{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T11:09:08Z","timestamp":1767092948564,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2015,5,4]],"date-time":"2015-05-04T00:00:00Z","timestamp":1430697600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper deals with three grading entropy-based rules that describe different soil structure stability phenomena: an internal stability rule, a filtering rule and a segregation rule. These rules are elaborated on the basis of a large amount of laboratory testing and from existing knowledge in the field. Use is made of the theory of grading entropy to derive parameters which incorporate all of the information of the grading curve into a pair of entropy-based parameters that allow soils with common behaviours to be grouped into domains on an entropy diagram. Applications of the derived entropy-based rules are presented by examining the reason of a dam failure, by testing against the existing filter rules from the literature, and by giving some examples for the design of  non-segregating grading curves (discrete particle size distributions by dry weight). A physical basis for the internal stability rule is established, wherein the higher values of base entropy required for granular stability are shown to reflect the closeness between the mean and maximum grain diameters, which explains how there are sufficient coarser grains to achieve a stable grain skeleton.<\/jats:p>","DOI":"10.3390\/e17052781","type":"journal-article","created":{"date-parts":[[2015,5,4]],"date-time":"2015-05-04T10:33:04Z","timestamp":1430735584000},"page":"2781-2811","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["The Grading Entropy-based Criteria for Structural Stability of Granular Materials and Filters"],"prefix":"10.3390","volume":"17","author":[{"given":"Janos","family":"L\u0151rincz","sequence":"first","affiliation":[{"name":"Tengizchevroil, Farnborough, Hampshire GU14 7BF, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Em\u00f6ke","family":"Imre","sequence":"additional","affiliation":[{"name":"Ybl Mikl\u00f3s Faculty of Architecture and Civil Engineering, Szent Istv\u00e1n University, Budapest 1146, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen","family":"Fityus","sequence":"additional","affiliation":[{"name":"School of Engineering, University of Newcastle, Callaghan 2308, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Phong","family":"Trang","sequence":"additional","affiliation":[{"name":"Budapest University of Technology and Economics, Budapest 1111, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tibor","family":"Tarnai","sequence":"additional","affiliation":[{"name":"Budapest University of Technology and Economics, Budapest 1111, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Istv\u00e1n","family":"Talata","sequence":"additional","affiliation":[{"name":"Ybl Mikl\u00f3s Faculty of Architecture and Civil Engineering, Szent Istv\u00e1n University, Budapest 1146, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vijay","family":"Singh","sequence":"additional","affiliation":[{"name":"Department of Biological and Agricultural Engineering, Texas A&M University, 321 Scoates Hall, MS 2117, College Station, TX 77843, USA"},{"name":"Zachry Department of Civil Engineering, Texas A&M University, 321 Scoates Hall, MS 2117, College Station, TX 77843, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,5,4]]},"reference":[{"key":"ref_1","unstructured":"L\u0151rincz, J. (1986). Grading Entropy of Soils. [Ph. D. Thesis, Technical University of Budapest]. In Hungarian."},{"key":"ref_2","unstructured":"L\u0151rincz, J. (1992, January 20\u201322). On particle migration with the help of grading entropy. Filters in Geotechnical and Hydraulic Engineering, Karlsruhe, Germany."},{"key":"ref_3","unstructured":"L\u0151rincz, J. (1992, January 20\u201322). On granular filters with the help of grading entropy. Filters in Geotechnical and Hydraulic Engineering, Karlsruhe, Germany."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1061\/(ASCE)0733-9410(1984)110:6(684)","article-title":"Basic properties of sand and gravel filters","volume":"110","author":"Sherard","year":"1984","journal-title":"J. Geotech. Eng."},{"key":"ref_5","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_6","doi-asserted-by":"crossref","first-page":"557","DOI":"10.3208\/sandf.46.557","article-title":"Seepage failure mechanism of the Gouhou rock-fill dam during reservoir water infiltration","volume":"46","author":"Zhang","year":"2006","journal-title":"Soils Found."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.3390\/e14061079","article-title":"Case Studies and Benchmark Examples for the Use of Grading Entropy in Geotechnics","volume":"14","author":"Imre","year":"2012","journal-title":"Entropy"},{"key":"ref_8","unstructured":"O\u2019Sullivan, C. (2012, January 29\u201330). Applying Micro-mechanical Analysis to Realistic Sands. Birmingham, UK."},{"key":"ref_9","unstructured":"K\u00e9zdi, \u00c1. (1975). Phase Movements in Granular Soils, Budapest University of Technology and Economics. manuscript."},{"key":"ref_10","unstructured":"Khomenko, V.P. (2006, January 6\u201310). Suffosion hazard: Today\u2019s and tomorrow\u2019s problem for cities. Nottingham, UK."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Bonelli, S. (2013). Erosion in Geomechanics Applied to Dams and Levees, Wiley-ISTE.","DOI":"10.1002\/9781118577165"},{"key":"ref_12","unstructured":"Bezuijen, A., and Mastbergen, D.R. (1989, January 13\u201318). Liquefaction of a sand body constructed by means of hydraulic fill. Rio de Janeiro, Brazil."},{"key":"ref_13","first-page":"1115","article-title":"Observations on the process of backward erosion piping in small-, medium- and full-scale experiments","volume":"15","author":"Knoeff","year":"2011","journal-title":"Eur. J. Environ. Civil Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1080\/19648189.2011.9714845","article-title":"Fine-tuning of the backward erosion piping model through small-scale, medium-scale and IJkdijk experiments","volume":"15","author":"Sellmeijer","year":"2011","journal-title":"Euro. J. Environ. Civil Eng."},{"key":"ref_15","unstructured":"Lubockov, E.A. The calculation of suffosion properties of non-cohesive soils when using the non-suffosion analogue, Brno, Czech Republic."},{"key":"ref_16","unstructured":"Korn, G.A., and Korn, T.M. (1975). Mathematical Handbook for Scientists and Engineers, McGraw-Hill. [2nd]."},{"key":"ref_17","unstructured":"Hales, T.C., and Ferguson, S.P. (2011). The Kepler Conjecture, Springer-Verlag."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"To, H., Torres, S.A.G., and Scheuermann, A. (2014). Primary fabric fraction analysis of granular soils. Acta Geotech.","DOI":"10.1007\/s11440-014-0353-9"},{"key":"ref_19","unstructured":"Gouhou Dam Failure Investigation Team (1996). Gouhou Concrete-faced Rockfill Dam\u2014Design, Construction, Operation, and Failure, Water Conservancy and Hydropower Press."},{"key":"ref_20","unstructured":"Cedergren, H.R. (1973). Embankment-dam Engineering, Wiley."},{"key":"ref_21","unstructured":"Schuler, U., and Brauns, J. (1992, January 20\u201322). Behaviour of coarse and well-graded filters. Filters in Geotechnical and Hydraulic Engineering, Karlsruhe, Germany."},{"key":"ref_22","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. Geoenviron. Eng."},{"key":"ref_23","unstructured":"Terzaghi, K., Peck, R.B., and Mesri, G. (1996). Soil Mechanics in Engineering Practice, Wiley."},{"key":"ref_24","unstructured":"US Bureau of Reclamation (1998). Earth Manual Part 1, U.S. Department of the Interior Bureau of Reclamation, Geotechnical Research Technical Service Center. [3rd]."},{"key":"ref_25","unstructured":"Bertram, G.E. (1940). An Experimental Investigation of Protective Filters, Graduate School of Engineering, Harvard University."},{"key":"ref_26","first-page":"45","article-title":"Zum Problem mechanischer Deformationen nichtbindiger Lockergesteine durch die Sickerwasserstr\u00f6mung in Erdd\u00e4mmen","volume":"2","author":"Cistin","year":"1967","journal-title":"Wasserwirtschaft Wassertechnik"},{"key":"ref_27","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_28","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 Res."},{"key":"ref_29","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_30","unstructured":"ASTM 2005 C136-06 (2003). Standard Test Method for Sieve Analysis of Fine and Coarse Aggregates, American Society for Testing and Materials."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2781\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:45:43Z","timestamp":1760215543000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2781"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,4]]},"references-count":30,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2015,5]]}},"alternative-id":["e17052781"],"URL":"https:\/\/doi.org\/10.3390\/e17052781","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,5,4]]}}}