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Santana, T., A. Antão, N. Guerra, and M. Vicente da Silva. "Upper bounds for the three-dimensional seismic active earth pressure coefficients." Géotechnique Letters. 13 (2023): 65-74. AbstractWebsite

A numerical implementation of the upper-bound theorem of limit analysis is applied to determine two-dimensional (2D) and three-dimensional (3D) active horizontal earth pressure coefficients considering seismic actions through a horizontal seismic coefficient. Results are obtained for vertical wall, horizontal soil, different friction angles of the soil, soil-to-wall friction ratios, horizontal seismic coefficients and wall width-to-height ratios. The few cases for which 3D active earth pressure coefficients are available in the literature using upper-bound methods were used for comparison with the corresponding earth pressure coefficients obtained in this study. This showed a general improvement of these results, which allows expecting a good accuracy for the set of cases studied. The ratios between the 3D and 2D horizontal active earth pressure coefficients are found to be practically independent of the soil-to-wall friction ratio. An equation is proposed for calculating these ratios. This equation can be easily used in the design of geotechnical structures requiring the determination of 3D active earth pressure coefficients.

Antão, A. N., Nuno M. Vicente da Silva, da Costa Guerra, and R. Delgado. "An upper bound-based solution for the shape factors of bearing capacity of footings under drained conditions using a parallelized mixed f.e. formulation with quadratic velocity fields." Computers and Geotechnics. 41 (2012): 23-35. Abstract

A strict upper-bound limit analysis finite element formulation is used to estimate shape factors s_gamma and s_q for determining the bearing capacity of shallow foundations using the classic bearing capacity formula. The finite element formulation uses a quadratic approximation for the velocity field, an extension of a previously published Augmented Lagrangian formulation with a linear velocity field, and was implemented for a parallel processing environment. Results from determining the limit loads under three-dimensional conditions are presented and compared with previously published data. The results obtained allow a strict upper-bound determination of the shape factors. Furthermore, a practical proposal for these factors is made and compared with other proposals made by other authors.

Vicente da Silva, M., and A. N. Antão. "Upper bound limit analysis with a parallel mixed finite element formulation." International Journal of Solids and Structures. 45 (2008): 5788-5804. AbstractWebsite

This paper addresses an implementation of the upper bound limit analysis theorem using a parallel mixed finite element formulation. The intrinsic characteristics of the adopted upper bound formulation proved to be suitable to adapt it to an efficient parallelization scheme. In order to illustrate the computational power provided by the new parallel processing method, accurate upper bound collapse load estimates, for 3D problems, are produced using a cluster of common PC machines.

Antão, A. N., M. Vicente da Silva, N. Monteiro, and N. Deusdado. "Upper and lower bounds for three-dimensional undrained stability of shallow tunnels." Transportation Geotechnics. 27 (2021): 100491. AbstractWebsite

This paper deals with the determination of upper and lower bounds for the three-dimensional undrained stability of shallow tunnels. The tunnel is circular and a distance between its face and its lining is considered. The soil shear strength is modeled using the Tresca criterion. Results of the upper and lower bounds of the stability number are presented, for several geometrical and resistance configurations and their comparison with previous results is made, showing the clear improvement obtained. Finally, equations approaching the stability number are proposed.

Antão, Nunes A., N. M. C. Guerra, Vicente M. da Silva, and T. Santana Upper and lower bounds for the bearing apacity of foundations on soft soils with reinforcement columns. Proceedings of the 17 th European Conference on Soil Mechanics and Geotechnical Engineering. Reykjavik, Islândia, 2019.