One-Dimensional Consolidation of Viscoelastic Soils Incorporating Caputo-Fabrizio Fractional Derivative
In this paper, the Caputo-Fabrizio fractional derivative is introduced to investigate the one-dimensional consolidation behavior of viscoelastic soils. Using the Caputo-Fabrizio operator, a novel four-element fractional-derivative model is proposed to capture the viscoelastic properties of the soils...
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| Format: | Article |
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MDPI AG
2021-01-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/3/927 |
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| author | Minghua Huang Chang Lv Suhua Zhou Shuaikang Zhou Jiatao Kang |
| author_facet | Minghua Huang Chang Lv Suhua Zhou Shuaikang Zhou Jiatao Kang |
| author_sort | Minghua Huang |
| collection | DOAJ |
| description | In this paper, the Caputo-Fabrizio fractional derivative is introduced to investigate the one-dimensional consolidation behavior of viscoelastic soils. Using the Caputo-Fabrizio operator, a novel four-element fractional-derivative model is proposed to capture the viscoelastic properties of the soils, and further the one-dimensional consolidation equation is derived to simulate the consolidation behavior of the soils. Using the techniques of eigenfunction expansion and Laplace transform, a series of analytical solutions are derived to calculate the excess pore-water pressure and the average degree of consolidation of the soils. The total vertical stress in the soil is assumed to change linearly with depth, and its distribution patterns are classified to rectangular pattern, trapezoidal pattern and inverse trapezoidal pattern. Four loading types including instantaneous loading, ramp loading, sinusoidal loading and general cyclic loading are considered. Then, a comparison for several special cases is presented to verify the correctness of the proposed solutions through comparing with existing theories. Moreover, two examples considering ramp and sinusoidal loadings are given to study the consolidation behavior of the viscoelastic soils incorporating the Caputo-Fabrizio fractional derivative. |
| first_indexed | 2024-03-09T04:12:33Z |
| format | Article |
| id | doaj.art-3786ee42d75f4df590d062f4dda148fd |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T04:12:33Z |
| publishDate | 2021-01-01 |
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| record_format | Article |
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| spelling | doaj.art-3786ee42d75f4df590d062f4dda148fd2023-12-03T13:58:49ZengMDPI AGApplied Sciences2076-34172021-01-0111392710.3390/app11030927One-Dimensional Consolidation of Viscoelastic Soils Incorporating Caputo-Fabrizio Fractional DerivativeMinghua Huang0Chang Lv1Suhua Zhou2Shuaikang Zhou3Jiatao Kang4Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education, Hunan University, Changsha 410082, ChinaCollege of Civil Engineering, Hunan University, Changsha 410082, ChinaKey Laboratory of Building Safety and Energy Efficiency of the Ministry of Education, Hunan University, Changsha 410082, ChinaCollege of Civil Engineering, Hunan University, Changsha 410082, ChinaDepartment of Architectural Engineering, Henan College of Transportation, Zhengzhou 450000, ChinaIn this paper, the Caputo-Fabrizio fractional derivative is introduced to investigate the one-dimensional consolidation behavior of viscoelastic soils. Using the Caputo-Fabrizio operator, a novel four-element fractional-derivative model is proposed to capture the viscoelastic properties of the soils, and further the one-dimensional consolidation equation is derived to simulate the consolidation behavior of the soils. Using the techniques of eigenfunction expansion and Laplace transform, a series of analytical solutions are derived to calculate the excess pore-water pressure and the average degree of consolidation of the soils. The total vertical stress in the soil is assumed to change linearly with depth, and its distribution patterns are classified to rectangular pattern, trapezoidal pattern and inverse trapezoidal pattern. Four loading types including instantaneous loading, ramp loading, sinusoidal loading and general cyclic loading are considered. Then, a comparison for several special cases is presented to verify the correctness of the proposed solutions through comparing with existing theories. Moreover, two examples considering ramp and sinusoidal loadings are given to study the consolidation behavior of the viscoelastic soils incorporating the Caputo-Fabrizio fractional derivative.https://www.mdpi.com/2076-3417/11/3/927viscoelastic soilsone-dimensional consolidationCaputo-Fabrizio fractional derivativeviscoelasticity |
| spellingShingle | Minghua Huang Chang Lv Suhua Zhou Shuaikang Zhou Jiatao Kang One-Dimensional Consolidation of Viscoelastic Soils Incorporating Caputo-Fabrizio Fractional Derivative Applied Sciences viscoelastic soils one-dimensional consolidation Caputo-Fabrizio fractional derivative viscoelasticity |
| title | One-Dimensional Consolidation of Viscoelastic Soils Incorporating Caputo-Fabrizio Fractional Derivative |
| title_full | One-Dimensional Consolidation of Viscoelastic Soils Incorporating Caputo-Fabrizio Fractional Derivative |
| title_fullStr | One-Dimensional Consolidation of Viscoelastic Soils Incorporating Caputo-Fabrizio Fractional Derivative |
| title_full_unstemmed | One-Dimensional Consolidation of Viscoelastic Soils Incorporating Caputo-Fabrizio Fractional Derivative |
| title_short | One-Dimensional Consolidation of Viscoelastic Soils Incorporating Caputo-Fabrizio Fractional Derivative |
| title_sort | one dimensional consolidation of viscoelastic soils incorporating caputo fabrizio fractional derivative |
| topic | viscoelastic soils one-dimensional consolidation Caputo-Fabrizio fractional derivative viscoelasticity |
| url | https://www.mdpi.com/2076-3417/11/3/927 |
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