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The Finite Element Method applied in the viscoelastic constitutive model of Kelvin–Voigt for characterization of the soil dynamic response to water leakage simulation

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Abstract

Sustainable water management is a highly relevant global topic; the existing problems in the area affect the human, social, environmental and economic development in any country. In Brazil, water distribution networks lose, on average, more than a third of their treated water, most of which is due to leakages along their supply system. As for the vibro-acoustic methods to detect and locate leaks, one of the factors that affect the acquisition of such signal is the response of the soil surrounding the pipe. In order to cooperate with the improvement of this scenario, the present work describes the development of the numerical model that simulates the soil’s response to low excitations like buried leaks. The soil is modeled as a viscoelastic solid using Kelvin–Voigt model, and the differential equations describing the problem were solved applying the Finite Element Method. The performance of the proposed model and the analysis framework are tested and validated through an experimental approach of the problem. Furthermore, it has been found that the leak noise spectra decay with a frequency power law close to 1/ω2 for the studied soil.

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Data availability

Some data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors are grateful for the support from National Council for Scientific and Technological Development (CNPq) and the Coordination for the Improvement of Higher Education Personnel (CAPES).

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Authors and Affiliations

  1. Department of Mechanical Engineering, UNESP, Ilha Solteira, São Paulo, 15385-000, Brazil

    Matheus S. Proença, Amarildo T. Paschoalini, João B. C. Silva, Daniel H. S. Obata, Luis P. M. Lima & Otávio D. Z. Boaventura

  2. Department of Civil Engineering, UNESP, Ilha Solteira, São Paulo, 15385-000, Brazil

    Adriano Souza

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  1. Matheus S. Proença
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  3. João B. C. Silva
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Correspondence to Matheus S. Proença.

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Overall procedure of the numeric workflow

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Proença, M.S., Paschoalini, A.T., Silva, J.B.C. et al. The Finite Element Method applied in the viscoelastic constitutive model of Kelvin–Voigt for characterization of the soil dynamic response to water leakage simulation. J Braz. Soc. Mech. Sci. Eng. 44, 470 (2022). https://doi.org/10.1007/s40430-022-03773-8

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