This section aims to define the seismic action used to perform structural analysis and to Clauses 3.2.1(1), design building systems according to the rules specified in the relevant parts of Eurocode 8. 3.2.1 (2)
Typical representations of seismic actions are described. These include basic (spectrum based) and alternative (accelerograms) formats. Also, expressions for combining the seismic action with other actions are given. Seismic zones are introduced along with the engineering seismological parameters utilized to define the hazard within each zone.
The estimation of future earthquake ground motions at a particular location can be carried out through the assessment of seismic hazard. There are a number of ways in which the hazard can be expressed; common approaches are either deterministic or probabilistic. A fairly comprehensive treatment of this subject is provided by Reiter7 and Lee et al.&
The seismic hazard at a site can be represented by a hazard curve showing the exceedence probabilities associated with different levels of a given engineering seismology parameter, e.g. peak ground acceleration (PGA), velocity (PGV), displacement (PGD) and duration, for a given period of exposure. Alternatively, the return period associated with different levels of the selected parameter can be used, which results from the probability of being exceeded and the period of exposure. PGAs are widely employed for hazard curves. More recently, spectral ordinates at a given response period have been used to characterize a hazard. Earthquakes cause inertial forces on structures; hence the effects can be assessed if the structural mass and the PGA are known.
The seismic hazard can also be presented in the form of regional maps. National authorities should perform seismic hazard assessments to subdivide national territories into seismic zones as a function of the local hazard. The hazard within each zone is assumed to be constant. This assumption tends to be over-conservative in the case of directivity of the fault rupture.8,9
Hazard maps are derived by employing attenuation relationships. These are empirical expressions describing ground motion variation with magnitude and source-site distance. Such relationships account for the mechanisms of energy loss of seismic waves during their travel through a path (soil hysteresis and scattering). They permit the estimation of both the ground motion at a site from a specified event and the uncertainty associated with the prediction. There is a large number of attenuation equations that have been developed by various researchers.10 Those used for hazard maps are generally based on values of PGAs. The basic functional form for attenuation relationships is as follows:
log(Y) = Iog(6,) + \ogUm] + log[/2(*)] + log[/3(M, R)] + log [/4(£;)] + log(e) (D3.2)
where Y is the ground motion parameter to be computed, for example the PGA, PGV or PGD, and b1 is a calibration factor. The second to fourth terms on the right-hand side are functions (/•) of the magnitude (M), source-to-site distance (R) and possible source, site and/or geologic structure effects (£,). Uncertainty and errors are quantified through the parameter e. Equation (D3.2) is an additive function based on the model for the ground motion regression equations defined by Campbell.11 It also accounts for the statistical log-normal distribution of a ground parameter (Y). Peak ground motion parameters decrease as the epicentral distance increases. The attenuation depends, however, on the magnitude; these variations may be expressed through equation (D3.2). Figure 3.2 shows variations of peak ground horizontal acceleration with magnitude and the effects of focal depth. Revised attenuation relationships for European countries and some regions in the Middle East have been proposed by Ambraseys and co-workers12'13 for different peak ground motion parameters.
In probabilistic seismic hazard assessment and for hazard maps, earthquakes are modelled as a Poisson process. The Poisson model is a continuous time, integer-value counting process with stationary independent increments.14 This means that the number of events occurring in an interval of time depends only on the length of the interval and does not change in time (stationarity). The probability of an event occurring in the interval is independent of the history and does not vary with the site. Thus, each earthquake occurs independently of any other seismic event; that is, earthquakes have no memory. The Poisson model is defined by a single parameter (v) which expresses the mean rate of occurrence of seismic events exceeding a certain threshold, e.g. earthquakes of magnitude greater than M over a given area.
The probability of earthquake occurrence modelled by the Poisson distribution is as follows:
0.01
1000
Distance (km)
1000
; | |
I h = 3.6 km | |
mb = 5.0 | |
5 krn^^» | |
; 20 km "— | |
I 40 km | |
. 1 MHIll |
Distance (km) Fig. 3.2. Attenuation of peak ground horizontal acceleration: (a) effect of magnitude and (b) focal depth7 20 40 60 80 Period of interest (years) 200 400 600 800 1000 Peak horizontal acceleration (cm/s2) Fig. 3.3. Relationship between (a) return period, lifetime of the structure and desired probability of exceedance and (b) hazard curves for peak ground accelerations7 20 40 60 80 Period of interest (years) 200 400 600 800 1000 Peak horizontal acceleration (cm/s2) Fig. 3.3. Relationship between (a) return period, lifetime of the structure and desired probability of exceedance and (b) hazard curves for peak ground accelerations7 where P = P[N = n, TJ is the probability of having n earthquakes with magnitude m greater than M over a reference time period TL in a given area. The value of v corresponds to the expected number N of occurrences per unit time for that area, i.e. the cumulative number of earthquakes greater than M. Recurrence relationships express the likelihood of earthquakes of a given size occurring in the given source during a specified period of time, for example one year. Therefore, the expected number of earthquakes N in equation (D3.3) can be estimated through statistical recurrence formulae. Gutenberg and Richter15 developed the following frequency-magnitude relationship: in which a and b are model constants that can be evaluated from seismological observational data through a least-square fit. They describe the seismicity of the area and the relative frequency of earthquakes of different magnitudes, respectively. From equation (D3.3), the probability of at least a seismic event exceeding a certain threshold can be expressed as the complement of no such occurrence (i.e. n = 0): The return period, TR, of seismic events that exceed a certain threshold can be estimated Clause 3.2.1 (3) as the average time between such occurrences: Low-magnitude earthquakes occur more often than high-magnitude events and are generally expected to produce less damage. Longer return periods lead to a lower probability of earthquake occurrence, which is often associated with a higher potential for economic loss (owing to a lack of seismic design provisions). The relationship between the return period Tr, the lifetime of the structure, TL, and the probability of exceedance of earthquakes with a magnitude m greater than M, P[m > M, TL], is plotted in Fig. 3.3a. Variations of the peak horizontal acceleration with the annual probability of exceedance are also included for the three percentiles 15, 50 and 85 in Fig. 3.3b. The design seismic action on rock (or, in Eurocode 8 terms, on type A ground) for structures of ordinary importance is the 'reference' seismic action. In EN 1998-1 the hazard is defined through the value of the 'reference peak ground acceleration' on type A ground, denoted by a R. This parameter will be derived from zonation maps in the National Annexes. Reference peak ground accelerations chosen by national authorities correspond to the reference return period (rNCR) of the design seismic action (for the no-collapse requirement) of structures of ordinary importance. For such structures it also corresponds to the reference probability of exceedance in TL = 50 years (PNCR). As explained in Section 2.1 of this guide, the reference values (period and probability of exceedance) selected by national authorities apply to the design of ordinary structures to fulfil the no-(local-)collapse requirement. Structures other than ordinary ones are designed to fulfil the no-(local-) collapse requirement under a design ground acceleration equal to ag = 7i«gR (D3.7) The value of the importance factor 7t in equation (D3.7) is by definition equal to 1.0 for structures of ordinary importance. Its recommended values for buildings other than ordinary ones have been given in Section 2.1. Values of 7, other than 1.0 are considered to correspond to mean return periods other than the reference, rNCR. It is noted, though, that ground motions with different TR values generally exhibit different seismological characteristics, especially frequency content and duration, in addition to a different PGA as per equation (D3.7). |
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