Design of Double-Curvature Arch Dams in Terms of Geometric and Stress Constraints by Using Script-Based Finite Element Modelling

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An arch dam is a curved surface structure that is designed to resist water pressure at the convex side. An arch dam is usually constructed in a narrow V-shape valley with strong rock foundations. Through the arched shape the water pressure is distributed from the upstream face of the dam to the abutment edges of the dam which are embedded in the rock-foundation. An arch dam is designed to be under compressive stresses when it is submitted to the dominant dead-weight and hydrostatic loadings. In comparison with other dam-types, such as an embankment dam, an arch dam is considerably thinner and requires less construction material, which can make this type of dam the most economical. Due to the thin shell structure, an arch dam cannot resist concentrated loadings resulting from strong variations of strength of the foundations or impact from e.g. falling rocks. Hence, a proper assessment of design conditions is essential and this also applies for other dam-types. To design an arch dam an initial dam layout is used, usually obtained from empirical methods, and it is reshaped until the essential constraints are satisfied within the design objectives. The application of finite element analysis during this iterative process is elaborative and therefore often postponed to the stage of design when the basic design parameters such as location, height and orientation of the dam have been defined. The aim of this master project is to develop a procedure that allows to define in an automatic way the generation of a finite element model of double-curved arch dams. In this way, the model can be efficiently used from the beginning of the design process taking into account the dam and excavation volume, the stresses and deformations in the dam body and the foundation for a variation of loading conditions for different basic design parameters of the dam. In this thesis guidelines applied in practice are the reference for the design of the shape of the dam. The general workflow consists of a preliminary and a final design stage. Through the first stage the best location of the dam and height must be defined such that geometric constraints as defined in the guidelines are satisfied. For this purpose, different potential locations for the dam are chosen by the designer. For each location an assessment must be made, considering many factors, such as state of the foundation, environmental and social conditions and also costs, which are predominantly defined by the volume of rock excavation and volume of the dam-body. When this information is collected for the chosen locations the best alternative can be defined. In the second stage, the dam of the best alternative is reshaped by modifying the entire geometry of the dam until stress constraints are satisfied. An important condition is to check and minimize the effect of design-changes on the costs under the condition that the shape of the dam remains smooth. This master project was done at TNO DIANA BV, this company develops the DIANA Finite Element software that is used by dam-engineering consultants and dam-owners to design new and assess existing dams. Based on Python scripting a procedure is defined for automatic generation of a finite element model of double-curved arch dam with rock foundation. The script starts with a topological surface. From the basic design parameters (location, orientation, height) a preliminary shape of the dam with abutments is defined following the US Army corps guidelines. With this model, the design engineer can perform efficiently different analyses, such as calculation of volume of dam-body and excavated rock, but also predict deformations and stresses and eigen-modes more accurately in the preliminary design stage. In the subsequent final design phase the same model can be optimized by including joints between different columns in the dam and define thickening at the edges of the dam to reduce stresses in the abutments. In the final design phase all kind of loadings and analysis types can be considered, such as thermal loadings during young-hardening phase of concrete or damage development during earthquake loadings. In this thesis first general information regarding double-curvature arch dams is given and their geometry is divided into four main parts from which the dam geometry is derived. Then the general workflow is introduced which describes the entire design process and is based on empirical methods used in practice. Each step in the geometry definition leads to mathematical expressions, which can be translated into Python commands. The entire process is inserted into the Finite Element software DIANA as a script and the dam is analyzed. The developed script is applied on a topographic surface which is based on real data. Three different locations are used and the most economical one is assessed. This design was reshaped based on the designer’s judgement. Finally, the analysis results are used to investigate the dependency of the theoretical with numerical volume and how basic design parameters influence the stresses and deformations of the structure. The conclusion of the thesis is that the developed procedure can sufficiently describe the design of double-curvature arch dams using any location, whereas the modelling effort is drastically reduced. It is recommended that further research is needed to further improve the code towards needs from dam-engineers in practice. When the developed procedure will be more integrated in the DIANA software it can be a very efficient tool to help dam-engineers around the world to make use of advanced finite element analysis already in the early preliminary design stage of curved arched dams.