Mathematical Modeling of Complex Granular Systems

Topic Information

Dear Colleagues,

Granular materials are ubiquitous in natural and engineering systems, and the physics and mechanics of them are crucial for understanding some aspects of geophysical flows, natural hazards (such as landslides and pyroclastic flows), food processing, chemical engineering, and pharmaceutical engineering. Granular materials can behave like a solid, a liquid, or a gas in different circumstances, which increases the difficulty in capturing their macroscopic behavior. Above all, granular materials are athermal, dissipative, and non-equilibrium. The thermal, mechanical behavior of granular assemblies and the phase transition when the system is subjected to different loading conditions, such as vibration, shaking, or shearing, bring huge difficulties in describing the general behavior of such a system. Additionally, there is still a long way to go to link the behavior of relatively simple mono- or bi- dispersed granular systems with regular particle shapes to the behavior of real natural or engineering system, such as different geomaterials, concrete, powders, etc., and to provide a proper mathematical model for simulating the macroscopic behavior of complex granular systems. This multidisciplinary topic presents a platform where academic and industry researchers can present methodologies, techniques, applications, experiments, and theoretical derivations that aim to increase our understanding of complex granular systems and their emergent behaviors, such as granular rheology, self-organizing criticality, granular segregation and percolation theory, and help link the behavior of granular system to more complex geomaterials. The focus of this Topic is both on modelling and simulation techniques but also on their practical application on various scenarios, and as such papers are welcome on a variety of topics including modelling, simulation, analysis, experimentation, and specific properties as defined above. Papers submitted on new and emerging topics within the general discipline are also encouraged.

Best regards,

Prof. Dr. Herbert Huppert
Dr. Teng Man
Dr. Xudong Zhang
Dr. Yiding Bao
Topic Editors

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Symmetry symmetry	2.2	5.4	2009	16.8 Days	CHF 2400	Submit
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17 pages, 4703 KiB  

Open AccessArticle

The Role of a New Stabilizer in Enhancing the Mechanical Performance of Construction Residue Soils

by Xin Chen, Jing Yu, Feng Yu, Jingjing Pan and Shuaikang Li

Materials 2024, 17(17), 4293; https://doi.org/10.3390/ma17174293 - 30 Aug 2024

Viewed by 466

Abstract

Urban construction generates significant amounts of construction residue soil. This paper introduces a novel soil stabilizer based on industrial waste to improve its utilization. This stabilizer is primarily composed of blast furnace slag (BFS), steel slag (SS), phosphogypsum (PG), and other additives, which [...] Read more.

Urban construction generates significant amounts of construction residue soil. This paper introduces a novel soil stabilizer based on industrial waste to improve its utilization. This stabilizer is primarily composed of blast furnace slag (BFS), steel slag (SS), phosphogypsum (PG), and other additives, which enhance soil strength through physical and chemical processes. This study investigated the mechanical properties of construction residue soil cured with this stabilizer, focusing on the effects of organic matter content (O_o), stabilizer dosage (O_c), and curing age (T) on unconfined compressive strength (UCS). Additionally, water stability and wet–dry cycle tests of the stabilized soil were conducted to assess long-term performance. According to the findings, the UCS increased with the higher stabilizer dosage and longer curing periods but reduced with the higher organic matter content. A stabilizer content of 15–20% is recommended for optimal stabilization efficacy and cost-efficiency in engineering applications. The samples lost their strength when immersed in water. However, adding more stabilizers to the soil can effectively enhance its water stability. Under wet–dry cycle conditions, the UCS initially increased and then decreased, remaining lower than that of samples cured under standard conditions. The findings can provide valuable data for the practical application in construction residual soil stabilization. Full article

(This article belongs to the Topic Mathematical Modeling of Complex Granular Systems)

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Figure 1

Figure 1
<p>The particle size distribution curve of the soil sample and the raw materials of the stabilizer.</p> Full article ">Figure 2
<p>The compaction curve of the soil sample.</p> Full article ">Figure 3
<p>The mineral phase of tested soil.</p> Full article ">Figure 4
<p>The methods of this study.</p> Full article ">Figure 5
<p>The relationship between the UCS of stabilized soil and the dosage of the stabilizer: (<b>a</b>) <span class="html-italic">T</span> = 7 d; (<b>b</b>) <span class="html-italic">T</span> = 14 d; (<b>c</b>) <span class="html-italic">T</span> = 21 d; (<b>d</b>) <span class="html-italic">T</span> = 28 d.</p> Full article ">Figure 6
<p>The variation in strength performance of stabilized soil with different organic matter contents: (<b>a</b>) <span class="html-italic">T</span> = 7 d; (<b>b</b>) <span class="html-italic">T</span> = 14 d; (<b>c</b>) <span class="html-italic">T</span> = 21 d; (<b>d</b>) <span class="html-italic">T</span> = 28 d.</p> Full article ">Figure 7
<p>The relationship between the UCS of stabilized soil and the dosage of the stabilizer: (<b>a</b>) <span class="html-italic">O</span>_c = 15%; (<b>b</b>) <span class="html-italic">O</span>_c = 20%; (<b>c</b>) <span class="html-italic">O</span>_c = 25%; (<b>d</b>) <span class="html-italic">O</span>_c = 30%.</p> Full article ">Figure 8
<p>The variation of UCS of stabilized soil with immersion time: (<b>a</b>) <span class="html-italic">O</span>_c = 20%; (<b>b</b>) <span class="html-italic">O</span>_c = 30%.</p> Full article ">Figure 9
<p>The strength residual coefficients of the new stabilized soil at different immersion periods.</p> Full article ">Figure 10
<p>The UCS of the new stabilized soil varied with the wet–dry cycle numbers: (<b>a</b>) <span class="html-italic">O</span>_c = 20%; (<b>b</b>) <span class="html-italic">O</span>_c = 30%.</p> Full article ">Figure 11
<p>The residual coefficients of stabilized soil under wet–dry cycling conditions.</p> Full article ">Figure 12
<p>The cumulative mass loss rate varies with the cycle numbers.</p> Full article ">

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27 pages, 14368 KiB  

Open AccessArticle

Parametric Modelling of the Crystalline Microstructure of the MCM41-Type Mesoporous Silica Modified with Derivatives of Alkyls

by Jarosław Stocki, Marcin Kuśmierz, Weronika Sofińska-Chmiel, Marek Stankevič, Marcin Puchała, Marek A. Kojdecki, Robert Gąska and Henryk Grajek

Materials 2024, 17(13), 3065; https://doi.org/10.3390/ma17133065 - 21 Jun 2024

Viewed by 555

Abstract

A siliceous material in which a framework order was established with a surfactant with sixteen carbon atoms in alkyl chains, MCM-41-C16, was synthesised, surface-modified, and tested regarding the selected physical properties. The pristine material was extracted in an acidic aqueous alcohol and then [...] Read more.

A siliceous material in which a framework order was established with a surfactant with sixteen carbon atoms in alkyl chains, MCM-41-C16, was synthesised, surface-modified, and tested regarding the selected physical properties. The pristine material was extracted in an acidic aqueous alcohol and then lined with different surface groups. The properties of four adsorbents were investigated using XRD, X-ray photoelectron spectroscopy, and N2 physisorption techniques. The unit–cell constant was determined from X-ray diffractograms, being in fixed relation to the edge length of the hexagonal frame. The specific surface areas of mesopores and whole crystallites were determined from low-temperature N2-physisorption isotherms. The novelty of this work is a mathematical model of a crystalline microstructure explaining the sizes and shapes of crystalline grains in relation to adsorption features, proposed and successfully tested with the aforementioned experimental data. The roughness of the surface is different from one that is necessary to explain the experimental characteristics quantitatively. Full article

(This article belongs to the Topic Mathematical Modeling of Complex Granular Systems)

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Figure 1

Figure 1
<p>Methods of synthesis and modifications of the surface of the MCM-41.</p> Full article ">Figure 2
<p>The N₂-physisorption isotherms on the tested MCM-41.</p> Full article ">Figure 3
<p>(<b>A</b>). The <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="sans-serif">α</mi> </mrow> <mrow> <mi mathvariant="normal">S</mi> </mrow> </msub> </mrow> </semantics></math>-plots, computed with respect to the sstandardisedsilica Nucleosil 1000. The plots for the pristine samples of MCM-41-SH, MCM-41-NH₂, MCM-41 are shifted by 100, 150, and 200 STP cm³ g⁻¹, respectively. (<b>B</b>). The <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="sans-serif">α</mi> </mrow> <mrow> <mi mathvariant="normal">S</mi> </mrow> </msub> </mrow> </semantics></math>-plots, computed with respect to the sstandardisedsilica LiChrospher Si-1000. The plots for the pristine samples of MCM-41-SH, MCM-41-NH₂ are shifted by 100, 150, and 200 STP cm³ g⁻¹, respectively. (<b>C</b>). The <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="sans-serif">α</mi> </mrow> <mrow> <mi mathvariant="normal">S</mi> </mrow> </msub> </mrow> </semantics></math>-plots, computed with respect to the standardised silica Fransil-I. The plots for the pristine samples of MCM-41-SH, MCM-41-NH₂ are shifted by 100, 150, and 200 STP cm³ g⁻¹, respectively.</p> Full article ">Figure 3 Cont.
<p>(<b>A</b>). The <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="sans-serif">α</mi> </mrow> <mrow> <mi mathvariant="normal">S</mi> </mrow> </msub> </mrow> </semantics></math>-plots, computed with respect to the sstandardisedsilica Nucleosil 1000. The plots for the pristine samples of MCM-41-SH, MCM-41-NH₂, MCM-41 are shifted by 100, 150, and 200 STP cm³ g⁻¹, respectively. (<b>B</b>). The <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="sans-serif">α</mi> </mrow> <mrow> <mi mathvariant="normal">S</mi> </mrow> </msub> </mrow> </semantics></math>-plots, computed with respect to the sstandardisedsilica LiChrospher Si-1000. The plots for the pristine samples of MCM-41-SH, MCM-41-NH₂ are shifted by 100, 150, and 200 STP cm³ g⁻¹, respectively. (<b>C</b>). The <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="sans-serif">α</mi> </mrow> <mrow> <mi mathvariant="normal">S</mi> </mrow> </msub> </mrow> </semantics></math>-plots, computed with respect to the standardised silica Fransil-I. The plots for the pristine samples of MCM-41-SH, MCM-41-NH₂ are shifted by 100, 150, and 200 STP cm³ g⁻¹, respectively.</p> Full article ">Figure 4
<p>The XPS survey spectra of MCM-41: pristine and lined with organised monolayers of functional molecules: MCM-41, MCM-41-SH, MCM-41-NH₂, and MCM-41-C₃H₇, respectively.</p> Full article ">Figure 5
<p>The XPS high-resolution O1s, Si2p, and C1s spectra of pristine MCM-41 and lined with organized monolayers of functional molecules. Details are given in <a href="#app1-materials-17-03065" class="html-app">(Supplementary Materials) Figures S5–S7</a>.</p> Full article ">Figure 6
<p>(<b>A</b>) Pristine MCM-41, and (<b>B</b>–<b>D</b>) MCM-41 silica lined with organised monolayers of functional molecules covalently bound to the mesoporous support—XRD diffraction patterns.</p> Full article ">Figure 7
<p>Smoothed background-corrected XRD diffraction patterns (<math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.15406</mn> <mo> </mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>) from (<b>A</b>) pristine MCM-41 silica and MCM-41 silica lined with organised monolayers of functional molecules (<b>B</b>) (-C₃H₆-NH₂), (<b>C</b>) (-C₃H₆-SH), (<b>D</b>) (-C₃H₆-C₃H₇) covalently bound to the mesoporous support, depicting marked peak maxima (for reflections 100, 110, 200, 210, 300, 220).</p> Full article ">Figure 8
<p>(<b>A</b>) Definition of mean crystallite: base (or cross-section) of a single silica crystallite, assumed to be a monocrystalline grain of the shape of a prism comprising rings of hexagonal nanotubes unified into a honeycomb structure around the central tube (two differently coloured rings are shown, and four vicinal unit cells are sketched), covered with an amorphous layer (white). (<b>B</b>) Basic parameters of crystallite base for one-ring crystallite with silica shell walls (grey) lined with another amorphous material (white).</p> Full article ">Figure 8 Cont.
<p>(<b>A</b>) Definition of mean crystallite: base (or cross-section) of a single silica crystallite, assumed to be a monocrystalline grain of the shape of a prism comprising rings of hexagonal nanotubes unified into a honeycomb structure around the central tube (two differently coloured rings are shown, and four vicinal unit cells are sketched), covered with an amorphous layer (white). (<b>B</b>) Basic parameters of crystallite base for one-ring crystallite with silica shell walls (grey) lined with another amorphous material (white).</p> Full article ">Figure 9
<p>(<b>A</b>) Diagrammatic representation of the suggested arrangement of the silica surface lined with organised monolayers of functional molecules (-C₃H₆-C₃H₇) covalently bound to the mesoporous siliceous support, resulting in a ‘upright posture’ for our surface-functionalized organosilanes [<a href="#B74-materials-17-03065" class="html-bibr">74</a>,<a href="#B75-materials-17-03065" class="html-bibr">75</a>,<a href="#B76-materials-17-03065" class="html-bibr">76</a>]. (<b>B</b>) Diagrammatic representation of the suggested arrangement of the silica surface lined with organised monolayers of functional molecules (-C₃H₆-NH₂) covalently bound to the mesoporous siliceous support, which would result in a ‘bent over posture’ for our surface-functionalized organosilanes [<a href="#B74-materials-17-03065" class="html-bibr">74</a>,<a href="#B75-materials-17-03065" class="html-bibr">75</a>,<a href="#B76-materials-17-03065" class="html-bibr">76</a>]. (<b>C</b>) Diagrammatic representation of the suggested arrangement of the silica surface lined with organised monolayers of functional molecules (-C₃H₆-SH) covalently bound to the mesoporous siliceous support, resulting in a ‘bent posture’ for our surface-functionalized organosilanes [<a href="#B74-materials-17-03065" class="html-bibr">74</a>,<a href="#B75-materials-17-03065" class="html-bibr">75</a>,<a href="#B76-materials-17-03065" class="html-bibr">76</a>].</p> Full article ">

15 pages, 1712 KiB  

Open AccessArticle

Mathematical Modeling of Pavement Gyratory Compaction: A Perspective on Granular-Fluid Assemblies

by Teng Man

Mathematics 2023, 11(9), 2096; https://doi.org/10.3390/math11092096 - 28 Apr 2023

Viewed by 1457

Abstract

The compaction of asphalt mixture is crucial to the performance of the pavement. However, the mix design (i.e., porosity, aggregate size distribution, binder content), which is based on compaction results, remains largely empirical. It is difficult to relate the aggregate size distribution and [...] Read more.

The compaction of asphalt mixture is crucial to the performance of the pavement. However, the mix design (i.e., porosity, aggregate size distribution, binder content), which is based on compaction results, remains largely empirical. It is difficult to relate the aggregate size distribution and the asphalt binder properties to the compaction curve in both the field and laboratory compaction of asphalt mixtures. In this paper, the author proposes a simple mathematical model from the perspective of granular physics to predict the compaction of asphalt mixtures. In this model, the compaction process is divided into two mechanisms: (i) viscoplastic deformation of an ordered granular-fluid assembly, and (ii) the transition from an ordered system to a disordered system due to particle rearrangement. This model could take into account both the viscous properties of the asphalt binder and the grain size distributions of the aggregates, where the viscous deformation is calculated with a proposed governing equation and the particle rearrangement effect is solved using simple DEM simulations. This model is calibrated based on the Superpave gyratory compaction tests in the pavement lab, and the R-squares of model predictions are all above 0.95. The model results are compared with experimental data to show that it can provide good predictions for the experiments, suggesting its potential for enhancing the design of asphalt mixtures. Full article

(This article belongs to the Topic Mathematical Modeling of Complex Granular Systems)
(This article belongs to the Section Engineering Mathematics)

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Figure 1

Figure 1
<p>Sketch of the Brovold Superpave gyratory compactor.</p> Full article ">Figure 2
<p>Sketch of the compaction process using the Brovold Superpave gyratory compactor.</p> Full article ">Figure 3
<p>Two parts of the deformation during the compaction of asphalt mixtures: (1) viscous deformation; (2) particle rearrangement.</p> Full article ">Figure 4
<p>Simplification of the viscous deformation induced by the FAM coatings on the surfaces of coarse aggregates.</p> Full article ">Figure 5
<p>Computational cell for calculating the change of volume fraction due to the viscous deformation of the FAM coatings, based on which we can form the differential equation for calculating the motion of particles so that we could also calculate the volume fraction versus time.</p> Full article ">Figure 6
<p>Comparison of the volume fraction/gyration number relationship as we change the thickness of the FAM coating.</p> Full article ">Figure 7
<p>Relationship between the solid fraction of particle rearrangement and the dimensionless time, <math display="inline"><semantics> <msup> <mi>t</mi> <mo>*</mo> </msup> </semantics></math>.</p> Full article ">Figure 8
<p>Grain size distribution of aggregates.</p> Full article ">Figure 9
<p>Comparison between experimental results and the results obtained from the proposed mathematical model: (<b>a</b>) results for 1N30, 1N50, and 1N100; (<b>b</b>) results for 2N30, 2N50, and 2N100.</p> Full article ">Figure 10
<p>The relationship between <math display="inline"><semantics> <msub> <mi>τ</mi> <mrow> <mi>r</mi> <mi>p</mi> </mrow> </msub> </semantics></math> and the median radius <math display="inline"><semantics> <msub> <mi>r</mi> <mn>50</mn> </msub> </semantics></math>.</p> Full article ">Figure 11
<p>Results of model validations.</p> Full article ">Figure 12
<p>Flowchart of the mathematical model for the gyratory compaction of asphalt mixtures.</p> Full article ">

22 pages, 5813 KiB  

Open AccessArticle

The Study on Mathematical Simulation and Analysis of the Molecular Discrete System of the Sulfurated Eucommia Ulmoides Gum

by Simeng Yan, Naisheng Guo, Xin Jin, Zhaoyang Chu and Sitong Yan

Mathematics 2023, 11(4), 964; https://doi.org/10.3390/math11040964 - 13 Feb 2023

Cited by 2 | Viewed by 1203

Abstract

In recent years, sulfurized eucommia ulmoides gum (SEUG) has been used and developed in many fields due to its good properties. The cross-linking degree is crucial to the performance of SEUG. In order to explore the effect of the cross-linking degree on SEUG [...] Read more.

In recent years, sulfurized eucommia ulmoides gum (SEUG) has been used and developed in many fields due to its good properties. The cross-linking degree is crucial to the performance of SEUG. In order to explore the effect of the cross-linking degree on SEUG in depth, this paper combines macroscopic and microscopic techniques, and molecular discrete system models of EUG and SEUG with different cross-linking degrees are calculated by molecular dynamics simulation, and the density and solubility parameters of EUG, glass transition temperature, radial distribution function and mechanical property parameters of SEUG are derived. The results show that (1) the suitable minimum degree of polymerization of EUG is N = 30; (2) the degree of cross-linking has a significant effect on the intramolecular radial distribution of SEUG, but it has a small effect on the intermolecular radial distribution of SEUG; (3) the degree of cross-linking of SEUG should be controlled to be between 40% and 80% because the mechanical properties of SEUG, namely the bulk modulus, shear modulus, elastic modulus, Poisson’s ratio, Corsi pressure, are the best ones. Therefore, the conclusions of this study provide a theoretical basis for engineering practices. Full article

(This article belongs to the Topic Mathematical Modeling of Complex Granular Systems)
(This article belongs to the Section Engineering Mathematics)

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Figure 1

Figure 1
<p>Macromolecular structures of NR and EUG. (<b>a</b>) The chemical structure of NR; (<b>b</b>) the chemical structure of EUG.</p> Full article ">Figure 2
<p>Schematic diagram of periodic boundary conditions. (<b>a</b>) In the three-dimensional example, molecules can freely traverse the faces of each multidimensional data set; (<b>b</b>) Intermolecular forces adopt the nearest mirror method.</p> Full article ">Figure 3
<p>The flow chart of MD simulation method.</p> Full article ">Figure 4
<p>Molecular structure fluxes of EUG.</p> Full article ">Figure 5
<p>Geometrically optimized EUG model.</p> Full article ">Figure 6
<p>Single chain molecular structure of EUG.</p> Full article ">Figure 7
<p>MS models of EUG with different polymerization degrees. (<b>a</b>) EUG model with aggregation degree of 5; (<b>b</b>) EUG model with aggregation degree of 10; (<b>c</b>) EUG model with aggregation degree of 15; (<b>d</b>) EUG model with aggregation degree of 20; (<b>e</b>) EUG model with aggregation degree of 25; (<b>f</b>) EUG model with aggregation degree of 30; (<b>g</b>) EUG model with aggregation degree of 35; (<b>h</b>) EUG model with aggregation degree of 40; (<b>i</b>) EUG model with aggregation degree of 45; (<b>j</b>) EUG model with aggregation degree of 50.</p> Full article ">Figure 7 Cont.
<p>MS models of EUG with different polymerization degrees. (<b>a</b>) EUG model with aggregation degree of 5; (<b>b</b>) EUG model with aggregation degree of 10; (<b>c</b>) EUG model with aggregation degree of 15; (<b>d</b>) EUG model with aggregation degree of 20; (<b>e</b>) EUG model with aggregation degree of 25; (<b>f</b>) EUG model with aggregation degree of 30; (<b>g</b>) EUG model with aggregation degree of 35; (<b>h</b>) EUG model with aggregation degree of 40; (<b>i</b>) EUG model with aggregation degree of 45; (<b>j</b>) EUG model with aggregation degree of 50.</p> Full article ">Figure 8
<p>Density of EUG models with different degrees of aggregation.</p> Full article ">Figure 9
<p>MD simulated and experienced values of solubility parameters for different degrees of polymerization of EUG.</p> Full article ">Figure 10
<p>Vulcanized dulcimer chains with different cross-linking degrees. (<b>a</b>) SEUG molecular chain model with 0% cross-linking degree; (<b>b</b>) SEUG molecular chain model with 20% cross-linking degree; (<b>c</b>) SEUG molecular chain model with 40% cross-linking degree; (<b>d</b>) SEUG molecular chain model with 60% cross-linking degree; (<b>e</b>) SEUG molecular chain model with 80% cross-linking degree; (<b>f</b>) SEUG molecular chain model with 100% cross-linking degree.</p> Full article ">Figure 11
<p>SEUG discrete system consisting of 100 SEUG monomers cross-linked with C-S-S-C bonds (<span class="html-italic">DC</span> = 20%).</p> Full article ">Figure 12
<p>Specific volume versus temperature for each system model.</p> Full article ">Figure 13
<p><span class="html-italic">T</span>_g of SEUG with different degrees of cross-linking.</p> Full article ">Figure 14
<p>Diagram of particle radial distribution function.</p> Full article ">Figure 15
<p>Intramolecular radial distribution functions of SEUG with different degrees of cross-linking.</p> Full article ">Figure 16
<p>Intermolecular radial distribution functions of SEUG with different degrees of cross-linking.</p> Full article ">Figure 17
<p>Relationship between cross-linking degree and mechanical parameters: (<b>a</b>) relationship between cross-linking degree and bulk modulus; (<b>b</b>) relationship between cross-linking degree and shear modulus; (<b>c</b>) relationship between cross-linking degree and elastic modulus; (<b>d</b>) relationship between cross-linking degree and Poisson ratio; (<b>e</b>) relationship between cross-linking degree and <b><span class="html-italic">C</span>₁₂-<span class="html-italic">C</span>₄₄</b>; (<b>f</b>) relationship between cross-linking degree and <span class="html-italic">K</span>/<span class="html-italic">G</span>.</p> Full article ">Figure 18
<p>The relationship between the content of S and tensile strength.</p> Full article ">Figure 19
<p>Relationship between the content of S and cross-link density.</p> Full article ">

25 pages, 9540 KiB  

Open AccessArticle

Analysis of Formation Mechanism of Slightly Inclined Bedding Mudstone Landslide in Coal Mining Subsidence Area Based on Finite–Discrete Element Method

by Jiaxin Zhong, Zhengjun Mao, Wankui Ni, Jia Zhang, Gaoyang Liu, Jinge Zhang and Mimi Geng

Mathematics 2022, 10(21), 3995; https://doi.org/10.3390/math10213995 - 27 Oct 2022

Cited by 3 | Viewed by 1679

Abstract

In this paper, the formation mechanism of a slightly inclined bedding mudstone landslide in the overlying mountain of the coal mining subsidence area of the Tanshan Coal Mine in Ningxia, China, is studied. By means of geotechnical investigation, indoor geotechnical tests, theoretical analysis [...] Read more.

In this paper, the formation mechanism of a slightly inclined bedding mudstone landslide in the overlying mountain of the coal mining subsidence area of the Tanshan Coal Mine in Ningxia, China, is studied. By means of geotechnical investigation, indoor geotechnical tests, theoretical analysis and other technical means, we find the geological environment background of the study area and obtain the physical and mechanical property indexes of the mining landslide in the Tanshan Coal Mine. By combining the numerical simulation of discrete elements and finite elements, the macro deformation and failure law of the mining mudstone landslide and the displacement and stress nephogram of the failure process are discussed. The results show that the slightly inclined bedding mudstone landslide in the Tanshan Coal Mine is 850 m long from east to west, 500 m wide from north to south and 10,875,000 m³ in volume. It is composed of Jurassic mudstone and is a traction landslide caused by the coal mining subsidence area. The formation of the landslide is affected by internal factors and inducing factors. The internal factors are mainly geotechnical types and engineering geological properties, and the inducing factors are mainly coal mining activities and rainfall. By analyzing and summarizing the calculation process of the slope model prior to the landslide in 2D-Block and GeoStudio numerical simulation software, the sliding process of the slightly inclined bedding mudstone landslide in the Tanshan Coal Mine is divided into four stages: slope creep, slope deformation, landslide movement and landslide accumulation. GeoStudio software is used to calculate the stability of the Tanshan Coal Mine landslide under natural and rainfall conditions. The landslide is in a stable state under natural conditions and is basically stable under rainfall conditions. By comparing the calculation results of the limit equilibrium method and the finite element limit equilibrium method, we find that the calculated stability coefficient is more accurate when the appropriate constitutive model is selected. The research results have important reference significance for the prevention and control of the gently inclined bedding mudstone landslide of the overlying mountain in the coal mining subsidence area of the Loess Plateau. Full article

(This article belongs to the Topic Mathematical Modeling of Complex Granular Systems)
(This article belongs to the Section Engineering Mathematics)

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Figure 1

Figure 1
<p>The shape of landslide in the Tanshan Coal Mine.</p> Full article ">Figure 2
<p>Geological map and section of landslide in coal mining subsidence area of Tanshan, China.</p> Full article ">Figure 3
<p>Discrete element model of the slope before the landslide in the Tanshan Coal Mine.</p> Full article ">Figure 4
<p>Finite element calculation model of slope before landslide and after mining in the Tanshan Coal Mine.</p> Full article ">Figure 5
<p>Numerical simulation results under the coal mining subsidence area.</p> Full article ">Figure 6
<p>Iterative 10,000-step numerical simulation results.</p> Full article ">Figure 7
<p>Iterative 200,000-step numerical simulation results.</p> Full article ">Figure 8
<p>Iterative 300,000-step numerical simulation results.</p> Full article ">Figure 9
<p>Iterative 607,693-step numerical simulation results.</p> Full article ">Figure 10
<p>Displacement vector of slope before sliding.</p> Full article ">Figure 11
<p>Displacement contour map of the slope in the X-direction before sliding.</p> Full article ">Figure 12
<p>Y-direction displacement contour map of slope before sliding.</p> Full article ">Figure 13
<p>The contour map of major principal stress after mining.</p> Full article ">Figure 14
<p>Local stability coefficient of landslide.</p> Full article ">

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