Simplex Algorithm for 3D Limit Analysis of Roman Groin Vaults

Abstract

In Roman Baths the Romans employed groin vaults of great dimensions, with maximum span more than 20 m; simple tools of structural analysis of ancient wide span vaulted halls are still lacking, due to geometrical and material complexity. In this paper we study the collapse behavior, under horizontal static action, of a corner cross vault of the Baths of Diocletian in Rome (Hall I). In the present modeling, masonry is discretized as a system of interacting rigid bodies in no-tension and frictional contact. The computational code consists in a linear programming approach which make use of a series of optimization packages via lower and upper bound techniques of limit analysis. In the paper, a solution strategy based on a modified simplex algorithm has been introduced in order to manage the large number of contacts given by a 3D block assembly. One more task of the proposed problem consists in a suitable description of the overall 3D geometry, here afforded with a specific pre-processing approach.

Full document

References

[1] Baggio, C. & Trovalusci, P. Collapse behaviour of three-dimensional brick-block systems using non-linear programming. Structural Engineering and Mechanics (2000), 10(2): 181- 195.

[2] Murty, Katta G. Linear programming, John Wiley & Sons (2000).

[3] Casapulla, C. & D’Ayala, D. Lower-bound approach to the limit analysis of 3D vaulted block masonry structures. In: TG. Hughes & GN. Pande (Eds): Computer Methods in Structural Masonry, Vol. 5, Swansea, Computers & Geotechnics Ltd (2001), pp. 177-183.

[4] Ferris, M. & Tin-Loi, F. Limit analysis of frictional block assemblies as a mathematical program with complementarity constraints. Int. J. Mech. Sci. (2001), 43: 209-224.

[5] Baggio, C. Il restauro antisismico dei centri storici e la regola d’arte. Ricerche di Storia dell’Arte (2009), 99, 2: 19-29.

[6] Jackson, M. D., Logan, J. M., Marra, F., Scheetz, B. E., Deocampo, D. M., Cawood, C. G. Composizione e caratteristiche meccaniche dei calcestruzzi della grande aula, L. Ungaro, M. P. Del Moro, M. Vitti (Eds), I mercati di Traiano restituiti – studi e restauri 2005-2007, Roma, Palombi (2010), pp. 145-153.

[7] Nizzi, I. & Baggio, C. Vulnerabilità sismica delle grandi aule delle terme di Diocleziano. In: A. Centroni & M.G. Filetici (Eds): Attualità delle aree archeologiche; Atti del VII Convegno ARCo, Roma, 2014.

[8] Block, P., Lachauer, L. Three-dimensional (3D) equilibrium analysis of gothic masonry vaults. Int. J. Architectural Heritage (2014), 8: 312-335.

[9] Baggio, C. & Trovalusci, P. 3D Limit analysis of Roman groin vaults, IBMAC 2016, Proc. 16th Int. Brick block Masonry Conf., Padua, Italy, CRC Balkema.