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With this method, the energy release rate of crack propagation under fracture grouting can be defined by the parameters of elastic\u2013plastic soils and the grouting pressure. In order to study the change of strain energy near the crack of elastic\u2013plastic soil under fracture grouting, a mechanical model of elastic\u2013plastic soil with crack was established based on non-associated Mohr\u2013Coulomb criterion model, and the SIF of crack with spring boundary was investigated. The influence of the crack depth ratio and crack aspect ratio on the SIF of cracks under the spring boundary were analyzed, and revealed the rule of crack growth under fracture grouting in elastic\u2013plastic soils. The results showed that the variation of the crack depth ratio and crack aspect ratio had an effect on the change of the SIF of cracks. Increasing the crack depth ratio and crack aspect ratio caused an increase in the SIF of the crack. The results can provide the reference for foundation reinforcement in elastic\u2013plastic soils.<\/jats:p>","DOI":"10.1038\/s41598-023-28649-2","type":"journal-article","created":{"date-parts":[[2023,1,25]],"date-time":"2023-01-25T11:03:48Z","timestamp":1674644628000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Fracture analysis-based mode-I stress intensity factors of crack under fracture grouting in elastic\u2013plastic soils"],"prefix":"10.1038","volume":"13","author":[{"given":"Long","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yousheng","family":"Deng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,1,25]]},"reference":[{"issue":"03","key":"28649_CR1","first-page":"550","volume":"31","author":"L-P Li","year":"2012","unstructured":"Li, L.-P., Li, S.-C. & Zhao, Y. 3D geomechanical model for progressive failure process of weak broken surrounding rock in super large section tunnel. 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