Application of Residue Theorem to evaluate real integrations.pptx
Earth quakes
1.
2.
3. An earthquake may be simply described as a
sudden shaking phenomenon of the earth’s
surface.
Earthquake is a natural force which originates
below the earth’s surface, works randomly and
creates irregularities on the earth’s surface.
Study of earthquakes is known as “seismology”.
The records of earthquakes are known as
“seismograms” and the recording instruments are
known as “seismographs” ( seismos means
shaking)
INTRODUCTION :
4. EARTHQUAKE TERMINOLOGY :
Focus or origin or centre or hypocentre : The place of origin of the earthquake in
the interior of the earth.
Epicentre : The place on earth’s surface, which lies exactly above the centre of
the earthquake.
Anticentre : The point on earth’s surface diametrically opposite to the epicentre.
Seismic vertical : The imaginary line which joins the centre and the epicentre.
Isoseismal : An imaginary line joining the points of same intensity of the
earthquake.
Coseismal : An imaginary line joining the points at which the earthquake waves
have arrived at the earth’s surface at the same time.
Seismic waves : The enormous energy released from the focus at the time of
earthquake in the form of waves and transmitted in all directions.
6. Shallow earthquakes : Earthquakes
with a focus depth less than 60 km.
Intermediate earthquakes : If the
depth is more than 60 km but less than
300 km, they are called intermediate
earthquakes.
Deep earthquakes : Earthquakes
originating at depths greater than 700 km
which are extremely rare.
BASED ON DEPTH OF THEIR ORIGIN :
7.
8. Tectonic earthquakes : Tectonic
earthquakes are exclusively due to
internal cause i.e., due to disturbances
or adjustments of geological formations
taking place in the earth’s interior.
They are less frequent, but more
intensive and hence more destructive in
nature.
BASED ON CAUSES RESPONSIBLE FOR
THEIR OCCURRENCE :
9. Non-tectonic earthquakes : These are generally due to
external or surfacial causes. This type of earthquake is very
frequent, but minor in intensity and hence generally not
destructive in nature. These occur due to various reasons as
follows :
• Due to huge waterfalls
• Due to avalanches
• Due to meteorites
• Due to the occurrence of sudden and major landslides
• Due to volcanic eruptions
• Due to tsunamis
• Due to man-made explosions
• Due to dams and reservoirs
10. SEISMIC BELTS AND SHIELD AREAS
Seismic belts are those places where earthquakes occurs frequently.
Occurrence of an earthquake in a place is an indication of underground instability
there.
Statistics have revealed that nearly 50% of earthquakes have occurred along
mountain ridges and 40% of earthquakes along steep coasts.
Earthquakes takes place on land most frequently along two well-defined tracts, i.e.,
seismic belts.
1. Circum Pacific belt : Accounts for 68% of earthquake occurrence.
2. Mediterranean belt : Accounts for 21% of earthquake occurrence. It extends east-
west from Portugal, through central Europe, Asia minor, Himalayas and Burma to
the East Indies with a branch through Tibet and China.
A minor belt of epicentres occurs along the mid-atlantic ridge.
11.
12. Shield areas are those places where earthquakes
occur either rarely or very mildly.
The regions where Archaean formations occur are
very stable and more or less free from earthquake
occurrences. Such areas are rightly described as shield
areas or aseismic areas.
In India, a major portion of Indo-Gangetic plains is
prone to the occurrence of major earthquakes.
The peninsular area is a stable shield area, though
some intense earthquakes like the Koyna earthquake
of 1967 have occurred.
15. Tectonic earthquakes are associated with the faulting
phenomena. The Elastic Rebound hypothesis has been
postulated by Reid to explain the mode of origin of
tectonic earthquakes. It is as follows :
“Underneath the earth’s surface, the beds or masses of
rocks are deformed and strained due to the differential
stresses.
In initial stages, accumulation of strain is accommodated
by bending.
When the stress acts further and exceeded the elastic
limit if formation, it is no longer bends, but breaks
suddenly along a fracture at the bend and broke, as a
result faulting appears.
During this the enormous energy stored gets released
instantaneously, causing severe vibrations which are
propagated in the form of earthquake waves”.
16. EARTHQUAKE WAVES
Earthquake vibrations originate from the focus
and are propagated in all directions. These
vibrations travel through the rock in the form of
elastic waves.
Mainly, there are three types of waves called
P waves, S waves and L waves.
17. These are variously called primary waves, push-pull waves,
preliminary waves, longitudinal waves, compressional waves,
etc.
These are fastest among the seismic waves.
They travel as fast as 8 to 13 km per second.
When an earthquake occurs, these are the first waves to
reach any seismic station and hence first to be recorded.
P waves resemble sound waves.
These waves are capable of travelling through solids, liquids
and gases.
P WAVES :
18.
19. These are also called shear waves, secondary waves,
transverse waves, etc.
Compared to P waves these are relatively slow.
They travel at the rate of 5 to 7 km per second.
In nature these are like light waves.
Transverse particle motion is characteristic of these
waves.
These waves are capable of travelling only through
solids.
S waves may sometimes show the polarization
phenomenon.
S WAVES :
20.
21. These are called long waves or surface waves.
These are slowest among the seismic waves.
They travel at the rate of 4 to 5 km per second.
Complex and elliptical particle motion is
characteristic of these waves.
These waves are capable of travelling through solids
and liquids.
These are called surface waves because their journey
is confined to the surface layers of the earth only.
They are complex in nature and are said to be one of
two kinds, namely, Raleigh waves and Love waves.
L WAVES :
22.
23.
24. The intensity of an earthquake refers to the degree
of destruction caused by it.
It depends upon some of the factors are as follows :
1. Distance from the epicentre
2. Type of construction
3. Compactness of the underlying ground
4. Magnitude of the earthquake
5. Duration of the earthquake
6. Depth of the focus
INTENSITY OF EARTHQUAKES
25.
26. MAGNITUDE OF THE EARTHQUAKE
The intensity of an earthquake is a function of the magnitude of that earthquake.
This magnitude may be defined as the rating of an earthquake based on the total
amount of energy released when the earthquake occurs.
In other words, the earthquake magnitude is a measure of the amount of energy
released by he earthquake.
Let, E = released energy ( erg ) M = magnitude
h = depth of focus ( km ) C = 0.625 ( constant )
a = ground acceleration
D = distance of the recording station from the epicentre ( km )
The relation between E, M and a is log E =4.4 + 2.14M – 0.054M^2
Where √E = C(a/h)(D^2 + h^2)
27. Charles Richter of the California Institute of Technology
proposed this scale, using the size of the surface waves as
recorded by Wood Anderson type torsion seismograph.
Earthquakes may have Richter magnitudes from 3 to 9 ( max.
8.9 only ).
No shock smaller than 5 cause severe damage.
Magnitude 2 is the smallest tremor that can be felt.
An earthquake of magnitude 5 may cause damage within a
radius of about 8 km, but that of magnitude 7 may cause
damage in a radius of 80 km, and that of 8 over a radius of
250 km.
THE RICHTER SCALE :
28. The energy released in earthquakes of different magnitudes is as follows :
M ( Richter ) = 5.0 ; 6.0 ; 6.5 ; 7.0 ; 7.5 ; 8.0 ; 8.4 ; 8.6
E ( 10^20 erg ) = 0.08 ; 2.5 ; 14.1 ; 80 ; 446 ; 2500 ; 10,000 ; 20,000
29. Approximate relationship between magnitude and and maximum intensity in the
epicentral area is as follows :
Richter scale → 5.0 ; 6.0 ; 6.5 ; 7.0 ; 7.5 ; 8.0
Maximum intensity VI-VII ; VII-VIII ; VIII-IX ; IX-X ; X-XI ; XI
31. To locate the epicenter of an earthquake, scientists must have
seismograms from at least three seismic stations.
The procedure for locating an epicenter has three steps:
1. Scientists find the difference between the arrival times of
the primary and the secondary waves at each of the three
stations.
2. The time difference is used to determine the distance of the
epicenter from each station. The greater the difference in
time, the farther away the epicenter is.
3. A circle is drawn around each station, with a radius
corresponding to the epicenter’s distance from that station.
The point where the three circles meet is the epicenter.
32.
33. DETERMINING THE DEPTH OF THE FOCUS OF AN
EARTHQUAKE
E (m ) d
Θ G (n)
h
r
F
E = epicentre
G = a station where the intensity is known
m = intensity at the epicentre
n = intensity at G
d = distance between E and G
h = depth of focus
Θ is calculated by ;
n/m = h^2/r^2 = sin^2 Θ
h = d tan Θ
34. EFFECTS OF EARTHQUAKES
Destruction of various civil engineering constructions like dams, bridges, tunnels,
roads and railway tracks.
Creation of irregularities and cracks on the ground, contributing problems for
communication systems.
Causing landslides and unstable conditions along hill slopes.
Changes in courses of rivers due to faulting across them.
Formation of new lakes, springs and waterfalls due to disturbances caused in surface
and subsurface conditions. It may cause disappearance of old lakes, springs etc.
Submarine earthquakes cause tsunamis, which are giant tidal waves.
Subsidence if land mass.
Heavy loss of life and property.
35. CIVIL ENGINEERING CONSIDERATIONS IN
SEISMIC AREAS
A civil engineer should think of his constructions immune to
earthquakes.
The difficulties in achieving this objective arise due to the fact that
it is not possible to predict crucial factors like :
i. The exact place of earthquake occurrence
ii. The magnitude of the earthquake
iii. The duration of the earthquake
iv. The direction of movement of the ground at the time of the
earthquake
36. Base shear force, F = a/g . W
a = acceleration due to expected earthquake
g = acceleration due to gravity
W = weight of the structure
a/g = seismic factor ( varies from 0.1 g to 0.001 g )
The overturning moment, M = FY
Y = vertical distance
Based on this value of M, safety factor is incorporated into
the design.
IS codes 1893-1970 gives guidelines to design in seismic areas.
SAFETY FACTOR :
38. CONSTRUCTION OF BUILDINGS
Buildings should be founded on hard bedrock only.
The foundation should be of the same depth throughout for continuity.
For large buildings, raft types of foundations are desirable.
Square foundations are more stable.
Buildings should have light walls.
Only rich cement mortar and reinforced concrete should be used.
Doors and windows should be kept to a minimum.
The building should have uniform height.
Building should have flat RCC roofs.
It is necessary to avoid resonance.
39. CONSTRUCTION OF DAMS
When an earthquake occurs, a dam is subjected to 2 types of forces which affect the
stability of dam.
1. Force due to dam
2. Force due to reservoir water
Horizontal inertia force of dam, Ve = w . c
w = concrete load
c = seismic factor i.e., a/g
Forces due to reservoir water is known as hydrodynamic forces.
It can be calculated by, Pe = C a . W . h
Pe = pressure at depth ‘y’ C = coefficient for shape of dam
h = maximum depth of the reservoir
40. The failure of a dam during an earthquake may be due to the
vibration effect or due to shearing forces or both.
It is essential to provide a clay core within the structure which
makes the dam impermeable and stable.
The general considerations for all types of dams are:
i. Dams should be designed in such a way that during an
earthquake they move along with the foundations below.
ii. Dams should not ordinarily be built along or across the faults
because possible slippage along these planes during
earthquakes will introduce additional complications.
iii. The resonance factor should also be given due consideration.
41. Reservoir- related Earthquakes
The magnitude of the earthquakes increased when the reservoirs
became full.
Example : Koyna earthquake in Maharashtra
The epicentres lay within the reservoir area.
To prevent the occurrence of earthquakes ;
Reservoirs can be filled to a limited safe level.
The pore pressure is reduced by draining the water from the weak zone.
42. PLATE TECTONICS
The earth’s outer shell (crust and upper mantle) consists of cool, brittle
rock called the lithosphere.
Seafloors make up the denser, thinner part of the
lithosphere. Continental crust makes up the less dense, thicker
part. The plastic layer beneath is called the asthenosphere.
Plates move by convection currents flowing in the warm, plastic
asthenosphere zone beneath the plates.
The lithosphere is broken up into separate plates, which include
continents and ocean basins.