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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.
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.
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.

Cardoso, António S., Nuno M. da Costa Guerra, Armando. N. Antão, and Manuel Matos Fernandes. "Cortinas tipo Berlim definitivas ancoradas em solos argilosos: a quest." Revista Portuguesa de Geotecnia. 100 (2004): 271-291. Abstract


Antão, A. N., M. Vicente da Silva, and N. M. C. Guerra. "Determination of depth factors for the bearing capacity of shallow foundations in sand." Soils and Rocks. 33 (2010): 47-52. Abstract
Leal, R., Nunes A. Antão, and N. M. C. Guerra Flexible retaining structures supported by anchor beams: the problem of tie-rod length. Proceedings of the 16th European Conference on Soil Mechanics and Geotechnical Engineering. Edimburgo, Escócia: 3, 2015.
Antão, Armando N., Nuno Costa M. da Guerra, Manuel Matos Fernandes, and António Cardoso. "Influence of tension cut-off on the stability of anchored concrete soldier-pile walls in clay." Canadian Geotechnical Journal. 45 (2008): 1036-1044. AbstractWebsite

A previous paper studied the stability of soldier-pile walls in clay under vertical loading using upper bound analyses. A classical Tresca yield criterion was assumed in that analysis. This paper extends that study by considering a tension truncated Tresca yield criterion in an upper bound numerical analysis of the problem. It shows that assuming zero tension soil strength has a significant influence on the values of the minimum soldier-pile resistance required to ensure stability.

Josefino, Santos C. J., Costa N. M. da Guerra, and Nunes A. Antão. "Influence of the Embedded Length on the Overall Stability of Single Anchored Retaining Walls." Soils & Rocks. 40.2 (2017): 133-145.
Cardoso, António S., Nuno M. da Costa Guerra, Armando. N. Antão, and Manuel Matos Fernandes. "Limit analysis of anchored concrete soldier-pile walls in clay under vertical loading." Canadian Geotechnical Journal. 43 (2006): 516-530. AbstractWebsite

The vertical stability of anchored concrete soldier-pile walls is highly influenced by the complexity of the interaction between the different parts of the structure, i.e., wall, anchors, and supported soil mass. The problem is analyzed using upper bound limit analysis through published solutions and proposed closed-form equations. A comparison is made between these equations and numerical limit analyses. An estimate of the theoretical minimum pile resistance required to avoid excavation collapse is presented. Published finite element elastoplastic results are used for comparison.Key words: anchored retaining wall, concrete soldier-pile walls, vertical equilibrium, finite elements, limit analysis, soil-to-wall interface shear forces.

Vicente da Silva, M., N. Deusdado, and A. N. Antão. "Lower and upper bound limit analysis via the alternating direction method of multipliers." Computers and Geotechnics. 124 (2020): 103571. AbstractWebsite

Computational limit analysis methods invariably lead to the need to solve a mathematical programming problem. The alternating direction method of multipliers (ADMM) is one versatile and robust technique to solve non-linear convex optimization problems that has recently found applications in a wide range of fields. Its solution scheme, based on an operator splitting algorithm, is not only easy to implement but also suitable to efficiently solve large-scale variational problems. Starting from the ADMM framework, we derive a strict upper bound finite element formulation using a two-(primal)-field approximation, one for the velocity field and the other for the plastic strain rate field. Next, following a similar approach, we develop a novel strict lower bound formulation. Here, the two-(primal)-field model is based on a redundant approximation of the stress field. Duality principles are then explored in order to unify these two formulations.The effectiveness of this approach is demonstrated on test problems and, to conclude, some considerations are made about the performance results.

Vicente da Silva, M., and A. N. Antão. "A new Hoek-Brown-Matsuoka-Nakai failure criterion for rocks." International Journal of Rock Mechanics and Mining Sciences. 172 (2023): 105602. AbstractWebsite

In the current paper, we propose a new three-dimensional strength criterion for rocks expressed in terms of the first principal stress invariant, I1, and the second and third invariants of the deviatoric stress tensor, J2 and J3. The design of this constitutive model conjugates the characteristics of two of the most well-known and widely used criteria in geotechnical engineering: Hoek-Brown and Matsuoka-Nakai. Its material parameters can be calibrated based on conventional axisymmetric compression and extension tests. Experimental polyaxial test data from a dozen different rock types were used to validate the current criterion.

Vicente da Silva, M., and A. N. Antão. "A non-linear programming method approach for upper bound limit analysis." International Journal for Numerical Methods in Engineering. 72 (2007): 1192-1218. AbstractWebsite

This paper presents a finite element model based on mathematical non-linear programming in order to determine upper bounds of colapse loads of a mechanical structure.The proposed formulation is derived within a kinematical approach framework, employing two simultaneous and independent field approximations for the velocity and strain rate fields. The augmented Lagrangian is used to establish the compatibility between these two fields. In this model, only continuous velocity fields are used.Uzawa's minimization algorithm is applied to determine the optimal kinematical field that minimizes the difference between external and dissipated work rate. The use of this technique allows to bypass the complexity of the non-linear aspects of the problem, since non-linearity is addressed as a set of small local subproblems of optimization for each finite element.The obtained model is quite versatile and suitable for solving a wide range of collapse problems. This paper studies 3D strut-and-tie structures, 2D plane strain/stress and 3D solid problems.

Vicente da Silva, M., and A. N. Antão. "A novel Augmented Lagrangian Approach for Limit Analysis Computations." IOP Conf. Ser.: Mater. Sci. Eng. 10. 10 (2010). AbstractWebsite


Vicente da Silva, M., and A. N. Antão. "A novel augmented Lagrangian based formulation for upper bound limit analysis." International Journal for Numerical Methods in Engineering. vol. 89.nº 12 (2012): pp. 1471-1496. Abstract

This paper describes a novel upper-bound formulation of limit analysis. This formulation is an innovative variant of an existing two-field mixed formulation based on the augmented Lagrangian method also developed by the authors. A natural approach is used to describe the deformation of each finite element. Furthermore, and in contrast to the previous formulation, two independent field approximations are now both used to define the velocity field, defined globally and at element level. It is shown that this feature allows a governing system of uncoupled linear equations to be obtained. Some numerical examples in plane strain conditions are presented in order to illustrate the current model performance. In conclusion, the potential and advantages of this new approach are discussed.

Gonçalves, Rodrigo, David Henriques, Armando Antão, and Manuel Ritto-Corrêa. "On non-uniform plastic torsion of steel I-section cantilevers." Thin-Walled Structures. 187 (2023): 110731. AbstractWebsite

This paper aims at contributing towards a better understanding of the non-uniform elastoplastic torsion mechanism of I-section beams. The particular case of cantilevers subjected to an end torque is analysed, which constitutes a simple yet interesting problem, since the maximum torque is very close to the so-called Merchant upper bound (MUB), with added independent maximum bishear and Saint-Venant torques. Consequently, it turns out that the maximum torque can be significantly higher than that for uniform plastic torsion. Besides the MUB, several solutions are presented and compared, namely (i) a stress resultant-based solution stemming from the warping beam theory differential equilibrium equation and (ii) solutions obtained with several beam finite elements that allow for a coarse/refined description of warping. It is found that all models are in very close agreement in terms of maximum torque (including the MUB) and stress resultants. However, the beam finite elements that allow for bishear, even with a simplified warping function, are further capable of reproducing quite accurately the stress field, as a comparison with a 3D solid finite element solution shows. Although the paper is primarily concerned with the small displacement case, the influence of considering finite rotations is also addressed.

Guerra, N. M. C., Santos C. Josefino, and Nunes A. Antão Overall stability of anchored retaining structures: revisiting Broms' method. Proceedings of the Edinburgh and Pune Workshops of TC207 of ISSMGE. Edimburgo, Escócia, 2016.
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).
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).
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.