tb lecture11 earthquakes

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EGN EGN -- 5439 The Design of Tall Buildings 5439 The Design of Tall Buildings

Lecture #11 Lecture #11

Earthquakes Earthquakes

© L. A. Prieto-Portar - 2008



On 8 October 2005, an

earthquake of magnitude 7.6hit Islamabad, Pakistan, killing

30,000 and seriously injuring

another 60,000.

Some structures collapsed nextto others of the same age that

remained intact.

This zone was classified as 2b

(magnitude 5.5 to 6.5)considered as only moderate.

The UBC was applied by

private consultants.



Seismic analysis and design is commonly based on the simplistic model of a structure’sbehavior under seismic “static” loads.

Important structures however, require that highly competent engineers know how to

analyze structures under complex dynamic loads, such as gusting high winds,

earthquakes and bomb blasts.

Examples of these dynamic loads are predominantly earthquakes. However, there is

an increasing interest on the effects from bomb blasts. Other common dynamic loads

are the operation of very heavy or unbalanced machinery, mining, construction (such

as pile driving, deep dynamic compaction, etc), heavy traffic, wind and wave actions.

The study of most dynamic loads show patterns that can be used to simplify their

study. Some of these simplifications are shown in the following slides.



This plot represents the intensity of the load from a low-speed

machine versus time upon its foundation.



The previous real-time plot is typically simplified to this type of

sinusoidal idealization.



This diagram shows the loading upon the soil below a foundation invert due to a

vibrating machine. Notice the static load offset.



A rotating machine that has an unbalanced mass will generate these centrifugal forces.



Dynamic loads vary in their magnitude, direction or position with time. It is possible

for more than one type of variation to coexist. Earthquake loads, for example, vary

both in magnitude and direction. Thus, they have three orthogonal directions and

their corresponding rotation components: a total of six component forces and

moments which each vary in magnitude with time.

The figure above could be a wheel load rolling over a bridge deck, and is the instance

of a force that varies in location with time. This is a periodic load, and the era of load

duration is a cycle of motion. The time taken for each cycle is the period. The inverse

of the period is the number of cycles per second, the frequency of the load.



A simplified loading diagram of the single impact of a steel hammer upon a steel plate.



Contrast the simple hammer plot on the previous slide to this plot that shows the

vertical acceleration of soil particles close to a pile driving hammer when it hits the

pile head-cushion interface.



The blast wave or shock wave that is caused by the detonation of a conventional

explosive such as TNT or ANFO (ammonium nitrate/fuel oil) results in the rapidrelease of a large amount of energy. This is shown by the peak overpressure (pressure

above atmospheric pressure) whose front consists of highly compressed air. The rapid

decrease occurs as the shock wave propagates outward from the center of the

explosion. Clearly, the effect of the shock is not only a function of the amount of

energy from the explosion, but also the distance. The overpressure rapidly decreasesbehind the wave front, and thus the pressure can become negative.



This plot is the North-South accelerogram of the El Centro, California earthquake that

took place on 18 May, 1940.



Acceleration, velocity and displacement and velocity plots from El Centro, CAearthquake, also N-S axis.



Similar oscillatory motions occur upon a building’s frame when loaded by steadywind loads and superimposed gusts.



The U.S. Geological Survey provided this National Seismic Hazard Map in 1996 for the

Continental United States. The map shows the level of ground shaking with a 10% probability of being exceeded in 50 years (a 475-year return period). The colors show PGA (the measure of

earthquake shaking) as a percent of the forge of gravity (g). Frankel, et al, 1997, GeotechnicalFabrics Report, May 2002.



The Nishinomiya bridge failure in January 17, 1995 was due to very large horizontal

displacement of the soil sub-grade. Notice the 2 meter displacement of the pier head.

2 m displacement



The Hanshin Expressway collapse was due to the very large horizontal components of

the Hyogo-Ken Nambu earthquake of January 17, 1995 in Kobe, Japan.



This Hanshin Expressway pier collapsed due to the very large vertical component of the Hyogo-Ken Nambu earthquake of January 17, 1995 in Kobe, Japan.



Definitions.

Focus – point of rupture of a fault

Focal depth

1. Shallow-focus: 0 to 70 km deep;(constitute about 75% of all earthquakes);

2. Intermediate-focus: 70 to 300 km deep;

(constitute about 22% of all earthquakes);

3. Deep-focus: 300 to 700 km deep;

(constitute about 3% of all earthquakes).

Epicenter

Epicentric distance

Hypocentric distance

L



The effective distance to the causative fault.

This distance is the epicentric distance should be to the midpoint of the fault length.

Length L of the

fault rupture.

Length L of the

fault rupture.

epicentric distance

epicentric distance



In the figure below, the hanging wall is thrust upward and over the footwall. This is

called a reverse thrust fault. Other types of faults between these two blocks can be

normal , oblique and strike-slip faults.



Recorded number of incidents and their magnitude for the island of Kauai.



P-wave map plotted on a world surface map.



Plot of the P-wave through a cross-

section of the earth’s sphere, showinghow the wave is both reflected and

refracted by the solid and liquid

core, upper and lower mantles and

the thin surface crust.

Notice that some zone do not receive

seismic waves due to the geometry of

the strata. This zone is called the

“shadow zone”.



A sudden displacement of the crust is called a slip. Slips are described according to

their movement. For example, when a person stands on either side of the San Andreas

fault in mid-California, and looks across the fault, that fault’s movement will towardsthat person’s right. Therefore, the San Andreas fault is a right-lateral movement. The

other three types of movements are left-lateral , normal and reverse.

The process where an oceanic plate slides beneath a continental plate is known as a

subduction. This is the case for the Pacific plate that is sliding beneath the NorthAmerica continental plate. The seismic activity common to the states of California,

Oregon and Washington ensues from this subduction.

The seismic waves radiate out of from the focus. The compression waves (primary or P-

waves) travel through the earth’s interior to reach the surface first. These compressionwaves displace materials directly behind or ahead of their path of travel.

The shear waves (secondary or S-waves) displace material at right angles to their line of

travel and reach the surface later. These shear waves have horizontal and vertical

components since their propagation path may be in any direction from the source.

The S-waves travel more slowly than the P-wave, but they transmit more energy. Thus,

S-waves cause the bulk of the damage to surface structures.



The three primary causes of seismic waves (vibrations) are, (1) the sudden

dislocations and changes within the earth’s crust plates due to their movements

against each other, (2) volcanic eruptions, and (3) deep artificially induced explosions.

During an earthquake, the sudden changes in the sea floor at depth (large rising and

dropping) set a massive wave in the water in motion. As the wave approaches a land

mass, the deep sea floor transitions gradually to a shallower floor. Since the wave has

a constant mass, this change causes the wave height to increase. Also, its velocitydecreases due to the increased friction with the shallower floor.

Sea waves are called tsunami (which means “sea wave” in Japanese). Other

synonymous terms are tidal wave and surface-water wave.

Seismic waves are measured with a seismometer. The seismometer measures the

actual displacement of the ground with respect to a fixed reference point. The

magnitude M of the earthquake can be calculated from the logarithm of the amplitude of the displacement.



Intensity. The Modified Mercalli Scale divides the intensity into an arbitrary scale of

12 levels of intensity. It is commonly used in the United States.



Date UTC Location Deaths Magnitude Comments

1556 01 23 China, Shansi 830000 ~8

2004 12 26 Sumatra 283106 9.1 Deaths from earthquakeand tsunami.

1976 07 27 China, Tangshan 255000(official) 7.5 Estimated death toll ashigh as 655,000.

1138 08 09 Syria, Aleppo 230000

856 12 22 Iran, Damghan 200000

1927 05 22 China, Tsinghai 200000 7.9 Large fractures.

1920 12 16 China, Gansu 200000 7.8 Major fractures, landslides.

893 03 23 Iran, Ardabil 150000

1923 09 01 Japan, Kanto

(Kwanto)

143000 7.9 Great Tokyo fire.

1948 10 05 USSR(Turkmenistan,Ashgabat)

110000 7.3

1908 12 28 Italy, Messina 70000 to100000

(estimated)

7.2 Deaths from earthquakeand tsunami.

1290 09 China, Chihli 100000

2005 10 08 Pakistan 80361 7.6

1667 11 Caucasia,Shemakha

80000

1727 11 18 Iran, Tabriz 77000

1932 12 25 China, Gansu 70000 7.6

1755 11 01 Portugal, Lisbon 70000 8.7 Great tsunami.

1970 05 31 Peru 66000 7.9 $530,000,000 damage,great rock slide, floods.

1935 05 30 Pakistan, Quetta 30000 to60000

7.5 Quetta almost completelydestroyed.

1693 01 11 Italy, Sicily 60000

1268 Asia Minor, Silicia 60000

1990 06 20 Western Iran 40000 to50000

7.7 Landslides.

1783 02 04 Italy, Calabria 50000

NOTE: Some sources list an earthquake that killed 300,00 people in Calcutta, India, on October 11, 1737.Recent studies indicate that these casualties were most likely due to a cyclone, not an earthquake.

(Source: The 1737 Calcutta Earthquake and Cyclone Evaluated by Roger Bilham, BSSA, Vol. 84, No. 5, 1650-1657, October 1994)



Largest Earthquakes in the World Since 1900.

Location Date UTC Magnitude Coordinates Reference:

1. Chile1960 05 229.5-38.24-73.05Kanamori, 19772. Prince William Sound, Alaska1964 03 289.261.02-147.65Kanamori, 19773. Off the West Coast of Northern Sumatra2004 12 269.13.3095.78PDE4. Kamchatka1952 11 049.052.76160.06Kanamori, 19775. Off the Coast of Ecuador1906 01 318.81.0-81.5Kanamori, 1977

6. Rat Islands, Alaska1965 02 048.751.21178.50Kanamori, 19777. Northern Sumatra, Indonesia2005 03 288.62.0897.01PDE

8. Andreanof Islands, Alaska1957 03 098.651.56-175.39Johnson, 19949. Assam - Tibet1950 08 158.628.596.5Kanamori, 197710. Kuril Islands1963 10 138.544.9149.6Kanamori, 197711. Banda Sea, Indonesia1938 02 018.5-5.05131.62Kanamori, 197712. Kamchatka1923 02 038.554.0161.0Kanamori, 1988

Updated 2006 May 02.

References:

Johnson, J.M., Y. Tanioka, L.J. Ruff, K. Sataki, H. Kanamori, and L.R. Sykes, 1994, The 1957 great Aleutian earthquake, Pureand Appl. Geophysics, 142, 3-28. Kanamori, H., 1977, The energy release of great earthquakes, J. Geophysical Res. 82, 2981-2987.

PDE (Preliminary Determination of Earthquakes) Monthly Listing, U.S. Geological Survey, Golden, CO.

Revisions:

The Andreanof Islands, Alaska earthquake of 1957 03 09, previously listed with a magnitude o f 9.1, has had its magnitudereviewed, and it was updated to 8.6. The Ningxia-Gansu, China earthquake of 1920 12 16, previously listed with a magnitude of 8.6 , has had its magnitude reviewed, and it was updated to 7.8. The Tonga earthquake of 1917 06 26, previously listed with amagnitude of 8.5, has had its magnitude reviewed, and it was updated to 8.4. The Chile-Argentina earthquake of 1922 11 11,previously listed with a magnitude of 8.5, has had its magnitude reviewed, and it was updated to 8.0.

U.S. Department of the Interior, U.S. Geological Survey. URL: http://earthquake.usgs.gov/regional/world/10_largest_world.php.



The earthquake’s magnitude M.

The magnitude M is a measure of the amplitude of the elastic waves generated by anearthquake.

In 1958, C.F. Richter proposed measuring the earthquake’s strength via its

magnitude M , which is related to the length of the fault slip L. His formula was,

log10 E = 11.4 + 1.5 M

where E is the energy released by the earthquake in ergs.

This equation was modified by Båth in 1966 to,

log10 E = 12.24 + 1.44 M

and again modified by Tocher (1958), Bonilla (1967) and Houser (1969) as,

log L = 1.02 M – 5.77

where L is the length of the fault’s rupture in kilometers.

Th i b t th Ri ht it d l d th M difi d M lli



The comparison between the Richter magnitude scale and the Modified Mercalli

intensity scale is approximately as follows,

A brief list of some recent major earthquakes is,

28 March 2005 Northern Sumatra (Indonesia) 8.7

26 December 2004 West coast of northern Sumatra 9.0

23 December 2004 Macquarie Island, Pacific Ocean 8.1

17 November 2003 Rat Islands, Alaska 7.8

25 September 2003 Hokkaido, Japan 8.303 November 2002 Denali Park, Alaska 7.9

23 June 2001 Coastal Peru 8.4

16 November 2000 Papua New Guinea 8.0



Example 1.

Using the Tocher equation, calculate the length of the fault rupture for an earthquakeof magnitudes 6, 7 and 8.

10

10

10

2 2

6

1 02 5 77 1 02 6 5 77 0 35

7

1 02 5 77 1 02 7 5 77 1 37

8

1 02 5 77 1

4

23 4

245

02 8 5 77 2 39

For a magnitude M ,

log L . M . . ( ) . .

For a magnitude M ,

log L . M . . ( ) . .

For a magnitude M ,

log L . M .

L . kilo

.

meters

L . kilometers

L ki

(

l

) .

o

.

=

= − = − =

∴

=

= − = − =

∴

=

=

=

− = − =

∴

=

=

meters

Note that each unit increase in magnitude corresponds to an increase of one order of

magnitude.



The amount of energy in a seismic wave decreases when it propagates through rock,

and this decrease is called attenuation.

Since attenuation is a decrease in the seismic energy, the factors that influence it are,

(1) the path line,

(2) the path length,

(3) the nature of the intervening geologic formations,(4) the focal depth, and

(5) the location of the epicenter.

The magnitude of an earthquake does not decrease the amount of energy.

Th ti f k d i th k



The motion of rocks during an earthquake.

The effects of an earthquake upon the surface are due primarily to the upwardpropagation of shear waves through the underlying soft rocks. The P-wave produces

vertical motion, but the S-wave is the one that produces the large two horizontal

components of the surface motions.

The typical shear wave velocity in a hard rock such as granite is about 10,000 to12,000 ft/s. In contrast, the velocity in a soft rock such as sandstone can be as low as

2,000 ft/s.

The nature of the surface ground motions were studied by Seed, Idriss and Kiefer in

1969 and they proposed that three factors need to be understood:

- (a) duration of the earthquake,

- (b) predominant period of the acceleration, and

- (c) maximum amplitude of the motion.

A Th d ti f th th k



A. The duration of the earthquake.

The duration is almost identical to the time taken by the fault to rupture. The rate of propagation of a fault rupture has been reported by Housner in 1965 to be

approximately 3.2 km/s. For a given magnitude, the duration can be found from the

Tocher equation that finds L.

Example 2.

If the epicentric distance from an earthquake of magnitude 7 is 88 km, what is the

probable duration of the event?

8827 5

3 2seconds= = =

dis tance km duration

rate of propagation of the fault rupture . km / s .

B The predominant period T of rock acceleration



B. The predominant period T of rock acceleration.

Seed, Idriss and Kiefer prepared in 1969 the graph shown below for thepredominant period T for maximum rock acceleration. The distance plotted below is

approximately the epicentric distance when the fault length is small. When the fault

length is large, the perpendicular distance to the fault line must be used.

Th i d T f th th k f t th d i t i d f th i i



The period T of the earthquake refers to the predominant period of the seismic wave.

It is determined by a Fourier analysis of its wave.

Both the site (local geology and surficial soils) and the building have their own

fundamental or natural periods. Therefore, these three periods are all different.

The site period is determined from geotechnical data. The building’s period is

determined from the analysis of the structure.

The structural damage due to an earthquake depends on (1) the ground acceleration,

(2) the duration of the motion, (3) the frequency content, (4) local soil conditions, (5)

the period of the site, (6) the distance between the focus and the structure, (7) the

intervening geological formations, and (8) the natural frequency of the structure andits damping.

Resonance results in an amplification of the response. It occurs when the earthquake,

the site and the building’s periods coincide with each other. An example of resonance

occurred during the 1985 Mexico City earthquake. The focus was 365 km from thecity, but although the acceleration amplitude was small, its period matched that of the

city’s underlying lake beds. In addition, some of the buildings had natural periods

similar to the seismic wave and local soils. The consequence was a major magnification

of the response, and major collapses of many buildings.

E l 3



Example 3.

What is the effect of placing permanent heavy air-conditioning equipment on the topfloor of a building? How does this affect the fundamental period of the building?

Since,

the stiffness of the building k will not be affected by the installation of the heavy air-

conditioning equipment. However, the mass m does increase, which in turn increases

the fundamental period T of the building.

2 m

T π ππ π =

C. The maximum amplitude of the acceleration. Gutenberg and Richter



C. The maximum amplitude of the acceleration. Gutenberg and Richter

proposed in 1956 a formula for the maximum amplitude of the acceleration a0 in the

rock in the epicenter region for shallow earthquakes, which have focal depths of lessthan 16 km,

log a0 = - 2.1 + 0.81 M – 0.027 M 2

When the earthquake is not shallow, the maximum amplitude decreases rapidly as

shown below,

Example 4



Example 4.

For the magnitudes 6, 7 and 8 earthquake discussed in Examples 1 and 2, what aretheir predominant periods for the maximum rock accelerations?

Using the plot on slide #45, and the distance of 88 km from the causative fault,

- For the magnitude 6 earthquake, the predominant period is 0.35 seconds;



Th it d M f th k h l ti ith ith th l ti



The magnitude M of an earthquake has no correlation with either the acceleration or

duration.

For example, the 1989 Loma Prieta earthquake in the San Francisco area had a

magnitude of 7.1 and registered a peak ground acceleration of 0.65g.

The 1994 Northridge earthquake in the Los Angeles area had a magnitude of 6.7 and

a peak ground acceleration of 1.80g.

The 1971 San Fernando earthquake had a magnitude of 6.6 and lasted only 7 sec.

The 1940 El Centro earthquake had a magnitude of 6.4 and lasted 16 seconds.

The frequency of a seismic wave, its duration and the ground acceleration all affect

the amount of structural damage.

The effects of an earthquake upon the soil’s structural performance



The effects of an earthquake upon the soil s structural performance.

Liquefation is one of the consequences of seismic waves traveling through saturatedloose granular surface soils. Liquefaction is the sudden and dramatic reduction of the

shear strength of the soil, a large increase in its pore water pressure, a complete loss

of the bearing capacity and a decrease in the effective stress of the soil.

Earthquakes can trigger the rapid consolidation of soft clays. The loss of the grain-to-grain contact and the excess pore water pressure leads to a complete loss of the

soil strength.

The soft clay strata tend to increase the amplitude of the earthquake motions, much

more than granular sites.

Earthquakes in California with magnitudes between 8.0 to 8.5 are associated with

ground accelerations of about 0.50g.

The maximum vibration of a single-degree-of-freedom system is measured in termsof acceleration, velocity or displacement. The maximum velocity of a structure

relative to the ground is known as the spectral velocity.

References



References.

Bonilla M.G., “Historic Surface Faulting in Continental United States and Adjacent Parts of Mexico”, Interagency Report, US Department of the Interior, Geological Survey, 1967;

Das, B., “Principles of Soil Dynamics”, PWS-Kent Publishing Co., Boston, 1993;

Gutenberg B., Richter C.F., “Earthquake Magnitude, Intensity, Energy and Acceleration”,Bulletin of the Seismological Society of America, Vol. 46, No. 2, 1956;

Seed H.B., Idriss I., Keifer F.W., “Characteristics of Rock Motion During Earthquakes”,

Journal of the Soil Mechanics and Foundation Division, ASCE, Vol. 95, No. SM5, 1969;

Richter C.F., “Elementary Seismology”, W.H. Freeman, San Francisco, CA, 1958;

Tocher J.E., “Earthquake Energy and Ground Breakage”, Bulletin of the Seismological Society

of America, Vol. 48, No. 2, 1958;

Wiegel R.W., “Earthquake Engineering”, Prentice-Hall, Englewood Cliffs, New Jersey, 1970;

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