Accurately predicting damping in the design phase of high-rise buildings is essential for reliable assessments of occupant comfort. To improve damping prediction models for Dutch high-rise buildings, it is important to assess the reliability of damping estimates derived from measured vibration responses. This thesis aims to evaluate the performance of the Random Decrement Technique ranked by peak amplitude (Peak RDT) in reliably estimating damping, for systems exhibiting constant and amplitude-dependent damping, excited by stationary and non-stationary loading conditions. Since this assessment requires a known ground truth, a series of numerical studies are conducted, producing a distribution of damping estimates.

Under stationary loading conditions, the mean damping estimates are accurate for both systems. However, the precision of damping estimates is significantly reduced at low and high relative amplitude ranges. At low amplitudes, the reduced precision in damping estimates arises because the Random Decrement Signatures (RDS) fail to accurately capture the system’s free decay, as segments are sampled at very low response levels. At high amplitudes, the lack of precision in damping estimates is primarily due to insufficient segment counts in the computation of the RDS, which prevents proper isolation of the system’s free vibration response.

Moreover, RDS corresponding to the system with amplitude-dependent damping exhibit a non-uniform decay, causing fitting errors when using non-linear Least Squares Minimization to estimate a constant damping value. These errors can be mitigated by reducing the length of the segments sampled by the Peak RDT algorithm.

Three types of non-stationarity are introduced in the excitation: time-varying mean, time-varying variance, and their combination. While the second case yields level-stationary response signals complying with the underlying assumptions of the Peak RDT, the other two introduce time-dependent non-zero means in the response data, leading to significant accuracy errors in mean damping estimates for both linear and non-linear systems.

In conclusion, the Peak RDT yields reliable damping estimates for systems with constant and amplitude-dependent damping only under stationary loading conditions. However, it must be acknowledged that the degrees of non-stationarity considered in this thesis is rather large. The Peak RDT might still produce reliable damping estimates for mildly non-stationary vibration responses.

The light and frequent earthquakes in the north of the Netherlands, particularly in the province of Groningen, have recently exposed the unreinforced masonry structures to seismic activities. Since these structures do not adhere to seismic regulations, they are considered vulnerable to seismicity. The ultimate state capacity of the structures is important for an individual's safety, however, these earthquakes are of low intensity and cause aesthetic damage.

In order to investigate the light damage initiation and development, TNO has performed shaking table tests on an unreinforced masonry (URM) cavity wall specimen in out-of-plane (OOP) one-way bending with small increments in intensity. The test specimen consisted of calcium silicate brick inner leaf and perforated clay brick outer leaf. The damage development in the outer leaf was monitored during these tests using a high-speed digital image correlation (DIC) technique to study the initiation and development of damage in the outer leaf of the specimen. The experimental tests showed damage initiation at the mid-height of the outer leaf. The tests could not capture the development of cracks through the thickness of the cavity wall.

The scope of this research is a numerical assessment of the experimental study by using a Non-Linear Time History (NLTH) analysis of light damage initiation and development of a URM cavity wall under out-of-plane loading. The high-resolution experimental results are used as a basis for the development and calibration of models which can better predict the crack initiation and development in URM. The finite element software DIANA 10.5 FEA was used to set up the numerical model and conduct transient analysis.

The seismic signal as an input loading and the top boundary condition of the test specimen. The acceleration data measured from the shaking table tests at the base was used as an input seismic signal for the transient analysis of the models. The input signal needed to be processed before application as the presence of low-frequency content leaded to inaccurate results. Different approaches are discussed in this thesis regarding the processing of the input acceleration signal.

The experimental tests were modeled along the cross-section of the test specimen, thereby highlighting the thickness of the inner leaf and the outer leaf. This enabled tracking the light damage initiation and propagation through the thickness of the cavity wall. A total of thirteen shaking table tests were conducted on the experimental setup. In order to gain insight into the behavior of the specimen during each shaking table test, a model was created corresponding to each shaking table test. Preliminary analysis schemes were set in order to check the validity of all thirteen models. The two cases of top boundary conditions were checked, roller support and spring-mass support. The roller boundary condition proved to be stiff in comparison to the experimental results.

The numerical results were calibrated on the basis of material properties. The results were compared to experimental results by checking the dynamic behavior at the mid-height, dynamic behavior over the height, and light damage initiation and development of the specimen. The results of the numerical models were stiff in comparison to the experimental results. According to the conclusions, it is recommended to research further regarding the boundary conditions, especially the bottom boundary condition due to the formation of a rocking crack. Another important aspect to focus on is the combination of all input signals, thereby, taking into consideration the damage accumulation.

As the world's population keeps increasing and the rate of urbanizations increases, The rate at which high-rise structures are being built is skyrocketing. In the Netherlands, this is no different. It is expected that the amount of high-rise structures taller than 70 meters will more than double in the coming 20 years. As these structures become taller and more slender, they also become more susceptible to wind-induced excitations. Where once the design of a structure was predominantly governed by the Ultimate Limit State (ULS) design criteria, for tall structures, the Serviceability Limit State (SLS) design criteria becomes as, if not more, important. Therefore, the accurate prediction of the dynamic characteristics are becoming increasingly important. One of these dynamic characteristics is the natural frequency, also called the eigen frequency, of the structure.

The natural frequency is a parameter which is largely influenced by the mass and the stiffness of the structure. One would think that after the completion of structure, that the magnitudes of parameters can be determined with a high level of certainty, and that the natural frequency can be calculated accurately, but this is not the case. When comparing the measured natural frequencies of several high-rise structures in the Netherlands, to their natural frequencies determined in the design phases, an underestimation of between 20\% to 50\% was seen. Although the likelihood that these underestimations will lead to structural failure are small, it does lead to larger design forces and higher peak accelerations, which are used in determining occupant comfort in the structures. The aim of this research is to find the reasons for the discrepancies between the measured and the calculated natural frequencies.

A literature study was performed to determine what the most common methods of determining the natural frequency are during the design phase. There are three main methods which are used throughout different stages of the design phase to approximate the natural frequencies. At the start of the design phase, when structural parameters have not yet been determined, the natural frequency is approximated using empirical formulae. These formulae mostly only depend on 1 or 2 spatial parameters.
As the design progresses and the structural parameters are specified, dynamic beam theory can be used to determine the natural frequency. These calculations take the stiffness of the super- and substructure, and the mass of the structure, into account. As the design nears completion, the structure is modelled in a FE software package. The natural frequency can then be calculated by the software to give a final impression of the natural frequency.

The main parameters influencing the natural frequency of a system are the stiffness and the mass. This is no different for high-rise structures, but how do these parameters affect the natural frequency, and which of these parameters has the greatest effect on the natural frequency? A sensitivity study, looking at 5 existing high-rise structures in the Netherlands, was performed. Each structure was represented by 5 different beam models. One structural parameter was added to each subsequent beam model as to be able to quantify the influence of the added parameter. Lower and upper bounds were determined for each structural parameter. By varying these parameters and calculating the natural frequencies, the effect this variation has on the natural frequency can be determined. It was found that there are 3 parameters which have significant influence on the natural frequencies, namely, the superstructure stiffness, the superstructure density and the rotational stiffness of the foundation.
For all cases with a flexible foundation, the measured natural frequencies could not be reached, even after determining the natural frequencies using the extreme parameter combination, the natural frequencies were still underestimated. The analyses were done for both uniform beam models and multibeam models. The general trend was that the multibeam model produced higher frequencies. This is due to more of the overall stiffness and mass of the structure being situated in the bottom sections of the structure. Using a multibeam can lead to an increase in natural frequency of up to 15\%. Although the natural frequencies were increased, they were still nowhere near the measured natural frequencies.

The underestimation of the natural frequencies using the beams models, led to the question if there are other factors which are not yet taken into account when determining the natural frequencies. In the calculation of the stiffness of the new Erasmus Medical Centre (NEMC), it was assumed that the beams, columns, non-structural elements and the low-rise structure have a negligible influence on the stiffness of the structure. The underestimation in the natural frequencies, led to the conclusion that the stiffness of the structure is underestimated. A complete model of the NEMC was modelled using the SCIA Engineer software. All the structural systems were added to the model. Modal analyses, including different combinations of structural systems and parameter magnitudes, were performed. It was found that for the NEMC the assumption that the beams and columns have a negligible contribution to the natural frequency, was correct. The main contributors to the stiffness of the superstructure were the outer tube and the central cores. The partition walls were added to the model using low stiffness wall elements, by added the walls, the natural frequency was increased by 8.5\%. Assumptions were made to include the influence of the low-rise structure. The determined natural frequency was increased past the measured natural frequency, however, this result might not be realistic.

The final conclusion of the thesis is that the stiffness of the superstructure is underestimated. This leads to the conclusion that there are certain elements which provide the structure with extra stiffness, which is not yet taken into account. At the end of the thesis several recommendations are made as to determine where this extra stiffness comes from.