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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 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.

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

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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.

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.
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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).
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).
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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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.
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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.
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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.
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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.
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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.
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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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.

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

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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
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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.

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.

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.
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.
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.