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3 Earthquake Engineering (continued) (shaking), inundation [tsunami, seiche (oscillating standing wave in a lake or bay), or dam failure], various kinds of perma- nent ground failure (liquefaction and landslide), and fire or hazardous materials release. In a particular event, any of these hazards can dominate, and historically each has caused major damage and great loss of life. The expected damage given a specified value of a hazard parameter is termed vulnerability, and the product of the hazard and the vulnerability is the ex- pected loss or seismic risk. For most earthquakes, shaking is the dominant and most wide- spread cause of damage. Shaking near the actual earthquake rupture lasts only during the time when the fault ruptures, a process that takes seconds or at most a few minutes. The seismic waves generated by the rupture propagate long after the movement on the fault has stopped, however, spanning the globe in about 20 min. Typically, earthquake ground mo- tions are powerful enough to cause damage only in the near field (that is, within a few tens of kilometers from the causative fault). In a few instances, long-period motions have caused significant damage at great distances to selected structures. A prime example of this was the 1985 Mexico City earthquake, in which numerous collapses of mid- and high-rise buildings were caused by a moment magnitude (MW) 8.1 earthquake, occur- ring at a distance of approximately 400 km from Mexico City. Damage can occur even farther away because of earthquake- induced phenomena, such as occurred in the MW 9.1 earth- quake and tsunami that occurred in 2004 in the Indian Ocean, in which not only were over a hundred thousand people killed in Indonesia, but tens of thousands more died in Sri Lanka and India due to the tsunami, at a distance greater than 1600 km from the causative fault. At present, the preferred scale for measuring earthquake mag- nitudes is the moment magnitude or MW scale, although many scales were used previously, such as body wave magnitude mb and surface wave magnitude or MS scale. Magnitude can be related to the total energy released by log10 E = 11.8 + 1.5 MS, where E is the total energy in ergs. Note that 101.5 = 31.6, so that an increase of one magnitude unit is equivalent to 31.6 times more total energy released, an increase of two magnitude units about 1000 times more total energy, and so on. Whereas mag- nitude is a measure of the overall size of a single earthquake, in- tensity is a measure of the effect, or strength, of an earthquake hazard at a specific location. Intensity scales in use include the Modified Mercalli Intensity (MMI) scale in the United States, the Medvedev-Sponheur-Karnik (MSK-81) scale in Europe, and the Japan Meteorological Agency (JMA) scale. Roman numer- als are traditionally used for intensity scales, to indicate the qualitative nature of the scales, which are based on subjective observations rather than instrumental records. The JMA scale is from 0 to 7, and uses Arabic numerals. For the MMI and MSK scales, 0 is no earthquake, VI is the initiation of damage to poor-to-average structures, and XII is total destruction. Earth- quake shaking at a site is recorded using a seismometer, which digitally (previously, on photographic film) records a time history of ground accelerations at the site. Statistical analysis of hundreds of such accelerograms provides the basis for ground- motion prediction equations (GMPEs), which permit estimation of the maximum acceleration, velocity, and/or displacement caused by an earthquake that a structure will experience at a site, as a function of the structure's natural period, site-specific soil properties, and the magnitude, distance, and depth of the hypothesized earthquake. In the United States, ground motions from all potential earthquakes have been analyzed by the U.S. Geological Survey, so that any U.S. site's seismic hazard can be quickly determined. Based on this hazard, or on building code requirements mapped at a regional scale, the seismic lateral force requirements against which a structure must be designed are determined. In the developed world, existing buildings and infrastructure constitute by far the preponderance of earthquake risk, so a major focus of earthquake engineering is on identification, analysis, and mitigation (reduction) of this risk. New con- struction is generally safer but is still a focus for earthquake engineers, especially for larger and unique structures. In the developing world, even recent and new construction is a sig- nificant contributor to seismic risk because of lack of building- code compliance. Figure 1 shows the collapse of reinforced concrete buildings in the M7.8 Gorkha, Nepal earthquake of April 25, 2015. The most seismically hazardous existing build- ing structures are low-strength masonry (for example, adobe in developing countries), unreinforced brick masonry (such as exists in older portions of U.S. cities), nonductile reinforced concrete (typically, concrete frames constructed prior to the 1980s), and certain kinds of precast concrete buildings. Steel and wood structures are not immune to earthquake damage, but typically are less collapse-prone. Building vulnerability is typically mitigated via structural retrofits involving strengthen- ing wall–diaphragm connections, adding shear walls or brac- ing, and improving the ductility of columns via steel jacketing or other methods. Structural Analysis and Design Earthquake analysis and design of a structure was traditionally performed assuming using elastic methods with seismic load- ing scaled accordingly (that is, the design neglected the struc- + ward ' s science