{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T17:25:01Z","timestamp":1773422701251,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T00:00:00Z","timestamp":1661126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42002266"],"award-info":[{"award-number":["42002266"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["30922010918"],"award-info":[{"award-number":["30922010918"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2020M673654"],"award-info":[{"award-number":["2020M673654"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Central Universities","award":["42002266"],"award-info":[{"award-number":["42002266"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["30922010918"],"award-info":[{"award-number":["30922010918"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2020M673654"],"award-info":[{"award-number":["2020M673654"]}]},{"name":"Chinese Postdoctoral Science Foundation","award":["42002266"],"award-info":[{"award-number":["42002266"]}]},{"name":"Chinese Postdoctoral Science Foundation","award":["30922010918"],"award-info":[{"award-number":["30922010918"]}]},{"name":"Chinese Postdoctoral Science Foundation","award":["2020M673654"],"award-info":[{"award-number":["2020M673654"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Energy is often dissipated and released in the process of rock deformation and failure. To study the energy evolution of rock discontinuities under cyclic loading and unloading, cement mortar was used as rock material and a CSS-1950 rock biaxial rheological testing machine was used to conduct graded cyclic loading and unloading tests on Barton\u2019s standard profile line discontinuities with different joint roughness coefficients (JRCs). According to the deformation characteristics of the rock discontinuity sample, the change of internal energy is calculated and analyzed. The experimental results show that under the same cyclic stress, the samples harden with the increase in the number of cycles. With the increase of cyclic stress, the dissipated energy density of each stage gradually exceeds the elastic energy density and occupies a dominant position and increases rapidly as failure becomes imminent. In the process of increasing the shear stress step-by-step, the elastic energy ratio shows a downward trend, but the dissipated energy is contrary to it. The energy dissipation ratio can be used to characterize the internal damage of the sample under load. In the initial stage of fractional loading, the sample is in the extrusion compaction stage, and the energy dissipation ratio remains quasi-constant; then the fracture develops steadily, the damage inside the sample intensifies, and the energy dissipation ratio increases linearly (albeit at a low rate). When the energy storage limit is reached, the growth rate of energy dissipation ratio increases and changes when the stress level reaches a certain threshold. The increase of the roughness of rock discontinuity samples will improve their energy storage capacity to a certain extent.<\/jats:p>","DOI":"10.3390\/ma15165784","type":"journal-article","created":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T21:30:34Z","timestamp":1661203834000},"page":"5784","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Experimental Study of Energy Evolution at a Discontinuity in Rock under Cyclic Loading and Unloading"],"prefix":"10.3390","volume":"15","author":[{"given":"Wei","family":"Zheng","sequence":"first","affiliation":[{"name":"Department of Civil Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linlin","family":"Gu","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhen","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junnan","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hujun","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hang","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/S1365-1609(02)00027-8","article-title":"Coalescence of multiple flaws in a rock-model material in uniaxial compression","volume":"39","author":"Sagong","year":"2002","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3873","DOI":"10.1007\/s00603-016-1077-y","article-title":"Effects of Acoustic Emission and Energy Evolution of Rock Specimens Under the Uniaxial Cyclic Loading and Unloading Compression","volume":"49","author":"Meng","year":"2016","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.ijrmms.2018.12.017","article-title":"Failure behavior and crack evolution mechanism of a non-persistent jointed rock mass containing a circular hole","volume":"114","author":"Yang","year":"2019","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.enggeo.2014.12.008","article-title":"Rockburst laboratory tests database\u2014Application of data mining techniques","volume":"185","author":"He","year":"2015","journal-title":"Eng. Geol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.1007\/s00603-017-1190-6","article-title":"Experimental Investigation of the Influence of Joint Geometric Configurations on the Mechanical Properties of Intermittent Jointed Rock Models under Cyclic Uniaxial Compression","volume":"50","author":"Liu","year":"2017","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s11431-011-4639-y","article-title":"Energy analysis for damage and catastrophic failure of rocks","volume":"54","author":"Xie","year":"2011","journal-title":"Sci. China Technol. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1061\/(ASCE)0733-9399(2003)129:7(793)","article-title":"Energy Release Rate due to Friction at Bimaterial Interface in Dams","volume":"129","author":"Sujatha","year":"2003","journal-title":"J. Eng. Mech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.ijrmms.2013.12.001","article-title":"Conversion of strain energy in triaxial unloading tests on marble","volume":"66","author":"Huang","year":"2014","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_9","first-page":"2603","article-title":"On energy analysis of rock failure","volume":"15","author":"Xie","year":"2005","journal-title":"Chin. J. Rock Mech. Eng."},{"key":"ref_10","first-page":"1729","article-title":"Energy mechanism of deformation and failure of rock masses","volume":"27","author":"Xie","year":"2008","journal-title":"Chin. J. Rock Mech. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.enggeo.2016.08.002","article-title":"New criteria for defining slope failure using the strength reduction method","volume":"212","author":"Tu","year":"2016","journal-title":"Eng. Geol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"106577","DOI":"10.1016\/j.engfracmech.2019.106577","article-title":"Effect of crack angles on energy characteristics of sandstones under a complex stress path","volume":"218","author":"Peng","year":"2019","journal-title":"Eng. Fract. Mech."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/S0886-7798(01)00030-X","article-title":"Comprehensive prediction of rockburst based on analysis of strain energy in rocks","volume":"16","author":"Wang","year":"2001","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_14","first-page":"836","article-title":"The evolution law of rock energy under different graded cyclic loading and unloading modes","volume":"37","author":"Wu","year":"2020","journal-title":"J. Min. Saf. Eng."},{"key":"ref_15","first-page":"1600","article-title":"Mechanical properties and energy evolution of dry and saturated sandstones under cyclic loading","volume":"38","author":"Wang","year":"2017","journal-title":"Rock Soil Mech."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4637","DOI":"10.1007\/s00603-019-01856-y","article-title":"Energy Evolution of Coal at Different Depths Under Unloading Conditions","volume":"52","author":"Jia","year":"2019","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.jngse.2016.05.020","article-title":"Theoretical analysis and experimental research on the energy dissipation of rock crushing based on fractal theory","volume":"33","author":"Deng","year":"2016","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_18","first-page":"1","article-title":"Confining pressure effect on rock energy","volume":"34","author":"Zhang","year":"2015","journal-title":"Chin. J. Rock Mech. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3343","DOI":"10.1007\/s00603-016-0986-0","article-title":"Rock Drilling Performance Evaluation by an Energy Dissipation Based Rock Brittleness Index","volume":"49","author":"Munoz","year":"2016","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4587","DOI":"10.1007\/s00603-016-1071-4","article-title":"Fracture Energy-Based Brittleness Index Development and Brittleness Quantification by Pre-peak Strength Parameters in Rock Uniaxial Compression","volume":"49","author":"Munoz","year":"2016","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1016\/j.ssci.2011.08.039","article-title":"Relationship between EMR and dissipated energy of coal rock mass during cyclic loading process","volume":"50","author":"Song","year":"2012","journal-title":"Saf. Sci."},{"key":"ref_22","unstructured":"Patton, F.D. (October, January 25). Multiple modes of shear failure in rock. Proceedings of the 1st ISRM Congress, Lisbon, Portugal."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.jsg.2019.06.016","article-title":"Shear stress relaxation behavior of rock discontinuities with different joint roughness coefficient and stress histories","volume":"126","author":"Wang","year":"2019","journal-title":"J. Struct. Geol."},{"key":"ref_24","first-page":"319","article-title":"Suggested methods for the quantitative description of discontinuities in rock masses: International Society for Rock Mechanics","volume":"15","author":"Barton","year":"1978","journal-title":"Int. J. Rock Mech. Min. Sci. Geomech. Abstr."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.ijrmms.2016.03.003","article-title":"Damage constitutive model based on energy dissipation for intact rock subjected to cyclic loading","volume":"85","author":"Liu","year":"2016","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"650","DOI":"10.1007\/s12665-019-8638-9","article-title":"Research on non-linear characteristics of rock energy evolution under uniaxial cyclic loading and unloading conditions","volume":"78","author":"Meng","year":"2019","journal-title":"Environ. Earth Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1857","DOI":"10.1007\/s11771-021-4735-5","article-title":"Energy evolution mechanism and failure criteria of jointed surrounding rock under uniaxial compression","volume":"28","author":"Li","year":"2021","journal-title":"J. Cent. South Univ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5471571","DOI":"10.1155\/2017\/5471571","article-title":"Energy Evolution Characteristics and Distribution Laws of Rock Materials under Triaxial Cyclic Loading and Unloading Compression","volume":"2017","author":"Zhang","year":"2017","journal-title":"Adv. Mater. Sci. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.engfracmech.2018.12.010","article-title":"Nonlinear behavior and damage model for fractured rock under cyclic loading based on energy dissipation principle","volume":"206","author":"Li","year":"2019","journal-title":"Eng. Fract. Mech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.ijmst.2015.03.009","article-title":"Experimental investigation on the energy evolution of dry and water-saturated red sandstones","volume":"25","author":"Zhang","year":"2015","journal-title":"Int. J. Min. Sci. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1007\/s00603-017-1389-6","article-title":"Acoustic Emission Characteristics of Red Sandstone Specimens under Uniaxial Cyclic Loading and Unloading Compression","volume":"51","author":"Meng","year":"2018","journal-title":"Rock Mech. Rock Eng."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/16\/5784\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:13:32Z","timestamp":1760141612000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/16\/5784"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,22]]},"references-count":31,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["ma15165784"],"URL":"https:\/\/doi.org\/10.3390\/ma15165784","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,22]]}}}