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Local Continuum Damage Mechanics models cannot represent the entire degradation process in materials exhibiting strain-softening behaviors. It is well known that the rate equilibrium problem becomes ill-posed when softening occurs, and an infinity of solutions exists. From a numerical point of view, finite element analyses suffer from mesh-dependent results. Non-local models are generally used to regularize the structural response and recover objectivity. However, some physical inconsistencies can be observed in numerical results, e.g., damage diffusion over large damaged bands and damage attraction on the boundary of the computational domain. Non-local formulations with evolving interactions may better describe the damaging process and overcome these issues. This paper uses the so-called spalling test to underline the main drawbacks and advantages of several regularized models with constant and evolving non-local interactions. Concerning non-local formulations with constant interactions, attention is focused on the integral non-local formulation on the internal variable of the constitutive model and an implicit gradient damage formulation. Regarding formulations with evolving non-local interactions, attention is focused on a “stress-based integral non-local” approach and the so-called “eikonal non-local” approach. In this latter case, both its integral-type and gradient-type variants are considered.

Archaeoseismology is one of the four issues usually involved to increase the knowledge of seismic risk. The three other issues are seismic records, historical seismicity, and palaeoseismicity. Archaeoseismology was founded as a discipline in the 1980s. It was developed and methodologically defined during the 1990s and 2000s, and its new developments and perspectives are based on two procedures. First, the numerical field, with tools like the database OPUR (Outil Pour Unités de Réparation), “Tool For Reparation Units”, conceived as a sort of atlas, to collect and index all the types of repairs identified in the Roman site of Pompeii, in Italy. Second, the focus on the evolution of ancient buildings and their pathologies, serves as a basis for the structural modelling, carried out by engineers. It allows to understand the behaviour of ancient buildings during seismic motion, to quantify the impact of seismic effects on cultural heritage and to propose a method of preservation. Major studies conducted in France as well as recent developments in this field are presented, in order to illustrate this collaboration between archaeoseismologists and engineers for the preservation of cultural heritage.

In the present work, a methodology is proposed to reassess the magnitude assigned to historical earthquakes thanks to a Bayesian updating approach. The initial information used to estimate the magnitude in the catalogue is supplemented by new data. The data is obtained with a combination of in situ observations and fragility characteristics of historical buildings. It is shown that no damage or low damage of buildings can be used to reduce the uncertainty on historical earthquakes. The methodology is applied to a case study in Southern France, the 1889 La-Tour-du-Pin earthquake. With the data and model considered, a small effect for the updating is obtained with an average value for the magnitude $M_w$ going from 4.4 to 4.39 and an uncertainty $\mathrm{err}_{M_w}$ going from 0.42 to 0.41. The impact of the choice of parameters of the Ground Motion Model (GMM) for this study is investigated. Indeed, collecting more information on the site in order to reduce uncertainty and using site-specific GMM could improve the accuracy of the estimations in future applications of the approach.

The menhir of Locmariaquer lays in four fragments 200 m north of Locmariaquer (Morbihan, Brittany, France). Several hypotheses have been raised over time to explain its fall. This study discusses a potential earthquake origin and investigates the associated ground motion features. The historical seismicity and the current instrumental seismicity support the concept of an active seismic area. Soil and subsurface characterization highlights a complex site response. Several models of the menhir based on archaeological observations are proposed to simulate the dynamic response of the menhir. A ground motion selection from the European Strong Motion database is used as inputs. An earthquake scenario is compatible with the fall of the menhir. The associated Intensity Measures are discussed. [ABSTRACT FROM AUTHOR]