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To study the freeze-thaw damage characteristics of Helankou relics carrier rocks, three dry-wet conditions (i.e., drying, pH = 2 and pH = 7) together with freeze-thaw experiments have been carried out at 0, 10, 20, 30, and 40 cycles. Additionally, a series of triaxial compression tests have been carried out at four different cell pressures of 4 MPa, 8 MPa, 16 MPa, and 32 MPa in tandem with a non-destructive acoustic emission technique. Subsequently, the rock damage variables were identified based on elastic modulus and acoustic emission ringing counts. It has been revealed that the acoustic emission positioning points reflected that the cracks would be concentrated near the surface of main fracture at higher cell pressures. Notably, the rock samples at 0 freeze-thaw cycles failed in pure shear. However, both shear slip and extension along the tensile cracks were observed at 20 freeze-thaw cycles, while tensile-oblique shear failure occurred at 40 freeze-thaw cycles. Not surprisingly, the decreasing order of deterioration inside the rock was observed to be (drying group) &gt; (pH = 7 group) &gt; (pH = 2 group). The peak values of damage variables in these three groups were also found to be consistent with the deterioration trend observed under freeze-thaw cycles. Finally, the semi-empirical damage model could rigorously ascertain stress and deformation behavior of rock samples, thus providing theoretical basis to establish a protection framework for Helankou relics.<\/jats:p>","DOI":"10.3390\/ma16114001","type":"journal-article","created":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T16:17:33Z","timestamp":1685204253000},"page":"4001","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Semi-Empirical Damage Model of Helankou Rocks Based on Acoustic Emission"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9622-4599","authenticated-orcid":false,"given":"Youzhen","family":"Yang","sequence":"first","affiliation":[{"name":"School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan 750021, China"},{"name":"Institute of Solid Mechanics, Ningxia University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingqing","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hailong","family":"Ma","sequence":"additional","affiliation":[{"name":"Institute of Ethnic Preparatory Education, Ningxia University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3927-4995","authenticated-orcid":false,"given":"Jahanzaib","family":"Israr","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan 750021, China"},{"name":"Department of Civil Engineering, University of Engineering and Technology, Lahore 54890, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yishen","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenguo","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan 750021, China"},{"name":"Institute of Solid Mechanics, Ningxia University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan 750021, China"},{"name":"Institute of Solid Mechanics, Ningxia University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongbo","family":"Li","sequence":"additional","affiliation":[{"name":"College of Civil and Hydraulic Engineering, Ningxia University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,26]]},"reference":[{"key":"ref_1","unstructured":"Men, X. 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