Seismic reliability assessment of classical columns subjected to near-fault ground motions

A methodology for the performance-based seismic risk assessment of classical columns is presented. Despite their apparent instability, classical columns are, in general, earthquake resistant, as proven from the fact that many classical monuments have survived many strong earthquakes over the centuries. Nevertheless, the quantitative assessment of their reliability and the understanding of their dynamic behavior are not easy, because of the fundamental nonlinear character and the sensitivity of their response. In this paper, a seismic risk assessment is performed for a multidrum column using Monte Carlo simulation with synthetic ground motions. The ground motions adopted contain a high- and low-frequency component, combining the stochastic method, and a simple analytical pulse model to simulate the directivity pulse contained in near source ground motions. The deterministic model for the numerical analysis of the system is three-dimensional and is based on the Discrete Element Method. Fragility curves are produced conditional on magnitude and distance from the fault and also on scalar intensity measures for two engineering demand parameters, one concerning the intensity of the response during the ground shaking and the other the residual deformation of the column. Three performance levels are assigned to each engineering demand parameter. Fragility analysis demonstrated some of the salient features of these spinal systems under near-fault seismic excitations, as for example, their decreased vulnerability for very strong earthquakes of magnitude 7 or larger. The analysis provides useful results regarding the seismic reliability of classical monuments and decision making during restoration process

Homogenization of interlocking masonry walls

International audienceIn a previous publication the authors proposed a continuous model for describing the mechanical behaviour of ‘Running Bond' masonry walls. Here a different masonry structure is considered. This structure is ‘bi-atomic' in the sense that its pattern consists in two kind of blocks with different. The homogenization by differential expansions technique is used for obtaining an equivalent Cosserat continuum. It is shown that the enriched kinematics of the Cosserat continuum is not sufficient to capture the full dynamic behaviour of this bi-atomic system. However, the Cosserat continuum model behaves well for low frequency waves and for wave lengths 5 to 10 times bigger the elementary cell

Chemically induced compaction bands: Triggering conditions and band thickness

International audienceDuring compaction band formation various mechanisms can be involved at different scales. Mechanical and chemical degradation of the solid skeleton and grain damage are important factors that may trigger instabilities in the form of compaction bands. Here we explore the conditions of compaction band formation in quartz- and carbonate-based geomaterials by considering the effect of chemical dissolution and grain breakage. As the stresses/deformations evolve, the grains of the material break leading to an increase of their specific surface. Consequently, their dissolution is accelerated and chemical softening is triggered. By accounting for (a) the mass diffusion of the system, (b) a macroscopic failure criterion with dissolution softening and (c) the reaction kinetics at the micro level, a model is proposed and the conditions for compaction instabilities are investigated. Distinguishing the micro-scale (grain level) from the macro-level (Representative Elementary Volume) and considering the heterogeneous microstructure of the REV it is possible to discuss the thickness and periodicity of compaction bands. Two case studies are investigated. The first one concerns a sandstone rock reservoir which is water flooded and the second one a carbonate rock in which CO2 is injected for storage. It is shown that compaction band instabilities are possible in both cases

Existence of a threshold for brittle grains crushing strength: two-versus three- parameter Weibull distribution fitting

International audienceGrain crushing plays an important role in the mechanical behavior of granular media, in chemo-hydro-thermo-mechanical couplings, in instabilities related to strain localization such as shear bands and compaction bands, in geophysical and geotechnical processes, in reservoir and petroleum engineering and in many other domains. The strength of brittle particles seems to be quite well described by a two-parameter Weibull distribution. Nevertheless, such a distribution predicts that failure is possible under any level of applied stress. On the contrary a three-parameter Weibull distribution contains a stress threshold under which grain failure is unlikely. Based on existing experiments on crushing of individual grains from various geomaterials and surrogate materials, and on new experiments performed on rock sugar particles, the present paper explores and compares the applicability of a two-versus a three parameter Weibull distribution. It is shown that in most of the cases the three-parameter Weibull distribution better describes the experimental results

Failure in shear bands for granular materials: thermo-hydro-chemomechanical effects

International audienceThe failure of geomaterials in localised shear bands is one of the most common features in geomechanics. Early studies have provided the necessary criteria for the conditions of localisation, inclination angle with respect to the loading axes and thickness of the shear bands, when loaded at room temperature. This work extends these criteria for the problem of simple shear of a chemically active granular cohesionless material at higher temperatures, where thermal or chemical pressurisation may set in and influence the response of the material. It is deduced that failure occurs at higher positive values of the hardening modulus as temperature increases, that the shear band thickness also depends on the chemical reaction characteristics and that micro-inertia due to grain translations and rotations introduce the necessary rate dependency to regularise the system

Modeling of fault gouges with Cosserat Continuum Mechanics: Influence of thermal pressurization and chemical decomposition as coseismic weakening mechanisms

International audienceIn this paper we study the impact of thermal pressurization and mineral decomposition reactions under seismic deformation conditions (e.g., slip rates of about 1 m/s) triggered by shear heating, to the stability of a saturated fault material. By using higher order continuum considerations, allowing for rotational degrees of freedom to the gouge material, we verify that the micro-inertia of the Cosserat Continuum may regularize the ill-posed problem of simple shear of a fault and that the thermal effects promote localization of deformation into ultra-thin shear bands. It is shown that the width of these structures depends on the parameters of the decomposition reaction considered, obtaining values as low as 100 μm, in agreement with microstructural evidence from natural and artificial faults

Passivity-based control of underactuated mechanical systems with Coulomb friction: Application to earthquake prevention

Passivity property gives a sense of energy balance. The classical definitions and theorems of passivity in dynamical systems require time invariance and locally Lipschitz functions. However, these conditions are not met in many systems. A characteristic example is nonautonomous underactuated, discontinuous systems due to friction. This paper presents an extended result for the negative feedback connection of two passive nonautonomous systems with a set-valued right-hand side based on an invariance-like principle. Such extension is the base of a structural passivity-based control synthesis for underactuated mechanical systems with Coulomb friction. The first step consists in designing the control able to restore the passivity in the considered friction law, achieving stabilization of the system trajectories to a domain with zero velocities. Then, an integral action is included to improve the latter result and perform a tracking over a reference. At last, the control is designed considering (slow) dynamics in the actuation. These control objectives are obtained using fewer control inputs than degrees of freedom, as a result of the underactuated nature of the plant. The presented control strategy is implemented in an earthquake prevention scenario, where a mature seismogenic fault represents the considered frictional underactuated mechanical system. Simulations are performed to show how the seismic energy can be slowly dissipated by tracking a slow reference, thanks to fluid injection far from the fault, accounting also for the slow dynamics of the fluid's diffusion

Οπτική Απόκριση Δισδιάστατων Περιοδικών Διατάξεων Στατικών και Δυναμικών Σφαιρικών Σωματιδίων

Στην εργασία αυτή, αναπτύσσεται αρχικά μια ακριβής μέθοδος Floquet για την περιγραφή της οπτικής απόκρισης ενός ισοτροπικού και ομοιογενούς σφαιρικού αντικειμένου με περιοδικά χρονικά μεταβαλλόμενο δείκτη διάθλασης, μέσω ενός πίνακα t που περιγράφει πλήρως όλες τις διαδικασίες ελαστικής και μη ελαστικής σκέδασης. Χρησιμοποιώντας μια κατάλληλη επέκταση της φωτονικής μεθόδου στρωματικής πολλαπλής σκέδασης για απλά και πολλαπλά δισδιάστατα πλέγματα τέτοιων δυναμικών διηλεκτρικών σκεδαστών, αναδεικνύονται ισχυρά και ελεγχόμενα φαινόμενα μη ελαστικής σκέδασης υπό τη συνθήκη τριπλού συντονισμού, που ικανοποιείται για οπτικές μεταβάσεις μεταξύ γειτονικών πλεγματικών καταστάσεων μεγάλου χρόνου ζωής, και κατάλληλης συμμετρίας, οι οποίες προέρχονται από πολυπολικούς συντονισμούς Mie.In this work, initially, an exact Floquet method for the description of the optical response of an isotropic and homogeneous spherical object characterized by a periodically time varying refractive index, by means of a t matrix that fully describes all elastic and inelastic scattering processes, is developed. By employing a proper extension of the photonic layer multiple scattering method for single and multiple two-dimensional lattices of such dynamic dielectric scatterers, strong and tunable inelastic scattering effects under the triple resonance condition, fulfilled for optical transitions between neighboring long-lifetime lattice modes of the appropriate symmetry, which originate from multipolar Mie resonances, are revealed