{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:54:13Z","timestamp":1787028853308,"version":"build-2736575974"},"reference-count":44,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,3,30]],"date-time":"2025-03-30T00:00:00Z","timestamp":1743292800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["51704015"],"award-info":[{"award-number":["51704015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The three-point bending test is a key method for determining parameters related to the mechanical fracture properties of rocks. In this study, shale outcrops from Changning County, Sichuan Province, China, were selected. Three-point bending experiments were performed on shale semi-circular disks with a central straight crack, tested both perpendicular and parallel to the bedding direction. The corresponding load\u2013displacement curves and crack opening displacements were obtained. The opening displacements of the specimens were measured through digital image technology, and the tensile strength and stiffness of the specimens were further calculated. A finite element model of the three-point bending test was developed. By integrating the finite element model with the experimentally obtained load\u2013displacement curves, the anisotropic elastic moduli of the shale were inversely determined. Fracture toughness was calculated using two approaches: a formula from the International Society for Rock Mechanics and numerical methods using the finite element model, which was appropriately configured with the previously obtained elastic modulus values. The stress intensity factors for each specimen were calculated and compared. The energy release rate of shale was computed based on the fracture toughness. Results showed that both the fracture toughness and energy release rate of shale were greater in the perpendicular bedding direction than in the parallel direction. As an example, one specimen\u2019s elastic modulus, opening displacement, and energy release rate obtained from experiments were input into the numerical simulation of the three-point bending test. The simulated load\u2013displacement curve matched the experimental results well. This study provides a comprehensive approach to evaluating the anisotropic mechanical fracture properties of shale formations, which is essential for improving the accuracy of hydraulic fracture prediction models and enhancing the efficiency of shale gas extraction.<\/jats:p>","DOI":"10.3390\/ma18071570","type":"journal-article","created":{"date-parts":[[2025,3,31]],"date-time":"2025-03-31T02:50:16Z","timestamp":1743389416000},"page":"1570","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Research on the Anisotropic Fracture Mechanical Properties of Shale Based on Three-Point Bending Experiments of Semi-Circular Disks"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-7881-1692","authenticated-orcid":false,"given":"Xinyue","family":"Wang","sequence":"first","affiliation":[{"name":"School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lianke","family":"Cui","sequence":"additional","affiliation":[{"name":"Petroleum Engineering Technology Research Institute, Sinopec Henan Oilfield Company, Nanyang 473132, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lianzhi","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fanmin","family":"He","sequence":"additional","affiliation":[{"name":"Chengdu Surveying Geotechnical Research Institute Co., Ltd. of MCC, Chengdu 610044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,30]]},"reference":[{"key":"ref_1","first-page":"13","article-title":"Progress in the development technology of continental shale oil and considerations on countermeasures for large-scale and cost-effective development","volume":"47","author":"Yuan","year":"2023","journal-title":"J. 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