{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T10:18:40Z","timestamp":1768472320274,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2016,12,27]],"date-time":"2016-12-27T00:00:00Z","timestamp":1482796800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>This paper numerically investigates the seismic response of the filled joint under high amplitude stress waves using the combined finite-discrete element method (FDEM). A thin layer of independent polygonal particles are used to simulate the joint fillings. Each particle is meshed using the Delaunay triangulation scheme and can be crushed when the load exceeds its strength. The propagation of the 1D longitude wave through a single filled joint is studied, considering the influences of the joint thickness and the characteristics of the incident wave, such as the amplitude and frequency. The results show that the filled particles under high amplitude stress waves mainly experience three deformation stages: (i) initial compaction stage; (ii) crushing stage; and (iii) crushing and compaction stage. In the initial compaction stage and crushing and compaction stage, compaction dominates the mechanical behavior of the joint, and the particle area distribution curve varies little. In these stages, the transmission coefficient increases with the increase of the amplitude, i.e., peak particle velocity (PPV), of the incident wave. On the other hand, in the crushing stage, particle crushing plays the dominant role. The particle size distribution curve changes abruptly with the PPV due to the fragments created by the crushing process. This process consumes part of wave energy and reduces the stiffness of the filled joint. The transmission coefficient decreases with increasing PPV in this stage because of the increased amount of energy consumed by crushing. Moreover, with the increase of the frequency of the incident wave, the transmission coefficient decreases and fewer particles can be crushed. Under the same incident wave, the transmission coefficient decreases when the filled thickness increases and the filled particles become more difficult to be crushed.<\/jats:p>","DOI":"10.3390\/ma10010013","type":"journal-article","created":{"date-parts":[[2016,12,28]],"date-time":"2016-12-28T11:22:14Z","timestamp":1482924134000},"page":"13","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Numerical Simulation on Seismic Response of the Filled Joint under High Amplitude Stress Waves Using Finite-Discrete Element Method (FDEM)"],"prefix":"10.3390","volume":"10","author":[{"given":"Xiaolin","family":"Huang","sequence":"first","affiliation":[{"name":"Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"Department of Civil Engineering, University of Toronto, Toronto, ON M5S 1A4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"Zhao","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, University of Toronto, Toronto, ON M5S 1A4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengwen","family":"Qi","sequence":"additional","affiliation":[{"name":"Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kaiwen","family":"Xia","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, University of Toronto, Toronto, ON M5S 1A4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giovanni","family":"Grasselli","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, University of Toronto, Toronto, ON M5S 1A4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuguang","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Engineering, Ocean University of China, Qingdao 266100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,12,27]]},"reference":[{"key":"ref_1","unstructured":"Goodman, R.E. (1976). Methods of Geological Engineering in Discontinuous Rocks, West Information Publishing Group."},{"key":"ref_2","unstructured":"Sun, G.Z. (1988). Rock Mass Structure Mechanics, Science Press. (In Chinese)."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1111\/j.1365-2478.1986.tb00522.x","article-title":"Experimental studies of elastic-wave propagation in a columnar-jointed rock mass","volume":"34","author":"King","year":"1986","journal-title":"Geophys. Prospect."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1449","DOI":"10.1002\/nag.772","article-title":"Considerations of the discontinuous deformation analysis on wave propagation problems","volume":"33","author":"Gu","year":"2009","journal-title":"Int. J. Numer. Anal. Methods Geomech."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1002\/nag.2209","article-title":"Application of the numerical manifold method for stress wave propagation across rock masses","volume":"38","author":"Zhao","year":"2014","journal-title":"Int. J. Numer. Anal. Methods Geomech."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1080\/17486025.2012.695402","article-title":"Modelling p-wave transmission across rock fractures by particle manifold method (pmm)","volume":"7","author":"Zhao","year":"2012","journal-title":"Geomech. Geoeng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/j.compgeo.2010.12.002","article-title":"Validation study of the distinct lattice spring model (DLSM) on p-wave propagation across multiple parallel joints","volume":"38","author":"Zhu","year":"2011","journal-title":"Comput. Geotech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1016\/S1365-1609(00)00013-7","article-title":"Effects of multiple parallel fractures on apparent attenuation of stress waves in rock masses","volume":"37","author":"Cai","year":"2000","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/S0148-9062(97)00322-7","article-title":"A study of udec modelling for blast wave propagation in jointed rock masses","volume":"35","author":"Chen","year":"1998","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_10","unstructured":"De Lemos, J.A.S.V. (1997). A Distinct Element Model for Dynamic Analysis of Jointed Rock with Application to Dam Foundations and Fault Motion, University Microfilms."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1007\/s00603-010-0098-1","article-title":"Micromechanical modelling of stress waves in rock and rock fractures","volume":"43","author":"Resende","year":"2010","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1007\/s00603-012-0287-1","article-title":"Some fundamental issues and verification of 3DEC in modeling wave propagation in jointed rock masses","volume":"45","author":"Deng","year":"2012","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1007\/s00603-006-0127-2","article-title":"Dynamic model of fracture normal behaviour and application to prediction of stress wave attenuation across fractures","volume":"41","author":"Zhao","year":"2007","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.compgeo.2007.01.001","article-title":"Udec modelling on wave propagation across fractured rock masses","volume":"35","author":"Zhao","year":"2008","journal-title":"Comput. Geotech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1429","DOI":"10.1007\/s00603-012-0352-9","article-title":"A numerical study on wave transmission across multiple intersecting joint sets in rock masses with udec","volume":"46","author":"Zhu","year":"2012","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_16","unstructured":"Barton, N. (1974). A Review of the Shear Strength of Filled Discontinuities in Rock, Norwegian Geotechnical Institute."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1016\/S1365-1609(00)00030-7","article-title":"Testing of rock joints filled with gouge using a triaxial apparatus","volume":"37","author":"Sinha","year":"2000","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.jappgeo.2013.06.009","article-title":"Seismic response of adjacent filled parallel rock fractures with dissimilar properties","volume":"96","author":"Wu","year":"2013","journal-title":"J. Appl. Geophys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1111\/j.1365-246X.2011.05110.x","article-title":"Seismic response of a single and a set of filled joints of viscoelastic deformational behaviour","volume":"186","author":"Zhu","year":"2011","journal-title":"Geophys. J. Int."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/j.ijrmms.2008.11.006","article-title":"Experimental study of stress wave propagation across a filled rock joint","volume":"46","author":"Li","year":"2009","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1007\/s00603-011-0212-z","article-title":"Loading rate dependency of dynamic responses of rock joints at low loading rate","volume":"45","author":"Wu","year":"2012","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.ijsolstr.2015.06.012","article-title":"Numerical simulation of stress wave propagating through filled joints by particle model","volume":"69","author":"Huang","year":"2015","journal-title":"Int. J. Solids Struct."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1002\/ggge.20076","article-title":"Laboratory observation of acoustic fluidization in granular fault gouge and implications for dynamic weakening of earthquake faults","volume":"14","author":"Xia","year":"2013","journal-title":"Geochem. Geophys. Geosyst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.soildyn.2006.06.004","article-title":"Evaluation of blast-induced ground vibration predictors","volume":"27","author":"Khandelwal","year":"2007","journal-title":"Soil Dynam. Earthq. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1016\/S1365-1609(02)00098-9","article-title":"Blast vibration damage to underground coal mines from adjacent open-pit blasting","volume":"39","author":"Singh","year":"2002","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.ijimpeng.2012.03.004","article-title":"Stress-strain behavior of sand at high strain rates","volume":"49","author":"Omidvar","year":"2012","journal-title":"Int. J. Impact Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jappgeo.2016.04.003","article-title":"Propagation of high amplitude stress waves through a filled artificial joint: An experimental study","volume":"130","author":"Huang","year":"2016","journal-title":"J. Appl. Geophys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1108\/02644409510799532","article-title":"A combined finite-discrete element method in transient dynamics of fracturing solids","volume":"12","author":"Munjiza","year":"1995","journal-title":"Eng. Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.ijrmms.2013.10.006","article-title":"Continuum\u2013discontinuum analysis of failure mechanisms around unsupported circular excavations in anisotropic clay shales","volume":"65","author":"Lisjak","year":"2014","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1007\/s00603-010-0092-7","article-title":"An example of realistic modelling of rock dynamics problems: Fem\/dem simulation of dynamic brazilian test on barre granite","volume":"43","author":"Mahabadi","year":"2010","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.cageo.2009.05.010","article-title":"Y-GUI: A graphical user interface and pre-processor for the combined finite-discrete element code, Y2D, incorporating material heterogeneity","volume":"36","author":"Mahabadi","year":"2010","journal-title":"Comput. Geosci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1061\/(ASCE)GM.1943-5622.0000216","article-title":"Y-geo: New combined finite-discrete element numerical code for geomechanical applications","volume":"12","author":"Mahabadi","year":"2012","journal-title":"Int. J. Geomech."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1016\/j.jrmge.2014.10.003","article-title":"Numerical simulation of hydraulic fracturing and associated microseismicity using finite-discrete element method","volume":"6","author":"Zhao","year":"2014","journal-title":"J. Rock Mech. Geotech. Eng."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/10\/1\/13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:29:21Z","timestamp":1760210961000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/10\/1\/13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,27]]},"references-count":33,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1]]}},"alternative-id":["ma10010013"],"URL":"https:\/\/doi.org\/10.3390\/ma10010013","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,12,27]]}}}