{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T10:30:38Z","timestamp":1760956238615,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,2]],"date-time":"2025-02-02T00:00:00Z","timestamp":1738454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["52174103","2023AH010023","2008085ME147"],"award-info":[{"award-number":["52174103","2023AH010023","2008085ME147"]}]},{"name":"Anhui Excellent Scientific Research and Innovation Team","award":["52174103","2023AH010023","2008085ME147"],"award-info":[{"award-number":["52174103","2023AH010023","2008085ME147"]}]},{"name":"Anhui Provincial Natural Science Foundation","award":["52174103","2023AH010023","2008085ME147"],"award-info":[{"award-number":["52174103","2023AH010023","2008085ME147"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This research aimed to detect the defects of anchoring agents\u2019 empty slurries in anchor support. The influence of anchoring defects on the propagation law of stress waves was comprehensively investigated using laboratory tests, theoretical calculations, and other methods. The characteristic modal components with symmetry and periodicity laws were extracted by adopting a variable modal decomposition (VMD) signal decomposition method. It was found that the bottom reflection time of stress waves had an inverse function relationship with the length of the anchorage flaw. The average propagation speed of the stress wave in the free rod was obtained as 5150 m\/s, and the average consolidation wave speed was 4198 m\/s. The calculation method of the bolt flaw length was finally proposed. After experimental verification, the average error rate was 2.65%, which meets the requirement of testing accuracy in the engineering field, which provides a guarantee for safe production.<\/jats:p>","DOI":"10.3390\/sym17020221","type":"journal-article","created":{"date-parts":[[2025,2,3]],"date-time":"2025-02-03T05:36:32Z","timestamp":1738560992000},"page":"221","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Research on the Method of Calculating Anchorage Flaw Length Based on the Propagation Characteristics of Bolt Excitation Stress Waves"],"prefix":"10.3390","volume":"17","author":[{"given":"Chuan","family":"Li","sequence":"first","affiliation":[{"name":"School of Mining Engineering, Anhui University of Science & Technology, Huainan 232000, China"}]},{"given":"Chuanming","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mining Engineering, Anhui University of Science & Technology, Huainan 232000, China"}]},{"given":"Qinghua","family":"Han","sequence":"additional","affiliation":[{"name":"School of Mining Engineering, Anhui University of Science & Technology, Huainan 232000, China"}]},{"given":"Wanrong","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Architecture and Engineering, Liaocheng University, Liaocheng 252059, China"}]},{"given":"Jianguo","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Mining Engineering, Anhui University of Science & Technology, Huainan 232000, China"}]},{"given":"Hu","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mining Engineering, Anhui University of Science & Technology, Huainan 232000, China"}]},{"given":"Yikai","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mining Engineering, Anhui University of Science & Technology, Huainan 232000, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Feng, C., Liu, S., Jia, H., Fu, M., and He, D. 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