Date of Award

December 2020

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Civil and Environmental Engineering


Eric M. Lui


continuous wavelet transform, endurance time analysis, incremental dynamic analysis, nonlinear dynamic analysis, performance-based seismic design, steel structure

Subject Categories



Earthquakes occur quite frequently around the world, but the number of reliable recorded ground motion data for a given site is often limited. In addition, the use of present methodologies to modify existing earthquake records to match site conditions could change the relationship between the recorded earthquake characteristics and their actual physical attributes. The result is that these modified earthquakes could have qualities not quite the same as those of the real earthquakes. Instead of using scaling and spectral matching of real earthquakes, artificial earthquakes capable of mimicking both the physical conditions and qualities of real earthquakes should be generated for use in seismic analysis and design.

The dynamic response of a system is highly dependent on the input ground motion characteristics, especially when system response is in the nonlinear range. There are two commonly used domains in characterizing ground motions: time and frequency. In the time domain, ground motion characteristics such as peak ground acceleration (PGA), the time at which PGA occurs, and the overall duration of the ground excitation can be obtained. On the other hand, analyzing ground motions in the frequency domain using Fourier Transform (FT) allows only the frequency content to be extracted. The temporal aspect of the dominant frequency and the range of frequencies that are considered the most important in affecting system response is lost.

In this dissertation, Morse wavelet is used to perform continuous wavelet transform (CWT) localized investigation of real ground motions to identify both time and frequency characteristics with the aim toward designing better artificially generated earthquakes. Using CWT, important earthquake attributes such as range of dominant frequencies and time span within which these frequencies occur are extracted. This information is then used to generate artificial earthquakes referred to as Endurance Time Excitation Functions (ETEFs) that can be used in an endurance time analysis (ETA). Detailed procedure for generating these ETEFs based on real ground motions with different magnitudes and soil site conditions are discussed.

Endurance time analysis is a methodology to perform earthquake analysis on structures subjected to an artificially generated ground motion (referred to as ETEF) that is being scaled up over time until the structures experience distress or failure. In the present work, the scaling used is a block-shaped envelope that increases in size by a factor of 3/2 over time. This scaling is relatively straightforward to apply and is shown to produce good results.

Endurance time analysis is considered more efficient when compared to another commonly used seismic analysis method called Incremental Dynamic Analysis (IDA). In using IDA, an excitation function is scaled progressively to various Intensity Measure (IM) levels, and at each level the largest Engineering Demand Parameter (EDP) is calculated. Analyzing structures using IDA is very computationally intensive and time consuming. The use of ETA in conjunction with the proper ETEF proposed in the present work allows for a noticeable reduction in computational time and effort without sacrificing accuracy, even for structures that experience high nonlinearity in both geometry and material.

Using the proposed method, nonlinear seismic analyses needed in a Performance-based Seismic Design (PBSD) for Single-Degree-of-Freedom (SDOF) and Multiple-Degrees-of-Freedom (MDOF) systems are performed. From the results of these analyses, it is observed the proposed method not only successfully predicts the base shear – roof displacement response of these, it also correctly identifies such behavior as weak story, concrete spalling, and core cracking.


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