Julien Baroth

Accounting for the variability of rock detachment conditions in designing rockfall protection structures

Abstract This study is based on the analysis of the residual rockfall hazard at the elements at risk and accounts for the variability of the rock release parameters influencing the trajectory. The design of protection structures is conducted in two phases: a functional design phase consisting of quantifying the structure height from the rock passing height distribution and a structural design phase where the structure required capacity is assessed from the rock passing energy distribution. This framework is used on a well-documented study site for identifying the effects of the definition of the rocks release conditions, limited to the rock volume and falling height, on the design and efficiency of protection fences. The rock volume is modeled using a random variable, with different probabilistic laws. A probabilistic method is also used to analyze the effect of the rock volume distribution. These sensitivity analyses are conducted using a point estimate method for saving computation time. In this work, the initial falling height is shown to have a negligible influence on both the functional and structural designs of the fence. On the contrary, the rock volume range appears to be the leading parameter. The influence of the distribution law is shown to be of second order. The proposed approach may be extrapolated to other uncertain or variable parameters, as well as to other types of passive rockfall protective structures.

Behavior of a RC Frame Under Differential Seismic Excitation

ABSTRACT Two very dense seismographic arrays were deployed in a seismically active area in Greece to incorporate the difference in amplitude and phase between two stations located within the dimension of a structure. The spatial variability in seismic ground motion is generally attributed to the wave passage effect, the incoherence effect, and the local site effect. It can cause severe damage on lifeline structures. This article studies the behavior of a reinforced concrete 2D frame structure subjected to differential seismic excitation at the supports. Both linear and nonlinear finite multifiber element models of the seismic behavior of this structure are used. The nonlinear behavior of the structure, under these different cases, displays different damage patterns and maximum displacements. This study allows evaluating the uncertainty that can be propagated through the finite element model, aiming at reducing variability for structural design purposes.Two very dense seismographic arrays were deployed in a seismically active area in Greece to incorporate the difference in amplitude and phase between two stations located within the dimension of a structure. The spatial variability in seismic ground motion is generally attributed to the wave passage effect, the incoherence effect, and the local site effect. It can cause severe damage on lifeline structures. This article studies the behavior of a reinforced concrete 2D frame structure subjected to differential seismic excitation at the supports. Both linear and nonlinear finite multifiber element models of the seismic behavior of this structure are used. The nonlinear behavior of the structure, under these different cases, displays different damage patterns and maximum displacements. This study allows evaluating the uncertainty that can be propagated through the finite element model, aiming at reducing variability for structural design purposes.

Development of a Size Effect Law for RC Structures

The work presented is a part of the french ANR (Agence Nationale pour la Recherche) project MACENA (Maitrise du Confinement en Accident), its main objective is to better present the role of concrete heterogeneities in RC structures in the cracking process. This paper aims to develop and use the size effect method (WL2) applicable to RC structures proposed by Sellier and Millard 2014 [1]. The originality of the method lies on introducing a weighting function defined in the direction of the maximum principal stress using a scale length. In this work, an inverse analysis of the method allows to identify this scale length using experimental test series of concrete specimens under tensile load and 3 point bending beams. The approach is then applied to predict the sensitivity of the mechanical behavior of a reinforced concrete tie under tensile load. The method is applied in the elastic phase and allows providing the structural tensile strength corresponding to the first crack which is affected by size effect and plays a key role because cracked and uncracked structures behave in severe environment in a very different way. In FE model, correlated random fields on the tensile strength of the concrete can be generated using the identified scale length to characterize the autocorrelation length.

Modelling strategies of prestressing tendons and reinforcement bars in concrete structures

This contribution presents an original approach to improve the modeling of steel rebars and prestressing tendons in concrete structures at a reduced cost. Classical 1D meshes and models typically used for civil engineering applications tend to provoke strain localization due to the geometrical singularity and are thus unable to reproduce local mechanical effects. Complete 3D models can be applied in some cases, however their accuracy at the local scale comes at the cost of engineering work on the meshes, especially for complex structures. The 1D-3D model presented in this contribution generates an equivalent volume for the steel bars, based on existing 1D models. Its 3D stiffness and stress state are computed, and then condensed on its interface with the concrete. The condensed degree of freedom are then linked to the surrounding concrete elements by kinematic relations. The presented approach is validated on different representative cases, and is able to predict the 3D effects of the bars and tendons at the local scale. In particular it provides the representativeness and mesh stability of a full 3D model, without the need for a complex mesh.

Adaptive Zooming Method for the Simulation of Quasi-Brittle Materials

A method to simulate concrete structures (quasi-brittle material) with localized nonlinearities is presented. Based on Guyan’s condensation, it consists in replacing the elastic zones of the structure by their equivalent rigidities (super-elements). The nonlinear computation is then performed only on the zones of interest (ie, damaged). As new damaged zones may appear, the proposed method monitors the evolution of the system and re-integrates previously condensed areas if necessary. This method, applied on different tests cases, allows a substantial computation economy.