Unit-1

1. What is the basic concept of vibration?

Ans. All bodies having mass and elasticity are capable of vibration. When external force is applied on the body, the internal forces are set up in the body which tend to bring the body in the original position. The internal forces which are set up are the elastic forces which tend to bring the body in the equilibrium position. Consider an example of swinging of pendulum. At extreme position whole of the kinetic energy of the ball is converted into elastic energy which tends to bring the ball in the equilibrium/mean position. At mean position whole of the, elastic

energy is converted into kinetic energy and body continues to move in opposite direction because of it. Now the whole of kinetic energy is converted into elastic energy and this elastic energy again brings the ball to the equilibrium position. In this way, vibratory motion is repeated indefinitely and exchange of energy takes place. This motion which repeats itself after certain interval of time is called vibration.

Q. 2. What are the main causes of vibration? Ans. The main causes of vibration are: 1. Unbalanced centrifugal force in the. system due to faulty design and poor manufacturing. 2. Elastic nature of system. 3. External excitation applied on the sysbm 4. Winds may cause vibration of cerim sv stem such as electricity lines, telephone lines etc.

Q. 3. What are the disadvantages of effects of vibration? Ans. Disadvantages harmful effects vibration: 1. Vibration causes excessive and unpleasant stresses in the rotating system. 2. Vibration causes rapid wear and tear of machine parts such as gears and bearings. 3. Vibration causes loosening of parts from the machine. 4. Due to vibrations locomotive can leave the track causing accident or heavy loss. 5. Earthquakes are the cause of vibration because of which buildings and other structures (like bridges) may collapse.

6. Proper readings of instruments cannot be taken because of heavy vibrations. 7. Resonance may take place if the frequency of excitation matches with the natural frequency of system causing large amplitudes of vibration thereby resulting in failure of systems e.g. — Bridges

Q. 4. (a) How can you eliminate/reduce unnecessary vibrations? Ans. Unwanted vibrations can be reduced by: 1. Removing external excitation if possible. 2. Using shock absorbers. 3. Dynamic absorbers. 4. Proper balancing of rotating parts. 5. Removing manufacturing defects and material inhomogeneities. 6. Resting the system on proper vibration isolators.

Q. 4. (b) What are the advantages of vibration? Ans. Advantages of vibration 1. Musical Instruments like guitar. 2. In study of earthquake for geological reasons. 3. Vibration is useful for vibration testing equipments. 4.. Propagation of sound is due to vibrations. 5. Vibratory conveyors are based on concept of vibration. 6. Pendulum clocks are based on the principle of vibration.

Q. 5. What is the importance of vibration study? Ans. Importance of vibration study. The imp of vibration study is to reduce or eliminate vibration effects over mechanical components by designing them suitably. Proper design and manufacture of parts will reduce.unbalance in engines which causes excessive and unpleasent stress in rotating system because of vibration, roper design of machine parts will reduce and tear due to vibration and loosening parts. The proper designing and material distribution prevent the locomotive m leaving the track due to excessive vibration which may result in accident or heavy loss. Proper designing of structure buildings can prevent the condition of resonance which causes dangerously large oscillations which may result in failure of that part.

Q. 6. Define the following: (i) Periodic Motion (ii) Time period (iii) Frequency (iv) Amplitude (v) Natural frequency (vi) Fundamental mode of vibration (vii) Degree of freedom (viii) Simple Harmonic Motion (S.H.M.) (ix) Resonance (x) Damping (xi) Phase Difference (xi,) Spring stiffness Ans. Definitions (i) Periodic motion: A motion which repeats itself after certain interval of time is

called periodic motion. (ii) Time Period : It is time taken to complete One cycle. (iii) Frequency: No’s of cycles in one sec. Units = H (iv) Amplitude: Maximum displacement of a vibrating body from mean position is called Amplitude. (v) Natural frequency: When there is no external force applied on the system and it is given a slight displacement the body vibrates. These vibrations are called free vibrations and frequency of free vibration is called Natural frequency.

(vi) Fundamental mode of vibration: Fundamental mode of vibr!sternis a mode (vii) Degree of freedom:

• The minimum no’s of co-ordinates required to specify motion of a system at any instant is called degree of freedom. (viii) Simple Harmonic Motion (S.H.M..) : The motion of a body “to” and “fro” about a fixed point is called S.H.M. S.FLM.. is a periodic motion and it is function of “Sine” or “Cosine”. Acceleration of S.H.M. is proportional to displacement from the mean position and is directed towards the centre.

In S.H.M. acceleration is directly proportional to the displacement from the mean position and is

directed towards the centre. (zx) Resonance : When the frequency of external force is equal to the natural frequency of a vibrating body, the amplitude of vibration becomes excessively large. This is known as “Resonance” . At resonance there are chances of machine part or structure to fail due to excessively large amplitude. It is thus important to find natural freuqencies of the system in order to avoid resonance. (x) Damping: It is resistance provided to the vibrating body and vibrations related to it are called damped vibration. (xi) Phase difference : Suppose there are two vectors

(xii) Spring stiffness : It is defined as unit deflection. Units : N/m.

Q. 7. What are the various parts of a vibrating system? Ans. Various parts of the mechanical system (vibratory system) are : — (A) Spring (B) Damper (C) Mass

Damping force c ± acting upwards Accelerating force m i acting downwards Spring force kx acting upwards

Q. 8. Explain different methods of vibration analysis ? Ans. Different methods of vibration analysis are: Energy method : According to this method total energy of the system remains constant i.e. sum of kinetic energy and potential energy always remains constant.

Rayleigh Method : This method is based on the principle that maximum kinetic energy of the term is equal to the maximum potential energy of the system.

According to this method the sum of forces and moments acting on the system is zero if no external force is applied on the system. Consider fig. I

Q. 9. Classify different types of vibrations. Ans. Types of Vibrations I. Free and Forced To and fro motion of the system when disturbed initially without any extornal force acting on it are called free vibrations. e.g. pendulum. To and fro motion of the system under the influence of external force are called forced vibrations. e.g. Bell, Earthquake. II. Linear and Non-linear vibrations Linear vibrations : The linear vibrations are those which obey law of superimposition. If a1 and a2 are the solutions of a differential equation, then a1 + a2 should also be the solution.

Non-linear vibrations : When amplitude of vibrations tends towards large value, then vibrations become non-linear in nature. They do not obey law of superimposition. III. Damped and Undamped vibrations Damped vibrations are those in which amplitude of vibration decreases with time. These vibrations are real and are also called transient vibrations.

Undamped vibrations are those in which amplitude of vibration remains constant. In ideal system there would be no damping and so amplitude of vibration is steady. 1V. Deterministic and Random vibrations (Non-Deterministic). Deterministic vibrations are those whose external excitation is known or can be determined whereas Random vibrations are those whose external excitation cannot be determined. e.g. Earthquake V. Longitudinal, Transverse and Torsional vibrations

Q. 10. What are beats? Ans. When two harmonic motions pass through some point in a medium simultaneously, the resultant is the sum of two motions. This superimposition of harmonics is called interference. When two harmonics are in phase then their resultant amplitude is maximum and the resultant amplitude is minimum when two harmonics are out of phase. This phenomenon continuously occurs i.e. amplitude becomes maximum and minimum repeatedly. This is called “beats”. For beats to occur, the difference

in frequencies of two waves should be very less.

Maximum amplitude = 2A Minimum amplitude 0. Q. 13. Split the harmonic motion x = 10 sin (wt + 2r/6) into two harmonic motions one having phase angle of 00 and other having 45° phase angle. Ans. Let the equations are:

Q. 14. Show that the resultant motion of three harmonic motions given below is zero.

Hence proved.

Q. 17. How can we make a system vibrate in one of its natural mode? Ans. When a system is displaced slightly from its equilibrium position and allowed to vibrate then these are called free vibrations and the system is said to vibrate m its natural mode without any external force impressed on it.

Q. 18. How does a continuous system differ from a discrete system in the nature of its equation of motion? Ans. Continuous systems have infinite degree of freedom and so the no. of solutions are infinite. The equation of motion for continuous system involve both displacement (x) as well as time (t). Discrete systems have finite degree of freedom and so the no. of solutions are finite. The discrete systems may be single degree of freedom system, 2 degree freedom system and so on. The number of equations depends upon the degree of freedom of discrete system. Further equation of motion of discrete systems involve only position (x) and not time (t).

Q. 1. What do you mean by undamped free vibrations? Ans. If the body vibrates with internal forces and no external force is included, it is Further during vibrations if there is no loss of energy due to friction or resistance, it is known as undamped free vibration.

Q. 2 Consider the relation for the frequency of spring mass system in vertical position. Ans.

Q. 3. What is D’Alembert’s Principle? Ans. D’Alembert’s principle states that if the resultant force acting on a body along with the inertia force is zero, then the body will be in static equilibrium. Inertia force acting on the body is given by

Assuming that the resultant force acting on body is F, then the body will be in static equilibrium if

Consider fig. 2.2., the spring force of the body Kx is acting upwards and acceleration of the body i is acting in downward direction. The accelerating force is acting downward so inertia force is acting upwards, so the body is M static equilibrium under the action of the two forces Kx and mi. Mathematically it can be written as

Q. 7. Determine the effect of mass of spring on natural frequency of the system as shown in Fig. 2.6. Ans. Let x be the displacement of mass m and so velocity will be x. The velocity of spring element at distance y from the fixed end is given by

where 1 is the total length of spring. Let p be the mass per unit length of spring element, the

Differentiating the above equation

Q. 9. A cylinder of diameter D and mass in floats vertically in a liquid of mass density p as shown in Fig. 2.8. Find the period of oscillation if it is depressed slightly and released. . Ans. Let us assume x be the displacement of the cylinder,

Q. 10. Determine the frequency of oscillation of the system shown in Fig. 2.9.

Q. 11. Determine the natural frequency of spring controlled simple pendulum as shown in Fig. 2.10.

Ans. Let us say the system is displaced by an angle 0 to the right. Equation of motion can be written as;

Q. 12. Determine the natural frequency of the system shown in Fig. 2.11.

Ans. Let m be the mass of circular cylinder and r be the radius of the cylinder.

Differentiating the above equation

Q. 13. The natural frequency of a. spring-mass system is 20 Hz and when extra 3 kg mass is attached to its mass the natural frequency reduces by 4 Hz. Determine the mass and stiffness of the system.

Q. 14. A spring-mass system has a time period of 0.25 sec. What will be the new time period if the spring constant is increased by 30%? Ans. We know

Q. 15. A car is having a mass of 1000 kg and its spring gets deflected 3 cm under its own load.. Find the natural frequency of car in vertical direction. Ans. Stiffness of spring is given by

Natural frequency of spring-mass system in vertical position is given by

Q. 17. Find the natural frequency of the system shown in Figure 2.12.

Ans. Since the three springs are in parallel1 their equivalent sfess can be calculated

Q. 18. A mass is suspended from a spring system as shown in figure 2.13. Determine the natural frequency of the system.

Ans. Since spring k2 and k3 are connected in parallel1 so their equivalent k is given as k = + k3. Again k and k1 are connected in series, so the equivalent ke is given as

The natural frequency

Q. 20. A cantilever beam of negligible mass is loaded with mass 4m’ at the free end. Find the natural frequency of the mass sm’.

Ans. Deflection of cantilever beam loaded at one end can be given as

and therefore stiffness of beam can be calculated as

General equation of motion for undamped free vibration is given as

Q. 21. Determine the natural frequency of the system as shown in figure. 2.16.

Ans. Deflection of such a system is given as

Equation of motion for undamped free vibration is given as

Q. 22. A simply supported beam of square cross section 5 mm x 5 mm and length 1 m, carrying a mass of 2.3 kg at the middle, is found to have a natural frequency of transverse vibrations of 30 rad/s. Determine the Young’s modulus of elasticity of the beam.

Q. 23. A simple pendulum of length L, bob mass m, and rod mass M, is vibrating in the vertical plane. Calculate the frequency of free vibrations.

Q. 1. What is damping? Ans. Damping is the resistance offered by a body to the motion of a vibratory system. The resistance may be applied to liquid or solid internally or externally At the start of the vibratory motion the amplitude of vibration is maximum wkij6es on decreasing with time. The rate of decreasing amplitude depends upon the amount of damping.

Q. 2. Classify different types of damping. Ans. Types of Damping 1. Viscous 2. Coulomb 3. Structural 4. Non-linear, Slip or interfacial damping 5. Eddy current-damping 1. Viscous damping: When the system is allowed to vibrate in viscous medium the damping is called viscous Viscosity is the property of the fluid by virtue of which it offers resistance to moment of one over the other. The force F required . to maintain the velocity x of plate is given by:

The force F can also be written as:

where c is called viscous damping coefficient From (1) and (2),

The main components of viscous damper are cylinder, piston and viscous fluid.

The damping resistance depends upon pressure difference on both sides of piston in viscous medium. The clearance is left between piston and cylinder walls. More the clearance, more will be the velocity of piston and less will be the value of viscous damping coefficient.

Equation of Motion

and B = specific damping capacity 2. Coulomb Damping: When a body is allowed to slide over the other body the surface of o offers resistance to the movement of 9Lod over it. This resisting force is called force of friction.

coefficient of friction

Some of the energy is wasted in friction and amplitude of vibrations goes on decreasing. Such type of damping is called coulomb damping. 3. Structural damping : This type of damping arises because of intermolecular friction beti- the molecules of structure which opposes its movement. The magnitude of this damping is very small as compared to other damping. Elastic materials during loading and unloading from a loop or stress strain curve known as_hysteresis loop. The area of this loop gives the amount of energy dissipated in one cycle during vibrations. This is also called hysteresis damping. The energy loss per cycle is given as;

If energy dissipated is treated equal to energy dissipated by viscous damping then;

The damping’force, F =

The amplitude decay is of exponential nature. 4. &on-linear, p or Interfacial damping : Machine elements are connected through various joints and microscopic slip occurs over the joints of machine elements which usdisspoint of energy when machine elements are in contact with fluctuating load. The energy dissipated per cycle depends upon coefficient of friction, pressure at contacting surface and amplitude of vibration. There is an optimum value of contact pressure at which energy dissipated is maximum for different amplitudes.

5. Eddy current damping : If a non-ferrous conducting object (e.g. plater d etc.) moves in a direction perpendicular lines of magnetic flux is produced by current is induced in the object.1iiiiIrent is proportional to vlocity of the object. The current induced is called eddy current which set up its own magnetic field opposite to original magnetic field that has induced it. This provides resistance to motion object It forms magnetic field . This type of damping produced by eddy currents is called eddy current damping. it is used in vibrometers and in some vibration control systems.

Q. 3. Derive the relation for energy dissipated in viscous damping per cycle. Ans. Energy dissipated in viscous damping per cycle

Q. 4. Prove that frequency of vibration of system having coulomb damping is same as that

of undamped system. Ans. Frequency of damped oscillations

• Free vibrations with dry friction or coulomb damping (b) Mass displaced towards rigit & moving towards right

The frequency of vibration of system having coulomb damping is same as that of undamped system

Q. 5. Prove that amplitude loss per cycle in c4 damping is :

Ans. Rate of Decay of oscillation: Let 1A be the amplitude of body from mean position to start and after half cycle, let x be its amplitude. The velocity of mass =0 at two extreme positions. (Refer Fig. 3.9) Therefore, total energy of the system at two extreme positions be

The difference between the two energies must be equal to energy dissipated or work done against friction.

Q. 6. Differentiate between Coloumb and Viscous damping. Ans. Differences between Viscous damping & Coulomb damping 1. In case of viscous damping ratio of any two successive amplitudes is constant whereas in coulomb damping difference between two successive amplitudes is constant.

2. In viscous damping envelope of the maximas in displacement-time plot is an exponential curve here as in coulomb damping envelope of maximise of displacement-time plot is a straight line. 3. In case of viscous damping the body once disturbed and from equilibrium position will come to rest in equilibrium position although it make theoretically infinite time to do so Whereas in case of coulomb damping the body may finally come to rest in equilibrium position or in displaced position depending upon initial amplitude and amount of friction present.

Q. 7. What is the response of single degree of freedom system with viscous damping when it is:

Ans. Differential equation of damped free vibrations

Solution of equation (1) can be written as

where A1, A2 = Arbitrary constants

Critical damping constant and damping ratio The critical damping c is defined as value of damping coefficient c for which

Depending upon the value of damping ratio e, the damped systems are categorized as:

This motion is also called a periodic motion. When t =0, x = A1 + A2. This system is non-vibratory in nature. When once the system is disturbed, it will take infinite time to come back to the equilibrium condition. The values of A1 and A2 can be found by initial conditions.

The value of displacement x goes on decreasing with time.

In critical damping both roots are equal and are equal to - (0. The solution of critically damped system is given as;

1

I.

The amplitude vary exponentially with time. As time increases amplitude decreases.

An underdamped system is an oscillatory system whose amplitude decreases with time. Theoretically the system will never come to rest although the amplitude of vibration may be very very small.

Q. 8. What is the importance of critical damping? Ans. Out of the three modes the vibrating body which has been displaced from its mean position would come to state of rest in smallest possible time without overshooting i.e. without executing oscillation about mean position in critical damping mode. So critical damping is used for practical applications in large guns so that after firing the returning to original position in minimum time without vibrating and ready for next firing without delay. If damping provided is overdamped or underdamped, then there will be delay. This property is also design of an instrument

Ans. Logarithmic Decrement (Underdamped system) It is defined as the natural logarithmic of ratio of any two successive amplitudes on same side of mean time. Consider fig. 3.13(a). Let us take two successive amplitudes be x1 and x2. Logarithmic decrement 6 is given by;

The time period of damped oscilliations

Q 10. If an underdamped system executes ‘n’ cycles then prove that logrithimic decrement

Q 11. A damping .force having magnitude 2 cos (23rt-44) N, gives 5 cos 2t m displacement. Calculate (a) Energy dissipated during first 5 seconds and (b) Energy dissipated during the first 3/4 sec. Ans. We know the force and displacement are given as:

Q. 14. In Question No. 13 if m = 1.5 kg, K 4900 N/m, a 6 cm and b = 14 cm, determine the value of c for which the system is critically damped. Ans. The equation of motion can be written as;

The system is critically damped when radical is zero

•

Unit-2 1.What are the two degree of freedom system? Ans. The system which requires two co-ordinates to describe its motion completely is called two degree of freedom system. In a two degree of freedom system there are two masses which have two natural frequencies and two co-ordinates are required to specify the configuration of the system completely.

Q. 2. Define ‘Normal mode of vibration’? Ans. In a two degree freedom system there are two natural frequencies of the system. The system at its lowest or first natural frequency its first and next higher i.e. second natural frequency is called its second mode. If the two masses vibrate at same frequency and in phase it is called principal mode of vibration. If prncipa1 mode of vibration the amplitude of one of the masses is then it is known as normal mode of vibration.

Q. 6. What are vibration absorbers ? Prove that spring force of the absorber system is equal and opposite to the excitition force for main system to be stationary? Ans.Vibration Absorber. When a structure which is excited by an external harmonic force has undesirable vibrations, it becomes necessary to eliminate them by coupling some vibrating system to it. The vibrating system is known as vibration absorber or dynamic vibration absorber. Vibration absorbers are used to control the structural resonance (consider the main figure)

The natural frequency of this system is

When forcing frequency (0 becomes equal to natural frequency of main system then resonance takes place. In order to reduce the amplitude of mass ‘nz1’ it is coupled with spring mass system (m2 — K2) called Vibration absorber. The spring mass system (ni2 — K2) will acts as vibration absorber andies the amplitude of ni1 to zero if its natural frequency is equal to the excitation frequency

Equations of Motion

Where

In order that amplitude of mass ni1 is zero Put A1 =0 (so that mass rn1 must not vibrate)

Simlilarly

when A1 0, from VII

Hence when the amplitude A1 = 0 i.e. main system becomes stationary the spring force of the absorber is equal and opposite to exciting force. The energy of the main system is absorbed by vibration absorber which is also called auxiliary system. Amplitude of the auxiliary system is inversely proportional to spring constant ‘K2’. This equation is used for design of absorber.

Q.7. Discuss the effect of mass ratio on natural frequency of the vibration absorber. Ans. We know that

By puffing w = W2 and equating denomination of the above equation equal to 0, we Get

Q. 10. Determine the two natural frequencies of vibration and the ratio of the amplitudes of motion of mass m1 and m2 for the system shown in Fig. 5.11.

Equations of motion can be written as

Assuming the solution of the form

The frequency equation can be written as

Q. 11. Solve the problem shown in Fig. 5.12; m1 10 kg, m2 = 15 kg, k = 320.N/m.

Ans. The equations of motion can be written as

Assuming the solution of the form

The frequency equation is obtained as

Q. 19. Derive the natural frequencies of the system shown in Fig. 5.19.

Ans. The equations of motion for the system shown in figure can be written as

Rearranging the above equations, we can write them as

Let us assume the solution of the form

The above equations can be written as

Q. 21. what is a two degree system? Ans. In a two degree freedom system, any point in the system may execute harmonic of the two natural frequencies and these are known of vibration. Let us assume the motion of two masses is simple harmonic and is represented as

where X1 and X2are the amplitudes of two masses respectively and are referred as principal co-ordinal.

Q. 23. What are various methods available for vibration control?

Ans. Various methods of vibration control are 1. Vibration Absorbers (centrifugal pendulum absorber, Lanchester damper, Houdaille damper). 2. Vibration Isolation materials like rubber, cork, felt, pad etc.

Q. 2. What are flexibility an stiffness matrix? Ans. If a system made of several points is acted by several forces F1, F2 .... F causing respective deflections x1, x2 x , it can be mathematically expressed as:

In matrix form it can be written as;

In short we can write as :

K12, are called stiffness influence coefficients

Q. 4. Determine the natural frequencies of the system shown in Fig. 6.2. using matrix method.

Ans. The equations of motion can be written as;

In matrix form, the equation can be written as;

Put

The solution of the above equation is

Solving, we get

From the above cubic equation we get;

• Q. 5. Determine the fundamental frequency and first mode of the system shown in Fig. 6.3 using matrix iteration method.

•

• • Ans. Influence coefficients are

• • Putting values of various influence coefficients

• • This can be written in matrix form as:

•

• • Now assume

• • Third iteration

• • Fourth Iteration

• • The ratio obtained in fourth iteration is very close to the initial value; so

•

• •

• Q. 16. What is generalized mass matrix? • Ans. Consider three degree freedom system as shown in figure. • The equations of motion can be written as

•

• • Rearranging, we get

• • Equation (I) can be written in matrix form as;

• • where [m] is called generalised mass matrix.

Unit-3

What causes the apparently solid and rigid Earth to move and so produce an

earthquake?

Earthquakes mainly occur when the different blocks or plates that make up the Earth's surface move relative to each other (Figure 2a), causing distortion in the rock (Figure 2b). The distortion builds up very slowly, over tens or hundreds of years. When rocks are distorted very slowly they behave as if they were springs, or pieces of elastic, in being able to store energy when they are stretched or compressed. Prior to an earthquake, the area is like a spring-loaded system waiting to go off. Eventually the distortion is enough to cause the rock to break and move, releasing energy in the form of an earthquake. The break is called a fault. It starts as a small fracture (Figure 2c), but grows rapidly (Figure 2d). In general, the larger the area of the fault, the greater is the size of the earthquake. The fault length (the length of the break along which rocks are displaced) can vary from metres for a small earthquake to about 1 000 km for a very large earthquake

Figure 2 above shows the cause of an earthquake, using block diagrams, illustrating both

the surface of the Earth and the Earth in cross-section.

(a)Part of the Earth where forces (shown by arrows) are trying to move the rock in opposite directions. (b)Before a fault breaks, the rocks stretch. (c)When the distortion is enough to cause the rocks to break, the break starts at one point (d) the break spreads rapidly along the fault, releasing energy. Note that faults are not always vertical and the forces causing movement can sometimes result in the rocks on either side of the fault moving up or down.

What causes the apparently solid and rigid Earth to move and so produce an earthquake?

Earthquakes mainly occur when the different blocks or plates that make up the Earth's surface move relative to each other (Figure 2a), causing distortion in the rock (Figure 2b). The distortion builds up very slowly, over tens or hundreds of years. When rocks are distorted very slowly they behave as if they were springs, or pieces of elastic, in being able to store energy when they are stretched or compressed. Prior to an earthquake, the area is like a spring-loaded system waiting to go off. Eventually the distortion is enough to cause the rock to break and move, releasing energy in the form of an earthquake. The break is called a fault. It starts as a small fracture (Figure 2c), but grows rapidly (Figure 2d). In general, the larger the area of the fault, the greater is the size of the earthquake. The fault length (the length of the break along which rocks are displaced) can vary from metres for a small earthquake to about 1 000 km for a very large earthquake

Figure 2 above shows the cause of an earthquake, using block diagrams, illustrating both the

surface of the Earth and the Earth in cross-section.

(a)Part of the Earth where forces (shown by arrows) are trying to move the rock in opposite directions. (b)Before a fault breaks, the rocks stretch. (c)When the distortion is enough to cause the rocks to break, the break starts at one point (d)The break spreads rapidly along the fault, releasing energy. Note that faults are not always vertical and the forces causing movement can sometimes result in the rocks on either side of the fault moving up or down.

Hypocenter

The hypocenter is the point within the earth where an earthquake rupture starts. The epicenter is the point directly above it at the surface of the Earth. Also commonly termed the focus. See also epicenter.

(1) Hypocenter: A hypocenter is the point within the Earth where an earthquake rupture starts. (2) Epicenter: An epicenter is the point at the surface that lies directly above a hypocenter in the Earth. * This diagram shows the position of a hypocenter and an epicenter.

Elastic-rebound theory

The elastic rebound theory is an explanation for how energy is spread during earthquakes. As rocks on opposite sides of a fault are subjected to force and shift, they accumulate energy and slowly deform until their internal strength is exceeded. At that time, a sudden movement occurs along the fault, releasing the accumulated energy, and the rocks snap back to their original undeformed shape.

In geology, the elastic rebound theory was the first theory to satisfactorily explain earthquakes. Previously it was thought that ruptures of the surface were the result of strong ground shaking rather than the converse suggested by this theory.

Ancient cultural explanations of earthquakes were often along the lines of the mythical Japanese Namazu: A giant catfish with the islands of Japan on his back. A demigod, or daimyojin, holds a heavy stone over his head to keep him from moving. Once in a while the daimyojin is distracted so Namazu moves and the Earth trembles.

The theory explained

Following the great 1906 San Francisco earthquake, Harry Fielding Reid examined the displacement of the ground surface around the San Andreas Fault.[1] From his observations he concluded that the earthquake must have been the result of the elastic rebound of previously stored elastic strain energy in the rocks on either side of the fault. In an interseismic period, the Earth's plates (see plate tectonics) move relative to each other except at most plate boundaries where they are locked. Thus, if a road is built across the fault as in the figure panel Time 1, it is perpendicular to the fault trace at the point E, where the fault is locked. The far field plate motions (large arrows) cause the rocks in the region of the locked fault to accrue elastic deformation, figure panel Time 2. The deformation builds at the rate of a few centimeters per

year, over a time period of many years. When the accumulated strain is great enough to overcome the strength of the rocks, an earthquake occurs. During the earthquake, the portions of the rock around the fault that were locked and had not moved 'spring' back, relieving the displacement in a few seconds that the plates moved over the entire interseismic period (D1 and D2 in Time 3). The time period between Time 1 and Time 2 could be months to hundreds of years, while the change from Time 2 to Time 3 is seconds. Like an elastic band, the more the rocks are strained the more elastic energy is stored and the greater potential for an event. The stored energy is released during the rupture partly as heat, partly in damaging the rock, and partly as elastic waves. Modern measurements using GPS largely support Reid’s theory as the basis of seismic movement, though actual events are often more complicated.

How are earthquakes recorded?

Earthquakes are recorded by instruments called seismographs. The recording they make is called a seismogram. The seismograph has a base that sets firmly in the ground, and a heavy weight that hangs free. When an earthquake causes the ground to shake, the base of the seismograph shakes too, but the hanging weight does not. Instead the spring or string that it is hanging from absorbs all the movement. The difference in position between the shaking part of the seismograph and the motionless part is what is recorded. Earthquakes generate seismic waves which can be detected with a sensitive instrument called a seismograph.

Advances in seismograph technology have increased our understanding of both earthquakes and the Earth itself.

Perhaps the earliest seismograph was invented in China A.D. 136 by a m an named Choko. is a

a Seismograph?

What is an earthquake?

An earthquake is what happens when two blocks of the earth suddenly slip past one another. The surface where they slip is called the fault or fault plane. The location below the earth’s surface

where the earthquake starts is called the hypocenter, and the location directly above it on the surface of the earth is called the epicenter.

Sometimes an earthquake has foreshocks. These are smaller earthquakes that happen in the same place as the larger earthquake that follows. Scientists can’t tell that an earthquake is a foreshock until the larger earthquake happens. The largest, main earthquake is called the mainshock. Mainshocks always have aftershocks that follow. These are smaller earthquakes that occur afterwards in the same place as the mainshock. Depending on the size of the mainshock, aftershocks can continue for weeks, months, and even years after the mainshock!

What causes earthquakes and where do they happen?

The earth has four major layers: the inner core, outer core, mantle and crust. (figure 2) The crust and the top of the mantle make up a thin skin on the surface of our planet. But this skin is not all in one piece – it is made up of many pieces like a puzzle covering the surface of the earth. (figure 3) Not only that, but these puzzle pieces keep slowly moving around, sliding past one another and bumping into each other. We call these puzzle pieces tectonic plates, and the edges of the plates are called the plate boundaries. The plate boundaries are made up of many faults, and most of the earthquakes around the world occur on these faults. Since the edges of the plates are rough, they get stuck while the rest of the plate keeps moving. Finally, when the plate has moved far enough, the edges unstick on one of the faults and there is an earthquake.

Why does the earth shake when there is an earthquake?

While the edges of faults are stuck together, and the rest of the block is moving, the energy that would normally cause the blocks to slide past one another is being stored up. When the force of the moving blocks finally overcomes the friction of the jagged edges of the fault and it unsticks, all that stored up energy is released. The energy radiates outward from the fault in all directions in the form of seismic waves like ripples on a pond. The seismic waves shake the earth as they move

through it, and when the waves reach the earth’s surface, they shake the ground and anything on it, like our houses and us! (see P&S Wave inset)

intensity of How do scientists measure the size of earthquakes?

The size of an earthquake depends on the size of the fault and the amount of slip on the fault, but that’s not something scientists can simply measure with a measuring tape since faults are many kilometers deep beneath the earth’s surface. So how do they measure an earthquake? They use the seismogram recordings made on the seismographs at the surface of the earth to determine how large the earthquake was (figure 5). A short wiggly line that doesn’t wiggle very much means a small earthquake, and a long wiggly line that wiggles a lot means a large earthquake. The length of the wiggle depends on the size of the fault, and the size of the wiggle depends on the amount of slip.

The size of the earthquake is called its magnitude. There is one magnitude for each earthquake. Scientists also talk about the shaking from an earthquake, and this varies depending on where you are during the earthquake.

How can scientists tell where the earthquake happened?

Seismograms come in handy for locating earthquakes too, and being able to see the P wave and the S wave is important. You learned how P & S waves each shake the ground in different ways as they travel through it. P waves are also faster than S waves, and this fact is what allows us to tell where an earthquake was. To understand how this works, let’s compare P and S waves to lightning and thunder. Light travels faster than sound, so during a thunderstorm you will first see the lightning and then you will hear the thunder. If you are close to the lightning, the thunder will boom right after the lightning, but if you are far away from the lightning, you can count several seconds before you hear the thunder. The further you are from the storm, the longer it will take between the lightning and the thunder.

P waves are like the lightning, and S waves are like the thunder. The P waves travel faster and shake the ground where you are first. Then the S waves follow and shake the ground also. If you are close to the earthquake, the P and S wave will come one right after the other, but if you are far away, there will be more time between the two. By looking at the amount of time between the P and S wave on a seismogram recorded on a seismograph, scientists can tell how far away the earthquake was from that location. However, they can’t tell in what direction from the seismograph the earthquake was, only how far away it was. If they draw a circle on a map around the station where the radius of the circle is the determined distance to the earthquake, they know the earthquake lies somewhere on the circle. But where?

Scientists then use a method called triangulation to determine exactly where the earthquake was (figure 6). It is called triangulation because a triangle has three sides, and it takes three seismographs to locate an earthquake. If you draw a circle on a map around three different seismographs where the radius of each is the distance from that station to the earthquake, the intersection of those three circles is the epicenter!

What Is Seismology?

Seismology is the study of earthquakes and seismic waves that move through and around the earth. A seismologist is a scientist who studies earthquakes and seismic waves.

What Are Seismic Waves?

Seismic waves are the waves of energy caused by the sudden breaking of rock within the earth or an explosion. They are the energy that travels through the earth and is recorded on seismographs.

Types of Seismic Waves

There are several different kinds of seismic waves, and they all move in different ways. The two main types of waves are body waves and surface waves. Body waves can travel through the earth's inner layers, but surface waves can only move along the surface of the planet like ripples on water. Earthquakes radiate seismic energy as both body and surface waves.

BODY WAVES

Traveling through the interior of the earth, body waves arrive before the surface waves emitted by an earthquake. These waves are of a higher frequency than surface waves.

P WAVES

The first kind of body wave is the P wave or primary wave. This is the fastest kind of seismic wave, and, consequently, the first to 'arrive' at a seismic station. The P wave can move through solid rock and fluids, like water or the liquid layers of the earth. It pushes and pulls the rock it moves through just like sound waves push and pull the air. Have you ever heard a big clap of thunder and heard the windows rattle at the same time? The windows rattle because the sound waves were pushing and pulling on the window glass much like P waves push and pull on rock. Sometimes animals can hear the P waves of an earthquake. Dogs, for instance, commonly begin barking hysterically just before an earthquake 'hits' (or more specifically, before the surface waves arrive). Usually people can only feel the bump and rattle of these waves. P waves are also known as compressional waves, because of the pushing and pulling they do. Subjected to a P wave, particles move in the same direction that the the wave is moving in, which is the direction that the energy is traveling in, and is sometimes called the 'direction of wave propagation'. Click here to see a P wave in action.

FIGURE 1 - A P WAVE TRAVELS THROUGH A MEDIUM BY MEANS OF COMPRESSION AND DILATION. PARTICLES ARE REPRESENTED BY CUBES IN THIS MODEL. IMAGE ©2000-2006 LAWRENCE BRAILE, USED WITH PERMISSION.

S WAVES

The second type of body wave is the S wave or secondary wave, which is the second wave you feel in an earthquake. An S wave is slower than a P wave and can only move through solid rock, not through any liquid medium. It is this property of S waves that led seismologists to conclude that the Earth's outer core is a liquid. S waves move rock particles up and down, or side-to-side--perpindicular to the direction that the wave is traveling in (the direction of wave propagation). Click here to see a S wave in action.

FIGURE 2 - AN S WAVE TRAVELS THROUGH A MEDIUM. PARTICLES ARE REPRESENTED BY CUBES IN THIS MODEL. IMAGE ©2000-2006 LAWRENCE BRAILE, USED WITH PERMISSION.

If you'd like to try your hand at making your own P and S waves, try this little experiment.

SURFACE WAVES

Travelling only through the crust, surface waves are of a lower frequency than body waves, and are easily distinguished on a seismogram as a result. Though they arrive after body waves, it is surface waves that are almost enitrely responsible for the damage and destruction associated with earthquakes. This damage and the strength of the surface waves are reduced in deeper earthquakes.

LOVE WAVES

The first kind of surface wave is called a Love wave, named after A.E.H. Love, a British mathematician who worked out the mathematical model for this kind of wave in 1911. It's the fastest surface wave and moves the ground from side-to-side. Confined to the surface of the crust, Love waves produce entirely horizontal motion.Click here to see a Love wave in action.

FIGURE 3 - A LOVE WAVE TRAVELS THROUGH A MEDIUM. PARTICLES ARE REPRESENTED BY CUBES IN THIS MODEL. IMAGE ©2000-2006 LAWRENCE BRAILE, USED WITH PERMISSION.

RAYLEIGH WAVES

The other kind of surface wave is the Rayleigh wave, named for John William Strutt, Lord Rayleigh, who mathematically predicted the existence of this kind of wave in 1885. A Rayleigh wave rolls along the ground just like a wave rolls across a lake or an ocean. Because it rolls, it moves the ground up and down, and side-to-side in the same direction that the wave is moving. Most of the shaking felt from an earthquake is due to the Rayleigh wave, which can be much larger than the other waves. Click here to see a Rayleigh wave in action.

FIGURE 4 - A RAYLEIGH WAVE TRAVELS THROUGH A MEDIUM. PARTICLES ARE REPRESENTED BY CUBES IN THIS MODEL. IMAGE ©2000-2006 LAWRENCE BRAILE, USED WITH PERMISSION.

Unit-4 Soil liquefaction

Some effects of liquefaction during the 1964 Niigata earthquake

Liquefaction allowed this sewer to float upward - 2004 Chūetsu earthquake

The effect of liquefaction in Christchurch, New Zealand, during the Mw 6.3 February 2011 Christchurch earthquake

Soil liquefaction describes a phenomenon whereby a saturated soil substantially loses strength and stiffness in response to an applied stress, usually earthquake shaking or other sudden change in stress condition, causing it to behave like a liquid.

In soil mechanics the term "liquefied" was first used by Hazen[1] in reference to the 1918 failure of the Calaveras Dam in California. He described the mechanism of flow liquefaction of the embankment dam as follows:

If the pressure of the water in the pores is great enough to carry all the load, it will have the effect of holding the particles apart and of producing a condition that is practically equivalent to that of quicksand… the initial movement of some part of the material might result in accumulating pressure, first on one point, and then on another, successively, as the early points of concentration were liquefied.

The phenomenon is most often observed in saturated, loose (low density or uncompacted), sandy soils. This is because a loose sand has a tendency to compress when a load is applied; dense sands by contrast tend to expand in volume or 'dilate'. If the soil is saturated by water, a condition that often exists when the soil is below the ground water table or sea level, then water fills the gaps between soil grains ('pore spaces'). In response to the soil compressing, this water increases in pressure and attempts to flow out from the soil to zones of low pressure (usually upward towards the ground surface). However, if the loading is rapidly applied and large enough, or is repeated many times (e.g. earthquake shaking, storm wave loading) such that it does not flow out in time before the next cycle of load is applied, the water pressures may build to an extent where they exceed the contact stresses between the grains of soil that keep them in contact with each other. These contacts between grains are the means by which the weight from buildings and overlying soil layers are transferred from the ground surface to layers of soil or rock at greater depths. This loss of soil structure causes it to lose all of its strength (the ability to transfer shear stress) and it may be observed to flow like a liquid (hence 'liquefaction').

Although the effects of liquefaction have been long understood, it was more thoroughly brought to the attention of engineers after the 1964 Niigata earthquake and 1964 Alaska earthquake. It was also a major factor in the destruction in San Francisco's Marina District during the 1989 Loma Prieta earthquake, and in Port of Kobe during the 1995 Great Hanshin earthquake. More recently liquefaction was largely responsible for extensive damage to residential properties in the eastern suburbs and satellite townships of Christchurch, New Zealand during the 2010 Canterbury earthquake[2] and more extensively again following the Christchurch earthquakes that followed in early and mid 2011.[3]

The building codes in many developed countries require engineers to consider the effects of soil liquefaction in the design of new buildings and infrastructure such as bridges, embankment dams and retaining structures.[4][5][6]

Contents

• 1 Technical definitions • 2 Liquefaction occurrence • 3 Earthquake liquefaction • 4 Effects • 5 Liquefaction mitigation methods • 6 Quicksand

• 7 Quick clay • 8 Turbidity currents • 9 See also

o 9.1 Events attributed to liquefaction • 10 References • 11 External links

[edit] Technical definitions

A state of 'soil liquefaction' occurs when the effective stress of a soil is reduced to essentially zero, which corresponds to a complete loss of shear strength. This may be initiated by either monotonic loading (e.g. single sudden occurrence of a change in stress - examples include an increase in load on an embankment or sudden loss of toe support) or cyclic loading (e.g. repeated change in stress condition - examples include wave loading or earthquake shaking). In both cases a soil in a saturated loose state, and one which may generate significant pore water pressure on a change in load are the most likely to liquefy. This is because a loose soil has the tendency to compress when sheared, generating large excess porewater pressure as load is transferred from the soil skeleton to adjacent pore water during undrained loading. As pore water pressure rises a progressive loss of strength of the soil occurs as effective stress is reduced. It is more likely to occur in sandy or non-plastic silty soils, but may in rare cases occur in gravels and clays (see quick clay)

A 'flow failure' may initiate if the strength of the soil is reduced below the stresses required to maintain equilibrium of a slope or footing of a building for instance. This can occur due to monotonic loading or cyclic loading, and can be sudden and catastrophic. A historical example is the Aberfan disaster. Casagrande[7] referred to this type of phenomena as 'flow liquefaction' although a state of zero effective stress is not required for this to occur.

The term 'cyclic liquefaction' refers to the occurrence of a state of soil when large shear strains have accumulated in response to cyclic loading. A typical reference strain for the approximate occurrence of zero effective stress is 5% double amplitude shear strain. This is a soil test based definition, usually performed via cyclic triaxial, cyclic direct simple shear, or cyclic torsional shear type apparatus. These tests are performed to determine a soils resistance to liquefaction by observing the number of cycles of loading at a particular shear stress amplitude before it 'fails'. Failure here is defined by the aforementioned shear strain criteria.

The term 'cyclic mobility' refers to the mechanism of progressive reduction of effective stress due to cyclic loading. This may occur in all soil types including dense soils. However on reaching a state of zero effective stress such soils immediate dilate and regain strength. Thus shear strains are significantly less than a true state of soil liquefaction whereby a loose soil exhibits flow type phenomena.

[edit] Liquefaction occurrence

Liquefaction is more likely to occur in loose to moderately saturated granular soils with poor drainage, such as silty sands or sands and gravels capped or containing seams of impermeable sediments.[8][9] During wave loading, usually cyclic undrained loading, e.g. seismic loading, loose sands tend to decrease in volume, which produces an increase in their pore water pressures and consequently a decrease in shear strength, i.e. reduction in effective stress.

Deposits most susceptible to liquefaction are young (Holocene-age, deposited within the last 10,000 years) sands and silts of similar grain size (well-sorted), in beds at least metres thick, and saturated with water. Such deposits are often found along stream beds, beaches, dunes, and areas where windblown silt (loess) and sand have accumulated. Some examples of soil liquefaction include quicksand, quick clay, turbidity currents, and earthquake induced liquefaction.

Depending on the initial void ratio, the soil material can respond to loading either strain-softening or strain-hardening. Strain-softened soils, e.g. loose sands, can be triggered to collapse, either monotonically or cyclically, if the static shear stress is greater than the ultimate or steady-state shear strength of the soil. In this case flow liquefaction occurs, where the soil deforms at a low constant residual shear stress. If the soil strain-hardens, e.g. moderately dense to dense sand, flow liquefaction will generally not occur. However, cyclic softening can occur due to cyclic undrained loading, e.g. earthquake loading. Deformation during cyclic loading will depend on the density of the soil, the magnitude and duration of the cyclic loading, and amount of shear stress reversal. If stress reversal occurs, the effective shear stress could reach zero, then cyclic liquefaction can take place. If stress reversal does not occur, zero effective stress is not possible to occur, then cyclic mobility takes place.[10]

The resistance of the cohesionless soil to liquefaction will depend on the density of the soil, confining stresses, soil structure (fabric, age and cementation), the magnitude and duration of the cyclic loading, and the extent to which shear stress reversal occurs.[11]

[edit] Earthquake liquefaction

Sand boils that erupted during the 2011 Christchurch earthquake.

The pressures generated during large earthquakes with many cycles of shaking can cause the liquefied sand and excess water to force its way to the ground surface from several metres below the ground. This is often observed as "sand boils" also called "sand blows" or "sand volcanoes" (as they appear to form small volcanic craters) at the ground surface. The phenomenon may incorporate both flow of already liquefied sand from a layer below ground, and a quicksand

effect whereby upward flow of water initiates liquefaction in overlying non-liquefied sandy deposits due to buoyancy.

A liquefaction susceptibility map - excerpt of USGS map for the San Francisco Bay Area. Many areas of concern in this region are also densely urbanized.

The other common observation is land instability - cracking and movement of the ground down slope or towards unsupported margins of rivers, streams, or the coast. The failure of ground in this manner is called 'lateral spreading', and may occur on very shallow slopes of angles of only 1 or 2 degrees from the horizontal. More is discussed on this aspect under the section 'Effects'.

One positive aspect of soil liquefaction is the tendency for the effects of earthquake shaking to be significantly damped (reduced) for the remainder of the earthquake. This is because liquids do not support a shear stress and so once the soil liquefies due to shaking, subsequent earthquake shaking (transferred through ground by shear waves) is not transferred to buildings at the ground surface.

Studies of liquefaction features left by prehistoric earthquakes, called paleoliquefaction or paleoseismology, can reveal a great deal of information about earthquakes that occurred before records were kept or accurate measurements could be taken.[12]

Soil liquefaction induced by earthquake shaking is also a major contributor to urban seismic risk.

[edit] Effects

The effects of lateral spreading (River Road in Christchurch following the 2011 Christchurch earthquake)

Damage in Brooklands from the 2010 Canterbury earthquake, where buoyancy caused by soil liquefaction pushed up an underground service including this manhole

The effects of soil liquefaction on the built environment can be extremely damaging. Buildings whose foundations bear directly on sand which liquefies will experience a sudden loss of support, which will result in drastic and irregular settlement of the building causing structural damage, including cracking of foundations and damage to the building structure itself, or may leave the structure unserviceable afterwards, even without structural damage. Where a thin crust of non-liquefied soil exists between building foundation and liquefied soil, a 'punching shear' type foundation failure may occur. The irregular settlement of ground may also break underground utility lines. The upward pressure applied by the movement of liquefied soil through the crust layer can crack weak foundation slabs and enter buildings through service ducts, and may allow water to damage the building contents and electrical services.

Bridges and large buildings constructed on pile foundations may lose support from the adjacent soil and buckle, or come to rest at a tilt after shaking.

Sloping ground and ground next to rivers and lakes may slide on a liquefied soil layer (termed 'lateral spreading'),[13] opening large cracks or fissures in the ground, and can cause significant damage to buildings, bridges, roads and services such as water, natural gas, sewerage, power and telecommunications installed in the affected ground. Buried tanks and manholes may float in the

liquefied soil due to buoyancy.[13] Earth embankments such as flood levees and earth dams may lose stability or collapse if the material comprising the embankment or its foundation liquefies.

[edit] Liquefaction mitigation methods

Main article: Dynamic compaction

Methods to mitigate the effects of soil liquefaction have been devised by earthquake engineers and include various soil compaction techniques such as vibro compaction (compaction of the soil by depth vibrators), dynamic compaction, and vibro stone columns.[14] These methods result in the densification of soil and enable buildings to withstand soil liquefaction.[15]

[edit] Quicksand

Main article: Quicksand

Quicksand forms when water saturates an area of loose sand and the ordinary sand is agitated. When the water trapped in the batch of sand cannot escape, it creates liquefied soil that can no longer support weight. Quicksand can be formed by standing or (upwards) flowing underground water (as from an underground spring), or by earthquakes. In the case of flowing underground water, the force of the water flow opposes the force of gravity, causing the granules of sand to be more buoyant. In the case of earthquakes, the shaking force can increase the pressure of shallow groundwater, liquefying sand and silt deposits. In both cases, the liquefied surface loses strength, causing buildings or other objects on that surface to sink or fall over.

The saturated sediment may appear quite solid until a change in pressure or shock initiates the liquifaction causing the sand to form a suspension with each grain surrounded by a thin film of water. This cushioning gives quicksand, and other liquefied sediments, a spongy, fluidlike texture. Objects in the liquefied sand sink to the level at which the weight of the object is equal to the weight of the displaced sand/water mix and the object floats due to its buoyancy.

[edit] Quick clay

Main article: Quick clay

Quick clay, also known as Leda Clay in Canada, is a unique form of highly sensitive clay, with the tendency to change from a relatively stiff condition to a liquid mass when it is disturbed. Undisturbed quick clay resembles a water-saturated gel. When a block of clay is held in the hand and struck, however, it instantly turns into a flowing ooze, a process known as spontaneous liquefaction. Quick clay behaves this way because, although it is solid, it has a very high water content, up to 80%. The clay retains a solid structure despite the high water content, because surface tension holds water-coated flakes of clay together in a delicate structure. When the structure is broken by a shock, it reverts to a fluid state.

Quick clay is only found in the northern countries such as Russia, Canada, Alaska in the U.S., Norway, Sweden, and Finland, which were glaciated during the Pleistocene epoch.

Quick clay has been the underlying cause of many deadly landslides. In Canada alone, it has been associated with more than 250 mapped landslides. Some of these are ancient, and may have been triggered by earthquakes.[16]

[edit] Turbidity currents

Main article: Turbidity current

Submarine landslides are turbidity currents and consist of water saturated sediments flowing downslope. An example occurred during the 1929 Grand Banks earthquake that struck the continental slope off the coast of Newfoundland. Minutes later, transatlantic telephone cables began breaking sequentially, farther and farther downslope, away from the epicenter. Twelve cables were snapped in a total of 28 places. Exact times and locations were recorded for each break. Investigators suggested that a 60-mile-per-hour (100 km/h) submarine landslide or turbidity current of water saturated sediments swept 400 miles (600 km) down the continental slope from the earthquake’s epicenter, snapping the cables as it passed.[17]

[edit] See also

• Paleoseismology • Dry quicksand • Atterberg limits • Mud volcano • Sand volcano or sand blow • Thixotropy • Earthquake engineering

[edit] Events attributed to liquefaction

• Aberfan disaster

Unit-5 It is easiest to see the principle at work by referring directly to the most widely used of these advanced techniques, known as base isolation. A base isolated structure is supported by a series of bearing pads, which are placed between the buildings and building foundation.

It is easiest to see the principle at work by referring directly to the most widely used of these advanced techniques, known as base isolation. A base isolated structure is supported by a series of bearing pads, which are placed between the buildings and building foundation.

Base Isolation Technique

The concept of base isolation is explained through an example building resting on frictionless rollers. When the ground shakes, the rollers freely roll, but the building above does not move.

Thus, no force is transferred to the building due to the shaking of the ground; simply, the building does not experience the earthquake.

Now, if the same building is rested on the flexible pads that offer resistance against lateral movements (fig 1b), then some effect of the ground shaking will be transferred to the building above. If the flexible pads are properly chosen, the forces induced by ground shaking can be a few times smaller than that experienced by the building built directly on ground, namely a fixed base building (fig 1c). The flexible pads are called base-isolators, whereas the structures protected by means of these devices are called base-isolated buildings. The main feature of the base isolation technology is that it introduces flexibility in the structure.

As a result, a robust medium-rise masonry or reinforced concrete building becomes extremely flexible. The isolators are often designed, to absorb energy and thus add damping to the system. This helps in further reducing the seismic response of the building. Many of the base isolators look like large rubber pads, although there are other types that are based on sliding of one part of the building relative to other. Also, base isolation is not suitable for all buildings. Mostly low to medium rise buildings rested on hard soil underneath; high-rise buildings or buildings rested on soft soil are not suitable for base isolation.

Concept of Base Isolation

Lead-rubber bearings are the frequently-used types of base isolation bearings. A lead rubber bearing is made from layers of rubber sandwiched together with layers of steel. In the middle of the solid lead “plug”. On top and bottom, the bearing is fitted with steel plates which are used to attach the bearing to the building and foundation. The bearing is very stiff and strong in the vertical direction, but flexible in the horizontal direction.

How it Works

To get a basic idea of how base isolation works, first examine the above diagram. This shows an earthquake acting on base isolated building and a conventional, fixed-base, building. As a result of an earthquake, the ground beneath each building begins to move. . Each building responds with movement which tends towards the right. The buildings displacement in the direction opposite the ground motion is actually due to inertia. The inertia forces acting on a building are the most important of all those generated during an earthquake.

In addition to displacing towards right, the un-isolated building is also shown to be changing its shape from a rectangle to a parallelogram. We say that the building is deforming. The primary cause of earthquake damage to buildings is the deformation which the building undergoes as a result of the inertial forces upon it.

Response of Base Isolated Buildings

The base-isolated building retains its original, rectangular shape. The base isolated building itself escapes the deformation and damage-which implies that the inertial forces acting on the base isolated building have been reduced. Experiments and observations of base-isolated buildings in earthquakes to as little as ¼ of the acceleration of comparable fixed-base buildings.

Acceleration is decreased because the base isolation system lengthens a buildings period of vibration, the time it takes for a building to rock back and forth and then back again. And in general, structures with longer periods of vibration tend to reduce acceleration, while those with shorter periods tend to increase or amplify acceleration.

Spherical Sliding Base Isolation

Spherical Sliding Base Isolation

Spherical sliding isolation systems are another type of base isolation. The building is supported by bearing pads that have a curved surface and low friction. During an earthquake the building is free to slide on the bearings. Since the bearings have a curved surface, the building slides both horizontally and vertically. The forces needed to move the building upwards limits the horizontal or lateral forces which would otherwise cause building deformations. Also by adjusting the radius of the bearings curved surface, this property can be used to design bearings that also lengthen the buildings period of vibration