1. Acceleration – Magnitude The Analysis of Accelerograms for the Earthquake Resistant Design of Structures

2. Preface The analysis of ground motions (displacements, velocities and accelerations) will be presented, focused to the seismic design. Their validity and applicability for the seismic design will be discussed also. The results presented here, will show that the relationships that exist between the important parameters: PGA, PGV, PGD and duration; and the earthquake magnitude, allow the prediction of the values for these parameters, in terms of the magnitude for future strong motions. These predictions can be very useful for seismic design. Particularly, the prediction of the magnitude associated to the critical acceleration, because the earthquakes with magnitude greater than this critical magnitude can produce serious damages in a structure (even its collapsing). The application of the relationships presented here must be very careful, because these equations are dependent on the source area, location and type of structure (Corchete, 2010).

3. Table of Contents Methodology and background Data, application and results Conclusions References

4. Methodology and Background The maximum acceleration A(cm/s 2 ) is related to the intensity of an earthquake by a linear equation (Bullen and Bolt, 1985). The intensity of an earthquake is also related to the magnitude by a linear equation (Howell, 1990). Thus, a linear relationship must exist between maximum acceleration and magnitude. This relation is given by Log 10 (A(cm/s 2 )) = a M(mb) + b (1) where A is the maximum acceleration, M is the magnitude and (a,b) are constants to be determined.

5. Methodology and Background For maximum velocity and maximum displacement also exist similar linear relationships (Doyle, 1995), given by Log 10 (V(cm/s)) = a ’ M(mb) + b ’ (2) Log 10 (D(cm)) = a ’’ M(mb) + b ’’ (3) where V is the maximum velocity, D is the maximum displacement, M is the magnitude and (a ’,b ’,a ’’,b ’’ ) are constants to be determined. Other important parameter is the time duration of the accelerations greater than 0.05 g registered in an accelerogram (time record of acceleration). For this time duration exists other linear relationship (Bullen and Bolt, 1985), given by Duration (s) = a ’’’ tanh(M(mb) – c) + b ’’’ (4) where (a ’’’,b ’’’,c) are constants to be determined.

6. Methodology and Background The Fourier spectrum of the strong ground motions can present several dominant periods (Figure 5). These dominant periods can be different for each component of the strong motion recorded and for each kind of record (displacements, velocities or accelerations). It is proved that the earthquake shaking can be most destructive, on structures having a natural period around any period of these dominant periods (Adalier and Aydingun, 2001). Thus, these dominant periods are important parameters to be known to reduce the damages in structures.

7. Data, Application and Results The constants of the equations (1), (2), (3) and (4), can be determined for a location (station) and a source area (a small area in which the epicenters can be grouped). The data to be used for this kind study must be time-series of acceleration, velocity and displacement, recorded at the same location (station), for seismic events with very closer epicentral coordinates. If there are not available any time-series of displacements, velocities or accelerations, these records can be obtained from the others using the AVD program. AVD Table 1 shows the data used as an example. Figures 1, 2, 3 and 4, show the results of the linear fit performed with the data listed in Table 1 for acceleration, velocity, displacement and duration.

8. Data, Application and Results Event (nº) Date (day month year) Origin Time (hour min. sec.) Latitude (ºN) Longitude (ºE) Magnitude (mb) 127 05 200317 11 32.536.8023.610 6.1 228 05 200311 26 31.637.1353.393 4.5 328 05 200319 05 22.236.9323.737 4.9 431 05 200311 44 46.337.0483.780 4.6 501 06 200302 54 21.036.9903.983 4.6 602 06 200308 20 24.237.0173.185 4.5 703 06 200323 17 46.237.2083.710 4.4 806 06 200303 13 47.037.0723.733 4.4 915 06 200301 06 10.836.8933.348 4.1 1017 06 200307 52 55.137.1133.838 4.5 1118 06 200319 36 13.136.9703.682 4.5 1221 06 200311 01 27.537.0383.467 4.1 1305 07 200320 03 35.937.2123.470 4.2 1406 07 200302 56 9.237.0123.758 4.4 1506 07 200308 50 20.636.9983.513 4.3 1614 07 200322 52 26.436.9253.308 4.2 1717 07 200321 07 50.336.6453.493 4.4 1818 07 200308 14 53.537.2023.725 4.4 1907 08 200308 23 11.737.1033.722 4.5 2011 08 200320 03 47.236.9233.328 4.6 2103 09 200314 04 49.837.1553.600 4.6 2212 10 200307 08 45.037.0453.418 4.4 Table 1. Near events recorded at the same station.

9. Data, Application and Results Fig. 1. Linear relationship between maximum accelerations and magnitude for near events recorded at the same station. The critical acceleration considered is 0.5 g.

10. Data, Application and Results Fig. 2. Linear relationship between maximum velocities and magnitude for near events recorded at the same station.

11. Data, Application and Results Fig. 3. Linear relationship between maximum displacements and magnitude for near events recorded at the same station.

12. Data, Application and Results Fig. 4. Linear relationship between duration and magnitude for near events recorded at the same station.

13. Data, Application and Results Fig. 5. Fourier amplitude spectra for the events listed in Table 1.

14. Conclusions The constants of the equations (1), (2), (3) and (4), can be determined for a location and a source area. The values for these constants can be different for different locations and/or different source areas. Formula (1) will be very useful to know the maximum acceleration, that can occur in a location, for earthquakes with high magnitudes which have not occurred up to now. For each building exists a critical acceleration, which is the maximum acceleration that this building can bear without damages (Corchete, 2010). Formula (1) allows to know in which magnitude the critical acceleration is reached (Figure 1). For earthquakes with magnitudes greater than this magnitude, the buildings can bear serious damages or collapse. Formulas (2), (3) and (4), allow to know important parameters for the seismic engineering.

15. References Adalier K. and Aydingun O., 2001. Structural engineering aspects of the June 27, 1998 Adana-Ceyhan (Turkey) earthquake. Engineering Structures, 23, 343-355. Bullen K. E. and Bolt A. B., 1985. An introduction to the theory of seismology. Cambridge University Press, Cambridge. Corchete V., 2010. The Analysis of Accelerograms for the Earthquake Resistant Design of Structures. International Journal of Geosciences, 2010, 32-37. Doyle H., 1995. Seismology. Wiley, New York. Howell B. F., 1990. An introduction to seismological research. History and development. Cambridge University Press, Cambridge.

16. Contact Prof. Dr. Víctor Corchete Department of Applied Physics Higher Polytechnic School - CITE II(A) UNIVERSITY OF ALMERIA 04120-ALMERIA. SPAIN FAX: + 34 950 015477 e-mail: corchete@ual.es