Theoretical investigation of interaction between a rectangular plate and fractional viscoelastic foundation
The interaction between plates and foundations is a typical problem encountered in geotechnical engineering. The long-term plate performance is highly dependent on the rheological characteristics of ground soil. Compared with conventional linear rheology, the fractional calculus-based theory is a mo...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2014-08-01
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| Series: | Journal of Rock Mechanics and Geotechnical Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1674775514000523 |
| _version_ | 1818148282375864320 |
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| author | Chengcheng Zhang Honghu Zhu Bin Shi Linchao Liu |
| author_facet | Chengcheng Zhang Honghu Zhu Bin Shi Linchao Liu |
| author_sort | Chengcheng Zhang |
| collection | DOAJ |
| description | The interaction between plates and foundations is a typical problem encountered in geotechnical engineering. The long-term plate performance is highly dependent on the rheological characteristics of ground soil. Compared with conventional linear rheology, the fractional calculus-based theory is a more powerful mathematical tool that can address this issue. This paper proposes a fractional Merchant model (FMM) to investigate the time-dependent behavior of a simply supported rectangular plate on viscoelastic foundation. The correspondence principle involving Laplace transforms was employed to derive the closed-form solutions of plate response under uniformly distributed load. The plate deflection, bending moment, and foundation reaction calculated using the FMM were compared with the results obtained from the analogous elastic model (EM) and the standard Merchant model (SMM). It is shown that the upper and lower bound solutions of the FMM can be determined using the EM. In addition, a parametric study was performed to examine the influences of the model parameters on the time-dependent behavior of the plate–foundation interaction problem. The results indicate that a small fractional differential order corresponds to a plate resting on a sandy soil foundation, while the fractional differential order value should be increased for a clayey soil foundation. The long-term performance of a foundation plate can be accurately simulated by varying the values of the fractional differential order and the viscosity coefficient. The observations from this study reveal that the proposed fractional model has the capability to capture the variation of plate deflection over many decades of time. |
| first_indexed | 2024-12-11T12:48:40Z |
| format | Article |
| id | doaj.art-20d934494c694839b45bf2a0d4d60828 |
| institution | Directory Open Access Journal |
| issn | 1674-7755 |
| language | English |
| last_indexed | 2024-12-11T12:48:40Z |
| publishDate | 2014-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Rock Mechanics and Geotechnical Engineering |
| spelling | doaj.art-20d934494c694839b45bf2a0d4d608282022-12-22T01:06:44ZengElsevierJournal of Rock Mechanics and Geotechnical Engineering1674-77552014-08-016437337910.1016/j.jrmge.2014.04.007Theoretical investigation of interaction between a rectangular plate and fractional viscoelastic foundationChengcheng Zhang0Honghu Zhu1Bin Shi2Linchao Liu3School of Earth Sciences and Engineering, Nanjing University, Nanjing 210023, ChinaSchool of Earth Sciences and Engineering, Nanjing University, Nanjing 210023, ChinaSchool of Earth Sciences and Engineering, Nanjing University, Nanjing 210023, ChinaSchool of Civil Engineering, Xinyang Normal University, Xinyang 464000, ChinaThe interaction between plates and foundations is a typical problem encountered in geotechnical engineering. The long-term plate performance is highly dependent on the rheological characteristics of ground soil. Compared with conventional linear rheology, the fractional calculus-based theory is a more powerful mathematical tool that can address this issue. This paper proposes a fractional Merchant model (FMM) to investigate the time-dependent behavior of a simply supported rectangular plate on viscoelastic foundation. The correspondence principle involving Laplace transforms was employed to derive the closed-form solutions of plate response under uniformly distributed load. The plate deflection, bending moment, and foundation reaction calculated using the FMM were compared with the results obtained from the analogous elastic model (EM) and the standard Merchant model (SMM). It is shown that the upper and lower bound solutions of the FMM can be determined using the EM. In addition, a parametric study was performed to examine the influences of the model parameters on the time-dependent behavior of the plate–foundation interaction problem. The results indicate that a small fractional differential order corresponds to a plate resting on a sandy soil foundation, while the fractional differential order value should be increased for a clayey soil foundation. The long-term performance of a foundation plate can be accurately simulated by varying the values of the fractional differential order and the viscosity coefficient. The observations from this study reveal that the proposed fractional model has the capability to capture the variation of plate deflection over many decades of time.http://www.sciencedirect.com/science/article/pii/S1674775514000523Viscoelastic foundationPlate deflectionGround settlementFractional derivativeMerchant modelRheologyLaplace transform |
| spellingShingle | Chengcheng Zhang Honghu Zhu Bin Shi Linchao Liu Theoretical investigation of interaction between a rectangular plate and fractional viscoelastic foundation Journal of Rock Mechanics and Geotechnical Engineering Viscoelastic foundation Plate deflection Ground settlement Fractional derivative Merchant model Rheology Laplace transform |
| title | Theoretical investigation of interaction between a rectangular plate and fractional viscoelastic foundation |
| title_full | Theoretical investigation of interaction between a rectangular plate and fractional viscoelastic foundation |
| title_fullStr | Theoretical investigation of interaction between a rectangular plate and fractional viscoelastic foundation |
| title_full_unstemmed | Theoretical investigation of interaction between a rectangular plate and fractional viscoelastic foundation |
| title_short | Theoretical investigation of interaction between a rectangular plate and fractional viscoelastic foundation |
| title_sort | theoretical investigation of interaction between a rectangular plate and fractional viscoelastic foundation |
| topic | Viscoelastic foundation Plate deflection Ground settlement Fractional derivative Merchant model Rheology Laplace transform |
| url | http://www.sciencedirect.com/science/article/pii/S1674775514000523 |
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