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<journal-id journal-id-type="publisher-id">Front. Earth Sci.</journal-id>
<journal-title>Frontiers in Earth Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Earth Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-6463</issn>
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<publisher-name>Frontiers Media S.A.</publisher-name>
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<article-id pub-id-type="publisher-id">1595035</article-id>
<article-id pub-id-type="doi">10.3389/feart.2025.1595035</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Earth Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Innovative application of optical fiber sensing technology for monitoring stope support pressure distribution in similar model tests</article-title>
<alt-title alt-title-type="left-running-head">Li et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/feart.2025.1595035">10.3389/feart.2025.1595035</ext-link>
</alt-title>
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<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Li</surname>
<given-names>Chao</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
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<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Jialin</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
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<contrib contrib-type="author">
<name>
<surname>Chen</surname>
<given-names>Yu</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
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<contrib contrib-type="author">
<name>
<surname>Hou</surname>
<given-names>Yabin</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
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<contrib contrib-type="author">
<name>
<surname>Shi</surname>
<given-names>Yong</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
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<xref ref-type="aff" rid="aff2">
<sup>2</sup>
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<contrib contrib-type="author">
<name>
<surname>Qu</surname>
<given-names>Yinghao</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
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<xref ref-type="aff" rid="aff2">
<sup>2</sup>
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<contrib contrib-type="author" corresp="yes">
<name>
<surname>Yuan</surname>
<given-names>Qiang</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
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<contrib contrib-type="author" corresp="yes">
<name>
<surname>Zhang</surname>
<given-names>Mingtian</given-names>
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<sup>3</sup>
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<aff id="aff1">
<sup>1</sup>
<institution>Chongqing Institute of Surveying and Mapping Science and Technology</institution>, <addr-line>Chongqing</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Technology innovation Center for Spatio-temporal Information and Equipment of Intelligent City, Ministry of Natural Resources</institution>, <addr-line>Chongqing</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>State Key Laboratory of Coal Mine Disaster Dynamics and Control, National Innovation Center for Industry-Education Integration of Energy Storage Technology, School of Resources and Safety Engineering, Chongqing University</institution>, <addr-line>Chongqing</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1639649/overview">Xin Yin</ext-link>, City University of Hong Kong, Hong Kong SAR, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1354881/overview">Zhanping Song</ext-link>, Xi&#x2019;an University of Architecture and Technology, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1487269/overview">Shaoke Feng</ext-link>, SINOPEC, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Qiang Yuan, <email>qiangyuan@cqu.edu.cn</email>; Mingtian Zhang, <email>cokexiaotian@126.com</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>29</day>
<month>08</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>13</volume>
<elocation-id>1595035</elocation-id>
<history>
<date date-type="received">
<day>17</day>
<month>03</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>05</day>
<month>08</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2025 Li, Zhang, Chen, Hou, Shi, Qu, Yuan and Zhang.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Li, Zhang, Chen, Hou, Shi, Qu, Yuan and Zhang</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>In order to explore the support pressure distribution law in the coal and rock mass around the stope and rock masses under an extremely thick conglomerate layer and evaluate the feasibility of different monitoring techniques, the study established the geometric size of a similar physical model as 3.6 m (length) &#xd7; 2.0 m (width) &#xd7; 2.0 m (height) in the laboratory. The test used pulse pre-pumped Brillouin optical time domain analysis (PPP-BOTDA) and pressure sensor technology to monitor distribution law. We placed pressure sensors and sensing elements at the bottom plate of the model to simulate the support pressure distribution around the stope under the thick conglomerate layer. And used theoretical calculations and numerical simulations to conduct comparative analysis. The test results showed that the distributed optical fiber support pressure test system can be used to characterize the variation law of support pressure in the model test. Compared with the pressure sensor, it had a good corresponding relationship. Both of them were basically consistent with the theoretical calculation results and simulation. The optical fiber test had the advantages of high precision and strong anti-interference ability, which were not available in the electric sensor. It provided a new idea for the support pressure test of the model experiment.</p>
</abstract>
<kwd-group>
<kwd>thick conglomerate layer</kwd>
<kwd>similar physical modeling</kwd>
<kwd>stope support pressure</kwd>
<kwd>fiber optic sensing</kwd>
<kwd>pressure sensor</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Geohazards and Georisks</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Coal had long served as the core pillar of China&#x2019;s energy structure (<xref ref-type="fig" rid="F1">Figure 1</xref>). It would continue to play a key role in economic growth for the foreseeable future (<xref ref-type="bibr" rid="B27">Yuan et al., 2013</xref>). While the advancement of energy transformation and carbon neutralization processes was reshaping the energy landscape, coal remains irreplaceable in China&#x2019;s energy consumption mix in the short term. Nevertheless, this reliance on coal poses significant environmental challenges, with mining operations causing substantial surface ecosystem damage and combustion processes releasing massive amounts of greenhouse gases, particularly carbon dioxide (<xref ref-type="bibr" rid="B14">Jing et al., 2025</xref>). And proportion was dominant in the energy structure. As shown in <xref ref-type="fig" rid="F1">Figure 1</xref>, the use of coal decreased from 2010 to 2022, but its overall share occupied a high level. This indicated that in the process of energy structure optimization and diversification, coal played an important role in China&#x2019;s economic development. However, with the increase of coal mining depth, the stability of deep surrounding rock had gradually emerged. It became a key factor restricting mine production safely and efficiently in areas with significant tectonic stress. While the stress level increased, the support became more difficult accordingly. It can lead to the increasingly prominent support problem in the mine operation. Therefore, it was necessary to continuously optimize the support design and strengthen the mine management to deal with the instability of deep surrounding rock.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>China&#x2019;s energy consumption priorities and priorities from 2010 to 2022. Note: The data was in China statistical yearbook (2010&#x2013;2022).</p>
</caption>
<graphic xlink:href="feart-13-1595035-g001.tif">
<alt-text content-type="machine-generated">Two charts show energy proportions from 2010 to 2022. The left is a stacked bar chart with four categories: coal, oil, natural gas, and primary power. Coal is the largest portion. The right is a bar chart with a decreasing trend in coal use from 69.2% in 2010 to 56.2% in 2022.</alt-text>
</graphic>
</fig>
<p>Domestic and foreign scholars had carried out a lot of research on the stability of surrounding rock and rock control. <xref ref-type="bibr" rid="B29">Zhang et al. (2024)</xref> used Comsol Multiphysics to simulate and analyze the influence of the layout, burial depth and temperature of the underground liquified natural gas (LNG) storage on the stability of the surrounding rock of the storage. Through theoretical analysis, similar material model tests, numerical simulation, field measurement and intelligent prediction, <xref ref-type="bibr" rid="B12">Hongwen et al. (2020)</xref>. Studied the stability of the surrounding loose rock circle in deep roadway and the corresponding support technology. <xref ref-type="bibr" rid="B26">Yuan et al. (2011)</xref> discussed the stability of surrounding rock of deep rock roadways in Huainan mining area under the condition of &#x201c;three high&#x201d; by means of laboratory test, numerical simulation and theory, and put forward the classification standard of surrounding rock and the corresponding stability control technology. <xref ref-type="bibr" rid="B18">Wang S. et al. (2024)</xref> proposed an innovative excavation method of &#x201c;excavation-filling-retaining&#x201d;, and applied it to the stability of surrounding rock in large-section roadway excavation. <xref ref-type="bibr" rid="B23">Xiao et al. (2014)</xref> analyzed the distribution law of surrounding rock displacement, stress and plastic zone by means of numerical simulation, and revealed the failure mechanism of coal roadway deformation in deep structural areas. <xref ref-type="bibr" rid="B19">Wang F. et al. (2024)</xref> applied the shear slider theory to explore the deformation mechanism of coal pillars under mining disturbance. <xref ref-type="bibr" rid="B21">Wu et al. (2019)</xref> explored the initiation, expansion and failure of cracks during the formation of coal pillars on the goaf side, and simulated the failure deformation and fracture distribution in the coal pillars. <xref ref-type="bibr" rid="B9">Frith and Reed (2019)</xref> analyzed the accident cases in the past 50 years and pointed out that the application of the empirical design method to the design of coal pillars under different conditions would lead to the instability of coal pillars. <xref ref-type="bibr" rid="B22">Wu et al. (2024)</xref> used a combination of theoretical analysis, numerical simulation and field tests to qualitatively analyze the failure characteristics of narrow coal pillars and the evolution law of damage degree, instability mechanism and size effect. <xref ref-type="bibr" rid="B24">Xie et al. (2019)</xref> used the borehole image method taken by the digital panoramic borehole camera to measure the surrounding rock cracks, and proposed a simple and fast support system. <xref ref-type="bibr" rid="B16">Shen (2014)</xref> found out that the main cause of roadway instability was the high-level stress and low strength of coal and surrounding rock strata, and put forward a new design method of roadway support. <xref ref-type="bibr" rid="B17">Tian et al. (2021)</xref> used field investigations, geological boreholes, numerical simulations, and so on to study the deformation characteristics of the Xiamaixi tunnel and slope. <xref ref-type="bibr" rid="B20">Wang H. Z. et al. (2024)</xref> used field monitoring and numerical simulations to investigate the formation pressure and deformation evolution. The above scholars&#x2019; research methods on the stability of surrounding rock mainly include numerical simulation, theoretical analysis and field tests. In addition, some scholars have studied the mine pressure and strata control after coal seam mining by combining optical fiber technology with a similar model test. For example, <xref ref-type="bibr" rid="B6">Du et al. (2021a)</xref> used optical fiber sensing technology and a physical similarity test model to explore the deformation law and internal stress evolution characteristics of overlying strata after coal seam mining. <xref ref-type="bibr" rid="B3">Chai et al. (2018)</xref> used the method of combining distributed optical fiber sensing technology with three-dimensional tests to explore the deformation and failure law of overlying strata in coal mines by analyzing the relationship between the Brillouin frequency shift value of the sensing fiber in the working face and the deformation and fracture of the overlying strata. <xref ref-type="bibr" rid="B11">Hao et al. (2024)</xref> studied the influence of non-uniform strain distribution on the measurement accuracy in the process of coal pillar deformation by using distributed optical fiber technology combined with FEM-DEM coupling numerical simulation, and verified the feasibility of the method through an indoor model test. Application of optical fiber sensing technology in a similar model test of shallow thick coal seam mining. <xref ref-type="bibr" rid="B30">Zhu et al. (2021)</xref> used Brillouin optical time-domain analysis (BOTDA) technology to carry out a physical similarity model test, analyzed the deformation and damage state of overlying strata above goaf, and deduced the partition interaction relationship of the optical monitoring strain curve. <xref ref-type="bibr" rid="B2">Chai et al. (2011)</xref> monitored the deformation of uncompacted strata by the optical fiber and physical model test. Based on distributed optical fiber and information entropy theory, <xref ref-type="bibr" rid="B5">Chai et al. (2023)</xref> analyzed the dynamic evolution law of mining overburden separation and water seepage fracture based on similar experiments. <xref ref-type="bibr" rid="B4">Chai et al. (2022)</xref> analyzed the mechanical properties and strain response of rock strata in elastic deformation and elastoplastic stage by establishing a mechanical model of the optical fiber and rock strata. <xref ref-type="bibr" rid="B5">Chai et al. (2023)</xref> proposed a method based on Brillouin optical time domain distributed optical fiber sensing technology combined with a similar model test to analyze the deformation law and pressure relief effect of overlying coal and rock mass during the mining of the upper protective layer and realized the accuracy analysis of optical fiber sensing monitoring system and the spatial positioning of sensors. <xref ref-type="bibr" rid="B7">Du et al. (2021b)</xref> used the method of fiber Bragg grating (FBG) and distributed optical fiber (BOTDA) to carry out a similar model test on the stability of mining overburden and analyzed the stability of the waterproof key layer in a shallow coal seam.</p>
<p>This study investigates the distribution law of the support pressure of the stope and the feasibility of technical methods in monitoring methodologies under the thick conglomerate layer.</p>
<p>We innovatively introduced distributed Pulse-PrePump Brillouin Optical Time Domain Analysis (PPP-BOTDA) fiber sensing technology to physical similarity simulation experiments. Fiber optic sensors were embedded in the hard coal seam floor. By monitoring the relationship between abutment pressure in the floor and the frequency shift of the optical fiber, thereby analyzing the evolution of pressure distribution beneath thick gravel strata. It contributes to achieving monitoring abutment pressure evolution in real time and continuously. This study integrates theoretical analysis, numerical simulation and similar indoor physical tests to analyze comprehensively. The research results could provide a theoretical basis and technical support for the analysis of support pressure of floor coal seams in similar projects.</p>
</sec>
<sec id="s2">
<title>2 Calculation of inclined support force</title>
<sec id="s2-1">
<title>2.1 Theoretical analysis of support pressure model</title>
<p>In the process of coal seam mining in the stope, the key strata of the roof strata of the coal seam move in the basic unit of the strata group, and the key strata play a leading role in controlling the overall movement in the strata group. With the mining of the coal seam, the original uniform load state of the roof strata was destroyed, which led to the transfer of load to both sides of the goaf. According to the key stratum theory and the load transfer characteristics of overlying strata, the calculation model of inclined support pressure was established (<xref ref-type="bibr" rid="B28">Zhang, 2017</xref>), as shown in <xref ref-type="fig" rid="F2">Figure 2</xref>.<disp-formula id="e1">
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<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Tendency bearing pressure model.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g002.tif">
<alt-text content-type="machine-generated">Diagram illustrating the structure of geological layers, including the i-th key layer marked by triangles. Dimensions are labeled: \(L_i\) (width), \(M_i\) (thickness), \(H_i\) (height of centerline), \(H_{max}\) (maximum height), and \(I\) (height of mining). The angle \(\alpha\) represents the fracture angle of overburden. The horizontal axis is labeled \(X\) and the base width is \(2I\).</alt-text>
</graphic>
</fig>
<p>Suppose that the weight of the <italic>i</italic>th key layer transferred to the front of one side of the work was half of its weight, and the key layer was broken or incompletely broken. It was characterized by a hanging or hinged state, the stress increment transferred to the inclined coal body was approximately an isosceles triangle distribution, and the isosceles triangle moved forward with the advance of the working face, then the <italic>i</italic> key layer was transferred to the stress in front of one side of the working face. The force increment was shown in <xref ref-type="disp-formula" rid="e2">Formula 2</xref>. If there were multiple key strata in the overlying strata of the stope roof, the stress increment generated by each key stratum could be superimposed to obtain <inline-formula id="inf1">
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</mml:mfenced>
</mml:mrow>
<mml:mtext>&#x2002;</mml:mtext>
<mml:mi>x</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>H</mml:mi>
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</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>cot</mml:mi>
<mml:mo>&#x2061;</mml:mo>
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<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi>H</mml:mi>
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<mml:mo>&#x2061;</mml:mo>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mi>x</mml:mi>
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<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
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<mml:msub>
<mml:mi>H</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>cot</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>&#x3b1;</mml:mi>
<mml:mo>,</mml:mo>
<mml:mo>&#x221d;</mml:mo>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
</p>
<p>In the formula, <inline-formula id="inf2">
<mml:math id="m4">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>max</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was the maximum support pressure (MPa) on the coal seam produced by the key layer of the first layer, and the calculation formula of <inline-formula id="inf3">
<mml:math id="m5">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>max</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was as follows<disp-formula id="e3">
<mml:math id="m6">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b1;</mml:mi>
<mml:mrow>
<mml:mi>max</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mrow>
<mml:mfenced open="{" close="}" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>I</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mstyle displaystyle="true">
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mstyle>
<mml:mtext>&#x200a;</mml:mtext>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>tan</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
</p>
<p>The support pressure <inline-formula id="inf4">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi mathvariant="normal">q</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> caused by the self-weight of roof strata was estimated.<disp-formula id="e4">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi mathvariant="normal">q</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="{" close="" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
<mml:mi>I</mml:mi>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mi>x</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>I</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>cot</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
<mml:mi>x</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>tan</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>&#x3b1;</mml:mi>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mi>x</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mi>cot</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>&#x3b1;</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mi>max</mml:mi>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>cot</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mi>max</mml:mi>
</mml:msub>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mi>x</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mi>max</mml:mi>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>cot</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>&#x3b1;</mml:mi>
<mml:mo>,</mml:mo>
<mml:mo>&#x221d;</mml:mo>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
<inline-formula id="inf5">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was the distance from the thickness center of the key layer of the first <italic>i</italic> layer to the coal seam floor, m; 2<italic>I</italic> was the inclined length of the working face, m; <inline-formula id="inf6">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was the thickness of the key layer of layer i, m; <italic>&#x3b1;</italic> was the fracture angle of rock strata, (&#xb0;); <italic>&#x3b3;</italic> was rock bulk density, <inline-formula id="inf7">
<mml:math id="m11">
<mml:mrow>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mo>&#xb7;</mml:mo>
<mml:msup>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>; <inline-formula id="inf8">
<mml:math id="m12">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was the exposed length (m) of the thickness center of the <italic>i</italic>th critical layer in the goaf area. It could be seen that the calculation formula of support pressure was a set of piecewise functions. The distribution characteristics of support pressure in the model were related to the number of key strata, the location of key strata, the thickness of each rock group, the oblique length of the working face, the fracture angle of rock strata and the buried depth.</p>
<p>The model established that the key layers were in an ideal overhang or hinged state during their establishment, and ignored the uncertainty of geological structures such as weak interlayers and faults. In actual engineering, due to the complexity of rock structure, changes in coal-rock mechanical parameters, and the diversity of roof failure modes, the model predict during on results might deviate from the field measurements. Therefore, the applicability of the model should be verified and modified in combination with specific geological conditions to improve its engineering promotion value.</p>
</sec>
<sec id="s2-2">
<title>2.2 Project profile and rated conditions</title>
<p>The main coal seam of a coal mine in Henan Province was the No. 2 coal seam. The thickness of the coal seam was 15&#x2013;24 m, and the total thickness of the overlying strata was 805.32 m. The thick conglomerate was developed at 209.5 m above the coal seam, with a total thickness of 410.2 m. It was divided into two groups: the upper group was 250 m thick and the lower group was 160 m thick. There was a weak interlayer of 0.2 m between the two groups. The conglomerate had high strength and hardness characteristics. The average elastic modulus was 32 &#xd7; 10<sup>3</sup> MPa, the tensile strength was 5.5 MPa, the average compressive strength was 75 MPa, and the maximum compressive strength can reach 95 MPa. It was a typical hard rock layer. The specific characteristics of the roof strata of the coal seam were detailed in <xref ref-type="table" rid="T1">Table 1</xref>. The geographical location of the coal mine was shown in <xref ref-type="fig" rid="F3">Figure 3</xref>.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Coal seam roof rock layer characteristics and key layer identification results.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Lithology</th>
<th align="center">Thickness/m</th>
<th align="center">Tensile strength/MPa</th>
<th align="center">Elastic modulus/GPa</th>
<th align="center">Rock layer bulk density (kN&#x22c5;m<sup>&#x2212;3</sup>)</th>
<th align="center">Remark</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">clay</td>
<td align="center">15</td>
<td align="center">1.5</td>
<td align="center">5.0</td>
<td align="center">25.6</td>
<td align="center">load layer</td>
</tr>
<tr>
<td align="center">muddy limestone</td>
<td align="center">5</td>
<td align="center">1.5</td>
<td align="center">5.0</td>
<td align="center">25.6</td>
<td align="center">load layer</td>
</tr>
<tr>
<td align="center">conglomerate</td>
<td align="center">65</td>
<td align="center">5.5</td>
<td align="center">32.0</td>
<td align="center">29.3</td>
<td align="center">load layer</td>
</tr>
<tr>
<td align="center">fine sandstone</td>
<td align="center">85</td>
<td align="center">4.0</td>
<td align="center">28.0</td>
<td align="center">26.7</td>
<td align="center">load layer</td>
</tr>
<tr>
<td align="center">conglomerate</td>
<td align="center">250</td>
<td align="center">5.5</td>
<td align="center">32.0</td>
<td align="center">27.2</td>
<td align="center">key layer</td>
</tr>
<tr>
<td align="center">broken zone</td>
<td align="center">1</td>
<td align="center">4.0</td>
<td align="center">28.0</td>
<td align="center">27.2</td>
<td align="center">load layer</td>
</tr>
<tr>
<td align="center">conglomerate</td>
<td align="center">160</td>
<td align="center">5.5</td>
<td align="center">32.0</td>
<td align="center">29.3</td>
<td align="center">key layer</td>
</tr>
<tr>
<td align="center">mudstone</td>
<td align="center">50</td>
<td align="center">1.2</td>
<td align="center">5.0</td>
<td align="center">31.5</td>
<td align="center">load layer</td>
</tr>
<tr>
<td align="center">fine sandstone</td>
<td align="center">40</td>
<td align="center">9.0</td>
<td align="center">35.0</td>
<td align="center">26.7</td>
<td align="center">load layer</td>
</tr>
<tr>
<td align="center">siltstone</td>
<td align="center">70</td>
<td align="center">4.0</td>
<td align="center">28.0</td>
<td align="center">27.2</td>
<td align="center">load layer</td>
</tr>
<tr>
<td align="center">fine sandstone</td>
<td align="center">25</td>
<td align="center">9.0</td>
<td align="center">35.0</td>
<td align="center">26.7</td>
<td align="center">key layer</td>
</tr>
<tr>
<td align="center">mudstone</td>
<td align="center">25</td>
<td align="center">1.2</td>
<td align="center">5.0</td>
<td align="center">31.5</td>
<td align="center">crush belt</td>
</tr>
<tr>
<td align="center">2&#x23; coal</td>
<td align="center">16&#x2013;25</td>
<td align="center">0.6</td>
<td align="center">3.5</td>
<td align="center">15.2</td>
<td align="center">excavate coal seams</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Coal mine location.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g003.tif">
<alt-text content-type="machine-generated">Map of China highlighting Henan province in green. The right side shows a detailed elevation map of Henan, with a coal mine marked by a red dot. The map includes a legend for elevation ranging from six to two thousand two hundred ninety-eight meters.</alt-text>
</graphic>
</fig>
<p>According to the parameters of each layer in <xref ref-type="table" rid="T1">Table 1</xref>, the conditions were calculated as follows: <inline-formula id="inf9">
<mml:math id="m13">
<mml:mrow>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mi>max</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 791 m, <italic>M</italic> &#x3d; 16 m, <italic>I</italic> &#x3d; 120 m, <italic>&#x3b1;</italic> &#x3d; 78&#xb0;, <inline-formula id="inf10">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 50 m, <inline-formula id="inf11">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 160 m, <inline-formula id="inf12">
<mml:math id="m16">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 250 m, <inline-formula id="inf13">
<mml:math id="m17">
<mml:mrow>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 37.5 m, <inline-formula id="inf14">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 290 m, <inline-formula id="inf15">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 496 m. The calculation conditions were inserted into the <xref ref-type="disp-formula" rid="e1">Formulas 1</xref>&#x2013;<xref ref-type="disp-formula" rid="e4">4</xref>. The corresponding variation curve of the inclined support pressure in the working face was drawn. As shown in <xref ref-type="fig" rid="F4">Figure 4</xref>.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Working surface inclination support pressure change curve.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g004.tif">
<alt-text content-type="machine-generated">Graph showing the support pressure estimation curve with support pressure in megapascals on the y-axis and distance from the coal wall in meters on the x-axis. The curve peaks at around 100 meters at approximately 35 MPa and stabilizes after 200 meters at about 20 MPa.</alt-text>
</graphic>
</fig>
<p>We observed the peak value of the inclined support pressure of the stope under the extremely thick conglomerate was about 35 MPa, the distance from the peak point to the coal wall was about 85 m, and the peak influence range was about 200 m. Compared with the traditional inclined support pressure, the distribution of inclined support pressure in the extremely thick conglomerate layer had the characteristics of a large distance from the peak position to the coal wall and a large influence range.</p>
</sec>
</sec>
<sec id="s3">
<title>3 Numerical simulation analysis</title>
<p>Based on the theoretical analysis of the inclined support pressure distribution, it is necessary to further verify and visualize the stress evolution process in a more detailed and quantitative manner. Therefore, we use numerical simulation as a supplementary tool in order to better understand the distribution law of the support pressure and rock mass around the stope after excavating the working face. This study used FLAC3D software to simulate the distribution of the tendency support pressure and the plastic zone characteristics of the working face during advancement. The Mohr-Coulomb elastoplastic yield criterion was adopted in the simulation, as it is widely used in rock mechanics to model the failure behavior of geological materials under shear and normal stress conditions. The diagram showed the stress distribution and plastic distribution of the model in the Z-axis direction. The specific analysis was as follows:</p>
<p>We observed the above simulation from <xref ref-type="fig" rid="F5">Figures 5</xref>&#x2013;<xref ref-type="fig" rid="F8">8</xref>. When the working face advances to 240 m, 480 m and 960 m, the surrounding rock stress of the working face was redistributed. The stress state at the top of the floor and directly above the working face was tensile. The peak values of support pressure were 33 MPa, 30 MPa and 38 MPa respectively, and the influence range was very large. The corresponding plastic distribution law was as follows: the plastic zone distribution indicated that plastic failure had occurred in roof strata. The maximum development height of the plastic zone was 40 m from the coal seam floor. The plastic zone of the roof had developed to the upper conglomerate layer. The lower conglomerate layer and the lower part of the upper conglomerate layer had serious and slight damage. The plastic zone of the roof had developed to the upper conglomerate layer, and the upper and lower conglomerate layers had been completely destroyed. At the same time, the surface had shown the plastic failure. When it was pushed to 720 m, the top of the working face and the model were still in the tensile stress state. The peak value of the support pressure was 31 MPa, and the influence range was still large. The corresponding plastic zone distribution was that the plastic failure of the roof had been extended to the upper conglomerate layer. The lower conglomerate layer and the upper conglomerate layer appeared seriously damaged.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Stress and plastic zone distribution of the 240 m model with working face advancement.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g005.tif">
<alt-text content-type="machine-generated">Simulation image showing a stress distribution map divided into two main sections. The left section displays a gradient from red to blue, indicating different stress levels, with a corresponding color scale. The right section is predominantly blue with some colored regions at the bottom. A legend identifies shear and tension types corresponding to colors.</alt-text>
</graphic>
</fig>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>The stress and plastic zone distribution of the model working face after the working face is advanced 480 m.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g006.tif">
<alt-text content-type="machine-generated">Two-panel image depicting stress analysis. The left panel shows a gradient-filled grid indicating stress levels, with colors from red to blue corresponding to high to low values, as per the legend. The right panel features a similar grid with varied colors representing different types of shear and tension failures. A legend beside the panel defines these failures: none, shear-n shear-p, shear-n shear-p tension-p, shear-p, shear-p tension-p, shear-n shear-p tension-p, and shear-p.</alt-text>
</graphic>
</fig>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>The stress and plastic zone distribution of the model working face after the working face is advanced 720 m.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g007.tif">
<alt-text content-type="machine-generated">Color-coded heat maps display stress distribution in a grid, with a scale ranging from high (red) to low (blue) values. The right side annotates different stress types using a legend, including &#x201C;shear-p&#x201D; and &#x201C;tension-p.&#x201D;</alt-text>
</graphic>
</fig>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Distribution status of stress and plastic zone of model with working face advancing 960 m.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g008.tif">
<alt-text content-type="machine-generated">Two side-by-side colored contour maps. The left map shows gradient bands from red to blue with a scale indicating values from 1.0510e&#x2b;06 to -3.8605e&#x2b;07. The right map displays a block pattern with colors corresponding to different types: None, shear-n shear-p, shear-n shear-p tension-p, shear-p, shear-p tension-p, shear-n shear-p tension-p, and shear-p, each represented by specific colors.</alt-text>
</graphic>
</fig>
<p>In summary, with the gradual advancement of the working face, the peak value of the support pressure and the development of the plastic zone showed significant changes. The peak support pressure fluctuates at different advancing distances, gradually decreasing from 33 MPa to 30 MPa and then rising to 38 MPa. It indicated that the support pressure was obviously affected by the advancing of the working face. At the same time, the range of the plastic zone also gradually expanded with the increase of advancing distance, which eventually led to the complete destruction of the upper and lower conglomerate layers and extended to the surface. This process revealed the complex evolution law of surrounding rock stress in the mining process, indicating that in different advancing stages. It was necessary to take targeted support measures according to the stress distribution to ensure the safety of the mining process. After the coal seam was mined, the lower conglomerate layer and the upper conglomerate layer in the overlying strata played a controlling role in the rock failure. In the process of model mining, the development of the plastic zone inhibited the expansion of overlying strata stress to the upper strata to a certain extent.</p>
</sec>
<sec id="s4">
<title>4 Similar physical models</title>
<sec id="s4-1">
<title>4.1 Test survey</title>
<p>To validate the simulation results and further explore the stress evolution process, a physical model experiment was carried out under similar geological conditions. The thick shale layer was a hard and special coal-bearing stratum structure. It is distributed mainly in provinces such as Shanxi and Shandong. In this study, the experiments&#x2019; geological conditions were based on the coal-bearing strata of a mine in Henan Province. The experiment selected the maximum thickness of the main coal seam in this coal mine, which was 24 m. Above the coal seam developed a 209.5 m thick schistose stratum, and it contained a 0.2 m thick weak interlayer in the middle. The scaling law or similarity theory, was the basis for conducting physical model experiments on stope support pressure. Based on the similarity theory, the results of the physical model could better reflect the pressure distribution law of thick shale formation. Therefore, the size of the test model was 3.6 m &#xd7; 2.0 m &#xd7; 2.0 m (length &#xd7; width &#xd7; height), the geometric similarity ratio of the model was 1:400, the length of the simulated single working face was 60 cm, the thickness of the coal seam was 6 cm, and the thickness of the overlying rock layer was 174 cm. River sand, gypsum and calcium carbonate were used as similar materials to build a three-dimensional physical model of the working surface and overlying rock strata. The model was built to a similar scale. The model materials were mixed proportionally, stirred thoroughly with water, and then placed in layers into the mold for compaction. The on-site physical picture of the model was shown in <xref ref-type="fig" rid="F9">Figure 9</xref>. Due to the model not simulating the surface, other rock layers were converted into a uniformly distributed load and loaded with sandbags. The characteristics and proportions of the roof rock strata in the model experiment were shown in <xref ref-type="table" rid="T2">Table 2</xref>.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Model site physical map.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g009.tif">
<alt-text content-type="machine-generated">A yellow metal container filled with bags of various colors is situated indoors. The bags appear to be packed tightly inside the container. Several tables are placed nearby, and the setting resembles an industrial or storage area.</alt-text>
</graphic>
</fig>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Model laying layers and ratio table (AT, Actual thickness; ACT, Actual Cumulative Thickness; MT, Model Thickness; MCT, Model Cumulative Thickness; CS, Compressive Strength; TS, Tensile Strength; EM, Elastic Modulus).</p>
</caption>
<table>
<thead valign="top">
<tr>
<th colspan="4" align="left">3D rock structure model</th>
<th colspan="7" align="left">Model size 3600 mm &#xd7; 2000 mm &#xd7; 2000 mm</th>
</tr>
<tr>
<th align="center">No.</th>
<th align="center">Lithology</th>
<th align="center">AT/m</th>
<th align="center">ACT/m</th>
<th align="center">MT/cm</th>
<th align="center">MCT/cm</th>
<th align="center">CS/MPa</th>
<th align="center">TS/MPa</th>
<th align="center">EM<break/>&#xd7;10<sup>3</sup>MPa</th>
<th align="center">Rock layer bulk density/<break/>(kN&#x22c5;m<sup>&#x2212;3</sup>)</th>
<th align="center">Proportion number</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">1</td>
<td align="center">mudstone</td>
<td align="center">40</td>
<td align="center">40</td>
<td align="center">10</td>
<td align="center">10</td>
<td align="center">50</td>
<td align="center">1.2</td>
<td align="center">5</td>
<td align="center">2.97</td>
<td align="center">828</td>
</tr>
<tr>
<td align="center">2</td>
<td align="center">conglomerate</td>
<td align="center">40</td>
<td align="center">40</td>
<td align="center">10</td>
<td align="center">10</td>
<td align="center">65</td>
<td align="center">3</td>
<td align="center">25</td>
<td align="center">2.83</td>
<td align="center">837</td>
</tr>
<tr>
<td align="center">3</td>
<td align="center">2 coal</td>
<td align="center">15</td>
<td align="center">15</td>
<td align="center">6</td>
<td align="center">6</td>
<td align="center">16</td>
<td align="center">0.6</td>
<td align="center">3.5</td>
<td align="center">0.95</td>
<td align="center">&#x2014;</td>
</tr>
<tr>
<td align="center">4</td>
<td align="center">mudstone</td>
<td align="center">25</td>
<td align="center">40</td>
<td align="center">4</td>
<td align="center">10</td>
<td align="center">50</td>
<td align="center">1.2</td>
<td align="center">5</td>
<td align="center">2.97</td>
<td align="center">828</td>
</tr>
<tr>
<td align="center">5</td>
<td align="center">fine sandstone</td>
<td align="center">25</td>
<td align="center">65</td>
<td align="center">6</td>
<td align="center">16</td>
<td align="center">40</td>
<td align="center">9</td>
<td align="center">35</td>
<td align="center">2.67</td>
<td align="center">946</td>
</tr>
<tr>
<td align="center">6</td>
<td align="center">siltstone</td>
<td align="center">70</td>
<td align="center">135</td>
<td align="center">17</td>
<td align="center">30</td>
<td align="center">45</td>
<td align="center">4</td>
<td align="center">28</td>
<td align="center">2.7</td>
<td align="center">837</td>
</tr>
<tr>
<td align="center">7</td>
<td align="center">fine sandstone</td>
<td align="center">40</td>
<td align="center">175</td>
<td align="center">10</td>
<td align="center">43</td>
<td align="center">40</td>
<td align="center">9</td>
<td align="center">35</td>
<td align="center">2.67</td>
<td align="center">946</td>
</tr>
<tr>
<td align="center">8</td>
<td align="center">mudstone</td>
<td align="center">50</td>
<td align="center">225</td>
<td align="center">12</td>
<td align="center">55</td>
<td align="center">50</td>
<td align="center">1.2</td>
<td align="center">5</td>
<td align="center">2.97</td>
<td align="center">828</td>
</tr>
<tr>
<td align="center">9</td>
<td align="center">conglomerate</td>
<td align="center">160</td>
<td align="center">385</td>
<td align="center">40</td>
<td align="center">95</td>
<td align="center">75</td>
<td align="center">5.5</td>
<td align="center">32</td>
<td align="center">2.83</td>
<td align="center">837</td>
</tr>
<tr>
<td align="center">10</td>
<td align="center">broken zone</td>
<td align="center">1</td>
<td align="center">386</td>
<td align="center">1</td>
<td align="center">96</td>
<td align="center">40</td>
<td align="center">4</td>
<td align="center">28</td>
<td align="center">2.7</td>
<td align="center">928</td>
</tr>
<tr>
<td align="center">11</td>
<td align="center">conglomerate</td>
<td align="center">250</td>
<td align="center">636</td>
<td align="center">62</td>
<td align="center">158</td>
<td align="center">75</td>
<td align="center">5.5</td>
<td align="center">32</td>
<td align="center">2.7</td>
<td align="center">837</td>
</tr>
<tr>
<td align="center">12</td>
<td align="center">fine sandstone</td>
<td align="center">85</td>
<td align="center">721</td>
<td align="center">22</td>
<td align="center">180</td>
<td align="center">45</td>
<td align="center">4</td>
<td align="center">28</td>
<td align="center">2.67</td>
<td align="center">946</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s4-2">
<title>4.2 Model excavation and test process</title>
<p>In the trial phase, the coal seam was replaced by a galvanized square tube. The size of the galvanized square tube was (40 mm &#xd7; 60 mm) length &#xd7; height. The excavation step was 40 mm. One galvanized square tube was removed each time. The advancement direction was shown in <xref ref-type="fig" rid="F10">Figure 10</xref>.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Model excavation advancement direction.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g010.tif">
<alt-text content-type="machine-generated">A large industrial machine with yellow framing and a transparent center featuring labeled measurements. A yellow arrow with the text &#x22;Advancement direction&#x22; points from left to right.</alt-text>
</graphic>
</fig>
<p>According to similarity theory, to ensure that the test model was comparable to the actual project. This study used the geometric similarity ratio for conversion. The advancing distance was set to 300 cm. The mining of 60 times was selected based on the preliminary experimental results, under the premise of satisfying the sensor response frequency and data continuity. The inclination length of the simulated excavation working face was 80 cm, the excavation step distance was 5 cm, In the experiment, as the overlying rock strata deformed and destroyed as the working face advanced, the working face experienced initial pressure and periodic pressure a total of 15 times, of which the initial pressure step was 550 mm and the average periodic pressure step was 115 mm, as shown in <xref ref-type="fig" rid="F11">Figure 11</xref>.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Comparison chart between model pressure step distance and actual working conditions.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g011.tif">
<alt-text content-type="machine-generated">Graph comparing working face advancement distance in centimeters to actual distance under working conditions in meters over 15 intervals. Black arrows represent advancement distance, blue dots signify actual distance. Initial pressure and periodic pressure are marked with red arrows. Measurements include various distances from first to fifteenth interval.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s4-3">
<title>4.3 Experimental test system</title>
<sec id="s4-3-1">
<title>4.3.1 Pressure sensor</title>
<p>The test used CL-YB-116B pressure sensor to test the support pressure change of the model floor. The sensors were arranged in two columns at different positions of the coal seam floor. The first column was No. 1 to No. 48, and the second column was No. 4 9 to No. 96. The numbers were arranged in turn. The total length of the sensor was the same as that of the coal seam excavation distance. The size of each sensor was 20 cm &#xd7; 5 cm &#xd7; 5 cm, and the range was 0&#x2013;200 kg. Due to the physical dimensions and deployment configurations of sensors, potential limitations in spatial resolution may arise, accompanied by measurement inaccuracies induced by stress concentration phenomena or dispersion effects. Furthermore, the measurement fidelity could be affected by stability issues associated with prolonged loading conditions and progressive deformation of model materials. In order to avoid the interference of the mining process to the sensor, a 2 cm thick model material was covered above the sensor. And this shielding layer serves dual functions: preserving sensor integrity during dynamic stress redistribution while maintaining measurement continuity in the excavation simulation phase. The arrangement was shown in <xref ref-type="fig" rid="F12">Figure 12</xref>.</p>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Floor pressure sensor layout.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g012.tif">
<alt-text content-type="machine-generated">Diagram of pressure sensor placement within a cuboid, showing two groups labeled &#x22;Working face 1&#x22; and &#x22;Working face 2,&#x22; with dimensions provided. Accompanying images include a pressure sensor, data analysis equipment with computers, and a sensor layout illustrating how sensors are embedded in a material.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s4-3-2">
<title>4.3.2 Sensing fiber support pressure test</title>
<p>In the unexcavated coal seam floor, three horizontal sensing optical fibers were arranged along the inclination of the coal seam to test the distribution of support pressure. The fiber numbers were D1, D2 and D3, which were 0.6 m, 1.2 m and 1.8 m away from the open off-cut, respectively. We chose a tight-sleeve single-mode fiber with a cross-section diameter of 2 mm. During the laying process of the test, it was necessary to ensure that the optical fiber was closely bonded to the model material and appropriate tensile prestress was applied.</p>
<p>In order to reduce errors, we could fix the optical fiber with a positioning fixture. It could enable its position in three-dimensional space. However, the uneven shrinkage of the model material during the curing process might affect strain transfer due to a slight separation occurring between the optical fiber and the medium. Meanwhile, uneven prestressing or the device being affected by the coal seam inclination might cause some errors. Thus, researchers should check the fiber continuity and signal strength before and after the test to eliminate interference factors. Some instruments and equipment were shown in <xref ref-type="fig" rid="F13">Figure 13</xref>. From left to right, they represented optical fiber, the NBX-6055 Photonic Nanoanalyzer, and the connecting line. The arrangement was shown in <xref ref-type="fig" rid="F14">Figure 14</xref>.</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Sensing optical fiber equipment.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g013.tif">
<alt-text content-type="machine-generated">Three images are shown side by side. The first image depicts a spool of pink optical fiber with a yellow label reading &#x22;optical fiber.&#x22; The second shows an NBX-6055 Photonometer with a laptop on top. The third image features a yellow connecting line coiled in a transparent plastic bag, labeled &#x22;connecting line.&#x22;</alt-text>
</graphic>
</fig>
<fig id="F14" position="float">
<label>FIGURE 14</label>
<caption>
<p>Coal seam floor inclination optical fiber and pressure sensor arrangement (mm).</p>
</caption>
<graphic xlink:href="feart-13-1595035-g014.tif">
<alt-text content-type="machine-generated">Diagram showing a rectangular layout with labeled sections including &#x22;Goaf&#x22; and &#x22;Unexcavated.&#x22; Two pressure sensors, labeled 48-1 and 96-49, are placed horizontally. Three labeled fiber cables, D1, D2, and D3, run vertically. An optical fiber cable connects to a data acquisition computer, depicted in the top right corner. Dimensions are marked in millimeters.</alt-text>
</graphic>
</fig>
</sec>
</sec>
<sec id="s4-4">
<title>4.4 Distributed fiber optic testing principle sensing principle</title>
<sec id="s4-4-1">
<title>4.4.1 Fiber optic sensing principle</title>
<p>This experiment used the Pulse-PrePump Brillouin Optical Time Domain Analysis (PPP-BOTDA) (<xref ref-type="bibr" rid="B15">Kishida and Li, 2006</xref>), which had more advantages than traditional technology. PPP-BOTDA was different from BOTDA (<xref ref-type="bibr" rid="B13">Horiguchi and Tateda, 1989</xref>; <xref ref-type="bibr" rid="B8">Fang et al., 2023</xref>; <xref ref-type="bibr" rid="B25">Yin et al., 2023</xref>) distributed optical fiber sensing technology in that it had higher frequency resolution, high-accuracy Brillouin frequency shift and good Brillouin spectrum morphology. When the strain and temperature of the measured object change, the principle of Brillouin frequency shift change was shown in <xref ref-type="disp-formula" rid="e5">Equation 5</xref>.<disp-formula id="e5">
<mml:math id="m20">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>&#x3f5;</mml:mi>
</mml:msub>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>&#x3b5;</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>T</mml:mi>
</mml:msub>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>
</p>
<p>In the formula, <inline-formula id="inf16">
<mml:math id="m21">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was the Brillouin frequency shift amount, MHz; <inline-formula id="inf17">
<mml:math id="m22">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>&#x3f5;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was the Brillouin frequency shift strain coefficient; <inline-formula id="inf18">
<mml:math id="m23">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>T</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was the Brillouin frequency shift temperature coefficient; &#x394;&#x3b5; was the strain change amount; <inline-formula id="inf19">
<mml:math id="m24">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> was the temperature change amount. Ordinary single-mode fiber, such as Corning SMF28 Brillouin line width temperature. The degree coefficient <inline-formula id="inf20">
<mml:math id="m25">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>T</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was about &#x2212;0.93MHz/&#xb0;c, and the strain coefficient <inline-formula id="inf21">
<mml:math id="m26">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>&#x3f5;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was about 0.0003MHz/<italic>&#x3bc;&#x3b5;</italic> (<xref ref-type="bibr" rid="B1">Brown et al., 2005</xref>).</p>
<p>The so-called &#x201c;strain&#x201d; referred to the strain change in the axial direction of the optical fiber, which was actually produced by the joint action of axial strain and radial strain. Within a small deformation range, the two were directly proportional and related to Poisson&#x2019;s ratio (<xref ref-type="bibr" rid="B10">Gu, 2013</xref>; <xref ref-type="bibr" rid="B31">Zuo et al., 2024</xref>). By monitoring changes in optical fiber transmission power, the Brillouin frequency shift of each section could be obtained, and then the strain or temperature information of the optical fiber could be obtained. This method had high measurement accuracy and small spatial resolution. The principles diagram of PPP-BOTDA distributed optical fiber sensing technology and optical fiber stimulated Brillouin scattering were shown in <xref ref-type="fig" rid="F15">Figures 15</xref>, <xref ref-type="fig" rid="F16">16</xref>.</p>
<fig id="F15" position="float">
<label>FIGURE 15</label>
<caption>
<p>PPP-BOTDA schematic diagram.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g015.tif">
<alt-text content-type="machine-generated">Diagram illustrating the process of Brillouin scattering in an optic fiber for strain and temperature variation detection. It shows a pump laser, labeled LD, directed into the fiber. An incident laser enters the fiber, resulting in Brillouin scattering, which is analyzed for frequency. A continuous wave from a probe laser is also depicted, emphasizing the role of pulsed light in exciting phonons and enhancing Brillouin scattering, with components labeled accordingly.</alt-text>
</graphic>
</fig>
<fig id="F16" position="float">
<label>FIGURE 16</label>
<caption>
<p>Stimulated Brillouin scattering principle diagram.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g016.tif">
<alt-text content-type="machine-generated">Graph illustrating light intensity over time and frequency, depicting stimulated Brillouin scattering (SBS) and Raman scattering. The central green peak shows Rayleigh scattering at the incident light frequency. SBS peaks flank it with a frequency shift of &#xB1;11 GHz, indicated in red. Purple curves represent Raman scattering on both ends.</alt-text>
</graphic>
</fig>
<p>Although PPP-BOTDA technology has high spatial resolution and stability, there may still be systematic deviations in long-term or complex environments. For example, temperature fluctuations may cause frequency shift errors, and the device itself may also have signal drift and connection port reflection loss and optical path bending, which will also affect the signal-to-noise ratio. In order to reduce the impact of errors, prestress control and signal verification measures were taken. In the future, it would still be necessary to strengthen error compensation and stability evaluation to improve data reliability.</p>
</sec>
<sec id="s4-4-2">
<title>4.4.2 Linear relationship between brillouin scattering frequency shift and strain</title>
<p>The optical fiber sensor monitored the axial strain based on the Brillouin scattering principle. When the fiber was subjected to axial stress, its Brillouin frequency shift changed. It was assumed that the Brillouin frequency shift was <inline-formula id="inf22">
<mml:math id="m27">
<mml:mrow>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> when the initial stress was not applied. When the strain <inline-formula id="inf23">
<mml:math id="m28">
<mml:mrow>
<mml:mi>&#x3f5;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> was applied, the Brillouin frequency shift became <inline-formula id="inf24">
<mml:math id="m29">
<mml:mrow>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>&#x3f5;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, and the frequency shift variation <inline-formula id="inf25">
<mml:math id="m30">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was expressed as <xref ref-type="disp-formula" rid="e6">Equation 6</xref>:<disp-formula id="e6">
<mml:math id="m31">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>&#x3f5;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>
</p>
<p>The variation <inline-formula id="inf26">
<mml:math id="m32">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> reflected the frequency shift difference of the fiber under stress. According to the Brillouin scattering theory, there was a linear relationship between Brillouin frequency shift and strain &#x3b5;, and the proportional coefficient <inline-formula id="inf27">
<mml:math id="m33">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>&#x3f5;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the relationship between the two, which was:<disp-formula id="e7">
<mml:math id="m34">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>&#x3f5;</mml:mi>
</mml:msub>
<mml:mo>&#xb7;</mml:mo>
<mml:mi>&#x3f5;</mml:mi>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
</p>
<p>Among them, <inline-formula id="inf28">
<mml:math id="m35">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>&#x3f5;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was the sensitivity coefficient of strain, which indicated the sensitivity of Brillouin frequency shift to strain. According to the experimental and theoretical derivation, the linear relationship between the Brillouin frequency shift change. <inline-formula id="inf29">
<mml:math id="m36">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and the strain <italic>&#x3b5;</italic> was obtained as follows <xref ref-type="disp-formula" rid="e8">Equation 8</xref>:<disp-formula id="e8">
<mml:math id="m37">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>4.88</mml:mn>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>&#x3f5;</mml:mi>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
</p>
<p>Among them, the change of the Brillouin frequency shift was proportional to the strain, and its proportional coefficient was 4.88 times the initial Brillouin frequency shift. Which <inline-formula id="inf30">
<mml:math id="m39">
<mml:mrow>
<mml:mi>&#x3f5;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> can be obtained from <xref ref-type="disp-formula" rid="e9">Equation 9</xref>
<disp-formula id="e9">
<mml:math id="m38">
<mml:mrow>
<mml:mi>&#x3f5;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>&#x3c3;</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>E</mml:mi>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>
</p>
<p>Among them, <italic>&#x3c3;</italic> was the local stress; <italic>E</italic> was the elastic modulus of the optical fiber. In general, the Brillouin frequency shift was mainly caused by the axial strain of the optical fiber, which in turn comes from the externally applied stress or support pressure. When the optical fiber was tightly bonded to the medium, the local pressure was transmitted to the optical fiber through the medium, generating axial strain, which leads to the change of the Brillouin frequency shift.</p>
</sec>
</sec>
</sec>
<sec id="s5">
<title>5 Test results and analysis</title>
<sec id="s5-1">
<title>5.1 Working surface bottom plate support pressure distribution</title>
<p>The peak value of support pressure can reflect the dynamic change process of support pressure around the working face. In the process of working face advancing, the first column (1 &#x23; &#x223c; 48 &#x23;) was arranged in the bottom plate pressure sensor and the second column (49 &#x23; &#x223c; 96 &#x23;) was arranged in the side of the sensor. The maximum value of the supporting pressure of the bottom plate and the corresponding stress concentration coefficient are recorded respectively. The results are shown in <xref ref-type="fig" rid="F17">Figure 17</xref>, and the abscissa was the advancing distance of the working face.</p>
<fig id="F17" position="float">
<label>FIGURE 17</label>
<caption>
<p>The peak change of support pressure on working face.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g017.tif">
<alt-text content-type="machine-generated">Line graph showing support pressure peaks in megapascals (MPa) across working surface advancement distance in meters. Two data sets are displayed: red for sensors one to forty-eight, and blue for sensors forty-nine to ninety-six. Peaks show fluctuations, with notable values such as 3.04 MPa in red and 2.48 MPa in blue. The x-axis ranges from 184 to 920 meters.</alt-text>
</graphic>
</fig>
<p>It can be seen that the support pressure concentration factor measured by the first column sensor was between 1.24 and 3.04. When the working face was advanced to 240 m, 378 m, 470 m, 608 m, 700 m and 746 m, the concentration coefficient exceeded 2.0, indicating that there was a significant increase in the strike support pressure at these locations, reflecting the large-scale violent movement of the rock strata and leading to serious damage to the model rock strata. In this process, the overlying strata repeatedly rotate and sink, and the load is transferred to the front of the working face, resulting in a large pressure on the working face and a significant increase in the frequency of pressure.</p>
<p>When the advancing distance of the working face is less than 470 m, the support pressure concentration coefficient measured by the No. 49&#x2013;96 pressure sensor was less than 1.3, indicating that the excavation at this stage has little effect on the inclined support pressure. However, when the propulsion distance reaches 470&#x2013;746 m, the stress concentration factor increases significantly, ranging from 1.44 to 2.23, and there are four times of pressure during this period in which the stress concentration factor exceeded 1.9. This shows that after the working face advances to the middle and rear part of the model, the range of rock movement expands, the overlying rock layer rotates and sinks many times, and the load gradually shifts to the inclined side of the coal body, resulting in a significant increase in the inclined support pressure. In addition, the measured peak value of the inclined support pressure was mainly located behind the working face, which was in line with the expectation of the traditional mine pressure theory.</p>
</sec>
<sec id="s5-2">
<title>5.2 Optical fiber frequency shift distribution of support pressure on working face floor</title>
<p>The experiment revealed the evolution law of the support pressure in the different advancing processes of the working face by monitoring the Brillouin frequency shift distribution of the inclined support pressure under different advancing distances. The monitoring resulted of D1, D2 and D3 optical fiber sensors were shown in (a) &#x223c; (c) of <xref ref-type="fig" rid="F17">Figure 17</xref>. It reflected the changing trend of Brillouin frequency shift of support pressure monitored by optical fiber sensors at different positions when the working face advances.</p>
<p>
<xref ref-type="fig" rid="F18">Figure 18a</xref> showed that the D1 optical fiber sensor was located 60 cm (240 m) in front of the open-off cut of the working face. The curve didn&#x2019;t change significantly before advancing to 42 cm (168 m). However, as the working face further advances to 94.5 cm (378 m) 96 cm (384 m), the Brillouin frequency shift reached a maximum. This showed that the support pressure reached the peak value at this time. It meant that the support pressure began to concentrate during the propulsion stage, and the rock structure had undergone significant deformation and failure.</p>
<fig id="F18" position="float">
<label>FIGURE 18</label>
<caption>
<p>Brillouin frequency shift distribution of fiber D1, D2 and D3 inclined to support pressure. <bold>(a)</bold> optical fiber D1, <bold>(b)</bold> optical fiber D2, <bold>(c)</bold> optical fiber D3.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g018.tif">
<alt-text content-type="machine-generated">Three graphs depict Brillouin shift in megahertz versus distance from the coal wall in meters, each with multiple data series labeled by advancement distances. Each graph includes a detailed inset showing specific data points and trends. Graph (a) presents six series, graph (b) presents five, and graph (c) presents six, each showing varying trends of Brillouin shifts across different distances from the coal wall. The line colors and markers differentiate the advancement measurements in each graph.</alt-text>
</graphic>
</fig>
<p>
<xref ref-type="fig" rid="F18">Figure 18b</xref> showed that the D2 fiber optic sensor was located 117.5 cm (470 m) in front of the working face. It was used to monitor the bearing pressure. Before advancing to 96 cm (384 m), the curve did not change significantly, and there was no obvious fluctuation. However, at this stage, the Brillouin frequency shift increased significantly and reached a maximum at 140.5 cm (562 m). This showed that the stress of the rock layer was significant. The bearing pressure was further concentrated. At the same time, the peak position of the support pressure in front of the working face was moved forward. It reflected that the goaf was gradually expanding, and the damage and collapse range of the rock stratum was developing to the high level.</p>
<p>
<xref ref-type="fig" rid="F18">Figure 18c</xref> showed that when the D3 sensing fiber was located 180 cm (720 m) in front of the open-off cut, the Brillouin frequency shift curve didn&#x2019;t change much before the working face advanced to 146 cm (584 m). As the working face advances to 186.5 cm (746 m), the Brillouin frequency shift of the optical fiber reached a peak. The main reason was that the second group of conglomerate layers in the overlying strata breaks for the fourth time during this advancement process, which made the support pressure peak on the side of the coal pillar behind the goaf increase significantly. Combined with the comprehensive analysis of the data, it could be seen that the influence range was about 43 cm (172 m), and the distance to the peak support pressure was about 17.5 cm (70 m).</p>
<p>Furthermore, the sensor responses across three monitored positions (D1&#x2013;D3) were systematically analyzed in <xref ref-type="table" rid="T3">Table 3</xref>. In <xref ref-type="table" rid="T3">Table 3</xref>, the onset and peak positions of Brillouin frequency shifts were quantitatively extracted and compared with the advancing distances of the working face. The overall performance of the Brillouin frequency shift curve was as follows: a stable frequency shift in early stages, followed by a significant increase and eventual peak, corresponding to concentrated support pressure zones. The spatial ranges of influence were estimated to be approximately 43&#x2013;54 cm (172&#x2013;216 m), and the distances to peak stress zones gradually increased with the sensor&#x2019;s distance from the initial cut-off. In general, these monitoring data showed that the change of Brillouin frequency shift could accurately identify the concentrated area of support pressure and its change law. This had important reference value for predicting and controlling the stability of rock strata in the process of coal seam mining.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Relationship between power sensor and bracket pressure.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Sensor number</th>
<th align="center">Distance from initial cut to working surface (cm/m)</th>
<th align="center">Brillouin frequency shift significant change starting point (cm/m)</th>
<th align="center">Frequency shift peak corresponding position (cm/m)</th>
<th align="center">Pressure influence range (cm/m)</th>
<th align="center">Bracket pressure explanation</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">D1</td>
<td align="center">60 cm (240 m)</td>
<td align="center">42 cm (168 m)</td>
<td align="center">96 cm (384 m)</td>
<td align="center">&#x2248;54 cm (216 m)</td>
<td align="center">Pressure concentration occurs, and the rock mass undergoes significant deformation and destruction</td>
</tr>
<tr>
<td align="center">D2</td>
<td align="center">117.5 cm (470 m)</td>
<td align="center">96 cm (384 m)</td>
<td align="center">140.5 cm (562 m)</td>
<td align="center">&#x2248;44.5 cm (178 m)</td>
<td align="center">Pressure moves forward, goaf expands, and the scope of damage to the overlying rock strata expands</td>
</tr>
<tr>
<td align="center">D3</td>
<td align="center">180 cm (720)</td>
<td align="center">146 cm (584 m)</td>
<td align="center">186.5 cm (746 m)</td>
<td align="center">186.5 cm (746 m)</td>
<td align="center">The overburden fracture layer is further broken, and the pressure on one side of the coal pillar increases significantly</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s5-3">
<title>5.3 Comparative analysis</title>
<sec id="s5-3-1">
<title>5.3.1 Comparative analysis of optical fiber frequency shift and sensor support pressure</title>
<p>In the test system, the sensing fiber D1 corresponded to the pressure sensor 2&#x23;60, the sensing fiber D2 corresponds to the pressure sensor 2&#x23;72, and the sensing fiber D3 corresponds to the pressure sensor 2&#x23;84. The average Brillouin frequency shift of the length (200 mm) of the pressure sensor corresponding to the sensing fiber and the change of the inclined support pressure measured by the pressure sensor are plotted as shown in <xref ref-type="fig" rid="F19">Figure 19</xref>. It indicated that the Brillouin frequency shift measured by the D1, D2 and D3 sensing fibers was consistent with the change trend of the support pressure measured by the pressure sensor.</p>
<fig id="F19" position="float">
<label>FIGURE 19</label>
<caption>
<p>Fiber frequency shift and sensor support pressure curve.</p>
</caption>
<graphic xlink:href="feart-13-1595035-g019.tif">
<alt-text content-type="machine-generated">Graph showing Brillouin shift in megahertz and pressure tendency in megapascal against distance from the coal wall in meters. It includes plots for three fibers and three pressure sensors. Fiber D1, D2, and D3 frequency shifts use black, red, and blue lines with markers. Pressure sensor readings, also labeled with numbers 60, 72, and 84, overlap and contrast these fiber shifts. Peaks and patterns vary with distance, indicating changes in both Brillouin shift and pressure tendency.</alt-text>
</graphic>
</fig>
<p>When the working face was advanced to 182 m, the Brillouin frequency shift value of the D1 sensing fiber began to increase. The working face was advanced to 363 m and the frequency shift value of the D1 sensing fiber reached the maximum value. When the working face was advanced to 693 m, the frequency shift value of the fiber was basically stable. Along the advancing direction of the working face, the advanced influence range of the support pressure measured by the D1 sensing fiber was 74 m, the peak point was 133 m behind the working face, and the lag influence distance reached 443 m. The corresponding No. 60 pressure sensor had tendency to advance the influence range of 60 m, the peak point was 177 m away from the rear of the working face, and the lag influence distance reached 450 m.</p>
<p>The working face advanced to 400 m, the Brillouin frequency shift value of the D2 sensing fiber began to increase. The working face advances to 551 m, the Brillouin frequency shift value of the D2 sensing fiber reached the maximum. When advancing to 858 m, the Brillouin frequency shift value of the D2 sensing fiber was basically stable. Along the advancing direction of the working face, the advance influence range of the support pressure measured by the D2 sensing fiber was 77 m, the peak point was 126 m away from the rear of the working face, and the lag influence range reached 347 m. The advanced influence range of the tendency measured by the No. 72 pressure sensor was 49 m, the peak point was 114 m behind the working face, and the lag influence distance was 258 m.</p>
<p>The working face advanced to 595 m, the frequency shift value of the D3 sensing fiber began to increase. At 748 m, the frequency shift value of the fiber reached the maximum value. When the working face advanced to 873 m, the frequency shift value of the fiber was basically stable, and excavation was completed at 920 m. The advance influence range of support pressure measured by the D3 sensing fiber was 93 m, the peak point was 85 m behind the working face, and the lag influence distance was 113 m. Corresponding to the No. 84 pressure sensor, the advanced influence range was 41 m, the peak point was 41 m away from the rear of the working face, and the lag influence distance was 150 m. The mentioned discrepancy suggests that fiber optic sensors might be more sensitive to micro-strain accumulation, capable of capturing earlier and more subtle stress variations in the surrounding rock. In contrast, pressure sensors could detect stress concentration at localized contact points and might underrepresent broader deformation fields. These differences might contribute to knowing the importance of support pressure distribution and rock behavior.</p>
<p>Fiber optic monitoring was based on the principles of light interference and scattering and had the advantages of high precision and strong anti-interference, while traditional pressure sensors relied on changes in electrical signals such as resistance and capacitance to achieve measurement. The fundamental difference in the measurement principles between the two made fiber optic monitoring more suitable for continuous monitoring over long distances and in plasma environments, while traditional sensors were more suitable for local monitoring.</p>
</sec>
<sec id="s5-3-2">
<title>5.3.2 Comparative analysis of optical fiber frequency shift and numerical simulation</title>
<p>By comparing the fiber frequency shift with the numerical simulation, it can be seen that the consistency of the two was mainly reflected in the evolution law of support pressure and the dynamic process of rock failure. First of all, both show that with the advancement of the working face, the pressure at different stages shows a peak change: the support pressure was not obvious at the initial stage, then gradually concentrated and reached the peak value, and finally the regression was stable. This process reflects the significant influence of working face advance on stress distribution. Secondly, both of them emphasize the destructive control of conglomerate layers. In the process of rock failure, the failure of the lower and upper conglomerate layers not only affects the concentration of support pressure but also leads to the complex evolution of stress transfer, which ultimately affects the surface deformation and the stability of the goaf. The above commonality shows that the optical fiber frequency shift monitoring method has good consistency with the numerical simulation, which can more comprehensively grasp the stress change and rock failure law in the process of coal seam mining and provide a scientific basis for support design and mine safety management. These monitoring data not only verify the reliability of the theoretical model but also provide more detailed pressure distribution information, which has important reference value for predicting rock damage and pressure concentration areas in the process of coal seam mining and helps to improve the accuracy and safety of support design.</p>
</sec>
<sec id="s5-3-3">
<title>5.3.3 Comparative analysis of optical fiber frequency shift and theoretical calculation value</title>
<p>In this section, we adopted a complementary analytical approach combined with theoretical calculation and testing. Fiber optic monitoring was mainly used to capture internal responses, such as internal strain or deformation. However, pressure sensors were used to record pressure changes outside the structure. This combination of internal and external monitoring methods helps to verify and supplement the theoretical analysis results from different angles. It helps to enhance the reliability of the conclusions. The influence distance of advance mining support pressure and the influence range of lag tendency support pressure/MPa Brillouin frequency shift/MHz 64 measured by D1, D2 and D3 sensing optical fibers and pressure sensors were drawn in <xref ref-type="table" rid="T4">Table 4</xref>. The comparative analysis of the data in the table showed that the average mining influence distance measured by the optical fiber was 81.3 m, while the result measured by the pressure sensor was 50 m. The average lag influence distance measured by the optical fiber was 301 m, while the result measured by the pressure sensor was 286 cm. The resulted measured by the two are basically the same. Among them, the mining influence distance measured by optical fiber D3 was 14 m different from that of pressure sensor, and the lag influence distance measured by optical fiber D2 was 89 m different from that of pressure sensor. The reason was that after the working face advances to 516 m, the pressure on the working face was more severe, the load of overlying strata was transferred in a large range, and the overlying strata behind the goaf are rebalanced many times.</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Comparative analysis of optical fiber monitoring and pressure sensor monitoring.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Monitoring methods</th>
<th colspan="3" align="center">Mining influence distance/m</th>
<th rowspan="2" align="center">Average value</th>
<th colspan="3" align="center">Hysteresis drive distance/m</th>
<th rowspan="2" align="center">Average value/m</th>
</tr>
<tr>
<th align="center">D1</th>
<th align="center">D2</th>
<th align="center">D3</th>
<th align="center">D1</th>
<th align="center">D2</th>
<th align="center">D3</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Optical fiber</td>
<td align="center">74</td>
<td align="center">77</td>
<td align="center">93</td>
<td align="center">81.3</td>
<td align="center">443</td>
<td align="center">347</td>
<td align="center">113</td>
<td align="center">301</td>
</tr>
<tr>
<td align="center">Pressure sensor</td>
<td align="center">60</td>
<td align="center">49</td>
<td align="center">41</td>
<td align="center">50</td>
<td align="center">450</td>
<td align="center">258</td>
<td align="center">150</td>
<td align="center">286</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>
<xref ref-type="table" rid="T4">Tables 4</xref>, <xref ref-type="table" rid="T5">5</xref> are the comparative analysis of the optical fiber tendency support pressure data and the theoretical calculation values. It can be seen that there was a high consistency between the optical fiber monitoring and the theoretical calculation results. Among them, the data in <xref ref-type="table" rid="T4">Table 4</xref> prove the stability of optical fiber monitoring on different monitoring indicators. In the monitoring of the mining influence range and lag influence range, there was a certain gap between the results of optical fiber monitoring and the pressure sensor. But the trend of the two was consistent. This indicated that the relationship between theoretical calculations and on-site monitoring was not antagonistic but complementary: the theoretical model provides reliable expectations for monitoring, while on-site monitoring captures more dynamic changes due to the complexity of geological conditions.</p>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Comparison of optical fiber monitoring results and theoretical calculations.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Name</th>
<th colspan="3" align="center">Mining influence distance/m</th>
<th rowspan="2" align="center">Average value</th>
</tr>
<tr>
<th colspan="3" align="center">Working face tendency peak influence range average</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Method</td>
<td align="center">D1</td>
<td align="center">D2</td>
<td align="center">D3</td>
<td align="left"/>
</tr>
<tr>
<td align="center">Fiber monitoring</td>
<td align="center">176</td>
<td align="center">287</td>
<td align="center">192</td>
<td align="center">218</td>
</tr>
<tr>
<td align="center">Theoretical calculation</td>
<td colspan="3" align="center">200</td>
<td align="center">200</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Accordingly, the optical fiber monitoring results of D1 and D3 points in <xref ref-type="table" rid="T5">Table 5</xref> were basically consistent with the influence range of the theoretical calculation of the peak value of the inclined support pressure, which indicated that the theoretical model can accurately predict the distribution of pressure during mining in these areas. Although the monitoring value of the D2 point (218 m) was higher than the theoretical calculation value (200 m), which was about 1.09 times, this deviation also had a reasonable explanation. Since the working face was mined to the middle of the model, the movement range of the rock stratum in the process of continuous rotary sinking was expanded, and the transfer of the load to the inclined side of the coal body was enhanced, so the influence range of the support pressure was increased. At the same time, this result showed that in the actual working conditions, the influence of the complexity of geological conditions and the non-uniformity of stress transfer on the pressure range may exceed the prediction of the theoretical model, that was, the theoretical calculation will have certain limitations, but the basic trends of the two were still consistent. This provided a strong verification for the reliability of optical fiber monitoring in practical engineering applications.</p>
<p>In addition, combined with the comprehensive analysis of <xref ref-type="table" rid="T4">Tables 4</xref>, <xref ref-type="table" rid="T5">5</xref>, it can be seen that the optical fiber monitoring technology had high reliability and sensitivity in the monitoring of mining, hysteresis effect and support pressure range. Optical fiber monitoring technology had obvious advantages in long-distance monitoring and was more suitable for long-distance monitoring in complex geological environments.</p>
<p>Optical fiber monitoring showed significant advantages over traditional pressure sensors and theoretical calculations in the monitoring of mining influence and support pressure peak influence. In terms of mining influence range, the average value of optical fiber monitoring (81.3 m) was higher than that of pressure sensor (50 m). At D3 point, the optical fiber monitoring range (93 m) was significantly higher than that of pressure sensor (41 m). This showed that optical fiber monitoring technology had obvious advantages in long-distance monitoring, and was more suitable for long-distance monitoring in complex geological environment. In addition, the performance of optical fiber monitoring in the lag influence range was better than that of the pressure sensor, with an average value of 301 m, while the pressure sensor was 286 m, indicating that optical fiber monitoring was more sensitive and stable in capturing the lag response.</p>
</sec>
</sec>
</sec>
<sec sec-type="conclusion" id="s6">
<title>6 Conclusion</title>
<p>
<list list-type="simple">
<list-item>
<p>1 The theoretical model indicated that the characteristics of the support pressure under the thick conglomerate are as follows: The peak pressure was high; the peak value was far away from the coal wall, and the influence range was wide.</p>
</list-item>
<list-item>
<p>2 Numerical simulation analysis showed that after coal mining, the lower and upper conglomerate layers in the overlying strata played a controlling role in rock failure, and the development of plastic zone inhibited the expansion of stress to the upper strata to a certain extent.</p>
</list-item>
<list-item>
<p>3 The trend of the frequency shift curve of the inclined support pressure of the working face was &#x201c;constant &#x2192; increase &#x2192; peak &#x2192; decrease &#x2192; constant&#x201d;; the monitoring results had a good correspondence with the results of the pressure sensor test and were basically consistent with the theoretical calculation results. Optical fiber monitoring was suitable for long-distance monitoring in complex geological environments.</p>
</list-item>
</list>
</p>
</sec>
<sec id="s7">
<title>7 Discussion and outlook</title>
<p>
<list list-type="simple">
<list-item>
<p>1. This study used PPP-BOTDA technology, which was more suitable to apply in high spatial resolution and long-distance measurement. But there were some limitations in dynamic response capability and demodulation accuracy under complex stress fields. In the future, multimodal sensing or optimized demodulation algorithms would be combined with the optical fiber to improve its adaptability and reliability in non-uniform stress environments.</p>
</list-item>
<list-item>
<p>2. This study was based on thick conglomerate conditions and was thus representative to a certain extent; however, stress transfer characteristics may vary across different geological settings. To improve the method&#x2019;s applicability, fiber layout density and orientation can be adjusted according to lithological differences, and the frequency shift&#x2013;stress relationship can be calibrated using parameters such as elastic modulus. Additionally, prestress control and signal verification can be implemented in future work to enhance error compensation and improve data stability and reliability.</p>
</list-item>
</list>
</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s8">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding authors.</p>
</sec>
<sec sec-type="author-contributions" id="s9">
<title>Author contributions</title>
<p>CL: Methodology, Writing &#x2013; original draft, Investigation. JZ: Conceptualization, Writing &#x2013; review and editing, Formal Analysis. YC: Writing &#x2013; original draft, Investigation, Software. YH: Conceptualization, Writing &#x2013; original draft, Supervision. YS: Writing &#x2013; original draft, Formal Analysis, Investigation. YQ: Writing &#x2013; original draft, Investigation, Validation. QY: Supervision, Conceptualization, Writing &#x2013; review and editing. MZ: Resources, Conceptualization, Writing &#x2013; review and editing.</p>
</sec>
<sec sec-type="funding-information" id="s10">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research and/or publication of this article. This work was funded in part by the National Natural Science Foundation of China, grant number 51804052; Chongqing Municipal Key Projects for Innovation and Application Development, grant number CSTB2022TIAD-KPX0105; Research Projects of Chongqing Planning and Natural Resources Bureau, grant number KJ2022-044.</p>
</sec>
<sec sec-type="COI-statement" id="s11">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="ai-statement" id="s12">
<title>Generative AI statement</title>
<p>The author(s) declare that no Generative AI was used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p>
</sec>
<sec sec-type="disclaimer" id="s13">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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