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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.

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.
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.

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).
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).