{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T02:05:35Z","timestamp":1768010735586,"version":"3.49.0"},"reference-count":46,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T00:00:00Z","timestamp":1690848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["52109113"],"award-info":[{"award-number":["52109113"]}]},{"name":"National Natural Science Foundation of China","award":["52209121"],"award-info":[{"award-number":["52209121"]}]},{"name":"National Natural Science Foundation of China","award":["cstc2021jcyj-msxmX1114"],"award-info":[{"award-number":["cstc2021jcyj-msxmX1114"]}]},{"name":"National Natural Science Foundation of China","award":["2020921002"],"award-info":[{"award-number":["2020921002"]}]},{"name":"National Natural Science Foundation of China","award":["LSDP202101"],"award-info":[{"award-number":["LSDP202101"]}]},{"name":"Natural Science Foundation of Chongqing, China","award":["52109113"],"award-info":[{"award-number":["52109113"]}]},{"name":"Natural Science Foundation of Chongqing, China","award":["52209121"],"award-info":[{"award-number":["52209121"]}]},{"name":"Natural Science Foundation of Chongqing, China","award":["cstc2021jcyj-msxmX1114"],"award-info":[{"award-number":["cstc2021jcyj-msxmX1114"]}]},{"name":"Natural Science Foundation of Chongqing, China","award":["2020921002"],"award-info":[{"award-number":["2020921002"]}]},{"name":"Natural Science Foundation of Chongqing, China","award":["LSDP202101"],"award-info":[{"award-number":["LSDP202101"]}]},{"name":"Postdoctoral special Funding Project of Chongqing, China","award":["52109113"],"award-info":[{"award-number":["52109113"]}]},{"name":"Postdoctoral special Funding Project of Chongqing, China","award":["52209121"],"award-info":[{"award-number":["52209121"]}]},{"name":"Postdoctoral special Funding Project of Chongqing, China","award":["cstc2021jcyj-msxmX1114"],"award-info":[{"award-number":["cstc2021jcyj-msxmX1114"]}]},{"name":"Postdoctoral special Funding Project of Chongqing, China","award":["2020921002"],"award-info":[{"award-number":["2020921002"]}]},{"name":"Postdoctoral special Funding Project of Chongqing, China","award":["LSDP202101"],"award-info":[{"award-number":["LSDP202101"]}]},{"name":"Ministry of Water Conservancy Embankment Safety and Disease Prevention Engineering Technology Research Center Open Subject Fund","award":["52109113"],"award-info":[{"award-number":["52109113"]}]},{"name":"Ministry of Water Conservancy Embankment Safety and Disease Prevention Engineering Technology Research Center Open Subject Fund","award":["52209121"],"award-info":[{"award-number":["52209121"]}]},{"name":"Ministry of Water Conservancy Embankment Safety and Disease Prevention Engineering Technology Research Center Open Subject Fund","award":["cstc2021jcyj-msxmX1114"],"award-info":[{"award-number":["cstc2021jcyj-msxmX1114"]}]},{"name":"Ministry of Water Conservancy Embankment Safety and Disease Prevention Engineering Technology Research Center Open Subject Fund","award":["2020921002"],"award-info":[{"award-number":["2020921002"]}]},{"name":"Ministry of Water Conservancy Embankment Safety and Disease Prevention Engineering Technology Research Center Open Subject Fund","award":["LSDP202101"],"award-info":[{"award-number":["LSDP202101"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, a modified maximum tangential stress criterion by considering T-stress and uniaxial compression tests have been utilized to theoretically and experimentally reveal the fracture initiation mechanism of a center-symmetric closed crack in compacted clay. The results show that wing cracks occur in the linear elastic phase of the stress-strain curve. In the plastic phase of the stress-strain curve, the wing cracks extend gradually and the shear cracks occur. The crack initiation stress and peak stress of compacted clay first decrease with the rise in pre-crack inclination angle (\u03b2 = 0\u00b0\u201340\u00b0), and then increase with the rise in pre-crack inclination angle (\u03b2 = 50\u00b0\u201390\u00b0). When the pre-crack inclination angle is relatively small or large (\u03b2 \u2264 10\u00b0 or \u03b2 \u2265 70\u00b0), the crack type is mainly tension cracks. Secondary shear cracks occur when the pre-crack inclination angle is 10\u00b0\u201380\u00b0. When the dimensionless crack length is larger than 0.35, the crack types include wing-type tension cracks and secondary shear cracks. The experimental results were compared with the theoretical values. It was found that the critical size rc of compacted clay under compression-shear loading was 0.75 mm, smaller than the value calculated by the empirical formula (12 mm). The MTS criterion considering T-stress can be used to predict the compression-shear fracture behavior of compacted clay.<\/jats:p>","DOI":"10.3390\/sym15081519","type":"journal-article","created":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T09:06:44Z","timestamp":1690880804000},"page":"1519","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Theoretical and Experimental Investigation on the Fracture Mechanism of Center-Symmetric Closed Crack in Compacted Clay under Compression\u2013Shear Loading"],"prefix":"10.3390","volume":"15","author":[{"given":"Shiyuan","family":"Huang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University, Chongqing 400074, China"},{"name":"School of Civil Engineering, Chongqing Jiaotong University, Chongqing 400074, China"},{"name":"Engineering Research Center of Diagnosis Technology and Instruments of Hydro-Construction, Chongqing Jiaotong University, Chongqing 400074, China"}]},{"given":"Xiaofeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Diagnosis Technology and Instruments of Hydro-Construction, Chongqing Jiaotong University, Chongqing 400074, China"}]},{"given":"Wenbing","family":"Yu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University, Chongqing 400074, China"},{"name":"School of Civil Engineering, Chongqing Jiaotong University, Chongqing 400074, China"}]},{"given":"Xudong","family":"Li","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Diagnosis Technology and Instruments of Hydro-Construction, Chongqing Jiaotong University, Chongqing 400074, China"}]},{"given":"Songyang","family":"Jin","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Diagnosis Technology and Instruments of Hydro-Construction, Chongqing Jiaotong University, Chongqing 400074, China"}]},{"given":"Hongbo","family":"Du","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Diagnosis Technology and Instruments of Hydro-Construction, Chongqing Jiaotong University, Chongqing 400074, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1007\/s11368-021-03082-y","article-title":"Investigation on desiccation cracking behavior of clayey soils with a perspective of fracture mechanics: A review","volume":"22","author":"Xu","year":"2022","journal-title":"J. Soil Sediment"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.clay.2010.01.011","article-title":"Landfill clay barrier subjected to cracking: Multi-scale analysis of bending tests","volume":"48","author":"Camp","year":"2010","journal-title":"Appl. Clay Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"106488","DOI":"10.1016\/j.enggeo.2021.106488","article-title":"Characteristics and causes of crest cracking on a high core-wall rockfill dam: A case study","volume":"297","author":"Zhang","year":"2022","journal-title":"Eng. Geol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1782686","DOI":"10.1155\/2018\/1782686","article-title":"Numerical Simulation of Hydraulic Fracturing in Earth and Rockfill Dam Using Extended Finite Element Method","volume":"2018","author":"Ji","year":"2018","journal-title":"Adv. Civ. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1680\/geot.2007.57.7.581","article-title":"Crack initiation in clay observed in beam bending","volume":"57","author":"Thusyanthan","year":"2007","journal-title":"G\u00e9otechnique"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.engfracmech.2018.03.024","article-title":"Dominant mode of planar fractures and the role of material properties","volume":"195","author":"Liu","year":"2018","journal-title":"Eng. Fract. Mech."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1680\/geot.1970.20.2.208","article-title":"Joints and Fissures in The London Clay at Wraysbury and Edgware","volume":"20","author":"Skempton","year":"1970","journal-title":"G\u00e9otechnique"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"109294","DOI":"10.1016\/j.engfracmech.2023.109294","article-title":"Experimental study on mode I fracture characteristics of compacted bentonite clay","volume":"285","author":"Qiao","year":"2023","journal-title":"Eng. Fract. Mech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"106814","DOI":"10.1016\/j.engfracmech.2019.106814","article-title":"Experimental study on fracture toughness of a compacted clay using semi-circular bend specimen","volume":"224","author":"Wang","year":"2020","journal-title":"Eng. Fract. Mech."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.engfracmech.2016.08.006","article-title":"Limit of crack depth in KIC testing for a clay","volume":"164","author":"Wang","year":"2016","journal-title":"Eng. Fract. Mech."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.enggeo.2007.06.005","article-title":"Experimental study on fracture toughness and tensile strength of a clay","volume":"94","author":"Wang","year":"2007","journal-title":"Eng. Geol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1139\/t11-031","article-title":"Determination of cohesive properties for mode I fracture from compacted clay beams","volume":"48","author":"Amarasiri","year":"2011","journal-title":"Can. Geotech. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/BF00191106","article-title":"Fracture under complex stress\u2014The angled crack problem","volume":"8","author":"Williams","year":"1972","journal-title":"Int. J. Fract. Mech."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"104433","DOI":"10.1016\/j.ijrmms.2020.104433","article-title":"Analytical solution of T-stresses for an inclined crack in compression","volume":"138","author":"Fan","year":"2021","journal-title":"Int. J. Rock Mech. Min."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"111484","DOI":"10.1016\/j.ijsolstr.2022.111484","article-title":"On the validation of mixed-mode I\/II crack growth theories for anisotropic rocks","volume":"241","author":"Sakha","year":"2022","journal-title":"Int. J. Solids Struct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4631","DOI":"10.1016\/j.engfracmech.2008.06.018","article-title":"On the use of Brazilian disc specimen for calculating mixed mode I\u2013II fracture toughness of rock materials","volume":"75","author":"Ayatollahi","year":"2008","journal-title":"Eng. Fract. Mech."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1007\/s12517-019-4628-1","article-title":"The compressive-shear fracture strength of rock containing water based on Druker-Prager failure criterion","volume":"12","author":"Zhao","year":"2019","journal-title":"Arab. J. Geosci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"103043","DOI":"10.1016\/j.tafmec.2021.103043","article-title":"Shear fracture (Mode II) toughness measurement of anisotropic rock","volume":"115","author":"Sun","year":"2021","journal-title":"Theor. Appl. Fract. Mec."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"106847","DOI":"10.1016\/j.engfracmech.2019.106847","article-title":"Fracture analysis of Beishan granite after high-temperature treatment using digital image correlation","volume":"225","author":"Miao","year":"2020","journal-title":"Eng. Fract. Mech."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1016\/j.engfracmech.2018.06.010","article-title":"Wing-crack initiation angle: A new maximum tangential stress criterion by considering T-stress","volume":"199","author":"Liu","year":"2018","journal-title":"Eng. Fract. Mech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1115\/1.3656897","article-title":"On the Crack Extension in Plates Under Plane Loading and Transverse Shear","volume":"85","author":"Erdogan","year":"1963","journal-title":"J. Basic Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1115\/1.4011547","article-title":"Analysis of Stresses and Strains Near End of a Crack Traversing a Plate","volume":"24","author":"Irwin","year":"1957","journal-title":"J. Appl. Mech."},{"key":"ref_23","first-page":"711","article-title":"Cracking Processes in Rock-Like Material Containing a Single Flaw Under Uniaxial Compression: A Numerical Study Based on Parallel Bonded-Particle Model Approach","volume":"45","author":"Zhang","year":"2011","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"102358","DOI":"10.1016\/j.tafmec.2019.102358","article-title":"Determination of the stress field and crack initiation angle of an open flaw tip under uniaxial compression","volume":"104","author":"Lin","year":"2019","journal-title":"Theor. Appl. Fract. Mec."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1046\/j.1460-2695.2001.00377.x","article-title":"The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading","volume":"24","author":"Smith","year":"2001","journal-title":"Fatigue Fract. Eng. M"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"103150","DOI":"10.1016\/j.tafmec.2021.103150","article-title":"On the role of fracture process zone size in specifying fracturing mechanism under dominant modeII loading","volume":"117","author":"Aminzadeh","year":"2022","journal-title":"Theor. Appl. Fract. Mec."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4965","DOI":"10.1007\/s00603-021-02541-9","article-title":"Influences of Loading Method and Notch Type on Rock Fracture Toughness Measurements: From the Perspectives of T-Stress and Fracture Process Zone","volume":"54","author":"Wei","year":"2021","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/BF00703881","article-title":"Brittle fracture in compression","volume":"8","author":"Cotterell","year":"1972","journal-title":"Int. J. Fract. Mech."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.engfracmech.2017.10.025","article-title":"T-stress effects on fatigue crack growth\u2014Theory and experiment","volume":"187","author":"Ayatollahi","year":"2018","journal-title":"Eng. Fract. Mech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1007\/s11431-016-0835-2","article-title":"Determination of T-stress using finite element analysis","volume":"60","author":"Tang","year":"2017","journal-title":"Sci. China Technol. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1023\/A:1020973802643","article-title":"Mode I cracks subjected to large T-stresses","volume":"117","author":"Ayatollahi","year":"2002","journal-title":"Int. J. Fract."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2581","DOI":"10.1016\/j.ijsolstr.2003.11.004","article-title":"Effect of T-stress on fatigue crack closure in 3-D small-scale yielding","volume":"41","author":"Roychowdhury","year":"2004","journal-title":"Int. J. Solids Struct."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2200","DOI":"10.1016\/j.engfracmech.2010.03.009","article-title":"Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading","volume":"77","author":"Aliha","year":"2010","journal-title":"Eng. Fract. Mech."},{"key":"ref_34","first-page":"77","article-title":"Crack growth path prediction for the angled cracked plate using higher order terms of Williams series expansion","volume":"1","author":"Aliha","year":"2013","journal-title":"Eng. Solid Mech."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"106199","DOI":"10.1016\/j.polymertesting.2019.106199","article-title":"On the use of edge cracked short bend beam specimen for PMMA fracture toughness testing under mixed-mode I\/II","volume":"81","author":"Mousavi","year":"2020","journal-title":"Polym. Test"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"102682","DOI":"10.1016\/j.tafmec.2020.102682","article-title":"Mixed mode notch fracture toughness assessment of quasi-brittle polymeric specimens at different scales","volume":"109","author":"Torabi","year":"2020","journal-title":"Theor. Appl. Fract. Mec."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"106830","DOI":"10.1016\/j.engfracmech.2019.106830","article-title":"Sub-sized short bend beam configuration for the study of mixed-mode fracture","volume":"225","author":"Aliha","year":"2020","journal-title":"Eng. Fract. Mech."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.ijsolstr.2020.02.017","article-title":"An extended edge-notched disc bend (ENDB) specimen for mixed-mode I+II fracture assessments","volume":"193\u2013194","author":"Bahmani","year":"2020","journal-title":"Int. J. Solids Struct."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1139\/cgj-2016-0214","article-title":"Brittle fracture of rock under combined tensile and compressive loading conditions","volume":"54","author":"Tang","year":"2017","journal-title":"Can. Geotech. J."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/BF00035493","article-title":"Strain-energy-density factor applied to mixed mode crack problems","volume":"10","author":"Sih","year":"1974","journal-title":"Int. J. Fract."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/BF00038891","article-title":"An energy release rate criterion for mixed mode fracture","volume":"11","author":"Nuismer","year":"1975","journal-title":"Int. J. Fract."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"100077","DOI":"10.1016\/j.finmec.2022.100077","article-title":"How to obtain a more accurate maximum energy release rate for mixed mode fracture","volume":"7","author":"Chen","year":"2022","journal-title":"Forces Mech."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.ijrmms.2015.06.009","article-title":"The effect of T-stress on the fracture of brittle rock under compression","volume":"79","author":"Tang","year":"2015","journal-title":"Int J Rock Mech Min"},{"key":"ref_44","unstructured":"Schmidt, R. (1980, January 27\u201330). A microcrack model and its significance to hydraulic fracturing and fracture toughness testing. Proceedings of the 21st U.S. Symposium on Rock Mechanics (USRMS), Rolla, MI, USA."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1016\/j.prostr.2018.12.122","article-title":"Crack path stability in brittle fracture under pure mode I loading","volume":"13","author":"Ayatollahi","year":"2018","journal-title":"Procedia Struct. Integr."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"3171","DOI":"10.1007\/s00419-023-02431-2","article-title":"Size effect on fracture behavior of quasi-brittle materials during uniaxial compression tests","volume":"93","author":"Wang","year":"2023","journal-title":"Arch. Appl. Mech."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/8\/1519\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:23:48Z","timestamp":1760127828000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/8\/1519"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,1]]},"references-count":46,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["sym15081519"],"URL":"https:\/\/doi.org\/10.3390\/sym15081519","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,1]]}}}