{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T10:36:10Z","timestamp":1760524570819,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,28]],"date-time":"2023-12-28T00:00:00Z","timestamp":1703721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100018542","name":"Natural Science Foundation of Sichuan Province","doi-asserted-by":"publisher","award":["2022NSFSC1169","Z211014","NERCRT202301","52204212","52204219","22375401D"],"award-info":[{"award-number":["2022NSFSC1169","Z211014","NERCRT202301","52204212","52204219","22375401D"]}],"id":[{"id":"10.13039\/501100018542","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific Research Foundation of Xihua University","award":["2022NSFSC1169","Z211014","NERCRT202301","52204212","52204219","22375401D"],"award-info":[{"award-number":["2022NSFSC1169","Z211014","NERCRT202301","52204212","52204219","22375401D"]}]},{"name":"National Engineering Research Center of Road Tunnel","award":["2022NSFSC1169","Z211014","NERCRT202301","52204212","52204219","22375401D"],"award-info":[{"award-number":["2022NSFSC1169","Z211014","NERCRT202301","52204212","52204219","22375401D"]}]},{"name":"National Natural Science Foundation of China","award":["2022NSFSC1169","Z211014","NERCRT202301","52204212","52204219","22375401D"],"award-info":[{"award-number":["2022NSFSC1169","Z211014","NERCRT202301","52204212","52204219","22375401D"]}]},{"name":"S&amp;T Program of Hebei","award":["2022NSFSC1169","Z211014","NERCRT202301","52204212","52204219","22375401D"],"award-info":[{"award-number":["2022NSFSC1169","Z211014","NERCRT202301","52204212","52204219","22375401D"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Rock strength parameters are usually indispensable for rock engineering design. Under the experimental testing conditions, the shape effect could significantly affect the measured results. Previous findings from uniaxial tests reveal that the measured rock strength gradually decreases with the increase in the slenderness ratio, which is mainly ascribed to the end effect. However, it is still unclear how strong the influence of the end effect on the shape effect is in true 3D tests. In the present study, rock mechanical behaviors in response to the variation in slenderness ratio are detailly examined in true 3D tests. The calculated results show that rock strength progressively decreases as the slenderness ratio increases. But the rock strength in true 3D tests still deviates far from the actual even though the slenderness ratio goes beyond 2, which is mainly caused by the interface friction along the two extra \u03c32-normal specimen faces. It is interesting that the slenderness ratio increases lead to an increase in the measured stiffness as well. The calculated results suggest that symmetry in the experimentally defined typical arc-shaped curves \u03c31(\u03c32) at constant \u03c33 are neglected most likely due to the stronger end effects in true 3D tests, and the accurate rock strength parameters are not obtained only through using slender specimens.<\/jats:p>","DOI":"10.3390\/sym16010040","type":"journal-article","created":{"date-parts":[[2023,12,28]],"date-time":"2023-12-28T09:35:21Z","timestamp":1703756121000},"page":"40","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Analysis of the Shape Effect on the Mechanical Behaviors of Rocks in True 3D Compression Test"],"prefix":"10.3390","volume":"16","author":[{"given":"Junchao","family":"Chen","sequence":"first","affiliation":[{"name":"School of Emergency Management, Xihua University, Chengdu 610039, China"}]},{"given":"Yuke","family":"Long","sequence":"additional","affiliation":[{"name":"School of Emergency Management, Xihua University, Chengdu 610039, China"}]},{"given":"Yulin","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Northeast Electric Power University, Jilin 132012, China"}]},{"given":"Xiaofei","family":"Liu","sequence":"additional","affiliation":[{"name":"Sichuan Institute of Safety Science and Technology, Chengdu 610000, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2551","DOI":"10.1007\/s10706-019-01168-6","article-title":"Influence of the Rock Length-to-Diameter Ratio and Failure Modes on Uniaxial Compression Strength","volume":"38","author":"Chen","year":"2020","journal-title":"Geotech. Geol. Eng."},{"key":"ref_2","unstructured":"Thuro, K., and Plinninger, R.J. (2001). Rock Mechanics-A Challenge for Society, ISRM."},{"key":"ref_3","first-page":"4765887","article-title":"3D Mechanical Characters and Their Fabric Evolutions of Granular Materials by DEM Simulation","volume":"2022","author":"Li","year":"2022","journal-title":"Math. Probl. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1007\/s10064-022-03013-2","article-title":"Effects of length-to-diameter ratio on energy storage characteristics of rock materials under uniaxial compression","volume":"81","author":"Yan","year":"2022","journal-title":"Bull. Eng. Geol. Environ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1016\/j.ijrmms.2008.11.001","article-title":"Study of failure and scale effects in rocks under uniaxial compression using 3D cellular automata","volume":"46","author":"Pan","year":"2009","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1669","DOI":"10.1007\/s10064-015-0811-0","article-title":"The effect of specimen shape and strain rate on uniaxial compressive behavior of rock material","volume":"75","author":"Liang","year":"2015","journal-title":"Bull. Eng. Geol. Environ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1695","DOI":"10.1007\/s00603-015-0899-3","article-title":"Size and Geometry Effects on the Mechanical Properties of Carrara Marble Under Dynamic Loadings","volume":"49","author":"Zou","year":"2016","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1007\/s12517-018-3957-9","article-title":"End and shape effects of brittle rock under uniaxial compression","volume":"11","author":"Gao","year":"2018","journal-title":"Arab. J. Geosci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.enggeo.2018.10.003","article-title":"A re-examination of slenderness ratio effect on rock strength: Insights from DEM grain-based modelling","volume":"246","author":"Peng","year":"2018","journal-title":"Eng. Geol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/0148-9062(71)90047-7","article-title":"Effects of inserts on the elastic behavior of cylindrical materials loaded between rough end-plates","volume":"8","author":"Brady","year":"1971","journal-title":"Int. J. Rock Mech. Min. Sci. G\u00e9om\u00e9ch. Abstr."},{"key":"ref_11","unstructured":"Labuz, J., and Bridell, J. (1991). Reducing Frictional Constraint in Compression Testing through Lubrication, University of Minnesota."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/0148-9062(93)91726-Y","article-title":"Reducing frictional constraint in compression testing through lubrication","volume":"30","author":"Labuz","year":"1993","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/S0148-9062(96)00031-9","article-title":"The effects of slenderness and lubrication on the uniaxial behavior of a soft limestone","volume":"34","author":"Pellegrino","year":"1997","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_14","first-page":"1159","article-title":"Analysis of end friction effect in true triaxial test","volume":"30","author":"Shi","year":"2009","journal-title":"Rock Soil Mech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.ijrmms.2017.04.002","article-title":"Evaluation and reduction of the end friction effect in true triaxial tests on hard rocks","volume":"97","author":"Feng","year":"2017","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1520\/GTJ20160242","article-title":"A Mogi-Type True Triaxial Testing Apparatus for Rocks With Two Moveable Frames in Horizontal Layout for Providing Orthogonal Loads","volume":"40","author":"Shi","year":"2017","journal-title":"Geotech. Test. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"862","DOI":"10.1139\/cgj-2016-0393","article-title":"Influence of end effect on rock strength in true triaxial compression test","volume":"54","author":"Xu","year":"2017","journal-title":"Can. Geotech. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9367","DOI":"10.1007\/s13369-020-04750-w","article-title":"Numerical Simulation of True 3D Rock Tests with Classical and New Three-Invariant Constitutive Models Focusing on the End Effects","volume":"45","author":"Chen","year":"2020","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"104353","DOI":"10.1016\/j.ijrmms.2020.104353","article-title":"A method to remove end effect for the determination of intrinsic 3D rock strength envelopes","volume":"131","author":"Xu","year":"2020","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_20","first-page":"3636","article-title":"Research on effect of loading conditions on failure processes of rocks with different sizes under uniaxial compression","volume":"27","author":"Pan","year":"2008","journal-title":"CJRME"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.ijrmms.2016.04.008","article-title":"Investigation into size and strain rate effects on the strength of rock-like materials","volume":"86","author":"Qi","year":"2016","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2255","DOI":"10.1007\/s00603-017-1231-1","article-title":"Influence of Loading System Stiffness on Post-peak Stress\u2013Strain Curve of Stable Rock Failures","volume":"50","author":"Xu","year":"2017","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_23","first-page":"135","article-title":"Suggested methods for determining the uniaxial compressive strength and deformability of rock materials","volume":"16","author":"Bieniawski","year":"1979","journal-title":"Int. J. Rock Mech. Min. Sci. G\u00e9om\u00e9ch. Abstr."},{"key":"ref_24","unstructured":"Philadelphia, P.A. (2014). Annual Book of ASTM Standards, American Society for Testing and Materials."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1029\/JB076i005p01255","article-title":"Fracture and flow of rocks under high triaxial compression","volume":"76","author":"Mogi","year":"1971","journal-title":"J. Geophys. Res."},{"key":"ref_26","first-page":"19","article-title":"Effect of the intermediate principal stress on strength and deformation behavior of sedimentary rocks at the depth shallower than 2000 m","volume":"30","author":"Takahashi","year":"1989","journal-title":"ISRM"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"18999","DOI":"10.1029\/2000JB900184","article-title":"True triaxial strength and deformability of the German Continental Deep Drilling Program (KTB) deep hole amphibolite","volume":"105","author":"Chang","year":"2000","journal-title":"J. Geophys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/S1365-1609(99)00106-9","article-title":"A new true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of Westerly granite","volume":"37","author":"Haimson","year":"2000","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1002\/jgrb.50084","article-title":"Response of Castlegate sandstone to true triaxial states of stress","volume":"118","author":"Ingraham","year":"2013","journal-title":"J. Geophys. Res."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1649","DOI":"10.1007\/s00603-015-0875-y","article-title":"A Novel Mogi Type True Triaxial Testing Apparatus and Its Use to Obtain Complete Stress\u2013Strain Curves of Hard Rocks","volume":"49","author":"Feng","year":"2016","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4647","DOI":"10.1007\/s00603-016-1060-7","article-title":"A Novel True Triaxial Apparatus to Study the Geomechanical and Fluid Flow Aspects of Energy Exploitations in Geological Formations","volume":"49","author":"Li","year":"2016","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"6477","DOI":"10.1002\/2016JB012979","article-title":"Failure characteristics of two porous sandstones subjected to true triaxial stresses","volume":"121","author":"Ma","year":"2016","journal-title":"J. Geophys. Res."},{"key":"ref_33","first-page":"2720","article-title":"End friction effect of Mogi type true-triaxial test apparatus","volume":"36","author":"Fan","year":"2017","journal-title":"Chin. J. Rock Mech. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2109","DOI":"10.1007\/s00603-018-1700-1","article-title":"Experimental Study of Failure Differences in Hard Rock Under True Triaxial Compression","volume":"52","author":"Feng","year":"2019","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.1007\/s00603-018-1414-4","article-title":"Failure Characteristics of Granite Influenced by Sample Height-to-Width Ratios and Intermediate Principal Stress Under True-Triaxial Unloading Conditions","volume":"51","author":"Li","year":"2018","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_36","first-page":"04019005","article-title":"Numerical Investigation of Hard Rock Strength and Fracturing under Polyaxial Compression Based on Mogi-Coulomb Failure Criterion","volume":"19","author":"Feng","year":"2019","journal-title":"Int. J. G\u00e9om\u00e9ch."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"104204","DOI":"10.1016\/j.ijrmms.2019.104204","article-title":"Strength and deformability of a low-porosity sandstone under true triaxial compression conditions","volume":"127","author":"Zhang","year":"2020","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1002\/(SICI)1099-1484(199601)1:1<115::AID-CFM6>3.0.CO;2-U","article-title":"Experimental investigation of concrete fracture under uniaxial compression","volume":"1","author":"Van","year":"1996","journal-title":"Mech. Cohes-Frict. Mat."},{"key":"ref_39","unstructured":"Itasca Consulting Group (2013). FLAC 3D (Fast Lagrangian Analysis of Continua in 3-Dimensions) 5.0 manual, Itasca Consulting Group."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.compgeo.2016.11.017","article-title":"Numerical study on the influence of cross-sectional shape on strength and deformation behaviors of rocks under uniaxial compression","volume":"84","author":"Xu","year":"2017","journal-title":"Comput. Geotech."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"5117","DOI":"10.1029\/JZ072i020p05117","article-title":"Effect of the intermediate principal stress on rock failure","volume":"72","author":"Mogi","year":"1967","journal-title":"J. Geophys. Res."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2011","DOI":"10.1007\/s00603-019-01782-z","article-title":"ISRM Suggested Method: Determining Deformation and Failure Characteristics of Rocks Subjected to True Triaxial Compression","volume":"52","author":"Feng","year":"2019","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.ijrmms.2013.08.009","article-title":"A note on the strength symmetry imposed by Mogi\u2019s true-triaxial criterion","volume":"64","author":"Jimenez","year":"2013","journal-title":"Int. J. Rock Mech. Min. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:43:22Z","timestamp":1760132602000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,28]]},"references-count":43,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["sym16010040"],"URL":"https:\/\/doi.org\/10.3390\/sym16010040","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,12,28]]}}}