S. Lenci, F. Clementi, E. Giordano, A. Ferrante
Department of Civil and Building Engineering, and Architecture, Polytechnic University of Marche, Ancona (Italy)
The conservation and the restoration of ancient buildings belonging to the cultural heritage, and preserving their main architectural features, are becoming a very important issue in Europe. This is especially true in Italy, which hosts the largest amount of monumental churches, monasteries and towers in the world, and where some earthquakes, occurred in the last few decades (Umbria-Marche 1997-1998, Abruzzo 2009, Emilia-Romagna 2012, Marche-Lazio-Umbria-Abruzzo 2016), severely damaged a number of unique pieces of the architectural heritage.
The vulnerability assessment of historical constructions against seismic actions, which is the necessary pre-requisite for their successive protection, is of strategic importance considering the richness of the European and Italian architectural heritage. Most historical constructions are masonry structures that were not conceived to resist lateral forces, as the old design concepts mostly focused on the effects of gravity loads and did not provide adequate lateral resistance and ductility. Furthermore, many historical and architectural structures are currently used with different functions, such as residential areas, offices, museums and headquarters of important civil activities. In particular, when the building has a strategic function during calamitous events, it has to guarantee safety to host the headquarters of rescue teams and to be a safe place for short-term hosting of people who lose their house. Hence, they require a high level of safety against both vertical and horizontal loads.
Masonry constructions are typically complex structures and there is a lack of knowledge concerning the behaviour of their structural systems, particularly about their seismic response. Typically, these structures are more massive than today's structures and they usually carry their actions primarily in compression. Successful modelling of a historical masonry structure is a prerequisite for a reliable earthquake-resistant design or assessment. For modern structures, with new industrial materials (reinforced concrete, steel, etc.), the development of a reliable mathematical model is possible, since materials and structural elements are more uniform and sufficiently well-known. Conversely, the seismic behaviour of old masonry structures is particularly difficult to be examined. It depends on many factors such as material properties, geometry of the structure, stiffness of the floors (diaphragm effect) and connection between orthogonal walls and structural and non-structural elements (Betti and Vignoli, 2011; Clementi et al., 2016).
One key point is the material behaviour modelling. Masonry is a composite material obtained joining natural or artificial bricks by means of mortar layers. The non-uniformity of the mixture is due to the variability of both components, mortar and bricks, that can vary very much from place to place due to different local construction technologies. For this reason, the stiffness and the resistance have a great dispersion, but it could be useful to characterise the masonry material of ancient constructions by means of average values provided in codes or manuals.
Furthermore, in addition to the heterogeneous nature of masonry, also the nonlinear response, often already triggered at low deformation levels, is a challenge for structural engineering, both from a scientific and from a professional point of view. Indeed, the formulation of models for reproducing the complex nonlinear mechanical behaviour of the masonry is an active research field. Experience shows that masonry mechanical behaviour is dominated by the nonlinear phase, characterised by cracks opening, dissipative and brittle behaviour with a softening branch. Nonlinear anisotropic constitutive laws are required and behaviour in tension and in compression is markedly different. Much focus is currently given to the formulation of nonlinear constitutive relationships for masonry and a large number of models are now available.
The most natural approach for describing the mechanical behaviour of masonry structural elements is the adoption of continuous material models. In this framework, a wide variety of continuous 2D and 3D nonlinear models have been proposed. These include complex nonlinear mechanisms such as friction-plasticity, cohesion, crushing, damage and so on (Clementi et al., 2017).
From a numerical point of view, elastic-plastic analyses may be used to simulate masonry nonlinear behaviour. However, they fail to simulate crack formation and the brittle behaviour when the material enters the softening regime. Limit analysis methods have been frequently applied in order to investigate the collapse mechanism of masonry structures subjected to given load distributions (Milani et al., 2007). Smeared crack approaches and/or damage models may be used to simulate the local loss of strength masonry material suffers when it enters the nonlinear behaviour. However, to the best of the authors' knowledge, the numerical analysis itself is still very demanding, especially when dealing with large and complex structures. For the sake of completeness, we mention that an alternative to modelling masonry as a homogenised continuum is the discrete element approach, which models the structure as an assembly of blocks with suitable interface laws (Lemos, 2007). This method focuses on the possible non-smooth nature of the dynamic response, which can come sliding and impacting between different blocks, and situation that is common just before and during the collapse.
In the present work, the importance of considering the exact nonlinear and three-dimensional behaviour of masonry structures is shown, in order to highlight all the structural deficiencies of different churches and towers damaged by the last Centre Italy earthquake (2016). For this purpose, the exact geometries of the structures are reconstructed, while information regarding the mechanical properties of masonry material are derived from previous investigations and literature references. Based on this information, different numerical models are used to reconstruct the damages.
Firstly, different three-dimensional FE models, endowed with an elastic plastic (softening) damage constitutive law, are adopted to determine the seismic vulnerability of the building by means of nonlinear static analyses using the smeared fracture energy approach. With this method it is possible to establish, with a right degree of approximation, the areas where the most important cracks are expected and, in general, the location of the potential damage caused by horizontal forces. Where possible, the dynamics of different churches is investigated using a distinct element code that implements the Non-Smooth Contact Dynamics method (NSCD). The main goal is to determine the weakness zones of the structures during seismic events, and the possible collapse mechanisms. Harmonic oscillations applied to the basement of the churches are considered first, and a systematic parametric study is done, aimed at correlating the vulnerability of the churches and/or towers to the amplitude and frequency of the excitation. Also, numerical analyses are performed to see the effects of the friction coefficient and the blocks geometry on the dynamics, and, in particular, on the collapse modes. Then, the study of the churches and towers stability against recorded seismic excitations is also addressed. Attention is paid to the occurrence of out-of-plane overturning mechanisms, and further comparisons of the damage obtained with the present approach and after real earthquakes are reported.
Betti, M., and Vignoli, A. (2011) Numerical assessment of the static and seismic behaviour of the basilica of Santa Maria all'Impruneta (Italy). Constr. Build. Mater. 25, 4308-4324. doi:10.1016/j.conbuildmat.2010.12.028.
Clementi, F., Gazzani, V., Poiani, M., and Lenci, S. (2016) Assessment of seismic behaviour of heritage masonry buildings using numerical modelling. J. Build. Eng. 8, 29-47. doi:10.1016/j.jobe.2016.09.005.
Clementi, F., Quagliarini, E., Monni, F., Giordano, E., and Lenci, S. (2017) Cultural Heritage and Earthquake: The Case Study of Santa Maria Della Carità in Ascoli Piceno. Open Civ. Eng. J. 11, 1079-1105. doi:10.2174/1874149501711011079.
Milani, G., Lourenco, P., and Tralli, A. (2007) 3D homogenized limit analysis of masonry buildings under horizontal loads. Eng. Struct. 29, 3134-3148.