Acceleration – Magnitude

The Analysis of Accelerogramsfor the Earthquake Resistant Design of Structures

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).

Table of Contents

• Methodology and background• Data, application and results• Conclusions• References

Methodology and Background• The maximum acceleration A(cm/s2) 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

Log10 (A(cm/s2)) = a M(mb) + b (1)

where A is the maximum acceleration, M is the magnitude and (a,b) are constants to be determined.

Methodology and Background• For maximum velocity and maximum displacement also exist similar

linear relationships (Doyle, 1995), given by

Log10 (V(cm/s)) = a’ M(mb) + b’ (2)

Log10 (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.

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.

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.

• 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.

Data, Application and Results

Event (nº)

Date(day month year)

Origin Time(hour min. sec.)

Latitude (ºN)

Longitude (ºE)

Magnitude (mb)

1 27 05 2003 17 11 32.5 36.802 3.610 6.12 28 05 2003 11 26 31.6 37.135 3.393 4.53 28 05 2003 19 05 22.2 36.932 3.737 4.94 31 05 2003 11 44 46.3 37.048 3.780 4.65 01 06 2003 02 54 21.0 36.990 3.983 4.66 02 06 2003 08 20 24.2 37.017 3.185 4.57 03 06 2003 23 17 46.2 37.208 3.710 4.48 06 06 2003 03 13 47.0 37.072 3.733 4.49 15 06 2003 01 06 10.8 36.893 3.348 4.1

10 17 06 2003 07 52 55.1 37.113 3.838 4.511 18 06 2003 19 36 13.1 36.970 3.682 4.512 21 06 2003 11 01 27.5 37.038 3.467 4.113 05 07 2003 20 03 35.9 37.212 3.470 4.214 06 07 2003 02 56 9.2 37.012 3.758 4.415 06 07 2003 08 50 20.6 36.998 3.513 4.316 14 07 2003 22 52 26.4 36.925 3.308 4.217 17 07 2003 21 07 50.3 36.645 3.493 4.418 18 07 2003 08 14 53.5 37.202 3.725 4.419 07 08 2003 08 23 11.7 37.103 3.722 4.520 11 08 2003 20 03 47.2 36.923 3.328 4.621 03 09 2003 14 04 49.8 37.155 3.600 4.622 12 10 2003 07 08 45.0 37.045 3.418 4.4

Table 1. Near events recorded at the same station.

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.

Data, Application and Results

Fig. 2. Linear relationship between maximum velocities and magnitude for near events recorded at the same station.

Data, Application and Results

Fig. 3. Linear relationship between maximum displacements and magnitude for near events recorded at the same station.

Data, Application and Results

Fig. 4. Linear relationship between duration and magnitude for near events recorded at the same station.

Data, Application and Results

Fig. 5. Fourier amplitude spectra for the events listed in Table 1.

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.

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.

Contact

Prof. Dr. Víctor CorcheteDepartment of Applied Physics

Higher Polytechnic School - CITE II(A)UNIVERSITY OF ALMERIA

04120-ALMERIA. SPAINFAX: + 34 950 015477e-mail: corchete@ual.es