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In response to most of the current constitutive models that fail to simulate the nonlinear fracture compaction deformation in the whole process of rock failure, especially brittle rocks, a piecewise constitutive model was proposed to represent the global constitutive relation of rocks in this study, which was composed of the fracture compaction empirical model and the damage statistical constitutive model. The fracture empirical compaction model was determined by fitting the expressions of fracture closure curves of various rocks, while the rock damage evolution equation was derived underpinned by the fracture growth. According to the effective stress concept and strain equivalence hypothesis, the rock damage constitutive model was deduced. The model parameters of the fracture compaction empirical model and damage statistical constitutive model were all calculated by the geometrical characteristics of the global axial stress\u2013strain curve to guarantee that the models are continuous and smooth at the curve intersection, which is also simple and ready to program. Finally, the uniaxial compression test data and the triaxial compression test data of different rocks in previous studies were employed to validate the models, and the determination coefficient was used to measure the accuracy. The results showed great consistency between the model curves and test data, especially in the pre-peak stage.<\/jats:p>","DOI":"10.3390\/ma16020589","type":"journal-article","created":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T05:57:14Z","timestamp":1673243834000},"page":"589","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Fracture Closure Empirical Model and Theoretical Damage Model of Rock under Compression"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4880-3489","authenticated-orcid":false,"given":"Yifan","family":"Chen","sequence":"first","affiliation":[{"name":"School of Resources and Safety Engineering, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5924-5163","authenticated-orcid":false,"given":"Hang","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Resources and Safety Engineering, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shijie","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Resources and Safety Engineering, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rihong","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Resources and Safety Engineering, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuwei","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Energy and Mining Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenhua","family":"Zha","sequence":"additional","affiliation":[{"name":"School of Civil and Architectural Engineering, East China University of Technology, Nanchang 330013, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2346-3097","authenticated-orcid":false,"given":"Yixian","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanlin","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Energy and Safety Engineering, Hunan University of Science and Technology, Xiangtan 411201, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huihua","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Resources and Safety Engineering, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s12665-021-09626-2","article-title":"Mechanical characteristics and deformation control of surrounding rock in weakly cemented siltstone","volume":"80","author":"Yu","year":"2021","journal-title":"Environ. 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