<?xml version="1.0"?>
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&#x431;&#x44E;&#x434;&#x436;&#x435;&#x442;&#x43D;&#x43E;&#x435; &#x443;&#x447;&#x440;&#x435;&#x436;&#x434;&#x435;&#x43D;&#x438;&#x435; &#x43D;&#x430;&#x443;&#x43A;&#x438; &#x424;&#x435;&#x434;&#x435;&#x440;&#x430;&#x43B;&#x44C;&#x43D;&#x44B;&#x439; &#x43D;&#x430;&#x443;&#x447;&#x43D;&#x44B;&#x439; &#x446;&#x435;&#x43D;&#x442;&#x440;  "&#x412;&#x43B;&#x430;&#x434;&#x438;&#x43A;&#x430;&#x432;&#x43A;&#x430;&#x437;&#x441;&#x43A;&#x438;&#x439; &#x43D;&#x430;&#x443;&#x447;&#x43D;&#x44B;&#x439; &#x446;&#x435;&#x43D;&#x442;&#x440; &#x420;&#x43E;&#x441;&#x441;&#x438;&#x439;&#x441;&#x43A;&#x43E;&#x439; &#x430;&#x43A;&#x430;&#x434;&#x435;&#x43C;&#x438;&#x438; &#x43D;&#x430;&#x443;&#x43A;"</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">1318</article-id><article-id pub-id-type="doi">10.46698/o0885-5581-1938-j</article-id><article-categories><subj-group subj-group-type="heading"><subject>&#x413;&#x435;&#x43E;&#x442;&#x435;&#x445;&#x43D;&#x43E;&#x43B;&#x43E;&#x433;&#x438;&#x44F;. &#x413;&#x435;&#x43E;&#x43C;&#x435;&#x445;&#x430;&#x43D;&#x438;&#x43A;&#x430;</subject></subj-group></article-categories><title-group><article-title>&#x410;&#x43D;&#x430;&#x43B;&#x438;&#x437; &#x441;&#x43E;&#x441;&#x442;&#x43E;&#x44F;&#x43D;&#x438;&#x44F; &#x43A;&#x440;&#x43E;&#x432;&#x43B;&#x438; &#x434;&#x43B;&#x44F; &#x432;&#x44B;&#x440;&#x430;&#x431;&#x43E;&#x442;&#x43E;&#x43A; &#x43F;&#x435;&#x440;&#x435;&#x434; &#x443;&#x433;&#x43E;&#x43B;&#x44C;&#x43D;&#x44B;&#x43C; &#x437;&#x430;&#x431;&#x43E;&#x435;&#x43C;: &#x43F;&#x440;&#x438;&#x43C;&#x435;&#x440; &#x443;&#x433;&#x43E;&#x43B;&#x44C;&#x43D;&#x43E;&#x439; &#x448;&#x430;&#x445;&#x442;&#x44B; &#xAB;&#x425;&#x430; &#x41B;&#x430;&#x43C;&#xBB;</article-title></title-group><contrib-group><contrib contrib-type="author"><name name-style="eastern" xml:lang="en"><surname>&#x424;&#x443;&#x43A;</surname><given-names>&#x41B;.&#x41A;.</given-names></name><email>nguyenkhaclinh@humg.edu.vn</email><xref ref-type="aff" rid="aff-aff-1"/></contrib><contrib contrib-type="author"><name name-style="eastern" xml:lang="en"><surname>&#x41B;&#x438;&#x43D;&#x44C;</surname><given-names>&#x41D;.&#x41A;.</given-names></name><xref ref-type="aff" rid="aff-aff-1"/></contrib><contrib contrib-type="author"><name name-style="eastern" xml:lang="en"><surname>&#x411;&#x430;&#x431;&#x44B;&#x440;&#x44C;</surname><given-names>&#x41D;.&#x412;.</given-names></name><xref ref-type="aff" rid="aff-aff-2"/></contrib><contrib contrib-type="author"><name name-style="eastern" xml:lang="en"><surname>&#x422;&#x445;&#x430;&#x43D;&#x433;</surname><given-names>&#x41D;.&#x412;.</given-names></name><xref ref-type="aff" rid="aff-aff-2"/></contrib></contrib-group><aff id="aff-aff-1">&#x425;&#x430;&#x43D;&#x43E;&#x439;&#x441;&#x43A;&#x438;&#x439; &#x443;&#x43D;&#x438;&#x432;&#x435;&#x440;&#x441;&#x438;&#x442;&#x435;&#x442; &#x433;&#x43E;&#x440;&#x43D;&#x43E;&#x433;&#x43E; &#x434;&#x435;&#x43B;&#x430; &#x438; &#x433;&#x435;&#x43E;&#x43B;&#x43E;&#x433;&#x438;&#x438;, &#x412;&#x44C;&#x435;&#x442;&#x43D;&#x430;&#x43C;, &#x433;. &#x425;&#x430;&#x43D;&#x43E;&#x439;, &#x443;&#x43B;. &#x424;&#x43E; &#x412;&#x44C;&#x435;&#x43D;, &#x414;&#x43E;&#x43D;&#x433; &#x41D;&#x433;&#x430;&#x43A;, 18</aff><aff id="aff-aff-2">&#x421;&#x430;&#x43D;&#x43A;&#x442;-&#x41F;&#x435;&#x442;&#x435;&#x440;&#x431;&#x443;&#x440;&#x433;&#x441;&#x43A;&#x438;&#x439; &#x433;&#x43E;&#x440;&#x43D;&#x44B;&#x439; &#x443;&#x43D;&#x438;&#x432;&#x435;&#x440;&#x441;&#x438;&#x442;&#x435;&#x442;, &#x420;&#x43E;&#x441;&#x441;&#x438;&#x44F;, 199106, &#x433;. &#x421;&#x430;&#x43D;&#x43A;&#x442;-&#x41F;&#x435;&#x442;&#x435;&#x440;&#x431;&#x443;&#x440;&#x433;, &#x412;&#x430;&#x441;&#x438;&#x43B;&#x44C;&#x435;&#x432;&#x441;&#x43A;&#x438;&#x439; &#x43E;&#x441;&#x442;&#x440;&#x43E;&#x432;, 21 &#x43B;&#x438;&#x43D;&#x438;&#x44F;, &#x434;. 2</aff><pub-date date-type="pub" iso-8601-date="2025-12-30" publication-format="electronic"><day>30</day><month>12</month><year>2025</year></pub-date><issue>4</issue><fpage>270</fpage><lpage>284</lpage><permissions><copyright-statement>Copyright (c) 2025 &#x413;&#x435;&#x43E;&#x43B;&#x43E;&#x433;&#x438;&#x44F; &#x438; &#x433;&#x435;&#x43E;&#x444;&#x438;&#x437;&#x438;&#x43A;&#x430; &#x42E;&#x433;&#x430; &#x420;&#x43E;&#x441;&#x441;&#x438;&#x438;</copyright-statement><copyright-year>2025</copyright-year><copyright-holder>&#x413;&#x435;&#x43E;&#x43B;&#x43E;&#x433;&#x438;&#x44F; &#x438; &#x433;&#x435;&#x43E;&#x444;&#x438;&#x437;&#x438;&#x43A;&#x430; &#x42E;&#x433;&#x430; &#x420;&#x43E;&#x441;&#x441;&#x438;&#x438;</copyright-holder></permissions><self-uri href="https://geosouth.ru/article/view/1318"/><abstract>&lt;p&gt;&#x420;&#x435;&#x437;&#x44E;&#x43C;&#x435;: &#x41F;&#x43E;&#x434;&#x437;&#x435;&#x43C;&#x43D;&#x430;&#x44F; &#x434;&#x43E;&#x431;&#x44B;&#x447;&#x430; &#x443;&#x433;&#x43B;&#x44F; &#x441;&#x432;&#x44F;&#x437;&#x430;&#x43D;&#x430; &#x441; &#x43E;&#x433;&#x440;&#x430;&#x43D;&#x438;&#x447;&#x435;&#x43D;&#x43D;&#x44B;&#x43C;&#x438; &#x443;&#x441;&#x43B;&#x43E;&#x432;&#x438;&#x44F;&#x43C;&#x438; &#x440;&#x430;&#x431;&#x43E;&#x442;&#x44B; &#x438; &#x437;&#x43D;&#x430;&#x447;&#x438;&#x442;&#x435;&#x43B;&#x44C;&#x43D;&#x44B;&#x43C;&#x438; &#x440;&#x438;&#x441;&#x43A;&#x430;&#x43C;&#x438; &#x431;&#x435;&#x437;&#x43E;&#x43F;&#x430;&#x441;&#x43D;&#x43E;&#x441;&#x442;&#x438; &#x442;&#x440;&#x443;&#x434;&#x430;. &#x412; &#x447;&#x430;&#x441;&#x442;&#x43D;&#x43E;&#x441;&#x442;&#x438;, &#x433;&#x43E;&#x440;&#x43D;&#x44B;&#x435; &#x432;&#x44B;&#x440;&#x430;&#x431;&#x43E;&#x442;&#x43A;&#x438;, &#x43F;&#x440;&#x43E;&#x432;&#x43E;&#x434;&#x438;&#x43C;&#x44B;&#x435; &#x43F;&#x43E; &#x443;&#x433;&#x43E;&#x43B;&#x44C;&#x43D;&#x43E;&#x43C;&#x443; &#x43F;&#x43B;&#x430;&#x441;&#x442;&#x443; &#x432;&#x43F;&#x435;&#x440;&#x435;&#x434;&#x438; &#x43E;&#x447;&#x438;&#x441;&#x442;&#x43D;&#x43E;&#x433;&#x43E; &#x437;&#x430;&#x431;&#x43E;&#x44F;, &#x43F;&#x440;&#x435;&#x434;&#x441;&#x442;&#x430;&#x432;&#x43B;&#x44F;&#x44E;&#x442; &#x441;&#x43E;&#x431;&#x43E;&#x439; &#x437;&#x43E;&#x43D;&#x443; &#x43F;&#x43E;&#x432;&#x44B;&#x448;&#x435;&#x43D;&#x43D;&#x43E;&#x433;&#x43E; &#x440;&#x438;&#x441;&#x43A;&#x430; &#x43E;&#x431;&#x440;&#x443;&#x448;&#x435;&#x43D;&#x438;&#x44F; &#x43A;&#x440;&#x43E;&#x432;&#x43B;&#x438; &#x438; &#x441;&#x43B;&#x43E;&#x436;&#x43D;&#x43E;&#x441;&#x442;&#x435;&#x439; &#x441; &#x443;&#x43F;&#x440;&#x430;&#x432;&#x43B;&#x435;&#x43D;&#x438;&#x435;&#x43C; &#x43A;&#x440;&#x43E;&#x432;&#x43B;&#x435;&#x439;. &#x426;&#x435;&#x43B;&#x44C;&#x44E; &#x434;&#x430;&#x43D;&#x43D;&#x43E;&#x433;&#x43E; &#x438;&#x441;&#x441;&#x43B;&#x435;&#x434;&#x43E;&#x432;&#x430;&#x43D;&#x438;&#x44F; &#x44F;&#x432;&#x43B;&#x44F;&#x435;&#x442;&#x441;&#x44F; &#x430;&#x43D;&#x430;&#x43B;&#x438;&#x437; &#x440;&#x430;&#x441;&#x43F;&#x440;&#x435;&#x434;&#x435;&#x43B;&#x435;&#x43D;&#x438;&#x44F; &#x43D;&#x430;&#x43F;&#x440;&#x44F;&#x436;&#x435;&#x43D;&#x438;&#x439; &#x438; &#x440;&#x430;&#x437;&#x432;&#x438;&#x442;&#x438;&#x44F; &#x437;&#x43E;&#x43D; &#x43F;&#x43B;&#x430;&#x441;&#x442;&#x438;&#x447;&#x435;&#x441;&#x43A;&#x43E;&#x439; &#x434;&#x435;&#x444;&#x43E;&#x440;&#x43C;&#x430;&#x446;&#x438;&#x438; &#x432;&#x43E; &#x432;&#x43C;&#x435;&#x449;&#x430;&#x44E;&#x449;&#x438;&#x445; &#x43F;&#x43E;&#x440;&#x43E;&#x434;&#x430;&#x445; &#x43D;&#x430; &#x43E;&#x441;&#x43D;&#x43E;&#x432;&#x435; &#x443;&#x441;&#x43B;&#x43E;&#x432;&#x438;&#x439; &#x43E;&#x442;&#x440;&#x430;&#x431;&#x43E;&#x442;&#x43A;&#x438; &#x43F;&#x43B;&#x430;&#x441;&#x442;&#x430; &#x2116; 10 &#x448;&#x430;&#x445;&#x442;&#x44B; &#xAB;&#x425;&#x430; &#x41B;&#x430;&#x43C;&#xBB;. &#x410;&#x43A;&#x442;&#x443;&#x430;&#x43B;&#x44C;&#x43D;&#x43E;&#x441;&#x442;&#x44C; &#x440;&#x430;&#x431;&#x43E;&#x442;&#x44B; &#x43E;&#x431;&#x443;&#x441;&#x43B;&#x43E;&#x432;&#x43B;&#x435;&#x43D;&#x430; &#x43D;&#x435;&#x43E;&#x431;&#x445;&#x43E;&#x434;&#x438;&#x43C;&#x43E;&#x441;&#x442;&#x44C;&#x44E; &#x43E;&#x431;&#x435;&#x441;&#x43F;&#x435;&#x447;&#x435;&#x43D;&#x438;&#x44F; &#x443;&#x441;&#x442;&#x43E;&#x439;&#x447;&#x438;&#x432;&#x43E;&#x441;&#x442;&#x438; &#x43F;&#x43E;&#x434;&#x433;&#x43E;&#x442;&#x43E;&#x432;&#x438;&#x442;&#x435;&#x43B;&#x44C;&#x43D;&#x44B;&#x445; &#x432;&#x44B;&#x440;&#x430;&#x431;&#x43E;&#x442;&#x43E;&#x43A; &#x432; &#x437;&#x43E;&#x43D;&#x435; &#x43E;&#x43F;&#x435;&#x440;&#x435;&#x436;&#x430;&#x44E;&#x449;&#x435;&#x433;&#x43E; &#x432;&#x43B;&#x438;&#x44F;&#x43D;&#x438;&#x44F; &#x43E;&#x447;&#x438;&#x441;&#x442;&#x43D;&#x44B;&#x445; &#x440;&#x430;&#x431;&#x43E;&#x442; &#x434;&#x43B;&#x44F; &#x43F;&#x43E;&#x432;&#x44B;&#x448;&#x435;&#x43D;&#x438;&#x44F; &#x431;&#x435;&#x437;&#x43E;&#x43F;&#x430;&#x441;&#x43D;&#x43E;&#x441;&#x442;&#x438; &#x438; &#x44D;&#x444;&#x444;&#x435;&#x43A;&#x442;&#x438;&#x432;&#x43D;&#x43E;&#x441;&#x442;&#x438; &#x434;&#x43E;&#x431;&#x44B;&#x447;&#x438;. &#x412; &#x43A;&#x430;&#x447;&#x435;&#x441;&#x442;&#x432;&#x435; &#x43E;&#x441;&#x43D;&#x43E;&#x432;&#x43D;&#x43E;&#x433;&#x43E; &#x43C;&#x435;&#x442;&#x43E;&#x434;&#x430; &#x438;&#x441;&#x43F;&#x43E;&#x43B;&#x44C;&#x437;&#x43E;&#x432;&#x430;&#x43D;&#x43E; &#x43A;&#x43E;&#x43C;&#x43F;&#x44C;&#x44E;&#x442;&#x435;&#x440;&#x43D;&#x43E;&#x435; &#x43C;&#x43E;&#x434;&#x435;&#x43B;&#x438;&#x440;&#x43E;&#x432;&#x430;&#x43D;&#x438;&#x435; &#x43D;&#x430;&#x43F;&#x440;&#x44F;&#x436;&#x435;&#x43D;&#x43D;&#x43E;&#x434;&#x435;&#x444;&#x43E;&#x440;&#x43C;&#x438;&#x440;&#x43E;&#x432;&#x430;&#x43D;&#x43D;&#x43E;&#x433;&#x43E; &#x441;&#x43E;&#x441;&#x442;&#x43E;&#x44F;&#x43D;&#x438;&#x44F; &#x43F;&#x43E;&#x440;&#x43E;&#x434;&#x43D;&#x43E;&#x433;&#x43E; &#x43C;&#x430;&#x441;&#x441;&#x438;&#x432;&#x430;, &#x432;&#x435;&#x440;&#x438;&#x444;&#x438;&#x446;&#x438;&#x440;&#x43E;&#x432;&#x430;&#x43D;&#x43D;&#x43E;&#x435; &#x434;&#x430;&#x43D;&#x43D;&#x44B;&#x43C;&#x438; &#x43D;&#x430;&#x442;&#x443;&#x440;&#x43D;&#x44B;&#x445; &#x43D;&#x430;&#x431;&#x43B;&#x44E;&#x434;&#x435;&#x43D;&#x438;&#x439;. &#x412; &#x440;&#x435;&#x437;&#x443;&#x43B;&#x44C;&#x442;&#x430;&#x442;&#x435; &#x443;&#x441;&#x442;&#x430;&#x43D;&#x43E;&#x432;&#x43B;&#x435;&#x43D;&#x43E;, &#x447;&#x442;&#x43E; &#x432;&#x44B;&#x440;&#x430;&#x431;&#x43E;&#x442;&#x43A;&#x430;, &#x440;&#x430;&#x441;&#x43F;&#x43E;&#x43B;&#x43E;&#x436;&#x435;&#x43D;&#x43D;&#x430;&#x44F; &#x432;&#x43F;&#x435;&#x440;&#x435;&#x434;&#x438; &#x43E;&#x447;&#x438;&#x441;&#x442;&#x43D;&#x43E;&#x433;&#x43E; &#x437;&#x430;&#x431;&#x43E;&#x44F;, &#x43F;&#x43E;&#x441;&#x442;&#x43E;&#x44F;&#x43D;&#x43D;&#x43E; &#x43D;&#x430;&#x445;&#x43E;&#x434;&#x438;&#x442;&#x441;&#x44F; &#x432; &#x443;&#x441;&#x43B;&#x43E;&#x432;&#x438;&#x44F;&#x445; &#x430;&#x441;&#x438;&#x43C;&#x43C;&#x435;&#x442;&#x440;&#x438;&#x447;&#x43D;&#x43E;&#x433;&#x43E; &#x43D;&#x430;&#x43F;&#x440;&#x44F;&#x436;&#x435;&#x43D;&#x43D;&#x43E;&#x433;&#x43E; &#x441;&#x43E;&#x441;&#x442;&#x43E;&#x44F;&#x43D;&#x438;&#x44F;, &#x43F;&#x440;&#x438; &#x44D;&#x442;&#x43E;&#x43C; &#x43A;&#x43E;&#x44D;&#x444;&#x444;&#x438;&#x446;&#x438;&#x435;&#x43D;&#x442; &#x441;&#x43E;&#x43E;&#x442;&#x43D;&#x43E;&#x448;&#x435;&#x43D;&#x438;&#x44F; &#x433;&#x43E;&#x440;&#x438;&#x437;&#x43E;&#x43D;&#x442;&#x430;&#x43B;&#x44C;&#x43D;&#x43E;&#x433;&#x43E; &#x438; &#x432;&#x435;&#x440;&#x442;&#x438;&#x43A;&#x430;&#x43B;&#x44C;&#x43D;&#x43E;&#x433;&#x43E; &#x43D;&#x430;&#x43F;&#x440;&#x44F;&#x436;&#x435;&#x43D;&#x438;&#x44F; &#x434;&#x43E;&#x441;&#x442;&#x438;&#x433;&#x430;&#x435;&#x442; &#x437;&#x43D;&#x430;&#x447;&#x435;&#x43D;&#x438;&#x439; &#x441;&#x432;&#x44B;&#x448;&#x435; 2,5. &#x417;&#x43E;&#x43D;&#x430; &#x43F;&#x43B;&#x430;&#x441;&#x442;&#x438;&#x447;&#x435;&#x441;&#x43A;&#x438;&#x445; &#x434;&#x435;&#x444;&#x43E;&#x440;&#x43C;&#x430;&#x446;&#x438;&#x439; &#x440;&#x430;&#x437;&#x432;&#x438;&#x432;&#x430;&#x435;&#x442;&#x441;&#x44F; &#x430;&#x441;&#x438;&#x43C;&#x43C;&#x435;&#x442;&#x440;&#x438;&#x447;&#x43D;&#x43E; &#x43C;&#x435;&#x436;&#x434;&#x443; &#x434;&#x432;&#x443;&#x43C;&#x44F; &#x431;&#x43E;&#x43A;&#x430;&#x43C;&#x438; &#x432;&#x44B;&#x440;&#x430;&#x431;&#x43E;&#x442;&#x43A;&#x438;, &#x447;&#x442;&#x43E; &#x43F;&#x440;&#x438;&#x432;&#x43E;&#x434;&#x438;&#x442; &#x43A; &#x43D;&#x435;&#x440;&#x430;&#x432;&#x43D;&#x43E;&#x43C;&#x435;&#x440;&#x43D;&#x43E;&#x439; &#x43D;&#x430;&#x433;&#x440;&#x443;&#x437;&#x43A;&#x435;. &#x412;&#x435;&#x43B;&#x438;&#x447;&#x438;&#x43D;&#x430; &#x43D;&#x430;&#x43F;&#x440;&#x44F;&#x436;&#x435;&#x43D;&#x438;&#x439; &#x438; &#x441;&#x442;&#x435;&#x43F;&#x435;&#x43D;&#x44C; &#x440;&#x430;&#x441;&#x43F;&#x440;&#x43E;&#x441;&#x442;&#x440;&#x430;&#x43D;&#x435;&#x43D;&#x438;&#x44F; &#x437;&#x43E;&#x43D;&#x44B; &#x43F;&#x43B;&#x430;&#x441;&#x442;&#x438;&#x447;&#x435;&#x441;&#x43A;&#x43E;&#x439; &#x434;&#x435;&#x444;&#x43E;&#x440;&#x43C;&#x430;&#x446;&#x438;&#x438; &#x432;&#x43E;&#x43A;&#x440;&#x443;&#x433; &#x432;&#x435;&#x43D;&#x442;&#x438;&#x43B;&#x44F;&#x446;&#x438;&#x43E;&#x43D;&#x43D;&#x43E;&#x439; &#x432;&#x44B;&#x440;&#x430;&#x431;&#x43E;&#x442;&#x43A;&#x438; &#x437;&#x43D;&#x430;&#x447;&#x438;&#x442;&#x435;&#x43B;&#x44C;&#x43D;&#x43E; &#x431;&#x43E;&#x43B;&#x44C;&#x448;&#x435;, &#x447;&#x435;&#x43C; &#x443; &#x442;&#x440;&#x430;&#x43D;&#x441;&#x43F;&#x43E;&#x440;&#x442;&#x43D;&#x43E;&#x439; &#x432;&#x44B;&#x440;&#x430;&#x431;&#x43E;&#x442;&#x43A;&#x438;. &#x421;&#x43B;&#x435;&#x434;&#x43E;&#x432;&#x430;&#x442;&#x435;&#x43B;&#x44C;&#x43D;&#x43E;, &#x43D;&#x435;&#x43E;&#x431;&#x445;&#x43E;&#x434;&#x438;&#x43C; &#x43F;&#x43B;&#x430;&#x43D; &#x434;&#x43E;&#x43F;&#x43E;&#x43B;&#x43D;&#x438;&#x442;&#x435;&#x43B;&#x44C;&#x43D;&#x43E;&#x433;&#x43E; &#x43A;&#x440;&#x435;&#x43F;&#x43B;&#x435;&#x43D;&#x438;&#x44F; &#x434;&#x43B;&#x44F; &#x43F;&#x43E;&#x432;&#x44B;&#x448;&#x435;&#x43D;&#x438;&#x44F; &#x443;&#x441;&#x442;&#x43E;&#x439;&#x447;&#x438;&#x432;&#x43E;&#x441;&#x442;&#x438; &#x432;&#x44B;&#x440;&#x430;&#x431;&#x43E;&#x442;&#x43A;&#x438; &#x43F;&#x43E; &#x43C;&#x435;&#x440;&#x435; &#x435;&#x435; &#x43F;&#x440;&#x438;&#x431;&#x43B;&#x438;&#x436;&#x435;&#x43D;&#x438;&#x44F; &#x43A; &#x43E;&#x447;&#x438;&#x441;&#x442;&#x43D;&#x43E;&#x43C;&#x443; &#x437;&#x430;&#x431;&#x43E;&#x44E;. &#x414;&#x430;&#x43D;&#x43D;&#x430;&#x44F; &#x441;&#x442;&#x430;&#x442;&#x44C;&#x44F; &#x441;&#x43B;&#x443;&#x436;&#x438;&#x442; &#x43D;&#x430;&#x434;&#x435;&#x436;&#x43D;&#x43E;&#x439; &#x43E;&#x441;&#x43D;&#x43E;&#x432;&#x43E;&#x439; &#x434;&#x43B;&#x44F; &#x448;&#x430;&#x445;&#x442;&#x44B; &#xAB;&#x425;&#x430; &#x41B;&#x430;&#x43C;&#xBB; &#x438; &#x434;&#x440;&#x443;&#x433;&#x438;&#x445; &#x43F;&#x43E;&#x434;&#x437;&#x435;&#x43C;&#x43D;&#x44B;&#x445; &#x443;&#x433;&#x43E;&#x43B;&#x44C;&#x43D;&#x44B;&#x445; &#x448;&#x430;&#x445;&#x442; &#x412;&#x44C;&#x435;&#x442;&#x43D;&#x430;&#x43C;&#x430; &#x43F;&#x440;&#x438; &#x440;&#x430;&#x437;&#x440;&#x430;&#x431;&#x43E;&#x442;&#x43A;&#x435; &#x43F;&#x43B;&#x430;&#x43D;&#x43E;&#x432; &#x43F;&#x43E; &#x43E;&#x431;&#x435;&#x441;&#x43F;&#x435;&#x447;&#x435;&#x43D;&#x438;&#x44E; &#x443;&#x441;&#x442;&#x43E;&#x439;&#x447;&#x438;&#x432;&#x43E;&#x441;&#x442;&#x438; &#x433;&#x43E;&#x440;&#x43D;&#x44B;&#x445; &#x432;&#x44B;&#x440;&#x430;&#x431;&#x43E;&#x442;&#x43E;&#x43A;, &#x43F;&#x43E;&#x432;&#x44B;&#x448;&#x435;&#x43D;&#x438;&#x44E; &#x44D;&#x444;&#x444;&#x435;&#x43A;&#x442;&#x438;&#x432;&#x43D;&#x43E;&#x441;&#x442;&#x438; &#x434;&#x43E;&#x431;&#x44B;&#x447;&#x438; &#x438; &#x431;&#x435;&#x437;&#x43E;&#x43F;&#x430;&#x441;&#x43D;&#x43E;&#x441;&#x442;&#x438; &#x442;&#x440;&#x443;&#x434;&#x430;.&lt;/p&gt;</abstract><kwd-group xml:lang="en"><kwd>coal face</kwd><kwd>roadway</kwd><kwd>numerical simulation</kwd><kwd>stress distribution</kwd><kwd>plastic deformation</kwd></kwd-group><kwd-group xml:lang="en"><kwd>&#x443;&#x433;&#x43E;&#x43B;&#x44C;&#x43D;&#x44B;&#x439; &#x437;&#x430;&#x431;&#x43E;&#x439;</kwd><kwd>&#x432;&#x44B;&#x440;&#x430;&#x431;&#x43E;&#x442;&#x43A;&#x430;</kwd><kwd>&#x447;&#x438;&#x441;&#x43B;&#x435;&#x43D;&#x43D;&#x43E;&#x435; &#x43C;&#x43E;&#x434;&#x435;&#x43B;&#x438;&#x440;&#x43E;&#x432;&#x430;&#x43D;&#x438;&#x435;</kwd><kwd>&#x440;&#x430;&#x441;&#x43F;&#x440;&#x435;&#x434;&#x435;&#x43B;&#x435;&#x43D;&#x438;&#x435; &#x43D;&#x430;&#x43F;&#x440;&#x44F;&#x436;&#x435;&#x43D;&#x438;&#x439;</kwd></kwd-group></article-meta></front><body>&lt;p&gt;&#xD;
    Introduction&lt;/p&gt;&#xD;
&lt;p&gt;The longwall&#xD;
    mining method is the primary approach adopted by underground coal mines [Babyr, 2024; Zuev et al.,&#xD;
    2020; Szurgacz, 2024]. It is considered one of the safest, most productive, and efficient methods&#xD;
    for coal extraction. In this approach, the stability of roadways along the seam plays a crucial role&#xD;
    in production efficiency and occupational safety [Kuranov et al., 2020; Kongar-Syuryun et al.,&#xD;
    2025], especially in the area ahead of the coal face and at the intersection between the coal face&#xD;
    and the roadway along the seam [Esterhuizen et al., 2019; Zhu et al., 2022]. According to studies,&#xD;
    this area is affected by the superimposition of static stress, lateral stress, and front support&#xD;
    stress at the coal face. The roadway along the seam is susceptible to deformation due to the&#xD;
    combined effects of support pressure exerted by the advancing coal face and the tendency of roof&#xD;
    strata to shift into the excavated space. This results in a significant risk of collapse, as&#xD;
    documented in references. Additionally, this area has a large space due to the intersection of the&#xD;
    coal face and the roadway along the seam, serving as a location for multiple transport equipment&#xD;
    installations, pedestrian access, and ventilation [Burtan et al., 2022; Kongar-Syuryun et al.,&#xD;
    2025].&lt;/p&gt;&#xD;
&lt;p&gt;Therefore, a critical task for&#xD;
    underground coal mines is maintaining the stability of the roadways to ensure safe and efficient&#xD;
    production [Linh et al., 2021; He et al., 2023]. The stress distribution patterns, surrounding rock&#xD;
    displacement, and deformation of the roadway at the coal face-roadway intersection and ahead of the&#xD;
    coal face in Vietnam&#x2019;s underground coal mines have yet to be the subject of comprehensive study.&#xD;
    Consequently, the measures for ensuring roadway stability have been based on production experience&#xD;
    rather than scientific grounds [Kovalsky et al., 2025]. Currently, single hydraulic props are used&#xD;
    as the reinforcement method in these areas at underground coal mines in Vietnam (see fig. 1).&#xD;
    However, the issue of maintaining roadway dimensions for production and safety, while reducing&#xD;
    repair costs, remains unresolved.&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="184" height="214" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_280.jpg" /&gt; &lt;img width="178"&#xD;
        height="214" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_281.jpg" /&gt;&#xD;
&lt;/p&gt;&#xD;
&lt;p&gt;Fig. 1.&#xD;
    Current support conditions at the coal face-roadway intersection and ahead of the coal face in some&#xD;
    underground coal mines in Vietnam&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;A number of studies have been&#xD;
    conducted on a global scale with the objective of gain- ing insight into the deformation mechanisms&#xD;
    of roadways and the technology employed for the control of surrounding rock. A mechanical model was&#xD;
    developed to provide sup- port for roadways ahead of the coal face [Esterhuizen et al., 2020]. This&#xD;
    was achieved by analysing the distribution of support pressure in hard roof rock, with the proposed&#xD;
    solu- tion being the use of cable bolts in place of single hydraulic props. A computational model&#xD;
&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;was established to&#xD;
    evaluate the support capability and potential for roof rock subsidence. A methodology for&#xD;
    determining the parameters of the support system to secure the road- way ahead of the coal face was&#xD;
    proposed [Tyulyaeva et al., 2024]. In their research works [Liu et al., 2022; Sasaoka et al., 2020;&#xD;
    Fan et al., 2023], the authors introduced active support technology, utilising cable bolts&#xD;
    throughout the entire lifespan of the roadway. This was achieved by establishing a prediction model&#xD;
    for the deformation of surrounding rock under the impact of longwall mining. Furthermore, the stress&#xD;
    and deformation of the surrounding rock at the coal face-roadway intersection and ahead of the coal&#xD;
    face were in- vestigated, with the suggestion that the support structure of the roadway should be&#xD;
    deter- mined based on the stress distribution and deformation characteristics of the surrounding&#xD;
    rock [Qiang et al., 2023; Mao et al., 2020]. The mechanical properties of the surrounding rock were&#xD;
    studied when the roadway was supported by hydraulic props combined with cable bolts, resulting in&#xD;
    the proposal of a heterogeneous support strategy [Koteleva et al., 2021]. A corresponding support&#xD;
    theory was proposed for the roadway position ahead of the coal face, along with a method for&#xD;
    relocating hydraulic supports. This was done in order to address issues where the roof and roadway&#xD;
    anchor system fail due to high support pressure and significant roof subsidence [Zhao et al., 2024,&#xD;
    Kongar-Syuryun et al., 2025]. Their research indicated that enhancing the adaptability of support&#xD;
    systems in roadways ahead of the coal face could improve stability. In addition, a movable support&#xD;
    device for roadways ahead of the coal face was developed, along with advanced mechanized support&#xD;
    principles [Guo et al., 2024; Kongar-Syuryun et al., 2025].&lt;/p&gt;&#xD;
&lt;p&gt;The preceding&#xD;
    analysis demonstrates that the extant research agenda is oriented towards elucidating the&#xD;
    relationship between the deformation of the surrounding rock and the sup- port system. However, it&#xD;
    should be noted that geological conditions vary significantly, which in turn gives rise to notable&#xD;
    differences in the deformation patterns of the surrounding rock. The deformation of roadways in the&#xD;
    coal face-roadway intersection area and ahead of the coal face, as well as the stress distribution&#xD;
    of surrounding rock in Vietnam&#x2019;s underground coal mines, are subjects that have yet to be adequately&#xD;
    addressed in the academic literature. It is therefore evident that further research is required in&#xD;
    order to develop advanced, safe and efficient support technologies. The present study focuses on&#xD;
    Seam 10 at the Ha Lam coal mine in Vietnam. In-depth analysis is conducted on the stress&#xD;
    distribution and defor- mation of the roadway situated ahead of the coal face, as well as at the&#xD;
    coal face-roadway intersection. The findings of this research will serve as a foundation for the&#xD;
    development and implementation of mechanized support systems in this region.&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;Methods&lt;/p&gt;&#xD;
&lt;h2 style="padding-top: 6pt;padding-left: 87pt;text-indent: 0pt;text-align: left;"&gt;Characteristics of&#xD;
    the Study Area&lt;/h2&gt;&#xD;
&lt;p&gt;The Ha Lam coal mine is located in&#xD;
    Ha Long City, Quang Ninh Province, Vietnam. The coal seam in the area has a gentle dip. The roof and&#xD;
    pillar rocks are primarily composed of siltstone and shale, while in many areas, the pillar and roof&#xD;
    rocks are sandstone, which is of low strength and unstable. The geological drill column is presented&#xD;
    (see fig. 2). The study area is the mechanized longwall face CGH 10.3 of Seam 10, with a thickness&#xD;
    ranging from 2 to 4 meters. The coal seam thickness across the entire longwall face is relatively&#xD;
    stable, with an average depth of approximately 300 m. The immediate roof of the seam is shale, with&#xD;
    a thickness varying from 0 to 6 meters. The preparation of the mining block is conducted through two&#xD;
    parallel roadways along the seam, one of which is designated to serve the adjacent mining block (see&#xD;
    fig. 3). The coal pillar between the&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;two roadways has a&#xD;
    width of 25 m.&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="197" height="242" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_282.jpg" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;Fig. 2.&#xD;
    Geological drill column in the study area&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="289" height="188" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_283.jpg" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;Fig. 3.&#xD;
    Roadway layout in the study area&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;Occurrence Range of Hazardous&#xD;
    Mining Stress Zones and Load Impact on Support Structures at the Intersection Area Ahead of the Coal&#xD;
    Face&lt;/p&gt;&#xD;
&lt;p&gt;Occurrence Range of&#xD;
    Hazardous Mining Stress Zones:&lt;/p&gt;&#xD;
&lt;p&gt;In the longwall mining system, a&#xD;
    hazardous stress zone (see fig. 4) always appears at the intersection between the coal face and the&#xD;
    roadway along the seam and ahead of it. The cause is believed to be the advancement of the coal face&#xD;
    and the collapse of the roof rock in the excavated space, which disrupts the structure of the roof&#xD;
    rock mass and continuously creates new equilibrium stress states. At the front abutment stress zone&#xD;
    ahead of the coal face, mining stress reaches a peak, generating a large load, and roof sagging&#xD;
    occurs, directly impacting the support structures of the roadway along the seam. At the intersection&#xD;
    between the coal face and the roadway along the seam, mining stress diminishes, resulting in roof&#xD;
    rock collapse and a tendency for the roadway to experience severe compression and deformation [Phuc&#xD;
    et al., 2022]. According to the collapse arch hypothesis, the occurrence range of the hazardous&#xD;
    mining stress zone ahead of the coal face can be determined by formula (1):&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="77" height="1" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_284.png" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="77" height="1" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_285.png" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;(1)&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;In which: n &#x2013;&#xD;
    coefficient for calculating the influence of other longwall faces in the calculation area,&#xD;
    determined by formula (2):&lt;/p&gt;&#xD;
&lt;p&gt; &lt;/p&gt;&#xD;
&lt;p&gt;&#xD;
&lt;p&gt;&#xD;
    &lt;u&gt; &lt;/u&gt;&#xD;
&lt;/p&gt;&#xD;
&lt;p&gt; &lt;/p&gt;&#xD;
&lt;p&gt;(2)&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&#xD;
    where: coefficient accounting for the influence of adjacent longwall face (if influ- enced, n1 = 1;&#xD;
    if not influenced, n1 = 0), &lt;img width="19" height="29" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_286.gif" /&gt;&#xD;
    &#x2013; coefficient accounting for the&#xD;
    influence of the adjacent upper coal seam; m1 &#x2013; thickness of the upper coal seam, in meters; h1 &#x2013;&#xD;
    dis- tance from the upper coal seam to the calculation area, in meters.&lt;/p&gt;&#xD;
&lt;p&gt;H &#x2013; depth of the working area, in&#xD;
    meters; &#x3B1; &#x2013; inclination angle of the coal seam, in degrees; f &#x2013; average firmness coefficient of the&#xD;
    roof rock (according to the Protodiakonov scale).&lt;/p&gt;&#xD;
&lt;p&gt;Under the conditions of Seam 10&#xD;
    with a thickness of 4 m, located beneath the previously mined CGH 10.2 longwall face (n1 = 1), with&#xD;
    the upper Seam 11 having an average thickness m1 = 6.0 m, an average distance between the two seams&#xD;
    h1 = 15 m, a working depth H = 300 m, a coal seam inclination angle &#x3B1; = 50, and an average firmness&#xD;
    coefficient of the roof rock f = 4, the hazardous stress zone range L is determined from formula (1)&#xD;
    as approximately L &#x2248; 3.0 m.&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="195" height="265" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_287.jpg" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;Fig. 4.&#xD;
    Diagram for determining the range of the hazardous stress zone&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;Mining Pressure Acting on&#xD;
    Support Structures in the Hazardous Stress Zone:&lt;/p&gt;&#xD;
&lt;p&gt;Mining pressure acts on the support&#xD;
    structures of the roadway along the seam at the intersection of the coal face-roadway along the seam&#xD;
    due to the load of both coal and roof rock in the collapse arch. The mining pressure on the support&#xD;
    structures can be determined by formula (3):&lt;/p&gt;&#xD;
&lt;p&gt; &lt;/p&gt;&#xD;
&lt;p&gt;&#xD;
&lt;p&gt;&#xD;
    &lt;u&gt; &lt;/u&gt; (3)&#xD;
&lt;/p&gt;&#xD;
&lt;p&gt; &lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;where: &#x3B3;t &#x2013; unit weight of coal,&#xD;
    T/m3; &#x3B3;&#x111; &#x2013; average unit weight of roof rock, T/m3;&#xD;
    Bt &#x2013; depth of the failure arch in the coal layer, which can be determined by formula (4):&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="21" height="1" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_288.png" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt; &#xD;
&lt;/p&gt;&#xD;
&lt;p&gt; &lt;/p&gt;&#xD;
&lt;p&gt;&#xD;
&lt;p&gt;&#xD;
&lt;/p&gt;&#xD;
&lt;p&gt;(4)&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;where: &#x3B7; &#x2013;&#xD;
    coefficient characterizing the inclination angle of the sliding prism; h &#x2013; width of the exposed coal&#xD;
    surface around the perimeter of the roadway, m; Kn &#x2013; stress concentration coefficient based on the&#xD;
    roadway shape, depending on the ratio of the roadway width in the inclined direction of the seam (A)&#xD;
    to the width of the exposed coal surface (h); ft &#x2013; coal firmness coefficient; k &#x2013; coefficient&#xD;
    accounting for the reduction in coal firmness over time; B&#x111; &#x2013; height of the failure arch in the roof&#xD;
    rock, determined by formula (5):&lt;/p&gt;&#xD;
&lt;p&gt; &lt;/p&gt;&#xD;
&lt;p&gt;&#xD;
&lt;p&gt;&#xD;
&lt;/p&gt;&#xD;
&lt;p&gt;&#xD;
&lt;/p&gt;&#xD;
&lt;p&gt;(5)&lt;/p&gt;&#xD;
&lt;p&gt;where: A &#x2013; roadway&#xD;
    width in the dip direction of the coal seam, m; f&#x111; &#x2013; average firmness coefficient of roof rock in&#xD;
    the collapse-prone area.&lt;/p&gt;&#xD;
&lt;p&gt;Y&#x111; &#x2013; allowable roof sag without&#xD;
    requiring additional support, Y&#x111; = 30-45mm; Y &#x2013; roof sag due to the influence of the coal face,&#xD;
    determined by the empirical formula (6):&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="78" height="1" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_289.png" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="115" height="4" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_290.png" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="78" height="1" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_291.png" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt; &lt;/p&gt;&#xD;
&lt;p&gt;&#xD;
&lt;ul id="l87"&gt;&#xD;
    &lt;li style="padding-top: 6pt;padding-bottom: 3pt;padding-left: 317pt;text-indent: -6pt;text-align: left;"&gt;&#xD;
        &lt;p&gt;(6)&lt;/p&gt;&#xD;
    &lt;/li&gt;&#xD;
&lt;/ul&gt;&#xD;
&lt;/li&gt;&#xD;
&lt;/ol&gt;&#xD;
&lt;/ol&gt;&#xD;
&lt;p&gt;&lt;img width="67" height="1" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_292.png" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;where X &#x2013; coal face width, m;&#xD;
    V &#x2013; average daily coal face advance rate; C &#x2013; width of a shear cut, m.&lt;/p&gt;&#xD;
&lt;p&gt;Under the conditions at coal face CGH 10.3, the&#xD;
    calculated mining pressure acting on the support structures is q = 22,3 T/m2.&lt;/p&gt;&#xD;
&lt;p&gt;This calculation result is quite consistent&#xD;
    with field measurements at the transport roadway. However, on the ventilation roadway side, there are&#xD;
    significant deviations (due to the absence of parameters reflecting the influence of the coal pillar and the&#xD;
    space mined out by the adjacent coal face). To clarify further, the method of numerical simulation analysis has&#xD;
    been applied to this study.&lt;/p&gt;&#xD;
&lt;h2 style="padding-top: 5pt;padding-left: 116pt;text-indent: 0pt;text-align: left;"&gt;Development of the Numerical&#xD;
    Simulation Model&lt;/h2&gt;&#xD;
&lt;p&gt;The Flac3D software was used to simulate the&#xD;
    longwall mining process. Flac3D, developed by ITASCA, is designed for continuous modeling of geomechanical&#xD;
    mining environments. Based on the geological conditions of Seam 10 at the Ha Lam coal mine, a typical geological&#xD;
    model was established. The lithology and thickness of the strata were selected and the chosen mechanical&#xD;
    properties of the surrounding rock (see table 1). The vertical and horizontal displacements at the base of the&#xD;
    model were fixed at zero, while the horizontal displacements of the four sides were constrained. Based on the&#xD;
    rock mass&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="280" height="252" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_293.jpg" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;density of 0.025 MN/m&#xB3;, a vertical static&#xD;
    stress of 7.5 MPa was applied to the top boundary of the model to simulate the static load of the rock mass.&#xD;
    Gravity was included in the model, and the Mohr-Coulomb failure criterion was used for the numerical simulation&#xD;
    (see fig. 5).&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;Fig. 5. Numerical simulation model&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;The simulation model was constructed based on a&#xD;
    case study of Seam 10 at the&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;Ha Lam coal&#xD;
    mine. The seam has an average thickness of 4.0 m, with an immediate roof and floor consisting of shale with a&#xD;
    thickness of 3 m. The main roof is siltstone with a thickness of 10 m. The roadway is located 300 m below the&#xD;
    surface, with a width of 4 m and a height of 3 m, and the coal pillar width is 25 m.&lt;/p&gt;&#xD;
&lt;p&gt;Table 1&lt;/p&gt;&#xD;
&lt;h3 style="padding-top: 5pt;padding-left: 245pt;text-indent: -117pt;text-align: left;"&gt;Lithology and mechanical&#xD;
    properties of rocks applied in the model [Cai et al., 2024]&lt;/h3&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;table&gt;&#xD;
    &lt;tr&gt;&#xD;
        &lt;td&#xD;
            style="width:142pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;Parameter&#xD;
                name&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:70pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                Sand-stone&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                Silt-stone&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                Shale&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;Coal&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
    &lt;/tr&gt;&#xD;
    &lt;tr&gt;&#xD;
        &lt;td&#xD;
            style="width:142pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;Tensile&#xD;
                Strength (MPa)&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:70pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                1.6&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                0.9&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                1.2&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;0.4&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
    &lt;/tr&gt;&#xD;
    &lt;tr&gt;&#xD;
        &lt;td&#xD;
            style="width:142pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;Bulk&#xD;
                Modulus (GPa)&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:70pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                7.456&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                2.333&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                1.822&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;0.748&#xD;
            &lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
    &lt;/tr&gt;&#xD;
    &lt;tr&gt;&#xD;
        &lt;td&#xD;
            style="width:142pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;Shear&#xD;
                Modulus (GPa)&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:70pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                3.244&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                0.955&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                0.607&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;0.484&#xD;
            &lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
    &lt;/tr&gt;&#xD;
    &lt;tr&gt;&#xD;
        &lt;td&#xD;
            style="width:142pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;Poisson&#x2019;s&#xD;
                Ratio, &#x3BD;&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:70pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                0.31&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                0.32&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                0.35&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;0.26&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
    &lt;/tr&gt;&#xD;
    &lt;tr&gt;&#xD;
        &lt;td&#xD;
            style="width:142pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;Cohesion, c&#xD;
                (MPa)&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:70pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                3.2&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                2.1&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                1.8&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;1.5&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
    &lt;/tr&gt;&#xD;
    &lt;tr&gt;&#xD;
        &lt;td&#xD;
            style="width:142pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;Friction&#xD;
                Angle, (&#xB0;)&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:70pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                34&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                30&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                26&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                19&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
    &lt;/tr&gt;&#xD;
    &lt;tr&gt;&#xD;
        &lt;td&#xD;
            style="width:142pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;Unit Weight&#xD;
                (kg/m&#xB3;)&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:70pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                2780&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                2550&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;&#xD;
                2250&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
        &lt;td&#xD;
            style="width:71pt;border-top-style:solid;border-top-width:1pt;border-top-color:#231F20;border-left-style:solid;border-left-width:1pt;border-left-color:#231F20;border-bottom-style:solid;border-bottom-width:1pt;border-bottom-color:#231F20;border-right-style:solid;border-right-width:1pt;border-right-color:#231F20"&gt;&#xD;
            &lt;p&gt;1450&lt;/p&gt;&#xD;
        &lt;/td&gt;&#xD;
    &lt;/tr&gt;&#xD;
&lt;/table&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;The numerical simulation&#xD;
    process was conducted in the following manner: (1) Setting up the static stress state and achieving the initial&#xD;
    equilibrium state; (2) Excavating the transport and ventilation roadways along the seam at the coal face; (3)&#xD;
    Mining the CGH&lt;/p&gt;&#xD;
&lt;p&gt;10.2 coal face; (4) Mining the CGH 10.3 coal&#xD;
    face. During the simulation, the stress-strain state of the transport and ventilation roadways along the seam&#xD;
    was extracted [Kongar- Syuryun et al., 2024; Kovalskiy et al., 2024; Tyulyaeva et al., 2024].&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;Simulation and Analysis Results&lt;/p&gt;&#xD;
&lt;p&gt;Stress&#xD;
    Distribution Patterns Ahead of the Coal Face and at the Coal Face-Roadway Intersection&lt;/p&gt;&#xD;
&lt;p&gt;In the area of the&#xD;
    intersection and in advance of the working face, the stress field within the surrounding rock mass becomes&#xD;
    disrupted [Han et al., 2023; Kazanin, 2023; Li et al., 2023]. The stress distribution patterns at the&#xD;
    intersection and ahead of the working face (see fig. 6). It can be observed that the stress distribution is&#xD;
    asymmetric due to the influence of front and lateral support pressures [Zeng et al., 2024; Linh et al., 2025;&#xD;
    Linh et al., 2024]. The peak stress near the coal wall or the primary coal pillar is typically located at the&#xD;
    intersection between the coal face and the roadway along the seam. Conversely, the peak stress near the coal&#xD;
    wall of the CGH-10.3 coal face is distributed 15 m ahead of the face.&lt;/p&gt;&#xD;
&lt;p&gt;At the transport roadway of&#xD;
    coal face CGH-10.3, on the left side, significant stress concentration occurs at the coal face-roadway&#xD;
    intersection and extends over a 35-meter length of the roadway ahead of the coal face. The maximum vertical&#xD;
    stress reaches&lt;/p&gt;&#xD;
&lt;p&gt;15.8 MPa at the intersection,&#xD;
    then increases to 17.2 MPa and decreases to 15.7 MPa at distances of 9 m and 24 m ahead of the coal face,&#xD;
    respectively. The maximum vertical stress concentration factor reaches k=2.3. Similarly, large horizontal stress&#xD;
    concentration is also found at this location. The horizontal stress value reaches 7.89 MPa at the intersection,&#xD;
    then increases to 8.6 MPa and decreases to 8.0 MPa at distances of 10 m and 25 m ahead of the coal face,&#xD;
    respectively.&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="275" height="247" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_294.jpg" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;Fig. 6.&#xD;
    Characteristics of stress distribution ahead of the coal face and at the coal face-roadway intersection: a &#x2013;&#xD;
    Vertical stress distribution; b &#x2013; Horizontal stress distribution&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;In contrast to the left side, on the right side&#xD;
    of the transport roadway, stress is significantly lower at the coal face-roadway intersection (vertical stress&#xD;
    is 4.5 MPa, and horizontal stress is 2.3 MPa). The peak stress is found 25 m ahead of the coal face, with values&#xD;
    of 16.4 MPa for vertical stress and 8.1 MPa for horizontal stress. Thus, it can be observed that due to the&#xD;
    influence of support pressure, both vertical and horizontal stresses are distributed asymmetrically on the two&#xD;
    sides of the roadway. This distribution leads to the formation of eccentric compressive forces acting on the&#xD;
    supports, making them more prone to failure.&lt;/p&gt;&#xD;
&lt;p&gt;Stress concentration intensifies when there is&#xD;
    a resonance between the front support pressure at the coal face and the support pressure formed by the&#xD;
    previously mined-out space. Specifically, in this study, stress distribution around the ventilation roadway of&#xD;
    coal face CGH-10.3 was examined. On the right side of the ventilation roadway (near the coal pillar), stress&#xD;
    concentration was observed from the coal face-roadway intersection and developed over a 60-meter length of the&#xD;
    roadway. At the intersection, the recorded vertical stress on the right side was 15.7 MPa (with a vertical&#xD;
    stress concentration factor of k=2.1) and horizontal stress was 6.9 MPa. At a position 15 m ahead of the coal&#xD;
    face, vertical stress increased to a peak of 18.3 MPa (with a stress concentration factor of k=2.44) and&#xD;
    horizontal stress was 7.9 MPa. In contrast, on the left side of the ventilation roadway of coal face CGH-10.3,&#xD;
    the vertical stress at the coal face-roadway intersection was only 2.2 MPa, and the horizontal stress was 1.05&#xD;
    MPa. This can be explained by the formation pattern of front support pressure at the coal face. The coal mass&#xD;
    adjacent to the intersection lies within the failure zone due to the intense development of a fracture system,&#xD;
    creating a stress relief zone. Subsequently, vertical stress peaks at 20.3 MPa (with a stress concentration&#xD;
    factor of k=2.7) at a distance of 27 m, and then decreases to 19.3 MPa (with a stress concentration factor of&#xD;
    k=2.57) at a distance of 50 m ahead of the coal face. Thus, vertical stress concentration on the left side is&#xD;
    1.1 times higher. Similarly, horizontal stress peaks at 10.1 MPa at a distance of 27 m ahead of the coal face.&#xD;
    Horizontal stress remains high (9.9 MPa) even further from the coal face.&lt;/p&gt;&#xD;
&lt;p&gt;Thus, the asymmetric&#xD;
    development of stress on both sides of the roadway was found in both the transport and ventilation roadways of&#xD;
    coal face CGH-10.3. This formation mechanism causes uneven displacement of the rock mass, resulting in&#xD;
    unbalanced forces&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;acting on the supports.&#xD;
    Additionally, the sustained high horizontal stress is the primary cause of roadway compression ahead of the coal&#xD;
    face.&lt;/p&gt;&#xD;
&lt;p&gt;When considering the stress environment in the&#xD;
    roof rock above the roadway, the distribution between horizontal and vertical stresses in the rock mass (see&#xD;
    fig. 7).&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="477" height="356" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_295.jpg" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;Fig. 7. Stress in&#xD;
    the rock masses 3 meters above the roadway: a &#x2013; Vertical stress distribution, MPa; b &#x2013; Horizontal stress&#xD;
    distribution, MPa; c &#x2013; Horizontal/Vertical stress ratio, MPa&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;The reduced stress magnitude in the rock&#xD;
    stratum located 3 m above the roadway is a consequence of its positioning within the stress relief region of the&#xD;
    collapse arch structure. In the collapse arch, a system of fractures develops significantly in the roof rock,&#xD;
    causing the rock layers to separate and crumple. Although the stress is not high, the entire rock mass within&#xD;
    the collapse arch will form a direct load acting on the roadway&#x2019;s support system. The stress distribution still&#xD;
    follows the pattern with peak stress located 10 m ahead of the coal face. Comparative analysis reveals elevated&#xD;
    roof rock stress in the ventilation roadway relative to the transport roadway. This stress elevation is a&#xD;
    consequence of the combined loading from dual support pressure zones in the ventilation roadway. The first&#xD;
    component is the lateral support pressure from the adjacent mined-out area above, which acts on the coal pillar&#xD;
    and ventilation roadway. This pressure formed during the coal extraction and roof collapse in the mining space&#xD;
    of the adjacent CGH-10.2 coal face. As the CGH-10.3 coal face advances forward, the ventilation roadway falls&#xD;
    within the second support pressure zone - the front support pressure of coal face CGH-10.3. The resonance of&#xD;
    both support pressure zones expands the collapse arch above the roadway and increases the load from the roof&#xD;
    rock acting on the support system. This explains why the support system of the ventilation roadway experiences&#xD;
    more severe destruction and deformation compared to the transport roadway.&lt;/p&gt;&#xD;
&lt;p&gt;Horizontal stress is consistently greater than&#xD;
    vertical stress in the zone ahead of the coal face (see fig. 7a and fig. 7b). As the distance from the coal face&#xD;
    increases, the ratio of horizontal to vertical stress rises. At the intersection between the coal face and the&#xD;
&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;roadway along the seam, this&#xD;
    ratio tends to approach the value of hydrostatic pressure (k=1). This may be because the roof rock mass has&#xD;
    reached its critical displacement, causing a new equilibrium state to be achieved behind the intersection. With&#xD;
    a horizontal- to-vertical stress ratio greater than 1, the rock mass tends to shift inward toward the roadway.&#xD;
    This is the primary cause of roadway deformation and support system failure near the coal face.&lt;/p&gt;&#xD;
&lt;p&gt;Development&#xD;
    Patterns of the Plastic Deformation Zone Around the Roadway&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="212" height="446" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_296.png" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;The distribution&#xD;
    characteristics of the plastic zones in the surrounding rock at various positions of the ventilation and&#xD;
    transport roadways of coal face CGH-10.3 (see fig. 8 and fig. 9). It can be observed that the shape and extent&#xD;
    of the plastic zone in the surrounding rock of these two roadways are entirely different.&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="186" height="378" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_297.png" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;a &#x2013; 0 m; b &#x2013; 10 m; c &#x2013; 20 m; d &#x2013; 30 m&#xD;
&lt;/p&gt;&#xD;
&lt;p&gt;1 &#x2013; Ventilation roadway of coal face&#xD;
    CGH-10.3 2 &#x2013; Coal pillar&lt;/p&gt;&#xD;
&lt;p&gt;3 &#x2013; Transport roadway of coal face&#xD;
    CGH-10.2 4 &#x2013; Coal face CGH-10.3&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;Fig. 8. Distribution of the plastic&#xD;
    zone in the rock surrounding the ventilation roadway at different positions ahead of the working face&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;The plastic deformation zone in the rock mass&#xD;
    within the ventilation roadway of coal face CGH-10.3 has reached a point where it covers the entire roadway area&#xD;
    and coal pillar. The roadway is subjected to lateral mining stress originating from the previous coal face and&#xD;
    front support pressure exerted by the current coal face. The extent of the plastic zone in the surrounding rock&#xD;
    is markedly increased in the vicinity of the coal face. At the intersection, the plastic zone has developed&#xD;
    extensively throughout the rock mass and coal pillar, resulting in significant deformation of the roadway. A&#xD;
    minor elastic zone&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="179" height="440" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_298.png" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;has manifested in the roof rock&#xD;
    above the coal face at a distance of approximately 10 m. Nevertheless, within a 15-metre radius surrounding the&#xD;
    roadway, the plastic deformation zone, characterized by the formation of fractures, can still be observed. At a&#xD;
    distance of 20 m ahead of the coal face, the elastic zone expands and persists in the roof rock, situated at a&#xD;
    height of 3 m above the roadway. The plastic deformation zone in the rock mass continues to expand on both sides&#xD;
    and beneath the roadway. At a distance of 30 m from the coal face, an elastic zone is visible on the right side&#xD;
    and beneath the roadway. However, in general, the extent of the plastic zone in the vicinity of the coal pillar&#xD;
    (on the left side) is greater than that on the coal wall side (on the right side), with both zones distributed&#xD;
    asymmetrically. The extent of the plastic deformation zone is observed to span the entire coal pillar, extending&#xD;
    for a distance of 25 m. The mining of the previous coal face has been identified as a factor that has disturbed&#xD;
    the stress field in the surrounding rock mass. The ratio of horizontal to vertical stress is estimated to be&#xD;
    approximately 1.5, and the direction of the principal stress is also observed to be skewed. As a result, the&#xD;
    plastic zone in the surrounding rock exhibits an asymmetric distribution.&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;&lt;img width="191" height="378" alt="image" src="&#x413;&#x435;&#x43E;&#x43B;_&#x436;&#x443;&#x440;&#x43D;__&#x2116;4_2025_&#x441; &#x43E;&#x431;&#x43B;_/Image_299.png" /&gt;&lt;/p&gt;&#xD;
&lt;p&gt;a &#x2013;&#xD;
    0 m; b &#x2013; 10 m; c &#x2013; 20 m; d &#x2013; 30 m&lt;/p&gt;&#xD;
&lt;p&gt;1 &#x2013; Transport roadway of coal face&#xD;
    CGH-10.3 2 &#x2013; Coal face CGH-10.3&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;Fig. 9. Distribution of the plastic&#xD;
    zone in the rock surrounding the transport roadway at different positions ahead of the working face&lt;/p&gt;&#xD;
&lt;p&gt;&lt;/p&gt;&#xD;
&lt;p&gt;The transport roadway on both sides of coal face&#xD;
    CGH-10.3 is comprised of solid coal, exhibiting no discernible impact from the mining activities associated with&#xD;
    coal face CGH-&lt;/p&gt;&#xD;
&lt;ol id="l88"&gt;&#xD;
    &lt;ol id="l89"&gt;&#xD;
        &lt;li style="padding-left: 70pt;text-indent: 0pt;text-align: justify;"&gt;&#xD;
            &lt;p&gt;The distribution of the plastic zone in the surrounding rock remains&#xD;
                asymmetric in proximity to the coal face, extending approximately 10 m beyond the active working&#xD;
                area. The plastic zone in the roof rock is primarily developed on the left side in the vicinity of&#xD;
                the coal wall, which is in close proximity to coal face CGH-10.3. As the distance from the&lt;/p&gt;&#xD;
            &lt;p&gt;&lt;/p&gt;&#xD;
            &lt;p&gt;working face&#xD;
                increases, the asymmetric distribution of the plastic zone in the surrounding rock transitions&#xD;
                towards a more symmetric distribution. The distribution of the roof, floor, and plastic zone on both&#xD;
                sides of the roadway is symmetrical.&lt;/p&gt;&#xD;
            &lt;p&gt;Therefore, in closer proximity to&#xD;
                the coal face, the surrounding rock mass of the roadway is situated within a non-uniform stress&#xD;
                field (horizontal/vertical stress ratio&lt;/p&gt;&#xD;
            &lt;p&gt;&#x2260; 1), wherein the plastic zone in&#xD;
                the surrounding rock transitions from symmetric to asymmetric. The horizontal-to-vertical stress&#xD;
                ratio can exceed 2.5, with the plastic zone developing throughout the surrounding rock mass over a&#xD;
                range of approximately 15 m. The zone of plastic failure primarily develops on the coal pillar side&#xD;
                (in the ventilation roadway) and on the coal wall side of coal face CGH-10.3 (in the transport&#xD;
                roadway). The zone of plastic deformation exhibits considerable growth within a distance of 30 m in&#xD;
                advance of the coal face. Approaching the coal face results in an increase in the extent of the&#xD;
                plastic deformation zone. This expansion increases the susceptibility to rock bursts, bilateral&#xD;
                roadway compression, and support system deterioration. In light of these findings, it is possible to&#xD;
                propose the implementation of enhanced support systems and the selection of appropriate supports in&#xD;
                order to guarantee the safety of the roadway situated in advance of the working face.&lt;/p&gt;&#xD;
            &lt;p&gt;&lt;/p&gt;&#xD;
            &lt;p&gt;Conclusion&lt;/p&gt;&#xD;
            &lt;p&gt;The proposed&#xD;
                technical solution serves as a reliable reference for Ha Lam coal mine and other underground coal&#xD;
                mines in Vietnam in developing plans to ensure roadway stability, improve production efficiency, and&#xD;
                enhance occupational safety. This solution allows for the delineation of the following conclusions:&#xD;
            &lt;/p&gt;&#xD;
            &lt;ul id="l90"&gt;&#xD;
                &lt;li style="padding-left: 99pt;text-indent: 17pt;text-align: justify;"&gt;&#xD;
                    &lt;p&gt;Due to the influence of front and lateral support pressures, the&#xD;
                        coal face-roadway intersection and the roadway ahead of the coal face are often in an&#xD;
                        asymmetric stress field. The ratio of horizontal to vertical stress in the roof rock of the&#xD;
                        roadway can reach up to 2.5, and the maximum vertical stress can be 2.57 times greater than&#xD;
                        hydrostatic stress. This leads to asymmetric damage in the roof rock of the roadway.&lt;/p&gt;&#xD;
                &lt;/li&gt;&#xD;
                &lt;li style="padding-left: 99pt;text-indent: 17pt;text-align: justify;"&gt;&#xD;
                    &lt;p&gt;The development range of the plastic deformation zone can extend&#xD;
                        over 15 m in the surrounding rock of the roadway and up to 30 m ahead of the working face.&#xD;
                        Particularly at the coal face-roadway intersection, the surrounding rock mass is almost&#xD;
                        entirely disturbed, with the collapse arch of the roof rock expanding and increasing the&#xD;
                        load on the roadway support system. Consequently, the risk of rock bursts and support&#xD;
                        failure increases on the roadway ahead of the coal face.&lt;/p&gt;&#xD;
                &lt;/li&gt;&#xD;
                &lt;li style="padding-left: 99pt;text-indent: 17pt;text-align: justify;"&gt;&#xD;
                    &lt;p&gt;Based on the case study of Seam 10 at the Ha Lam mine, Vietnam,&#xD;
                        within 30 m ahead of the coal face, the roadway must be supplemented with high-load bearing&#xD;
                        supports to ensure the stability of the roof rock in the plastic deformation zone.&#xD;
                        Specifically, suitable supports must be selected for the coal face-roadway intersection,&#xD;
                        where the surrounding rock mass of the roadway is completely disturbed.&lt;/p&gt;&#xD;
                &lt;/li&gt;&#xD;
            &lt;/ul&gt;&#xD;
        &lt;/li&gt;&#xD;
    &lt;/ol&gt;&#xD;
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