{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T19:51:28Z","timestamp":1775073088226,"version":"3.50.1"},"reference-count":58,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,5,24]],"date-time":"2021-05-24T00:00:00Z","timestamp":1621814400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>When the fracture is not developed and the connectivity is poor, the original single medium simulation cannot meet the accuracy requirements. Now, the seepage simulation of fractured rock mass has gradually developed from equivalent continuous medium to dual medium and multiple medium. However, it is still difficult to establish the connection between a discrete fracture network model and a continuous medium model, which makes it difficult to simulate the influence of fracture location on the seepage field of rock mass. As the excavation direction of the shaft is vertically downward, the surrounding strata are symmetrical around the plane of the shaft axis, which is different from the horizontal tunnel. Taking the auxiliary shaft of the No.1 Shaft in HighLiGongshan as the engineering background, combined with Monte Carlo methods and DFN generator built in FLAC3D5.01, a discrete fracture network is generated. Based on the dual medium theory, MIDAS is used to optimize the modeling of each fracture group. At the same time, the concept of \u201cFracture Weakening area\u201d is introduced, and the simulation is carried out based on a fluid\u2013solid coupling method. It is found that the simulation effect is close to the reality. The water inflow increases with the increase of shaft excavation depth, and the water inflow at the end of excavation is nearly three times larger than the initial value. Combined with Legendre equation, a new analytical formula of water inflow prediction is proposed. It is found that this analytical formula is more sensitive to permeability and has a greater safety reserve.<\/jats:p>","DOI":"10.3390\/sym13060930","type":"journal-article","created":{"date-parts":[[2021,5,24]],"date-time":"2021-05-24T23:35:05Z","timestamp":1621899305000},"page":"930","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Study on Water Inflow Variation Law of No.1 Shaft Auxiliary Shaft in HighLiGongshan Based on Dual Medium Model"],"prefix":"10.3390","volume":"13","author":[{"given":"Jiabin","family":"Li","sequence":"first","affiliation":[{"name":"Key Laboratory of Urban Underground Engineering, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"},{"name":"School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yonghong","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Urban Underground Engineering, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"},{"name":"School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongsheng","family":"Tan","sequence":"additional","affiliation":[{"name":"Key Laboratory of Urban Underground Engineering, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"},{"name":"School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen","family":"Du","sequence":"additional","affiliation":[{"name":"Key Laboratory of Urban Underground Engineering, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"},{"name":"School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenyu","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Urban Underground Engineering, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"},{"name":"School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,24]]},"reference":[{"key":"ref_1","first-page":"996","article-title":"The relationship of the degree of interconnection to permeability in fractured networks","volume":"90","author":"Long","year":"1985","journal-title":"J. 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