{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T14:52:21Z","timestamp":1763563941829,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2016,8,11]],"date-time":"2016-08-11T00:00:00Z","timestamp":1470873600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51578212"],"award-info":[{"award-number":["51578212"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the 973 Program of China","award":["2012CB417005"],"award-info":[{"award-number":["2012CB417005"]}]},{"name":"the Postgraduate Research and Innovation Projects in Jiangsu Province","award":["(KYZZ_0141)"],"award-info":[{"award-number":["(KYZZ_0141)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Owing to the randomness in the fracture flow system, the seepage system beneath a complex rock mass dam is inherently complex and highly uncertain, an investigation of the dam leakage by estimating the spatial distribution of the seepage field by conventional methods is quite difficult. In this paper, the entropy theory, as a relation between the definiteness and probability, is used to probabilistically analyze the characteristics of the seepage system in a complex rock mass dam. Based on the principle of maximum entropy, an equation for the vertical distribution of the seepage velocity in a dam borehole is derived. The achieved distribution is tested and compared with actual field data, and the results show good agreement. According to the entropy of flow velocity in boreholes, the rupture degree of a dam bedrock has been successfully estimated. Moreover, a new sampling scheme is presented. The sampling frequency has a negative correlation with the distance to the site of the minimum velocity, which is preferable to the traditional one. This paper demonstrates the significant advantage of applying the entropy theory for seepage velocity analysis in a complex rock mass dam.<\/jats:p>","DOI":"10.3390\/e18080293","type":"journal-article","created":{"date-parts":[[2016,8,11]],"date-time":"2016-08-11T10:29:29Z","timestamp":1470911369000},"page":"293","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Characterization of Seepage Velocity beneath a Complex Rock Mass Dam Based on Entropy Theory"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7994-0166","authenticated-orcid":false,"given":"Xixi","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Water Environment, China Institute of Water Resources and Hydropower Research, Beijing 100038, China"},{"name":"College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China"}]},{"given":"Jiansheng","family":"Chen","sequence":"additional","affiliation":[{"name":"Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, China"},{"name":"Geotechnical Research Institute of Hohai University, Nanjing 210098, China"}]},{"given":"Tao","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, China"},{"name":"Geotechnical Research Institute of Hohai University, Nanjing 210098, China"}]},{"given":"Huaidong","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Water Environment, China Institute of Water Resources and Hydropower Research, Beijing 100038, China"}]},{"given":"Linghua","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Water Environment, China Institute of Water Resources and Hydropower Research, Beijing 100038, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,8,11]]},"reference":[{"key":"ref_1","first-page":"305","article-title":"Hydrogeological uncertainties in delineation of leakage at karst dam sites, the Zagros Region, Iran","volume":"69","author":"Mohammadi","year":"2007","journal-title":"J. Cave Karst Stud."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s12665-011-1069-x","article-title":"Water leakage paths in the Doosti Dam, Turkmenistan and Iran","volume":"65","author":"Mozafari","year":"2012","journal-title":"Environ. Earth Sci."},{"key":"ref_3","first-page":"8","article-title":"Study on the disaster-causing mechanism of the tailings dam falling","volume":"5","author":"Zheng","year":"2008","journal-title":"J. Saf. Sci. Technol."},{"key":"ref_4","first-page":"368","article-title":"Lattice Boltzmann modeling for tracer test analysis in a fractured Gneiss aquifer","volume":"5","author":"Abdelaziz","year":"2013","journal-title":"Nat. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"657","DOI":"10.4236\/jwarp.2012.48076","article-title":"Analytical and numerical modeling of flow in a fractured gneiss aquifer","volume":"4","author":"Abdelaziz","year":"2012","journal-title":"J. Water Resour. Prot."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1286","DOI":"10.1016\/0021-8928(60)90107-6","article-title":"Basic concepts in theory of seepage of homogeneous liquids in fissured rocks","volume":"24","author":"Ge","year":"1960","journal-title":"J. Appl. Math. Mech."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.enggeo.2009.11.006","article-title":"Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis","volume":"110","author":"Srivastava","year":"2010","journal-title":"Eng. Geol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.enggeo.2012.02.013","article-title":"Probabilistic analysis of seepage that considers the spatial variability of permeability for an embankment on soil foundation","volume":"133","author":"Cho","year":"2012","journal-title":"Eng. Geol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.compgeo.2012.07.010","article-title":"Two-dimensional probabilistic infiltration analysis with a spatially varying permeability function","volume":"48","author":"Zhu","year":"2013","journal-title":"Comput. Geotech."},{"key":"ref_10","first-page":"1","article-title":"The entropy theory as a tool for modelling and decision-making in environmental and water resources","volume":"26","author":"Singh","year":"2000","journal-title":"Water SA"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1007\/s11069-014-1515-7","article-title":"Entropy weight-set pair analysis based on tracer techniques for dam leakage investigation","volume":"76","author":"Wang","year":"2015","journal-title":"Nat. Hazards"},{"unstructured":"Contreras, I.A., and Hern\u00e1ndez, S.H. Techniques for prevention and detection of leakage in dams and reservoirs. Available online: http:\/\/ussdams.com\/proceedings\/2010Proc\/785-814.pdf.","key":"ref_12"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/19648189.2013.834582","article-title":"Experimental study of seawall piping under water level fluctuation","volume":"17","author":"Chen","year":"2013","journal-title":"Eur. J. Environ. Civ. Eng."},{"key":"ref_14","first-page":"1131","article-title":"Experimental study of low temperature water seepage detection model of embankment dam","volume":"24","author":"Chen","year":"2015","journal-title":"Fresenius Environ. Bull."},{"key":"ref_15","first-page":"230","article-title":"Radioactive or Natural Tracer Techniques for Leak Determining of Dam Abutment","volume":"6","author":"Chen","year":"1995","journal-title":"Nucl. Sci. Tech."},{"key":"ref_16","first-page":"100","article-title":"Generalized physical model of tracer dilution for measuring seepage velocity in well","volume":"9","author":"Chen","year":"2002","journal-title":"J. Hydraul. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.jconhyd.2007.09.001","article-title":"A New Tracer Technique for Monitoring Groundwater Fluxes: The Finite Volume Point Dilution Method","volume":"95","author":"Brouyere","year":"2008","journal-title":"J. Contam. Hydrol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s10064-011-0379-2","article-title":"Water seepage beneath dams on soluble evaporite deposits: A laboratory and field study (Caspe Dam, Spain)","volume":"71","author":"Piqueras","year":"2001","journal-title":"Bull. Eng. Geol. Environ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"952","DOI":"10.1111\/gwat.12151","article-title":"Characterization of Focused Seepage through an Earthfill Dam Using Geoelectrical Methods","volume":"52","author":"Ikard","year":"2014","journal-title":"Ground Water"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1302","DOI":"10.1139\/t02-068","article-title":"A dual fracture model to simulate large-scale flow through fractured rocks","volume":"39","author":"Wang","year":"2002","journal-title":"Can. Geotech. J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1186\/cc2948","article-title":"Complex systems and the technology of variability analysis","volume":"8","author":"Seely","year":"2005","journal-title":"Crit. Care"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/0309-1708(86)90015-1","article-title":"Derivation of some frequency distributions using the principle of maximum entropy (POME)","volume":"9","author":"Singh","year":"1986","journal-title":"Adv. Water Resour."},{"key":"ref_23","first-page":"353","article-title":"Some recent advances in the application of the principle of maximum entropy (POME) in hydrology","volume":"164","author":"Singh","year":"1987","journal-title":"IAHS Publ."},{"doi-asserted-by":"crossref","unstructured":"Singh, V.P., and Fiorentino, M. (1992). Entropy and Energy Dissipation in Water Resources, Kluwer Academic Publishers.","key":"ref_24","DOI":"10.1007\/978-94-011-2430-0"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.2134\/jeq2000.2931019x","article-title":"Entropy-Based Parameter Estimation in Hydrology","volume":"29","author":"Singh","year":"2000","journal-title":"J. Environ. Qual."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1061\/(ASCE)0733-9429(1987)113:5(583)","article-title":"Entropy and probability concepts in hydraulics","volume":"113","author":"Chiu","year":"1987","journal-title":"J. Hydraul. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1061\/(ASCE)0733-9429(1988)114:7(738)","article-title":"Entropy and 2-D velocity distribution in open channels","volume":"114","author":"Chiu","year":"1988","journal-title":"J. Hydraul. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1061\/(ASCE)0733-9429(1989)115:5(576)","article-title":"Velocity Distribution in Open Channel Flow","volume":"115","author":"Chiu","year":"1989","journal-title":"J. Hydraul. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1061\/(ASCE)0733-9429(1991)117:5(615)","article-title":"Application of Entropy Concept in Open-channel Flow Study","volume":"117","author":"Chiu","year":"1991","journal-title":"J. Hydraul. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1080\/00221686.2011.635889","article-title":"Entropy approach for 2D velocity distribution in open-channel flow","volume":"49","author":"Marini","year":"2011","journal-title":"J Hydraul. Res."},{"doi-asserted-by":"crossref","unstructured":"Greco, M., and Mirauda, D. (2015). Entropy Parameter Estimation in Large-Scale Roughness Open Channel. J. Hydrol. Eng., 20.","key":"ref_31","DOI":"10.1061\/(ASCE)HE.1943-5584.0001009"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3960","DOI":"10.1016\/j.physa.2008.01.044","article-title":"Application of spectral methods for high-frequency financial data to quantifying states of market participants","volume":"387","author":"Sato","year":"2007","journal-title":"Physica A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"765","DOI":"10.2166\/wst.2008.674","article-title":"Assessment of the groundwater salinity monitoring network of the Tehran region: Application of the discrete entropy theory","volume":"58","author":"Masoumi","year":"2008","journal-title":"Water Sci. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"453","DOI":"10.30638\/eemj.2009.061","article-title":"Theoretical analysis of the economy-ecology-environment system","volume":"8","author":"Nicolae","year":"2009","journal-title":"Environ. Eng. Manag. J."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1108\/03684920910973234","article-title":"Characterizing Cantorian sets by entropy-like quantities","volume":"38","author":"Karamanos","year":"2009","journal-title":"Kybernetes"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"30007","DOI":"10.1209\/0295-5075\/88\/30007","article-title":"Non-extensitivity vs. informative moments for financial models\u2014A unifying framework and empirical results","volume":"88","author":"Herrmann","year":"2009","journal-title":"Europhys. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s10661-008-0418-z","article-title":"Design of on-line river water quality monitoring systems using the entropy theory: A case study","volume":"155","author":"Karamouz","year":"2009","journal-title":"Environ. Monit. Assess."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1029\/2009WR008193","article-title":"Entropy theory for derivation of infiltration equations","volume":"46","author":"Singh","year":"2010","journal-title":"Water Resour. Res."},{"key":"ref_39","first-page":"1560","article-title":"Entropy-based approach for estimation of natural recharge in Kodaganar River basin, Tamil Nadu, India","volume":"99","author":"Mondal","year":"2010","journal-title":"Curr. Sci. India"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communications","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"unstructured":"Shannon, C.E., and Wyner, A.D. (1993). Claude Elwood Shannon: Collected Papers, Wiley.","key":"ref_41"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1287\/opre.38.2.362","article-title":"Generalized Entropy-Based Weights for Multiattribute Value Models","volume":"38","author":"Soofi","year":"1990","journal-title":"Oper. Res."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","article-title":"Information Theory and Statistical Mechanics","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"unstructured":"Levine, R.D., and Tribus, M. (1979). The Maximum Entropy Formalism, MIT Press.","key":"ref_44"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/TIT.1980.1056144","article-title":"Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy","volume":"26","author":"Shore","year":"1980","journal-title":"IEEE Trans. Inform. Theory"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/8\/293\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:28:15Z","timestamp":1760210895000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/8\/293"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,11]]},"references-count":45,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2016,8]]}},"alternative-id":["e18080293"],"URL":"https:\/\/doi.org\/10.3390\/e18080293","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2016,8,11]]}}}