1. Concepts

The concept of Endurance Time

Endurance time method is a seismic structural analysis method using intensifying dynamic loads. The structural response is monitored as the intensity of excitation is increased. Structural performance is assessed based on the response as a function of the excitation intensity.

The concept of the endurance time method is quite simple and can be easily explained by a hypothetical shaking table experiment. Let’s assume that three different structures are placed on a shaking table and subjected to an intensifying dynamic loading. In the beginning and at low shaking levels, all structures remain stable and intact. As the intensity of shaking is gradually increased, structural failures develop and structures collapse at intensity levels that are beyond their capacity levels. Let’s assume that in this case structure "A" fails first followed by structure “C” and ultimately structure “B” (see Figure 1). Accordingly, it can be concluded that structure “A” which showed least endurance time has worst performance and structure “B” which endures longest has best performance regarding the collapse under applied loading.

If the applied intensifying loading is designed in such a way as to have a reasonable correspondence to earthquake ground motions, then, one can readily identify structure “B” as the best and structure “A” as the worst performer regarding the seismic collapse resistance. Moreover, differences among the endurance time of these structures can indicate their relative risk of collapse in earthquake events. Endurance Time (ET) method puts the simple concepts described above into a practical framework for seismic assessment and design of structures.

Putting the concept into a practical framework

The results of this hypothetical experiment can be explained in terms of response v.s. intensity plot as shown in Figure 2. The horizontal axis shows time from the start of load application and the vertical axis shows the response parameter of interest. Since the applied load is intensifying, time becomes a representative of the intensity of load. In practice, time can be mapped into a more convenient intensity measure such as PGA, Hazard Return Period, or other intensity measure of interest. The response parameter can be relevant simple or complicated structural response, or a function of structural response such as maximum displacements, interstory drift ratios, stresses, plastic rotations, damage indexes, damage costs, etc. In case of the shaking table test explained above, if a damage index (DI) that is indicator of the collapse of the structure is considered, Figure 2 shows that structure "A" has passed the limiting value of the DI at about t=7s and by t=15s, structures "A" and "C" have failed while structure "B" has endured.

Endurance Time Excitation Functions

Successful implementation of the ET concept is dependent on the characteristics of the applied loading function. There are many paths to follow in order to produce working intensifying dynamic load functions. The concept of response spectrum leads to a very effective strategy for this purpose. Response spectrum strongly reflects most important characteristics of ground motions, i.e. the intensity and the frequency content. Two dynamic excitations with similar response spectrum, produce mostly similar maximum responses in most structures. Almost all concurrent seismic design codes define seismic load requirements based on spectral intensities. Development of preliminary Endurance Time Excitation Functions (ETEFs) started by concentrating on spectral characteristics of the excitation functions. If the response spectrum of the applied loading at a particular time matches a particular response spectrum of interest, maximum structural responses are also expected to match. This target spectrum can be in the form of design spectra, average spectra of a set of ground motions, or any other spectra of interest. This idea turns out to be a good starting point in producing useful intensifying acceleration functions. Initial ETEFs were produced by considering a seismic code based design spectra as a template and trying to produce an intensifying excitation function that has the property of producing a response spectrum that tends to remain proportional to this target spectrum at all times. The coefficient of proportionality was assumed to increase linearly with time. The response spectra produced by a typical such ETEF is shown in figure 3.

A typical Endurance Time Excitation Function (ETEF) in the form of ground acceleration function is shown in Figure 4. From practical viewpoint, maximum time span of these records is in the order of 20~50 seconds. However, it should be noted that normally, no theoretical end is defined for these functions.