Seismic Bearing Capacity Solution for Strip Footings in Unsaturated Soils with Modified Pseudo-Dynamic Approach
In engineering mathematics, the unsaturated nature of soil has a significant impact on the seismic bearing capacity solution. However, it has generally been neglected in the published literature to date. Based on the kinematic approach of limit analysis, the present study proposes a method for calcu...
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/12/2692 |
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| author | Sheng Xu De Zhou |
| author_facet | Sheng Xu De Zhou |
| author_sort | Sheng Xu |
| collection | DOAJ |
| description | In engineering mathematics, the unsaturated nature of soil has a significant impact on the seismic bearing capacity solution. However, it has generally been neglected in the published literature to date. Based on the kinematic approach of limit analysis, the present study proposes a method for calculating the bearing capacity of shallow strip footings located in unsaturated soils, taking four common types of soils as examples. The modified pseudo-dynamic (MPD) approach is used to calculate the seismic forces varying with time and space, and the layerwise summation method is used to derive the power generated by the seismic forces. In the calculation of internal energy dissipation, this paper introduces the effective stress based on the suction stress to derive the cohesion expression at different depths. The analytical formula of bearing capacity is obtained by the principle of virtual work, and its value is optimized by the Sequential Quadratic Programming (SQP) algorithm. In order to verify the validity of the proposed method, the present results are compared with the solutions published so far and a good agreement is obtained. Finally, a parametric study is performed to investigate the influence of different types of parameters on the bearing capacity. |
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| language | English |
| last_indexed | 2024-03-11T02:11:07Z |
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| spelling | doaj.art-2c883725b1d74789ade506dc98c83f2d2023-11-18T11:28:27ZengMDPI AGMathematics2227-73902023-06-011112269210.3390/math11122692Seismic Bearing Capacity Solution for Strip Footings in Unsaturated Soils with Modified Pseudo-Dynamic ApproachSheng Xu0De Zhou1School of Civil Engineering, Central South University, Changsha 410075, ChinaSchool of Civil Engineering, Central South University, Changsha 410075, ChinaIn engineering mathematics, the unsaturated nature of soil has a significant impact on the seismic bearing capacity solution. However, it has generally been neglected in the published literature to date. Based on the kinematic approach of limit analysis, the present study proposes a method for calculating the bearing capacity of shallow strip footings located in unsaturated soils, taking four common types of soils as examples. The modified pseudo-dynamic (MPD) approach is used to calculate the seismic forces varying with time and space, and the layerwise summation method is used to derive the power generated by the seismic forces. In the calculation of internal energy dissipation, this paper introduces the effective stress based on the suction stress to derive the cohesion expression at different depths. The analytical formula of bearing capacity is obtained by the principle of virtual work, and its value is optimized by the Sequential Quadratic Programming (SQP) algorithm. In order to verify the validity of the proposed method, the present results are compared with the solutions published so far and a good agreement is obtained. Finally, a parametric study is performed to investigate the influence of different types of parameters on the bearing capacity.https://www.mdpi.com/2227-7390/11/12/2692seismic bearing capacityupper boundunsaturated soilsmodified pseudo-dynamic approach |
| spellingShingle | Sheng Xu De Zhou Seismic Bearing Capacity Solution for Strip Footings in Unsaturated Soils with Modified Pseudo-Dynamic Approach Mathematics seismic bearing capacity upper bound unsaturated soils modified pseudo-dynamic approach |
| title | Seismic Bearing Capacity Solution for Strip Footings in Unsaturated Soils with Modified Pseudo-Dynamic Approach |
| title_full | Seismic Bearing Capacity Solution for Strip Footings in Unsaturated Soils with Modified Pseudo-Dynamic Approach |
| title_fullStr | Seismic Bearing Capacity Solution for Strip Footings in Unsaturated Soils with Modified Pseudo-Dynamic Approach |
| title_full_unstemmed | Seismic Bearing Capacity Solution for Strip Footings in Unsaturated Soils with Modified Pseudo-Dynamic Approach |
| title_short | Seismic Bearing Capacity Solution for Strip Footings in Unsaturated Soils with Modified Pseudo-Dynamic Approach |
| title_sort | seismic bearing capacity solution for strip footings in unsaturated soils with modified pseudo dynamic approach |
| topic | seismic bearing capacity upper bound unsaturated soils modified pseudo-dynamic approach |
| url | https://www.mdpi.com/2227-7390/11/12/2692 |
| work_keys_str_mv | AT shengxu seismicbearingcapacitysolutionforstripfootingsinunsaturatedsoilswithmodifiedpseudodynamicapproach AT dezhou seismicbearingcapacitysolutionforstripfootingsinunsaturatedsoilswithmodifiedpseudodynamicapproach |