Asinou Monument – Numerical Modelling
In order to numerically examine the structural response of the Asinou church, a Finite Element (FE) model was developed in Abaqus/CAE. For the simulation of the masonry, the stone-mortar composite was treated as a homogenous continuum whose mechanical properties average the effects of the two interacting materials. The response of the homogenized masonry medium was modelled using an isotropic elasticity constitutive model. The mechanical characteristics assigned to the medium were derived from calculation models and experimental data reported in the literature. More specifically, the weight density of the masonry was set as 2500 kg/m3, while the modulus of elasticity (E) was approximated based on the estimated value of compressive strength (fc) as E = 500fc. Using equation
fc = 2/3fb1/2 + 0.6fm - 2.5 proposed by Tassios (2013) for rubble masonry construction and taking fb = 55 MPa (Rigopoulos et al., 2011) and fm = 1 MPa as the compressive strengths of the ophiolithic stones and of the lime-based mortar composing the structure, gave fc = 3 MPa and E = 1.5 GPa. A value of v = 0.25 was assumed for the Poisson’s ratio (EN 1996-1-1). The timber composing the truss roof and the ties installed at the interior of nave was assumed to be elastic isotropic with a density of 700 kg/m3 and an elastic modulus of 7 GPa.
All load-bearing masonry components (i.e. walls, arches, vaults) were modelled using shell elements based. The FE model was thus discretized into 3-noded shell elements with 6 degrees of freedom per node and 5 Gauss integration points through the thickness to account for out-of-plane bending. Section properties corresponding to different shell thicknesses were defined based on the actual construction configuration of the various parts of structure. The approximate global size of the elements’ sides was set as 0.4 m. Common nodes were assigned at all cross-walls assuming that the connections between intersecting masonry members enable full transfer of shear and flexural stresses. The roof members and the timber ties at the interior of the church were modelled using 2-noded truss elements. Pinned supports were defined along the walls’ base. The FE model is shown in Figure 1.
The FE model was subjected to time-history analysis using a real-time accelerogram representing the seismic motion recorded during the June 20th 1978 Thessaloniki earthquake. The duration of the selected seismic event is 30.59 s and the peak ground accelerations in the x and y directions are 0.139g and 0.146g, respectively. These magnitudes of seismic acceleration are approximately equal to the 0.15g peak ground acceleration prescribed in the Cyprus National Annex to EN 1998-1 for the Troodos area where the monument is located. Dynamic analysis was completed in two successive numerical steps taking into account geometric non-linearity effects. Initially, the structure was analyzed under dead loads using a general static solution procedure. Then, the seismic load was imposed adopting a dynamic implicit procedure with direct integration and a full Newton equation solver scheme. Upon transition from the static to the dynamic step, the basal translational constraints along the x and y axes were replaced by ground accelerations acting in the same directions. The accelerations’ amplitudes were defined in accordance with the selected accelerograms.
The numerical results obtained enabled examining the dynamic response of the structure and identifying the areas of the masonry which are prone to seismic damage. The prediction of damage was based on the hypothesis that the fictitious elastic principal stresses computed at the elements’ integration points should not exceed the compressive and tensile capacity (ft) of the masonry. The latter was taken as ft = 5%fc = 0.15 MPa. In addition, exceedance of the shear stress capacity of the masonry was examined. The maximum permissible shear stress was taken as fv = 0.065 fc = 0.2 MPa (EN 1996-1-1).
According to the outcomes of the analysis, damage of the structure’s masonry sections is primarily due tensile cracking, rather than shearing. The computed distribution of maximum principal stresses at the time step these attain their maximum values are shown in the contour diagrams of Figure 2. As it was pretty much expected, the parts of the church which are more prone to damage are the parapets, the base of the dome of the narthex and the apex of the nave’s vault. The analysis predicted only limited tensile damage along the longitudinal wings of the church, due to the presence of buttresses and of shear walls resisting the seismic forces in the transversal direction. At the level of seismic loading examined, structural response is characterized by the development of localized damage, rather than the propagation of extensive damage which can result to instability at the global level. The parapets in particular are susceptible to out-of-plane collapse as they tend to behave as unrestrained cantilever structures. Although the failure of these elements is not expected to critically affect the overall seismic capacity of the structure, localized collapse mechanisms can jeopardize the safety of visitors and will certainly result to loss of historic fabric.