Patent Application
20200157762
Each year, on average, a major magnitude-8 earthquake strikes somewhere in the world. In addition, 10,000 earthquake-related deaths occur annually, where collapsing buildings claim the most lives, by far. Moreover, industry activity, such as oil extraction and wastewater reinjection, are suspected to cause earthquake swarms that threaten high-value oil pipeline networks, U.S. oil storage reserves, and civilian homes. Earthquake engineering building structural designs and materials have evolved over many years to attempt to minimize the destructive effects of seismic surface waves. However, even under the best engineering practices, significant damage and numbers of fatalities can still occur.
In particular, damage caused by earthquakes to critical structures, such as nuclear power plants, regional hospitals, military installations, airport runways, pipelines, dams, and other infrastructure facilities, exacerbates an earthquake disaster and adds tremendous cost and time of recovery. Even low-energy earthquakes resulting from human activity can cause significant damage. For example, wastewater reinjection practices used by the oil industry resulted in over 900 earthquakes in 2014-2015 in the state of Oklahoma, with a recent 2016 earthquake of magnitude 5.8. These continual earthquakes, although many may be small, can threaten extremely high-value above- and below-ground pipelines that control oil supply, storage, and transport in the U.S. This can present major economic and environmental concerns.
Certain structures have been proposed to protect buildings or other areas from the effects of seismic waves. In one way or another, however, all of those structures previously proposed are inadequate, in that they can only protect against a certain amount of seismic energy and still allow passage, or support propagation, of a certain amount of seismic energy. Previously proposed structures, therefore, are inadequate in that they allow certain types or amounts of seismic waves to enter an area that is intended to be protected.
Earthquake engineering building practices apply primarily to new construction to decouple seismic energy traveling in the ground between the ground and building foundation, whereas existing high-value structures are typically unlikely to be retrofitted because this is cost prohibitive and because there is typically difficulty in accessing the structures. Historically, there were no free standing subsurface structures used to protect existing high value assets from incoming hazardous earthquake waves. More recently, some research groups have investigated investigating the possibility of using boreholes in front of an area to protect from seismic waves. These efforts have been primarily computer simulations, with one group conducting a small scaled field test. This field test involved using a surface seismic source, which is not representative of a location for an earthquake, because earthquake sources are at depth. This test examined the ability of a few holes to block the seismic energy in its near field. These attempts have been very limited in their usefulness and are not representative of earthquakes, their geometries, raypaths, hypocenters, or seismic wavelengths or amplitudes.
Structures described herein can overcome these challenges by providing broadband redirection and attenuation of ground motion amplitudes caused by earthquakes. Structures can provide for this by implementing an engineered, subsurface, seismic barrier (elastic wave attenuation structure), for example. In some structures, a form of a metamaterial is created. A metamaterial is a material engineered to have a property that is not found in nature. Metamaterials are made from assemblies of multiple elements fashioned from materials not found in the media in which they are embedded. In the case of the earth, boreholes and trenches would be considered metamaterials since they are air-filled or specialized, viscous, attenuating, fluid-filled.
As disclosed herein, a seismic barrier (or metamaterial) can include borehole array complexes or trench complexes that reflect, refract, absorb, divert, or otherwise impede destructive seismic surface waves from a designated “protection zone.” Seismic surface waves against which disclosed wave damping structures can protect include Rayleigh waves (ground-roll), shear waves, Love waves, and compressional waves.
Further, disclosed wave damping structures can overcome the limitations of using a vertical borehole structure only in front of an intended protection zone. Use of a vertical borehole structure only in front of an intended protection zone (between a seismic wave incoming toward the protection zone and the protection zone itself) is not effective enough, since most seismic waves will diffract around a vertical borehole structure vertically and still strike the protection area with considerable force. However, with respect to structures described herein, boreholes or trenches (example “elements” as used herein) formed at an angle with respect to the vertical, with lateral offset into the earth and toward a zone and surface structure to be protected, can better divert seismic waves farther away from the intended protection zone than straight, deep boreholes. In addition, seismic wave damping structures described herein and incorporating such borehole or trench elements have been demonstrated, through numerical modeling and bench scale measurements, to provide broadband seismic wave amplitude reduction.
By using angles for holes that point down below a structure to be protected, seismic wave power can be effectively diverted far underneath the structure. Angled holes forming groupings or tapered structures can be particularly helpful due to the vertical depths that surface waves can reach, which can be hundreds of meters or greater. Moreover, by using angled holes on multiple sides of a structure, an aperture between protective holes can be made small, effectively blocking most seismic energy from diffraction toward the protected zone, thereby significantly limiting any need for deep boring, which can be cost-prohibitive. A structural arrangement formed of at least two angled borehole elements with opposing orientations with respect to a vertical, thus forming a tapered aperture, can be referred to herein as a “muffler.” Such structures are described hereinafter in greater detail with respect to the drawings.
Furthermore, retrofitting a building area with embodiment wave attenuation structures can be done with much flexibility, because disclosed structures can be implemented farther from a structure to be protected, at least at the Earth's surface. Further, certain periodic groupings of boreholes, such as sawtooth-shaped groupings or other geometric groupings, may be employed and can increase a range of seismic wavelengths against which a disclosed structure can be made effective. Such layout geometries can advantageously be configured to cause reflected self-interference of a traveling seismic wave, thus reducing the waves's effective ground motion amplitude. Still further, structures described herein can be used in protecting areas of the ocean or ocean front from the destructive effects of sea waves, such as tsunamis.
In one structure described herein, a seismic wave damping structure includes a structural arrangement of at least two elements, each element defining an inner volume and containing therein a medium resistant to passage of an anticipated seismic wave having a wavelength at least one order of magnitude greater than a cross-sectional dimension of the inner volume of the elements. The structural arrangement can taper from an upper aperture to a lower aperture, the structural arrangement defining a protection zone at the upper aperture, the upper aperture being larger than the lower aperture. The structural arrangement can be configured to attenuate power from the anticipated seismic wave within the protection zone relative to power from the anticipated seismic wave external to the protection zone.
The structural arrangement can be further configured to attenuate power from a Rayleigh wave, or from at least one of a compressional, shear, or Love elastic wave.
The at least two elements can be boreholes in earth, and the upper aperture can be closer to a surface of the earth than the lower aperture. As an alternative, the at least two elements can be trenches in earth, while the upper aperture can still be closer to the surface of the earth than the lower aperture.
The anticipated seismic wave can be a seismic wave in earth, and the medium resistant to passage of the anticipated seismic wave can be air or at least one of a gas, water, or viscous fluid. The anticipated seismic wave can be a water wave, and the medium resistant to passage of the water wave can include a solid material. The upper aperture can be closer to an upper surface of the water in the absence of the anticipated water wave. As an alternative, the upper aperture can be in air, and the lower aperture can be in earth or water in absence of the anticipated water wave.
A depth of the lower aperture in earth or water can be on the order of 100 meters. Each element can further include a structural lining between the inner volume and an exterior of the element. A width of the upper aperture can be on the order of 0.5 km. Particular preferred dimensions for particular upper apertures can be predicted using expressions given hereinafter.
Each of the at least two elements can include a plurality of discrete sub-elements, each of the sub-elements defining a respective sub-element inner volume and containing therein the medium resistant to passage of the seismic wave. Cross-sections of respective discrete sub-elements corresponding to at least one of the elements can be located at points collectively defining a hexagon.
The damping structure can also include a plurality of structural arrangements defining a superstructure, and the protection zone can encompass, at least partially, upper apertures of respective arrangements of the plurality of structural arrangements. The superstructure can be configured to attenuate power from the elastic wave within the protection zone relative to power from the seismic wave external to the protection zone. The protection zone can extend, in length, from one of the at least two elements to the other at the upper aperture. The protection zone can have a width, measured perpendicular to the length, of approximately 5%, 10%, 25%, 50%, 75%, or 100% of the length. The protection zone can be defined by a region, bounded at least partially by the at least two elements, within which the structural arrangement is configured to attenuate power from the seismic wave by at least 10 dB in power within the protection zone relative to power from the seismic wave external to the protection zone. Larger reductions in power have also been demonstrated by the authors using numerical simulations and scaled measurements.
The damping structure can also include an incident grouping of elements situated at a border of the protection zone expected to receive the seismic wave, as well as a transmission grouping of elements situated at a border of the protection zone opposite the incident grouping. The structural arrangement of at least two elements can include one element of the incident grouping and one element of the transmission grouping. Each element of the incident and transmission groupings of elements can have upper and lower ends thereof, and each element of the incident and transmission groupings of elements can define an inner volume and contain therein the medium resistant to passage of the anticipated seismic wave. The incident and transmission groupings can form a superstructure.
Upper ends or lower ends of respective elements of the incident or transmission grouping may be situated along an element row. Upper ends or lower ends of respective elements of the incident or transmission grouping may further be situated along a plurality of substantially parallel rows to form an element array. Upper ends or lower ends of respective elements of the incident or transmission grouping may be situated to form a substantially periodic pattern. The substantially periodic pattern may be a substantially sawtooth pattern, or the pattern may be configured to cause constructive or destructive interference of diffracted portions of the anticipated seismic wave diffracted from respective elements.
The damping structure can also include an electro-mechanical generator configured to generate or store electrical power using mechanical power from the anticipated seismic wave.
In another disclosed seismic wave damping structure the structure may include a structural grouping of elements, each element of the structural grouping defining an inner volume and containing therein a medium resistant to passage of an anticipated elastic wave having a wavelength at least one order of magnitude greater than a cross-sectional dimension of the inner volume of the elements. Each element of the structural grouping may have an upper end and a lower end thereof defining a first line from the upper end to the lower end. The first line can form an acute angle with a second line defining a direction of travel of the anticipated elastic wave toward a protection zone. The structural grouping of elements may be configured to attenuate power from the seismic wave within the protection zone relative to power from the seismic wave external to the protection zone.
The grouping of elements can be further configured to attenuate power from a Rayleigh elastic wave, or from at least one of a compression, shear, or Love seismic wave. Each element may be a borehole in earth or a trench in earth, with the upper end closer to a surface of the earth than the lower end.
At least one of the elements can include a plurality of discrete sub-elements substantially parallel to each other, each of the sub-elements defining a respective sub-element inner volume and containing therein the medium resistant to passage of the elastic wave. Cross-sections of respective discrete sub-elements may be located at points in a cross-sectional plane collectively defining a hexagon.
Upper ends or lower ends of respective elements can be situated along an element row. Furthermore, upper ends or lower ends of respective elements can be situated along a plurality of substantially parallel rows to form an element array. Upper ends or lower ends of respective elements can be situated to form a substantially periodic pattern, and the substantially periodic pattern may be a substantially sawtooth pattern. The substantially periodic pattern may also be configured to cause constructive or destructive interference of diffracted portions of the anticipated seismic wave diffracted from respective elements.
The grouping of elements can be an incident grouping of elements situated at a border of the protection zone at which the anticipated seismic wave is expected to be incident. The damping structure can further include a transmission grouping of elements situated at an opposite border of the protection zone opposite the incident grouping. Each element of the transmission grouping can define an inner volume and contain therein a medium resistant to passage of the anticipated seismic wave having a wavelength at least one order of magnitude greater than a cross-sectional dimension of the inner volume of the element. Each element of the transmission grouping may have an upper end and a lower end thereof defining a first line from the upper end to the lower end, the first line forming an obtuse angle with a second line defining a direction of travel of an attenuated anticipated seismic wave away from the protection zone. The transmission grouping of elements can be configured to attenuate power from the elastic wave within the protection zone relative to power from the elastic (e.g., seismic) wave external to the protection zone and transmitted through or around the incident grouping of elements.
A separation of upper ends of elements of the incident grouping from upper ends of respective elements of the transmission grouping can be on the order of 0.5 km. The protection zone can be further defined by a region, bounded at least partially by the incident and transmission groupings, within which the incident and transmission groupings are configured to attenuate power from the seismic wave by at least 10 dB within the protection zone relative to power from the seismic wave external to the protection zone.
Also disclosed is an elastic wave damping structure that can include first means for damping an anticipated seismic wave and second means for damping an anticipated seismic wave, wherein a combination of the first means and the second means forms an upper aperture and a lower aperture. The upper aperture can taper to lower aperture, the combination defining a protection zone at the upper aperture. The structural arrangement can be configured to attenuate power from the anticipated seismic wave within the protection zone relative to power from the anticipated seismic wave external to the protection zone.
Still another disclosed seismic wave damping structure can include first means configured to attenuate power from an anticipated seismic wave and at least one second means configured to attenuate power from the seismic wave. Each of the first and second means can define a first line from an upper end of the means to a lower end of the means, the first line forming an acute angle with a second line defining a direction of travel of the anticipated seismic wave toward a protection zone.
One limitation of the seismic wave damping structures described above is that they do not block or attenuate all power from an anticipated seismic wave from entering a protection zone. Some seismic power may still enter the protection zone, particularly higher frequencies. Specifically, a seismic wave damping structure is described in the examples above and in other parts of this specification can be very effective at attenuating power from an anticipated seismic wave in lower frequency ranges. Nonetheless, the seismic wave damping structures described above may permit propagation of frequencies, particularly frequencies in a higher frequency range, within the protection zone.
Advantageously, as described herein, the seismic wave damping structures described above may have resonant frequencies that can be predicted based on parameters of the structure and based on properties of the protection zone, particularly earth, soil, ground, etc. within the protection zone, in which the seismic wave damping structure is embedded. As further described hereinafter, the disclosed seismic wave damping structures may be advantageously combined with anti-resonance damping structures described hereinafter according to various embodiments. These combinations may form a seismic wave damping system that is extremely effective at preventing seismic waves from damaging protected structures in a protection zone. While some of the damping structures described herein have previously been known, they have not been used in the sense or combination described in this specification, namely as anti-resonance damping structures. As described hereinafter, when used as anti-resonance damping structures, they may be configured to address, specifically, resonance frequencies supported by the disclosed seismic damping structures, as described above.
When used in combined systems as noted above, and as described further hereinafter, seismic wave damping structures and anti-resonance damping structures have particular synergistic effects when used in combination with each other. On one hand, anti-resonance damping structures described herein may increase effectiveness of seismic wave damping structures described herein in damping residual seismic waves that propagate within the protection zone, which may be allowed to pass the seismic wave damping structures. On the other hand, synergistically, based on properties of a host medium in which the seismic damping structure is embedded, resonance frequencies supported by a given seismic wave damping structure may be specifically predicted based on one or more properties of the host medium and on one or more physical properties of the seismic damping structure. A corresponding anti-resonance damping structure may, therefore, be configured to dampen specifically a residual wave propagating within the protection zone at the resonance frequency. A synergy of this arrangement is that the anti-resonance damping structure need not be configured to address all possible seismic frequencies, potentially requiring more complex and extensive engineering. Instead, the anti-resonance damping structure may be built and configured to dampen, specifically, only one or more resonance frequencies supported by the seismic damping structure, where these resonance frequencies may be specifically predicted based on properties of the host medium and seismic damping structure. Accordingly, according to embodiments described hereafter, particular synergies may be obtained, which have not been contemplated or described before.
In one particular embodiment disclosed herein, a seismic wave damping system includes elements, embedded within a host medium. The elements define a seismic damping structure and are arranged to form a border of a protection zone. The seismic wave damping structure (also referred to herein as “seismic damping structure”) is configured to attenuate power of a seismic wave, traveling from a distal medium outside of the protection zone to the host medium in which the seismic damping structure is embedded. Thus, the seismic wave is incident at the seismic damping structure, at the protection zone. The seismic wave damping structure is characterized by one or more resonance frequencies that may be predetermined (i.e., known by prediction or modeling or calculation).
The resonance frequency may be a function of a depth of the elements embedded in the host medium and of a property (i.e., a physical property) of the host medium.
The anti-resonance damping structure may be configured to dampen the residual wave by being mechanically tuned to the resonance frequency. In other words, the anti-resonance damping structure may be built according to dimensions and specifications that will allow it to specifically dampen the resonance frequency, or the anti-resonance damping structure may be built, and then calibrated in such a manner that it absorbs or scatters preferentially at the resonance frequency, a harmonic of the resonance frequency, or a subharmonic of the resonance frequency. The anti-resonance damping structure may be configured to dampen the residual wave by being mechanically tuned to a harmonic of the resonance frequency or to a subharmonic of the resonance frequency. The anti-resonance damping structure may include two or more anti-resonance damping structures that are configured to dampen the residual wave by being mechanically tuned to two or more respective frequencies selected from the group consisting of (i) the resonance frequency, (ii) harmonics of the resonance frequency, and (iii) sub harmonics of the resonance frequency.
The anti-resonance damping structure may include one or more Helmholtz resonators positioned on or within the host medium within the protection zone. The one or more Helmholtz resonators may be filled with a gas, such as air, or with water or a viscous fluid. The anti-resonance damping structure may be an array of cylinders or other shaped elements, such as meta-concrete cylinders, buried within the host medium within the protection zone.
The anti-resonance damping structure may be a seismic wave absorbing structure configured to dampen the residual wave by absorption. The seismic wave absorbing structure may be a mass-in-mass lattice. The host medium may be earth, and the anti-resonance damping structure may include an array of trees that are not placed in order naturally, but are rather planted in the earth in a specific configuration that includes being spaced periodically within the protection zone. The anti-resonance damping structure may include an array of scattering components that are positioned periodically on or within the host medium within the protection zone. The anti-resonance damping structure may include one or more towers positioned on the host medium within the protection zone. The one or more towers may be one or more flexible, steel-girded towers. The one or more towers may have heights, extending vertically from a surface of the host medium, such as a ground surface, between a few meters and hundreds of meters. In various examples, heights may be on the order of 300 m, on the order of 200 m or, on the order of 100 m, on the order of 50 m, on the order of 25 m, or on the order of 10 m, for example. The one or more towers may have heights, extending vertically from a surface of the host medium, of 100 m or less, such as between about 10 m and about 100 m. Heights of the one or more towers may be specifically configured such that the towers dampen the residual wave at the resonance frequency by dampening one or more harmonics or subharmonics of the resonance frequency. The one or more towers may have, each, a cross-sectional dimension, such as a diameter, on the order of 1 m, on the order of 5 m, on the order of 10 m, or on the order of 15 m, for example.
In another embodiment, a method of constructing a seismic wave protection zone includes embedding elements within a host medium, thus defining a seismic wave damping structure characterized by a resonance frequency and forming a border of a protection zone. The seismic wave damping structure is built or otherwise configured to attenuate power of a seismic wave traveling from a distal medium to the host medium, where the seismic wave may be anticipated to be incident at the protection zone. The method also includes positioning an anti-resonance damping structure within the protection zone and configuring the anti-resonance damping structure to dampen a residual wave propagating within the protection zone at the resonance frequency.
The method may further include positioning the anti-resonance damping structure within the protection zone and configuring the anti-resonance damping structure to dampen a residual wave by building or tuning the anti-resonance damping structure to dampen the resonance frequency, where the resonance frequency is predicted based on one or more properties of the host medium and one or more dimensions or other properties of the elements embedded within the host medium forming the seismic wave damping structure. Configuring the anti-resonance damping structure to dampen the residual wave propagating within the protection zone at the resonance frequency may include configuring the anti-resonance damping structure based on one or more properties of the host medium, such as a wave propagation velocity, and one or more properties of the elements, such as length (depth) in the host medium, such as depth in earth.
In a further embodiment, a method of seismic wave damping includes converting an incident seismic wave propagating in a distal medium outside a protection zone into a residual seismic wave propagating within the protection zone at one or more resonant frequencies. The method further includes dampening the residual wave within the protection zone via anti-resonance damping. The method may optionally include use or incorporation of any of the methods; elements; seismic wave damping structures, superstructures, or arrangements; and anti-resonance damping structures summarized hereinabove pertaining to other embodiments or further described hereinafter in relation to other embodiments.
The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawings will be provided by the Office upon request and payment of the necessary fee.
The foregoing will be apparent from the following more particular description of example embodiments of the invention, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments of the present invention.
FIG. 2D is a top-view illustration two structural groupings of elements, namely an incident structural grouping to 304a of elements that are arranged into substantially parallel element rows 226 on the incident side of the protection zone.
A description of example embodiments of the invention follows.
The structural arrangement 100 tapers from an upper aperture 104 to a lower aperture 106. The structural arrangement 100 defines a protection zone, also referred to herein as a “structural protection zone” 112, at the upper aperture 104. The structural arrangement 100 is configured to attenuate power from the anticipated, incident elastic wave 114 within the protection zone 112, relative to power from the anticipated elastic wave external to the protection zone. Thus, outside of the protection zone 112, the incident elastic wave 114 has a given power, which can be referred to as seismic power, where the elastic wave 114 propagates in earth 118. However, due to the attenuation of power within the protection zone 112, which is caused by the structural arrangement 100, a component 114′ of the elastic wave 114, which is transmitted into the protection zone 112, has an attenuated seismic power relative to the incident elastic wave 114 that is incident at the structural arrangement 100. In particular, the elastic wave 114 is incident at the element 102a of the structural arrangement 100.
The upper ends of the elements 102a and 102b are located at greater (more positive) Z values along the Z axis that is illustrated in
The structural arrangement 100 can be configured to attenuate power from a Rayleigh wave, or from at least one of a compressional, share, or love elastic wave. Thus, where the elastic weight 114 is a seismic wave, for example, the structural arrangement 100 is, advantageously, effective for attenuating surface seismic waves, as well as seismic waves of other types.
The elements 102a-b can be boreholes in earth, and, as described hereinabove, the upper aperture 104 can be closer to a surface 120 of the earth 118 than the lower aperture 110. However, in other embodiments, the two elements 102a and 102b can be trenches in the earth 118, as described hereinafter in connection with
Furthermore, continuing to refer to
The limited-size, lower aperture 106 helps to prevent leakage of seismic power around the element 102a, at which the seismic wave 114 is incident, and up to the protection zone. Such leakage presents some limitation on the effectiveness of the element 102a as a seismic shield; however, it should also be recognized that, in other embodiments, such as that illustrated in
The structural arrangement 100 illustrates a key feature of many embodiments, the ability to be effective in broadband shielding against a wide range of seismic wavelengths. In particular, broadband wavelengths longer than the lower aperture 106 are most effectively blocked by the structural arrangement 100. While higher frequency, shorter wavelength seismic waves with wavelengths shorter than the lower aperture 106 are not as effectively shielded by the arrangement 100, the majority of seismic power is typically present at the very low frequencies and longer wavelengths that are less able to enter through the lower aperture.
The protection zone 112 can also have a width 224 that can extend, measured perpendicular to the length 222, approximately 5%, 10%, 25%, 50%, 75%, or 100% of the length 222, for example the region defined as the protection zone 112 can also be defined in terms of a particular degree of attenuation of the seismic waves 114 that can be achieved. For example, the protection zone 112 can be defined by a region, bounded by at least partially by the elements 102a and 102b, within which the structural arrangement 100 is configured to attenuate power from the elastic wave 114 by at least 10 dB. This attenuation can be within the protection zone 112, relative to power from the elastic wave 114 external to the protection zone 112. Furthermore, other criteria can be used to select the protection zone, such as the region within which a 3 dB attenuation of seismic power is obtained, or within which more than another given value, such as more than 30 dB of attenuation is obtained, for example.
As is understood in the art of mechanical engineering, the hexagon formation for structural elements can be particularly strong. However, it should be understood that discrete sub-elements can be arranged in other orientations, such as in groups of four, in pentagon or other polygon shapes, or in other arrangements, for example.
FIGS. 2D-2F illustrate other embodiment arrangements of elements. In particular, the arrangements illustrated in the top-view illustrations of FIGS. 2D-2F, in which there are a plurality of structural arrangements, constitute other example orientation patterns.
FIG. 2D, in particular, illustrates two structural groupings of elements, namely an incident structural grouping to 234a of elements that are arranged into substantially parallel element rows 226 on the incident side of the protection zone 112, which is the side at which the anticipated seismic wave 114 is anticipated to arrive toward the protection zone. Similarly, at the opposite side of the protection zone 112, the superstructure 240a includes two additional, substantially parallel element rows 226 of elements 102b that include a transmission structural grouping 234b of elements, at the side of the protection zone 112 that receives seismic power transmitted (leaked) through the protection zone 112. The elements 102a on the incident side, in the incident structural grouping 234a, and corresponding elements on the transmission side, in the transmission structural grouping 234b, form respective, structural arrangements similar to the arrangement 100 shown in
The element rows of the respective groupings that are closest to the protection zone 112 may be considered to form respective structure arrangements, while the remaining, outer rows can be considered to form respective wider structural arrangements. However, alternatively, an inner row from one grouping may be considered to correspond to an outer row from the opposite grouping, and vice versa, such that all structural arrangements have similar aperture sizes.
As can also be seen in FIG. 2D, the protection zone 112 encompasses, at least partially, upper apertures of respective structural arrangements. It should be noted that, while the elements 102a and 102b each form regular, periodic arrays of elements, in other embodiments, the elements 102a and 102b can each have other formations, and do not need to be situated in element rows. Furthermore, it should be understood that, in other superstructures within the scope of the present disclosure, there can be unequal numbers of elements in an incident structural grouping and a transmission structural grouping. In particular, respective incident-side elements and transmission-side elements can still form upper apertures of one or more respective, structural arrangements, similar to that shown in
In
The elements 302a-b each form an inner volume containing therein a medium resistant to passage of the wave 314. For the case of water waves, this material can be a solid, for example. In this way, the elements 302a-b may be formed of wood, metal, or another structure. The elements 302a-b can be similar to pylons, for example.
It should be understood that embodiment elastic wave damping structures that are used to protect against water waves are not limited to a single structural arrangement, such as the one shown in
A grouping of two or more of the elements 102a, with the acute angle for 440 a, can form an elastic wave damping structure having an incident structural grouping of elements. As described hereinabove, the acute angle 440a serves to redirect power from the seismic wave 114 around (below) the elements 102a. Where a depth 119 of the elements 102a (illustrated in
The elements 102a also include an optional structural lining 439 between the inner volume of the element and the exterior of the element (the earth 118). Structural linings may be helpful when used in certain types of earth where there is danger of the structural elements collapsing, or where there is danger of the structural elements filling with water in an undesirable manner, for example. Such structural linings can include PVC, other types of plastic, metal jackets, or any other suitable type of lining material known in the art of civil and mechanical engineering, for example.
While an incident structural grouping, such as the grouping 434a, can provide some protection, it may be useful to include the transmission structural grouping of elements 434b, which is optional. The grouping 434b includes elements 102b, with a line 438b extending from the upper end thereof to the lower end thereof forming an obtuse angle 440b with the line 436 defining the direction of travel of the elastic wave. In this way, an upper aperture and a lower aperture are formed, with the protection zone 112 at the upper aperture. The lower aperture is smaller than the upper aperture, thus preventing leakage of seismic power up into the protection zone 112. It should be understood that, while the incident structural grouping 434a is oriented with successive elements oriented along the X direction, arrays of elements oriented along the Y direction, such as those illustrated in
While a superstructure is not specifically annotated in
The substantially periodic, substantially sawtooth pattern 642 has the additional advantage of including more than a single row of elements in order to provide additional attenuation. Furthermore, the multiple-sawtooth pattern can extend a greater width along the y-axis, for example, thus providing a wider protection zone 112.
The reflected seismic wavelength wavelets 748 also can interfere constructively or destructively with the incident seismic wave 114, creating zones of the incident region in which seismic power is potentially greater than that which is incident, and also regions in which incident and reflected waves destructively interfere with each other to diminish significantly the intensity of seismic waves that are present in a given position. This effect can be exploited to protect certain positions on the incident side of the protection zone 112 having elements that are desired to be protected.
Interference effects can also be exploited advantageously to generate electrical power electro-mechanically. In particular, as illustrated in
Finite element modeling has been employed to predict attenuation of waves of various embodiments seismic wave damping structures.
The finite element analysis performed on the analytical models illustrated in
Superstructures as described herein, and as exemplified by the superstructure 840 in
In particular, the diagram 1160 shows an areal view of seismic wave snapshots without cloaking, while the diagram 1161 shows the effect of a single, frontal vertical borehole 1164. Further, the diagram 1162 is a depth view snapshot of the effect of cloaking using a structural arrangement including two angled borehole elements 102a, 102b as described in relation to
As illustrated in the comparison, using a single vertical borehole array or trench may significantly reduce the direct surface wave energy reaching a protected region. However, energy is still able to diffract around the barrier and enter the protected region. Using a V-shaped muffler (structural arrangement) formed of elements 102a and 102b is much more effective in blocking surface waves in the 3D extent. The graph 1163 of seismic power as a function of time reaching the protection zone further bears out this fact. A curve 1164 corresponds to graph 1160, with no boreholes and the highest power; a curve 1165 corresponds to graph 1161 with one vertical borehole and somewhat diminished power reaching the protection zone. However, a curve 1166 corresponds to the angled boreholes case of graph 1162, with greatly diminished power entering the protection zone between the angular boreholes.
The muffler 1200 includes a tapered funnel with a subwavelength opening (entrance; lower aperture) 1206 with respect to a wavelength of an acoustic radiation source 1214. The mathematical expressions shown in
In general, the calculations for mufflers suggest that small entrance, shallow depth and steep angle can all help to maximize attenuation of acoustic waves incident at the entrance aperture. Specific trends observed in calculations such as those shown in
The solid model was composed of Delrin® plastic 1464 with a P-wave speed of 1700 m/s, S-Wave speed of 855 m/s, and a density of 1.41 g/cm3. Delrin® blocks were machined to contain boreholes in prescribed patterns or trenches defining a V-shaped muffler and compared with homogeneous solid blocks. The Delrin® blocks contained boreholes in prescribed patterns or trenches defining a V-shaped muffler.
The model muffler was aimed at significantly reducing the elastic wave power reaching a ‘protected keep-out’ zone from a controlled elastic wave source. Each borehole had a diameter of 3 mm and was separated 3 mm apart from neighboring boreholes, forming a single line, where the line extended the entire length of the block. A near and far borehole line V-shaped pattern was formed where the near and far borehole line spacing is 3 inches apart on the Delrin® surface, the boreholes are sloped with a 5 inch length (4 inch vertical depth), and provided an aperture opening at the V-borehole barrier structure base of 0.5 inches.
Similarly, a V-trench barrier structure was machined in a separate Delrin® block where the 3 mm diameter boreholes were in contact, forming continuous hollow walls on both sides of the barrier structure. A Modal-Shop® variable transducer 1462 was used to vertically load on the Delrin® block surface to prescribed loading functions. A 10 kHz Ricker waveform was used to act as the seismic input function to generate the elastic wave propagation in the Delrin® blocks. PCB® model 352C33 accelerometers 1460 were used to measure the temporal and spatial vibration distributions observed on the Delrin® surface. An IOTECH® wavebook 516E was used to record each time series trace using a synchronized 70 kHz sample rate per channel.
In addition to the seismic wave damping structures described hereinabove, embodiments may include seismic wave damping systems that provide significant benefits beyond the benefits of the structures alone. Seismic wave damping structures, together with anti-resonance damping structures described herein, have particular synergistic effects when used in combination with each other.
On one hand, seismic wave damping structures described above can provide significant protection against damaging seismic power, particularly against the most damaging, lower-frequency range of seismic waves. On the other hand, separately, various alternative types of earthquake protection that may be generally less-effective against lower-frequency waves have been proposed, including Helmholtz resonators, tree or tower arrays, meta-concrete arrays, etc. A problem of the various proposed alternative types of protection is that they may particularly effective only at particular frequencies for which they are designed. Thus, these alternatives may not provide protection for a given expected earthquake, whose specific seismic frequencies may not be known in advance. Further, while various proposed alternative types of protection may be built in the same location to address different frequencies, engineering in this manner is redundant and expensive.
A problem of the seismic wave damping structures described above is that they may be characterized by one or more resonant frequencies that may propagate well within a protection zone defined by the structures. The present inventors have recognized that this problems of both the seismic wave damping structures and the various proposed alternative types of protection may become special advantages in a system that incorporates both a seismic wave damping structure, as described hereinabove, and also one or more of the various proposed alternative types of earthquake protection, which are referred to in the context of the embodiment systems of the present application as “anti-resonance damping structures” and by other terms describing specific examples thereof
An advantage of the seismic wave damping structures described hereinabove is that their resonant frequencies may be predicted in advance. Then, with that knowledge, it is not only helpful, but also especially advantageous to configure an anti-resonance damping structure to address the particular resonant frequencies supported by the seismic wave damping structures. Thus, when used together, the two structures act synergistically to increase protection against seismic waves in significant manner, beyond the benefits that could be expected from either seismic wave damping structures or anti-resonant damping structures acting individually.
Further, when combined as described herein, the benefits are beyond those that may be predicted simply from a hypothetical combination of any two given earthquake protection structures. As noted above, both the seismic wave damping structures and the anti-resonance damping structures have disadvantages when used separately, namely that higher-frequency resonances are allowed to propagate, and that only protection against particular frequencies is generally provided, respectively. However, the inventors have realized that when used in combination, these very disadvantages each become advantageous. Particularly, there is a way described to predict resonance frequencies that may be supported by a seismic wave damping structure, and instead of attempting to engineer an alternative earthquake protection structure to protect against primary (incident) seismic waves, an alternative structure (“anti-resonance damping structure,” as used herein) may be engineered to protect against specific resonant frequencies predicted for the seismic wave damping structure.
Based on properties of a host medium in which the seismic damping structure is embedded, resonance frequencies supported by a given seismic wave damping structure may be specifically predicted based on one or more properties of the host medium and on one or more physical properties of the seismic damping structure. A corresponding anti-resonance damping structure may, therefore, be configured to dampen specifically a residual wave propagating within the protection zone at the resonance frequency. A synergy of this arrangement is that the anti-resonance damping structure need not be configured to address all possible seismic frequencies, potentially requiring more complex and extensive engineering. Instead, the anti-resonance damping structure may be built and configured to dampen, specifically, only one or more resonance frequencies supported by the seismic damping structure, where these resonance frequencies may be specifically predicted based on properties of the host medium and seismic damping structure. Accordingly, according to embodiments described hereafter, particular synergies may be obtained, which have not been recognized previously.
As noted hereinabove in the Summary section, a certain amount of seismic wave power will be able to enter a disclosed seismic damping structure. In
Example anti-resonance damping structures 1770 may include a Helmholtz resonator or array of Helmholtz resonators, as illustrated in
The host medium 1718 shown in
It should be further understood that the anti-resonance damping structure 1770 may be configured to dampen the residual wave 1760′ at the resonance frequency by being tuned to dampen, and being mechanically tuned to a harmonic or subharmonic of the resonance frequency. Furthermore, in some embodiments, anti-resonance damping structures may be configured to dampen a residual wave by being mechanically tuned to the resonance frequency, one or more harmonics of the resonance frequency, one or more sub harmonics of the resonance frequency, or any combination thereof. An example harmonic of a resonance frequency of 5 Hz is 10 Hz, for example. An example subharmonic of a resonance frequency 5 Hz is a frequency of 2.5 Hz, for example.
These resonance frequencies characterizing an example V-shaped muffler (seismic wave damping structure) may be determined by numerical modelling, as will be understood by one of skill in the art in view of this disclosure. Alternatively, the resonance frequencies may be calculated more easily as follows. We separate the description of the total transmission loss (Eqn. (1)) into the entrance loss TLent (Kinsler et al., 2000) and the loss through the conical muffler TLcon (Easwaran and Munjal, 1992). In terms of seismology, the entrance loss is the frequency dependent reflected wave power that does not couple into the muffler inlet. The transmission loss through the muffler as the coupled wave travels within the muffler to its outlet (exit) is attenuation.
TL=TL
con
+TL
ent (1)
The entrance loss is caused by the acoustic impedance of the open pipe with the subwavelength opening, as described by the lumped element theory (Kinsler et al., 2000).
Furthermore, the transmission loss through the conical muffler can be expressed in terms of a transfer matrix relating the pressure and velocity at muffler inlet (entrance) (p1, v1) to those at the muffler outlet (exit) (p2, v2).
Using the above transfer matrix, we can describe the TLcon term in Eqn. (1) for a conical muffler as follows (Easwaran and Munjal, 1992):
in which the terms in the Eqn. (4) are in turn defined below:
Term definitions for the muffler characteristics specified in Eqns. (1)-(11) are described in Table 1.
The above formalism of the conical muffler depicted in Eqns. (1)-(11) was used to estimate elastic wave transmission and attenuation performance for various muffler geometries and sizes scaled to nominal areas for example infrastructure protection vulnerable to damage from earthquakes, treating seismic waves as example elastic waves. Muffler (seismic wave damping structure) performance results calculated based on Eqns. (1)-(11) are depicted in
In particular, the one or more resonance frequencies of a seismic wave damping structure may be determined as a function of depth of the elements forming the muffler (L, as used in Table 1 and illustrated in
In summary, in order to achieve the maximum attenuation of seismic motion for a broadband frequency response, the muffler parameters should include small inlet diameters, shallow depths with shorter lengths, and steep muffler wall angle (shallow slope). In these calculations, a 25-30 dB transmission loss through the muffler was possible for a shallow, steep angle structure at 1 Hz of seismic frequency, with greater reductions at frequencies less than 1 Hz. Seismic frequencies from 0.1 to 1 Hz are common for many large magnitude earthquakes. This frequency band appears to be well suited for the muffler structure. The predicted transmission loss at these frequencies indicates that the impact of larger earthquakes can be reduced to a less destructive level by the employment of conical mufflers.
Additional details regarding these calculations may be obtained in “Seismic Muffler Protection of Critical Infrastructure from Earthquakes,” Robert W. Haupt, et al., Bulletin of the Seismological Society of America, Vol. 108, No. 6, pp. 3625-3644, Dec. 2018, which is hereby incorporated herein by reference in its entirety.
The following are two examples for how to use the equations in
In some embodiments, anti-resonance damping of residual waves in a protection zone may be accomplished by mechanically tuning an anti-resonance damping structure to a harmonic or subharmonic of the resonance frequency. Furthermore, as will be understood in view of this description, a seismic wave damping structure may be characterized by two or more resonance frequencies. Accordingly, two or more resonance frequencies for residual seismic waves may be targeted for attenuation by mechanically tuning one or more anti-resonance damping structures to two or more respective frequencies, whether resonance frequencies, harmonics or subharmonics thereof, or any combination of these.
In the case of a seismic damping structure having a resonance frequency at 5 Hz, the Helmholtz resonator array anti-resonance damping structure may be built with cylinder width of 1.7 m, cylinder height of 1.3 m, neck width of 0.1 m, and neck height of 0.2 m. As a second example, for a resonance frequency of a seismic damping structure at 10 Hz, a cylinder width for the Helmholtz resonator array may be 1.7 m, with cylinder height 1.3 m, neck width of 0.24 m, and neck height of 0.2 m. Additional details regarding parameters for Helmholtz resonators may be found, for example, in Wang et al., J. Appl. Phys. 103 (2008) 064907, which is hereby incorporated herein by reference in its entirety.
Heights H of various embodiments, extending vertically from the surface of the host medium, may be between a few meters and hundreds of meters, such as 100 m or less, for example. A particular advantage of embodiment systems is that an anti-resonance damping structure need not be built to attempt to counteract the direct influence of incident seismic waves, the most destructive frequencies of which are usually at the lower end of the seismic frequency range, such as between 0.1 Hz and 3 Hz, as an example. Instead, in embodiment systems, anti-resonance damping structures are configured to dampen seismic waves propagating at the resonance frequency or frequencies of the respective seismic damping structures. The seismic damping structures are particularly effective at damping lower seismic frequencies, while the resonance frequencies tend to be higher, such as above 3 Hz, above 5 Hz, or above 10 Hz, for example. For damping at higher frequencies, towers, trees, or other structures may generally be smaller, shorter, and more feasible and inexpensive to construct.
For exemplary wood towers, example parameters can include vp=2200 m/s, pr=450 kg/m3, vs=1200 m/s, and A=0.071 m2. Example ground host medium parameters can include vp=900 m/s, pg=1200 kg/m3, and vs=500 m/s, with r=vs/vp, L=50, μg=1×108 for a shear modulus of soil, and Er=1×109 for Young's modulus of the wood. With these parameters, in particular examples, where an example height of the resonators is 50 m, the resonant frequency addressed will be 5 Hz, while in a second example, with a height of 25 m, the resonant frequency addressed will be 10 Hz. Furthermore, assuming that a resonant frequency is 5 Hz for example, a height of 25 m may still be used, thus tuning the array of resonators 2472 to dampen the harmonic frequency 10 Hz, which will still dampen a residual wave propagating within the protection zone at 5 Hz. Further information regarding these calculations may be found, for example, in Colombi et al. (2016), “A seismic meta-material: The resonance meta-wedge,” Sci. Rep. 6, 27717, which is hereby incorporated herein by reference in its entirety.
At 2686, an anti-resonance damping structure is positioned within the protection zone and is configured to dampen a residual wave propagating within the protection zone at the resonance frequency. As described hereinabove, configuring the anti-resonance damping structure to dampen the residual wave propagating within the protection zone at the resonance frequency may include determining the resonance frequency as a function of a depth of the elements in the host medium and of a physical property of the host medium.
It should be understood that the procedure 2600, in other embodiments, may be modified to use or take advantage of any embodiment structure or system described hereinabove.
In a further embodiment not directly illustrated in the drawings, but which will be clearly understood by those skilled in the art in view of the other illustrations in the drawings and description herein, a procedure for seismic wave damping includes converting an incident seismic wave propagating in a distal medium outside a protection zone into a residual seismic wave propagating within the protection zone at one or more resonant frequencies. The procedure further includes dampening the residual wave within the protection zone via anti-resonance damping. The method may optionally include use or incorporation of any of the methods; elements; seismic wave damping structures, superstructures, or arrangements; and anti-resonance damping structures summarized hereinabove pertaining to other embodiments or further described hereinafter in relation to other embodiments. For example, the distal medium may be earth, and also the protection zone may earth or another building foundation or medium. The conversion may occur via the incident seismic waves of any of the types described hereinabove being incident at a seismic wave damping structure, superstructure, arrangement, or grouping formed by elements such as borehole elements embedded in the earth. A casing (i.e., liner) may be inserted into each borehole to maintain its shape and structure. Dampening the residual wave within the protection zone via anti-resonance damping may include use of any of the anti-resonance damping within the scope of the claims listed hereinafter or within the scope of the embodiments otherwise described hereinabove.
The teachings of all patents, published applications and references cited herein are incorporated by reference in their entirety.
While this invention has been particularly shown and described with references to example embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.
This application claims the benefit of U.S. Provisional Application No. 62/769,517, filed on Nov. 19, 2018. The entire teachings of the above application are incorporated herein by reference.
This invention was made with Government support under Contract No. FA8721-05-C-0002 awarded by the U.S. Air Force. The Government has certain rights in the invention.
| Number | Date | Country | |
|---|---|---|---|
| 62769517 | Nov 2018 | US |
