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

Discrete element modeling of masonry structures: Validation and application

The failure mechanism and maximum collapse load of masonry structures may change significantly under static and dynamic excitations depending on their internal arrangement and material properties. Hence, it is important to understand correctly the nonlinear behavior of masonry structures in order to adequately assess their safety and propose efficient strengthening measures, especially for historical constructions. The discrete element method (DEM) can play an important role in these studies. This paper discusses possible collapse mechanisms and provides a set of parametric analyses by considering the influence of material properties and cross section morphologies on the out of plane strength of masonry walls. Detailed modeling of masonry structures may affect their mechanical strength and displacement capacity. In particular, the structural behavior of stacked and rubble masonry walls, portal frames, simple combinations of masonry piers and arches, and a real structure is discussed using DEM. It is further demonstrated that this structural analysis tool allows obtaining excellent results in the description of the nonlinear behavior of masonry structures

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

Numerical modelling of masonry gravity dams considering the internal structure of the material

Frequently, numerical models of masonry dams disregard the discontinuous nature of the material. In some cases, those discontinuities control the structural and hydraulic behaviour of the masonry dam. The masonry proprieties are influenced by the quality of the material and the laying scheme of the stones on the external faces as well as in the inner material. The Discrete Element Method (DEM) has been used on analyses of gravity masonry dams. The capacity to model the discontinuities explicitly and the ability to perform coupled analyses are two significant benefits of the DEM. The DEM application used in this paper is presented, stressing the description of the calculation cycle. Seven examples of numerical analyses of gravity masonry dams are presented. Three of them consider the discontinuous nature of the dam body, in order to study the loss of cohesion scenario, the crack propagation scenario and the seismic performance of a masonry dam. The remainder four examples are aimed at stress analysis, global stability, hydromechanical analysis and the permanent sliding resulting from a seismic event

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

Desenvolvimento de um modelo de elementos discretos para o estudo de barragens gravidade em alvenaria

Tese de doutoramento em Engenharia Civil / EstruturasEm 1853, J. Sazilly publicou o primeiro documento científico na área da Engenharia de Barragens. Neste artigo, Sazilly propõe um novo método para a definição do perfil de barragens gravidade em alvenaria, com base na análise de tensões. Quase 40 anos depois, em 1895, após o acidente da barragem de Bouzey, M. Lévy publicou um relatório em que descreve o importante efeito da subpressão na estabilidade global das barragens gravidade. Apenas nos anos 1960, R. Clough e E. Wilson desenvolveram as primeiras análises de barragens através do Método dos Elementos Finitos, para tratar de problemas térmicos e sísmicos. Esta introdução histórica descreve o período no qual a maioria das barragens gravidade em alvenaria foi construída. Muitas destas barragens apresentam alguma fragilidade estrutural que reflecte o conhecimento disponível na época em que foram projectadas, para além de outras fragilidades, relacionadas com problemas de deterioração. Hoje em dia, a exploração destas barragens representa um desafio, pois a segurança estrutural deve ser garantida de acordo com os regulamentos modernos. A maioria das aplicações numéricas existentes no mercado, não permitem a modelação realista dos mecanismos de rotura específicos das barragens gravidade em alvenaria, pois foram desenvolvidos para a análise de estruturas correntes. Neste contexto, foi elaborada uma aplicação numérica, através da linguagem de programação C++, com base no método dos elementos discretos (MED), designada por DEC-DAM. A aplicação foi elaborada especificamente para tratar dos problemas relacionados com barragens gravidade, especialmente as barragens gravidade em alvenaria, apesar de a sua utilização também ser válida para as barragens gravidade em betão. A aplicação permite a realização de análises estáticas, dinâmicas e de escoamento, com acoplamento hidromecânico, para além da análise do processo de injecção de calda e do reforço estrutural com ancoragens. Os modelos desenvolvidos através desta aplicação podem ser discretizados em blocos com três ou quatro lados, rígidos ou deformáveis. A associação entre blocos pode ocorrer de forma semelhante a uma malha de elementos finitos ou através do estabelecimento de contactos entre blocos, constituindo um meio descontínuo. Foi desenvolvida uma solução completa para a detecção, actualização e eliminação de contactos ao longo da análise. A solução numérica utilizada corresponde a integração da equação de movimento, através do método das diferenças centrais, em associação as técnicas das massas escaladas e de relaxação dinâmica. A análise dinâmica baseia-se na mesma solução numérica da análise estática, excepto no que se refere à utilização das massas escaladas e da relaxação dinâmica, que é substituída pela aplicação do amortecimento de Rayleigh. Foram elaboradas diversas ferramentas para a aplicação das solicitações dinâmicas e respectivas condições de fronteira. Para a aplicação simultânea das componentes de corte e de compressão foi implementada uma solução designada por free-field. A aplicação permite ainda a realização de análises hidromecânicas. A estrutura de dados, nomeadamente a concepção da malha de escoamento, possibilita a integração do cálculo hidráulico e mecânico. O cálculo hidromecânico foi estendido para tratar das questões relacionadas com a injecção de calda. O modelo desenvolvido permite, numa mesma análise, efectuar o estudo do escoamento de água por uma fissura, a substituição da água pela calda por meio da simulação do processo de injecção e, posteriormente, o endurecimento da calda e a avaliação do seu efeito no comportamento estrutural da barragem. Para além disto, a aplicação admite a aplicação de pregagens e ancoragens que, em conjunto com a injecção de calda, permite avaliar a grande parte das obras de reforço e reparação de barragens. Foram ainda analisadas cinco barragens, das quais três estão localizadas em Portugal, barragem de Guilhofrei, de Lagoa Comprida e da Póvoa, uma na Índia, barragem de Bhandardara, e uma no Canadá. Estes estudos permitem demonstrar mais amplamente as capacidades da aplicação desenvolvida.In 1853, J. Sazilly published the first scientific paper on the field of Dam Engineering. In this paper, Sazilly proposes a novel method to define the profile of masonry gravity dams, based on stress analysis. Almost 40 years later, in 1895, after the accident of Bouzey Dam, M. Lévy published the report which describes the great effect of the uplift in the global stability of gravity dams. Only in the 1960's, R. Clough and E. Wilson developed the first analyses of dams by means of the Finite Elements Method to solve thermal and seismic problems. This historical introduction describes the period of time along which the majority of masonry gravity dams was constructed. Many of these dams present some structural fragility that reflects the knowledge available in the period of time that dams were designed. Other fragilities are present, such as deterioration problems. Nowadays, the exploitation of these dams represents a challenge, since the structural safety should be achieved according to modern regulations. The majority of numerical applications in the market, does not allow to model actual failure mechanisms typical of masonry gravity dams since it was developed for the analysis of general structures. In this context, a numerical application using the Discrete Element Method (DEM) was developed, designated as DEC-DAM. The application was designed specifically to address the problems associated with gravity dams, especially in masonry gravity dams, although its use also is valid for concrete gravity dams. The application enables to perform static, dynamic and flow analyses, with hydro-mechanical coupling, in addition to analyzing the process of grouting and structural strengthening with anchors. The models developed through this application can be discretized into blocks with three or four sides, rigid or deformable. The association between the blocks may be similar to a finite element mesh to create a continuum or through the contacts between blocks, forming a discontinuous medium. A complete solution was developed for the detection, updating and deletion of contacts throughout the analysis. The numerical solution used corresponds to integration of the motion equation, through the central difference method, together with scaled masses and dynamic relaxation procedures The dynamic analysis is based on the same numerical solution as the static analysis, except as regards the use of scaled mass and dynamic relaxation, which is replaced by the application of Rayleigh damping. Several tools for the application of dynamic loads and their boundary conditions were developed. For the simultaneous application of the shear and compression components, a free-field solution was implemented. The application also allows the realization of hydro-mechanical analysis. The data structure, namely the design of the flow mesh enables the integration of mechanical and hydraulic calculation. The hydro-mechanical calculation has been extended to address issues related to the grouting. The model allows to combine in a single analysis, the study of water flow through a crack, replacement of water by the grout by simulating the injection process and then hardening of the grout and assessing their effect on structural behavior the dam. In addition, the application allows the application of passive and active anchors that, together with the grouting solution, allows the evaluation of much of the work of strengthening and repair of dams. Five real dams were also analyzed, three of them are located in Portugal, the Guilhofrei Dam, the Lagoa Comprida Dam and the Póvoa Dam, one in India, the Bhandardara Dam, and one in Canada. These analyses allow to fully demonstrate the capabilities of the developed application

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

Hydromechanical analysis of masonry gravity dams and their foundations

A numerical model for the hydromechanical analysis of masonry dams based on the discrete element method is presented. The dam and the rock foundation are represented as block assemblies, and a coupled flow-stress analysis is performed in an integrated manner for the entire system. Complex block shapes may be obtained by assembling elementary blocks into macroblocks, allowing the application of the model to situations ranging from equivalent continuum to fully discontinuum analysis. A contact formulation was developed based on an accurate edge-edge approach, incorporating mechanical and hydraulic behavior. The main numerical aspects are described, with an emphasis in the flow analysis explicit algorithm. An application to an existing masonry dam is presented, analyzing its present condition, with excessive seepage, and the proposed rehabilitation intervention. An evaluation of sliding failure mechanisms was also performed, showing the expected improvement in the safety of the structure.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

Analysis of a gravity dam considering the application of passive reinforcement

Small concrete gravity dams are sometimes built using passive steel anchors to enhance their stability for the applied loads. It is important to assess the amount of internal tensile and shear forces resisted by the anchors to verify their structural adequacy. This paper presents the application of the distinct element method to study the magnitude and distribution of internal anchor forces. Comprehensive parametric analyses considering the anchor shear stiffness and the friction angle of the dam-foundation interface have been performed on a small dam 3 m high. The case of several anchors along the section was also investigated. It is shown that (a) the required displacements to induce anchor loads are very small (of the order of 10x10-3 mm of crack opening), (b) that the anchor shear stiffness has small impact in the load share between anchor and concrete, and finally (c) that strength properties of rock-concrete interface play a key role in the structure behavior.(undefined