Analysis of earth dam-flexible canyon interaction by 3D hybrid FEM-SBFEM

La géométrie et la flexibilité d'un canyon sont les paramètres qui affectent grandement la valeur des périodes naturelles dans les barrages en terre. Le canyon entourant des barrages peut être considéré comme un domaine illimité. Pour prendre en compte ces deux effets, le canyon a été modélisé par SBFEM et le barrage en terre, à géométrie limitée, par FEM. La technique hybride SBFEM-FEM pour l'analyse tridimensionnelle dynamique de l'interaction sol-barrage a été validée avec les résultats disponibles dans la littérature. Comme la matrice de rigidité dynamique du domaine non borné est complexe et dépendante de la fréquence, la méthode classique de superposition de modes n'est pas simple pour le système d'interaction sol-structure. Ainsi, pour obtenir la fréquence propre fondamentale, le barrage a été excité en direction amont-aval. Les périodes naturelles du barrage de terre pour des canyons de formes géométriques et de coefficient de impédance différents ont été obtenues. Ils se sont avérés avoir des effets significatifs sur la période naturelle. Les résultats ont été comparés aux données enregistrées réelles. Il a été constaté que les graphiques proposés dans cette étude peuvent être utilisés par des concepteurs de barrages pour l'estimation des périodes naturelles des barrages en terre dans des canyons de formes et de propriétés matérielles différentes. Plusieurs fonctions d'amplification correspondant à différentes conditions de canyon ont été obtenues en appliquant un déplacement uniforme à la limite du canyon. Une étude approfondie a été réalisée pour examiner les effets de la géométrie et de la flexibilité du canyon sur la réponse en régime permanent du barrage. Ces deux effets ont influencé de manière importante les fonctions d'amplification. Alors que la flexibilité du canyon affecte de manière significative la valeur de la fonction d'amplification maximale, cette valeur ne change pas pour les barrages en terre dans lesquels les canyons ont des formes différentes et la même longueur. De plus, la réponse latérale du barrage de terre dans le domaine temporel a été calculée pour analyser les effets susmentionnés lors d'un tremblement de terre réel. Les fonctions d'amplification proposées ont été utilisées pour comparer les spectres de réponse enregistrés du barrage d'El Infiernillo lors des tremblements de terre de 1966 avec la fonction d'amplification calculée. Un accord raisonnable a été observé entre eux. La méthode linéaire équivalente (EQL) a été implémentée dans le FEM. La technique FEMSBFEM a été étendue pour prendre en compte l'effet du comportement non linéaire des barrages en terre. Il a été observé que le comportement non linéaire affecte grandement la fréquence naturelle, la fonction d'amplification et l'accélération de crête maximale du barrage de terre situé dans les canyons. Les effets de la géométrie et de la flexibilité du canyon sur le comportement non linéaire ont été examinés, et on a vu qu'en augmentant la flexibilité du canyon, l'effet de la non-linéarité était diminué. Le barrage d'El Infiernillo a été modélisé par FEM-SBFEM non linéaire 3D, et une comparaison de la fonction d'amplification de crête obtenue par la méthode proposée avec les données enregistrées montre la précision du FEM-SBFEM non linéaire.The canyon surrounding a dam can be assumed as an unbounded domain, and the geometry and flexibility of a canyon are parameters that greatly affect the values of natural periods in earth dams. In this thesis, in order to take into account these two effects, canyons are modeled by SBFEM, and earth dams, which have limited geometries, are modeled by FEM. The hybrid FEM-SBFEM technique used for the dynamic three-dimensional analysis of soil-earth dam interactions is validated with results available in the literature. Because the dynamic-stiffness matrix of the unbounded domain is complex and frequency-dependent, the classical mode-superposition method is not straightforward for a soil-structure interaction system, and thus, to obtain their fundamental natural frequencies, the modeled dams were excited in the upstream-downstream direction. The natural periods of earth dams in canyons with different geometries shapes and impedance ratios are obtained, and are found to have significant effects on the dams' natural periods. The results are compared with actual recorded data, and it is found that the graphs put forward in this study may be used by practical engineers for the estimation of natural periods of earth dams in canyons with different shapes and material properties. Several amplification functions corresponding to different canyon conditions are obtained by applying a uniform displacement at the canyons' boundaries. A comprehensive study is performed to examine the effects of canyon geometry and flexibility on the steady-state responses of the dams, and it is found that these two effects significantly influence the amplification functions. While the flexibility of the canyon does affect the maximum amplification function value, this value does not change for earth dams in canyons that have different shapes but the same length. In addition, the lateral responses of earth dams in the time domain are computed in order to analyze the aforementioned effects under an actual earthquake. The proposed amplification functions are used to compare the recorded response spectra of the El Infiernillo dam under the two 1966 earthquakes with the calculated amplification function, and a reasonable agreement is observed between them. The equivalent linear method (EQL) is implemented into the FEM, and the FEM-SBFEM technique is extended in order to take into consideration the effect of earth dams' nonlinear behavior. It is observed that such nonlinear behavior greatly affects the natural frequency, the amplification function, and peak crest acceleration of earth dams located in canyons. The effects of canyon geometry and flexibility on the nonlinear behavior are examined, and it is found that by increasing canyon flexibility, the effect of nonlinearity is decreased. The El Infiernillo dam is modeled by the 3D nonlinear FEM-SBFEM, and comparison of the crest amplification function obtained by the proposed method with the recorded data shows the accuracy of the nonlinear FEM-SBFEM

Effects of thermal and seepage actions on seismic response of roller compacted concrete dams

Roller compacted concrete (RCC) dams have been developed for their rapid construction and low cost. However, some issues associated with the analysis and design of RCC dams are related to the seismically induced damages and possible failure of the dam, seepage due to the weakness of roller compacted layers and thermal stresses due to massive concreting. Large seismic events, in addition to the thermal and seepage effects, can cause the cracking and nonlinear behaviour where these cracks may expand further under the water pressure inside them to affect the stability of the structure. Therefore, developing a suitable constitutive material model and a reliable computational procedure for the safety evaluation and prediction of cracking risk of these structures has been a challenging and demanding task. This research aims to present a new comprehensive numerical procedure to evaluate the seismically induced cracking of RCC dams under the effects of thermal and seepage actions. It takes into account the coupling effect of water pressure and the crack formation during an earthquake. In addition, more relevant features of the behaviour of concrete such as ageing, temperature, confining pressure and adiabatic temperature effects have been considered in the analysis. A purposeful comprehensive numerical system consists of several individual features and in combination. The system includes a combination of field problems (thermal and seepage fields), continuum mechanics (stress analysis), seismic hazard assessment and safety evaluation. The combination uses finite elements to introduce compatible units capable of analysing infrastructure, such as RCC dams, to evaluate and predict level of safety in terms of crack pattern development. The method, which is based on a principle of birth and death process, is capable of simulating and assessing safety of RCC dams during the construction and the operation phase. The constitutive material model for concrete is based on the combination of damage mechanics and plasticity. The mathematical models for mechanical behaviour of materials are given in the form of constitutive equations. The proposed constitutive models have been reformulated and presented in convenient forms for RCC materials. Ageing, temperature and confining pressure effects were taken into account and implemented in the proposed constitutive models. All the developments and analyses are performed using coded subprograms written in FORTRAN and developed in finite element program ABAQUS. Then, the validity of the proposed computational procedures and models has been confirmed by analysing and comparing the results obtained based on available experimental and analytical evidences. After the verification process, the material nonlinearity and proposed models are applied to analyse and evaluate the related dam safety against the cracking of an existing full-size dam. Finally, conclusions are drawn and recommendations are made based on the present research. Based on the conclusions, it is revealed that the numerical procedure developed in this study for the seismic evaluation of RCC gravity dams under thermal and seepage actions provides a general framework for the analysis and design of these critical structures. The results of the evaluation indicate that different response patterns result when considering and neglecting THM (thermos-hydro-mechnical) model in seismic analysis, suggesting the significance of incorporating the thermal and seepage fields into the seismic assessment and design of concrete gravity dams

Seismic Analysis of Post-tensioned Gravity Dams using Scaled Boundary Finite Element Method

Dams are hydraulic structures built across rivers to create reservoirs, which provide essential services to society such as flood control, human water supply, and electricity generation. A dam shall be designed to ensure stability against overturning and sliding caused by the hydro-pressure of the reservoir. A common type of dam is the concrete gravity dam that mainly relies on its self-weight and resistance to sliding on the foundation to maintain its stability. Installing post-tensioned anchors (PTAs) is a practical and cost-effective technique in dam engineering. It provides an additional stabilizing force and improves the shear resistance at the dam-foundation interface. Seismic safety evaluation of post-tensioned concrete gravity dams is necessary for new dam designs or strengthened existing dams to guarantee that the structures will survive at specified seismic hazard levels. This thesis presents the development of an efficient numerical framework for the seismic analysis of post-tensioned concrete gravity dam-reservoir-foundation systems. This framework is realized by implementing the scaled boundary finite element method (SBFEM) in the well-known commercial FEM software ABAQUS as user elements (UEL). Polytope elements (polygonal elements in 2D and polyhedral elements in 3D) are as versatile as standard FEM solid elements, while they provide greater flexibility in mesh generation for bounded domains. Unbounded user elements (UEL) are derived to model wave propagation in far-fields. An unbounded UEL only requires discretization with a small number of faces at the near-field/far-field interface and can rigorously satisfy the radiation condition at infinity. The ABAQUS software enhanced with the UELs is employed for two-dimensional seismic analysis of gravity dams, overcoming the difficulties encountered in standard FEM, for example, local mesh refinement for geometrical features, generating matching interfacial meshes for weak joints, and simulation of anchor-structure interactions. The overall system consists of a near-field containing the dam body and its neighboring reservoir and foundation, and a far-field of the reservoir and foundation continua. The near-field dam and foundation are discretized as quadtree meshes assigned with polygonal UELs. Quadtree meshes allow rapid and smooth transitions in element size, which facilitates the local mesh refinement for dam lift joints, anchor boreholes, drainage systems, etc. An unbounded UEL represents the far-field foundation in terms of displacement unit-impulse response matrices. It captures free-field motions and transfers them as equivalent seismic inputs acting at the near-field/far-field interface. The reservoir is modeled by ABAQUS built-in acoustic elements. At the far end of the reservoir, a non-reflecting acoustic boundary embedded in ABAQUS is employed to satisfy the radiation condition of the unbounded reservoir. Comprehensive considerations have been taken in the numeral simulation of post-tensioned gravity dams, such as weak joint behaviors, anchor-structure interaction, and concrete damage. Weak joints in a concrete gravity dam, such as the dam-foundation interface and the dam lift joints, are the most likely places where the sliding and cracking occur. A cohesive-frictional contact scheme is utilized to simulate the non-linear behaviors of these weak joints. A PTA is usually grouted with the structure along a portion of the length, called bond length. At the grouting interface, the bond stress develops with the slippage between the anchor and structure, and then transfers the prestressing in the anchor to the structure. Cohesive elements connected with the anchor and structure are generated along the bond length to simulate the bond-slip interaction. A Mazars' damage evolution law for dynamic loading is applied to simulate the quasi-brittle behaviors of the concrete. To avoid mesh sensitivity, a partially regularized local damage model is introduced into this application. Automatic re-meshing algorithms to generate conforming interfacial meshes are developed for the sake of the simulation of interfacial problems. For the weak joints, the domains in contact are allowed to be discretized individually, and then the existing meshes at the interfaces are re-meshed to be node-to-node matching. The anchor is embedded automatically in the structure by inserting additional nodes into the existing structural meshes along the anchor layout. By duplicating the inserted nodes and connecting the duplicated nodes, beam elements conforming with structural meshes are formed naturally. These re-meshing procedures are easily operated on the polygonal meshes allowing arbitrary numbers of nodes and edges. Cohesive elements can be generated with the matching nodes at interfaces, and no constraints are required to connect them with the surrounding elements. The proposed approach is verified by performing seismic analysis of a post-tensioned gravity dam with simple geometry, and comparing the results obtained from the model using ABAQUS built-in elements. The advantages of the proposed approach in handling complex problems are demonstrated through dams with multiple inclined anchors. Applications of this method can be extended to three-dimensional cases, and composite materials with randomly spread fiber inclusions

Risk Assessment of Concrete Gravity Dams under Earthquake Loads

Dams are important structures to supply water for irrigation or drinking, to control flood, and to generate electricity. In seismic regions, the structural safety of concrete gravity dams is important due to the high potential of life and economic loss if they fail. Therefore, the seismic analysis of existing dams in seismically active regions is very crucial to predict responses of dams to ground motions. In this thesis, earthquake response of concrete gravity dams is investigated using the finite element (FE) method. The selected dam is the Pine Flat Dam which is located in the Central Valley of Fresno County, California. The dam-water-foundation rock interaction is taken into account in developed FE model by considering compressible water, flexible foundation effects, and absorptive reservoir bottom materials. In addition, Dams are usually analyzed using deterministic analysis method; however, several uncertainties affecting the results should be considered in the analyses of dams, such as material properties, inaccuracies of modeling, the water level in the reservoir, and the aleatoric nature of earthquakes. Therefore, the uncertainties regarding structural data and external actions are considered to obtain the fragility curves of the dam-water-foundation rock system. The structural uncertainties are sampled using Latin Hypercube Sampling method as a practical and efficient way for addressing such a complex problem. The fragility curves for base sliding and tensile cracking limit states are obtained performing non-linear time history analyses. Normal, Log-Normal and Weibull distribution types are used in order to fit fragility curves. The effect of the minimum principal stress on tensile strength is considered and found to be insignificant. It is also found that the probability of failure of tensile cracking is higher than that for base sliding of the dam. In addition, the loss of reservoir control is unlikely for a moderate earthquake

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

Reliability Analysis of Concrete Gravity Dams under Earthquake Loads

Dams are infrastructure assets of extreme importance; the failure of which can have catastrophic consequences on adjacent communities. Therefore, it is prudent for authorities to evaluate the safety of existing dams in seismically active regions. This thesis focuses on carrying out a reliability analysis of concrete gravity dams under earthquake loads using an enhanced finite element model. For many years, reliability studies on concrete gravity dams were performed using a finite element model that considered a massless foundation and assumed that water is incompressible. Moreover, the design ground motion was applied without any modification either at the bottom fixed boundary of the foundation domain or at the dam-foundation-rock interface. As these assumptions do not accurately represent real-life conditions, investigations incorporating realistic constraints are necessary. In this study, a finite element model that considers three subdomains is employed - namely the dam, its foundation domain that includes mass, stiffness, and material damping, and a fluid domain that includes water compressibility. The interactions between the different subdomains is also included in the model. The truncated boundaries of the foundation-rock and fluid domains are modeled using standard viscous-damper boundaries. In addition, effective earthquake forces obtained by deconvolving ground motion are specified at these boundaries. Non-linear time-history analyses are performed using the developed model by considering uncertainties associated with material data as well as the aleatoric nature of earthquakes. Fragility curves are then obtained for the limit states - base sliding, excessive deformation, and tensile cracking at the upstream face and at the neck - with the goal of using them to assess the risk of the dam under earthquake loads. The results are compared with that of Sen and Okeil [1]. It is observed that the differences in modeling assumptions have a significant impact on the probabilities of failures for the limit states. The critical limit state in this study was found to be excessive deformation. In contrast, in the study by Sen and Okeil [1], tensile cracking was identified to be the critical limit state. Among both the studies, the tensile cracking limit state was the least different. It was also observed that a loss of reservoir control could occur in the event of a moderate to strong earthquake

Dynamic modelling of arch dams in the ambient state

Includes bibliographical references.To date, dam failures have resulted in significant losses in the commercial economy and in human life. Raising awareness in the field of structural health monitoring is neccesary to develop contemporary structural analysis and monitoring methods to ensure the integrity of these structures. Hence, the research aims at developing an analytical formulation that can be used in the dynamic modelling of arch dams, for structural health monitoring purposes. A hypothetical arch dam model was created to investigate the influence of a reservoir’s orientation and geometry on the dam’s dynamic properties, and the discrepancies between the Westergaard and Fluid Structure Interaction (FSI) analysis methods. The two analysis methods were then utilized to develop an updatable finite element model, in a case study pertaining to the 72m high Roode Elsberg concrete-arch dam. Thereafter, ambient vibration tests were conducted on the Roode Elsberg dam to measure its dynamic properties and validate the finite element models. The excitation on the dam was provided by the wind and the reservoir flowing over the spillway. Vibrations of the dam were measured and recorded by accelerometers placed on the cantilevered arch blocks. Finally, the Frequency Domain Decomposition (FDD) algorithm was used to analyse the acquired data and identify the natural frequencies of the dam

Modelling the Eddy Pattern in the harbour of Zeebrugge

Hydrodynamic