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27 pages, 6572 KiB  
Article
Predictive Models for Correlation of Compaction Characteristics of Weakly Cohesive Soils
by Carmen Nicoleta Debeleac, Andrei Buraga and Daniel Sorin Miron
Appl. Sci. 2024, 14(24), 11647; https://doi.org/10.3390/app142411647 - 13 Dec 2024
Viewed by 170
Abstract
In this paper, an investigation was conducted to characterize the behavior of weakly cohesive soil subjected to vibratory compaction. Thus, the authors developed a model for weakly cohesive soils, defined by inter-parametric laws that consider their initial state and predict the evolution of [...] Read more.
In this paper, an investigation was conducted to characterize the behavior of weakly cohesive soil subjected to vibratory compaction. Thus, the authors developed a model for weakly cohesive soils, defined by inter-parametric laws that consider their initial state and predict the evolution of state parameters resulting from static and vibratory compaction processes, depending on the number of equipment passes. Four types of soil were proposed for testing, with different initial characteristics such as dry density, longitudinal modulus, and moisture content. Some correlations between main parameters involved in the compaction process were established, considering soil mechanical properties, compaction equipment, and in situ technology applied. The results obtained in the computational environment were implemented to predict the performance compaction process for an overall assessment. This research contributes to database development by offering valuable insights for specialists aiming to apply Industry 4.0 digitalization practices, which stipulate the use of predictability laws in pre-assessing the degree of soil compaction (or settlement) to estimate and maximize the efficiency of road construction or foundation works. These insights help optimize design processes, enhance functional performance, improve resource utilization, and ensure long-term sustainability in large infrastructure projects built on these soils. Full article
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Figure 1

Figure 1
<p>The location of the compacted section and the measurement points and the method of carrying out the tests on the experimental ground polygon built on the construction site.</p>
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<p>Steps for developing a mathematical model of a mechanical system.</p>
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<p>Voigt–Kelvin model description.</p>
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<p>Dependence of the static modulus of linear deformation on the dry density for weakly cohesive soils (experiments under static conditions).</p>
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<p>Comparative representation of the law E<sub>st</sub> = f(ρ<sub>d</sub>): experimental results (in blue) versus the proposed analytical model (in red).</p>
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<p>Representation of the law E<sub>st</sub> = f(ρ<sub>d</sub>) for the four types of soil, corresponding to the four measurement points: (<b>a</b>) F; (<b>b</b>) G; (<b>c</b>) H; (<b>d</b>) I.</p>
Full article ">Figure 7
<p>The law of variation of the density in the dry state as a function of the soil moisture content with the layer thickness for: (<b>a</b>) h<sub>c</sub> = 26.4 cm (point F); (<b>b</b>) h<sub>c</sub> = 24.5 cm (point G); (<b>c</b>) h<sub>c</sub> = 28 cm (point H); (<b>d</b>) h<sub>c</sub> = 29.5 cm (point I).</p>
Full article ">Figure 7 Cont.
<p>The law of variation of the density in the dry state as a function of the soil moisture content with the layer thickness for: (<b>a</b>) h<sub>c</sub> = 26.4 cm (point F); (<b>b</b>) h<sub>c</sub> = 24.5 cm (point G); (<b>c</b>) h<sub>c</sub> = 28 cm (point H); (<b>d</b>) h<sub>c</sub> = 29.5 cm (point I).</p>
Full article ">Figure 8
<p>The law of variation of the contact area according to the degree of soil compaction (experimental measurements in the soil channel).</p>
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<p>The law of variation of the contact area according to soil settlement (experimental measurements in the soil channel).</p>
Full article ">Figure 10
<p>The approximation laws for the variation of the width of the contact area of the front vibratory drum of the ABG DD16 roller, during soil compaction (after the first three passes made in static working regime with the VV 170 roller).</p>
Full article ">Figure 11
<p>The regression curve and its analytical expression for the function Δh/h<sub>c</sub> − p, corresponding to the determinations on loess from Giurgiu (DN 2—km 39 + 200—Movilița site) [<a href="#B6-applsci-14-11647" class="html-bibr">6</a>].</p>
Full article ">Figure 12
<p>Current and cumulative settlement variation for compactor passes.</p>
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<p>Compaction degree variation in function by roller passes for the soil with different initial compaction degree: (<b>a</b>) point F with D<sub>i</sub> = 74.5%; (<b>b</b>) point G with D<sub>i</sub> = 79.7%; (<b>c</b>) point H with D<sub>i</sub> = 78.5%; (<b>d</b>) point I with D<sub>i</sub> = 81.7%.</p>
Full article ">Figure 14
<p>Comparison between approximation laws for the degree of compaction, for the first three static passes, corresponding to measurements from point F (<b>a</b>), point G (<b>b</b>), and point H (<b>c</b>).</p>
Full article ">Figure 15
<p>The variation of the degree of compaction according to the initial condition of the soil, the thickness of the layer and the number of passes of the compactor, corresponding to the measurements from points F, G, H, I.</p>
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<p>Curves of the main parameters that characterized the overall compaction process.</p>
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<p>Simulation results: (<b>a</b>) A = f(c,k); (<b>b</b>) Q<sub>0</sub> = f(c,k); (<b>c</b>) T = f(c,k).</p>
Full article ">
16 pages, 3392 KiB  
Article
Long-Term Dynamics of Water Droplet Impact on Rotating Hydrophilic Disk
by Wen Yang, Yunbo Zhang, Tian Deng and Chuanyang Liu
Appl. Sci. 2024, 14(24), 11608; https://doi.org/10.3390/app142411608 - 12 Dec 2024
Viewed by 250
Abstract
Ice accretion from the impingement of supercooled water droplets on the rotating components of aero-engines reduces engine efficiency and poses significant in-flight safety risks. In the present study, we experimentally investigate the impact of water droplets on the center of a rotating disk [...] Read more.
Ice accretion from the impingement of supercooled water droplets on the rotating components of aero-engines reduces engine efficiency and poses significant in-flight safety risks. In the present study, we experimentally investigate the impact of water droplets on the center of a rotating disk to gain insights into the icing mechanisms on these components. The effects of impact velocity and disk rotation speed on dynamic behaviors are systematically explored by visualizing the phenomena and quantitatively analyzing the evolution of droplet diameters during long time durations. Three distinct regimes of impact dynamics are identified based on the final states: stable rotation, stable ring, and ring ejection. The experimental results reveal that the spreading phase is primarily governed by inertial effects, with minimal influence from disk rotation, while the latter significantly affects the retraction phase. The maximum spreading factor increases with the impact velocity and shows little dependence on rotation, and the spreading time remains nearly unchanged. Scaling laws for the maximum and equilibrium spreading factors as functions of the Weber number and rotational Bond number are established. While the maximum spreading factor increases with impact velocity on static disks, the retraction time decreases as both the impact velocity and rotation speed increase. Full article
(This article belongs to the Section Fluid Science and Technology)
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Figure 1

Figure 1
<p>Experimental set-up.</p>
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<p>Selected snapshots of droplets impacting stationary disk at various Weber numbers.</p>
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<p>Snapshots of a water droplet impacting a rotating disk at <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>o</mi> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>.</p>
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<p>Droplet snapshots at <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> <mo>=</mo> <mn>166</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>o</mi> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>.</p>
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<p>Droplet snapshots at <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> <mo>=</mo> <mn>166</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>o</mi> <mo>=</mo> <mn>10.5</mn> </mrow> </semantics></math>.</p>
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<p>Distribution of droplets’ final states.</p>
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<p>The evolution of the spreading factor <math display="inline"><semantics> <mi>β</mi> </semantics></math> for droplet impact on the disk at different Weber numbers.</p>
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<p>Evolution of the spreading factor <math display="inline"><semantics> <mi>β</mi> </semantics></math> under various working conditions.</p>
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<p>Evolution of inner and exterior diameters of the ring-like droplets during the retraction phase. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>o</mi> <mo>=</mo> <mn>0.3</mn> <mo>,</mo> <mo> </mo> <mn>1.2</mn> </mrow> </semantics></math> and 2.6 and the same <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> <mo>=</mo> <mn>166</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> <mo>=</mo> <mn>133</mn> <mo>,</mo> <mo> </mo> <mn>166</mn> <mo>,</mo> <mo> </mo> <mn>200</mn> </mrow> </semantics></math> and the same <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>o</mi> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math>.</p>
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<p>The relationship of <math display="inline"><semantics> <msub> <mi>β</mi> <mi>max</mi> </msub> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>o</mi> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <msub> <mi>β</mi> <mi>max</mi> </msub> </semantics></math> as a function of <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> </mrow> </semantics></math> for different <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>o</mi> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>β</mi> <mi>max</mi> </msub> </semantics></math> as a function of <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>o</mi> </mrow> </semantics></math> for different <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> </mrow> </semantics></math> [<a href="#B26-applsci-14-11608" class="html-bibr">26</a>].</p>
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<p>The relationship of the equilibrium spreading factor <math display="inline"><semantics> <msub> <mi>β</mi> <mi>eq</mi> </msub> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>o</mi> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <msub> <mi>β</mi> <mi>eq</mi> </msub> </semantics></math> as a function of <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>o</mi> </mrow> </semantics></math> for different <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>β</mi> <mi>eq</mi> </msub> </semantics></math> as a function of <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> </mrow> </semantics></math> for different <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>o</mi> </mrow> </semantics></math>.</p>
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<p>Variation of spreading time (<b>a</b>) <math display="inline"><semantics> <msub> <mi>t</mi> <mi mathvariant="normal">d</mi> </msub> </semantics></math> and (<b>b</b>) retraction time <math display="inline"><semantics> <msub> <mi>t</mi> <mi mathvariant="normal">r</mi> </msub> </semantics></math> with respect to <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>o</mi> </mrow> </semantics></math>.</p>
Full article ">
15 pages, 3412 KiB  
Article
Prediction of Fretting Wear Lifetime of a Coated System
by Kyungmok Kim
Machines 2024, 12(12), 910; https://doi.org/10.3390/machines12120910 - 11 Dec 2024
Viewed by 231
Abstract
This article proposes a model of predicting the fretting wear lifetime of a low-friction coating. The proposed model incorporates multiple factors that influence the fretting wear damage of coatings: the imposed contact load, imposed average velocity, coating hardness, and initial surface roughness of [...] Read more.
This article proposes a model of predicting the fretting wear lifetime of a low-friction coating. The proposed model incorporates multiple factors that influence the fretting wear damage of coatings: the imposed contact load, imposed average velocity, coating hardness, and initial surface roughness of counterparts. The fretting wear lifetime of coatings, defined as the number of cycles critical to friction coefficient evolution, was collected from the literature. For the purpose of identifying parameters in the model, experimental fretting wear lifetime data were analyzed. The results show that the fretting wear lifetime of a coating can be described by an inverse power law regarding the contact load, imposed average velocity, and initial surface roughness of counterparts. In contrast, the fretting wear lifetime of a coating was observed to increase with increased coating hardness. It was observed that the exponents of the inverse power law varied with respect to the type of coating. The proposed fretting wear lifetime model enables the prediction of coating lifetime under various fretting conditions. Full article
(This article belongs to the Special Issue Design and Characterization of Engineered Bearing Surfaces)
Show Figures

Figure 1

Figure 1
<p>COF evolutions of electro-deposited coatings against different counterparts under a gross slip regime (displacement amplitude of 0.2 mm and frequency of 1 Hz), redrawn from [<a href="#B13-machines-12-00910" class="html-bibr">13</a>]: (<b>a</b>) AISI52100 ball; (<b>b</b>) SUS316L ball; (<b>c</b>) ZrO<sub>2</sub> ball.</p>
Full article ">Figure 1 Cont.
<p>COF evolutions of electro-deposited coatings against different counterparts under a gross slip regime (displacement amplitude of 0.2 mm and frequency of 1 Hz), redrawn from [<a href="#B13-machines-12-00910" class="html-bibr">13</a>]: (<b>a</b>) AISI52100 ball; (<b>b</b>) SUS316L ball; (<b>c</b>) ZrO<sub>2</sub> ball.</p>
Full article ">Figure 2
<p>Number of fretting cycles at COF of 0.45 versus contact load scatters: (<b>a</b>) AISI52100 ball; (<b>b</b>) SUS316L ball; (<b>c</b>) ZrO<sub>2</sub> ball.</p>
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<p>Relationship between fretting wear lifetime (<span class="html-italic">N<sub>f</sub></span>) and imposed contact load (<span class="html-italic">P</span>) on the bilogarithmic scale: (<b>a</b>) AISI52100 ball; (<b>b</b>) SUS316L ball; (<b>c</b>) ZrO<sub>2</sub> ball. <span class="html-italic">Nr</span> and <span class="html-italic">Pr</span> denote the reference lifetime and the reference load, respectively.</p>
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<p>COF evolutions of an aromatic thermosetting copolyester-MoS<sub>2</sub> coating under a gross slip regime (a frequency of 10 Hz), redrawn from [<a href="#B14-machines-12-00910" class="html-bibr">14</a>]. (<b>a</b>) COF evolutions at different imposed contact loads. Note that the value in parenthesis denotes the displacement amplitude. (<b>b</b>) Number of fretting cycles at a COF of 0.5 versus the contact load.</p>
Full article ">Figure 5
<p>Relationship between fretting wear lifetime (<span class="html-italic">N<sub>r</sub></span>) and imposed contact load (<span class="html-italic">P</span>) on the bilogarithmic scale: (<b>a</b>) a displacement amplitude of 1.5 mm; (<b>b</b>) a displacement amplitude of 2 mm. <span class="html-italic">N<sub>r</sub></span> and <span class="html-italic">P<sub>r</sub></span> denote the reference lifetime and the reference load, respectively.</p>
Full article ">Figure 6
<p>COF evolutions of electro-deposited coatings at various average velocities (a contact load of 50 N), redrawn from [<a href="#B15-machines-12-00910" class="html-bibr">15</a>]: (<b>a</b>) 0.2 mm/s; (<b>b</b>) 0.3 mm/s; (<b>c</b>) 0.4 mm/s; (<b>d</b>) 0.6 mm/s; (<b>e</b>) 0.8 mm/s; (<b>f</b>) number of fretting cycles at a COF of 0.45 versus the imposed average velocity. Note that the imposed average velocity was defined as 4 × displacement amplitude × frequency.</p>
Full article ">Figure 7
<p>COF evolutions of a thermal sprayed coating under a gross slip regime (a contact load of 10.3 kN and a frequency of 2.5 Hz), redrawn from [<a href="#B9-machines-12-00910" class="html-bibr">9</a>]: (<b>a</b>) COF evolutions at three different average velocities; (<b>b</b>) number of fretting cycles at a COF of 0.33 versus the imposed average velocity; v is equal to 4 × displacement amplitude × frequency.</p>
Full article ">Figure 8
<p>COF evolutions of an epoxy coating in a gross slip regime (a contact load of 20 N), redrawn from [<a href="#B16-machines-12-00910" class="html-bibr">16</a>]: (<b>a</b>) COF evolutions at three average velocities; (<b>b</b>) number of fretting cycles at a COF of 0.7 versus the imposed average velocity; v is equal to 4 × displacement amplitude × frequency.</p>
Full article ">Figure 9
<p>COF evolutions of an aluminum bronze coating under a gross slip regime (a contact load of 10 N), redrawn from [<a href="#B17-machines-12-00910" class="html-bibr">17</a>]: (<b>a</b>) COF evolutions; (<b>b</b>) number of fretting cycles at a COF of 0.6 versus the imposed average velocity; v is equal to 4 × displacement amplitude × frequency.</p>
Full article ">Figure 10
<p>Relationship between fretting wear lifetimes and imposed average velocity on the bilogarithmic scale: (<b>a</b>) electro-deposited coating; (<b>b</b>) thermally sprayed coating; (<b>c</b>) epoxy coating; (<b>d</b>) aluminum bronze coating. <span class="html-italic">N<sub>r</sub></span> and <span class="html-italic">v<sub>r</sub></span> denote the reference lifetime and the reference average velocity, respectively.</p>
Full article ">Figure 11
<p>COF evolutions of graphite-like carbon coatings at various hardness values, redrawn from [<a href="#B19-machines-12-00910" class="html-bibr">19</a>]: (<b>a</b>) COF evolutions in dry air and N<sub>2</sub> conditions; (<b>b</b>) number of fretting cycles at a COF of 0.6 versus coating hardness.</p>
Full article ">Figure 12
<p>Relationship between fretting wear lifetimes (<span class="html-italic">N<sub>f</sub></span>) and coating hardness (<span class="html-italic">H</span>) on the bilogarithmic scale: (<b>a</b>) in air condition; (<b>b</b>) in N<sub>2</sub> condition. <span class="html-italic">N<sub>r</sub></span> and <span class="html-italic">H<sub>r</sub></span> denote the reference lifetime and the reference hardness, respectively.</p>
Full article ">Figure 13
<p>Fretting wear lifetime of a rubber coating with respect to the arithmetic average surface roughness (R<sub>a</sub>), redrawn from [<a href="#B18-machines-12-00910" class="html-bibr">18</a>]: (<b>a</b>) number of fretting cycles at COF of 0.3; (<b>b</b>) relationship between fretting wear lifetimes and average roughness on the bilogarithmic scale. <span class="html-italic">N<sub>r</sub></span> and <span class="html-italic">R<sub>ar</sub></span> denote the reference lifetime and the reference surface roughness, respectively.</p>
Full article ">
16 pages, 6184 KiB  
Article
A Study on the Influence of the Rotating Speed and Load on the Grain Structure and Wear Properties of Bearing Steel GCr15 During Bearing Service
by Li Cui, Donghui Wang, Chenxu Zhang and Xin Wang
Metals 2024, 14(12), 1408; https://doi.org/10.3390/met14121408 - 9 Dec 2024
Viewed by 471
Abstract
In order to study the wear failure mechanism and structure evolution law of bearings under different speeds and contact loads, an elastoplastic model of a 7009AC bearing was established in this paper. The stress, temperature rise and grain size during dry friction and [...] Read more.
In order to study the wear failure mechanism and structure evolution law of bearings under different speeds and contact loads, an elastoplastic model of a 7009AC bearing was established in this paper. The stress, temperature rise and grain size during dry friction and wear of the bearing inner ring were simulated with the finite element method. The effects of the inner ring speed, load pressure and other parameters on the wear rate were studied. The relationship between the grain size and yield strength of GCr15 bearing steel was obtained. The effects of the initial grain size, rotational speed and load pressure on the bearing wear failure were studied. The evolutions of the grain size during service were predicted by means of the dynamic grain recrystallization (DRX), static grain recrystallization (SRX) and grain growth (GG) subprogram. The results show that the contact stress has a more significant effect on the early failure wear than the bearing speed, and the increase in the contact stress will aggravate the wear rate of the bearing inner ring. Under the same working conditions, the smaller the grain size, the more significant the influence of the cycle times on wear was. The heat-affected zone produced a local high temperature in the contact area, temperature flashes of up to 580 °C could occur in the central contact area, and the temperature decreased gradually with the increase in the depth from the contact area. It is noteworthy that both the surface and the subsurface of the material produced grain refinement; the grain size was refined from 20 μm to 0.4–12 μm under different working conditions. And the degree of refinement of the subsurface was higher than that of the surface. Full article
Show Figures

Figure 1

Figure 1
<p>7009AC bearing geometry model: (<b>a</b>) geometrical model of bearing; (<b>b</b>) simplified finite element model; (<b>c</b>) model representativeness analysis position.</p>
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<p>Experimental schematic diagram and device: (<b>a</b>) schematic diagram of the experimental chamber; (<b>b</b>) experimental facility.</p>
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<p>Hall–Petch fitting relationship of GCr15.</p>
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<p>Influence of contact load and speed of GCr15 on the number of cycles (wear rate): (<b>a</b>) effect of bearing contact load; (<b>b</b>) effect of speed under 1 GPa; (<b>c</b>) effect of speed under 1.5 GPa; (<b>d</b>) effect of speed under 2 GPa.</p>
Full article ">Figure 4 Cont.
<p>Influence of contact load and speed of GCr15 on the number of cycles (wear rate): (<b>a</b>) effect of bearing contact load; (<b>b</b>) effect of speed under 1 GPa; (<b>c</b>) effect of speed under 1.5 GPa; (<b>d</b>) effect of speed under 2 GPa.</p>
Full article ">Figure 5
<p>Temperature distribution of the bearing under 12,000 rpm and 2000 MPa working conditions: (<b>a</b>) 3D morphology; (<b>b</b>) the contact influence zone.</p>
Full article ">Figure 6
<p>GCr15 contact area temperature variation trend under different working conditions: (<b>a</b>) 2000 rpm, 1000 MPa; (<b>b</b>) 2000 rpm, 1500 MPa; (<b>c</b>) 2000 rpm, 2000 MPa; (<b>d</b>) 12,000 rpm, 1000 MPa; (<b>e</b>) 12,000 rpm, 1500 MPa; (<b>f</b>) 12,000 rpm, 2000 MPa.</p>
Full article ">Figure 7
<p>Grain distributions of GCr15 under different working conditions. (<b>a</b>) 2000 rpm, 1000 MPa; (<b>b</b>) 2000 rpm, 1500 MPa; (<b>c</b>) 2000 rpm, 2000 MPa; (<b>d</b>) 12,000 rpm, 1000 MP; (<b>e</b>) 12,000 rpm, 1500 MP; (<b>f</b>) 12,000 rpm, 2000 MPa.</p>
Full article ">Figure 8
<p>Grain evolution of the bearing inner ring at an initial grain size of 20 μm.</p>
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<p>Effect of grain evolution on wear rate at an initial grain size of 20 μm.</p>
Full article ">Figure 10
<p>OM with different numbers of cycles: (<b>a</b>) original sample surface; (<b>b</b>) 2.5 × 106 times; (<b>c</b>) 5 × 106 times.</p>
Full article ">Figure 11
<p>Wear modes and mechanisms during the dry sliding wear test. (<b>a</b>) Original sample surface; (<b>b</b>) after a period of wear and tear; (<b>c</b>) end of wear test.</p>
Full article ">Figure 12
<p>SEM and EDS with different numbers of cycles. (<b>a</b>) Initial sample surface; (<b>b</b>) Sample surface of 2.5 × 10<sup>6</sup> cycles; (<b>c</b>) Sample surface of 5 × 10<sup>6</sup> cycles; (<b>d</b>) Initial EDS detection; (<b>e</b>) EDS detection of 2.5 × 10<sup>6</sup> cycles; (<b>f</b>) EDS detection of 5 × 10<sup>6</sup> cycles.</p>
Full article ">Figure 13
<p>XRD patterns with different numbers of cycles.</p>
Full article ">
15 pages, 8914 KiB  
Article
Numerical Simulation and Engineering Application of Temporary Stress Field in Coal Mine Roadway
by Heng Zhang, Hongwei Ma, Chuanwei Wang, Qinghua Mao and Xusheng Xue
Appl. Sci. 2024, 14(23), 11420; https://doi.org/10.3390/app142311420 - 8 Dec 2024
Viewed by 580
Abstract
The imbalance between excavation and mining is significant as it restricts the efficient development of coal resources. Slow tunneling speed is primarily due to the inability to concurrently conduct excavation and permanent support operations, and temporary support is considered a key solution to [...] Read more.
The imbalance between excavation and mining is significant as it restricts the efficient development of coal resources. Slow tunneling speed is primarily due to the inability to concurrently conduct excavation and permanent support operations, and temporary support is considered a key solution to this problem. However, the mechanism by which temporary support affects the surrounding rock in unsupported are as remains unclear, hindering the assurance of stability in these areas and the determination of a reasonable unsupported span. To address this issue, this work proposed a stress distribution model as temporary support, elucidating the distribution law of support forces within the surrounding rock. By analyzing the stress differences between areas with and without temporary support, the stress field distribution characteristics of temporary support were determined. Subsequently, the evolution of stress and strain in the surrounding rock within unsupported areas was analyzed concerning changes in temporary support length, support force, and unsupported distance. The results indicated that, although temporary support does not directly act on unsupported areas, it still generates a supportive stress field within them. The maximum unsupported distance should not exceed 3 m, and there is a strong linear relationship between the optimal temporary support force and the unsupported span. Furthermore, the length of temporary support should not exceed 17 m from the tunnel face. The successful application of the shield tunneling robot system verifies that temporary support can ensure the stability of the surrounding rock in unsupported areas, confirming the validity of the temporary support stress distribution model. This research can be used to design and optimize cutting parameters and temporary support parameters, arrange equipment, and design and optimize tunnel excavation processes to achieve safe and efficient tunneling. Full article
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<p>Relationship between tunneling system and surrounding rock (a—unexcavated area; b—unsupported area; c—temporary support area; d—permanent support area; 1—excavating system; 2—temporary support system; 3—anchor drilling system;).</p>
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<p>Temporary support stress distribution model.</p>
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<p>Stress change regulation along excavation direction (<b>a</b>) and height direction (<b>b</b>) of the roadway.</p>
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<p>Stress nephogram at different heights from the roof.</p>
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<p>Comparison of stress curves at different heights from the roof.</p>
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<p>Influence of different temporary supporting forces on different empty roof spacing.</p>
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<p>Linear fitting relationship.</p>
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<p>Roof displacements conditions with different unsupported distance.</p>
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<p>Roof displacements under different temporary support lengths and unsupported distances.</p>
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<p>Relationship between robot system and surrounding rock (a—unexcavated area; b—unsupported area; c—temporary support area; d—permanent support area; 1—excavating robot; 2—temporary support robot I; 3—temporary support robot II; 4—anchor drilling platform; 5—electro-hydraulic control platform; 6—ventilation and transportation system).</p>
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<p>Tunneling face conditions. (<b>a</b>) Shield tunneling robot system. (<b>b</b>) Road header. (<b>c</b>) Tunnel 112204 face roof support condition. (<b>d</b>) Tunnel 112202 face roof support condition. (<b>e</b>) Tunnel 112204 face sidewall support conditions. (<b>f</b>) Tunnel 112202 face sidewall support conditions.</p>
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<p>On-site monitoring data. (<b>a</b>) Excavation distance monitoring. (<b>b</b>) Roof strain monitoring.</p>
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14 pages, 3760 KiB  
Article
Heat Transfer Mechanism Study of an Embedded Heat Pipe for New Energy Consumption System Enhancement
by Yuanlin Cheng, Hu Yu, Yi Zhang, Shu Zhang, Zhipeng Shi, Jinlin Xie, Silu Zhang and Changhui Liu
Energies 2024, 17(23), 6162; https://doi.org/10.3390/en17236162 - 6 Dec 2024
Viewed by 364
Abstract
Aiming at the demand for new energy consumption and mobile portable heat storage, a gravity heat pipe with embedded structure was designed. In order to explore the two-phase heat transfer mechanism of the embedded heat pipe, CFD numerical simulation technology was used to [...] Read more.
Aiming at the demand for new energy consumption and mobile portable heat storage, a gravity heat pipe with embedded structure was designed. In order to explore the two-phase heat transfer mechanism of the embedded heat pipe, CFD numerical simulation technology was used to study the internal two-phase flow state and heat transfer process of the embedded heat pipe under different working conditions. The evolution law of the internal working medium of the heat pipe under different working conditions was obtained. With the increase in heating power, it is easier to form large bubbles and large vapor slugs inside the heat pipe. When the heating power increases to a certain extent, the shape of the vapor slugs can no longer be maintained at the bottom of the adiabatic section, and the vapor slugs begin to break and merge, forming local annular flow. When the filling ratio (FR) is relatively low, the bubble is easy to break through the liquid level and rupture, unable to form a vapor slug. With the increase in FR, the possibility of projectile flow and annular flow in the heat pipe increases. Under the same heating power, the temperature uniformity of the heat pipe becomes stronger with the increase in heating time. The velocity distribution in the heat pipe is affected by the FR. The heating power has almost no effect on the distribution of the velocity field inside the heat pipe, but the maximum velocity is different. At an FR of 30%, there are two typical velocity extremes in the tube near positions of 120 mm and 160 mm, respectively, and the velocity in the tube is basically unchanged above a position of 200 mm. There are also multiple velocity extremes at an FR of 70%, with the maximum velocity occurring near 240 mm. Full article
(This article belongs to the Collection Advances in Heat Transfer Enhancement)
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<p>(<b>a</b>) Real picture, (<b>b</b>) dimensions and (<b>c</b>) mesh of the embedded heat pipe.</p>
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<p>Mesh independence test.</p>
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<p>The (<b>a</b>) temperature validation and (<b>b</b>) internal flow field validation of the embedded heat pipe.</p>
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<p>Contours of vapor phase and liquid phase distribution at heating power of 30 W (<b>a</b>) FR = 30% (<b>b</b>) FR = 50% (<b>c</b>) FR = 70%.</p>
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<p>Contours of vapor and liquid phase in heat pipe under different (<b>a</b>) heating power and (<b>b</b>) FRs.</p>
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<p>Contours of temperature distribution in heat pipe at different moments (FR = 70%, Heat power = 30 W).</p>
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<p>Comparison of axial velocity distribution of heat pipe under different heating powers.</p>
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<p>Comparison of heat pipe axial velocity distribution under different FRs.</p>
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24 pages, 9936 KiB  
Article
Research on the Correlation Between Overburden Rock Fracture Development and High-Energy Events During Deep Mining in Extremely Thick and Weakly Consolidated Strata for Regional Coal Mining Safety
by Jingchao Sun, Huaizhan Li, Guangli Guo, Yonghua Hu, Chao Tang, Tiening Wang, Hui Zheng, Liangui Zhang and Hang Sun
Sustainability 2024, 16(23), 10705; https://doi.org/10.3390/su162310705 - 6 Dec 2024
Viewed by 358
Abstract
The environmental damage and mining accidents caused by water inrush accidents and rock burst are two major problems faced in the safe and sustainable deep mining of extremely thick weakly cemented overlying strata. Mastering the fracture development law of the overlying strata, the [...] Read more.
The environmental damage and mining accidents caused by water inrush accidents and rock burst are two major problems faced in the safe and sustainable deep mining of extremely thick weakly cemented overlying strata. Mastering the fracture development law of the overlying strata, the evolution characteristics of high-energy events, and their correlative relationships in the deep mining of extremely thick weakly cemented overlying strata is the key to solving the above two problems, which is directly related to the sustainable development of regional coal and the protection of underground water resources in mining areas. By integrating the geological characteristics of extremely thick and weakly cemented overburdens in the Shaanxi–Inner Mongolia mining region of China, this study adopts methods such as field measurements, numerical simulations, and theoretical analyses to investigate the energy evolution characteristics of regional mining-induced tremors, as well as the correlation and mutual influence mechanisms between overburden fracture development and high-energy events. The results indicate a positive correlation between high-energy events and the development height of overburden fractures, suggesting that the occurrence of high-energy events can increase the height of overburden fracture development. Furthermore, high-energy events occurring before and after the “parallel joining” of two working faces have a relatively minor impact on the development height of overburden fractures, with an increase in the fracture-to-mining ratio (FMR) ranging from 1.56 to 2.78. In contrast, high-energy events occurring during the “parallel joining” of two working faces significantly affect the development height of overburden fractures, resulting in an FMR increase of 10.33 to 13.44, approximately one-third of the FMR measured through boreholes. The research results can provide a scientific basis for the safe and sustainable coal mining and the protection of underground water resources in similar mining areas with extremely thick weakly cemented overlying strata. Full article
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<p>The layout of the working face.</p>
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<p>Concept diagram of the seismic monitoring system in Shilawusu mining area.</p>
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<p>Mine earthquake monitoring data during the advancing of the 1208 working face.</p>
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<p>Location map of high-energy events during the mining process of the 1208 working face.</p>
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<p>Energy distribution during the mining process of the 1208 working face.</p>
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<p>Initial model diagram.</p>
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<p>Strike direction slice of the model.</p>
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<p>Subsidence and movement curves of various points along the strike observation line (line H) of the 1208 working face during mining.</p>
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<p>Simulated subsidence and movement curves of various points along the strike observation line (line H) of the 1208 working face during mining.</p>
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<p>Energy accumulation profiles along the strike direction during working face mining. (<b>a</b>) Advance distances of 400 m, 900 m, and 1400 m; (<b>b</b>) advance distances of 1900 m, 2400 m, and 2700 m.</p>
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<p>Curve of energy extreme values along the strike direction of rock strata at different advance distances of the 1208 working face.</p>
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<p>Comparison of overburden fracture development before and after high-energy events at an X-coordinate of 2050 m. (<b>a</b>) Before the high-energy event at an advance distance of 2400 m on the working face; (<b>b</b>) after the high-energy event at an advance distance of 2500 m on the working face; (<b>c</b>) before the high-energy event at an advance distance of 2600 m on the working face; (<b>d</b>) after the high-energy event at an advance distance of 2700 m on the working face.</p>
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<p>Comparison of overburden fracture development before and after high-energy events at an X-coordinate of 2050 m. (<b>a</b>) Before the high-energy event at an advance distance of 2400 m on the working face; (<b>b</b>) after the high-energy event at an advance distance of 2500 m on the working face; (<b>c</b>) before the high-energy event at an advance distance of 2600 m on the working face; (<b>d</b>) after the high-energy event at an advance distance of 2700 m on the working face.</p>
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<p>Comparison of overburden fracture development before and after high-energy events at an X-coordinate of 2075 m. (<b>a</b>) Before the high-energy event at an advance distance of 2400 m on the working face; (<b>b</b>) after the high-energy event at an advance distance of 2500 m on the working face; (<b>c</b>) before the high-energy event at an advance distance of 2600 m on the working face; (<b>d</b>) after the high-energy event at an advance distance of 2700 m on the working face.</p>
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<p>Comparison of overburden fracture development before and after high-energy events at an X-coordinate of 2150 m. (<b>a</b>) Before the high-energy event at an advance distance of 2700 m on the working face; (<b>b</b>) after the high-energy event at an advance distance of 2800 m on the working face.</p>
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<p>Comparison of overburden fracture development before and after high-energy events at an X-coordinate of 2425 m. (<b>a</b>) Before the high-energy event at an advance distance of 2400 m on the working face; (<b>b</b>) after the high-energy event at an advance distance of 2500 m on the working face.</p>
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<p>Comparison of overburden fracture development before and after high-energy events at an X-coordinate of 2625 m. (<b>a</b>) Before the high-energy event at an advance distance of 2600 m on the working face; (<b>b</b>) after the high-energy event at an advance distance of 2700 m on the working face.</p>
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<p>Comparison of overburden fracture development before and after high-energy events at an X-coordinate of 2775 m. (<b>a</b>) Before the high-energy event at an advance distance of 2700 m on the working face; (<b>b</b>) after the high-energy event at an advance distance of 2800 m on the working face.</p>
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<p>Height of overburden fractures before and after high-energy events at different times along the X-coordinate of the 1208 working face.</p>
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<p>Development process of overburden fractures triggered by high-energy events.</p>
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16 pages, 3962 KiB  
Article
Full Spectrum Electrochromic WO3 Mechanism and Optical Modulation via Ex Situ Spectroscopic Ellipsometry: Effect of Li+ Surface Permeation
by Buyue Zhang, Jintao Wang, Shuhui Jiang, Meng Yuan and Xinyu Chen
Micromachines 2024, 15(12), 1473; https://doi.org/10.3390/mi15121473 - 5 Dec 2024
Viewed by 451
Abstract
Tungsten oxide (WO3) electrochromic devices are obtaining increasing interest due to their color change and thermal regulation. However, most previous work focuses on the absorption or transmission spectra of materials, rather than the optical parameters evolution in full spectrum in the [...] Read more.
Tungsten oxide (WO3) electrochromic devices are obtaining increasing interest due to their color change and thermal regulation. However, most previous work focuses on the absorption or transmission spectra of materials, rather than the optical parameters evolution in full spectrum in the electrochromic processes. Herein, we developed a systematic protocol of ex situ methods to clarify the evolutions of subtle structure changes, Raman vibration modes, and optical parameters of WO3 thin films in electrochromic processes as stimulated by dosage-dependent Li+ insertion. We obtained the below information by ex situ spectroscopic ellipsometry. (1) Layer-by-layer Li+ embedding mechanism demonstrated by individual film thickness analysis. (2) The details of its optical leap in the Brillouin zone in the full spectral. (3) The optical constants varied with the Li+ insertion in the ultraviolet, visible, and near-infrared bands, demonstrating the potential for applications in chip fabrication, deep-sea exploration, and optical measurements. (4) Simulated angular modulation laws of WO3 films for full spectra in different Li+ insertion states. This ex situ method to study the optical properties of electrochromic devices are important for monitoring phase transition kinetics, the analysis of optical leaps, and the study of ion diffusion mechanisms and the stoichiometry-dependent changes in optical constants over the full spectral. This work shows that electrochromic films in Li+ surface permeation can be applied in the field of zoom lenses, optical phase modulators, and other precision optical components. Our work provides a new solution for the development of zoom lenses and a new application scenario for the application of electrochromic devices. Full article
(This article belongs to the Special Issue Energy Conversion Materials/Devices and Their Applications)
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<p>(<b>a</b>) Planar and (<b>b</b>) cross-sectional photographs of field emission scanning electron microscopy of WO<sub>3</sub> thin film. The as-fabricated WO<sub>3</sub> film is composed of uniformly distributed small particles that are difficult to discern with a diameter smaller than 10 nm. The as-coated WO<sub>3</sub> layer shows an average thickness of 380 nm uniformly and compactly on the top surface of the ITO layer.</p>
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<p>The XRD results of the Li<sub>x</sub>WO<sub>3</sub> films (0.10 ≤ x ≤ 0.35). To show the structural changes more clearly, we drew a detailed view of the main diffraction peaks of the sample and the contour of the film. Blue lines represent (002) crystal surfaces and red lines represent (200) crystal surfaces.</p>
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<p>The Raman spectra of the Li<sub>x</sub>WO<sub>3</sub> (0.10 ≤ x ≤ 0.35).</p>
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<p>The model of (<b>a</b>) the FTO substrate and (<b>b</b>) the fit result of it. The model of (<b>c</b>) γ-WO<sub>3</sub> films on the FTO substrate and (<b>d</b>) Li<sub>x</sub>WO<sub>3</sub> films, respectively.</p>
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<p>(<b>a</b>) Schematic structure of thin film after lithiation. (<b>b</b>) Relationship between Li<sup>+</sup> insertion value x and film thickness.</p>
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<p>Using the Second derivatives of the pseudo dielectric function numerically calculated spectra of Li<sub>x</sub>WO<sub>3</sub> (blue) thin films at 300K. The <span class="html-italic">E</span><sub>cp1</sub>, <span class="html-italic">E</span><sub>cp2</sub>, <span class="html-italic">E</span><sub>cp3</sub>, <span class="html-italic">E</span><sub>cp4</sub>, and <span class="html-italic">E</span><sub>cp5</sub> transition features are indicated by arrows. (<b>a</b>–<b>f</b>) is the calculated spectra of Li<sub>x</sub>WO<sub>3</sub> for x = 0.10, x = 0.15, x = 0.20, x = 0.25, x = 0.30, x = 0.35, respectively.</p>
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<p>(<b>a</b>) The absorption and (<b>b</b>) transmission spectra for different values of x. The illustration is the optical bandgaps by simulated. Absorption peaks in the red area is attributed to the absorption of W (VI) (d<sup>0</sup>). Absorption peaks in the blue area is attributed to the absorption of W (V) (d<sup>1</sup>). Absorption peaks in the green area is attributed to the absorption of W (IV) (d<sup>2</sup>).</p>
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<p>(<b>a</b>) The refractive index and (<b>b</b>) extinction coefficient of the Li<sub>x</sub>WO<sub>3</sub> film for different x values. As a comparison, the values of the γ-WO<sub>3</sub> layer are also given. In fitting Li<sub>x</sub>WO<sub>3</sub> layers, the optical constants of the γ-WO<sub>3</sub> layer are fixed.</p>
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<p>Simulated and experimental absorption coefficient spectra of thin films on the FTO substrate in the visible region with x = 0.10, 0.20, and 0.30.</p>
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27 pages, 13275 KiB  
Article
Seismic Response Analysis of a Vibrating Stirred Steel Fiber Concrete Frame Structure Based on Probability Density Evolution
by Liang Huang, Shuaitao Li, Di Zhang, Wenze Wang, Jianguo Xu and Shizhan Xu
Buildings 2024, 14(12), 3862; https://doi.org/10.3390/buildings14123862 - 30 Nov 2024
Viewed by 459
Abstract
In this paper, an experimental study of steel fiber concrete using vibration mixing technology and the probability density evolution theory is applied to establish a nonlinear stochastic seismic response model for multistory concrete frame structures considering the randomness of structural parameters. The random [...] Read more.
In this paper, an experimental study of steel fiber concrete using vibration mixing technology and the probability density evolution theory is applied to establish a nonlinear stochastic seismic response model for multistory concrete frame structures considering the randomness of structural parameters. The random evolution characteristics of the structural response are studied and analyzed, and a reliability analysis method for concrete frame structures based on PDEM theory is proposed. The equations are solved by the finite difference method in the TVD format, and the probability distribution of the deformation index of the concrete frame structure is obtained by summation, where the reliability is given according to the limit value of the index. The results confirm that the PDEM theory can accurately assess the functional reliability of the structure, and it is also found that the randomness of the structural parameters has a significant effect on its nonlinear dynamic response law, and that consideration of the randomness of the structural parameters at the early stage of the design can be of great help to the seismic resistance of the structure. This study not only provides a scientific basis for the optimization of the performance of steel fiber concrete but also provides a new perspective and tool for the analysis of probability density evolution in the field of structural earthquake engineering. Full article
(This article belongs to the Section Building Materials, and Repair & Renovation)
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<p>Concrete mixing curve.</p>
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<p>The scattered distribution of gelling material (<b>a</b>) and the ideal distribution (<b>b</b>).</p>
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<p>Self-falling mixer and forced mixer working diagram. (<b>a</b>) Self-falling mixer. (<b>b</b>) Forced mixer.</p>
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<p>Stirring working model and speed gradient schematic. (<b>a</b>) Stirring working model. (<b>b</b>) Speed gradient schematic.</p>
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<p>Concrete microstructure.</p>
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<p>Vibrating and stirring energy wavefront and energy gradient map. (<b>a</b>) Vibrating and stirring energy wavefront. (<b>b</b>) Energy gradient map.</p>
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<p>The theoretical model of fiber spacing. (<b>a</b>) Mechanical action model of fibers. (<b>b</b>) Distribution of interface bonding forces.</p>
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<p>The feeding and mixing process of steel-fiber-reinforced concrete.</p>
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<p>Morphology of plain concrete slurry. (<b>a</b>) Comparison of conventional mixing specimens. (<b>b</b>) Vibrational mixing specimens.</p>
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<p>Morphology of steel-fiber-reinforced concrete slurry. (<b>a</b>) Comparison of conventional mixing specimens. (<b>b</b>) Vibrational mixing specimens.</p>
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<p>Compressive damage pattern of plain concrete. (<b>a</b>) Specimen 1. (<b>b</b>) Specimen 2.</p>
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<p>Compressive damage form of ordinary mixed steel fiber concrete. (<b>a</b>) Specimen 3. (<b>b</b>) Specimen 4.</p>
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<p>Vibration mixing steel fiber concrete compressive damage morphology. (<b>a</b>) Specimen 5. (<b>b</b>) Specimen 6.</p>
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<p>Joint concrete stress–strain curve.</p>
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<p>Flowchart of reliability solution for probability density evolution method of stochastic structure.</p>
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<p>Elevation arrangement and beam–column section reinforcement of concrete frame structures. (<b>a</b>) Elevation layout diagram. (<b>b</b>) Beam–column section reinforcement diagram.</p>
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<p>Stress–strain curve comparison chart.</p>
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<p>Schematic diagram of the OpenSEES model.</p>
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<p>Mean parameter curve of stress–strain relationship.</p>
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<p>Stress–strain time course curves of structures during seismic response.</p>
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<p>Ground floor shear—inter-story displacement hysteresis recovery force curve.</p>
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<p>Time course curves of interlayer displacement angles at the top layer of all samples under seismic effects.</p>
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<p>Mean and mean square deviation curves of the top displacement angle. (<b>a</b>) Mean curve. (<b>b</b>) Mean square deviation curve.</p>
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<p>Probability density surfaces.</p>
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<p>Probability density contour plot.</p>
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<p>Different cutoff probability density functions.</p>
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<p>The extreme value distribution. (<b>a</b>) The top inter-story displacement angle. (<b>b</b>) The bottom side column turning angle.</p>
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<p>Cumulative distribution function. (<b>a</b>) The top inter-story displacement angle. (<b>b</b>) The bottom side column turning angle.</p>
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<p>Hysteresis curve comparison chart.</p>
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28 pages, 12115 KiB  
Article
Energy Evolution and Fractal Characteristics of Sandstones Under True Triaxial Cyclic Loading and Unloading
by Qihang Zhang, Xiangrui Meng and Guangming Zhao
Fractal Fract. 2024, 8(12), 714; https://doi.org/10.3390/fractalfract8120714 - 30 Nov 2024
Viewed by 512
Abstract
To study the fractal characteristics and energy evolution of sandstones under true three-dimensional stress states, a true triaxial compression test and a cyclic loading and unloading test of sandstone specimens under different loads were carried out using a self-developed true triaxial disturbance testing [...] Read more.
To study the fractal characteristics and energy evolution of sandstones under true three-dimensional stress states, a true triaxial compression test and a cyclic loading and unloading test of sandstone specimens under different loads were carried out using a self-developed true triaxial disturbance testing system. Based on the evolution law of true triaxial cyclic loading and unloading stress–strain, the types of loading and unloading in the cyclic loading and unloading test were delineated, and the reasons for the change in peak maximum principal stress intensity under different paths were analyzed. By analyzing the crushing characteristics of rock samples under different paths, it was found that the staged cyclic loading and unloading caused the greatest damage to the rock mass, while the equal-amplitude and unequal-lower-limit staged loading and unloading caused the least damage to the rock mass. Based on fractal theory, it was found that the rock samples under path V had the highest fractal dimension D. The elastic energy density, dissipated energy density, and input energy density of true triaxial cyclic loading and unloading under different paths were calculated by graphical area integration and superposition methods, respectively, to analyze the evolution of the three with the increase in the loading and unloading cycles and the energy distribution during the loading and unloading process. True triaxial cyclic loading and unloading tests revealed a linear relationship between the elastic energy density and total input energy density of the rock mass, and the energy storage coefficient exceeded 0.5, regardless of the loading path. Full article
(This article belongs to the Special Issue Fractal Analysis and Its Applications in Rock Engineering)
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<p>True triaxial disturbance unloading rock testing system.</p>
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<p>Rock sample and installation schematic.</p>
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<p>True triaxial compression test path.</p>
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<p>Diagram of the true triaxial cyclic loading and unloading test path.</p>
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<p>True triaxial compression stress–strain curve.</p>
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<p>Variation curves of principal strain in different directions with peaks and valleys of maximum principal stress.</p>
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<p>True triaxial cyclic loading and unloading stress−strain curves under different paths.</p>
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<p>Maximum primary stress intensity at peak under various cyclic loading and unloading trajectories.</p>
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<p>Energy calculation under true triaxial loading and unloading cycles.</p>
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<p>Energy density vs. loading and unloading cycle index.</p>
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<p>Evolution laws of the elastic and dissipated energy ratios with the number of cycles.</p>
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<p>Correlation of elastic energy density and total input energy density under different cyclic loading and unloading cycles.</p>
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<p>Correlation of elastic energy density and total input energy density under different cyclic loading and unloading cycles.</p>
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<p>Sandstone specimen morphology after true triaxial cyclic loading and unloading.</p>
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<p>Sandstone specimen sieving results.</p>
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<p>Sandstone specimen sieving results.</p>
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<p>Distribution pattern of broken particles in rock samples.</p>
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<p>The values of D under different true triaxial cyclic loading and unloading cycles.</p>
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17 pages, 11075 KiB  
Article
Uniaxial Compressive Failure Characteristics and Fractal Analysis of Mud–Sand Composite Rock Samples Based on Acoustic Emission Tests
by Changzheng Zhao, Shenggen Cao, Shihui Lang, Shuyu Du and Chiyuan Che
Fractal Fract. 2024, 8(12), 713; https://doi.org/10.3390/fractalfract8120713 - 30 Nov 2024
Viewed by 489
Abstract
In order to study the influence of rock combination types on their mechanical properties and failure characteristics, uniaxial compression tests of single rock samples and combined rock samples were conducted. Acoustic emission (AE) signals during the test process were collected, and the differences [...] Read more.
In order to study the influence of rock combination types on their mechanical properties and failure characteristics, uniaxial compression tests of single rock samples and combined rock samples were conducted. Acoustic emission (AE) signals during the test process were collected, and the differences in AE signals of single rock samples and combined rock samples were studied based on the fractal theory. The results showed that the peak strength, elastic modulus, peak strain, and failure degree of the combined rock samples are all between those of the two single rock samples. The AE ringing count gradually increases with the loading process and suddenly increases to the maximum when the rock sample fails. During this process, the phase trajectory volume corresponding to the ringing count shows an evolution law of first decreasing and then increasing, while the correlation dimension corresponding to the ringing count signal shows an overall evolution law of first increasing and then decreasing. The results indicate that the phase trajectory volume, correlation dimension, and crack changes have a consistent dynamic change. Therefore, the phase trajectory and correlation dimension are effective tools to describe the pore change characteristics of rock combinations. Full article
(This article belongs to the Special Issue Applications of Fractal Analysis in Underground Engineering)
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<p>Geographical location of a mine.</p>
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<p>Rock samples.</p>
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<p>Uniaxial and acoustic emission experimental equipment.</p>
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<p>Position diagram of acoustic emission sensor.</p>
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<p>Stress–strain curve and failure mode of rock samples. (<b>a</b>) Mudstone. (<b>b</b>) Sandstone. (<b>c</b>) Mudstone–sandstone combined rock.</p>
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<p>Acoustic emission ringing count and cumulative ringing count. (<b>a</b>) Mudstone. (<b>b</b>) Sandstone. (<b>c</b>) Mudstone–sandstone combined rock.</p>
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<p>Distribution of RA-AF. (<b>a</b>) Mudstone. (<b>b</b>) Sandstone. (<b>c</b>) Mudstone–sandstone combined rock.</p>
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<p>Distribution of RA-AF. (<b>a</b>) Mudstone. (<b>b</b>) Sandstone. (<b>c</b>) Mudstone–sandstone combined rock.</p>
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<p>Location diagram of acoustic emission at different stages. (<b>a</b>) Mudstone. (<b>b</b>) Sandstone. (<b>c</b>) Mudstone–sandstone combined rock.</p>
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<p>Correlation dimension and phase trajectory change trend of mudstone. (<b>a</b>) Correlation dimension. (<b>b</b>) Phase trajectories.</p>
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<p>Correlation dimension and phase trajectory change trend of Sandstone. (<b>a</b>) Correlation dimension. (<b>b</b>) Phase trajectories.</p>
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<p>Correlation dimension and phase trajectory change trend of mudstone–sandstone combined rock. (<b>a</b>) Correlation dimension. (<b>b</b>) Phase trajectories.</p>
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14 pages, 565 KiB  
Article
A Parameter Study of 1D Atmospheric Models of Pulsating AGB Stars
by Henry A. Prager, Lee Anne M. Willson, Joyce A. Guzik, Michelle J. Creech-Eakman and Qian Wang
Galaxies 2024, 12(6), 81; https://doi.org/10.3390/galaxies12060081 - 29 Nov 2024
Viewed by 311
Abstract
Using the atmospheric pulsation code written by George Bowen, we have performed a parameter study examining the effects of modifying various parameters of models of oxygen-rich AGB atmospheres pulsating in the fundamental and first-overtone modes. For each pulsation mode, we have examined the [...] Read more.
Using the atmospheric pulsation code written by George Bowen, we have performed a parameter study examining the effects of modifying various parameters of models of oxygen-rich AGB atmospheres pulsating in the fundamental and first-overtone modes. For each pulsation mode, we have examined the effects of adjusting the dust condensation temperature, dust condensation temperature range, pulsation amplitude, dust opacity, and metallicity. Our model grids are generated with the constraint that their luminosities are chosen to span the range of observed mass loss rates at a chosen mass. The dust condensation temperature, pulsation amplitude, and dust opacity have strong effects on the ultimate location and shape of the final model grids in the mass luminosity plane. The mass loss rate evolution of the fundamental and first-overtone mode models show a significant difference in behavior. While the fundamental mode models exhibit the typically assumed power–law relation with mass and luminosity, the first-overtone mode models show significant non-power law behavior at observed mass loss rates. Effectively, models in the first-overtone mode require somewhat higher luminosities to reach the same mass loss rates seen in fundamental mode models of the same mass, consistent with observed AGB stars. Full article
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Figure 1
<p>This diagram depicts the location of observed AGB stars (contours) and models generated using reference values (markers) in <math display="inline"><semantics> <mrow> <mo form="prefix">log</mo> <mi>M</mi> </mrow> </semantics></math> vs. <math display="inline"><semantics> <mrow> <mo form="prefix">log</mo> <mi>L</mi> </mrow> </semantics></math> in solar units. Solid blue contours depict the location of fundamental mode M-type stars in the LMC and dashed red contours depict the location of first-overtone mode M-type stars in the LMC from Riebel et al. [<a href="#B14-galaxies-12-00081" class="html-bibr">14</a>]; contours are the percentile of stars included in steps of 20, starting from 90 working inward. Blue dots are fundamental mode M-type star models and red crosses are first-overtone-mode M-type star models within the established mass loss rate ranges.</p>
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<p>These figures depict the effects of adjusting model parameters on the ratio of the power law exponents |B/C|, and thus the orientation of the model grid. Shifts due to the maximum dust opacity <math display="inline"><semantics> <msub> <mi>κ</mi> <mrow> <mi mathvariant="normal">D</mi> <mo>,</mo> <mi>max</mi> <mo>.</mo> </mrow> </msub> </semantics></math> are found in (<b>a</b>), the dust condensation temperature <math display="inline"><semantics> <msub> <mi>T</mi> <mrow> <mi>con</mi> <mo>.</mo> </mrow> </msub> </semantics></math> in (<b>b</b>), a constant piston amplitude <math display="inline"><semantics> <msub> <mi>u</mi> <mrow> <mi>amp</mi> <mo>.</mo> </mrow> </msub> </semantics></math> in (<b>c</b>), the factor <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math> from Equation (<a href="#FD3-galaxies-12-00081" class="html-disp-formula">3</a>) in (<b>d</b>), and the range of condensation and evaporation temperatures <math display="inline"><semantics> <msub> <mi>δ</mi> <mi>T</mi> </msub> </semantics></math> in (<b>e</b>). The fundamental mode fit line can be seen in solid blue with individual grids marked by blue dots, and the first-overtone mode fit line can be seen in dashed red with individual model grids marked by red crosses.</p>
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<p>These figures depict the effects of adjusting model parameters on the position of the death line, and thus the position of the model grid. Shifts due to the maximum dust opacity <math display="inline"><semantics> <msub> <mi>κ</mi> <mrow> <mi mathvariant="normal">D</mi> <mo>,</mo> <mi>max</mi> <mo>.</mo> </mrow> </msub> </semantics></math> are found in (<b>a</b>), the dust condensation temperature <math display="inline"><semantics> <msub> <mi>T</mi> <mrow> <mi>con</mi> <mo>.</mo> </mrow> </msub> </semantics></math> in (<b>b</b>), a constant piston amplitude <math display="inline"><semantics> <msub> <mi>u</mi> <mrow> <mi>amp</mi> <mo>.</mo> </mrow> </msub> </semantics></math> in (<b>c</b>), the factor <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math> from Equation (<a href="#FD3-galaxies-12-00081" class="html-disp-formula">3</a>) in (<b>d</b>), and the range of condensation and evaporation temperatures <math display="inline"><semantics> <msub> <mi>δ</mi> <mi>T</mi> </msub> </semantics></math> in (<b>e</b>). The fundamental mode fit line can be seen in solid blue with individual grids marked by blue dots, and the first-overtone mode fit line can be seen in dashed red with individual model grids marked by red crosses.</p>
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<p>This figure depicts the necessary change in energy factor <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math> or maximum dust opacity <math display="inline"><semantics> <msub> <mi>κ</mi> <mrow> <mi mathvariant="normal">D</mi> <mo>,</mo> <mi>max</mi> <mo>.</mo> </mrow> </msub> </semantics></math> necessary for a grid of models generated using the Bowen atmospheric pulsation code to match the observed population of AGB stars in the LMC. The blue shaded region spans the shifts for the fundamental mode, with the solid curve being the shift, assuming no error in Prager et al. [<a href="#B18-galaxies-12-00081" class="html-bibr">18</a>], and the dashed lines bounding the maximum spread, as described by Equation (<a href="#FD5-galaxies-12-00081" class="html-disp-formula">5</a>). The red shaded region and corresponding curves show the same for the first-overtone mode. Note that this figure extends beyond the bounds discussed in <a href="#sec2-galaxies-12-00081" class="html-sec">Section 2</a> to show which combination of parameters is implied to replicate the observed range of AGB stars.</p>
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<p>This figure depicts an extreme (<span class="html-italic">not physical</span>) combination of the explored parameters chosen to shift the death line position as close to observations as possible, <math display="inline"><semantics> <mrow> <mi>ϵ</mi> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>κ</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>max</mi> <mo>.</mo> </mrow> </msub> <mo>=</mo> <mn>50</mn> <mspace width="4pt"/> <msup> <mi>cm</mi> <mn>2</mn> </msup> <mo>/</mo> <mi mathvariant="normal">g</mi> </mrow> </semantics></math>. The contours depict the same data as in <a href="#galaxies-12-00081-f001" class="html-fig">Figure 1</a>. Fundamental-mode models are represented by blue dots and first-overtone models are represented by red crosses. The fundamental-mode models have moved closer to the observed population, but are not yet in agreement. While the first-overtone mode models are within error bounds, neither they nor the fundamental mode are as extensive as expected, implying the mass loss rate increases too quickly with luminosity.</p>
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<p>Comparisons of pulsation period <span class="html-italic">P</span> to acoustic cut-off period <math display="inline"><semantics> <msub> <mi>P</mi> <mi>ac</mi> </msub> </semantics></math> in AGB atmospheres of a 1 <math display="inline"><semantics> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </semantics></math> star, as a function of luminosity. Blue compares these in the fundamental mode while red compares these in the first-overtone mode. Dots track the pulsation period of the modeled stars, and triangles track the acoustic cut-off period at the photosphere for the modeled stars. The acoustic cut-off period varies between modes due to differences in the effective scale height—the initial <span class="html-italic">e</span>-folding distance in the dynamic atmosphere—between the different pulsation modes.</p>
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<p>These figures depict locations of shock fronts relative to the stellar radius (<math display="inline"><semantics> <mrow> <mi>R</mi> <mo>/</mo> <msub> <mi>R</mi> <mo>★</mo> </msub> </mrow> </semantics></math>) in <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> <mspace width="4pt"/> <msub> <mi mathvariant="normal">M</mi> <mo>⊙</mo> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>6309</mn> <mspace width="4pt"/> <msub> <mi mathvariant="normal">L</mi> <mo>⊙</mo> </msub> </mrow> </semantics></math> AGB atmospheres. (<b>a</b>) displays these in the fundamental mode, (<b>b</b>) displays these in the first-overtone mode. Note that these models share an RML relation (see <a href="#sec2-galaxies-12-00081" class="html-sec">Section 2</a>) and are thus the same mean radius, but have different cycle time scales due to differences in their pulsation period. These models are evaluated to a distance of over 80 stellar radii, with some variation as models are rezoned (see Bowen [<a href="#B10-galaxies-12-00081" class="html-bibr">10</a>] for details).</p>
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<p>This figure demonstrate the inverse correlation between the mass loss rate <math display="inline"><semantics> <mover accent="true"> <mi>M</mi> <mo>˙</mo> </mover> </semantics></math> (y-axis) and <math display="inline"><semantics> <mrow> <mi>P</mi> <mo>/</mo> <msub> <mi>P</mi> <mi>ac</mi> </msub> </mrow> </semantics></math> (x-axis) in AGB atmospheres of 1 <math display="inline"><semantics> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </semantics></math> models assuming the reference parameters in <a href="#galaxies-12-00081-t001" class="html-table">Table 1</a>. Blue dots are the fundamental mode models and red crosses are the first-overtone mode models. This plot is limited to models that fall within the observed mass loss rate range (see <a href="#sec2-galaxies-12-00081" class="html-sec">Section 2</a>). The luminosity of each model in solar units is included in the plot; (4466, 4731, 5011, 5308, 5623, 5956, 6309, 6683, 7079, 7498, 7943) is the fundamental mode set and (4731, 5011, 5308, 5623, 5956, 6309, 6683, 7079, 7498, 7943, 8413, 8912, 9440, 9999, 10,592) is the first-overtone mode set.</p>
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18 pages, 20080 KiB  
Article
Driving Factors for Vegetation NDVI Changes in a Cold Temperate Zone: Climate, Topography, and Land Use
by Dandan Zhao, Weijia Hu, Jianmiao Wang and Jiping Liu
Forests 2024, 15(12), 2098; https://doi.org/10.3390/f15122098 - 27 Nov 2024
Viewed by 640
Abstract
Exploring the spatio-temporal evolution and driving mechanism of the NDVI (Normalized Difference Vegetation Index) is important in order to understand the operating forces of the ecosystem and the response process of environmental change. We analyzed spatio-temporal vegetation changes by using the trend analysis [...] Read more.
Exploring the spatio-temporal evolution and driving mechanism of the NDVI (Normalized Difference Vegetation Index) is important in order to understand the operating forces of the ecosystem and the response process of environmental change. We analyzed spatio-temporal vegetation changes by using the trend analysis method during 2001–2020 based on the MODIS NDVI, the meteorological data, the DEM (Digital Elevation Model) and land use types data. We quantitatively revealed the influence degree and mechanism of each detection factor and their interaction on the spatial differentiation of vegetation by using the geographical detector model. Results showed that the vegetation NDVI showed an increasing trend with an increasing rate of 0.021/10 a during 2001–2020 and mainly distributed in the northwest and southwest of the Greater Khingan Mountains. The explanatory power values of each driving factor are as follows: land use (0.384) > elevation (0.193) > slope (0.159) > annual precipitation (0.104) > aspect (0.069) > average annual temperature (0.056). The explanatory power of interaction between driving factors were relatively high, as follows: Land use ∩ Aspect (0.490) > Land use ∩ Slope (0.471) > Land use ∩ Annual precipitation (0.460) > Land use ∩ elevation (0.443) > Land use ∩ Annual temperature (0.421) > Aspect ∩ elevation (0.408). Our research was of great significance for understanding the growth law of vegetation, protecting the ecological environment, and sustainable development in cold temperate zones. Full article
(This article belongs to the Section Forest Ecology and Management)
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<p>The Greater Khingan Mountains area of China.</p>
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<p>(<b>a</b>) NDVI variation trends (<b>b</b>) Annual average NDVI (<b>c</b>) Slope variation trends of NDVI during 2001–2020 in the Greater Khingan Mountains.</p>
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<p>Annual NDVI changes of different land use in the Greater Khingan Mountains.</p>
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<p>Spatial distribution of land use transformation in the Greater Khingan Mountains during 2001–2020.</p>
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<p>Interannual changes of mean NDVI and average temperature (<b>a</b>) and interannual changes of mean NDVI and annual precipitation (<b>b</b>) during 2001–2020.</p>
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<p>Spatial distribution of correlation between annual NDVI and average temperature (<b>a</b>) Spatial distribution of correlation between annual NDVI and annual precipitation (<b>b</b>).</p>
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<p>Variation trend of NDVI with elevation (<b>a</b>), slope (<b>b</b>), and aspect (<b>c</b>) in the Greater Khingan Mountains during 2001–2020.</p>
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<p>Explanatory power of driving factors of the NDVI spatial differentiation in the Greater Khingan Mountains.</p>
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<p>Explanatory power of interactive detection of driving factors in the Greater Khingan Mountains.</p>
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26 pages, 9559 KiB  
Article
Damage Evolution and NOx Photocatalytic Degradation Performance of Nano-TiO2 Concrete Under Freeze–Thaw Cycles
by Zongming Jia, Yanru Zhao and Hengmao Niu
Buildings 2024, 14(12), 3763; https://doi.org/10.3390/buildings14123763 - 26 Nov 2024
Viewed by 360
Abstract
The internal pore structure of nano-TiO2 concrete deteriorates gradually during freeze–thaw (F–T) cycles. The deterioration process can reveal the F–T damage mechanism and the deterioration law of photocatalytic performance. The evolution law of the pore structure of nano-TiO2 concrete during F–T [...] Read more.
The internal pore structure of nano-TiO2 concrete deteriorates gradually during freeze–thaw (F–T) cycles. The deterioration process can reveal the F–T damage mechanism and the deterioration law of photocatalytic performance. The evolution law of the pore structure of nano-TiO2 concrete during F–T damage was investigated. Moreover, this paper defined the microscopic F–T damage factor based on porosity and fractal dimension. The results showed that a 2% dosage of nano–TiO2 concrete had better frost resistance and lower porosity in this experiment. Its porosity only increased by 13.3% after 200 F–T cycles, which was much smaller than that of ordinary concrete. Furthermore, the presence of nano-TiO2 enhanced the volume fractal dimension of concrete pores larger than 100 nm, increasing the complexity of the pore structure and contributing to improved frost resistance. F–T damage led to a decrease in the photocatalytic performance of nano–TiO2 concrete. Still, it helped the nitrate on the surface of the concrete to dissolve and disappear more quickly under rainwater washout. Finally, a thermodynamic theory-based concrete F–T damage correction model was constructed, and the model was used to predict F–T damage values for some scholars. The results showed that the correlation between the model values and the experimental values was more than 0.95, which could accurately reflect the degree of F–T damage of concrete. In addition, a prediction model of photocatalytic NO reduction by nano-TiO2 concrete based on microscopic damage factor was established. It provides a theoretical basis for the application of nano-TiO2 concrete in the field of gas pollutant treatment. Full article
(This article belongs to the Section Building Materials, and Repair & Renovation)
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Figure 1
<p>Forming and curing process of nano-TiO<sub>2</sub> concrete specimens.</p>
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<p>Rapid F–T test: (<b>a</b>) F–T testing machine, (<b>b</b>) concrete dynamic modulus of elasticity tester, and (<b>c</b>) F–T cycle regime.</p>
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<p>(<b>a</b>) NOx photocatalytic degradation experiment system. (<b>b</b>) Schematic diagram of gas flow in the reactor.</p>
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<p>Variation of NOx and NO concentration in photocatalytic test.</p>
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<p>Flow chart of nitrate elution test.</p>
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<p>(<b>a</b>) NMR specimen preparation process. (<b>b</b>) MesoMR23-060H-I NMR tester.</p>
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<p>The mass loss rate of nano-TiO<sub>2</sub> concrete during F–T cycles.</p>
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<p>Mechanism of the effect of nano-TiO<sub>2</sub> admixture on concrete mass loss during F–T cycles.</p>
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<p>RDEM change of nano-TiO<sub>2</sub> concrete in F–T cycles.</p>
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<p>NO removal from nano-TiO<sub>2</sub> concrete for various numbers of F–T cycles.</p>
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<p>NOx removal rate of nano-TiO<sub>2</sub> concrete for various numbers of F–T cycles.</p>
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<p>Nitrogen content in nano-TiO<sub>2</sub> concrete eluent in a freeze–thaw environment.</p>
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<p>Porosity of nano-TiO<sub>2</sub> concrete at various numbers of F–T cycles.</p>
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<p>Volume fraction of different pore sizes of concrete before F–T cycles.</p>
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<p>Pore volume fraction of nano-TiO<sub>2</sub> concrete at various numbers of F–T cycles. (<b>a</b>) NC. (<b>b</b>) NT-2. (<b>c</b>) NT-4. (<b>d</b>) NT-6.</p>
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<p>Pore volume fraction of nano-TiO<sub>2</sub> concrete at various numbers of F–T cycles. (<b>a</b>) NC. (<b>b</b>) NT-2. (<b>c</b>) NT-4. (<b>d</b>) NT-6.</p>
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<p>Growth rate of volume fraction of pores larger than 100 nm after 200 F–T cycles of concrete.</p>
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<p>Evolution law of fractal dimension of pores above 100 nm during the F–T cycle of concrete.</p>
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<p>Evolution law of the macroscopic F–T damage factor of concrete during the F–T process.</p>
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<p>Evolution law of microscopic freeze–thaw damage factor of concrete during freeze–thaw process.</p>
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<p>Comparison of modeled and experimental values of concrete damage at different numbers of F–T cycles.</p>
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<p>Comparison between the modified and experimental values of concrete damage models for different numbers of F–T cycles.</p>
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<p>Comparison of F–T damage test values of some scholars with the damage prediction model values in this paper. (<b>a</b>) R0, R50, and R100. (<b>b</b>) R50P, R50T, R100P, and R100.</p>
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<p>Correlation analysis of NO removal from nano-TiO<sub>2</sub> concrete with dosage and pore structure damage influence coefficient. (<b>a</b>) NT-2. (<b>b</b>) NT-4. (<b>c</b>) NT-6.</p>
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<p>Comparison between experimental and model-predicted values of NO removal of nano-TiO<sub>2</sub> concrete.</p>
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25 pages, 19929 KiB  
Article
Coupled Elastic–Plastic Damage Modeling of Rock Based on Irreversible Thermodynamics
by Xin Jin, Yufei Ding, Keke Qiao, Jiamin Wang, Cheng Fang and Ruihan Hu
Appl. Sci. 2024, 14(23), 10923; https://doi.org/10.3390/app142310923 - 25 Nov 2024
Viewed by 481
Abstract
Shale is a common rock in oil and gas extraction, and the study of its nonlinear mechanical behavior is crucial for the development of engineering techniques such as hydraulic fracturing. This paper establishes a new coupled elastic–plastic damage model based on the second [...] Read more.
Shale is a common rock in oil and gas extraction, and the study of its nonlinear mechanical behavior is crucial for the development of engineering techniques such as hydraulic fracturing. This paper establishes a new coupled elastic–plastic damage model based on the second law of thermodynamics, the strain equivalence principle, the non-associated flow rule, and the Drucker–Prager yield criterion. This model is used to describe the mechanical behavior of shale before and after peak strength and has been implemented in ABAQUS via UMAT for numerical computation. The model comprehensively considers the quasi-brittle and anisotropic characteristics of shale, as well as the strength degradation caused by damage during both the elastic and plastic phases. A damage yield function has been established as a criterion for damage occurrence, and the constitutive integration algorithm has been derived using a regression mapping algorithm. Compared with experimental data from La Biche shale in Canada, the theoretical model accurately simulated the stress–strain curves and volumetric–axial strain curves of shale under confining pressures of 5 MPa, 25 MPa, and 50 MPa. When compared with experimental data from shale in Western Hubei and Eastern Chongqing, China, the model precisely fitted the stress–strain curves of shale at pressures of 30 MPa, 50 MPa, and 70 MPa, and at bedding angles of 0°, 22.5°, 45°, and 90°. This proves that the model can effectively predict the failure behavior of shale under different confining pressures and bedding angles. Additionally, a sensitivity analysis has been performed on parameters such as the plastic hardening rate b, damage evolution rate Bω, weighting factor r, and damage softening parameter a. This research is expected to provide theoretical support for the efficient extraction technologies of shale oil and gas. Full article
(This article belongs to the Section Civil Engineering)
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Figure 1
<p>Map of basins with assessed shale oil and shale gas formations [<a href="#B5-applsci-14-10923" class="html-bibr">5</a>].</p>
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<p>Loading direction and bedding plane angle <span class="html-italic">θ</span>.</p>
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<p>Principle of the regression mapping algorithm.</p>
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<p>Schematic of the calculation process for the elastoplastic damage coupled model.</p>
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<p>Stress–strain curves of theoretical and experimental for La Biche shale [<a href="#B18-applsci-14-10923" class="html-bibr">18</a>].</p>
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<p>Volumetric–axial strain curves of theoretical and experimental for La Biche shale [<a href="#B18-applsci-14-10923" class="html-bibr">18</a>].</p>
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<p>Location of Eastern Yunnan–Western Chongqing shale.</p>
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<p>Field sampling (modified from Zhang [<a href="#B110-applsci-14-10923" class="html-bibr">110</a>]).</p>
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<p>Samples in different bedding plane orientations.</p>
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<p>Fitting curve of <span class="html-italic">f</span>(<span class="html-italic">θ</span>) at 0 MPa confining pressure [<a href="#B110-applsci-14-10923" class="html-bibr">110</a>].</p>
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<p>Stress–strain curves of theoretical and experimental for Eastern Yunnan–Western Chongqing shale: (<b>a</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 0°; (<b>b</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 22.5°; (<b>c</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 45°; (<b>d</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 90° [<a href="#B110-applsci-14-10923" class="html-bibr">110</a>].</p>
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<p>Stress–strain curves of theoretical and experimental for Eastern Yunnan–Western Chongqing shale: (<b>a</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 0°; (<b>b</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 22.5°; (<b>c</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 45°; (<b>d</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 90° [<a href="#B110-applsci-14-10923" class="html-bibr">110</a>].</p>
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<p>Sensitivity analysis of <span class="html-italic">b</span>: (<b>a</b>) The relationship between axial strain and deviatoric stress; (<b>b</b>) The relationship between axial strain and damage variable <span class="html-italic">D</span>.</p>
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<p>Sensitivity analysis of <span class="html-italic">B<sub>ω</sub></span>: (<b>a</b>) The relationship between axial strain and deviatoric stress; (<b>b</b>) The relationship between axial strain and damage variable <span class="html-italic">D</span>.</p>
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<p>Sensitivity analysis of <span class="html-italic">r</span>: (<b>a</b>) The relationship between axial strain and deviatoric stress; (<b>b</b>) The relationship between axial strain and damage variable <span class="html-italic">D</span>.</p>
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<p>Sensitivity analysis of <span class="html-italic">a</span>: (<b>a</b>) The relationship between axial strain and deviatoric stress; (<b>b</b>) The relationship between axial strain and damage variable <span class="html-italic">D</span>.</p>
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