Keywords: historic masonry, coastal towers, structural settlement, conservation mortars, masonry failure, biaxial failure.

The tower of San Andrés in Tenerife partially collapsed in 1898 due to subsidence caused by floods, leaving today the issue of the conservation of the ruins [1]. The main walls are made of squared rubble masonry of volcanic rock, enclosing a coarse core. The initial aim of this project is to assess the strength of the masonry and the collapse is investigated as an effect of the soil conditions. The instability of the tower due to settlement is demonstrated in this paper with a non-linear geometric and material analysis of a finite element (FE) model of the intact form, using suitable user subroutines in the FE program Abaqus [2].

The randomness of the material properties will require complex analytical methods during later stages when conservation of the ruined state is examined. The FE model should therefore be developed in a way to avoid unnecessary geometrical non-linearities and concentrate on the effect of the material and the applied loadings. In this initial stage, the masonry is considered as homogeneous and orthotropic [3]. The non-linear analysis is carried out using a biaxial failure criterion developed for brickwork [4] and the brittle failure of stone masonry is simulated with a smeared crack approach, as has already been tested in historic vaulted structures [5].

The deformation of the tower under its own weight is shown to be small and the stresses overall are low and well below the strength limits discussed earlier. So far as settlement modelling is concerned, the erosion of the various soil strata and their 3D interaction with the planar layout of the building requires a very complex model and closed expressions to evaluate the settlement exist only for tunnelling works [6]. As an initial attempt to model the settlement of the foundations in the tower, a linear development was assumed, starting from the outermost tip of the base line and propagating with an angle equal to the friction angle of the gravel.

This simple model gave satisfactory insight into the progression of the failure, which initiated quite early as a hoop crack along the middle of the east wall, the area directly affected by the subsidence. Collapse of the wall ultimately occurred when two hinge lines form at the left and right ends of this wall, resulting in a mechanism. Study of the failure rate enabled a reconstruction of the collapse that agrees with observations on site. A further examination of the tower in its ruined condition confirmed also the stability of the present state.

The ultimate aim of the project is to propose a conservation methodology for this type of ruins using the tower as a case study. The FE model can be then utilised to examine the application of conservation mortars developed by two of the authors [7] based upon the mechanical properties of the constituent materials of the masonry [8]. The problem of long-term deformations under permanent load requires a complex probabilistic analysis [9] and the plain FE model and failure mode provided at this stage facilitates this. In the future, the analytical method can also be applied to a wider range of non-planar structures such as vaults.

1

de Luxán, M.P., Dorrego, F., Río, O., Monge, M.J., Pelaez, L., Larraz, A., Prada, J.L., "Las técnicas constructivas militares en fortificaciones históricas a través de la investigación de estructuras y materiales. Un caso singular en el siglo XVIII: la Torre de San Andrés en Tenerife", Conf. Proc. Conservación del Patrimonio, Santo Domingo, 2001.

2

"ABAQUS/ Standard v. 6.4", ABAQUS Inc, Pawtucket, RI, USA 2003

3

Hendry, A.W., Sinha, B.P., Davies, S.R., "Design of masonry structures", E&FN Spon, London 1997.

4

Sinha, B.P., Ng, C.L., Pedreschi, R.F., "Failure criterion and behaviour of brickwork in biaxial bending", J. Mater. Civ. Eng., ASCE, 9(2), 70-75. 1995. doi:10.1061/(ASCE)0899-1561(1997)9:2(70)

5

Theodossopoulos, D., Sinha, B.P., Usmani, A.S., "Case Study of the Failure of a Cross Vault: Church of Holyrood Abbey". J. Architectural Engrg, ASCE, vol. 9(3), pgs. 109-117, 2003. doi:10.1061/(ASCE)1076-0431(2003)9:3(109)

6

Rots, J.G., Invernizzi, S., "Prevision of settlement-induced cracking in historical building masonry façades", Proc. Int. Conf. Structural Analysis of Historical Structures, pp. 687-694, Padova, 2004.

7

Ruiz de Antón, M., de Luxán, M.P., Sánchez de Rojas, I., Dorrego, F., "Original protective renderings in the Cathedral of León", Cons. of Iberian and Latin American cultural heritage: IIC congress, pp 130-34, Madrid, 1992.

8

Lourenço, P.B., "Computational Strategies for Masonry Structures", Delft University Press, Delft, 1996.

9

Garavaglia, E., Anzani, A., Binda, L., "A probabilistic model for the assessment of historic buildings under permanent load" Proc. Int. Conf. Structural Analysis of Historical Structures, pp. 589-596, Padova, 2004.

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