Prediction of Seismic Bearing Capacity Considering Nonlinearity and Dilatancy by Sequential Quadratic Programming
Most of the published literature regarding bearing capacity are often focused on linear and associative soils. Concerning the intrinsic strength nonlinearity in dilatancy soils, this study investigates the problem of the seismic bearing capacity in the framework of the kinematic theorem of limit ana...
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MDPI AG
2023-03-01
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| author | Hong Liao De Zhou |
| author_facet | Hong Liao De Zhou |
| author_sort | Hong Liao |
| collection | DOAJ |
| description | Most of the published literature regarding bearing capacity are often focused on linear and associative soils. Concerning the intrinsic strength nonlinearity in dilatancy soils, this study investigates the problem of the seismic bearing capacity in the framework of the kinematic theorem of limit analysis. The conventional linear Mohr–Coulomb criterion is substituted with a nonlinear power law criterion to depict the nonlinearity of the soil strength. The non-associative feature of soil materials is considered by defining a nonlinear dilatancy coefficient. A generalized tangential technique is accordingly introduced to linearize the strength envelope for making the nonlinear criterion tractable in the analysis. A non-symmetrical translational failure mechanism that is comprised of several rigid wedges is used to characterize the failure of the foundation at the limit state. Moreover, the seismic action is considered by the classic pseudo-static method. Based upon the energy equilibrium theory of the upper-bound limit analysis, new analytical solutions are derived from the work-balanced equation with nonlinearity and dilatancy. This rigorous upper-bound solution is formulated as a multivariate optimization problem and is readily addressed by sequential quadratic programming (SQP). To verify the reliability of the new expressions, the present results are compared with already posted solutions and the original pseudo-dynamic solutions. The comparative results show a good agreement with previous works, and the correctness and rationality of the new analytical solutions are validated. The detailed parametric study reveals that, in the non-associative flow soils, the ultimate bearing capacity is significantly decreased with a reduction in the dilatancy coefficient. Particularly in the linear condition, namely m = 1, the larger the internal friction angle is, the more obvious the influence of the non-associative feature on the bearing capacity is. |
| first_indexed | 2024-03-11T07:30:21Z |
| format | Article |
| id | doaj.art-06aa6250babd4243827056202955c065 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-11T07:30:21Z |
| publishDate | 2023-03-01 |
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| series | Applied Sciences |
| spelling | doaj.art-06aa6250babd4243827056202955c0652023-11-17T07:20:48ZengMDPI AGApplied Sciences2076-34172023-03-01135321510.3390/app13053215Prediction of Seismic Bearing Capacity Considering Nonlinearity and Dilatancy by Sequential Quadratic ProgrammingHong Liao0De Zhou1School of Civil Engineering, Central South University, Changsha 410075, ChinaSchool of Civil Engineering, Central South University, Changsha 410075, ChinaMost of the published literature regarding bearing capacity are often focused on linear and associative soils. Concerning the intrinsic strength nonlinearity in dilatancy soils, this study investigates the problem of the seismic bearing capacity in the framework of the kinematic theorem of limit analysis. The conventional linear Mohr–Coulomb criterion is substituted with a nonlinear power law criterion to depict the nonlinearity of the soil strength. The non-associative feature of soil materials is considered by defining a nonlinear dilatancy coefficient. A generalized tangential technique is accordingly introduced to linearize the strength envelope for making the nonlinear criterion tractable in the analysis. A non-symmetrical translational failure mechanism that is comprised of several rigid wedges is used to characterize the failure of the foundation at the limit state. Moreover, the seismic action is considered by the classic pseudo-static method. Based upon the energy equilibrium theory of the upper-bound limit analysis, new analytical solutions are derived from the work-balanced equation with nonlinearity and dilatancy. This rigorous upper-bound solution is formulated as a multivariate optimization problem and is readily addressed by sequential quadratic programming (SQP). To verify the reliability of the new expressions, the present results are compared with already posted solutions and the original pseudo-dynamic solutions. The comparative results show a good agreement with previous works, and the correctness and rationality of the new analytical solutions are validated. The detailed parametric study reveals that, in the non-associative flow soils, the ultimate bearing capacity is significantly decreased with a reduction in the dilatancy coefficient. Particularly in the linear condition, namely m = 1, the larger the internal friction angle is, the more obvious the influence of the non-associative feature on the bearing capacity is.https://www.mdpi.com/2076-3417/13/5/3215seismic bearing capacityshallow foundationsmulti-block mechanismkinematic theorem |
| spellingShingle | Hong Liao De Zhou Prediction of Seismic Bearing Capacity Considering Nonlinearity and Dilatancy by Sequential Quadratic Programming Applied Sciences seismic bearing capacity shallow foundations multi-block mechanism kinematic theorem |
| title | Prediction of Seismic Bearing Capacity Considering Nonlinearity and Dilatancy by Sequential Quadratic Programming |
| title_full | Prediction of Seismic Bearing Capacity Considering Nonlinearity and Dilatancy by Sequential Quadratic Programming |
| title_fullStr | Prediction of Seismic Bearing Capacity Considering Nonlinearity and Dilatancy by Sequential Quadratic Programming |
| title_full_unstemmed | Prediction of Seismic Bearing Capacity Considering Nonlinearity and Dilatancy by Sequential Quadratic Programming |
| title_short | Prediction of Seismic Bearing Capacity Considering Nonlinearity and Dilatancy by Sequential Quadratic Programming |
| title_sort | prediction of seismic bearing capacity considering nonlinearity and dilatancy by sequential quadratic programming |
| topic | seismic bearing capacity shallow foundations multi-block mechanism kinematic theorem |
| url | https://www.mdpi.com/2076-3417/13/5/3215 |
| work_keys_str_mv | AT hongliao predictionofseismicbearingcapacityconsideringnonlinearityanddilatancybysequentialquadraticprogramming AT dezhou predictionofseismicbearingcapacityconsideringnonlinearityanddilatancybysequentialquadraticprogramming |