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Vibration 101
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Every one of us experiences vibrations constantly. If we are not hearing-impaired, the sounds we hear are vibrations in air. The waves in a pool, lake or the ocean are vibrations in water. We all feel that we understand what the term "vibration" means, because we are so familiar with various forms of it. However, many people may not be aware of what vibration means in the technical sense, especially when it comes to ground vibrations experienced in the home. Because an understanding of vibration in that sense is important for what comes after in the CVDG, we will present in this chapter some definitions, examples and analogies that provide a better, though mostly non-technical, understanding of the properties of ground vibration, how they are measured and their effects. Vibration in Physics A vibration in the scientific sense is a passage of motional energy in a material that causes oscillations (movements) about the average position of the particles or molecules which make up a material, item or structure. A vibration must travel in some physical material. In that respect, it differs from visible light and other forms of "electromagnetic radiation" (X-rays, radio, ultraviolet, etc.), which can move through total vacuum. Sufficiently low intensity vibration passages produce no permanent change in the relative position of particles in an item or structure. Introductory physics often talks about "ideal materials" in which vibrations, once started, persist indefinitely. Vibrations in "real materials" eventually fade away due to damping effects, which ultimately convert the vibration energy to heat. You can show the effect of damping just by tapping a glass; initially the sound is relatively loud, but dies away quickly because the energy of the vibration is lost mostly to creating the sound you hear when you tap the glass. Some of that energy also goes into ultimately producing a very slight temperature increase in the glass itself. This transformation of the motional energy of vibration to heat energy is the reason that articles which undergo continuous vibration can become warm or even hot. The repeated vibrations impart more and more energy to the vibrating material, which appears as heat (a faster and more disordered movement in the molecules of a substance). The conversion of the vibration energy of motion to the disordered energy of heat is an example of the operation of the famous Second Law of Thermodynamics, which says that "entropy" (a scientific measure of the amount of disorder in a system) increases over time. Vibrations and Waves
In real-world materials, vibration waves often look different, both in shape
and intensity, along the three different possible directions of movement (up-down, back-forth, side-side).
Scientific seismographs are designed to record the vibrations in all three perpendicular
dimensions at the same time. These differences are also important from the damage
standpoint; vibrations in the side-side ("transverse") and back-forth ("longitudinal",
sometimes seen written as "radial") directions cause potentially damaging "shear"
(differing directions or speeds of movement within the material) in structures.
Properties of Waves Simple waves can be characterized by something called the "frequency", usually quoted in Hertz (Hz or cycles per second). It is just the number of wave peaks passing a given point per second. You can see mathematical sine waves of different frequencies, but the same size, in the diagram at right. The wave sin (1/2x) has half the frequency of sin (x) (the sine wave from high school geometry and algebra), while sin (2x) has twice the frequency.[8] Lower frequency waves look more "spread out", while higher frequency ones look more densely packed. Physical waves with higher frequencies carry more energy per unit of time than those with lower frequencies of the same intensity. Sound vibrations and ground vibrations are typically very complex in their wave structure, being comprised of multiple "components" of different frequencies. But, they still look like waves, albeit seemingly irregular ones, when they are visualized with the proper equipment. Complex ground vibration waves can be viewed and understood as the sum of multiple simpler waves of different frequencies and "amplitudes" (sizes). Such complex waves can be analyzed mathematically to reveal their multiple "frequency components", which, when added together, make up the complex wave seen. The frequency components of a given complex wave can be extracted from the shape of the wave using a minicomputer (personal computer, tablet or even a smart phone) running a "Fast Fourier Transform" (FFT) program. More discussion about vibration frequencies and how they are determined from seismograph data is found on the CVDG chapter, Vibration Frequencies and in the Fourier Transform chapter of the CVDG Pro. A more detailed description of wave phenomena can be found in almost any college-level physics text.[3] Ground vibration components with different frequencies travel differently and are absorbed and dissipated ("attenuated") to different degrees in different materials, leading to changes in the overall vibration shape and frequency distribution with distance traveled through the ground. If you have a sound system in your home, you know that the deep bass notes (low frequency) travel further than the high notes (high frequency). The same thing happens in ground vibration. Unlike the sound vibrations produced by your home sound system, the ground vibration frequencies of most concern and interest are not those that can be heard well by most people; they are low in frequency and more felt than heard. Typically, construction vibrations have components which range in frequency from about 100 Hz down to below 10 Hz. Ground vibration frequencies below about 40 Hz in frequency are the ones of most concern in causing damage to structures. Ground Vibration
Seismographs for earthquake measurement, although they operate on the same principles, are somewhat different from those used for man-made ground vibration measurements. In part, this is because they must be able to measure a far greater range of ground vibration intensities than those produced by human activities. This is the reason that the "Richter Scale", used to describe the source energy ("intensity") of earthquakes, is both "open-ended" (i.e. having no upper limit) and exponential, meaning that every unit increase in Richter intensity indicates an energy which is ten times greater than the next lower one. You can learn more about ground vibration measurement and scales in the CVDG Pro chapter, Vibration Measures. In spite of their design differences, the purpose for both kinds of seismographs is the same - to provide a reliable record of ground movement. Vibration and Damage Unlike the "ideal" vibrations discussed above, which involve movement of particles or molecules back and forth about one unchanged position, both earthquake vibrations and some man-made ones can produce permanent changes in the relative positions of "particles" comprising structures. Since these permanent changes are essentially always unwanted, we refer to them as damage. In earthquakes, such damage can be seen as cracks in the ground and, in a large earthquake, collapsed buildings and infrastructure. The larger the vibration (i.e. the higher the ground movement speed), the greater is the potential for these permanent changes in particle positions. See Vibration and Damage in the CVDG for much more on this topic. In materials like a body of water, which is the same pretty much everywhere (i.e. "isotropic" or "homogeneous"), the vibration intensity decreases with distance approximately according to the same "1/r2" law that Sir Isaac Newton found for both light intensity and gravitational attraction with distance from the source. The reason for this is fundamentally geometric. As a given amount of motional energy spreads out from a source, it can be thought of as passing through a "sphere" of continually increasing size. The surface area of that sphere increases proportional to the radius squared (r2) and, over which, the source energy spreads. This part of the decrease in vibration wave intensity with distance is often referred to in the scientific literature as "geometric damping". Ground vibration intensities at the ground surface usually don't follow the "1/r2" law with any exactness, even though vibrations generally decrease in intensity with distance from the source. Typically, surface vibrations decay more slowly with the distance, r, than 1/r2 (inverse square dependence), often approaching a 1/r (inverse linear) distance dependence, due, again to a geometric effect. Body vibration waves (see below) can come close to obeying the "1/r2" law. Just how fast vibrations die off with distance is a critical factor in estimating damage potential for vibrations. You can learn more about some of the ways that vibration intensities can change with distance in the CVDG chapter, Vibration and Distance. A basic understanding of vibration decrease with distance also must account for the properties of the soil and rock through which the vibration waves move. Different types of ground composition cause a lesser or greater loss in the vibration intensity through attenuation of the vibration energy in the soil. Such "material damping" can be quite complex when viewed scientifically. But, beyond causing a further decrease of vibration energy, it has at least one important characteristic. As we have seen, ground vibrations are usually mixtures of waves of different frequencies. Material damping generally reduces higher frequency components of the vibration waves more than low frequency ones. This means that the properties of a vibration wave measured at some distance will be different, not only in intensity but in frequency, as well, from those measured close to the source of the vibration. The difference between geometric damping and material damping can be clarified by an analogy. We all know that the further we are from a bright light, the dimmer it appears to our eyes. That's an effect of geometric damping of the light intensity. However, if we are in sunlight, we use sunglasses, which, as the soil does with vibrations, selectively remove ("damp") some parts of the light, while letting some through to reach our eyes. The sunglasses' effect on light are broadly similar to material damping of vibrations in the soil, which removes some parts of the vibration selectively. Note that vibration energy spreads in all directions, even though it does not necessarily spread equally in all directions, unless the transmission is through a single isotropic material. Most materials, especially the ground, are anything but isotropic. Different types of rock and soil transmit vibrations differently, in intensity, frequency, and speed. Clay soils, because of their greater coherence, transmit vibration more efficiently than sandy or loamy soils. Even soils with different amounts of moisture can behave differently in vibration transmission.[7] Layering of the soil can produce both reflections and amplifications of the ground vibration, due to an effect similar to intensification of light by a lens. Differences in vibration transmission and reflection in rock are pretty well-understood by geologists, particularly those at oil companies. They use such differences in a geophysical technique called "seismic profiling" to reveal underlying rock structures and search for possible oil deposits. Being at a greater distance from a vibration source can't always be seen as much comfort, if your home is close enough to hear the vibration source.[6] Indeed, it is well-known that some types of lesser vibrations at a greater distance can be more damaging than those closer in. This is due to the well-documented lowering of the ground vibration frequency with distance, a result of the soil absorbing selectively the higher frequency components. These lower frequency vibrations often have special, more efficient, interactions (called "resonances") with the house structure that other, higher frequency, vibrations lack. Wave Propagation, Interference, Reflection and Focusing Ground vibrations can take multiple paths from the source of the vibration to a house or a seismograph. These paths can be divided into two basic groups, surface waves and body waves. There are several different types of "surface waves" ("Rayleigh waves", "Love waves", among others) which differ in the specific pattern of particle movement with respect to the overall direction of movement ("propagation") of the wave. Others vibrations can travel through the thickness of soil or rock ("body waves"). Body waves can become surface waves, due to reflection (see below) from underlying rock or soil layers. The different paths taken by waves lead to different arrival times for the vibration waves and different wave shapes for the two different components. Since the foundations of homes are, for all intents and purposes, at the surface of the ground, surface waves are of most interest in their interactions with homes. When vibration waves are reflected from some underlying soil or rock layers, they can create "interference" patterns with later, slower moving, incoming parts of the vibrations. Interference can be easily seen by dropping a single drop in a bowl of water; as waves reach the walls and reflect back onto the incoming waves, they produce a more "jumbled" pattern of waves. In this and all other forms of wave movement, wave peaks and valleys in multiple waves interact to produce a larger or smaller sum wave, depending on whether wave peaks coincide with wave peaks ("constructive interference") or wave peaks coincide with wave valleys ("destructive interference"). Just as a lens can focus light waves by bending of the light ("refraction"), ground vibration waves can be locally refracted and focused as a result of the differing vibration transmission properties of the topsoil and the subsoil.[15] Such focusing effects, like those of a lens, are often highly localized. Ground vibration focusing can sometimes mean that two homes the same distance away from the same vibration source may be subjected to different vibration velocities, with different degrees of damage.
Calculating Vibration Intensities It is possible to calculate vibration intensities, using equations which take into account the basic properties of wave propagation. Vibration velocities are often "estimated" using "scaled distance" or other vibration propagation equations like those proposed by the U.S. Federal Transit Administration.[1] These can be valuable when they are validated in the local soil environment. But, they can be nearly worthless without such validation, because vibration propagation depends strongly on the local ground conditions (including the structures present) and local geology. Such vibration estimation equations are often used without any significant validation through confirming measurements or consideration of the real complexities of vibration transmission. They, and conclusions based upon them, should be considered as approximate, at best, when used without explicit experimental knowledge of the local vibration "attenuation" (i.e. decrease in ground vibration velocity with distance) conditions.
Causes of Man-made Vibration Most people know that vibration can be produced in many different ways and transmitted through all kinds of different materials. However, most kinds of human-caused vibrations, including those created by people walking on floors in a house, slamming doors and exercising, are too small in intensity, last for too short a time and/or affect too small an area to be of much concern in causing significant damage to an entire structure.[14] From the standpoint of damage to structures, there are only three important sources of man-made vibration: blasting, operation of heavy equipment and, in some extreme cases, traffic and other transportation (e.g. railroad traffic). Some might add oilfield hydraulic fracturing ("fracking") and oilfield underground wastewater disposal activities to this list. Small earthquakes, most below the limit of sensation, have been attributed to oilfield activities. Much like those involved in construction, those who do fracking claim that their work doesn't cause damage. There is a good deal of scientific documentation that shows small earthquakes occurring in previously geologically stable areas where fracking or wastewater disposal is being done. However, the cause of those earthquakes is still hotly disputed. Of course, any technology capable of breaking rock at depth, as fracking and wastewater disposal do, would have to be considered a possible cause for small earthquakes and a matter calling for further study. For more information on vibrations caused by activities other than the three sources listed above see the CVDG's Non-construction Vibrations.
Vibrations from construction operations are increasingly being recognized as causes of damage to homes and other structures. In many ways, they are more worrisome than blasting, because of their much longer vibration durations and lower frequency component distributions, magnifying resonance and fatigue effects in a house. The graphic at right of measured FFT dominant frequencies, for heavy equipment operations in one road reconstruction job, shows that most of the vibration intensity is in the sub-40 Hz frequency range of most concern for causing damage. Of course, vibration generation and suppression is important in many other areas (e.g. machine tool operation), constituting a science in their own right. However, many of these other sources are insignificant in terms of vibration transmission to and through the ground, the focus of Vibrationdamage.com. For that reason, I simply note these other forms of vibration in passing. Ground Vibration and Homes Damage to homes from ground vibration can occur by three basic types of interaction. The first is the direct interaction of the ground vibration with the house, without any of the resonant interactions discussed above. If a vibration is large enough and lasts long enough, it can do damage even though its frequency composition does not "excite" directly the natural vibration frequencies of the house ("resonant frequencies"). The second type of interaction with ground vibration is that of ground vibrations with frequencies which overlap the natural vibration frequencies of the home, i.e. those which are "in resonance" with the home. Such resonant interactions are self-reinforcing in the home, growing with each passing wave. Therefore, resonant vibrations are potentially damaging, if the they last long enough. Resonance effects are discussed in more detail on the CVDG page, Resonance/Fatigue. Finally, the ground vibration can cause damage by bringing about settling of the soil around the home, with corresponding settling of the house foundation. Ground settling effects are often indicated by cracks in the soil around the home or shifting of soil around house supports, with possible damage to home support structures (slabs, foundations) themselves. Vibration can produce damage without noticeable settling, through the resonant and non-resonant interactions indicated above. Vibration "Safety"
Because the potential for vibration damage is linked to distance from the vibration source, vibration safety estimates often use quantities called "safe distances". Distances are more easily measured than ground vibration peak particle velocities (PPV's), which are considered to be the best indicators of damage potential. Safe distances usually are arrived at by considering the likely velocities of vibrations of a given type and their distance dependence, which can be calculated, albeit with limited accuracy. Thus, "safe distances" are closely linked to vibration standards, which set allowable ground vibration velocities for various activities and structure types. Construction vibration standards set much lower PPV limits than the ones established for blasting, with corresponding larger safe distances. This means that, for a given ground vibration PPV in a given area, the probability of damage is generally higher for construction vibration than for blasting vibration, with a correspondingly higher safe distance. For more on this somewhat complicated topic, see the CVDG chapter, Vibration and Damage. The CVDG Pro section, Vibration Safety, discusses ways in which vibration standards can be used to set "safe distances" from vibration-causing work and the limitations of these approaches. Hard materials like rock, or to a somewhat lesser extent, a home, transmit passing vibrations well, in the sense that they damp (attenuate) vibrations less efficiently than soil. If the vibration is sufficiently large or continues long enough, they will be damaged, since all real materials possess limited strengths. One can decrease (mitigate) vibration transmission and buildup, usually by directing the vibration to a flexible material which can move without damage, thereby converting the vibration energy to movement and, ultimately, to heat. There are many examples of this approach in our everyday world. Many cars use shock absorbers of various sorts filled with gas or liquid. Vibrations from the wheels are transmitted into the shock absorber, where most of the intensity is absorbed in the movement of the fill material. Most car engines are mounted on large blocks of special rubber, which move slightly while the engine is running, absorbing the engine vibrations. These approaches are also used, to some degree, in earthquake-proofing large buildings in earthquake-prone zones, albeit on a huge scale. Since rock is a good vibration transmitter, a different approach is used in mine blasting to reduce vibrations. Most mines and quarries use small, specifically-patterned, multiple explosive charges to break the rock first, then a second set of charges a few thousandths of a second later to heave the broken rock away from the mine face, where it can be loaded and transported. Since the rock is already broken, the opened cracks absorb a good deal of the vibration of the second blast. By timing the second blast correctly, one can also take advantage of wave interference effects, like those discussed above, to reduce the vibration still further. These multiple small blasts occurring within a small fraction of a second are known collectively as a "shot" in the mining industry. U. S. Bureau of Mines publications have specific instructions for mitigation of mining blast vibration, and, by implication, those from construction-related blasting.[2],[5] You can find out more about blasting and the vibrations it produces by looking at the CVDG chapter, Blasting Vibrations.
The Federal Transit Administration's Noise and Vibration Manual provides a list of steps to be taken and procedures to be avoided in mitigating construction vibration.[1] Another, more extensive, discussion of such recommendations from the U.S. state of California is also valuable.[11] Vibration mitigation in construction settings is further discussed in the CVDG's Avoiding Damage chapter and in the CVDG Pro page, Mitigating Vibration. Mitigation techniques are well understood and publicly available for free over the Internet to any contractor. There are almost always ways to carry out a given operation in a manner which produces less vibration than the "standard" way of doing it; this situation creates a moral, if not contractual and legal, obligation to mitigate vibration, especially from those operations known to be of particular concern in vibration damage (blasting, pile driving, vibratory compaction, ground impacts generally). The CVDG
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The vibration of water to form waves shows one of the prime properties of vibrations,
that they move as repeated "displacements" (i.e. changes in position) in the
particles or molecules which compose the material. Waves in water are relatively
simple, in part because water is pretty much the same everywhere in the local "neighborhood"
and has relatively low loss of vibration energy (damping). We can see waves in water, but visualizing vibrations
in other materials requires specialized equipment (e.g. a microphone and an oscilloscope or computer
for sound waves, a 
The up-down
("vertical") movement is usually less damaging, though not entirely without consequence, because structures are built
to withstand the generally higher vertical force of gravity. The seismograph trace at right above shows the vibration traces for an impact on the ground. A close examination will show that the traces for the three axes of measurement are similar, but differ in detail
both in velocity (intensity) and specific shape.
Ground
vibration can be either natural (from earthquakes) or man-made (from blasting, construction,
equipment, traffic, etc.) in source. In both cases, "seismographs" (see blasting seismograph
example at left) are used to record the ground vibration. To accomplish this meaningfully,
seismograph detectors must be firmly anchored to the ground (i.e. they must achieve
good "ground coupling") so that, as the ground moves, the detector moves
in exactly the same way. In absence of a certainty of proper ground coupling, seismograph data are
meaningless. 
The graphic at right shows the
interference effects of summing two mathematical sine waves
of different peak-to-peak distances (frequencies). For some values of x, the red sum wave has a
value of zero, because the positive and negative peaks of the two components (sin(x)
and sin(1.4x)) cancel each other, due to destructive interference. For other values,
the red sum wave is much larger than either simple wave, due to 
Much of the scientific literature of vibration effects is based on studies of surface mine blasting,
because damage effects were recognized earlier in mine blasting vibration than in construction.
The mining vibration studies provide much useful information on vibration effects,
even though they are not directly useful in estimating likelihood of damage from
construction activities. An introduction to blasting and the vibrations it produces can be found in the CVDG 
People can feel vibration at much lower levels than
those necessary to cause damage in most structures, so the mere presence of vibration doesn't imply that damage is occurring. Because of design and building material differences, structures of different types also respond differently to vibration. The result
is that there is no one guaranteed "safe" or "unsafe" level of vibration for all buildings and all vibration causes. 
Probably the best way to reduce vibration in construction operations is to conduct them in known ways which decrease
vibration generation at the source. For example, oscillatory compactors (or rollers) bring about faster compaction with less vibration generated than the more common vibratory ones. In pile driving, sonic or resonance pile drivers generate less
vibration than impact ("hammer") pile drivers.
