An Analytical Elastic Solution for Right-Angle Trapezoidal Opening in Steeply Inclined Coal Seam
In the process of underground mining, steeply inclined rocks or coal seams are often encountered, forming the openings of right-angle trapezoid. According to the geological conditions of a mining project in China, an analytical elastic solution of stress and displacement around right-angle trapezoid...
Gespeichert in:
Veröffentlicht in: | Processes 2022-01, Vol.10 (1), p.110 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | |
---|---|
container_issue | 1 |
container_start_page | 110 |
container_title | Processes |
container_volume | 10 |
creator | Bu, Wankui Xu, Hui Ji, Ming |
description | In the process of underground mining, steeply inclined rocks or coal seams are often encountered, forming the openings of right-angle trapezoid. According to the geological conditions of a mining project in China, an analytical elastic solution of stress and displacement around right-angle trapezoidal opening in a homogeneous, isotropic, and linear elastic geomaterial is presented, which is based on the evaluation of the conformal mapping representation by an appropriate numerical calculation and the complex potential functions. The different results from other shaped openings are shown as follows. In a right-angle trapezoidal opening, the maximum displacements of roof falling occur on the low side, while the most horizontal displacements on the low side are around the roof and the most horizontal displacements on the high side are around the middle of the high side in this opening. These results are also compared with the numerical calculations in FLAC software, illustrating that the solution may be easily applied to rock mechanics or rock engineering for understanding the deformation of floor heave and roof falling down. The solution is also suitable for optimum design of bolt supporting in a right-angle trapezoidal opening, which is different from the traditional concept of symmetrical bolt supporting. Finally, a methodology is proposed for the estimation of conformal mapping coefficients for a given cross-sectional shape of an opening without symmetrical axis. |
doi_str_mv | 10.3390/pr10010110 |
format | Article |
fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2621348240</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2621348240</sourcerecordid><originalsourceid>FETCH-LOGICAL-c295t-afa56cde5542dd3d18497bb3200be74912c94ed3e6fb6ba53933920f5c25c24d3</originalsourceid><addsrcrecordid>eNpNkE1LAzEYhIMoWGov_oKAN2E1n7vNcSlVC4WCrec1m2RrSpqsyfaw_nojFXR4Yebw8MIMALcYPVAq0GMfMUIYYYwuwIQQUhWiwtXlv3wNZikdUJbAdM7LCXivPay9dONglXRw6WTKCW6DOw02eNiFCF_t_mMoar93Bu6i7M1XsDrDm9546_fQergdjOndCFdeOeuNhouQga2Rxxtw1UmXzOzXp-DtablbvBTrzfNqUa8LRQQfCtlJXiptOGdEa6rxnImqbSlBqDUVE5gowYympuzaspWcilyZoI4rko9pOgV35799DJ8nk4bmEE4xN0sNKQmmbE4YytT9mVIxpBRN1_TRHmUcG4yanxGbvxHpNzUpY3M</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2621348240</pqid></control><display><type>article</type><title>An Analytical Elastic Solution for Right-Angle Trapezoidal Opening in Steeply Inclined Coal Seam</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>MDPI - Multidisciplinary Digital Publishing Institute</source><creator>Bu, Wankui ; Xu, Hui ; Ji, Ming</creator><creatorcontrib>Bu, Wankui ; Xu, Hui ; Ji, Ming</creatorcontrib><description>In the process of underground mining, steeply inclined rocks or coal seams are often encountered, forming the openings of right-angle trapezoid. According to the geological conditions of a mining project in China, an analytical elastic solution of stress and displacement around right-angle trapezoidal opening in a homogeneous, isotropic, and linear elastic geomaterial is presented, which is based on the evaluation of the conformal mapping representation by an appropriate numerical calculation and the complex potential functions. The different results from other shaped openings are shown as follows. In a right-angle trapezoidal opening, the maximum displacements of roof falling occur on the low side, while the most horizontal displacements on the low side are around the roof and the most horizontal displacements on the high side are around the middle of the high side in this opening. These results are also compared with the numerical calculations in FLAC software, illustrating that the solution may be easily applied to rock mechanics or rock engineering for understanding the deformation of floor heave and roof falling down. The solution is also suitable for optimum design of bolt supporting in a right-angle trapezoidal opening, which is different from the traditional concept of symmetrical bolt supporting. Finally, a methodology is proposed for the estimation of conformal mapping coefficients for a given cross-sectional shape of an opening without symmetrical axis.</description><identifier>ISSN: 2227-9717</identifier><identifier>EISSN: 2227-9717</identifier><identifier>DOI: 10.3390/pr10010110</identifier><language>eng</language><publisher>Basel: MDPI AG</publisher><subject>Civil engineering ; Coal ; Coal mining ; Conformal mapping ; Deformation ; Displacement ; Elastic analysis ; Mapping ; Mining engineering ; Numerical analysis ; Rock mechanics ; Roofs ; Underground mining</subject><ispartof>Processes, 2022-01, Vol.10 (1), p.110</ispartof><rights>2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c295t-afa56cde5542dd3d18497bb3200be74912c94ed3e6fb6ba53933920f5c25c24d3</citedby><cites>FETCH-LOGICAL-c295t-afa56cde5542dd3d18497bb3200be74912c94ed3e6fb6ba53933920f5c25c24d3</cites><orcidid>0000-0002-5549-0639</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,778,782,27911,27912</link.rule.ids></links><search><creatorcontrib>Bu, Wankui</creatorcontrib><creatorcontrib>Xu, Hui</creatorcontrib><creatorcontrib>Ji, Ming</creatorcontrib><title>An Analytical Elastic Solution for Right-Angle Trapezoidal Opening in Steeply Inclined Coal Seam</title><title>Processes</title><description>In the process of underground mining, steeply inclined rocks or coal seams are often encountered, forming the openings of right-angle trapezoid. According to the geological conditions of a mining project in China, an analytical elastic solution of stress and displacement around right-angle trapezoidal opening in a homogeneous, isotropic, and linear elastic geomaterial is presented, which is based on the evaluation of the conformal mapping representation by an appropriate numerical calculation and the complex potential functions. The different results from other shaped openings are shown as follows. In a right-angle trapezoidal opening, the maximum displacements of roof falling occur on the low side, while the most horizontal displacements on the low side are around the roof and the most horizontal displacements on the high side are around the middle of the high side in this opening. These results are also compared with the numerical calculations in FLAC software, illustrating that the solution may be easily applied to rock mechanics or rock engineering for understanding the deformation of floor heave and roof falling down. The solution is also suitable for optimum design of bolt supporting in a right-angle trapezoidal opening, which is different from the traditional concept of symmetrical bolt supporting. Finally, a methodology is proposed for the estimation of conformal mapping coefficients for a given cross-sectional shape of an opening without symmetrical axis.</description><subject>Civil engineering</subject><subject>Coal</subject><subject>Coal mining</subject><subject>Conformal mapping</subject><subject>Deformation</subject><subject>Displacement</subject><subject>Elastic analysis</subject><subject>Mapping</subject><subject>Mining engineering</subject><subject>Numerical analysis</subject><subject>Rock mechanics</subject><subject>Roofs</subject><subject>Underground mining</subject><issn>2227-9717</issn><issn>2227-9717</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNpNkE1LAzEYhIMoWGov_oKAN2E1n7vNcSlVC4WCrec1m2RrSpqsyfaw_nojFXR4Yebw8MIMALcYPVAq0GMfMUIYYYwuwIQQUhWiwtXlv3wNZikdUJbAdM7LCXivPay9dONglXRw6WTKCW6DOw02eNiFCF_t_mMoar93Bu6i7M1XsDrDm9546_fQergdjOndCFdeOeuNhouQga2Rxxtw1UmXzOzXp-DtablbvBTrzfNqUa8LRQQfCtlJXiptOGdEa6rxnImqbSlBqDUVE5gowYympuzaspWcilyZoI4rko9pOgV35799DJ8nk4bmEE4xN0sNKQmmbE4YytT9mVIxpBRN1_TRHmUcG4yanxGbvxHpNzUpY3M</recordid><startdate>20220101</startdate><enddate>20220101</enddate><creator>Bu, Wankui</creator><creator>Xu, Hui</creator><creator>Ji, Ming</creator><general>MDPI AG</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JG9</scope><scope>KB.</scope><scope>LK8</scope><scope>M7P</scope><scope>PDBOC</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><orcidid>https://orcid.org/0000-0002-5549-0639</orcidid></search><sort><creationdate>20220101</creationdate><title>An Analytical Elastic Solution for Right-Angle Trapezoidal Opening in Steeply Inclined Coal Seam</title><author>Bu, Wankui ; Xu, Hui ; Ji, Ming</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c295t-afa56cde5542dd3d18497bb3200be74912c94ed3e6fb6ba53933920f5c25c24d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Civil engineering</topic><topic>Coal</topic><topic>Coal mining</topic><topic>Conformal mapping</topic><topic>Deformation</topic><topic>Displacement</topic><topic>Elastic analysis</topic><topic>Mapping</topic><topic>Mining engineering</topic><topic>Numerical analysis</topic><topic>Rock mechanics</topic><topic>Roofs</topic><topic>Underground mining</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bu, Wankui</creatorcontrib><creatorcontrib>Xu, Hui</creatorcontrib><creatorcontrib>Ji, Ming</creatorcontrib><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>Materials Research Database</collection><collection>Materials Science Database</collection><collection>ProQuest Biological Science Collection</collection><collection>Biological Science Database</collection><collection>Materials Science Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><jtitle>Processes</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bu, Wankui</au><au>Xu, Hui</au><au>Ji, Ming</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Analytical Elastic Solution for Right-Angle Trapezoidal Opening in Steeply Inclined Coal Seam</atitle><jtitle>Processes</jtitle><date>2022-01-01</date><risdate>2022</risdate><volume>10</volume><issue>1</issue><spage>110</spage><pages>110-</pages><issn>2227-9717</issn><eissn>2227-9717</eissn><abstract>In the process of underground mining, steeply inclined rocks or coal seams are often encountered, forming the openings of right-angle trapezoid. According to the geological conditions of a mining project in China, an analytical elastic solution of stress and displacement around right-angle trapezoidal opening in a homogeneous, isotropic, and linear elastic geomaterial is presented, which is based on the evaluation of the conformal mapping representation by an appropriate numerical calculation and the complex potential functions. The different results from other shaped openings are shown as follows. In a right-angle trapezoidal opening, the maximum displacements of roof falling occur on the low side, while the most horizontal displacements on the low side are around the roof and the most horizontal displacements on the high side are around the middle of the high side in this opening. These results are also compared with the numerical calculations in FLAC software, illustrating that the solution may be easily applied to rock mechanics or rock engineering for understanding the deformation of floor heave and roof falling down. The solution is also suitable for optimum design of bolt supporting in a right-angle trapezoidal opening, which is different from the traditional concept of symmetrical bolt supporting. Finally, a methodology is proposed for the estimation of conformal mapping coefficients for a given cross-sectional shape of an opening without symmetrical axis.</abstract><cop>Basel</cop><pub>MDPI AG</pub><doi>10.3390/pr10010110</doi><orcidid>https://orcid.org/0000-0002-5549-0639</orcidid><oa>free_for_read</oa></addata></record> |
fulltext | fulltext |
identifier | ISSN: 2227-9717 |
ispartof | Processes, 2022-01, Vol.10 (1), p.110 |
issn | 2227-9717 2227-9717 |
language | eng |
recordid | cdi_proquest_journals_2621348240 |
source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; MDPI - Multidisciplinary Digital Publishing Institute |
subjects | Civil engineering Coal Coal mining Conformal mapping Deformation Displacement Elastic analysis Mapping Mining engineering Numerical analysis Rock mechanics Roofs Underground mining |
title | An Analytical Elastic Solution for Right-Angle Trapezoidal Opening in Steeply Inclined Coal Seam |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-15T13%3A08%3A37IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=An%20Analytical%20Elastic%20Solution%20for%20Right-Angle%20Trapezoidal%20Opening%20in%20Steeply%20Inclined%20Coal%20Seam&rft.jtitle=Processes&rft.au=Bu,%20Wankui&rft.date=2022-01-01&rft.volume=10&rft.issue=1&rft.spage=110&rft.pages=110-&rft.issn=2227-9717&rft.eissn=2227-9717&rft_id=info:doi/10.3390/pr10010110&rft_dat=%3Cproquest_cross%3E2621348240%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2621348240&rft_id=info:pmid/&rfr_iscdi=true |