## Alternative representations of the seismic action

3.2.3.1. Time-history representation Clauses There are three approaches to obtain earthquakes or earthquake-like ground motion

3.2.3.1.1(1), records (acceleration versus time functions) for the purposes of assessment by advanced 3.2.3.1.1(3) analysis. Natural records of earthquakes have increased exponentially in the past decade or so, leading to the availability of high-quality strong-motion (acceleration) data for different locations around the world, archived by many agencies. Another approach is to generate a signal that fits, with a certain degree of approximation, a target spectrum. Finally, use of mathematical source models (point, line or area source representations) to generate strong-motion-like time series is increasing in popularity since the ensuing records resemble natural records more than records generated to fit a target spectrum.

Records of a quantity versus time as described above may also be expressed as ground velocity or displacement.

Clause For planar structural models, horizontal and vertical components of earthquake motions

3.2.3.1.1(2) can be considered to act simultaneously. For spatial models, the seismic action should consist of three simultaneously acting accelerograms, two horizontal and one vertical. It is recommended that the most demanding combination of motions applied in all the different directions is used.

Clauses

Artificial accelerograms

Artificial accelerograms are an option for generating signals that satisfy engineering criteria unrelated to the physics of earthquake motion generation and propagation. Accelerograms can be mathematically simulated through random vibration theory. Both stationary and non-stationary random processes have been suggested.30'31 Strong motions include transitional phases at the initial and final stages, respectively, moving from rest to maximum shaking and vice versa (non-stationary processes). Small earthquakes can also be described by such processes. By contrast, the middle portion, i.e. the nearly uniform part of the vibration, can be modelled by means of stationary processes, such as white noise.32'33

The most widely used approach is to develop a signal with a response spectrum that matches a target response spectrum with a predefined accuracy (e.g. 3-5% margin of error). The target spectrum is either a uniform hazard spectrum or a code spectrum. An example of such acceleration signals (a response-spectrum-compatible accelerogram) is shown in Fig. 3.7. It is noteworthy that the level of accuracy of the match depends on the number of iterations carried out during the generation process.

Time (s)

Period (s)

Fig. 3.7. (a) Acceleration artificial record matched to (b) a code spectrum

Period (s)

Fig. 3.7. (a) Acceleration artificial record matched to (b) a code spectrum

In EN 1998-1 it is required that artificial accelerograms should be generated so as to match the elastic response spectrum given in clauses 3.2.2.2 and 3.2.2.3 for 5% viscous damping. Moreover, the duration of the generated records should be consistent with the magnitude and the other relevant seismological features consistent with the establishment of the ground acceleration (a ), e.g. frequency content and duration. The stationary part of the accelerograms should possess a minimum duration of 10 s. A minimum number of three accelerograms should be generated; their mean PGA should not be less than the value agS for a given site. In addition, mean 5% damping elastic spectral values should not be less than 90% of the corresponding value of the 5% damping elastic response spectrum. These requirements are meant to ensure deriving records that would provide conservative estimates of the response of structures and foundations. Relationships between magnitude and duration from the literature (e.g. Naeim,25 among others) may be consulted. Three elements are necessary to generate artificial (or synthetic) accelerograms:

• power spectral density

• a random phase angle generator

• an envelope function.

The simulated motion can be calculated as the sum of several harmonic excitations. Thus, the consistency of the artificial motion is assessed through an iterative algorithm which examines the frequency content. The latter check can be carried out either with the response spectrum of the signal or its power spectral density. A detailed description of the procedures for generating artificial records can be found in Clough and Penzien.34 Several computer programs that generate such records have been developed (e.g. SIMQKE-l33). Inherent difficulties in the generation process are: (1) the assumption of the phase distribution between the various single-frequency waves and (2) the duration of the record. Therefore, signals that match the same spectrum may look different and, more importantly, may lead to different structural response quantities. A closer fit between the spectrum of the generated signal and that of the target spectrum should be sought in the vicinity of the structural fundamental period (0.2-2.0 times the fundamental period). It should also be recognized that artificial records often exhibit a larger number of cycles than natural records. As a consequence, such records may lead to over-conservative demand quantities for inelastic systems.

3.2.3.2. Recorded or simulated accelerograms Clauses When using natural earthquake records, EN 1998-1 recommends the use of a minimum of

3.2.3.1.3(I), three different accelerometer recordings, scaled to the required PGA. Otherwise, artificially 3.2.3.1.3(2), generated records can be used, provided the distribution of frequencies associated with high 3.2.3.1.3(3) energy is relevant to the fundamental period of the structure. This can be ensured by generating a record which conforms to an approved spectral shape.

It is instructive to note that the features of strong motions that affect structural response are many and their inter-relationship is complex. It is thus of importance to highlight the regional differences in strong-motion data and the criteria for the selection and scaling of natural records.

The ideal procedure for the selection of strong motion for use in analysis is to obtain records generated under conditions that are identical to those of the design earthquake scenario. Bolt36 showed that if all the characteristics of the design earthquake could be matched to those of a previous earthquake, the probability of the characteristics of the record matching would be 100%. The design earthquake, however, is usually defined in terms of only a few parameters. Hence, it is difficult to guarantee that the selected records will closely model all of the characteristics of the design earthquake at the source, along the path and through the site to the surface. Furthermore, even if the design earthquake scenario was defined in all aspects, it is unlikely that a record could be found in the available data banks which would also match all of the characteristics. To select records with a reasonable probability of bracketing the response, it is necessary to identify the most important parameters that characterize the conditions under which an earthquake record is produced, and match as many of these as possible to the design earthquake scenario. It is emphasized that records giving seemingly consistent response parameters, i.e. with the lowest coefficients of variation, may yield much higher variations due to period shifts due to inelasticity.

The parameters that characterize the conditions under which strong-motion records are generated can be grouped into three sets representing the earthquake source, the path from the source to the bedrock under the recording site and the nature of the site. The important parameters in the above sets are as follows:

9 Source: magnitude, rupture mechanism, directivity and focal depth

• Path: distance and azimuth

• Site: surface geology, topography and structures.

The above list is not exhaustive, but it does include the parameters that have been established as having a notable influence on ground motion characteristics.7 These parameters influence different characteristics of the recorded motion in different ways and to different degrees. Hence, the most appropriate selection of parameters depends on which characteristics of the selected motion are considered most important from a system- response viewpoint.

3.2.3.3. Spatial model of the seismic action Clauses Structural systems frequently do not experience the same displacements at all ground-

3.2.2.1 (8), system contact points. This is referred to as asynchronous motion. Asynchronous motion is

3.2.3.2(1), caused by the spatial variability of ground motions. The latter can be represented primarily

3.2.3.2(2) by three mechanisms, namely:

• loss of coherence

• local site conditions.

The wave passage effect is due to the time delay of waves because of the finite velocity of seismic waves, while loss of coherence is caused by the reflection and refraction of waves in soil layers underlying the structure. The local properties of soil at the construction site may filter seismic ground motion, thus amplifying or damping wave amplitudes and modifying the frequency content.

If the plan dimensions of a structure are large with respect to the wavelength of the seismic waves, the foundation-structure system is subjected to non-uniform shaking. Asynchronous motion at the support points is a common problem in the design of long-span bridges, large dams and pipelines that extend over considerable areas. Conversely, for ordinary structures, the ground motion at the base can be considered coherent, provided that the structure is supported by rigid foundation systems. For structures in which the excitation at the support points is incoherent, spatial models of the seismic action should be used. Such models should employ the elastic spectra defined in clauses 3.2.2.2 and 3.2.2.3.