Analytical Solutions for the Radial Consolidation of Unsaturated Foundation with Prefabricated Vertical Drain Based on Fourier Series Expansion Theory
This paper presents the analytical solution of the radial consolidation of a prefabricated vertical drain (PVD) foundation under the unsaturated condition. In the proposed modeling, air and water phases in the foundation are thought to dissipate horizontally toward to the drain, and the smear effect...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-10-01
|
| Series: | Applied Sciences |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2076-3417/11/19/9285 |
| _version_ | 1797516816996630528 |
|---|---|
| author | Qiang Meng Qianwei Xu Xianmin Luo Yang Chen Tianyi Li |
| author_facet | Qiang Meng Qianwei Xu Xianmin Luo Yang Chen Tianyi Li |
| author_sort | Qiang Meng |
| collection | DOAJ |
| description | This paper presents the analytical solution of the radial consolidation of a prefabricated vertical drain (PVD) foundation under the unsaturated condition. In the proposed modeling, air and water phases in the foundation are thought to dissipate horizontally toward to the drain, and the smear effect, drain resistance and external time-dependent loading are fully considered. The analytical mathematical tools, namely the general integration method, Fourier series expansion method, decoupling method and the constant variation method, are utilized to solve the partial differential equations. Moreover, the current solutions are verified with existing solutions in the literature. Finally, a case study considering the ramp loading and exponential loading is conducted to investigate the consolidation patterns under various loading parameters. The results show that smear effect and drain resistance can significantly hinder the dissipation process of excess pore pressures, and different external loading types will lead to various dissipation characteristics (i.e., peak values). |
| first_indexed | 2024-03-10T07:06:09Z |
| format | Article |
| id | doaj.art-d87b144a4c744d1b968cdc5c910dedfe |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T07:06:09Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-d87b144a4c744d1b968cdc5c910dedfe2023-11-22T15:50:26ZengMDPI AGApplied Sciences2076-34172021-10-011119928510.3390/app11199285Analytical Solutions for the Radial Consolidation of Unsaturated Foundation with Prefabricated Vertical Drain Based on Fourier Series Expansion TheoryQiang Meng0Qianwei Xu1Xianmin Luo2Yang Chen3Tianyi Li4Guangxi Airport Construction Engineering Co., Ltd., Nanning 530048, ChinaCollege of Transportation Engineering, Tongji University, Shanghai 201804, ChinaGuangxi Nanning Airport Comprehensive Transportation Hub Construction Co., Ltd., Nanning 530048, ChinaSchool of Navy Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, ChinaSchool of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, ChinaThis paper presents the analytical solution of the radial consolidation of a prefabricated vertical drain (PVD) foundation under the unsaturated condition. In the proposed modeling, air and water phases in the foundation are thought to dissipate horizontally toward to the drain, and the smear effect, drain resistance and external time-dependent loading are fully considered. The analytical mathematical tools, namely the general integration method, Fourier series expansion method, decoupling method and the constant variation method, are utilized to solve the partial differential equations. Moreover, the current solutions are verified with existing solutions in the literature. Finally, a case study considering the ramp loading and exponential loading is conducted to investigate the consolidation patterns under various loading parameters. The results show that smear effect and drain resistance can significantly hinder the dissipation process of excess pore pressures, and different external loading types will lead to various dissipation characteristics (i.e., peak values).https://www.mdpi.com/2076-3417/11/19/9285unsaturated PVD foundationradial dissipationsmear effectdrain resistanceequal strain assumptionanalytical solution |
| spellingShingle | Qiang Meng Qianwei Xu Xianmin Luo Yang Chen Tianyi Li Analytical Solutions for the Radial Consolidation of Unsaturated Foundation with Prefabricated Vertical Drain Based on Fourier Series Expansion Theory Applied Sciences unsaturated PVD foundation radial dissipation smear effect drain resistance equal strain assumption analytical solution |
| title | Analytical Solutions for the Radial Consolidation of Unsaturated Foundation with Prefabricated Vertical Drain Based on Fourier Series Expansion Theory |
| title_full | Analytical Solutions for the Radial Consolidation of Unsaturated Foundation with Prefabricated Vertical Drain Based on Fourier Series Expansion Theory |
| title_fullStr | Analytical Solutions for the Radial Consolidation of Unsaturated Foundation with Prefabricated Vertical Drain Based on Fourier Series Expansion Theory |
| title_full_unstemmed | Analytical Solutions for the Radial Consolidation of Unsaturated Foundation with Prefabricated Vertical Drain Based on Fourier Series Expansion Theory |
| title_short | Analytical Solutions for the Radial Consolidation of Unsaturated Foundation with Prefabricated Vertical Drain Based on Fourier Series Expansion Theory |
| title_sort | analytical solutions for the radial consolidation of unsaturated foundation with prefabricated vertical drain based on fourier series expansion theory |
| topic | unsaturated PVD foundation radial dissipation smear effect drain resistance equal strain assumption analytical solution |
| url | https://www.mdpi.com/2076-3417/11/19/9285 |
| work_keys_str_mv | AT qiangmeng analyticalsolutionsfortheradialconsolidationofunsaturatedfoundationwithprefabricatedverticaldrainbasedonfourierseriesexpansiontheory AT qianweixu analyticalsolutionsfortheradialconsolidationofunsaturatedfoundationwithprefabricatedverticaldrainbasedonfourierseriesexpansiontheory AT xianminluo analyticalsolutionsfortheradialconsolidationofunsaturatedfoundationwithprefabricatedverticaldrainbasedonfourierseriesexpansiontheory AT yangchen analyticalsolutionsfortheradialconsolidationofunsaturatedfoundationwithprefabricatedverticaldrainbasedonfourierseriesexpansiontheory AT tianyili analyticalsolutionsfortheradialconsolidationofunsaturatedfoundationwithprefabricatedverticaldrainbasedonfourierseriesexpansiontheory |