{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T09:08:50Z","timestamp":1775812130038,"version":"3.50.1"},"reference-count":83,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,14]],"date-time":"2021-01-14T00:00:00Z","timestamp":1610582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"German Research Foundation (DFG)","award":["257344691"],"award-info":[{"award-number":["257344691"]}]},{"name":"Bavarian-French University Cooperation Centre (BFHZ-CCUFB)","award":["FKZ8_2017"],"award-info":[{"award-number":["FKZ8_2017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>For the selective paste intrusion (SPI) method, thin layers of aggregate are locally bound by cement paste where the structure shall arise. After completion of the printing process, the structure is excavated from the particle-bed and the unbound particles are removed. However, for a sufficient layer bonding and shape accuracy, the rheology of the cement paste must be adapted to the flow resistance of the particle-bed. For practical application, that means mostly time and material consuming \u201ctrial and error\u201d tests. To prevent that, analytical models can help to predict the penetration of the cement paste. This paper presents four analytical models to calculate the penetration depth of a cement paste into a particle packing. Based on Darcy\u2019s law, an already existing model is slightly modified (model A+) and a generalized (model C), an advanced generalized (model D) as well as a simplified model (model B\/B+) are developed. Compared to conducted tests on the penetration depth, model B showed good accuracy (deviation &lt;1.5 mm) for pastes with a yield stress \u22658.2 Pa, model A+\/B+\/C for \u2265 5.4 Pa and model D even for &lt;5.4 Pa. Finally, an application guide for each model for practical use will be given.<\/jats:p>","DOI":"10.3390\/ma14020389","type":"journal-article","created":{"date-parts":[[2021,1,14]],"date-time":"2021-01-14T11:39:14Z","timestamp":1610624354000},"page":"389","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Penetration of Cement Pastes into Particle-Beds: A Comparison of Penetration Models"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3762-5592","authenticated-orcid":false,"given":"Daniel","family":"Weger","sequence":"first","affiliation":[{"name":"Chair of Materials Science and Testing, Centre for Building Materials (CBM), Technical University of Munich, 81245 Munich, Germany"}]},{"given":"Alexandre","family":"Pierre","sequence":"additional","affiliation":[{"name":"L2MGC, EA4114, CY Cergy Paris Universit\u00e9, 95031 Cergy-Pontoise, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7105-4212","authenticated-orcid":false,"given":"Arnaud","family":"Perrot","sequence":"additional","affiliation":[{"name":"Institut de Recherche Dupuy de L\u00f4me (IRDL), Universit\u00e9 de Bretagne Sud, UMR CNRS 6027, IRDL, 56100 Lorient, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5650-3825","authenticated-orcid":false,"given":"Thomas","family":"Kr\u00e4nkel","sequence":"additional","affiliation":[{"name":"Chair of Materials Science and Testing, Centre for Building Materials (CBM), Technical University of Munich, 81245 Munich, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8626-918X","authenticated-orcid":false,"given":"Dirk","family":"Lowke","sequence":"additional","affiliation":[{"name":"Institute of Building Materials, Concrete Construction and Fire Safety (iBMB), Technische Universit\u00e4t Braunschweig, 38106 Braunschweig, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1214-3960","authenticated-orcid":false,"given":"Christoph","family":"Gehlen","sequence":"additional","affiliation":[{"name":"Chair of Materials Science and Testing, Centre for Building Materials (CBM), Technical University of Munich, 81245 Munich, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,14]]},"reference":[{"key":"ref_1","unstructured":"UNEP (2017). 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