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OBJECTIVE/SCOPE
To give an introduction to seismicity, seismic hazard, seismic risk, and seismic measures.
PREREQUISITES
None.
RELATED LECTURES
None.
SUMMARY
The lecture introduces seismicity, explaining the origins of earthquakes and summarises their characteristics in both general and engineering
terms. The need for probabilistic assessments is demonstrated and the concept of response spectra is introduced. The basic approaches for
design against earthquakes and Eurocode 8[1] are presented.
1. INTRODUCTION
Among the natural phenomena that have worried human kind, earthquakes are without doubt the most distressing one. The fact that, so far, the
occurrence of earthquakes has been unpredictable, makes them especially feared by the common citizen, for he feels there is no way to assure
an effective preparedness.
The most feared effects of earthquakes are collapses of constructions, for they not only usually imply human casualties but represent huge
losses for individuals as well as for the community. Thus, although other consequences of earthquakes may include landslides, soil liquefaction
and tsunamis, it is the aim in this lecture to study seismic motion from the point of view of the natural hazard it poses to construction, and
particularly to steel structures.
The fundamental goals of any structural design are safety, serviceability and economy. Achieving these goals for design in seismic regions is
especially important and difficult. Uncertainty and unpredictability of when, where and how a seismic event will strike a community increases
the overall difficulty. In addition, lack of understanding and ability to estimate the performance of constructed facilities makes it difficult to
achieve the above mentioned goals.
The future occurrence of earthquakes can be regarded as a seismic hazard, whose consequences represent what can be defined as seismic risk.
The separate study of these two concepts is important. The first represents the action of nature and the second the effects on mankind and manmade
structures.
2. THE SEISMIC EVENT
2.1 General
The knowledge and study of past seismic events is an important way of predicting the potential seismic hazard for the different zones of the
earth. Earthquakes have been reported as far back as during the Babylonian Empire or in 780 BC in China.
A region which has suffered large earthquakes (Figure 1) is the circumPacific belt including New Zealand, the Tonga and NewHebrides
Archipelagos, the Philippines, Taiwan, Japan, the Kurile and Aleutian Isles, Alaska, the western coasts of Canada and the United States, Mexico, all the countries in Central America and the western coast of South America from Colombia to Chile. Other regions of the world that
also have been subject to devastating earthquakes in the past are the northern and eastern zones of China, northern India, Iran, the south of the
Arabian Peninsula, Turkey, all the southern part of Europe including Greece, Yugoslavia, Italy and Portugal, the north of Africa and some of
the Caribbean countries.
Worldwide, the most devastating seismic event which has ever happened is believed to be the 1556, January 23rd earthquake in the Shaanxi
Province of China. That earthquake may have caused more than half a million casualties. More recently, two other Chinese provinces, the
Ningxia province in 1920 and the Hebei province in 1976, were hit by earthquakes that may have caused several hundreds of thousands of
dead.
In Europe, earthquakes are reported as far back as 373 BC in Helice, Greece. Other catastrophic earthquakes in Europe occurred in 365, 1455
and 1626 in Naples, 1531 and 1755 in Portugal, 1693 in Sicily, 1783 in Calabria and 1908 in Messina. Each one of these earthquakes is
believed to have caused between 30000 and 60000 deaths. Even if these figures are not totally reliable, they give a dimension of the
consequences or the risk that may result from the seismic hazard in some European countries.
These major earthquakes have each caused not only a large number of human casualties due to the collapse of houses and other buildings, but
also have caused huge economical losses which in some cases took long periods to recover. The large losses, human and economic, that can be
expected from the occurrence of future earthquakes justify special attention being given to the study of earthquake phenomena and the
earthquake hazard.
2.2 Origins of Earthquakes
Earthquakes have their origin in the sudden release of accumulated energy in some zones of the earth's crust and the resulting propagation of
seismic waves.
Wegener introduced the concept of continental drift to explain the origin of the continents, and why the earth's crust is divided into interacting
plates. The zones of the earth where most earthquakes are generated are at the boundaries of the plates. Earthquakes occur in some cases due to
subduction movements between two plates, as is the case of the Pacific plate which moves underneath the South American continent, and in
other cases due to sliding movements between the two plates, as is the case of San Andreas fault in California. In Southern Europe the
boundary between the African and the Euroasiatic plates is responsible for some very large earthquakes, as for example the 1755 earthquake
that destroyed most of the city of Lisbon.
Other zones where earthquakes occur are at the faults in the intraplate regions, due to the accumulation of strains caused by the pressures in the
plate's boundaries. Most of the Chinese earthquakes are generated in the intraplate region. In Europe a similar region is involved for most of
the southern part of the continent but also for some other central and northern areas.
The point or the zone at which the earthquake slip first occurs is commonly designated as the focus or hypocentre. The earthquake focus is
usually at a certain depth, known as the focal depth. The intersection of a vertical line through the focus with the ground surface is known as
the epicentre (Figure 2). Obviously the most affected zones are the ones closer to the focus, showing that distance to the epicentre (or
hypocentre) is a significant factor of seismic hazard.
The sudden release of energy at the focus generates seismic waves that propagate through the rock and soil layers. There are three basic types
of seismic waves; P waves, S waves and surface waves which include the Love and Rayleigh waves. The difference of velocity between the P
and the S waves allows, by means of the difference in the arrival time, the determination of the hypocentral distance. Typical velocities of P
and S waves vary from 100m/sec for S waves in unconsolidated soils (300m/sec for P waves) to 4000m/sec for S waves in igneous rocks
(7500m/sec for P waves).
2.3 Earthquake Characteristic
The "size" of the earthquake or what could be seen as a seismic scale is a very important factor for a correct characterization of its potential
hazard. Intensity and magnitude are two different means of "measuring" an earthquake which are often confused by the media.
The concept of magnitude which was first introduced by Richter and which still carries his name, represents a measure of the earthquake that is
supposed to be independent of the location at which the measurement is obtained. It is related to the amplitude of the seismic waves corrected
with respect to distance. It represents a universal measure of the size of the earthquake, independently of its effects. Although there is no
maximum value for the magnitude of an earthquake, the two largest magnitudes ever observed correspond to the 1906 earthquake off the coast
of Ecuador and the 1933 earthquake off the Sanriku coast in Japan with magnitudes of 8,9. The 1755 earthquake, off the coast of Portugal, is
believed to have been the largest earthquake in Europe with a magnitude of 8,6.
The magnitude of an earthquake can be related to other physical measures of earthquakes such as the total released energy, the length of the
fault rupture, the fault rupture area and the fault slippage or relative displacement suffered between the two sides of the fault. Several
relationships have been proposed by different authors. The ones presented here are merely an indication of the types of relationships. More
accurate expressions can probably be presented for different seismic zones. Approximate relationships between magnitude (M), total energy (E
in ergs), fault rupture length (L in meters), fault rupture area (A in Km2
) and fault slippage displacement (D in meters) are:
Log E = 9,9 + 1,9 M 0,024 M2
M = 1,61 + 1,182 log L
M = 4,15 + log A
M = 6,75 + 1,197 log D
The relationship between energy and magnitude shows that an earthquake of magnitude 8 releases as much as about 37 times the energy
released by a magnitude 7 earthquake. The same observation can be made for the relationships between magnitude and measures of the fault,
showing that an increase of one degree in the Richter scale corresponds to a considerable increase in terms of seismic hazard.
A different way of measuring an earthquake, has been adopted, based on a scale initially proposed by Mercalli and later modified, known as
the Modified Mercalli Intensity (MMI). According to this scale (Table 1), which varies between I and XII, the intensity of an earthquake is
dependent on the observed effects on landscape, structures and people at a given site. Thus, the intensity is variable from place to place and
relies on a subjective appreciation of the earthquake consequences.
3. EARTHQUAKE INPUT FOR STRUCTURAL DESIGN
The fact that, for a given earthquake source and site, there have been no observed earthquakes with a magnitude, intensity, or peak ground
acceleration larger than certain values, does not mean that larger values will not be observed in future. Thus, the maximum possible or
probable values have to be derived using a probabilistic approach. Furthermore, if one derives probabilistic maximum values for earthquakes
that may occur during a certain future period of time, the values will differ from the ones relating to a different period of time. The return
period of an earthquake with given characteristics, can be defined as the inverse of the annual probability of occurrence of that event. The
larger the seismic event, the larger the corresponding return period as shown by the recurrence formulae already presented.
If the earthquake for which the structure has to be designed and its return period are known, and if the period for which the structure is
designed is also known, the probability of the structure being subjected to the earthquake during its lifetime can be determined. Evaluating this
probability is a matter of assessing a parameter of seismic risk. To evaluate the global seismic risk, one should combine this type of
information with the information regarding the single probability of collapse or malfunctioning of the structure if designed according to certain
levels and standards of resistance and ductility.
Different earthquakes lead to dissimilar response spectra. Not only different maximum values of the ground acceleration (ag
) lead to different
maximum spectrum values, but also different accelerograms will result in dissimilar shapes of spectra even with the same ag
. So, the use of
response spectra to characterize a certain potential seismic event, has to take into account the influence of important aspects such as the nature
and distance of the seismic source and the characteristics of the soil.
For these reasons, the evaluation of response spectra for design purposes must include a probabilistic study of the seismic occurrences. The
study will define the maximum ground acceleration and the shape of the spectra to be considered, for each seismic source and each different
kind of soil. This definition is usually obtained by statistical means. The spectra used for design purposes, and the spectra presented in
regulations are usually the smoothed graphs of the maximum credible values of the corresponding spectra, for a certain level of risk
acceptance, in terms of seismic origin and local soil conditions, obtained for different earthquakes.
The different levels of risk acceptance are also related to the importance of the structure to be designed. The catastrophic consequences arising
as a result of collapse or malfunctioning of important buildings and other structures, such as hospitals, fire stations, power plants, schools,
dams, main bridges, etc. requires design to a lower level of risk than for normal structures. This lower level is achieved by designing these
structures to a larger earthquake return period and consequently to higher values of seismic input. This approach corresponds to designing
them to a lower probability of damage and collapse in the event of future earthquakes.
Similarly, different levels of probability of occurrence of earthquakes can also be used for different design philosophies. For regular structures,
the choice of an earthquake level with a very low probability of being exceeded is usually associated with a design aimed at avoiding structural
collapse, and thus human casualties, even if the structure undergoes major damage and has to be rebuilt. For earthquake levels with higher
probability of occurrence, and that may thus occur more often during the lifetime of the structure, the design goal is not to avoid collapse but
rather to guarantee that no substantial damage occurs and that the structure maintains its serviceability.
Usually, the response spectra are presented in normalized form, as is the case of the normalized elastic response spectrum of Eurocode 8. It is
normalized to the peak ground acceleration (ag
), i.e. it is independent of ag and so can be used for different values of the maximum expected
acceleration for the site. This approach allows for the use of the same spectra for different conditions of severity of the ground motion. In other
words, it enables the consideration of earthquakes corresponding to different return periods and thus to different acceptance of seismic risk.
According to Eurocode 8 and other national regulations, the elastic response spectrum to be used for design purposes depends on several
parameters such as the seismic zone, the type of seismic action, the local soil conditions and the viscous damping ratio of the structure.
The seismic zone can be characterized by means of the severity of the seismic action. This characterization is accomplished by normalizing the
response spectra to a certain level of ag
. Usually, the response spectrum for the vertical motion is defined as a percentage of the response
spectrum for the two orthogonal horizontal directions. In Eurocode 8 the suggested percentage is 70%.
The maximum acceleration to be used in each region in Europe is defined according to microzonation studies for each zone, depending on the
local seismic hazard parameters. It is the responsibility of the National Authorities.
The normalized elastic response spectrum e
(T) (Figure 8) is defined by means of four parameters, o
, T1 T2 and k, according to the
following expressions:
0 < T < T1 e
(T) = 1 + T/T1
(o
1)
T1 < T < T2 e
(T) = o
T2 < T e
(T) = (T2
/T)
k o
where
T is the natural vibration period of the structure, or the inverse of the natural frequency (Hz)
o
is the maximum value of the normalised spectral value assumed constant for periods between T1 and T2
k is an exponent which influences the shape of the response spectrum for vibration periods larger than T2
.
The values of the transition periods T1 and T2
, also known as the inverses of the corner frequencies, depend essentially on the magnitude of
the earthquake and on the ratios between the maximum ground acceleration, ground velocity and ground displacement.