Pierre Léger

Finite element analysis of concrete swelling due to alkali-aggregate reactions in dams

Many concrete dams throughout the world are suffering from deteriorations induced by alkali-aggregate reaction (AAR) that impair the durability, serviceability, and might also affect, in the long term, the safety of the installation. AAR produces concrete expansion, and generally leads to a loss of strength, stiffness (cracking), and generates undesirable deformations and disturbances in the equilibrium of internal forces. This paper first presents a brief review of the physical processes that control the structural behaviour of concrete dams suffering from AAR. A methodology to distribute the observed concrete expansion in proportion to the compressive stress state, temperature, moisture, and reactivity of the constituents is then proposed for the numerical modelling of AAR concrete swelling in dams. A case study on a concrete spillway pier that is affected by AAR is presented to illustrate some features of the proposed methodology.

Multiple-support seismic analysis of large structures

Abstract The effect of the spatial variation of earthquake ground motion on the dynamic response of multiple-support structures may be important. The relative performance of two simple analytical methods to model multiple-support seismic analysis of large structures is investigated. These are the relative motion method (RMM), which divides the structural response into a dynamic response component and a pseudo-static response component, and the large mass method (LMM), which attributes fictitious large mass values at each driven nodal degree of freedom (DOF) to obtain the total response of the structure. The seismic response of a four-span bridge using the traveling wave assumption is used to illustrate the practical application of the methods. It is found that the LMM is able to yield results that are almost identical to those of the RMM using large mass values equal to approximately 10 7 times the total mass of the bridge. Parametric analyses where the travel wave speed is systematically varied show that the structural response tends to increase as the wave velocity decreases and can become significantly larger than the response obtained from synchronous excitation.

Initial versus tangent stiffness‐based Rayleigh damping in inelastic time history seismic analyses

In the inelastic time history analyses of structures in seismic motion, part of the seismic energy that is imparted to the structure is absorbed by the inelastic structural model, and Rayleigh damping is commonly used in practice as an additional energy dissipation source. It has been acknowledged that Rayleigh damping models lack physical consistency and that, in turn, it must be carefully used to avoid encountering unintended consequences as the appearance of artificial damping. There are concerns raised by the mass proportional part of Rayleigh damping, but they are not considered in this paper. As far as the stiffness proportional part of Rayleigh damping is concerned, either the initial structural stiffness or the updated tangent stiffness can be used. The objective of this paper is to provide a comprehensive comparison of these two types of Rayleigh damping models so that a practitioner (i) can objectively choose the type of Rayleigh damping model that best fits her/his needs and (ii) is provided with useful analytical tools to design Rayleigh damping model with good control on the damping ratios throughout inelastic analysis. To that end, a review of the literature dedicated to Rayleigh damping within these last two decades is first presented; then, practical tools to control the modal damping ratios throughout the time history analysis are developed; a simple example is finally used to illustrate the differences resulting from the use of either initial or tangent stiffness-based Rayleigh damping model.

Earthquake input mechanisms for time-domain analysis of dam—foundation systems

Abstract The seismic design of concrete dam-foundation-reservoir systems must be able to ensure the survivability of these structures to extreme magnitude earthquakes for which nonlinear behaviour can be expected. This study is concerned with the evaluation of four different earthquake input mechanisms that are suitable for time-domain analysis of dam-foundation systems. These are the standard rigid-base input model, the massless-foundation input model, the deconvolved-base-rock input model, and the free-field dam—foundation interface input model. Parametric studies have been conducted by applying the four proposed input mechanisms to simplified two-dimensional finite element models of gravity dam-foundation systems. The principal parameters retained in the analysis were the ratio of the modulus of elasticity between the foundation and the concrete dam and the damping ratio of the foundation. It was shown that the use of the standard rigid-base input model is not acceptable, producing significant amplifications. The deconvolved and the free-field input models produced very similar results for the complete range of selected parameters. The massless-foundation input model, although not as accurate as the deconvolved and the free-field input models, can be used for practical analyses if a proper modelling of the energy dissipation characteristics of the foundation is provided in the mathematical formulation.

Evaluation of earthquake ground motions to predict cracking response of gravity dams

Abstract Smooth design spectra are generally used to describe the seismic excitation imparted by the maximum design earthquake for safety evaluation of critical facilities such as concrete dams. When earthquake induced stresses exceed the elastic strength capacity of the structure, dynamic nonlinear analyses in the time-domain are recommended to determine the potential path of crack extension and failure mechanism. Spectrum-compatible ground motion acceleration time histories, that might be defined using different approaches, must then be specified as input to perform crack propagation analyses. However, the cracking response is sensitive to the details of the time variations of the input motions. This paper presents a study of the cracking response of gravity dams subjected to: (i) historical records scaled to the smooth spectrum intensity; (ii) spectrum-compatible accelerograms generated by random vibration theory; and (iii) spectrum-compatible accelerograms obtained from the modification of the Fourier spectrum coefficients of historical records while preserving the original phase angles. The crest displacements, the seismic energy response, and the cracking profiles are examined in parametric analyses to identify the type of input motion that is critical for the earthquake resistant design of gravity dams.

Shake Table Testing of Slender RC Shear Walls Subjected to Eastern North America Seismic Ground Motions

AbstractThis paper presents shake table test results on two identical 1:0.429 scaled, 8-story moderately ductile RC shear wall specimens under the expected high-frequency ground motion in eastern North America. The walls were designed and detailed according to the seismic provisions of the NBCC 2005 and CSA-A23.3-04 standards. The objectives were to validate and understand the inelastic responses and interaction of shear and flexure and axial loads in the plastic hinge zones of the walls taking into consideration the higher-mode effects. One specimen was tested under incremental ground motion intensities ranging from 40 to 120% of the design level. The intensity range was increased from 100 to 200% for the second specimen. The response of the walls was significantly affected by the second mode, causing an inelastic flexural response to develop at the base as well as at the sixth level. Dynamic amplification of the base shear forces was also observed in both walls. In the second wall, which was tested in t...

Modeling and Testing Influence of Scaling Effects on Inelastic Response of Shear Walls

Monotonic and cyclic quasi-static testing was performed on ductile reinforced concrete shear-wall specimens designed and detailed according to the seismic provisions of the National Building Code of Canada and CSA-A23.3-04. The tests were carried out on full-scale and 1:2.37 reduced-scale wall specimens. The behavior under cyclic loading was characterized by ductile flexural response up to a displacement ductility of 4.0. At this deformation level, inelastic shear deformations in the plastic hinge contributed to approximately 20% of the total deformation. In the subsequent cycles, strength degradation took place due to shear sliding developing along the large flexural cracks at the wall base. Shear sliding was not observed under monotonic loading and the specimens exhibited significantly higher ductility capacity. Excellent agreement was found between prototype and reduced-scale walls. The inelastic response and failure mode observed under cyclic loading could be adequately reproduced using a finite element analysis program. Simpler models with frame elements and lumped plastic hinges could capture the wall flexural response well, but shear deformations could not be reproduced.

Computer aided stability analysis of gravity dams: CADAM

This paper presents the main features and organisation of CADAM, a computer program, freely available, that has been developed for the static and seismic stability evaluations of concrete gravity dams. CADAM is based on the gravity method using rigid body equilibrium and beam theory to perform stress analyses, compute crack lengths, and safety factors. Seismic analyses could be done using either the pseudostatic or a simplified response spectrum method. CADAM is primarily designed to provide support for learning the principles of structural stability evaluation of gravity dams. It could also be used for research and development on stability of gravity dams. In adopting several different world-wide published dam safety guidelines, a large number of modelling options have been implemented. These include (i) crack initiation and propagation, (ii) effects of drainage and cracking under static, seismic, and post-seismic uplift pressure conditions, and (iii) safety evaluation procedures using deterministic, allowable stresses and limit states probabilistic analyses (Monte-Carlo simulations). Structural stability evaluation of a 30 m dam is presented to illustrate the use of CADAM.

Numerical Modeling of Slender Reinforced Concrete Shear Wall Shaking Table Tests Under High-Frequency Ground Motions

This article presents the numerical modeling of large-scale shake table tests of slender 8-story reinforced concrete (RC) shear wall specimens. Nonlinear time history analyses are carried out using reinforced concrete fiber elements (OpenSees, OS) and the finite element (FE) methods (VecTor2, VT2). The effects of the modeling assumptions are investigated, including: (a) the tension stiffening effect, (b) damping, (c) smeared vs. lumped reinforcement, and (d) the use of effective shear stiffness in OS. Good agreements are obtained between the numerical and experimental results. Using the proposed numerical modeling strategy, it is possible to investigate the nonlinear dynamic responses of slender RC wall structures with confidence.

Reduced frequency-independent models for seismic analysis of concrete gravity dams

Abstract A methodology is presented to allow a consistent and rational transition from linear frequency-domain model of concrete gravity dam-foundation-reservoir systems to time-domain models suitable for nonlinear seismic analysis. Two types of reservoir models are considered. These are an added mass approach based on the Westergaard method, and a finite element formulation using displacements as nodal variables to represent the reservoir. Coordinate reduction techniques are used to reduce the number of degrees-of-freedom needed to represent properly the reservoir and the foundation. A simplified time-domain model of energy dissipation in the reservoir and the foundation is developed by providing boundary dampers at the interface of the different media along with added stiffness and mass matrices. The added system matrices are calibrated to provide low level (elastic) time-domain response compatible to that obtained by using frequency-dependent system properties. The application to a typical gravity dam shows that the seismic response in time-domain can be properly predicted using the proposed methodology to develop frequency-independent system properties.