Appendix Magnitude and Intensity of Earthquakes*

Transcription

1 Appendix Magnitude and Intensity of Earthquakes* Alberto Sarria M. A.1 INTRODUCTION The concepts of magnitude and intensity are used in seismology and in earthquake engineering to compare seismic events and to quantify the energy that is released during an earthquake. It is important that the engineer have a precise understanding of the terminology that is employed in order to have a basis for uniformly evaluating and comparing different seismic events. A.2 MAGNITUDE The original concept of earthquake magnitude was introduced in the year 1935 by C. F. Richter (1958) with the objective of comparing the energy liberated by different earthquakes. Seismologists have found many limitations in the use of this concept of magnitude. Therefore, it may be possible that the use of Richter's concept of magnitude will decrease in the years to come, even though it currently continues to be the most used parameter for the estimation of energy released by earthquakes. Richter expressed ~he magnitude, M, of an earthquake by the followmg formula: in which M = 10g(A/1) + [(.:1, h) + Cs + Cn (A.1) A = maximum amplitude of vibration registered by a seismograph, expressed in thousandths of millimeters T = period of the seismic wave, in seconds.:1 = distance to the epicenter, in grades h = focal depth, in kilometers Cs = correction factor for the seismological station Cr = regional correction factor. The determination of 1(11, h) as a function of distance and depth is based on a combination of analytical and empirical studies, in which the attenuation is considered as well as the particular type of wave. The magnitude of an earthquake determined by eq.(a.1) should provide a unique value for a specific seismic event. Although the magnitude M does not have an upper limit, natural seismic events have a maximum value of M = 8 or slightly higher. Since the publication in 1935 of the original Richter magnitude [eq.(a.1)], several other scales have been proposed that consider the different types of waves propagating from the same seismic source. The following paragraphs recapitulate the different scales for earthquake magnitude that are in use at the present time. A.2.1 Local Magnitude ML The local magnitude M L corresponds to the original formulation proposed by Richter in 1935 for local seismic events in southern California. The magnitude M L is defined as the logarithm of the maximum amplitude that is obtained from the record of a seismic event using a Wood-Anderson torsional seismograph located at 100 kilometers from the epicenter of the earthquake. This seismograph must have a natural period of 0.8 second, magnification of 2,800, and -Translated from Ingenieria Sismica (Alberto Sarria M., 1990) 536

2 Appendix 537 damping coefficient of 80% of critical damping. The magnitude for seismic events registered at locations other than 100 kilometers from the epicenter may be determined on the basis of the variation of the amplitude as a function of distance. and for any location in South America: A.3 SEISMIC MOMENT Ms = 2. 18Mb (A.6) A.2.2 Surface Magnitude Ms The surface magnitude Ms was proposed by Gutenberg and Richter in the year 1945 as a result of detailed studies. It is currently the magnitude scale most widely used for great epicentral distances, but it is valid for any epicentral distance and for any type of seismograph. The magnitude Ms requires a more precise knowledge of the variation of the wave amplitude as a function of distance. In order to utilize different seismographs, the amplitude of vibration of the soil should be used, not the amplitude recorded. Ms may be evaluated for surface waves with periods in the order of 20 seconds by the following expression, known as the Praga formula: where Ms = log (AI 7) gd (A. 2) A = spectral amplitude, the horizontal component of the Rayleigh wave, with a period of 20 seconds, measured on the ground surface in microns T = period of the seismic wave in seconds d = epicentral distance in degrees. After a detailed study of the Praga formula, Okal (1989) concluded that it could be extended to longer periods at an appropriate epicentral distance, for which eq.(a.2) would require some modifications. A.2.3 Magnitude Mb Gutenberg has proposed another method to measure the magnitude of an earthquake based on the amplitude of internal waves with periods in the order of one second. The following expressions (Bath 1973) relate the value of Mb to that of Ms or M L : Ms = ML - O.01(ML? (A. 3) Mb = 0.56Ms (A.4) Special expressions have been developed for specific geographic locations. For northwest South America: Ms = 1.51Mb (A.5) A concept known as seismic moment has been introduced recently to quantify and compare seismic events; it is evaluated by the expression in which Mo = ADG (ton-m) (A. 7) Mo = seismic moment A = fault area (length x depth) (m2) D = longitudinal displacement of the fault (m) G = modulus of rigidity (approximately 3 x 10 6 m2 = 3 x 1011 dyna/cm2) A.3.1 Seismic Moment Magnitude Mw toni The magnitude Mw (seismic moment) of an earthquake is expressed as (Kanamori and Anderson 1975): Mw = 2/310gMo (A. 8) According to Bullen and Bolt (1985), the Alaska earthquake of 1964 had the following magnitude: Ms = 8.4 or Mw = 9.2 A.1i RELEASED ENERGY The energy E, in joules, released by an earthquake can be estimated from the magnitude Ms as [Newmark and Rosenblueth (1971)] E = M, (joules) (A.9) According to Newmark and Rosenblueth (1971), the energy released by an earthquake is comparable to that of a nuclear explosion. A nuclear explosion of one megaton releases 5 X joules; thus, by eq.(a.9), to release the equivalent amount of energy released by an earthquake of magnitude Ms = would require a nuclear explosion of 50 megatons. This brief calculation helps to demonstrate the enormous destructive power of a strong earthquake; the vast amount of energy that accumulates along a fault for many years, even centuries, is suddenly released in a short interval of time, about 60 seconds or less. 1Earthquakes of magnitude Ms = 7.3 or greater occur worldwide at an average of seven per year.

3 538 Appendix Table A.1. Modified Mercalli Intensity (MMI) Scale (Abbreviated Version) Intensity Evaluation Description I Insignificant Only detected by instruments II III Very light Light Only felt by sensitive persons; oscillation of hanging objects Small vibratory motion IV V VI Moderate Slightly strong Strong Felt inside buildings; noise produced by moving objects Felt by most persons; some panic; minor damages Damage to nonseismic-resistant structures VII Very strong People running; some damages in seismic-resistant structures and serious damage to unreinforced masonry structures VIII Destructive Serious damage to structures in general IX X Ruinous Disastrous XI Disastrous in extreme General panic; almost total destruction; the ground cracks and opens XII Catastrophic Total destruction.. Serious damage to well-built structures; almost total destruction of nonseismic-resistant structures Only seismic-resistant structures remain standing Table A.2_ Intensity I II III IV V VI VII VIII IX X XI XII International Macroseismic Intensity Scale (MSK) (Abbreviated Version) Description Not perceptible by humans, only detected by seismographs. Perceptible only by some people at rest, particularly in the upper stories of buildings. Perceptible by some people inside buildings, but only under favorable conditions. Perceptible by many people inside buildings and some outside. Hanging objects swing. Perceptible by most people inside buildings and by many outside. Movement of objects. Some light damage to Type A structures. Perceptible by most people inside buildings and outside. Moderate damage to Type A structures and damage to some Type B structures. Most people running in the street. Many Type A structures highly damaged. Moderate damage to Type B structures. Damage to some Type C structures. General panic. Many Type A structures are destroyed and many Type B structures experience serious damage. Also, many Type C structures suffer moderate damage. General panic. Many Type C structures collapse. Earth displacements and large waves in lakes and reservoirs occur. Most Type A structures and many Type B structures suffer complete collapse. Many Type C structures experience destruction. Ground opens; displacements of sand on sea cause change in the water levels of wells. Important damage to all kinds of structures including well-designed ones. Virtually complete destruction of all structures including those underground. A.5 INTENSITY Although the magnitude of an earthquake provides a measure of the total energy released, it does not describe the damaging effects caused by the earthquake at a particular locality. Therefore, it is necessary to distinguish between the magnitude and intensity of an earthquake. Magnitude refers to the energy liberated, while intensity measures the effect that an earthquake produces at a given geographic location. Several intensity scales have been proposed. The one most widely used is the intensity scale of Mercalli Cancani, modified by Wood-Newman (Newman 1954), now known as the Modified Mercalli Intensity scale or MMI scale. A.5.1 Modified Merc:aIliintensity (MMI) Scale The value assigned to the MMI scale at a particular location is based on the observations of the damage produced by the earthquake. The MMI scale has a total of 12 intensity values usually expressed in Roman numerals as described in Table A.I. Intensities up to VI usually do not produce damage, while intensities from VI to XII result in progressively greater damage to buildings and other structures. A.5.2 International Macroseismic Intensity Scale (MSI{) The International Macroseismic Intensity Scale (MSK) proposed by Medvedev-Sponheuer-Karnik, which is similar to the Modified Mercalli Intensity (MMI) scale, provides an empirical appraisal of the effects of an earthquake based on observed damage. The degrees in the MSK are defined by: (a) effects felt by people, (b) damage produced in different types of structures, and (c) changes observed in nature after the earthquake. Damages are observed in three types of structures not designed to resist seismic action: Type A: with masonry walls of adobe or similar materials;

4 Appendix 539 Type B: with brick walls, concrete blocks, or masonry with wood reinforcement; and Type C: steel or reinforced concrete structures. Table A.2 presents an abbreviated description of the 12 degrees of the International Macroseismic Intensity Scale (MSK). REFERErtCES BATH, MARKUS (1973) Introduction to Seismology. John Wiley and Sons, New York, NY. BULLEN, K. E., and BOLT, BRUCE (1985) An Introduction to the Theory of Seismology. 4th ed. Cambridge University Press, London and New York. KANAMORI, H., and ANDERSON, DON L. (1975) "Theoretical Basis of Some Empirical Relations in Seismology." Bulletin of the Seismological Society of America, Vol. 65, #5. NEWMAN, F. (1954) Earthquake Intensities and Related Ground Motions. University of Washington Press, Seattle, WA. NEWMARK, NATHAN, and ROSENBLUETH, EMILIO (1971) Fundamentals of Earthquake Engineering. Prentice Hall, Englewood Cliffs, NJ. OKAL, EMILE (1989) "A Theoretical Discussion of Time Domain Magnitude: The Praga Formula for Ms and the Mantle Magnitude Mm." Journal of Geophysical Research, Vol. 94. RICHTER, CHARLES F. (1958) Elementary Seismology. W. H. Freeman and Company, San Francisco, CA. SARRIA M., ALBERTO (1990) Ingenierfa Sismica. Ediciones Uniandes, Universidad de Los Andes, Bogota, Colombia.

5 Diskette Order Form Professor Mario Paz P.O. Box Louisville, KY USA Date Please send to: Name Street Address City, State, Zip code Country Earthquake Resistant Design Programs: Implementing Seismic Codes for 25 Countries in this Handbook Set of Programs, source and compiled versions (menu driven) 20% discount to a purchaser of the Handbook Shipping charge $ $192 Total (check enclosed) USA shipping and handling, add $5 Overseas shipping, add $15 Canada shipping, add $10

6 Index Angular Frequency, 13 Aspect Ratio, 31 ATC,25 Base Shear Force: Algeria, 61 Argentina, 72 Australia, 89 Canada, 113 Chile, 128 China, 145 Egypt, 196 Greece, 235, 245 India, 262 Indonesia, 278 Iran, 298 Israel, 310 New Zealand, 365 Puerto Rico, 405 Taiwan, 447 Thailand, 455 Turkey, 463 United States of America (USA), 488, 502,509 Venezuela, 520 Yugoslavia (former), 529 BOCA, 502, 505 BSSC,486 Building Occupancy or Importance Categories: Algeria, 59 Argentina, 67 Australia, 88 Canada, 116 Chile, 129 China, 144 Colombia, 161 Costa Rica, 178 Egypt, 197 El Salvador, 207 France, 220 Greece, 242 Hungary, 250 India, 260 Indonesia, 280 Iran, 297, 300 Israel, 310 Italy, 319 Mexico, 343 Peru, 382 Puerto Rico, 403 Romania, 419 Taiwan, 448 Thailand,457 Turkey, 463 United States of America (USA), 488, 502 Venezuela, 517 Yugoslavia (former), 529 Building Seismic Codes: Canada, 111 Chile, 128 China, 143 El Salvador, 207 France, 216, 226, 231 Greece, 232, 239 Hungary, 249 India, 256 Indonesia, 277 Iran, 296 Israel, 308 Italy, 318 Japan, 331 Mexico, 343 New Zealand, 361 Peru, 377 Portugal, 390 Puerto Rico, 401 Romania, 416 Spain, 432, 438 Taiwan, 447 Thailand, 454 Turkey, 462 United States of America (USA), 485, 501 USSR (former), 472 Venezuela, 515 Yugoslavia (former), 528 Center of Rigidity, 507 Characteristic Equation, 40 Circular Frequency, 6 Combination of Modes: CQC (Complete Quadratic Combination), 51 SRSS (Square Root Sum of Squared Values), 51 Complete Quadratic Combination (CQC), 51 Computer Program: Argentina, 79 Australia, 97 Bulgaria, 109 Canada, 120 Chile, 136 China, 154 Colombia, 169 Costa Rica, 191 France, 225 Greece, 247 Hungary, 253 India, 272 Indonesia, 291 Italy, 324 Mexico, 358 New Zealand, 371 Peru, 386 Portugal, 398 Puerto Rico, 413 Romania, 425 Spain, 443 Thailand, 458 Turkey, 469 United States of America (USA), 494, 500,505,511 USSR (former), 482 Venezuela, 525 Yugoslavia (former), 535 Condensation: Dynamic, 45 Modified dynamic, 47 Static,42 Construction of elastic spectra, 15, 16 Housner design spectra, 15 Mohraz design spectrum, 18 Critical Damping, 6 Damped: Free vibration, 5 Frequency, 5 Recommended values, 6 Damping: Coefficient, 3 Critical,5 Ratio, 5 Degrees of Freedom, 3 Design Philosophies: Canada, 112 Chile, 128 Costa Rica, 176 India, 275 Iran, 297 Israel,309 Japan, 337 New Zealand, 363 Portugal, 390 Puerto Rico, 408 Spain, 438 Turkey, 462 United States of America (USA), 496 USSR (former), 472 Venezuela, 517 Design Spectrum, 2 Direct Method, 6 Duhamel's Integral, 8 Dynamic Modal Method: Chile, 134 Egypt, 201 France, 229 Greece, 247 India, 263 Indonesia, 282 Israel,

7 544 Index Dynamic Modal Method-contd. Italy, 320 Mexico, 353 New Zealand, 370 Peru, 383 Portugal, 396 Puerto Rico, 408 Spain, 438 United States of America (USA), 497, 504 USSR (former), 477 Venezuela, 522 Yugoslavia (former), 532 Earthquake: Effective force, 4 Effective modal weight, 49 Elastic design spectra, 14 El Centro,CA (1940), 13 Imperial Valley (1940), 14 San Fernando, CA (1971), 16 Tripartite response spectra, 13 Earthquake Energy, 537 Effective Weight: Argentina, 74 Chile, 136 Colombia, 165 Israel, 312 United States of America (USA), 498 Elastic Design Spectra, 14 Housner,15 Influence of soil conditions, 18 Mohraz,18 Newmark and Hall, 15, 16 Normalized (UBC), 19 Peng, Elghadamsi and Mohraz, 21 Sadigh's relationship, 23 Element: Overturning moment, 510 Shear force, 510 Energy: Kinetic, 43 Potential, 43 Equivalent Lateral Forces: Algeria, 61 Argentina, 72 Australia, 90 Bulgaria, 104 Canada, 118 Chile, 129 China, 146 Egypt, 199 France, 216, 223 Greece, 235, 245 Hungary, 251 India, 262 Indonesia, 281 Iran, 301 Israel, 311 Italy, 319 Japan, 334 Mexico, 351 New Zealand, 366 Peru, 382 Portugal, 394 Puerto Rico, 405 Romania, 420 Spain, 437 Taiwan, 449 Thailand, 455 Turkey, 466 United States of America (USA), 489, 504,509 USSR (former), 473 Venezuela, 521 Yugoslavia (former), 529 FEMA,25 Forces and Moments on Structural Elements, 510 Free Vibration: Damped, 5 Undamped, 5 Fundamental Period: Algeria, 60 Australia, 89 Canada, 116 Chile, 130 China, 152 Colombia, 162 Costa Rica, 183 Egypt, 199 El Salvador, 209 France, 219 Greece, 242 Hungary, 252 India, 261 Indonesia, 279, 288 Iran, 300 Israel, 309 Italy, 319 Japan, 332 Mexico, 351 New Zealand, 366 Peru, 381 Portugal, 393 Puerto Rico, 403 Romania, 420 Spain, 434 Taiwan, 448 Thailand, 457 Turkey, 466 United States of America (USA), 489 USSR (former), 478 Venezuela, 520 Yugoslavia (former), 534 Gauss-Jordan, 43 Generalized: Coordinates, 30 Equation of motion, 30 Properties, 30 Generalized Coordinates, 3 Impulsive Force, 8 Intensity of Earthquakes: International Macroseismic Scale (MSK), 538 Modified Mercalli-Intensity Scale (MMI), 538 Lateral Displacements: Australia, 92 Canada, 119 Chile, 135 China, 152 Colombia, 165 Costa Rica, 187 Egypt, 203 El Salvador, 211 France, 225 Indonesia, 283, 287 Iran, 302 Japan, 334 Mexico, 354 New Zealand, 367 Peru, 384 Portugal, 395 Puerto Rico, 407 Romania, 422 Spain, 438 Taiwan, 450 Turkey, 469 United States of America (USA), 493, 510 USSR (former), 480 Venezuela, 523 Yugoslavia (former), 532 Lateral Stiffness: Cantilever structure, 38 Story, 32 Magnitude of Earthquake: Local (Md, 536 Magnitude (Mb)' 537 Richter (M), 536 Surface (Ms), 537 Mathematical Model, 3 Mercalli, 538 Methods of Analysis: Argentina, 71 China, 144 Colombia, 162 Egypt, 195 Greece, 245 Hungary, 251 Indonesia, 282 Iran, 298 Mexico, 350 New Zealand, 365 Portugal, 392 Puerto Rico, 402 United States of America (USA), 505 Venezuela, 520 Modal: Displacement, 50 Effective weight, 49 Equation, 48 Lateral force, 50 Overturning moment, 50 Shape, 41 Shear force, 48 Story drift, 50 Superposition method, 47 Torsional moment, 50 Natural Frequency: Multi-degree-of-freedom system, 39 Single-degree-of-freedom system, 6 Natural Period, 13 Newton's Law of Motion, 4 Overturning Moments: Argentina, 72 Australia, 91 Canada, 118 Chile, 129 Egypt, 200 France, 225 Greece, 246 Indonesia, 281 Iran, 301 Israel, 313 Italy, 323 Japan, 334 Mexico, 353

8 Index 545 Overturning Moments--contd. Peru, 383 Portugal, 395 Puerto Rico, 407 Romania, 421 Spain, 437 Taiwan, 450 Thailand,457 Turkey, 466 United States of America (USA), 490, 504,509 USSR (former), 479 Venezuela, 521 Yugoslavia (former), 532 Participation Factor, 31, 48 P-delta Effect, 51 Argentina, 71 Australia, 92 El Salvador, 211 France, 231 Greece, 236 Israel, 312 Mexico, 353 New Zealand, 371 Puerto Rico, 406 United States of America (USA), 490 Venezuela, 522 Predictive Attenuation Relationship, 23 Pseudo-acceleration, 11 Pseudo-velocity, 11 Rayleigh Method, 34, 509 Reduced: Damping matrix, 43 Dynamic matrix, 45 Mass matrix, 43, 45, 47 Stiffness matrix, 43, 45, 47 Response: Direct integration, 6 Duhamel integral, 8 Response Spectra, 2, 12 Elastic system, 12 Inelastic design spectra, 25 Inelastic systems, 25 Lai and Biggs, 27 Newmark and Hall, 26 Tripartite, 13 Uniform Building Code, 18 Rotational Stiffness, 508 Sadigh's Relationship, 23 SEAOC, 25, 486 Seismic Factor, 503 Seismic Moment, 537 Seismic Zones: Algeria, 59 Argentina, 66 Canada, 112 Colombia, 157 Costa Rica, 177 El Salvador, 208 Greece, 222, 241 Hungary, 250 India,258 Indonesia, 279 Iran, 299, 304 Israel,308 Japan,332 Mexico, 345 Peru, 378 Portugal, 391 Puerto Rico, 402 Romania, 419 Spain, 432 Taiwan, 448 Thailand,456 Turkey, 463 United States of America (USA), 486 USSR (former), 472 Venezuela, 517 Yugoslavia (former), 530 Shape Function, 31 Single-Degree-of-Freedom System, 4 Soil Classification: Algeria, 61 Argentina, 67 Australia, 89 Bulgaria, 103 Canada, 117 Chile, 129 China, 144 Colombia, 161 Costa Rica, 182 Egypt, 197 France, 229 Greece, 235, 242 Hungary, 252 India, 260 Indonesia, 279 Iran, 299 Israel,310 Mexico, 346 Peru, 379 Portugal, 391 Puerto Rico, 403, 404 Spain, 436 Thailand,457 Turkey,465 United States of America (USA), 488 USSR (former), 477 Venezuela, 519 Yugoslavia (former), 530 Spectral: Acceleration, 11 Pseudo-velocity, 11 SRSS Method, 51 Story Drift: Australia, 92 Canada, 119 Chile, 135 China, 152 Colombia, 165 Costa Rica, 187 Egypt, 203 El Salvador, 211 France, 222, 225 Greece, 235, 246 India, 263 Indonesia, 287 han, 302 Japan, 334 Mexico, 354 Portugal, 394 Puerto Rico, 407 Romania, 422 Spain, 438 Taiwan, 450 Turkey, 469 United States of America (USA), 490, 510 USSR (former), 482 Yugoslavia (former), 534 Story Lateral Stiffness, 32 Story Shear Force: Australia, 90 Bulgaria, 105 Chile, 130 China, 153 Egypt, 202 France, 224 Greece, 235 India, 263 Indonesia, 285 Iran, 303 Israel,313 Portugal, 394 Puerto Rico, 410 Romania, 421 Spain, 437 Taiwan, 452 Thailand, 457 Turkey, 468 United States of America (USA), 490, 503 USSR (former), 479 Venezuela, 524 Yugoslavia (former), 532 Structural Wall, 38 Torsional Moments Argentina, 72 Australia, 91 Bulgaria, 106 Canada, 118 Chile, 130 China, 147 Egypt, 200 France, 224 Greece, 244, 246 India, 263 Indonesia, 281 Iran, 301 Israel,311 Italy, 320 Mexico,352 NewZealand, 371 Peru, 383 Portugal, 394 Puerto Rico, 405 Romania, 421 Spain, 437 Taiwan, 449 Turkey, 467 United States of America (USA), 490, 510 USSR (former), 479 Venezuela, 522 Yugoslavia (former), 531 UBC, 486 Vertical Seismic Action China, 148 Costa Rica, 177 France, 218 Greece, 246 Iran, 302 Israel,311 Italy, 320 Peru, 383 Romania, 417 Spain, 434 USSR (former), 475 Yugoslavia (former), 531 Virtual Work, 43