Definitions. Seismic Risk, R (Σεισμική διακινδύνευση) = risk of damage of a structure

SEISMIC HAZARD

Definitions Seismic Risk, R (Σεισμική διακινδύνευση) = risk of damage of a structure Seismic Hazard, Η (Σεισμικός κίνδυνος) = expected intensity of ground motion at a site Vulnerability, V (Τρωτότητα) = vulnerability of a structure depending on its resistance R = H V

METHODOLOGY 1. Identification of seismic sources around the site under examination. 2. Determination of number and magnitude of earthquake events for each seismic source according to historic data 3. Determination of an attenuation model in order to calculate ground motion parameters for given magnitude and distance from the site of a particular earthquake 4. Determination of the stochastic model for the appearance of earthquake events. Usually the Poisson distribution is considered. 5. Evaluation of seismic hazard curve associating a particular ground motion parameter (i.e. peak ground acceleration) with an annual frequency of exceedence or a probability of exceedence in a given time period.

The determination of the number and magnitude of earthquake events for a particular seismic source is performed through a Guttenberg-Richter relationship with the following form: where: log 10 N = a b M N = the number of earthquakes with magnitude larger than M during a time period T. a = a constant that measures the total number of earthquakes at the given source b = a measure of the number of small versus large events. The number of events N can be divided by the T years in order to get the annual frequency of exceeding the M event magnitude: N 1 (M) = N(M) / T Furthermore, N 1 can be divided by the source area A (or length L) in order to define the annual frequency of exceedence per unit source area: N 2 (M) = N 1 M) / A

Effect of faults that produce large earthquakes Faults tend to produce essentially the same size or characteristic earthquakes having a relative narrow range of magnitudes near the maximum. Large earthquakes on the fault are more probable than indicated by the G-R relationship

For each seismic source a table is constructed, where the columns represent different event magnitudes and the lines different distances from the examined site. At a bin of magnitude M i and distance R j is given the annual frequency of having an earthquake in the range of magnitude M i, (Μ i -dm/2 < M < M i +dm/2) and distance R j (R j -dr/2 < R < R j +dr/2). This annual frequency is calculated from: N 1,ij = [ N 1 (Μ i -dm/2) - N 1 (M i +dm/2) ]da where da is at the portion of the source area between R j -dr/2 and R j +dr/2. R min Μ min Μ i Μ max Different tables are obtained for each source and finally a global table is constituted by adding the values in the corresponding bins of the particular tables. R j N 1,ij R max

Another table is created by giving in each (M i, R j ) bin the ground motion value obtained from a corresponding attenuation relationship. Such relationships are those given for peak ground acceleration and spectral accelerations by Boore and Atkinson. A similar but simpler relationship is the one given by Papazachos, in the form: lna g = 3.88 + 1.12 M s 1.65 ln(r+15) where a g = peak ground acceleration in cm/sec 2 R = distance from the source in km s ij s k If we consider as s ij the values of the chosen ground motion parameter for the M i, R j pair we can define a region of bins at which the s ij values are larger or equal to a target value s k. R min Μ min Μ i Μ max R j s ij The addition of the corresponding N 1,ij values from the first table gives the annual frequency of exceedence N 1,k for the target value s k. R max

Considering that the appearance of earthquake events follows the Poisson distribution, the probability of exceeding s k in t years is given by the relationship: p(t) = 1 exp( N 1,k t) Accordingly, for different s k values a hazard curve can be obtained with the s k value on the vertical axis and on the horizontal either the probability of exceedence of s k or the return period of events larger than s k which is the inverse of N 1,k. s s d sσχ T R t ln( 1 p) p t T R TE, σχ TE T (έτη) R (years) 10 100 1000 10000 100000

DEAGGREGATION Determine earthquake parameters, principally magnitude and distance, to consider in seismic-resistant design Choose the most likely magnitude distance pair

Example A seismic hazard analysis showed that: The site is affected by earthquakes that happen within a region of radius R = 80 km from the site. The probability of occurrence of a seismic event is the same at every point in this region. The G-R relation for the earthquakes that have occurred in a period T = 120 years in this region is: logn = 6.55 0.85 M (Ν = number of earthquakes Μ) 1. Every how many years (in the average) an earthquake happens with Μ 6.5. Answer logn = 6.55 0.85 M Annual rate: Ν 1 = Ν/T = N/120 logn 1 = logn log120 logn 1 = 6.55 0.85 M 2.079 logn 1 = 4.471 0.85 M For Μ = 6.5 logn 1 (M 6.5) = 4.471 0.85 6.5 = 1.054 N 1 (M 6.5) = 10 1.054 = 0.0883 Return period: Τ R (Μ 6.5) = 1/Ν 1 = 11.3 years.

Example (cont.) 2. Calculate the probability of occurrence of at least one earthquake of magnitude Μ 7.5 in the next 100 years. Answer p(t) = 1 e N1 t For Μ = 7.5, t = 100: logn 1 (M 7.5) = 4.471 0.85 7.5 = 1.904 N 1 (M 7.5) = 10 1.904 = 0.0125 p(t=100) = 1 e 0.0125 100 = 0.713 = 71.3% 3. Calculate the probability of occurrence of at least one earthquake of magnitude Μ 6.0 in the next 50 years and in a distance less than 20 km from the site. Answer logn 1 (M 6.0) = 4.471 0.85 6.0 = 0.629 N 1 (M 6.0) = 10 0.629 = 0.235 A 1 = π 20 2, Α = π 80 2 Ν 1 (Α 1 ) = Ν 1 (Α) (Α 1 /Α) = 0.235 20 2 /80 2 = 0.01469 p(t=50) = 1 e 0.01469 50 = 0.520 = 52.0%

EXERCISE 10 SOURCE AREA WITH A RADIUS OF 200 km GUTTENBERG RICHTER RELATIONSHIP log N = 7.1 M GRID 2 2 km CALCULATE PROBABILITY OF EXCEEDENCE OF 0.50 g AT 50 YEAR PERIOD

Consider as attenuation relationship the one given by Papazachos: lna g = 3.88 + 1.12 M s 1.65 ln(r+15) Define the area that must be taken into account Evaluate the seismicity of each square of the grid from the Guttenberg Richter relationship: logn = 7.1 - M Define for each of the selected squares the minimum magnitude that produces a 0.50 g acceleration at the examined site. Evaluate the annual frequency of exceedence of the referred minimum magnitude for each square. Calculate the annual frequency of exceedence of 0.50 g at the examined site. Calculate the probability of exceedence in a 50 year period of the 0.50 g ground acceleration.

EXERCISE 11 SOURCE AREA WITH RADIUS 40 km PRODUCES A CHARACTERISTIC EARTHQUAKE OF MAGNITUDE 6.0 WITH A RETURN PERIOD OF 10 YEARS. LINE SOURCE WITH A LENGTH OF 40 km PRODUCES A CHARACTERISTIC EARTHQUAKE OF MAGNITUDE 7.5 WITH A RETURN PERIOD OF 100 YEARS. CALCULATE PROBABILITY OF EXCEEDENCE OF 0.25 g AND 0.50 g AT 50 YEAR PERIOD.

Define for each source the portion of its area or length that produces the target acceleration at the examined site as a result of the characteristic earthquake. Define the annual frequency of appearance of the characteristic earthquake at the defined portions. Calculate the annual frequency of exceedence of the target acceleration at the examined site. Calculate the probability of exceedence of the target acceleration in a 50 year period.