EEE: 1.4: Intensity of Earthquake (Theory part)

INTENSITY OF AN EARTHQUAKE:

                        “ Intensity of an earthquake is an evaluation of the severity of ground motion at a  given location and is represented by numerical index”

      Generally destruction is described in terms of the damage caused to buildings, dams, bridges and so on as reported by witnesses.

      Initially is generally represented by Roman capital numbers.

Quantitative alignment of numerical value to the earthquake intensity:

Intensity	Observed effects
I	Not felt, except by very few people under special conditions. Detected by Instruments
II	Felt by a few people, especially those on upper floors of buildings. Suspended objects may swing
III	Felt noticeably indoor, parked automobiles may rock slightly
IV	Felt by many people indoors and by a few outdoors. At night, some are awakened. Dishes, windows and doors rattle
V	Felt by nearly everyone. Many are awakened and some dishes and windows are broken. Unstable objects are overturned.
VI	Felt by everyone. Many people are frightened and run outdoors. Some heavy furniture is moved. Some plaster falls.
VII	Most of the people alarmed and run outside. Damage is negligible in buildings of good construction
VIII	Damage is slight in specially designed structures, considerable in ordinary buildings, great in poorly built structures. Heavy furniture is overturned
IX	Damage is considerable in specially designed structures. Buildings shift from their foundations and partially collapse. Underground pipes are broken
X	Some well built wooden structures are destroyed. Most masonry structures are destroyed. The ground is badly cracked. Considerable landslides occur on steep slopes
XI	Few, if any, masonry structures remain standing. Rails are bent. Broad fissures appear in the ground.
XII	Virtually total destruction. Waves are soon on the ground surface. Objects are thrown in the air.

      The intensity of earthquake at specific location depends on various factors, important among them is the total amount of energy released.

Measurement of Intensity:

                        Intensity of earthquake is measured by two scales

1. Modified Mercalli (MM) Intensity scale, 1931

2. Medvedev –spoonheuer-Karnik (MSK-64) intensity scale, 1964, are generally used.

1. MODIFIED MERCALLI SCALE:

      It is usually assessed by distribution of questionnaires to or interviewing persons in the affected areas, in addition to the observations of the earthquake’s effects by experience personnel.

      It is apparent that the determination of intensity at a particular site involves considerable subjective judgements and is greatly influence by the type and quality of structures as well as the geology of that area.

      Thus comparison of intensity ratings made by different people in different countries or under different conditions can be misleading.

      From the point of view of a structural engineer, the reported MM intensities mentioned in the following table can be considered only as a very crude quantitative measure of the destructiveness of an earthquake since they do not provide specific information on damage corresponding to the structures of interest in terms of the relevant structural parameters.

Intensity by scale	Mercalli Intensity	Description of characteristic effects	Corresponding Richter magnitude
I	Instrumental	Detected only by seismographs	--
II	Feeble	Noticed only by sensitive people	3.5-4.2
III	Slight	Like the vibrations due to a passing lorry; felt by people at rest, especially on upper floors.	3.5-4.2
IV	Moderate	Felt by people while walking, rocking of loose objects, including parked vehicles	4.3-4.8
V	Rather strong	Felt generally; most people sleeping are awakened and bells ring	4.9-5.4
VI	Strong	Trees, sway and all suspended objects swing; damage by overturning and falling loose objects	4.9 – 5.4
VII	Very strong	General alarm; walls crack, plaster falls	5.5-6.1
VIII	Destructive	Car drivers seriously disturbed; masonry fissures; chimneys fall; poorly constructed buildings damaged	6.2-6.9
IX	Ruinous	Some houses collapse where ground begins to crack, and pipes break open	6.2-6.9
X	Disastrous	Ground cracks badly; many buildings get destroyed and railway lines bet bent; landslides on steep slopes	7.0-7.3
XI	Very disastrous	Few buildings remain standing; bridges get destroyed; all services (Railway, pipes, and cables ) are put out of action ; great landslides and floods	7.4-8.1
XII	Catastrophic	Total destruction; objects thrown in to air, ground rises and falls in waves	>8.1 (Maximum known 8.9)

2. MEDVEDEV – SPOONHEUER – KARNIK Intensity scale (MSK-64 Scale):

      The MSK – 64 intensity scale is prevalent in India and central and eastern Europe.

      Quantitative nature of MSK – 64 scale is apparent from the description of each intensity level which takes into account the type of structure, grade of damage to the structure, and the description of characteristic effects.

      The scale is more comprehensive than MM intensity scale and describes the intensity of earthquakes more precisely.

Intensity	Feature	Description
I	Noticeable	The intensity of the vibration is below the limits of sensibility; the tremor is detected and recorded by seismograph only.
II	Scarcely noticeable (Very slight	Vibration is felt only by individuals at rest in houses, especially on upper floors of buildings
III	Weak, partially observed	The earthquake is felt indoors by a few people, outdoors, only in favorable circumstances. The vibration is similar to the passing of a light truck. Attentive observers notice a slight swinging of hanging objects, somewhat more heavily on upper floors.
IV	Largely observed	The earthquake is felt indoors by many people and outdoors by few. None is frightened. Vibration is similar to heavily loaded truck. Windows, doors, dishes rattle and walls crack. Furniture shakes,. Hanging objects swing. Shock is noticeable in parked cars.
V	Awakening	Felt indoors by all and outdoors by many. People awake. Few run outdoors. Animals become uneasy Buildings tremble throughout. Hanging objects will swing considerably The sensations of vibration are similar to heavy objects falling inside the buildings Slight damage may occur to buildings of Type A
VI	Frightening	Felt by most people indoors and outdoors. Few persons lose their balance. Domestic animals run out of their stalls Dishes, glassware may break. Heavy furniture moves, bells ring Cracks up to widths of 1cm are possible on wet grounds Landslides in mountain areas Grade 1 damage to Type B buildings Grade 2 damage to Type A buildings
VII	Damage of buildings	Many people run outdoors and many find it difficult to stand. The vibration is noticed by persons driving motor cars. Landslides on steep slopes Cracks in roads Underground pipelines are damaged Cracks in stonewalls are observed Water in well get turbid by mud stirrup Grade 1 damage to type C buildings Grade 2 damage to type B buildings Grade 3 damage to type A buildings
VIII	Destruction of buildings	Persons driving motor cars are disturbed Branches of trees break off Heavy furniture moves and overturns. Hanging lamps are damaged Memorials and monuments will twist Stonewalls collapse Landslips on steep slopes Cracks in ground up to width of several centimeters are observed Grade 2 damage to type C buildings Grade 3 damage to type B buildings Grade 4 damage to type A buildings
IX	General damage of buildings	Considerable damage to buildings. Animals run in confusion. Monuments and columns fail Considerable damage to reservoirs Underground pipes are broken Railway lines bent Roadways damaged. Overflow of sand, water and mud Fall of rocks and land slides Dry wells renew their flow and wet wells may dry up Grade 3 and 4 damages to type C buildings Grade 4 and 5 damages to type B buildings Grade 5 damages to type A buildings
XI	Destruction	Severe damage to well built buildings, water dams, and heavy railway lines. Highways become useless Underground pipes are destroyed Ground is considerably destroyed by broad cracks and fissures and movement in horizontal and vertical directions Numerous landslips and landfalls occur The intensity of earthquake required to be investigated specifically.
XII	Landscape changes	All structures above and below ground are greatly damaged and destroyed The surface of ground is radically changed Considerable ground cracks with extensive vertical and horizontal movements. Lakes are damaged Rivers are deflected. This intensity of earthquake required special investigation

Note1:Types of Buildings Type A buildings: Building in field stone, rural structures, unburnt brick houses, clay houses etc Type B buildings: Ordinary brick buildings, buildings of large blocks and prefabricated type, half timbered structures, buildings in natural hewn stone. Type C buildings: Reinforced buildings, well built wooden structures Note 2: Types of damages Grade 1 : Slight damage: Slight cracks in plaster, fall of small pieces of plastering Grade 2: Moderate damage:  Small cracks in plaster, fairly large pieces of plaster falls, cracks in chimneys, parts of chimneys fall down Grade 3: Heavy Damage: Large and deep cracks in plaster, fall of chimneys Grade 4: Destruction: Gaps in walls, parts of buildings may collapse, separate parts of buildings lose their cohesion, inner wall collapse Grade 5:Total damage: Total collapse of buildings

 

EEE: 1.3: Magnitude of Earthquake and its measurement

MAGNITUDE OF EARTHQUAKE:

      The magnitude of earthquake is a measure of the amount of energy released.

      It is actually a measure of earthquake size and is determined from the logarithm of the maximum displacement or amplitude of the earthquake signal as seen on the seismogram, with a correction for the distance between the focus and seismometer.

      Earthquake magnitudes are based on direct measurement of size amplitude of seismic waves, made with recording instruments.

      The total energy released by an earthquake can be calculated from the amplitude of waves and distance from epi-center.

      The amount of ground shaking is related to the magnitude of earthquake

      Earthquake magnitude and most often reported using the RICHTER magnitude scale.

Amplitude: Amplitude of a wave is its maximum disturbance from its undisturbed position

 

      

     The Richter magnitude is based on the energy release of earthquake which is closely related to the length of the fault on which slippage occurs.

      A magnitude number is assigned to an earthquake on the basis of the amount of ground displacement or vibration procedures as measured by seismograph.

      The Richter scale is a logarithmic scale, meaning that an earthquake of magnitude 4 causes 10 times as much as one of the magnitude 2 and so on.

      To say simply, the magnitude ‘x’ is 33 times more than previous one.

Fig: Richter scale graphic representation

      Technically there is no upper limit for Richter scale.

      It must be noted that the Richter scale number is not a good measure of damage potential of an earthquake the longer duration of shaking may produce greater damage.

MEASUREMENT OF MAGNITUDE:

      The magnitude (M) of the earthquake is given by

M  =   log10(A)

 

                                   

Where,            

A= Maximum amplitude (µm) at a point 100km from epicenter

      However a standard seismometer is not always set at a point 100km from the epi-center in which case one may use the logarithmic form of Richter magnitude scale, ‘M’ is given as

M   =   log10(A)  - log10 (A0)

 

               Where, A₀ à Amplitude for a particular earthquake selected as standard

                        A à Maximum recorded trace amplitude for a given earthquake at a distance.

      We have another equation to calculate the magnitude using special factors, which is better than previous one. Because the magnitude is a measure of seismic energy related, which is proportional to A/T.

M   =  log10(A/T)max  +  σ(δ, h)  +  Cr  +  Cs

 

                       Where,

                       A = Ground displacement amplitude

                       T= Time period of considered wave

                       σ(δ, h)  = Distance correction factor at epi central distance (δ) and focal depth (h)

                       δ = Epicentral distance

                       h = Focal depth

                       C_r= Regional source correction factor

                       C_r = Station correction factor.

      The Magnitude can also be expressed in terms of length of fault line ‘L’ as

M   =  0.98 log10 (L) + 5.65

 

Where, L =  Length of fault line.

      The Magnitude in terms of slip ‘U’ in the fault line can be given as

M = 1.32 log10 (U) + 4.27

 

Where, U = Slip in the fault line

      The value of surface wave magnitude is given by

M = log10 (As/T)max­  +  1.66 log10 δ  +  3.3

 

                   Where,

                   A_s à Amplitude of horizontal ground motion in μm.

                   T à Time period (20±2 s)

                   δ à Epicentral distance indegrees

      Body wave Magnitude is given by equation

Mb  =  log (As/T)max  + σ(δ, h)

 

                     Where,

                     σ(δ, h) à correction factor

                     δ à Epi central distance

                     h à Focal depth

      Gutenberg and Richter have given following relationship between energy of seismic waves and magnitude of surface waves, M_s.

Log10(E)  =  4.4 + 1.5 Ms

 

                            Where,

                            E à Energy of seismic wave

                            M_s à Magnitude of surface wave

•       All the magnitudes numerically give similar results.
•      
  Additional magnitude scales such as moment magnitude (M_w) have been introduced to improve the standards.
•       The moment magnitude may be calculated using the relationship given by Kanamore.

M  =  2/3 [log10(M0 – 16)

 

                        Where,

                        M_w à Moment magnitude

                        M₀ à Seismic moment in (dyne-cm)

                        M₀  = μAd

                        A à Area of rupture

                        d à Displacement