was investigated in conjunction with the rock strength damage theory. Next, the influence of rock sample size and loading rate on different standard point load strength evaluation methods was analyzed to find a reasonable evaluation method and loading rate and range of rock sample size. Finally, the relationship between standard point load strength and uniaxial compressive strength was analyzed on this basis to obtain its empirical conversion formula. The results show that: (1) With the increase in the loading rate of point load, the tensile and compressive stresses in the loading axis increase, and the compressive stresses near the center of the loading axis of the rock sample are more influenced by the loading rate; the standard point load strength increases with the increase in the loading rate, but the increase in the standard point load strength decreases when the loading rate increases to a certain range. (2) With the increase in size, the standard point load strength solved by method I, method III, and method IV has an obvious size effect, while the size effect of standard point load strength solved by method II is not obvious. (3) The conversion factors of fine-crystalline granite, coarse-crystalline granite, and siltstone were obtained by zero-intercept linear regression analysis as 16.80, 15.32, and 14.60, respectively, which indicated that the conversion factors of rocks with high strength were higher than those of rocks with low strength. The present research results can provide theoretical support for revising the existing point load strength calculation equations. Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
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<p>Physical view of the new electro-hydraulic servo point load instrument.</p>
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<p>Rock parameter setting—English interface.</p>
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<p>Test—English interface.</p>
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<p>Images of point load damage in the three rock samples.</p>
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<p>Images of uniaxial compression damage in the three rock samples.</p>
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<p>Stress distribution of three rock samples of different sizes under different loading rates.</p>
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<p>Relationship between I<sub>s(50)</sub> and loading rate for three rock samples with different sizes.</p>
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<p>Relationship between I<sub>s(50)</sub> and loading rate for three rock samples with different sizes.</p>
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<p>Relationship between two point load strength indexes I<sub>s</sub> and size for the three rock samples under different loading rates.</p>
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<p>Three correction factors versus size for the three rock samples at different loading rates.</p>
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<p>Three correction factors versus size for the three rock samples at different loading rates.</p>
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<p>The relationship between I<sub>s(50)</sub> and size of the three rock samples under different loading rates.</p>
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19 pages, 7461 KiB  
Article
Effect of Freeze-Thaw Damage on the Physical, Mechanical, and Acoustic Behavior of Sandstone in Urumqi
by Junce Xu, Hai Pu and Ziheng Sha
Appl. Sci. 2022, 12(15), 7870; https://doi.org/10.3390/app12157870 - 5 Aug 2022
Cited by 6 | Viewed by 1439
Abstract
The Urumqi area in China is a seasonally cold region, and the rock structures in the region are susceptible to freeze-thaw (F-T) weathering. Therefore, this study investigated the effect of F-T on the physical, mechanical, and fracture behavior of sandstone from Urumqi. The [...] Read more.
The Urumqi area in China is a seasonally cold region, and the rock structures in the region are susceptible to freeze-thaw (F-T) weathering. Therefore, this study investigated the effect of F-T on the physical, mechanical, and fracture behavior of sandstone from Urumqi. The acoustic emission method (AE) was used to determine the stress thresholds for the initiation and development of cracks in the samples under cyclic F-T action. The results suggested that parameters such as P-wave velocity, elastic modulus, and peak stress presented a significant negative correlation with F-T damage, while porosity exhibited a close positive correlation. The elastic modulus of the sample was more sensitive to the F-T action with the smallest half-life (27 cycles) and the largest decay factor (0.0254). In addition, the stress threshold for micro-cracks development and macro-cracks initiation in the samples decreased with increasing F-T damage. After 30 F-T cycles, the stress threshold for micro-cracks propagation in the samples decreased from 20.73 MPa to 5.02 MPa by approximately 76%. The normalized stress threshold for the macro-cracks initiation was also decreased from 0.93 to 0.71. Moreover, the macro-cracks damage zone of the samples showed an increasing trend with F-T damage, from 7% under natural conditions to 29% after 30 cycles. It is concluded that F-T action lowers the stress thresholds for cracks development in sandstone in the Urumqi area, posing serious safety concerns for mass rock engineering in this area. Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
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<p>Location of the Xinjiang province from where the sandstone samples were obtained: (<b>a</b>) Location in China; (<b>b</b>) Detailed map of Xinjiang Province, China; (<b>c</b>) Actual view; (<b>d</b>) Satellite map of sampling point; (<b>e</b>) Samples. Red circle: rough location of the tested sandstone.</p>
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<p>X-ray diffraction results for the tested sandstone.</p>
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<p>Thin section photomicrographs. (<b>a</b>) 0 F-T cycle; (<b>b</b>) 15 F-T cycles.</p>
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<p>Experimental procedure and equipment.</p>
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<p>Failure patterns of the tested sandstone that was subjected to different numbers of F-T cycles. (<b>a</b>) Before loading; (<b>b</b>) After loading.</p>
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<p>The average porosity and loss rate with cycles in tested sandstone.</p>
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<p>SEM micrographs of sandstone samples under F-T actions. Orange frame 1: pore; Red frame 1: intergranular fracture; Red frame 2: transgranular fracture.</p>
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<p>The average P-wave velocity and loss rate with cycles in the tested sandstone.</p>
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<p>The average dry density and loss rate with cycles in the tested sandstone.</p>
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<p>Stress-strain curves of the tested samples that were subjected to different F-T cycles.</p>
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<p>Change in the peak stress and loss rate with F-T action in the tested sandstone.</p>
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<p>F-T damage mechanism.</p>
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<p>Variation of the elastic modulus (<b>a</b>) and damage (<b>b</b>) with F-T cycles.</p>
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<p>The relationship between the AE signal and stress with rock deformation (after [<a href="#B39-applsci-12-07870" class="html-bibr">39</a>]).</p>
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<p>Relationship between the AE counts, cumulative AE counts, and the time of samples with different numbers of F-T cycles under uniaxial compression condition: (<b>a</b>–<b>d</b>) represent the tested samples that were subjected to 0, 5, 15, and 30 F-T cycles, respectively.</p>
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<p>The relationship between the AE behavior and the stress of samples with different F-T cycles under uniaxial compression conditions: (<b>a</b>–<b>d</b>) represent the samples that were subjected to 0, 5, 15, and 30 F-T cycles, respectively.</p>
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<p>Changes in the acoustic behavior and stress with different F-T cycles. (<b>a</b>) Stress; (<b>b</b>) Normalized stress.</p>
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<p>Acoustic behavior of the sandstone that was subjected to different F–T action. (<b>a</b>) Micro-cracks; (<b>b</b>) Macro-cracks.</p>
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13 pages, 3550 KiB  
Article
Experimental Study on Mechanical Properties of High Temperature Granite with Different Cooling Methods
by Jin-Song Zhang, Yu Lu, Jian-Yong Pang and Yi-Shun Bu
Appl. Sci. 2022, 12(12), 5968; https://doi.org/10.3390/app12125968 - 11 Jun 2022
Cited by 7 | Viewed by 1643
Abstract
Due to various factors, high-temperature rocks are often affected by different cooling methods. They will lead to changes in rock mechanical properties, which firmly connect with the safety and stability of practical projects. At present, there are many studies of the microscopic characteristics [...] Read more.
Due to various factors, high-temperature rocks are often affected by different cooling methods. They will lead to changes in rock mechanical properties, which firmly connect with the safety and stability of practical projects. At present, there are many studies of the microscopic characteristics of rocks under different cooling methods, but few on the mechanical characteristics of rocks under the same conditions. Therefore, it is necessary to carry out experimental research on the mechanical properties of rock under different cooling methods. The study shows that the deterioration degree of the sample increases gradually with temperature rising and the cooling methods have different effects on the change of the sample in mass, volume and density. The stress–strain curve of the sample is divided into the crack compaction stage, elastic deformation stage, nonlinear deformation stage and failure stage. The peak strength of the naturally cooled sample is higher than that of the water cooled. The peak strength comes with a trend that goes up first, and then down with the temperature increasing. The uniaxial compression failure of the sample under uniaxial action is tensile failure. The failure characteristic of the sample is influenced both by the cooling modes and the temperature. Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
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<p>Granite Sample.</p>
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<p>WAW-1000 universal testing machine.</p>
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<p>Surface morphology of granite with different cooling methods. (<b>a</b>) is the surface morphology of granite under natural cooling; (<b>b</b>) is the surface morphology of granite under cooling in water.</p>
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<p>Mass change after different cooling methods.</p>
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<p>Volume change under different cooling methods.</p>
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<p>Density change under different cooling methods.</p>
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<p>Stress–strain curves of samples under different cooling methods. (<b>a</b>) The stress–strain curve of the sample in natural cooling mode; (<b>b</b>) The stress–strain curve of the sample cooled in water.</p>
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<p>Change of peak strength of sample after different cooling methods.</p>
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<p>Change of elastic modulus of samples after different cooling methods.</p>
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<p>Change of deformation modulus of sample after different cooling methods.</p>
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<p>Failure modes of granite with different cooling modes. (<b>a</b>) Failure modes of granite under natural cooling; (<b>b</b>) Failure modes of granite under cooling in water.</p>
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<p>Damage process of granite sample under different cooling modes.</p>
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20 pages, 7092 KiB  
Article
Characteristics of Acoustic Emission Caused by Intermittent Fatigue of Rock Salt
by Yao Cui, Changjun Liu, Nan Qiao, Siyu Qi, Xuanyi Chen, Pengyu Zhu and Yongneng Feng
Appl. Sci. 2022, 12(11), 5528; https://doi.org/10.3390/app12115528 - 29 May 2022
Cited by 1 | Viewed by 1575
Abstract
This paper compares classic (continuous) fatigue tests and fatigue tests carried out with time intervals of no stress in rock salt using a multifunctional testing machine and acoustic emission equipment. The results show that time intervals of no stress have a strong impact [...] Read more.
This paper compares classic (continuous) fatigue tests and fatigue tests carried out with time intervals of no stress in rock salt using a multifunctional testing machine and acoustic emission equipment. The results show that time intervals of no stress have a strong impact on the fatigue activity of rock salt. In fatigue tests with intervals, the residual strain in circles following an interval (α circles) is generally larger than that in circles before the intervals (β circles). The insertion of a time interval with no stress in the fatigue process accelerates the accumulation of residual strain: the longer the interval, the faster the residual strain accumulates during the fatigue process and the shorter the fatigue life of the rock salt. α circles produce a greater number of acoustic emission counts than β circles, which demonstrates that residual stress leads to internal structural adjustment of rock salt on a mesoscopic scale. During intervals of no stress, acoustic emission activity becomes more active in α circles because of reverse softening caused by the Bauschinger effect, which accelerates the accumulation of plastic deformation. A qualitative relationship between the accumulated damage variable and the time interval is established. A threshold in the duration of the time interval exists (around 900 s). Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
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<p>(<b>a</b>) The triaxial loading system.1—salt rock sample; 2—limber; 3—compression plate; 4—compression plate; 5—engine base; 6—strut; 7—cylinder; 8—servo hydraulic station; 9—confining pressure chamber; 10—axial compression; 11—dissolved liquid cylinder; 12—brine pump; 13—flow meter; 14—relief valve; 15—dissolved liquid container; 16—heat tape; 17—temperature sensor; 18—temperature controller. (<b>b</b>) The actual triaxial loading apparatus. (<b>c</b>) Acoustic emission test and analysis system.</p>
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<p>(<b>a</b>) The triaxial loading system.1—salt rock sample; 2—limber; 3—compression plate; 4—compression plate; 5—engine base; 6—strut; 7—cylinder; 8—servo hydraulic station; 9—confining pressure chamber; 10—axial compression; 11—dissolved liquid cylinder; 12—brine pump; 13—flow meter; 14—relief valve; 15—dissolved liquid container; 16—heat tape; 17—temperature sensor; 18—temperature controller. (<b>b</b>) The actual triaxial loading apparatus. (<b>c</b>) Acoustic emission test and analysis system.</p>
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<p>1,2,3,4 are positions of AE sensors with respect to the rock salt specimens: (<b>a</b>) top view and (<b>b</b>) side view.</p>
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<p>(<b>a</b>) The real rock salt samples. (<b>b</b>) Components of rock salt used in the tests.</p>
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<p>Stress paths of (<b>a</b>) classic fatigue and (<b>b</b>) fatigue as a function of time interval.</p>
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<p>Fatigue strain path as a function of time interval.</p>
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<p>Residual axial strain for each loading circle for (<b>a</b>) the classic fatigue experiment and (<b>b</b>) the control group experiment with a time interval of 5 s.</p>
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<p>Strain curves and (<b>a</b>) AE counts, (<b>b</b>) AE energy features for the fatigue tests carried out with a 30 s interval.</p>
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<p>(<b>a</b>) Failure condition of rock salt after experiment. SEM images of micro cracks for (<b>b</b>) the first circle and (<b>c</b>) the complete circle.</p>
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<p>Features of AE counts for tests carried out with fatigue intervals of (<b>a</b>) 5 s, (<b>b</b>) 10 s, (<b>c</b>) 60 s, (<b>d</b>) 120 s, (<b>e</b>) 600 s, (<b>f</b>) 900 s, and (<b>g</b>) 1200 s.</p>
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<p>Features of AE counts for tests carried out with fatigue intervals of (<b>a</b>) 5 s, (<b>b</b>) 10 s, (<b>c</b>) 60 s, (<b>d</b>) 120 s, (<b>e</b>) 600 s, (<b>f</b>) 900 s, and (<b>g</b>) 1200 s.</p>
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<p>Features of AE counts for tests carried out with fatigue intervals of (<b>a</b>) 5 s, (<b>b</b>) 10 s, (<b>c</b>) 60 s, (<b>d</b>) 120 s, (<b>e</b>) 600 s, (<b>f</b>) 900 s, and (<b>g</b>) 1200 s.</p>
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<p>Partial enlarged detail of <a href="#applsci-12-05528-f007" class="html-fig">Figure 7</a>a for test carried out with a 30 s fatigue interval.</p>
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<p>Area graphs showing the accumulated AE counts produced in each circle for fatigue tests with intervals of (<b>a</b>) 5 s, (<b>b</b>) 10 s, (<b>c</b>) 30 s, (<b>d</b>) 60 s, (<b>e</b>) 120 s, (<b>f</b>) 600 s, (<b>g</b>) 900 s, and (<b>h</b>) 1200 s.</p>
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<p>Area graphs showing the accumulated AE counts produced in each circle for fatigue tests with intervals of (<b>a</b>) 5 s, (<b>b</b>) 10 s, (<b>c</b>) 30 s, (<b>d</b>) 60 s, (<b>e</b>) 120 s, (<b>f</b>) 600 s, (<b>g</b>) 900 s, and (<b>h</b>) 1200 s.</p>
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<p>Area graphs showing the accumulated AE counts produced in each circle for fatigue tests with intervals of (<b>a</b>) 5 s, (<b>b</b>) 10 s, (<b>c</b>) 30 s, (<b>d</b>) 60 s, (<b>e</b>) 120 s, (<b>f</b>) 600 s, (<b>g</b>) 900 s, and (<b>h</b>) 1200 s.</p>
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<p>Area graphs showing the accumulated AE counts produced in each circle for fatigue tests with intervals of (<b>a</b>) 5 s, (<b>b</b>) 10 s, (<b>c</b>) 30 s, (<b>d</b>) 60 s, (<b>e</b>) 120 s, (<b>f</b>) 600 s, (<b>g</b>) 900 s, and (<b>h</b>) 1200 s.</p>
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<p>Trends of N<span class="html-italic"><sub>i</sub></span>(X) as a function of fatigue interval duration.</p>
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<p>Accumulated damage curves-D<span class="html-italic"><sub>i</sub></span>.</p>
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<p>Relationship between the slope of the linear equation (k<span class="html-italic"><sub>d</sub></span>) and the time intervals during the stable damage phases.</p>
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20 pages, 9105 KiB  
Article
Dynamic Analysis of the Seismo-Dynamic Response of Anti-Dip Bedding Rock Slopes Using a Three-Dimensional Discrete-Element Method
by Zhanghao Ren, Congxin Chen, Chaoyi Sun and Yue Wang
Appl. Sci. 2022, 12(9), 4640; https://doi.org/10.3390/app12094640 - 5 May 2022
Cited by 10 | Viewed by 1609
Abstract
Earthquakes are a major external factor that induce landslides. In order to systematically study the dynamic effects and failure mechanism of anti-dip bedding rock slopes (the slope trend is the same as the joint trend, while the slope dip direction is opposite to [...] Read more.
Earthquakes are a major external factor that induce landslides. In order to systematically study the dynamic effects and failure mechanism of anti-dip bedding rock slopes (the slope trend is the same as the joint trend, while the slope dip direction is opposite to the joint dip direction) under seismic action (as well as the spatial effects of the structural planes in the anti-dip bedding rock slopes), three-dimensional (3D) discrete-element numerical calculations were performed to analyze anti-dip bedding rock slopes with different slope angles, joint angles, and joint trends subjected to the action of natural seismic and sinusoidal waves. The results were analyzed to investigate the amplification effect, change in Fourier spectrum, failure mechanism, and permanent displacement of the slope under the applied seismic action. The permanent displacement of the slope was calculated using Newmark’s method and the results obtained were discussed and compared with those obtained from a dynamic analysis performed using the 3D discrete-element method. The results showed that the regularity of the spatial distribution of the amplification effect was less clear than that encountered in the planar problem (unidirectional or bidirectional dynamical loading), and this leads to the effect of having an overall rhythmical nature. The seismic wave decays in the high-frequency part from the bottom up of the slope, while the dominant frequency of the seismic wave decreases. The value of the permanent displacement obtained using Newmark’s method is much smaller than that obtained using the dynamic 3D discrete-element analysis approach. The angle between the joint and slope trends has a significant effect on the amplification effect, failure mode, permanent displacement, and stability of slopes subjected to seismic action. Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
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<p>Side view of the discrete-element model of the slope.</p>
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<p>Three-dimensional view of the slope model.</p>
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<p>Schematic diagrams illustrating the dynamic boundary conditions imposed on the 3D discrete-element models showing: (<b>a</b>) a side view of the model, and (<b>b</b>) a 3D spatial view.</p>
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<p>The input acceleration history of the sinusoidal wave used. The holding time is assumed to be 5 s, the amplitude 3.14 m/s<sup>2</sup>, and the period (<span class="html-italic">T</span>) 0.2 s.</p>
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<p>The nature of the input acceleration used in this work (Wolong waves of the Wenchuan earthquake), showing: (<b>a</b>) the acceleration history with a holding time of 5 s and E–W, U–P, and N–S PGA values of 9.28, 6.39, and −6.08 m/s<sup>2</sup>, respectively, and (<b>b</b>) the corresponding Fourier spectra and earthquake dominant frequency range (1.5–6 Hz).</p>
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<p>Spatial locations of the acceleration (A) and displacement (D) monitoring points and the profiles upon which they are located in the slope model.</p>
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<p>Variation of the acceleration amplification factors at different acceleration monitoring points due to the action of natural seismic and sinusoidal waves for points along profiles: (<b>a</b>) 1, (<b>b</b>) 2, (<b>c</b>) 3, and (<b>d</b>) 4.</p>
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<p>Variation of the peak acceleration amplification factors at four different points in slopes subjected to the action of sinusoidal waves. The values are plotted as functions of the angle <span class="html-italic">γ</span> and the points chosen are: (<b>a</b>) A5 and A9, and (<b>b</b>) A7 and A8.</p>
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<p>Variation of the three-directional peak AAF values at point A8 with slope angle <span class="html-italic">α</span> and joint angle <span class="html-italic">β</span>: (<b>a</b>) under the action of sinusoidal waves, and (<b>b</b>) under the action of natural seismic waves.</p>
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<p>Fourier spectra components and their dominant frequencies at different elevations within a slope subjected to the action of a natural seismic wave. The data are arranged in order of increasing elevation from bottom to top (points A12, A10, and A8 along profile 2).</p>
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<p>Contour plots of the displacement in the <span class="html-italic">Y</span>-direction of a slope (<span class="html-italic">α</span> = 40° and <span class="html-italic">β</span> = 60°) subjected to a natural seismic wave. The plots show the displacements in the plane corresponding to <span class="html-italic">x</span> = 10 m at different times after the onset of the seismic disturbance: (<b>a</b>) 1 s, (<b>b</b>) 2 s, (<b>c</b>) 3 s, (<b>d</b>) 4 s, (<b>e</b>) 5 s, and (<b>f</b>) 6 s.</p>
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<p>Contour plots of the displacement in the <span class="html-italic">Y</span>-direction of a slope (<span class="html-italic">α</span> = 40° and <span class="html-italic">β</span> = 70°) subjected to a sinusoidal wave. The plots show the displacements in the plane corresponding to <span class="html-italic">x</span> = 10 m at the end of the period of disturbance (<span class="html-italic">t</span> = 5 s) for different values of <span class="html-italic">γ</span>: (<b>a</b>) 0°, (<b>b</b>) 5°, (<b>c</b>) 10°, (<b>d</b>) 15°, and (<b>e</b>) 20°.</p>
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<p>Example of the use of Newmark’s method: (<b>a</b>) acceleration history (<span class="html-italic">Y</span>-direction) at point A6, (<b>b</b>) corresponding relative velocity history, and (<b>c</b>) cumulative displacement history.</p>
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<p>Displacement history of point D5 in the <span class="html-italic">Y</span>-direction for different slopes subjected to the action of a natural seismic wave. The slopes are labeled <span class="html-italic">α</span>_<span class="html-italic">β</span> according to their <span class="html-italic">α</span> and <span class="html-italic">β</span> angles.</p>
Full article ">Figure 15
<p>Displacement history of point D5 in the <span class="html-italic">Y</span>-direction for slopes subjected to the action of a sinusoidal wave. Each slope has <span class="html-italic">α</span> = 40° and <span class="html-italic">β</span> = 70° but different values of <span class="html-italic">γ</span>.</p>
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<p>Comparison of the permanent displacements of point D5 (in the <span class="html-italic">Y</span>-direction) under the action of a natural seismic wave as calculated using Newmark’s method and dynamic 3D discrete-element method.</p>
Full article ">

Review

Jump to: Editorial, Research

11 pages, 2541 KiB  
Review
Effect of Methane Adsorption on Mechanical Performance of Coal
by Feng Cai, Jingwen Yin and Juqiang Feng
Appl. Sci. 2022, 12(13), 6597; https://doi.org/10.3390/app12136597 - 29 Jun 2022
Cited by 3 | Viewed by 1353
Abstract
Understanding the influence of methane adsorption on coal mechanical properties is an important prerequisite for preventing coal mining and gas mining disasters. In the present research, meager coal and gas coal samples were obtained from Huaneng Yunnan Diandong Energy Co., Ltd. The triaxial [...] Read more.
Understanding the influence of methane adsorption on coal mechanical properties is an important prerequisite for preventing coal mining and gas mining disasters. In the present research, meager coal and gas coal samples were obtained from Huaneng Yunnan Diandong Energy Co., Ltd. The triaxial compression tests were carried out under different methane adsorption equilibrium pressures and confining pressures. The influence laws of different factors on the mechanical properties of coal were analyzed. The results show that the triaxial stress-strain curve of adsorbed methane coal has similar morphology with that of non-adsorbed coal. Under the same confining pressure, the stress-strain curve morphology of coal before and after adsorbing methane is basically the same but the compressive strength of coal after adsorbing methane decreases. The greater the adsorption equilibrium pressure of methane, the smaller the compressive strength of coal. The change in the mechanical properties (compressive strength and elastic modulus) of coal caused by methane adsorption can be described by the Langmuir curve and the correlation coefficient is more than 0.99. Under any stress environment, high-rank coal shows greater strength and lower elastic modulus than low-rank coal, which is mainly due to the existence of a developed cleat system in high-rank coal that provides more conditions for methane adsorption. The research results provide important data-based support for the prevention of coal and gas outbursts. Full article
(This article belongs to the Special Issue Mechanical Properties of Rocks under Complex Stress Conditions)
Show Figures

Figure 1

Figure 1
<p>Structure diagram of test system.</p>
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<p>Meager coal triaxial compression stress-strain curve. (<b>a</b>) Stress-strain curve of Meager coal when confining pressure is 0 MPa. (<b>b</b>) Stress-strain curve of Meager coal when confining pressure is 3 MPa. (<b>c</b>) Stress-strain curve of Meager coal when confining pressure is 6 MPa. (<b>d</b>) Stress-strain curve of Meager coal when confining pressure is 9 MPa.</p>
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<p>Gas coal triaxial compression stress-strain curve. (<b>a</b>) Stress-strain curve of Gas coal when confining pressure is 0 MPa. (<b>b</b>) Stress-strain curve of Gas coal when confining pressure is 3 MPa. (<b>c</b>) Stress-strain curve of Gas coal when confining pressure is 6 MPa. (<b>d</b>) Stress-strain curve of Gas coal when confining pressure is 9 MPa.</p>
Full article ">Figure 3 Cont.
<p>Gas coal triaxial compression stress-strain curve. (<b>a</b>) Stress-strain curve of Gas coal when confining pressure is 0 MPa. (<b>b</b>) Stress-strain curve of Gas coal when confining pressure is 3 MPa. (<b>c</b>) Stress-strain curve of Gas coal when confining pressure is 6 MPa. (<b>d</b>) Stress-strain curve of Gas coal when confining pressure is 9 MPa.</p>
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<p>Longitudinal wave speed. (<b>a</b>) Meager coal. (<b>b</b>) Gas coal.</p>
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<p>Reduction in compressive strength of coal sample vs. methane adsorption equilibrium pressure.</p>
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<p>Reduction in elastic modulus vs. equilibrium pressure for methane adsorption.</p>
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<p>Prediction of compressive strength and elastic modulus of coal samples under different methane adsorption equilibrium pressures. (<b>a</b>) Lean coal. (<b>b</b>) Gas coal.</p>
Full article ">Figure 7 Cont.
<p>Prediction of compressive strength and elastic modulus of coal samples under different methane adsorption equilibrium pressures. (<b>a</b>) Lean coal. (<b>b</b>) Gas coal.</p>
Full article ">
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