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 (SLPT&S) 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 SLPT&S 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.

Alexandre Jean Pachoud

High-head steel lined pressure tunnels and shafts may be considered as critical infrastructures especially when rock overburden is small. In the case of lining failure, catastrophic damages can occur when a large amount of water can reach the steep valley slopes and induce dangerous mud and debris flow. In the last decades, high-strength steel has been used more frequently for such high-head pressure tunnels and shafts mainly for economic and construction reasons. Under the more and more rough operation conditions of storage hydropower plants, high-strength steels, which are generally thinner than lower grade steels, are more prone to fail by fatigue. Design guidelines for the application of high-strength steel for steel liners are still missing. With his research project, Dr Alexandre Pachoud made an important and novel contribution for the design of pressure tunnels and shafts considering the influence of anisotropic behavior of rock as well as the geometrical imperfections and flaws at welds on the fatigue resistance of the steel liners. For the first time, Dr Pachoud studied systematically the influence of rock anisotropy on the deformation of the lining system comprising steel liner, backfill concrete and near as well as far field rock mass. He performed an extensive parametric study with the finite element method (FEM) over a wide range of geometrical and material parameters. Normalized stresses and displacements were analyzed in the steel liner and the far-field rock mass and correction factors to be included in the analytical solution for isotropic rock conditions could be derived. For transversely anisotropic rock mass the analytical solution allows a simple and fast estimation of the maximum stresses in the steel liner by a correction applied to the isotropic analytical solution with a high accuracy. Based on extensive FEM simulations Dr Pachoud derived in a further step parametric correction factors, which allow estimating stress concentrations and structural stresses in steel liners considering geometrical imperfections. Dr Pachoud obtained also Stress Intensity Factors (SIF) for axial cracks in the weld material of the longitudinal joints by means of computational Linear Elastic Fracture Mechanics (LEFM) and could propose new parametric equations for the weld shape correction. For fatigue assessment, a probabilistic model for steel liner crack growth and fracture was developed by using the above mentioned new parametric equations for considering geometrical imperfections. Finally, Dr Pachoud illustrated the implementation of all the developed parametric equations in a probabilistic model for crack growth in the steel liner under dynamic loading with a case study for a high-head power plant. The probabilistic model allows determining the acceptable undetected initial crack sizes in the steel liner depending on the choice of the steel grade, which is crucial for engineering practice using high-strength steels for pressure tunnels and shafts.

EPFL-LCH2017

Shape changes through geometric nonlinear control as a strategy for structural adaptation

Arka Prabhata Reksowardojo

Adaptive structures modify their geometry and internal forces through sensing and mechanical actuation in order to maintain optimal performance under changing actions. Previous work has shown that well-conceived adaptive design strategies achieve substantial whole-life energy savings compared to traditional passive designs. The whole-life energy comprises an embodied part in the material and an operational part for structural adaptation This thesis presents a new method to design adaptive structures capable of large and reversible shape changes achieved through actuation. To this end, linear actuators are strategically fitted within selected elements of reticular (e.g. trusses and frames) structures. Structural adaptation through controlled large shape changes allows a significant stress redistribution so that the design is not governed by extreme loads with long return periods. This way, material utilization is maximized and thus, embodied energy is reduced. A set of target shapes that counteract the effect of peak loads are first obtained through geometry and sizing optimization. Strategies have been developed to reduce the uncertainty due to the presence of multiple local minima so that the computational efficiency is improved and the convergence is guaranteed. A method is formulated to obtain a suitable actuator layout in order to control the structure into the target shapes. This is a challenging task due to the combinatorial nature of the actuator placement process which, in this case, includes geometric nonlinearity. A heuristic for near-neighbor generation based on the actuator control efficacy is employed to explore effectively the large search space. The heuristic has significantly improved convergence, which is important for structures with complex topologies that are made of many elements. A framework for real-time control combining shape optimization and nonlinear force method is proposed. The objective of the control framework is to minimize the operational energy for shape adaptation while satisfying stress and element buckling limits. A linear-sequential formulation is presented, allowing a computationally-efficient implementation of real-time shape control through a mechanics-based formulation. Through a nested univariate optimization scheme, an adaptive structure with minimum whole-life energy requirements is synthesized. Numerical case studies demonstrate that whole-life energy savings can be achieved compared to weight-optimized passive structures for the configurations studied in this thesis. Structures that adapt to loading through large shape changes achieve marginal whole-life energy savings with respect to structures that adapt to loading through small shape changes. Nevertheless, significant embodied energy (and thus material mass) savings are achieved with respect to weight-optimized passive structures as well as to structures that adapt through small shape changes. Experimental studies at various scales are carried out to verify numerical findings and investigate the feasibility of the design method. Experimental testing has demonstrated that significant stress homogenization through large-shape changes is achievable. The control framework allows for real-time shape adaptation to achieve stress homogenization under various loading conditions. An energy appraisal carried out on a near-full-scale prototype confirms that considerable savings of the total energy can be achieved by adaptive solutions.

EPFL2020

Experimental Testing of a Small-Scale Truss Beam That Adapts to Loads Through Large Shape Changes

Arka Prabhata Reksowardojo, Gennaro Senatore, Ian Smith

Adaptive structures have the ability to modify their shape and internal forces through sensing and actuation in order to maintain optimal performance under changing actions. Previous studies have shown that substantial whole-life energy savings with respect to traditional passive designs can be achieved through well-conceived adaptive design strategies. The whole-life energy comprises an embodied part in the material and an operational part for structural adaptation. Structural adaptation through controlled large shape changes allows a significant stress redistribution so that the design is not governed by extreme loads with long return periods. This way, material utilization is maximized and embodied energy is reduced. A design process based on shape optimization has been formulated to obtain shapes that are optimal for each load case. A geometrically non-linear force method is employed to control the structure into required shapes. This paper presents the experimental testing of a small-scale prototype adaptive structure produced by this design process. The structure is a simply supported planar truss. Shape adaptation is achieved through controlled length changes of turnbuckles that strategically replace some of the structural elements. The stress is monitored by strain sensors fitted on some of the truss elements. The nodal coordinates are monitored by an optical tracking system. Numerical predictions and measurements have a minimum Pearson correlation of 0.86 which indicates good accordance. Although scaling effects have to be further investigated, experimental testing on a small-scale prototype has been useful to assess the feasibility of the design and control methods outlined in this work. Results show that stress homogenization through controlled large shape changes is feasible.

2019

Shape changes through geometric nonlinear control as a strategy for structural adaptation

Arka Prabhata Reksowardojo

EPFL2020

Influence of geometrical imperfections and flaws at welds of steel liners on fatigue behavior of pressure tunnels and shafts in anisotropic rock

Alexandre Jean Pachoud

EPFL-LCH2017