How Buildings Respond to Earthquakes

Ground Acceleration and Building Damage

Comparatively speaking, the absolute movement of the ground and buildings during an earthquake is not actually all that large, even during a major earthquake. That is, they do not usually undergo displacements that are large relative to the building's own dimensions. So, it is not the distance that a building moves which alone causes damage.

Rather, it is because a building is suddenly forced to move very quickly that it suffers damage during an earthquake. Think of someone pulling a rug from beneath you. If they pull it quickly (i.e., accelerate it a great deal), then they needn't pull it very far to throw you off balance. On the other hand, if they pull the rug slowly and only gradually increase the speed of the rug, they can move (displace) it a great distance without that same unfortunate result.

figure 1: Accelerogram

In other words, the damage that a building suffers primarily depends not upon its displacement, but upon acceleration. Whereas displacement is the actual distance the ground and the building may move during an earthquake, acceleration is a measure of how quickly they change speed as they move. During an earthquake, the speed at which both the ground and building are moving will reach some maximum. The more quickly they reach this maximum, the greater their acceleration.

It's worthwhile mentioning here that in order to study the earthquake responses of buildings, many buildings in earthquake-prone regions of the world have been equipped with strong motion accelerometers. These are special instruments which are capable of recording the accelerations of either the ground or building, depending upon their placement.

The recording of the motion itself is known as an accelerogram. Figure 1 shows an accelerogram recorded in a hospital building parking lot during the Northridge, California earthquake of January 17, 1994.

In addition to providing valuable information about the characteristics of the particular earthquake recorded or the building where the accelerogram was recorded, accelerograms recorded in the past are also often used in the earthquake response analysis and earthquake design of buildings yet to be constructed.

Newton's Law

Acceleration has this important influence on damage, because, as an object in movement, the building obeys Newton' famous Second Law of Dynamics. The simplest form of the equation which expresses the Second Law of Motion is F = MA.

This states the Force acting on the building is equal to the Mass of the building times the Acceleration. So, as the acceleration of the ground, and in turn, of the building, increase, so does the force which affects the building, since the mass of the building doesn't change.

Of course, the greater the force affecting a building, the more damage it will suffer; decreasing F is an important goal of earthquake resistant design. When designing a new building, for example, it is desirable to make it as light as possible, which means, of course, that M, and in turn, F will be lessened. As we've seen in the discussion of Advanced Earthquake Resistant Techniques, various techniques are now also available for reducing A.

Inertial Forces

figure 2: Acceleration, Inertial Forces

It is important to note that F is actually what's known as an inertial force, that is, the force is created by the building's tendency to remain at rest, and in its original position, even though the ground beneath it is moving. This is in accordance with another important physical law known as D'Alembert's Principle, which states that a mass acted upon by an acceleration tends to oppose that acceleration in an opposite direction and proportionally to the magnitude of the acceleration (See Figure 2.)

This inertial force F imposes strains upon the building's structural elements. These structural elements primarily include the building's beams, columns, load-bearing walls, floors, as well as the connecting elements that tie these various structural elements together. If these strains are large enough, the building's structural elements suffer damage of various kinds.

figure 3: Simple Rigid Block

To illustrate the process of inertia generated strains within a structure, we can consider the simplest kind of structure imaginable--a simple, perfectly rigid block of stone. (See Figure 3.) During an earthquake, if this block is simply sitting on the ground without any attachment to it, the block will move freely in a direction opposite to that of the ground motion, and with a force proportional to the mass and acceleration of the block.

If the same block, however, is solidly founded in the ground and no longer able to move freely, it must in some way absorb the inertial force internally. In Figure 3, this internal uptake of force is shown to result in cracking near the base of the block.

Of course, real buildings do not respond as simply as described above. There are a number of important characteristics common to all buildings which further affect and complicate a building's response in terms of the accelerations it undergoes, and the deformations and damages that it suffers.

Building Frequency and Period

To begin with, as we discussed in the How Earthquakes Affect Buildings, the magnitude of the building response – that is, the accelerations which it undergoes – depends primarily upon the frequencies of the input ground motion and the building's natural frequency. When these are near or equal to one another, the building's response reaches a peak level.

In some circumstances, this dynamic amplification effect can increase the building acceleration to a value two times or more that of the ground acceleration at the base of the building. Generally, buildings with higher natural frequencies, and a short natural period, tend to suffer higher accelerations but smaller displacement. In the case of buildings with lower natural frequencies, and a long natural period, this is reversed as the buildings will experience lower accelerations but larger displacements.

Building Stiffness

The taller a building, the longer its natural period tends to be. But the height of a building is also related to another important structural characteristic: the building flexibility. Taller buildings tend to be more flexible than short buildings. (Only consider a thin metal rod. If it is very short, it is difficulty to bend it in your hand.

If the rod is somewhat longer, and of the same diameter, it becomes much easier to bend. Buildings behave similarly.) We say that a short building is stiff, while a taller building is flexible. (Obviously, flexibility and stiffness are really just the two sides of the same coin. If something is stiff, it isn't flexible and vice-versa.)

Stiffness greatly affects the building's uptake of earthquake generated force. Reconsider our first example above, of the rigid stone block deeply founded in the soil. The rigid block of stone is very stiff; as a result it responds in a simple, dramatic manner. Real buildings, of course, are more inherently flexible, being composed of many different parts.

Furthermore, not only is the block stiff, it is brittle; and because of this, it cracks during the earthquake. This leads us to the next important structural characteristic affecting a building's earthquake response and performance— ductility.

Ductility

figure 4: Metal Rod Ductility

Ductility is the ability to undergo distortion or deformation – bending, for example – without resulting in complete breakage or failure. To take once again the example of the rigid block in Figure 3, the block is an example of a structure with extremely low ductility. To see how ductility can improve a building's performance during an earthquake, consider Figure 4.

For the block, we have substituted a combination of a metal rod and a weight. In response to the ground motion, the rod bends but does not break. (Of course, metals in general are more ductile than materials such as stone, brick and concrete.) Obviously, it is far more desirable for a building to sustain a limited amount of deformation than for it to suffer a complete breakage failure.

The ductility of a structure is in fact one of the most important factors affecting its earthquake performance. One of the primary tasks of an engineer designing a building to be earthquake resistant is to ensure that the building will possess enough ductility to withstand the size and types of earthquakes it is likely to experience during its lifetime.

Damping

The last of the important structural characteristics, or parameters, which we'll discuss here is damping. As we noted earlier, ground and building motion during an earthquake has a complex, vibratory nature. Rather than undergoing a single "yank" in one direction, the building actually moves back and forth in many different horizontal directions.

All vibrating objects, including buildings, tend to eventually stop vibrating as time goes on. More precisely, the amplitude of vibration decays with time. Without damping, a vibrating object would never stop vibrating, once it had been set in motion. Obviously, different objects possess differing degrees of damping. A bean bag, for example, has high damping; a trampoline has low damping.

In a building undergoing an earthquake, damping – the decay of the amplitude of a building's vibrations – is due to internal friction and the absorption of energy by the building's structural and nonstructural elements. All buildings possess some intrinsic damping.

The more damping a building possesses, the sooner it will stop vibrating--which of course is highly desirable from the standpoint of earthquake performance. Today, some of the more advanced techniques of earthquake resistant design and construction employ added damping devices like shock absorbers to increase artificially the intrinsic damping of a building and so improve its earthquake performance.