During the past two decades, the use of ambient vibrations for modal analysis of structures has increased as compared to the traditional techniques (forced vibrations). The Frequency Domain Decomposition method is nowadays widely used in modal analysis because of its accuracy and simplicity. In this paper, we first present the physical meaning of the FDD method to estimate the modal parameters. We discuss then the process used for the evaluation of the building stiffness deduced from the modal shapes. The models considered here are 1D lumped-mass beams and especially the shear beam. The analytical solution of the equations of motion makes it possible to simulate the motion due to a weak to moderate earthquake and then the inter-storey drift knowing only the modal parameters (modal model). This process is finally applied to a 9-storey reinforced concrete (RC) dwelling in Grenoble (France). We successfully compared the building motion for an artificial ground motion deduced from the model estimated using ambient vibrations and recorded in the building. The stiffness of each storey and the inter-storey drift were also calculated.
Knowing the dynamic parameters of a structure (e.g. a building or a bridge) may be useful:
(1) to calibrate its elastic properties for numerical modelling, (2) to detect the modification of its behaviour after retrofitting or damage, (3) and, finally, to predict its behaviour under earthquakes. The linear dynamic behaviour can be fully described by the modal parameters: resonance frequencies, modal shapes and damping ratios. These parameters mainly depend on the storey masses, which remain unchanged whatever the state of the structure, and the storey stiffnesses, which are influenced by the structural modifications such as reinforcing and damage. It can also be representative of the quality of the material (e.g. the equivalent Young’s modulus of the cracked or undamaged concrete) and of the structural design (e.g. irregularity of the shear resistance or soft storey). All large-scale vulnerability assessment methods (e.g. [1,2,3]) identify the stiffness regularity of buildings as one of the main parameters controlling their seismic resistance. The stiffness is also the basic parameter needed to draw the capacity curve of buildings, which is the basis of recent large-scale vulnerability assessment methods (e.g. [1,3,4]). One of the greatest difficulties within such methods is the lack of information on existing buildings. Within vulnerability assessment, we have to deal with questions on, for example, ageing, structural design, quality of materials and the building state.
Assessing the stiffness of each storey, and therefore the modal shapes of the structure, is then a critical point for the evaluation of the dynamic properties of existing buildings and hence to predict their seismic response and vulnerability. The ratio between transverse and longitudinal frequencies can, for example, provide information on the relative stiffness in perpendicular directions that may expose a lack of stiffness and may help in structural design understanding.
Comparing the frequencies and mode shape before and after the shaking [5,6,7] allows the evaluation of damage. This method requires knowledge of the initial state of the structure in such a way that the modification due to damage can be observed. For example, comparisons of frequencies among a group of identical buildings can quantify the damage level of each building [8]. Based on the integrity threshold concept [9], and with only limited structural information, the integrity of the building under seismic shaking can be estimated using the experimental modal shape deduced from forced or ambient vibrations. Ambient vibrations provide information about the modal parameters of a structure that we can extract using Modal Analysis methods. There are many different techniques to identify the “natural” modes of a structure, which can be divided into parametric and non-parametric methods. In the first category, the parameters of the considered model are updated to fit the recorded data in frequency or in time domain (see [10] for details). In the second category, the methods use only signal processing tools so that they are more user-friendly and easier to implement. Moreover, existing civil engineering structures are often difficult to model relevantly so that it is necessary to test these approaches before any more complicated method. For example, the Peak Picking (PP) method consists in taking the frequency peaks of average spectra for each sensors placed at different points. The Frequency Domain Decomposition (FDD [11]) is an improvement of the PP method. It consists of decomposing the power spectral density matrices into single-degrees-of-freedom systems by singular value decomposition.
The main goal of this paper is to demonstrate the utility of techniques using ambient vibration recordings to complement and improve seismic vulnerability investigations of existing buildings. Ambient vibrations recorded in buildings are processed for estimating the dynamic parameters of the building based on modal parameter estimates (Fig. 1). Because of its low cost and the efficiency of operational modal analysis, the ambient vibration method is well adapted to large-scale analysis for which a large set of buildings has to be analyzed. We first describe the FDD method we used in this study, one method among a large set of others existing methods. Then we propose the shear beam model, adapted to our recording layout to approximate the motion of a building. An analytical solution is proposed to estimate the stiffness at each story as a function of the modal shapes. We apply this theoretical work to a building located in Grenoble (France). We estimate its modal properties using ambient vibration tests and recordings of a ground motion induced by a bridge demolition in the same area. We then validate the modal model derived using modal parameters estimated from ambient vibrations by comparing the simulation results of the bridge collapse with real data.
Finally we estimate the stiffness
This content is AI-processed based on open access ArXiv data.