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A
Viana, L. A., Nunes A. Antão, Vicente M. da Silva, and N. M. C. Guerra The application of limit analysis to the study of the basal failure of deep excavations in clay considering the spatial distribution of soil strength. Proceedings of the 17 European Conference on Soil Mechanics and Geotechnical Engineering. Reykjavik, Islândia, 2019.
Deusdado, N., Nunes A. Antão, Vicente M. da Silva, and N. M. C. Guerra Application of the Upper and Lower-Bound Theorems to Three-Dimensional Stability of Soil Slope. 3 th International Conferen e on Transportation Geotechnics. Guimarães., 2016.
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Franco, F., Nunes A. Antão, Vicente M. da Silva, and N. M. C. Guerra Bearing capacity of shallow impervious footing in soil under sub-vertical seepage. Pro eedings of the 18 th International Conference on Soil Mechanics and Geotechnical Engineering. Seoul, Coreia, 2017.
C
da Silva, Vicente M., and A. N. Antão. "Computational Upper- and Lower-Bound 3D Limit Analysis Using the Hoek–Brown Yield Criterion." International Journal of Geomechanics. 24 (2024): 04024036. AbstractWebsite

The Hoek–Brown failure criterion has been widely applied to predict the strength of rock masses, demonstrating its relevance in diverse geotechnical contexts. This paper presents a novel 3D numerical implementation of the Hoek–Brown criterion in a finite-element limit analysis code. The proposed formulation is unique in its ability to produce strict upper and lower bounds for 3D problems, providing more accurate and reliable predictions of failure mechanisms compared to previous formulations. The validity of the formulation is demonstrated through comparisons with known analytical solutions or other authors’ numerical solutions. Furthermore, the proposed numerical tool is used to determine the stability of shallow circular tunnels in rock masses, highlighting its practical applicability in engineering design.

P
Deusdado, N., Vicente M. da Silva, and Nunes A. Antão Parallel 3D limit analysis via the alternating direction method of multipliers. Computational Plasticity XIII, COMPLAS2015. Barcelona, Espanha, 2016.
Antão, Armando N., T. Santana, M. Vicente da Silva, and N. M. C. Guerra. "Passive earth-pressure coefficients by upper-bound numerical limit analysis." Canadian Geotechnical Journal. 48 (2011): 767-780. Abstract

A three-dimensional (3D) numerical implementation of the limit analysis upper-bound theorem is used to determine passive horizontal earth-pressure coefficients. An extension technique allowing determination of the 3D passive earth pressures for any width-to-height ratios greater than 7 is presented. The horizontal passive earth-pressure coefficients are presented and compared with solutions published previously. Results of the ratio between the 3D and two-dimensional horizontal passive earth-pressure coefficients are shown and found to be almost independent of the soil-to-wall friction ratio. A simple equation is proposed for calculating this passive earth-pressure ratio.

Simões, J. T., L. C. Neves, Nunes A. Antão, and Costa N. M. da Guerra. "Pro- babilisti analysis of bearing apa ity of shallow foundations using three-dimensional limit analyses." International Journal of Computational Methods. 11.2 (2014).
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Simões, J. T., L. C. Neves, Nunes A. Antão, and Costa N. M. da Guerra. "Reliability assessment of shallow foundations on undrained soils considering soil spatial variability." Computers and Geotechnics. 119 (2020).
T
Antão, Nunes A., T. Santana, Vicente M. da Silva, and Costa N. M. da Guerra. "Three-dimensional active earth pressure coefficients by upper bound numerical limit analysis." Computers and Geotechnics. 79 (2016): 96-104.
Santana, T., Vicente M. da Silva, Nunes A. Antão, and N. M. C. Guerra Two dimensional upper and lower-bound numerical analysis of the basal stability of deep excavations in clay. Pro eedings of the 9 th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE 2018). Porto, 2018.
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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.
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.