{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T05:13:22Z","timestamp":1771305202017,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,1,21]],"date-time":"2021-01-21T00:00:00Z","timestamp":1611187200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,21]],"date-time":"2021-01-21T00:00:00Z","timestamp":1611187200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003593","name":"CNPq","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100008530","name":"FEDER","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"crossref"}]},{"name":"FCT"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Acta Geotech."],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s11440-021-01141-9","type":"journal-article","created":{"date-parts":[[2021,1,21]],"date-time":"2021-01-21T18:02:56Z","timestamp":1611252176000},"page":"1879-1894","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Nonlinear porodynamic analysis by adaptive semi-explicit\/explicit time marching formulations"],"prefix":"10.1007","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5756-9359","authenticated-orcid":false,"suffix":"Jr.","given":"Delfim","family":"Soares","sequence":"first","affiliation":[]},{"given":"Luis","family":"Godinho","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,21]]},"reference":[{"key":"1141_CR1","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/BF01436561","volume":"20","author":"I Babuska","year":"1973","unstructured":"Babuska I (1973) The finite element method with Lagrange multiplier. Numer Math 20:179\u2013192","journal-title":"Numer Math"},{"key":"1141_CR2","doi-asserted-by":"crossref","unstructured":"Brezzi F (1974) On the existence, uniqueness and approximation of saddle point problems arising from Lagrangian multipliers. RAIRO 8-R2 129\u2013151","DOI":"10.1051\/m2an\/197408R201291"},{"key":"1141_CR3","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1145\/321439.321446","volume":"15","author":"H Dubner","year":"1968","unstructured":"Dubner H, Abate J (1968) Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform. J Assoc Comput Mach 15:115\u2013123","journal-title":"J Assoc Comput Mach"},{"key":"1141_CR4","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1016\/0022-460X(72)90452-X","volume":"22","author":"I Fried","year":"1972","unstructured":"Fried I (1972) Bounds on the extremal eigenvalues of the finite element stiffness and mass matrices and their spectral condition number. J Sound Vib 22:407\u2013418","journal-title":"J Sound Vib"},{"key":"1141_CR5","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/S0267-7261(00)00105-6","volume":"21","author":"M Huang","year":"2001","unstructured":"Huang M, Wu S, Zienkiewicz OC (2001) Incompressible or nearly incompressible soil dynamic behavior\u2014a new staggered algorithm to circumvent restrictions of mixed formulation. Soil Dyn Earthq Eng 21:169\u2013179","journal-title":"Soil Dyn Earthq Eng"},{"key":"1141_CR6","doi-asserted-by":"publisher","first-page":"1421","DOI":"10.1002\/nme.1115","volume":"61","author":"M Huang","year":"2004","unstructured":"Huang M, Yue ZQ, Tham LG, Zienkiewicz OC (2004) On the stable finite element procedure for dynamic problems of saturated porous media. Int J Numer Methods Eng 61:1421\u20131450","journal-title":"Int J Numer Methods Eng"},{"key":"1141_CR7","volume-title":"The finite element method: linear static and dynamic finite element analysis","author":"TJR Hughes","year":"2000","unstructured":"Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis. Dover Publications INC., New York"},{"key":"1141_CR8","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/BF01446812","volume":"46","author":"A Hurwitz","year":"1895","unstructured":"Hurwitz A (1895) \u00dcber die Bedingungen unter welchen eine Gleichung nur Wurzeln mit negativen reellen Teilen besitzt. Math Ann 46:273\u2013284","journal-title":"Math Ann"},{"key":"1141_CR9","volume-title":"The mathematical theory of viscous incompressible flow","author":"OA Ladyshenskaya","year":"1969","unstructured":"Ladyshenskaya OA (1969) The mathematical theory of viscous incompressible flow, 2nd edn. Gordon and Breach, New York","edition":"2"},{"key":"1141_CR10","volume-title":"Computational methods in ordinary differential equations","author":"JD Lambert","year":"1973","unstructured":"Lambert JD (1973) Computational methods in ordinary differential equations. Wiley, Chichester (ISBN 978-0471511946)"},{"key":"1141_CR11","volume-title":"The finite element method in the static and dynamic deformation and consolidation of porous media","author":"RW Lewis","year":"1998","unstructured":"Lewis RW, Schrefler BA (1998) The finite element method in the static and dynamic deformation and consolidation of porous media, 2nd edn. Wiley, Chichester","edition":"2"},{"key":"1141_CR12","doi-asserted-by":"publisher","first-page":"3845","DOI":"10.1016\/S0045-7825(03)00378-5","volume":"192","author":"X Li","year":"2003","unstructured":"Li X, Han X, Pastor M (2003) An iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics. Comput Methods Appl Mech Eng 192:3845\u20133859","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1141_CR13","doi-asserted-by":"publisher","first-page":"733","DOI":"10.1002\/nag.829","volume":"34","author":"X Li","year":"2010","unstructured":"Li X, Zhang X, Han X, Sheng DC (2010) An iterative pressure-stabilized fractional step algorithm in saturated soil dynamics. Int J Numer Anal Met 34:733\u2013753","journal-title":"Int J Numer Anal Met"},{"key":"1141_CR14","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1002\/nme.2789","volume":"82","author":"B Markert","year":"2010","unstructured":"Markert B, Heider Y, Ehlers W (2010) Comparison of monolithic and splitting solution schemes for dynamic porous media problems. Int J Numer Methods Eng 82:341\u20131383","journal-title":"Int J Numer Methods Eng"},{"key":"1141_CR15","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s11440-012-0168-5","volume":"7","author":"CR McGann","year":"2012","unstructured":"McGann CR, Arduino P, Mackenzie-Helnwein P (2012) Stabilized single-point 4-node quadrilateral element for dynamic analysis of fluid saturated porous media. Acta Geotech 7:297\u2013311","journal-title":"Acta Geotech"},{"key":"1141_CR16","doi-asserted-by":"publisher","first-page":"1488","DOI":"10.1002\/nag.2923","volume":"43","author":"L Monforte","year":"2019","unstructured":"Monforte L, Navas P, Carbonell JM, Gens MAA (2019) Low-order stabilized finite element for the full Biot formulation in soil mechanics at finite strain. Int J Numer Anal Methods Geomech 43:1488\u20131515","journal-title":"Int J Numer Anal Methods Geomech"},{"key":"1141_CR17","doi-asserted-by":"publisher","unstructured":"Navas P, Pastor M, Yag\u00fce A, Stickle MM, Manzanal D, Molinos M (2020) Fluid stabilization of the u\u2212w Biot\u2019s formulation at large strain. Int J Numer Anal Methods Geomech 1\u201317. https:\/\/doi.org\/10.1002\/nag.3158","DOI":"10.1002\/nag.3158"},{"key":"1141_CR18","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1002\/1099-1484(200010)5:7<511::AID-CFM87>3.0.CO;2-S","volume":"5","author":"M Pastor","year":"2000","unstructured":"Pastor M, Li T, Liu X, Zienkiewicz OC, Quecedo M (2000) A fractional step algorithm allowing equal order of interpolation for coupled analysis of saturated soil problems. Mech Cohes-Frict Mater 5:511\u2013534","journal-title":"Mech Cohes-Frict Mater"},{"key":"1141_CR19","volume-title":"A treatise on the stability of a given state of motion: particularly steady motion","author":"EJ Routh","year":"1877","unstructured":"Routh EJ (1877) A treatise on the stability of a given state of motion: particularly steady motion. Macmillan and Co., New York City"},{"key":"1141_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01453641","volume":"145","author":"M Schanz","year":"2000","unstructured":"Schanz M, Cheng AHD (2000) Transient wave propagation in a one-dimensional poroelastic column. Acta Mech 145:1\u201318","journal-title":"Acta Mech"},{"key":"1141_CR21","doi-asserted-by":"publisher","first-page":"4645","DOI":"10.1016\/j.cma.2008.06.002","volume":"197","author":"D Soares","year":"2008","unstructured":"Soares D (2008) A time-domain FEM approach based on implicit Green\u2019s functions for the dynamic analysis of porous media. Comput Methods Appl Mech Eng 197:4645\u20134652","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1141_CR22","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1002\/nag.2214","volume":"38","author":"D Soares","year":"2014","unstructured":"Soares D (2014) Iterative analysis of pore-dynamic models discretized by finite elements. Int J Numer Anal Methods Geomech 38:391\u2013405","journal-title":"Int J Numer Anal Methods Geomech"},{"key":"1141_CR23","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1016\/j.cma.2019.05.040","volume":"354","author":"D Soares","year":"2019","unstructured":"Soares D (2019) An adaptive semi-explicit\/explicit time marching technique for nonlinear dynamics. Comput Methods Appl Mech Eng 354:637\u2013662","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1141_CR24","doi-asserted-by":"publisher","first-page":"112593","DOI":"10.1016\/j.cma.2019.112593","volume":"357","author":"D Soares","year":"2019","unstructured":"Soares D (2019) A simple non-iterative uncoupled algorithm for nonlinear pore-dynamic analyses. Comput Methods Appl Mech Eng 357:112593","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1141_CR25","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.compstruc.2019.01.004","volume":"214","author":"D Soares","year":"2019","unstructured":"Soares D, Wrobel LC (2019) A locally stabilized explicit approach for nonlinear heat conduction analysis. Comput Struct 214:40\u201347","journal-title":"Comput Struct"},{"key":"1141_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cma.2015.08.012","volume":"297","author":"D Soares","year":"2015","unstructured":"Soares D, Gro\u00dfeholz G, von Estorff O (2015) An efficient staggered time-marching procedure for porodynamics. Comput Methods Appl Mech Eng 297:1\u201317","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1141_CR27","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/0045-7825(93)90184-Y","volume":"106","author":"E Turska","year":"1993","unstructured":"Turska E, Schrefler BA (1993) On convergence conditions of partitioned solution procedures for consolidations problems. Comput Methods Appl Mech Eng 106:51\u201363","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1141_CR28","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/0045-7825(94)90168-6","volume":"144","author":"E Turska","year":"1994","unstructured":"Turska E, Wisniewski K, Schrefler BA (1994) Error propagation of staggered solution procedures for transient problems. Comput Methods Appl Mech Eng 144:177\u2013188","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1141_CR29","doi-asserted-by":"publisher","first-page":"4353","DOI":"10.1016\/j.cma.2008.05.015","volume":"197","author":"J White","year":"2008","unstructured":"White J, Borja RI (2008) Stabilized low-order finite elements for coupled solid-deformation\/fluid-diffusion and their application to fault zone transients. Comput Methods Appl Mech Eng 197:4353\u20134366","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1141_CR30","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1016\/j.compgeo.2008.05.001","volume":"36","author":"K Xia","year":"2009","unstructured":"Xia K, Masud A (2009) A stabilized finite element formulation for finite deformation elastoplasticity in geomechanics. Comput Geotech 36:396\u2013405","journal-title":"Comput Geotech"},{"key":"1141_CR31","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1002\/nag.2538","volume":"41","author":"SY Yi","year":"2017","unstructured":"Yi SY, Bean ML (2017) Iteratively coupled solution strategies for a four-field mixed finite element method for poroelasticity. Int J Numer Anal Methods Geomech 41:159\u2013179","journal-title":"Int J Numer Anal Methods Geomech"},{"key":"1141_CR32","doi-asserted-by":"publisher","first-page":"1859","DOI":"10.1007\/s11440-019-00879-7","volume":"15","author":"Y Zhang","year":"2020","unstructured":"Zhang Y, Pedroso DM, Li L, Scheuermann A, Ehlers W (2020) Accurate and stablised time integration strategy for saturated porous media dynamics. Acta Geotech 15:1859\u20131879","journal-title":"Acta Geotech"},{"key":"1141_CR33","doi-asserted-by":"publisher","first-page":"113225","DOI":"10.1016\/j.cma.2020.113225","volume":"369","author":"Y Zhao","year":"2020","unstructured":"Zhao Y, Borja RI (2020) A continuum framework for coupled solid deformation\u2013fluid flow through anisotropic elastoplastic porous media. Comput Methods Appl Mech Eng 369:113225","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1141_CR34","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1002\/nag.1610080106","volume":"8","author":"OC Zienkiewicz","year":"1984","unstructured":"Zienkiewicz OC, Shiomi T (1984) Dynamic behavior of saturated porous media: the generalized Biot formulation and its numerical solution. Int J Numer Anal Methods Geo-mech 8:71\u201396","journal-title":"Int J Numer Anal Methods Geo-mech"},{"key":"1141_CR35","first-page":"1871","volume":"23","author":"OC Zienkiewicz","year":"1986","unstructured":"Zienkiewicz OC, Qu S, Taylor RL, Nakzawa S (1986) The patch test for mixed formulation. Int J Numer Methods Eng 23:1871\u20131883","journal-title":"Int J Numer Methods Eng"},{"key":"1141_CR36","doi-asserted-by":"publisher","first-page":"1039","DOI":"10.1002\/nme.1620260504","volume":"26","author":"OC Zienkiewicz","year":"1988","unstructured":"Zienkiewicz OC, Paul DK, Chan AHC (1988) Unconditionally stable staggered solution procedure for soil\u2013pore fluid interaction problems. Int J Numer Methods Eng 26:1039\u20131055","journal-title":"Int J Numer Methods Eng"},{"key":"1141_CR37","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1098\/rspa.1990.0061","volume":"429","author":"OC Zienkiewicz","year":"1990","unstructured":"Zienkiewicz OC, Chan AHC, Pastor M, Paul DK, Shiomi T (1990) Static and dynamic behavior of soils: a rational approach to quantitative solutions. I. Fully saturated problems. Proc R Soc Lond A 429:285\u2013309","journal-title":"Proc R Soc Lond A"},{"key":"1141_CR38","volume-title":"Computational geomechanics with special reference to earthquake engineering","author":"OC Zienkiewicz","year":"1999","unstructured":"Zienkiewicz OC, Chan AHC, Pastor M, Schrefler BA, Shiomi T (1999) Computational geomechanics with special reference to earthquake engineering. Wiley, Chichester"}],"container-title":["Acta Geotechnica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11440-021-01141-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11440-021-01141-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11440-021-01141-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T20:22:07Z","timestamp":1724358127000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11440-021-01141-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,21]]},"references-count":38,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["1141"],"URL":"https:\/\/doi.org\/10.1007\/s11440-021-01141-9","relation":{},"ISSN":["1861-1125","1861-1133"],"issn-type":[{"value":"1861-1125","type":"print"},{"value":"1861-1133","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,21]]},"assertion":[{"value":"18 May 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 January 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 January 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}