Grand canonical ensemble of a dd-dimensional Reissner-Nordstr\"om black hole in a cavity

The grand canonical ensemble of a $d$-dimensional Reissner-Nordstr\"om black hole space in a cavity is analyzed. The realization of this ensemble is made through the Euclidean path integral approach by giving the Euclidean action for the black hole with the correct topology, and boundary conditions corresponding to a cavity, where the fixed quantities are the temperature and the electric potential. One performs a zero loop approximation to find and analyze the stationary points of the reduced action. This yields two solutions for the electrically charged black hole, $r_{+1}$, which is the smaller and unstable, and $r_{+2}$, which is the larger and stable. One also analyzes the most probable configurations, which are either a stable charged black hole or hot flat space, mimicked by a nongravitating charged shell. Making the correspondence between the action and the grand potential, one can get the black hole thermodynamic quantities, such as the entropy, the mean charge, the mean energy, and the thermodynamic pressure, as well as the Smarr formula, shown to be valid only for the unstable black hole. We find that thermodynamic stability is related to the positivity of the heat capacity at constant electric potential and area of the cavity. We also comment on the most favorable thermodynamic phases and phase transitions. We then choose $d = 5$, which is singled out naturally from the other higher dimensions as it provides an exact solution for the problem, and apply all the results previously found. The case $d = 4$ is mentioned. We compare thermodynamic radii with the photonic orbit radius and the Buchdahl-Andr\'easson-Wright bound radius in $d$-dimensional Reissner-Nordstr\"om spacetimes and find they are unconnected, showing that the connections displayed in the Schwarzschild case are not generic, rather they are very restricted holding only in the pure gravitational situation.Comment: 28 pages, 5 figure

Modeling the dynamic behaviour of masonry walls as rigid blocks

This paper addresses the numerical modeling of masonry walls as rigid blocks. Models based on rigid block assemblies provide a suitable frame work for understanding their dynamic behavior under seismic actions. In this context, the problem is primarily concerned with Rocking Motion dynamics. The numerical tool is based on the Discrete Element Method (DEM) specially effective for the numerical modeling of rigid blocks. Some authors have been used successfully the DEM in the study of block structures. However, they have used experimental test to calibrate their models and to obtain the parameters used in the DEM; because these parameters cannot be obtained directly form the characteristics of the stones. In this context, a new methodology is proposed to find the parameters of the DEM by using the parameters of the classical theory. Special attention regards about the damping factor, since in the DEM a viscous damping is considered, but in reality the damping is due to impulsive forces that they can be considered as a type of Dirac-б forces. An extensive comparison between numerical and experimental data has been carried out to verified the proposed methodology. Very good agreement between the numerical model and experimental data is achieved.Fundação para a Ciência e Tecnologia (FCT) - SFRH/BPD/17449/2004

3D stability analysis of gravity dams on sloped rock foundations using the limit equilibrium method

A convenient approach to performing stability analysis of concrete gravity dams is the so-called two dimensional ‘‘gravity method.’’ However, concrete gravity dams located in valleys with sloped rock foundation abutments behave as three-dimensional (3D) structures and are often able to share compressive and shear loads between adjacent monoliths, especially when shear keys are present. A general 3D limit equilibrium method was developed in this study to compute global sliding safety factors (SSFg) by considering sequential load redistribution among adjacent monoliths when individual monoliths have mobilized their sliding strength. Two validation examples of the sliding safety assessment of existing dams are presented to illustrate the accuracy and efficiency of the proposed approach compared to that of the full 3D numerical analyses conducted using the distinct element method. It is shown that gravity dams may be formed by individual monoliths on sloped rock foundations that will slide if considered as isolated structures but will constitute a stable assembly when the load-sharing capabilities of monoliths are recognized in the analysis.The financial support provided by FCT (the Portuguese Foundation for Science and Technology), through the PhD Grant SFRH/BD/43585/2008, and by the Natural Science and Engineering Research Council of Canada is acknowledged

Masonry gravity dams : a numerical application for stability analysis

This work presents a numerical application for stability analysis of masonry gravity dams. From the geometrical dimensions, the material characteristics, hydrostatic loads and seismic loads, the application automatically determines the following results: thrust line for the dead weight load and the dead weight together with the other loads; stress diagram and safety factors for the failure of the damfoundation contact as part of an overall analysis; safety factors for the failure of horizontal planes along the body of the dam; parametric properties analysis (volumetric mass) and the resistant characteristics (friction angle) on the base of the dam. The analyses of three historical masonry dams located in Algeria was made. This work highlights the versatility of the numerical application as it can work with different section geometry, including curved and discontinuous sections, and the importance of assessing several scenarios in order to obtain a safe result

Conformal entropy from horizon states: Solodukhin's method for spherical, toroidal, and hyperbolic black holes in D-dimensional anti-de Sitter spacetimes

A calculation of the entropy of static, electrically charged, black holes with spherical, toroidal, and hyperbolic compact and oriented horizons, in D spacetime dimensions, is performed. These black holes live in an anti-de Sitter spacetime, i.e., a spacetime with negative cosmological constant. To find the entropy, the approach developed by Solodukhin is followed. The method consists in a redefinition of the variables in the metric, by considering the radial coordinate as a scalar field. Then one performs a 2+(D-2) dimensional reduction, where the (D-2) dimensions are in the angular coordinates, obtaining a 2-dimensional effective scalar field theory. This theory is a conformal theory in an infinitesimally small vicinity of the horizon. The corresponding conformal symmetry will then have conserved charges, associated with its infinitesimal conformal generators, which will generate a classical Poisson algebra of the Virasoro type. Shifting the charges and replacing Poisson brackets by commutators, one recovers the usual form of the Virasoro algebra, obtaining thus the level zero conserved charge eigenvalue L_0, and a nonzero central charge c. The entropy is then obtained via the Cardy formula.Comment: 21 page

Seismic analysis of masonry gravity dams using the discrete element method: Implementation and application

Much research in recent years has focused on the seismic analysis of concrete and earthfill dams, and few works have addressed the case of masonry dams. The structural behaviour of masonry dams is controlled essentially by its discontinuous nature, which may induce significant non-linear response during an intense earthquake. In this paper a numerical tool based on the Discrete Element Method is presented, aimed at the static, dynamic and hydromechanical analysis of masonry gravity dams. The use of discontinuous models is mandatory for the study of failure mechanisms involving the masonry discontinuities, the dam-rock interface or the rock mass joints. The Discrete Element Method is able to assemble continuous and discontinuous meshes simultaneously in the same model, providing a versatile tool to consider various assumptions and levels of analysis, ranging from simplified to detailed structural representations. A comprehensive study of the seismic behaviour of Lagoa Comprida Dam, located in Portugal, is presented. Both continuous and discontinuous models were developed to assess the main failure mechanisms, including overstress, partial and global sliding and overturning.Permission by EDP – Energias de Portugal, to present the dam modelling results is gratefully acknowledged

A DEM based tool for the safety analysis of masonry gravity dams

A numerical model for analysis of masonry gravity dams based on the discrete element method is presented. The dam and the rock foundation are represented as block assemblies, using elementary 3- and 4-node blocks. Complex block shapes are obtained by assembling the elementary blocks into macroblocks, allowing the model to be applied in various situations ranging from equivalent continuum to fully discontinuum analysis. A contact formulation was developed, which represents the interaction between macroblocks in terms of contacts established between elementary blocks, based on an accurate edge-edge approach. The main numerical aspects of the model are described, addressing in particular the contact creation and update procedures, and the numerical devices that support an efficient explicit solution algorithm. An application to the safety evaluation of an existing masonry dam is discussed, including stress analysis in the structure, and the assessment of sliding failure mechanisms, involving different paths in the vicinity of the dam-rock interface.Permission by EDP to present the example data is gratefully acknowledged. The first author also acknowledges the financial support of the Portuguese Science Foundation (Fundacao de Ciencia e Tecnologia, FCT), through Grant SFRH/BD/43585/2008

Avaliação da propagação de fissuras na superfície de fundação de barragens gravidade

Neste trabalho apresenta-se um processo iterativo de cálculo, com base na análise limite, para determinação do comprimento de fissuras nos planos horizontais de barragens gravidade sujeitos a esforços de tracção e, em consequência, alteração das condições de aplicação da subpressão. Esta ferramenta baseia-se num modelo de dados proveniente de uma aplicação mais vasta que, a partir da geometria da barragem, características do material, nível da água a jusante e montante, condições de drenagem e solicitação sísmica, permite a determinação das condições de estabilidade da estrutura. Faz-se a análise dos dois acidentes ocorridos na barragem de Bouzey, um por deslizamento pela base e o outro por derrubamento parcial da secção, em que a ocorrência de fissuração e o efeito da subpressão tiveram papel determinante.This paper presents an iterative process of calculation, based on limit analysis, to determine the length of cracks in horizontal planes of gravity dams subjected to tension and, consequently, changes in the uplift resultant. This tool is based on a data model from a wider application that, from the dam geometry, material properties, downstream and upstream water level, drainage effectiveness and seismic load, allows the determination of the structure stability conditions. The analysis of the two accidents with the Bouzey dam is also made. One accident occurred by sliding through the base and the other by partial overturning of the cross section, where the occurrence of cracking and the effect of uplift played a key role