Parametric Study of Steel-Lined pressure Shafts in Anisotropic Rock
Steel-lined pressure tunnels and shafts are used to convey water from the reservoir to the turbines in high-head hydroelectric power plants. An axisymmetrical multilayer model is of-ten considered by engineers for the design of the steel liner. Stresses and deformations can then be computed with a closed-form analytical solution in isotropic rock. When the rock is anisotropic, the lowest elastic modulus of the rock measured in situ is often considered in the analytical solu-tion, which is regarded as conservative. In this work, the behaviour of steel liners in anisotropic rock was studied systematically by means of the Finite Element Method (FEM). The materials, namely steel, backfill concrete, near-field rock and far-field rock were modelled as linear and elas-tic, and a tied contact was assumed between the layers. The influence of geometrical and material parameters under a quasi-static internal water pressure was studied through an extensive para-metric study. It was observed that, compared to the corresponding results in isotropic rock, maxi-mum stresses in the steel-liner can be reduced up to 25% when anisotropy is considered. On the contrary, the maximum stresses in the far-field rock can be largely underestimated, namely up to 65%.
Influence of geometrical imperfections and flaws at welds of steel liners on fatigue behavior of pressure tunnels and shafts in anisotropic rock
The recent development of high-strength (HSS) weldable steels has enlarged the range of design alternatives for the optimization of high-head steel-lined pressure tunnels and shafts (SLPTS) in the hydropower industry. With the liberalization of the European energy market and increasing contribution of new renewable volatile energies in the electricity grid due to high subsidies, storage hydropower and pumped-storage plants are subject to more and more severe operation conditions resulting in more frequent transients. The use of HSS allows the design of thinner and thus more economic steel liners. However, welded HSS do not provide higher fatigue resistance than lower steel grades, and may be particularly subject to the risk of cold cracking in the weld material as dramatically illustrated by the failure of the Cleuson-Dixence pressure shaft in 2000. Fatigue behavior may become the leading limit state criterion. This research project aims at improving the comprehension of the mechanical behavior of SLPTS and at developing a framework for probabilistic fatigue crack growth and fracture assessment of crack-like flaws in the weld material of longitudinal butt welded joints, considering all possible steel grades for high-head hydropower schemes. The influence of anisotropic rock behavior and geometrical imperfections at the longitudinal joints on the structural stresses have been studied by means of the finite element method accounting for the interaction with the backfill concrete-rock multilayer system. Parametric correction factors have been derived to estimate stress concentrations and structural stresses in steel liners with ease in practice, allowing the use of $S$-$N$ based engineering fatigue assessment approaches. Stress intensity factors (SIF) for axial cracks in the weld material of the longitudinal joints have also been obtained by means of computational linear elastic fracture mechanics (LEFM). The use of the previously developed parametric equations in the classical formulas for SIF in cracked plated structures has been validated, and new parametric equations for the weld shape correction have been proposed. A probabilistic model for fatigue crack growth assessment has been developed in the framework of LEFM in combination with the Paris-Erdogan law. The probability of failure is estimated by means of the Monte Carlo simulation procedure, in which the crack growth rate parameters and the crack shape ratio are defined as stochastic variables. A week-long normalized loading spectrum derived from prototype measurements on an alpine pumped-storage hydropower plant in Switzerland is used. This approach provides relative and quantitative results through parametric studies, giving new insights on the fatigue behavior of steel liners containing cracks in the weld material of the longitudinal joints. Finally, a fatigue assessment case study is presented, detailing the entire calculation procedures developed in this research. It aims at ensuring the transfer of knowledge toward practitioners.
The Inca Occupation of the South Coast of Peru
like the others, however; it forks into several nearly parallel ravines of which the largest are Huayuri, Rio Grande-Palpa, Ingenio (called Collao in ancient times), Nasca proper (the ancient Caxamarca), Taruga, and Poroma. Due to peculiarities of the local topography, the irrigated areas in Ica and the ravines of Nasca are located inland, at the foot of the mountains, rather than at the mouths of the rivers as is more usual in Peruvian coastal valleys. No sharp natural or cultural boundary separates the valley of Chincha from the valleys of Cafiete (ancient Huarco and Runahuana), Asia, and Mala, the next valleys going up the coast to the northwest. At the other end of the area we are considering, however, there is a sharp break; beyond Yauca the Andean foothills reach out to the sea, natural conditions are quite different, and there are important differences in the archaeological picture as well. The historical sources which mention the south coast are not particularly helpful, except in so far as they provide us with a few dates. To begin with, no chronicler gives an explicit account of the political organization of the south coast at the time it came into contact with the Incas. It can, perhaps, be inferred from Cabello Balboa's statements about common policy toward the Inca invaders that there was some sort of political connection between the valleys of Mala, Cafiete, and Chincha, but the connection need have been no more than a temporary military alliance. Cabello makes no mention at all of Pisco. The valleys of Ica, Nasca, and 125