{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T13:47:52Z","timestamp":1790948872787,"version":"4.1.0"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,3,21]],"date-time":"2024-03-21T00:00:00Z","timestamp":1710979200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2021YFB2601000"],"award-info":[{"award-number":["2021YFB2601000"]}]},{"name":"National Key Research and Development Program of China","award":["52208415"],"award-info":[{"award-number":["52208415"]}]},{"name":"National Key Research and Development Program of China","award":["2021JQ-255"],"award-info":[{"award-number":["2021JQ-255"]}]},{"name":"National Key Research and Development Program of China","award":["2022JQ-303"],"award-info":[{"award-number":["2022JQ-303"]}]},{"name":"National Key Research and Development Program of China","award":["2021M693752"],"award-info":[{"award-number":["2021M693752"]}]},{"name":"National Natural Science Foundation of China","award":["2021YFB2601000"],"award-info":[{"award-number":["2021YFB2601000"]}]},{"name":"National Natural Science Foundation of China","award":["52208415"],"award-info":[{"award-number":["52208415"]}]},{"name":"National Natural Science Foundation of China","award":["2021JQ-255"],"award-info":[{"award-number":["2021JQ-255"]}]},{"name":"National Natural Science Foundation of China","award":["2022JQ-303"],"award-info":[{"award-number":["2022JQ-303"]}]},{"name":"National Natural Science Foundation of China","award":["2021M693752"],"award-info":[{"award-number":["2021M693752"]}]},{"name":"Natural Science Foundation of Shaanxi Province","award":["2021YFB2601000"],"award-info":[{"award-number":["2021YFB2601000"]}]},{"name":"Natural Science Foundation of Shaanxi Province","award":["52208415"],"award-info":[{"award-number":["52208415"]}]},{"name":"Natural Science Foundation of Shaanxi Province","award":["2021JQ-255"],"award-info":[{"award-number":["2021JQ-255"]}]},{"name":"Natural Science Foundation of Shaanxi Province","award":["2022JQ-303"],"award-info":[{"award-number":["2022JQ-303"]}]},{"name":"Natural Science Foundation of Shaanxi Province","award":["2021M693752"],"award-info":[{"award-number":["2021M693752"]}]},{"name":"Chinese Postdoctoral Science Foundation","award":["2021YFB2601000"],"award-info":[{"award-number":["2021YFB2601000"]}]},{"name":"Chinese Postdoctoral Science Foundation","award":["52208415"],"award-info":[{"award-number":["52208415"]}]},{"name":"Chinese Postdoctoral Science Foundation","award":["2021JQ-255"],"award-info":[{"award-number":["2021JQ-255"]}]},{"name":"Chinese Postdoctoral Science Foundation","award":["2022JQ-303"],"award-info":[{"award-number":["2022JQ-303"]}]},{"name":"Chinese Postdoctoral Science Foundation","award":["2021M693752"],"award-info":[{"award-number":["2021M693752"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>In order to study the influence of an unsupported sleeper on the vertical bearing characteristics of heavy-haul railway ballast, a three-dimensional discrete element model (DEM) was established for a ballasted track, by removing ballast particles that come into contact with the bottom of the sleeper from the model to simulate the unsupported sleeper. Vertical bearing characteristics for ballast on different types of unsupported sleepers were studied. The results showed that an unsupported sleeper could reduce the bearing area of the ballast below the sleeper and reduce the number of ballast particles that were in contact. It could also lead to an increase in the maximum contact force between the particles, accelerating the deterioration of the particles (thus affecting the overall performance of the ballast) and reducing the vertical stiffness of the ballast. As the unsupported length and width increased, vertical stiffness gradually decreased. The vertical ballast stiffness for an unsupported sleeper was then used in a dynamic coupled vehicle\/track model, and the effect of the unsupported sleeper on wheel\/rail interaction was analyzed. Results showed that increasing the unsupported length and width leads to a decrease in the supporting force on the unsupported sleeper and to an increase in the supporting force on the adjacent sleepers.<\/jats:p>","DOI":"10.3390\/ma17061434","type":"journal-article","created":{"date-parts":[[2024,3,21]],"date-time":"2024-03-21T04:34:46Z","timestamp":1710995686000},"page":"1434","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["The Influence of an Unsupported Sleeper on the Vertical Bearing Characteristics of Heavy-Haul Railway Ballast"],"prefix":"10.3390","volume":"17","author":[{"given":"Dan","family":"Liu","sequence":"first","affiliation":[{"name":"School of Highway, Chang\u2019an University, Xi\u2019an 710064, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chengguang","family":"Su","sequence":"additional","affiliation":[{"name":"China Railway First Survey and Design Institute Group Co., Ltd., Xi\u2019an 710043, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3300-0969","authenticated-orcid":false,"given":"Dawei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automobile, Chang\u2019an University, Xi\u2019an 710064, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Caihao","family":"Lan","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of High-Speed Railway Engineering, Southwest Jiaotong University, Chengdu 610031, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,21]]},"reference":[{"key":"ref_1","unstructured":"Lu, Z. (2002). Railway Track Structure and Maintenance, China Railway Publishing House."},{"key":"ref_2","first-page":"104","article-title":"Experimental Study on Resistance of Granular Ballast Bed under Periodic Longitudinal Load","volume":"39","author":"Liu","year":"2017","journal-title":"J. China Railw. Soc."},{"key":"ref_3","unstructured":"Olsson, E.L., and Zack RIsson, P. (2002). Long-Term Measurement Results, Final Report, Banverket. Technical Report."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"80","DOI":"10.2219\/rtriqr.40.80","article-title":"Influence of loose sleeper on track dynamics and bending fatigue of rail welds","volume":"40","author":"Ishida","year":"1999","journal-title":"Q. Rep. RTRI"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Auguetin, S., Gudehus, G., Huber, G., and Sch\u00fcnemann, A. (2003). Numerical Model and Laboratory Tests on Settlement of Ballast Track, Springer.","DOI":"10.1007\/978-3-540-45476-2_19"},{"key":"ref_6","first-page":"715","article-title":"Evaluation of the influence factors on the ballast settlement by using the discrete element method","volume":"36","author":"Kim","year":"2016","journal-title":"J. Korean Soc. Civ. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1243\/09544097JRRT141","article-title":"Investigation of free vibrations of voided concrete sleepers in railway track system","volume":"221","author":"Kaewunruen","year":"2007","journal-title":"Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1006\/jsvi.1995.0564","article-title":"Dynamic modeling of concrete railway sleepers","volume":"187","author":"Grassie","year":"1995","journal-title":"J. Sound Vib."},{"key":"ref_9","first-page":"8","article-title":"Research on the Responses of Vertical Vibration of Train-Track System due to Voided Sleeper","volume":"4","author":"Xiang","year":"2007","journal-title":"J. Railw. Sci. Eng."},{"key":"ref_10","first-page":"67","article-title":"Effect of Track Support Failure on Dynamic Response of Tangent Track","volume":"40","author":"Xiao","year":"2008","journal-title":"Chin. J. Theor. Appl. Mech."},{"key":"ref_11","first-page":"203","article-title":"Effect of Unsupported Sleepers on Sleeper Dynamic Performance Response","volume":"45","author":"Zhang","year":"2010","journal-title":"J. Southwest Jiaotong Univ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1115\/1.2424978","article-title":"Effect of disabled fastening systems and ballast on vehicle derailment","volume":"129","author":"Xiao","year":"2007","journal-title":"J. Vib. Acoust."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1016\/j.soildyn.2007.08.006","article-title":"Effect of unsupported sleepers on wheel\/rail normal load","volume":"28","author":"Zhang","year":"2008","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_14","first-page":"1","article-title":"Effect of Unsupported Sleepers on the Wheel\/Rail Interaction of Heavy-Haul Railway lines","volume":"36","author":"Zhang","year":"2017","journal-title":"J. Vib. Shock."},{"key":"ref_15","first-page":"517","article-title":"Influence of Unsupported Sleeper on Wheel-Rail Contact at Rail Weld Irregularity","volume":"49","author":"Wei","year":"2021","journal-title":"J. Tongji Univ. (Nat. Sci. Ed.)"},{"key":"ref_16","first-page":"521","article-title":"Dynamic Evolution Process of Voided Sleeper","volume":"47","author":"Zhou","year":"2019","journal-title":"J. Univ. Stat. (Nat. Sci. Ed.)"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2289","DOI":"10.1007\/s12206-015-0521-3","article-title":"Influence of unsupported and partially supported sleepers on dynamic responses of train\u2013track interaction","volume":"29","author":"Zakeri","year":"2015","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1177\/0954409716664932","article-title":"Effects of train bogie patterns on the mechanical performance of ballasted railway tracks with unsupported sleepers","volume":"232","author":"Mosayebi","year":"2018","journal-title":"Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit"},{"key":"ref_19","first-page":"171","article-title":"DEM Analysis of Effect of Unsupported Sleepers on Dynamic Characteristics of Ballast Beds","volume":"39","author":"Cui","year":"2020","journal-title":"J. Vib. Shock."},{"key":"ref_20","first-page":"1481","article-title":"Discrete element simulation and its validation on vibration and deformation of railway ballast","volume":"5","author":"Zhang","year":"2017","journal-title":"Rocks Soil Mech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1016\/j.conbuildmat.2012.09.007","article-title":"Discrete element modeling of ballast settlement under trains moving at \u201cCritical Speeds\u201d","volume":"38","author":"Huang","year":"2013","journal-title":"Constr. Build. Mater."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1061\/(ASCE)MT.1943-5533.0000839","article-title":"Image-Aided Element Shape Generation Method in Discrete-Element Modeling for Railroad Ballast","volume":"26","author":"Huang","year":"2013","journal-title":"J. Mater. Civ. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2841","DOI":"10.1016\/j.cma.2005.07.006","article-title":"Modelling ballast behaviour under dynamic loading. Part 1: A 2D polygonal discrete element method approach","volume":"195","author":"Saussine","year":"2005","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_24","first-page":"688","article-title":"Effect of flakiness-elongation index on shear behavior of railway ballast","volume":"55","author":"Jing","year":"2020","journal-title":"J. Southwest Jiaotong Univ."},{"key":"ref_25","first-page":"110","article-title":"The effect of rail corrugation on dynamic characteristics of heavy haul railway ballast bed","volume":"49","author":"Cui","year":"2021","journal-title":"J. Huazhong Univ. Sci. Technol. Nat. Sci."},{"key":"ref_26","unstructured":"(2008). Railway Ballast (Standard No. TB\/T 2140-2008)."},{"key":"ref_27","unstructured":"(2017). Code for Design of Heavy Haul Railway (Standard No. TB10625-2017)."},{"key":"ref_28","unstructured":"(2017). Code for Design of Raiway Track (Standard No. TB 10082-2017)."},{"key":"ref_29","unstructured":"Han, H. (2023). Research on under Ballast Mats: Mesoscopic Contact Behavior and Influence on Mechanical Properties of the Ballast Bed. [Master\u2019s Thesis, China Academy of Railway Sciences Corporation Limited]."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"041009","DOI":"10.1115\/1.4001908","article-title":"Lateral Hunting Stability of Railway Vehicles Running on Elastic Track Structures","volume":"5","author":"Zhai","year":"2010","journal-title":"J. Comput. 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