{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T14:43:52Z","timestamp":1779115432797,"version":"3.51.4"},"reference-count":52,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2020,10,22]],"date-time":"2020-10-22T00:00:00Z","timestamp":1603324800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Displacements of landfills play an important role in the reclamation process and geotechnical safety improvement of such sites. Landfill settlements are defined as a vertical displacement of waste body due to compression, degradable nature of the waste, and creep phenomenon of the waste particles. Waste composition is more diverse than natural soil. Thus, it has to be properly placed and compacted since the landfill body will continuously settle down. Several models of the landfill displacement estimation have already been developed. The aim of the present study was: (i) to review the methods of landfill settlements computation and (ii) to propose the model allowing landfill body displacements simulation based on monitoring datasets applying a Global Navigation Satellite Systems (GNSS) measurement. The new model employs Gauss-Newton iteration and Runge-Kutta methods to estimate landfill surface displacements. The objectives were to analyse and mathematically describe the landfill body displacements. The GNSS geodetic survey and computations allowed concluding that the landfill body has been transformed over the years. The results revealed that the curves of waste displacement are in agreement with the measured total displacement of the landfill, and all curves corresponding to waste displacement are perpendicular to the active edge of the landfill. In the period of a maximum of 4.5 years after the waste deposition with a layer of up to 16.2 m thickness, the phenomenon of expansion was observed, which then disappears, and more settlement occurs due to the gravity of upper layers. The analysed landfill as a whole does not experience significant displacements. Neither of the slope failures are observed, even for large inclination.<\/jats:p>","DOI":"10.3390\/s20215998","type":"journal-article","created":{"date-parts":[[2020,10,22]],"date-time":"2020-10-22T20:51:00Z","timestamp":1603399860000},"page":"5998","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Analytical Modelling of MSW Landfill Surface Displacement Based on GNSS Monitoring"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6778-4634","authenticated-orcid":false,"given":"Dana","family":"Adamcov\u00e1","sequence":"first","affiliation":[{"name":"Faculty of AgriSciences, Mendel University in Brno, Zem\u011bd\u011blsk\u00e1 1, 613 00 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7213-6498","authenticated-orcid":false,"given":"Stanislav","family":"Barto\u0148","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering Automatic Control and Informatics, Opole University of Technology, Pr\u00f3szkowska 76, 45-758 Opole, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1503-7650","authenticated-orcid":false,"given":"Piotr","family":"Osinski","sequence":"additional","affiliation":[{"name":"Institute of Civil Engineering, Warsaw University of Life Sciences\u2014SGGW, Nowoursynowska 159, 02-776 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7320-6347","authenticated-orcid":false,"given":"Grzegorz","family":"Pasternak","sequence":"additional","affiliation":[{"name":"Institute of Civil Engineering, Warsaw University of Life Sciences\u2014SGGW, Nowoursynowska 159, 02-776 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0326-5672","authenticated-orcid":false,"given":"Anna","family":"Podlasek","sequence":"additional","affiliation":[{"name":"Institute of Civil Engineering, Warsaw University of Life Sciences\u2014SGGW, Nowoursynowska 159, 02-776 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2384-6207","authenticated-orcid":false,"given":"Magdalena Daria","family":"Vaverkov\u00e1","sequence":"additional","affiliation":[{"name":"Faculty of AgriSciences, Mendel University in Brno, Zem\u011bd\u011blsk\u00e1 1, 613 00 Brno, Czech Republic"},{"name":"Institute of Civil Engineering, Warsaw University of Life Sciences\u2014SGGW, Nowoursynowska 159, 02-776 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3895-960X","authenticated-orcid":false,"given":"Eugeniusz","family":"Koda","sequence":"additional","affiliation":[{"name":"Institute of Civil Engineering, Warsaw University of Life Sciences\u2014SGGW, Nowoursynowska 159, 02-776 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.wasman.2015.10.020","article-title":"Landfill area estimation based on integrated waste disposal options and solid waste forecasting using modified ANFIS model","volume":"55","author":"Younes","year":"2016","journal-title":"Waste Manag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3674","DOI":"10.1002\/ldr.3119","article-title":"The use of vegetation as a natural strategy for landfill restoration","volume":"29","author":"Radziemska","year":"2018","journal-title":"Land Degrad. Dev."},{"key":"ref_3","first-page":"76","article-title":"Settlements\u2014The short and the long of it. Geotechnical Characterization, Field Measurement and Laboratory Testing of Municipal Solid Waste","volume":"209","author":"McDougall","year":"2011","journal-title":"ASCE Geotech. Spec. Publ."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Koda, E., Kiersnowska, A., Kawalec, J., and Osi\u0144ski, P. (2020). Landfill Slope Stability Improvement Incorporating Reinforcements in Reclamation Process Applying Observational Method. Appl. Sci., 10.","DOI":"10.3390\/app10051572"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1080\/10934529.2016.1212556","article-title":"Settlement behavior of municipal solid waste due to internal and external environmental factors in a lysimeter","volume":"51","author":"Melo","year":"2016","journal-title":"J. Environ. Sci. Health Part A Toxic Hazard. Subst. Environ. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/0148-9062(75)90051-0","article-title":"Settlement of Waste Disposal Fills","volume":"12","author":"Sowers","year":"1975","journal-title":"Int. J. Rock Mech. Min. Sci. Geomech. Abstr."},{"key":"ref_7","unstructured":"Koda, E., and Zakowicz, S. (1998, January 7\u201311). Physical and hydraulics properties of the MSW for water balance of the landfill. Proceedings of the 3rd International Congress on Environmental Geotechnics, Lisboa, Portugal."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1016\/j.wasman.2012.10.001","article-title":"Monitoring and modeling of long-term settlements of an experimental landfill in Brazil","volume":"33","author":"Catapreta","year":"2013","journal-title":"Waste Manag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1016\/j.wasman.2016.09.016","article-title":"Geotechnical properties of municipal solid waste at Laogang Landfill, China","volume":"63","author":"Feng","year":"2017","journal-title":"Waste Manag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1139\/cgj-2017-0558","article-title":"Modelling deformation and strains induced by waste settlement in a centrifuge test","volume":"55","author":"Yu","year":"2018","journal-title":"Can. Geotech. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1390","DOI":"10.1002\/nag.2687","article-title":"Model for degradation induced settlements as part of a coupled landfill model","volume":"41","author":"Bente","year":"2017","journal-title":"Int. J. Numer. Anal. Methods Geomech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1007\/s40891-016-0082-2","article-title":"Modeling coupled processes in municipal solid waste landfills: An overview with key engineering challenges","volume":"3","author":"Reddy","year":"2017","journal-title":"Int. J. Geosynth. Ground Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"153","DOI":"10.30955\/gnj.002982","article-title":"Investigation of solid waste characteristics in field-scale landfill test cells","volume":"21","author":"Top","year":"2019","journal-title":"Glob. Nest. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.wasman.2017.07.048","article-title":"A practical approach for calculating the settlement and storage capacity of landfills based on the space and time discretization of the landfilling process","volume":"69","author":"Gao","year":"2017","journal-title":"Waste Manag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1018","DOI":"10.1016\/j.wasman.2008.08.018","article-title":"Effects of gas and moisture on modeling of bioreactor landfill settlement","volume":"29","author":"Hettiarachchi","year":"2009","journal-title":"Waste Manag."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1080\/10473289.2007.10465318","article-title":"Analysis of long-term settlement of municipal solid waste landfills as determined by various settlement estimation methods","volume":"57","author":"Hyun","year":"2007","journal-title":"J. Air Waste Manag. Assoc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"11","DOI":"10.22630\/ASPA.2019.18.2.17","article-title":"Impact assessment of the municipal solid landfill on environment: A case study","volume":"18","year":"2019","journal-title":"Acta Sci. Pol. Archit."},{"key":"ref_18","first-page":"159","article-title":"Long-term settlement behavior of landfills with refuse decomposition","volume":"24","author":"Park","year":"1997","journal-title":"J. Solid Waste Technol. Manag."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1016\/j.compgeo.2007.11.008","article-title":"Constitutive model for long-term municipal solid waste mechanical behaviour","volume":"35","author":"Machado","year":"2008","journal-title":"Comput. Geotech."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"942","DOI":"10.1061\/(ASCE)1090-0241(2002)128:11(940)","article-title":"Constitutive model for municipal solid waste","volume":"128","author":"Machado","year":"2002","journal-title":"J. Geotech. Geoenviron. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1061\/(ASCE)1090-0241(2003)129:4(372)","article-title":"Composite compressibility model for municipal solid waste","volume":"129","author":"Marques","year":"2003","journal-title":"J. Geotech. Geoenviron. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"952","DOI":"10.1016\/j.wasman.2008.05.011","article-title":"Geotechnical properties of fresh municipal solid waste at Orchard Hills Landfill, USA","volume":"29","author":"Reddy","year":"2009","journal-title":"Waste Manag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1080\/10643380091184200","article-title":"Modeling settlement in MSW landfills: A critical review","volume":"30","author":"Khoury","year":"2000","journal-title":"Crit. Rev. Environ. Sci. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/j.wasman.2015.08.016","article-title":"Simulating settlement during waste placement at a landfill with waste lifts placed under frozen conditions","volume":"46","author":"Murray","year":"2015","journal-title":"Waste Manag."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"51","DOI":"10.28927\/SR.401051","article-title":"Statistical Modeling of Municipal Solid Waste Settlement from a Lysimeter","volume":"40","author":"Sousa","year":"2017","journal-title":"Soils Rocks"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.wasman.2015.04.011","article-title":"Assessment of municipal solid waste settlement models based on field-scale data analysis","volume":"42","author":"Bareither","year":"2015","journal-title":"Waste Manag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1080\/22797254.2019.1683471","article-title":"UAV for monitoring the settlement of a landfill","volume":"52","author":"Baiocchi","year":"2019","journal-title":"Eur. J. Remote Sens."},{"key":"ref_28","first-page":"12","article-title":"Simulation of the solid waste landfill settlement taking into account underlying soil","volume":"3","author":"Remez","year":"2016","journal-title":"East Eur. J. Enterp. Technol."},{"key":"ref_29","unstructured":"Esteban-Altabella, J., McDougall, J., Colomer-Mendoza, F.J., Gallardo, A., and Edo-Alc\u00f3n, N. (2017, January 2\u20136). Review and application of a settlement model for landfills. Proceedings of the Sardinia 16th International Waste Management and Landfill Symposium, Cagliari, Italy."},{"key":"ref_30","first-page":"267","article-title":"Municipal solid waste settlement (MSWS) model with account for integrated creep and degradation process","volume":"51","author":"Topolnicki","year":"2004","journal-title":"Arch. Hydro Eng. Environ. Mech."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1061\/(ASCE)GT.1943-5606.0000835","article-title":"Compression of municipal solid waste in bioreactor landfills: Mechanical creep and biocompression","volume":"139","author":"Bareither","year":"2013","journal-title":"J. Geotech. Geoenviron. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1680\/warm.2008.161.3.121","article-title":"The long-term settlement of landfill waste","volume":"Volume 161","author":"Ivanova","year":"2008","journal-title":"Proceedings of the Institution of Civil Engineers\u2013Waste and Resource Management"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.15244\/pjoes\/29940","article-title":"Long-Term Temperature Monitoring of a Municipal Solid Waste Landfill","volume":"24","year":"2015","journal-title":"Pol. J. Environ. Stud."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"109809","DOI":"10.1016\/j.jenvman.2019.109809","article-title":"Performance comparison of a MSW settlement prediction model in Tehran landfill","volume":"254","author":"Tahmoorian","year":"2020","journal-title":"J. Environ. Manag."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.wasman.2017.10.043","article-title":"Analysis of landfill design variables based on scientific computing","volume":"71","author":"Cuartas","year":"2018","journal-title":"Waste Manag."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1061\/(ASCE)1090-0241(1998)124:1(21)","article-title":"Estimation of municipal solid waste landfill settlement","volume":"1","author":"Ling","year":"1998","journal-title":"J. Geotech. Geoenviron. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1177\/0734242X18788149","article-title":"Identification of initial settlement of municipal solid waste layers in Indonesian landfill","volume":"36","author":"Hadinata","year":"2018","journal-title":"Waste Manag. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11431-019-1439-2","article-title":"Comparison of settlement behaviors of high-food-waste-content (HFWC) and low-food-waste-content (LFWC) MSWs and assessment of their prediction models","volume":"62","author":"Xu","year":"2019","journal-title":"Sci. China Technol. Sci."},{"key":"ref_39","unstructured":"Bjarngard, A., and Edgers, L. (1990, January 19\u201320). Settlement of Municipal Solid Waste Landfills. Proceedings of the 13th Annual Madison Waste Conference, Madison, WI, USA."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Hossain, M.S., and Gabr, M.A. (2005). Prediction of municipal solid waste landfill settlement with leachate recirculation. Waste Containment and Remediation, ASCE.","DOI":"10.1061\/40789(168)50"},{"key":"ref_41","first-page":"1","article-title":"A Theory for Soils Exhibiting Secondary Compression","volume":"296","author":"Gibson","year":"1961","journal-title":"Acta Polytech. Scand."},{"key":"ref_42","first-page":"475","article-title":"Sanitary landfill settlement rates","volume":"101","author":"Yen","year":"1975","journal-title":"J. Geotech. Geoenviron. Eng."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Edil, T.B., Ranguette, V.J., and Wuellner, W.W. (1990). Settlement of municipal refuse. Geotechnics of Waste Fills\u2014Theory and Practice, ASTM International.","DOI":"10.1520\/STP25309S"},{"key":"ref_44","first-page":"1","article-title":"Assessing Geotechnical Risks in the Frame of Landfill Engineering in Eastern Europe","volume":"1","author":"Schneider","year":"2017","journal-title":"J. Geol. Res. Eng."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Liu, Z., Liu, P., Zhou, C., Huang, Y., and Zhang, L. (2019). Structural Health Monitoring of Underground Structures in Reclamation Area Using Fiber Bragg Grating Sensors. Sensors, 19.","DOI":"10.3390\/s19132849"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Wilk, A., Koc, W., Specht, C., Judek, S., Karwowski, K., Chrostowski, P., Czaplewski, K., Dabrowski, P.S., Grulkowski, S., and Licow, R. (2020). Digital Filtering of Railway Track Coordinates in Mobile Multi\u2013Receiver GNSS Measurements. Sensors, 20.","DOI":"10.3390\/s20185018"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Chang, L., Niu, X., and Liu, T. (2020). GNSS\/IMU\/ODO\/LiDAR-SLAM Integrated Navigation System Using IMU\/ODO Pre-Integration. Sensors, 20.","DOI":"10.3390\/s20174702"},{"key":"ref_48","first-page":"923928","article-title":"Monitoring displacements of an earthen dam using GNSS and remote sensing","volume":"Volume 9239","author":"Dardanelli","year":"2014","journal-title":"Remote Sensing for Agriculture, Ecosystems and Hydrology XVI"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1736","DOI":"10.1109\/TPWRD.2019.2919927","article-title":"Application of Gauss\u2013Newton Iteration Algorithm on Winding Radial Deformation Diagnosis","volume":"34","author":"Ren","year":"2019","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.jcp.2019.03.027","article-title":"When topological derivatives met regularized Gauss-Newton iterations in holographic 3D imaging","volume":"388","author":"Carpio","year":"2019","journal-title":"J. Comput. Phys."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Agarwal, R.P., Hodis, S., and O\u2019Regan, D. (2019). Runge-Kutta Method. 500 Examples and Problems of Applied Differential Equations, Springer.","DOI":"10.1007\/978-3-030-26384-3"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1144\/qjegh2017-103","article-title":"Atmosphere\u2013vegetation\u2013soil interactions in a climate change context; impact of changing conditions on engineered transport infrastructure slopes in Europe","volume":"51","author":"Tang","year":"2018","journal-title":"Q. J. Eng. Geol. Hydrogeol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/21\/5998\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:26:30Z","timestamp":1760178390000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/21\/5998"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,22]]},"references-count":52,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["s20215998"],"URL":"https:\/\/doi.org\/10.3390\/s20215998","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,22]]}}}