{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T05:20:12Z","timestamp":1776144012527,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2012,6,18]],"date-time":"2012-06-18T00:00:00Z","timestamp":1339977600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The grading entropy concept can be adapted to the field of geotechnics, to establish criteria for phenomena such as particle packing, particle migration and filtering, through a quantified expression of the order\/disorder in the grain size distribution, in terms of two entropy-based parameters. In this paper, the grading entropy theory is applied in some geotechnical case studies, which serve as benchmark examples to illustrate its application to the characterisation of piping, softening and dispersive soils, and to filtering problems in the context of a leachate collection system for a landfill site. Further, since unstable cohesive (dispersive) soils are generally improved by lime, the effect of lime addition is also considered, on the basis of some measurements and a further application of the grading entropy concept, which allows evolutions in the entropy of a soil to be considered as its grading is modified. The examples described support the hypothesis that the potential for soil erosion and particle migration can be reliably identified using grading entropy parameters derived from grading curve data, and applied through an established soil structure stability criteria and a filtering rule. It is shown that lime modification is not necessarily helpful in stabilizing against particle migration.<\/jats:p>","DOI":"10.3390\/e14061079","type":"journal-article","created":{"date-parts":[[2012,6,18]],"date-time":"2012-06-18T14:31:40Z","timestamp":1340029900000},"page":"1079-1102","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Case Studies and Benchmark Examples for the Use of Grading Entropy in Geotechnics"],"prefix":"10.3390","volume":"14","author":[{"given":"Em\u00f6ke","family":"Imre","sequence":"first","affiliation":[{"name":"Ybl Mikl\u00f3s Faculty of Architecture and Civil Engineering, Szent Istvan University, Thokoly 74, Budapest, 1146, Hungary"},{"name":"Geotechnical Department, Budapest University of Technology and Economics, Bp 1111 Muegyetem rkp 3, Budapest 1111, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00e0nos","family":"L\u00f6rincz","sequence":"additional","affiliation":[{"name":"Geotechnical Department, Budapest University of Technology and Economics, Bp 1111 Muegyetem rkp 3, Budapest 1111, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Janos","family":"Szendefy","sequence":"additional","affiliation":[{"name":"Geotechnical Department, Budapest University of Technology and Economics, Bp 1111 Muegyetem rkp 3, Budapest 1111, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Phong Q.","family":"Trang","sequence":"additional","affiliation":[{"name":"Geotechnical Department, Budapest University of Technology and Economics, Bp 1111 Muegyetem rkp 3, Budapest 1111, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laszlo","family":"Nagy","sequence":"additional","affiliation":[{"name":"Geotechnical Department, Budapest University of Technology and Economics, Bp 1111 Muegyetem rkp 3, Budapest 1111, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vijay P.","family":"Singh","sequence":"additional","affiliation":[{"name":"Deptartment of Biological and Agricultural Engineering, Texas A&M University, College Station, TX 77843, USA"},{"name":"Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX 77843, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen","family":"Fityus","sequence":"additional","affiliation":[{"name":"School of Engineering, the University of Newcastle, Callaghan 2308, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,6,18]]},"reference":[{"key":"ref_1","unstructured":"L\u0151rincz, J. (1986). Grading entropy of soils (in Hungarian). [Ph.D. Thesis, Technical University of Budapest]."},{"key":"ref_2","unstructured":"L\u0151rincz, J. (1993). Filters in Geotechnical and Hydraulic Engineering: Proceedings of the First International Conference \u201cGeo-Filters\u201d Karlsruhe\/Germany\/20\u201322 October 1, A.A. Balkema."},{"key":"ref_3","unstructured":"L\u0151rincz, J. (1993). Filters in Geotechnical and Hydraulic Engineering: Proceedings of the First International Conference \u201cGeo-Filters\u201d, Karlsruhe, Germany, 20\u201322 October 1992, A.A. Balkema."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1061\/(ASCE)1532-3641(2005)5:4(311)","article-title":"Grading entropy variation due to soil crushing","volume":"5","author":"Imre","year":"2005","journal-title":"Int. J. Geomech."},{"key":"ref_5","unstructured":"Lambe, T.W., and Whitman, R.V. (1969). Soil Mechanics, John Wiley and Sons."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1071\/SR9670047","article-title":"A classification of soil aggregates based on their coherence in water","volume":"5","author":"Emerson","year":"1967","journal-title":"Aust. J. Soil Res."},{"key":"ref_7","first-page":"53","article-title":"The role of clay fraction in the particle arrangement and stability of soil aggregates\u2014A review","volume":"3","author":"Rengasamy","year":"1984","journal-title":"Clay Research"},{"key":"ref_8","first-page":"1193","article-title":"Interparticle action and rheology of dispersive clays","volume":"105","author":"Yong","year":"1979","journal-title":"J. Geotech. Eng."},{"key":"ref_9","first-page":"45","article-title":"Seepage phenomena along flood protection dams (in Hungarian)","volume":"2","author":"Galli","year":"1955","journal-title":"V\u00edz\u00fcgyi K\u00f6zlem\u00e9nyek"},{"key":"ref_10","unstructured":"Khomenko, V.P. (2006, January 6\u201310). Suffosion hazard: Today's and tomorrow's problem for cities. Proceedings of IAEG2006, Nottingham, UK. No. 577."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1139\/t85-029","article-title":"Internal stability of granular filters","volume":"22","author":"Kenney","year":"1985","journal-title":"Can. Geotech. J."},{"key":"ref_12","unstructured":"Terzaghi, K., Peck, R.B., and Mesri, G. (1996). Soil Mechanics in Engineering Practice, John Wiley and Sons."},{"key":"ref_13","unstructured":"Jones, J.A.A. (1981). British Geomorphological Research Group Monograph Series 3, Geo Books."},{"key":"ref_14","unstructured":"ASTM C136-06 Standard Test Method for Sieve Analysis of Fine and Coarse Aggregates, ASTM International."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s12205-009-0257-7","article-title":"Some dry density transfer function for sands","volume":"13","author":"Imre","year":"2009","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"L\u0151rincz, J., K\u00e1rp\u00e1ti, L., Trang, P.Q., Imre, E., and Fityus, S. (2011, January 12\u201315). Some comments on the grading entropy variation and crushing of various sands. Proceedings of the 15th European Conference on Soil Mechanics and Geotechnical Engineering, Athens, Greece.","DOI":"10.3233\/978-1-60750-801-4-215"},{"key":"ref_17","unstructured":"Schuler, U., and Brauns, J. (1993). Filters in Geotechnical and Hydraulic Engineering: Proceedings of the First International Conference \u201cGeo-Filters\u201d, Karlsruhe, Germany, 20\u201322 October 1992, A.A. Balkema."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Middlebrooks, T.A. (1953). Earth dam practice in the United States. Transaction, ASCE Centennial Volume, 697\u2013722. Paper 2620.","DOI":"10.1061\/TACEAT.0006946"},{"key":"ref_19","unstructured":"Imre, E. (, January June). Characterization of dispersive and piping soils. Proceedings of the XI European Committee on Soil Mechanics and Foundation Engineering Conference, Copenhagen, Denmark."},{"key":"ref_20","unstructured":"Szepessy, J., Bog\u00e1rdi, I., and Vastagh, G. (1973). Literature Review about River Dike Failures (in Hungarian), VITUKI Research Report B203."},{"key":"ref_21","unstructured":"Nagy, G. (2010). Budapest University of Technology and Economics. Student Research Manuscript."},{"key":"ref_22","unstructured":"Feh\u00e9r, \u00c1. (1973). Improvement of River Dike Stability. B.209.2. Piping (in Hungarian), VITUKI Research Report B209."},{"key":"ref_23","unstructured":"Szepessy, J., and Szilv\u00e1ssy, K. (A k\u00f6rtv\u00e9lyesi g\u00e1tszakasz er\u0151s\u00edt\u00e9s\u00e9vel kapcsolatban v\u00e9gzett vizsg\u00e1latok, 1977). A k\u00f6rtv\u00e9lyesi g\u00e1tszakasz er\u0151s\u00edt\u00e9s\u00e9vel kapcsolatban v\u00e9gzett vizsg\u00e1latok, VITUKI Report 3.7."},{"key":"ref_24","unstructured":"Smoltczyk, U. (2003). Geotechnical Engineering Handbook, Wiley-VCH."},{"key":"ref_25","unstructured":"Nagy, L. (2011). Zbornik Radova Gradevinskog Fakukteta 20, Universitet u Novum Sadu Gradevinski Fakultet. ISSN 0352\u20136852."},{"key":"ref_26","unstructured":"T\u00f6r\u00f6k, \u00c1., and V\u00e1s\u00e1rhelyi, B. Buzg\u00e1rb\u00f3l kimosott talaj szemeloszl\u00e1sa (in Hungarian). Proceedings of the M\u00e9rn\u00f6kgeol\u00f3gia K\u0151zetmechanika Konferencia 2011; M\u00e9rn\u00f6kgeol\u00f3gia-k\u0151zetmechanika Kisk\u00f6nyvt\u00e1r 12, ISBN: 978-615-5086-04-5."},{"key":"ref_27","first-page":"23","article-title":"Tunnel erosion and liquefaction of granular and plastic soils in river dikes (in Hungarian)","volume":"29","author":"Szepessy","year":"1983","journal-title":"V\u00edz\u00fcgyi K\u00f6zlem\u00e9nyek"},{"key":"ref_28","unstructured":"Koorevaar, P., Menelik, G., and Dirksen, C. (1983). Elements of Soil Physics, Elsevier."},{"key":"ref_29","first-page":"69","article-title":"Pinhole test for identifying dispersive soils","volume":"102","author":"Sherard","year":"1976","journal-title":"J. Geotech. Eng.-ASCE"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Sherard, I.L., and Decker, R.S. (1977). Dispersive Clays, Related Piping, and Erosion in Geotechnical Projects, ASTM. STP 623.","DOI":"10.1520\/STP623-EB"},{"key":"ref_31","first-page":"26","article-title":"Trends and debatable aspects in embankment dam engineering","volume":"36","author":"Sherard","year":"1984","journal-title":"International Water Power Dam Construction"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Sherard, I.L., and Decker, R.S. (1977). Dispersive Clays, Related Piping, and Erosion in Geotechnical Projects, ASTM. STP 623.","DOI":"10.1520\/STP623-EB"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Sherard, I.L., and Decker, R.S. (1977). Dispersive Clays, Related Piping, and Erosion in Geotechnical Projects, ASTM. STP 623.","DOI":"10.1520\/STP623-EB"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Sherard, I.L., and Decker, R.S. (1977). Dispersive Clays, Related Piping, and Erosion in Geotechnical Projects, ASTM. STP 623.","DOI":"10.1520\/STP623-EB"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Sherard, I.L., and Decker, R.S. (1977). Dispersive Clays, Related Piping, and Erosion in Geotechnical Projects, ASTM. STP 623.","DOI":"10.1520\/STP623-EB"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1061\/(ASCE)0733-9410(1983)109:2(244)","article-title":"Failure of an earth dam","volume":"109","author":"Khan","year":"1983","journal-title":"A case study. J. Geotech. Eng.-ASCE"},{"key":"ref_37","first-page":"1017","article-title":"Dispersive soil problem at the Los Esteros Dam","volume":"105","author":"McDaniel","year":"1979","journal-title":"J. Geotech. Eng.-ASCE"},{"key":"ref_38","unstructured":"K\u00e9zdi, \u00c1. (1975). Phase movements in granular soils, unpublished material."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1061\/(ASCE)1090-0241(2008)134:3(267)","article-title":"From theory to practice in geotechnical filter design","volume":"134","author":"Fannin","year":"2008","journal-title":"J. Geotech. Eng.-ASCE"},{"key":"ref_40","unstructured":"US Bureau of Reclamation (1998). Earth Manual Part 1."},{"key":"ref_41","unstructured":"Imre, E., Kov\u00e1cs, M., Czap, Z., Trang, P.Q., and Szab\u00f3, I. (2007, January 22\u201324). Leachate collection system of municipal landfills in Hungary. Proceedings of Geo-Environmental Engineering 2007, the 7th Japan-Korean-French Seminar, Grenoble, France."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1139\/t99-036","article-title":"Field observations of clogging in a landfill leachate collection system","volume":"36","author":"Fleming","year":"1999","journal-title":"Can. Geotech. J."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1139\/t03-070","article-title":"Laboratory studies of clogging of landfill leachate collection and drainage systems","volume":"41","author":"Fleming","year":"2004","journal-title":"Can. Geotech. J."},{"key":"ref_44","unstructured":"Wong, D.K.H. (1986). A report on the review phase of the lime-modified clay research program, internal report."},{"key":"ref_45","unstructured":"Diamond, S., and Kinter, E.B. (1965). Mechanisms of Soil-Lime Stabilization, Transportation Research Board."},{"key":"ref_46","unstructured":"Trang, P.Q., K\u00e1rp\u00e1ti, L., Ny\u00e1ri, I., Szendefy, J., Imre, E., and L\u00f5rincz, J. (, January October). Entropy concept to explain particle breakage and soil improvement. Proceedings of the Young Geotechnical Engineers Conference, Alexandria, Egypt."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/6\/1079\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:50:50Z","timestamp":1760219450000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/6\/1079"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,18]]},"references-count":46,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2012,6]]}},"alternative-id":["e14061079"],"URL":"https:\/\/doi.org\/10.3390\/e14061079","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,18]]}}}