A mathematical approach for predicting the consolidation of saturated clays

Authors

DOI:

https://doi.org/10.5902/2179460X66836

Keywords:

Consolidation, Viscosity, Non-linearity, Saturated clay

Abstract

The saturated clay layers subjected to a vertical load undergo vertical deformations over time, that is, consolidation. These deformations, when accentuated, cause structural, functional or aesthetic damage to buildings. In this sense, here a mathematicalmodel is proposed and developed to predict the consolidation of saturated clays taking into account the concepts presented by Terzaghi e Frohlich (1936), Taylor (1942) e Barden (1965). The mathematical formulation considers the existence of a viscous portion of the effective vertical tension and incorporates in the modeled partial differential equation a non-linear viscosity lawas a fundamental property. This consolidation equation is obtained in terms of dissipating excess normalized poropressure. Inview of the complexity of the model, the numerical technique of finite divided differences is used to obtain the theoretical solution considering variations in time and space. The numerical solution shows that the viscous portion of the effective vertical tension acts by slowing down the phenomenon of consolidation. Furthermore, the adjustment of theoretical to experimental values shows that the modeling for the viscosity factor equal to one is more promising than the proposals by Terzaghi e Frohlich (1936) and Andrade (2014).

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Author Biographies

Joabby da Costa Biz, Universidade Tecnológica Federal do Paraná, Curitiba, PR

Possui graduação em Engenharia Civil pela Universidade Tecnológica Federal do Paraná (2021). Atualmente é aluno de Pós-Graduação na Universidade Estadual de Londrina.

Maurício do Espirito Santo Andrade, Universidade Tecnológica Federal do Paraná, Curitiba, PR

Possui graduação em Engenharia Civil pela Universidade Federal de Sergipe (2007), mestrado em Engenharia Civil pela Universidade Federal do Rio de Janeiro (2009) e doutorado em Engenharia Civil pela Universidade Federal do Rio de Janeiro (2014). Atualmente é professor da Universidade Tecnológica Federal do Paraná. Tem experiência na área de métodos matemáticos (analíticos) aplicados a problemas de adensamento de solos. Associado efetivo da Sociedade Brasileira de Matemática desde 2010. Associado efetivo da Sociedade Brasileira de Matemática Aplicada e Computacional.

Elmagno Catarino Santos Silva, Universidade Tecnológica Federal do Paraná, Curitiba, PR

É professor da área de Geotecnia da Universidade Tecnológica Federal do Paraná (UTFPR), campus Toledo. Possui formação em Tecnologia da Construção Civil, pela Universidade Estadual de Campinas (UNICAMP), com destaque na modalidade de Obras e Solos. Possui graduação em Engenharia Civil com realização de trabalhos relativos à erosão laminar em sub-bacia Pirapitinga-Sarandi. Concluiu Mestrado em Geotecnia pela Universidade de Brasília (UnB), na temátia de erosao laminar na bacia hidrográfica do reservatório Corumbá IV e doutorado, na mesma instiuição, no entando com trabalhos voltados aos impactos dos resíduos sólidos em redes de águas pluviais urbanas. Atualmente leciona as disciplinas de Mecânica dos Solos 1, Projeto de Pavimentação e Gerenciamento de Resíduos Sólidos. Atua nas seguintes áreas: Processos Erosivos, Pavimentação, 

References

ANDRADE, M. E. S. (2014). Adensamento unidimensional considerando a resistência viscosa à compressão. PhD dissertation,Universidade Federal do Rio de Janeiro.

BARDEN, L. (1965). Consolidation of clay with non-linear viscosity. Géotechnique, 15(4), 345–362.

BRAJA, M. (2011). Fundamentos de Engenharia Geotécnica, 6º edn. Cengage Learning.

CARVALHO, S. R. L. (1997). Uma teoria de adensamento com compressão secundária. PhD dissertation, Universidade Federal doRio de Janeiro.

TAYLOR, D. W. (1942). Research on Consolidation of Clays, 1º edn. Massachusetts Institute of Technology.

TERZAGHI, K., FROHLICH, O. K.(1936). Theorie der Setzung von Tonschichten, 1º edn. Franz Deuticke.

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Published

2021-11-08 — Updated on 2022-06-27

How to Cite

Biz, J. da C., Andrade, M. do E. S., & Silva, E. C. S. (2022). A mathematical approach for predicting the consolidation of saturated clays. Ciência E Natura, 43, e2. https://doi.org/10.5902/2179460X66836

Issue

Vol. 43 (2021): Special Edition: X ERMAC RS

Section

Special Edition

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