U.S. patent application number 16/688997 was filed with the patent office on 2020-05-21 for seismic wave damping system.
The applicant listed for this patent is Massachusetts Institute of Technology. Invention is credited to Robert W. Haupt, Vladimir Liberman, Mordechai Rothschild.
Application Number | 20200157762 16/688997 |
Document ID | / |
Family ID | 70727550 |
Filed Date | 2020-05-21 |
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United States Patent
Application |
20200157762 |
Kind Code |
A1 |
Haupt; Robert W. ; et
al. |
May 21, 2020 |
Seismic Wave Damping System
Abstract
A seismic wave damping system, and a corresponding method,
includes elements, embedded within a host medium, the elements
defining a seismic damping structure, and the elements being
arranged to form a border of a protection zone. The seismic damping
structure is configured to attenuate power of a seismic wave,
traveling from a distal medium to the host medium, that is incident
at the protection zone. The seismic damping structure is
characterized by a resonance frequency. The system further includes
an anti-resonance damping structure positioned within the
protection zone and configured to dampen a residual wave
propagating within the protection zone at the resonance frequency.
Embodiment systems offer synergistic advantages because resonance
frequencies of seismic wave damping structures may be predicted by
calculation and an anti-resonance damping structure may be built to
attenuate waves of primarily only specific resonance frequencies
supported by the seismic wave damping structure.
Inventors: |
Haupt; Robert W.;
(Lexington, MA) ; Rothschild; Mordechai; (Newton,
MA) ; Liberman; Vladimir; (Reading, MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Massachusetts Institute of Technology |
Cambridge |
MA |
US |
|
|
Family ID: |
70727550 |
Appl. No.: |
16/688997 |
Filed: |
November 19, 2019 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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62769517 |
Nov 19, 2018 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
E04H 9/00 20130101; E02B
17/0017 20130101; E04B 1/98 20130101; E04H 9/027 20130101; E02D
31/08 20130101 |
International
Class: |
E02D 31/08 20060101
E02D031/08; E04B 1/98 20060101 E04B001/98 |
Goverment Interests
GOVERNMENT SUPPORT
[0002] 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.
Claims
1. A seismic wave damping system comprising: elements, embedded
within a host medium, defining a seismic damping structure, the
elements arranged to form a border of a protection zone, the
seismic damping structure configured to attenuate power of a
seismic wave, traveling from a distal medium to the host medium,
that is incident at the protection zone, the seismic damping
structure characterized by a resonance frequency; and an
anti-resonance damping structure positioned within the protection
zone and configured to dampen a residual wave propagating within
the protection zone at the resonance frequency.
2. The seismic wave damping system of claim 1, wherein the
resonance frequency is a function of a depth of the elements in the
host medium and of a physical property of the host medium.
3. The seismic wave damping system of claim 1, wherein the
anti-resonance damping structure is configured to dampen the
residual wave by being mechanically tuned to the resonance
frequency.
4. The seismic wave damping system of claim 1, wherein the
anti-resonance damping structure is configured to dampen the
residual wave by being mechanically tuned to a harmonic of the
resonance frequency.
5. The seismic wave damping system of claim 1, wherein the
anti-resonance damping structure is configured to dampen the
residual wave by being mechanically tuned to a subharmonic of the
resonance frequency.
6. The seismic wave damping system of claim 1, wherein the
anti-resonance damping structure includes two or more
anti-resonance damping structures 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)
subharmonics of the resonance frequency.
7. The seismic wave damping system of claim 1, wherein the
anti-resonance damping structure includes one or more Helmholtz
resonators positioned on or within the host medium within the
protection zone.
8. The seismic wave damping system of claim 1, wherein the
anti-resonance damping structure is an array of cylinders within
the host medium within the protection zone.
9. The seismic wave damping system of claim 1, wherein the
anti-resonance damping structure is a seismic wave absorbing
structure configured to dampen the residual wave by absorption.
10. The seismic wave damping system of claim 9, wherein the seismic
wave absorbing structure is a mass-in-mass lattice.
11. The seismic wave damping system of claim 1, wherein the host
medium is earth, and wherein the anti-resonance damping structure
includes an array of trees planted in the earth within the
protection zone and spaced periodically.
12. The seismic wave damping system of claim 1, wherein the
anti-resonance damping structure includes an array of scattering
components positioned periodically.
13. The seismic wave damping system of claim 1, wherein the
anti-resonance damping structure includes one or more towers
positioned on the host medium within the protection zone.
14. The seismic wave damping system of claim 13, wherein the one or
more towers are one or more flexible, steel-girded towers.
15. The seismic wave damping system of claim 13, wherein the one or
more towers have heights, extending vertically from a surface of
the host medium, between a few meters and hundreds of meters.
16. The seismic wave damping system of claim 13, wherein the one or
more towers have heights, extending vertically from a surface of
the host medium, of 100 m or less.
17. The seismic wave damping system of claim 13, wherein each of
the one or more towers has a cross-sectional dimension on the order
of 1 m or on the order of 10 m.
18. A method of constructing a seismic wave protection zone, the
method comprising: 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,
wherein the seismic wave damping structure is configured to
attenuate power of a seismic wave traveling from a distal medium to
the host medium and incident at the protection zone; and
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.
19. The method of claim 18, wherein configuring the anti-resonance
damping structure to dampen the residual wave propagating within
the protection zone at the resonance frequency includes configuring
the anti-resonance damping structure based on one or more
properties of the host medium and one or more properties of the
elements.
20. A method of seismic wave damping, the method comprising:
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; and
dampening the residual wave within the protection zone via
anti-resonance damping.
Description
RELATED APPLICATION
[0001] 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.
BACKGROUND
[0003] 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.
[0004] 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.
[0005] 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.
SUMMARY
[0006] 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.
[0007] 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.
[0008] 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.
[0009] 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.
[0010] 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.
[0011] 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.
[0012] 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.
[0013] 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.
[0014] 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.
[0015] 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.
[0016] 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.
[0017] 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.
[0018] 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.
[0019] 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.
[0020] 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.
[0021] 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.
[0022] 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.
[0023] 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.
[0024] 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.
[0025] 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.
[0026] 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.
[0027] 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.
[0028] 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.
[0029] 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.
[0030] 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.
[0031] 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.
[0032] 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.
[0033] 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).
[0034] 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.
[0035] 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.
[0036] 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.
[0037] 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.
[0038] 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.
[0039] 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.
[0040] 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.
BRIEF DESCRIPTION OF THE DRAWINGS
[0041] 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.
[0042] 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.
[0043] FIG. 1A is a cross-sectional side view of an embodiment
elastic wave damping structure that includes a downward-tapered,
V-shaped structural arrangement with two elements.
[0044] FIG. 1B is a diagram of the embodiment of FIG. 1A without
the above-ground building structure and with additional
below-ground details as compared to FIG. 1A.
[0045] FIG. 2A is a top-view illustration of the structural
arrangement of FIG. 1B.
[0046] FIG. 2B is a top-view illustration of a linear structural
grouping of elements forming an embodiment elastic wave damping
structure.
[0047] FIG. 2C is a top-view illustration of an embodiment elastic
wave damping structure including an arrangement of two elements
formed of pluralities of discrete sub-elements in hexagonal
clusters.
[0048] 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.
[0049] FIG. 2E is a top-view illustration of an embodiment wave
damping structure including a superstructure with two of the
structural arrangements illustrated in FIG. 1B.
[0050] FIG. 2F is a top-view illustration of a superstructure
includes trench elements instead of borehole elements.
[0051] FIG. 3 is a cross-sectional side-view diagram showing how
embodiments can be advantageously used to protect structures in the
sea, such as an oil platform.
[0052] FIG. 4A is a cross-sectional, side-view illustration of
incident and transmission structural element groupings,
respectively, of elements on either side of a protection zone.
[0053] FIG. 4B is a cross-sectional, side-view illustration of an
incident structural grouping of elements that can be employed to
protect against incident water waves, such as tsunami waves.
[0054] FIG. 5 is a top-view illustration of an arrangement of
elements forming an incident structural grouping of the elements in
a sawtooth pattern.
[0055] FIG. 6 is a top-view illustration of an embodiment wave
damping structure with a substantially sawtooth, substantially
periodic pattern of elements that form an incident structural
grouping.
[0056] FIG. 7 is a top-view illustration of an additional incident
structural grouping of elements showing interference between
reflected wavelets and showing constructive interference used to
generate electrical power.
[0057] FIG. 8A is a top-view illustration of a protection zone
formed between modeled arrays of borehole elements.
[0058] FIG. 8B is a three-dimensional (3D) illustration of the
protection zone and borehole elements shown in FIG. 8A.
[0059] FIG. 8C is a 3D view of modeled trench elements in a 3D
finite element meshing.
[0060] FIG. 9A shows model equations used in finite element
analysis of embodiments.
[0061] FIG. 9B is a 3D representation of the finite element
analysis.
[0062] FIG. 9C is a graph showing a source time function for
rupture velocity of an earthquake measured and used as a source
time function for the finite element analysis.
[0063] FIG. 9D is a graph showing power reduction calculated in a
protection zone with and without embodiment wave damping
structures.
[0064] FIG. 9E is collection of areal and depth view seismic wave
snapshots calculated with and without embodiment seismic wave
damping structures.
[0065] FIG. 10 is a table showing various high-value assets that
may be protected, as examples, using embodiment elastic wave
damping structures, with expected upper aperture and lateral extent
sizes and numbers of boreholes for corresponding structures.
[0066] FIG. 11 is a series of diagrams and a graph showing the
comparative effects of seismic cloaking on seismic wave propagation
for a single, vertical barrier element compared with an embodiment
angled structural element, as calculated using a finite difference
2D model of the barrier structures.
[0067] FIGS. 12A-12B show a diagram and equations illustrating
semi-analytical simulation of acoustic propagation through a
"tapered muffler" geometry.
[0068] FIGS. 13A and 13B are graphs showing transmission loss as a
function of frequency for various acoustic "muffler" parameters, as
calculated using the analytical tools shown in FIGS. 12A-12B.
[0069] FIG. 14 is a collage of photographs showing apparatus used
to study, on a model scale, non-naturally occurring, man-made
structures such as borehole arrays and trenches embedded in elastic
media analogous to rock and compact soil using a machined,
table-top scaled physical model.
[0070] FIGS. 15A-15C show measured results that illustrate the
effects of a model V-trench machined in Delrin.RTM. block table-top
experimental configuration. In particular, FIG. 15A and FIG. 15B
show accelerometer time series traces measured in a center line
across a homogeneous solid Delrin.RTM. block relative to the
transducer source location, and FIG. 15C shows the model trench
barrier structure in schematic form, along with accelerometer
locations corresponding to the traces in FIGS. 15A-15B.
[0071] FIG. 16 shows earthquake magnitude reduction expected due to
subsurface barrier structures, based on extrapolation from the
measured and modelled results.
[0072] FIG. 17A is a schematic diagram illustrating an embodiment
seismic wave damping system in its environment of use.
[0073] FIG. 17B is a schematic diagram illustrating, more
particularly, the seismic wave damping system of FIG. 17A, without
it's contextual environment of use.
[0074] FIG. 18A is a perspective, colored or shaded illustration of
a V-shaped seismic muffler (seismic damping structure) used in
connection with the anti-resonance damping structure of FIGS.
17A-17B to form an embodiment seismic wave damping system.
[0075] FIG. 18B is a color-coded or shaded, side-view graphical
drawing illustrating particle velocity, in unit length per second,
over a cross-sectional area showing the seismic damping structure
of FIG. 18A.
[0076] FIG. 19A is a cross-sectional diagram illustrating geometry
and terms terminology for an example conical shaped muffler seismic
damping structure.
[0077] FIG. 19B is a diagram illustrating for different muffler
geometries and their respective dimensions.
[0078] FIG. 19C is a graph illustrating elastic wave transmission
loss as a function of wavelength corresponding to seismic
frequencies spanning from 0.1-10 Hz for the muffler geometries
illustrated in FIG. 19B.
[0079] FIG. 19D is a graph illustrating P and S wave transmission
loss behavior for the four muffler examples illustrated in FIG. 19B
as a function of seismic frequency.
[0080] FIG. 20A illustrates four different muffler geometries,
wherein the inlet diameter is 0.1 km and the muffler wall slope is
constant for all cases except the last case, which shows vertical a
vertical wall muffler for comparison.
[0081] FIG. 20B is a graph illustrating wave transmission loss as a
function of seismic wavelength corresponding to seismic frequencies
from 0.1 Hz to 10 Hz.
[0082] FIG. 20C is a graph illustrating P and S wave transmission
loss for the four muffler examples illustrated in FIG. 20A as a
function of seismic wave incident frequency.
[0083] FIG. 21A is a diagram illustrating cross-sectional muffler
geometry for a shallow sloping muffler model (a) having a wall
slope and for a vertical wall muffler model (d).
[0084] FIG. 21B is a cross-sectional illustration of the example
structures in FIG. 21A, along with color-coded or shaded
illustration of numerically calculated damping characteristics.
[0085] FIG. 21C is a graph illustrating transmission loss as a
function of seismic frequency for the two example structures
illustrated in FIG. 21A.
[0086] FIG. 22A illustrates a time source a source time function
from the Hector Mine 1999 earthquake.
[0087] FIG. 22B is a graph showing amplitude as a function of
frequency for the Hector Mine earthquake.
[0088] FIG. 23A is a color-coded or shaded, cross-sectional
illustration of a seismic wave field in presence of an embodiment
seismic wave damping system that includes a Helmholtz resonator
array anti-seismic damping structure as part of the system.
[0089] FIG. 23B is a graph showing the source function for the
Hector Mine earthquake, injected by simulation into the model
represented in the graph of FIG. 23A.
[0090] FIG. 23C illustrates calculations by which damping of a
Helmholtz resonator array may be determined.
[0091] FIG. 23D is a schematic diagram illustrating the Helmholtz
resonator array, anti-resonance damping structure graphically
illustrated in FIG. 23A.
[0092] FIG. 23E is a graph illustrating seismic amplitude as a
function of frequency, as reduced by a seismic wave damping
structure alone, and as reduced by the seismic wave damping
structure in combination with the Helmholtz resonator array example
anti-resonance damping structure of FIG. 23A.
[0093] FIG. 24A is a color-coded or shaded, vertical view
cross-sectional graph of a seismic wave damping structure
embodiment including a tower or tree array example anti-resonance
damping structure in presence of a shear wave of the Hector Mine
earthquake.
[0094] FIG. 24B is a graph showing the source function for the
Hector Mine earthquake, which was injected into the model
illustrated in FIG. 24A.
[0095] FIG. 24C shows an equation that can be used to calculate
damping frequency for the array of resonators (towers or trees,
e.g.) illustrated in FIG. 24A.
[0096] FIG. 24D is a more detailed illustration of the array of
resonators illustrated in FIG. 24A.
[0097] FIG. 24E is a graph illustrating damping, particularly
seismic amplitude decrease, obtained by using the combination of
seismic wave damping structure and anti-resonance damping structure
of the embodiment system illustrated in FIG. 24A.
[0098] FIG. 25A is a cross-sectional illustration of a
meta-concrete array example of buried cylinders used as an
anti-resonance damping structure as part of an embodiment system,
illustrated in presence of the Hector Mine earthquake source
function used in the model.
[0099] FIG. 25B is a graph illustrating the Hector Mine earthquake
source function injected into the model illustrated in FIG.
25A.
[0100] FIG. 25C is a cross-sectional view of the meta-concrete
array example anti-resonance damping structure illustrated in FIG.
25A.
[0101] FIG. 25D is an equation illustrating how resonance frequency
of the medic concrete array of FIG. 25A may be calculated.
[0102] FIG. 25E is a graph illustrating seismic amplitude reduction
damping that may be obtained using the meta-concrete array example
seismic anti-resonance damping structure as part of an embodiment
seismic wave damping system illustrated in FIG. 25A.
[0103] FIG. 26 is a flow diagram illustrating an embodiment
procedure for seismic wave damping.
DETAILED DESCRIPTION
[0104] A description of example embodiments of the invention
follows.
Seismic Wave Damping Structures
[0105] FIG. 1A is a cross-sectional side view of an embodiment
elastic wave damping structure that includes a downward-tapered,
V-shaped structural arrangement with two elements 30a and 30b. The
structural arrangement defines a protection zone 40 between the
elements 30a and 30b, where a building 20 that is desired to be
protected is located above the protection zone. The damping
structure is configured to protect the building 20 from incident
surface waves 60 that initially impinge on the element 30a as a
result of an earthquake 50. A small amount of seismic wave power
still enters the protection zone 40, such that there are attenuated
surface waves 60' under the building 20. Some wave energy also
travels underneath and around the elements 30a and 30b to become
transmitted surface waves 60''.
[0106] FIG. 1B is a cross-sectional side view of an embodiment
elastic wave damping structure that includes a structural
arrangement 100 with two elements 102a and 102b. Each of the
elements 102a and 102b defines an inner volume 116 that contains
therein a medium resistant to passage of an anticipated incident
elastic wave 114. The wave 114 has a wavelength at least one order
of magnitude greater than a cross-sectional dimension of the inner
volume of the elements, such as the diameter d of the element 102a.
The element 102a may be referred to as having an upper end 108 and
a lower end 110. Likewise, while not marked in FIG. 1B, the element
102b has upper and lower ends similar to those of element 102a.
[0107] 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.
[0108] 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 FIG. 1B, while the lower ends 110 are located at
smaller positive (more negative), Z values than the upper ends
108.
[0109] 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.
[0110] 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 FIG. 2F. For either boreholes or trenches, or other
configurations of the elements 102a-b, the upper aperture 104 can
be closer to a surface 120 of the earth 118 than the lower aperture
110, as illustrated in FIG. 1B. The lower aperture 110 is at a
depth 119 in the earth below the surface 120. In many embodiments,
the length of the upper aperture, as also illustrated in FIG. 2A
and described below, can be on the order of 0.5 km, for
example.
[0111] Furthermore, continuing to refer to FIG. 1B, in cases where
the anticipated incident elastic wave 114 is a seismic wave in the
earth, the medium contained in the inner volume 116 and resistant
to passage of the wave 114 can be air, for example. However, in
other embodiments, the medium contained in the inner volume 116 can
be at least one of a gas, water, or viscous fluid. In all of these
cases of air, gas, water, or viscous fluid, for example, the medium
does not transmit seismic power nearly as well as the earth 118.
Hence, the medium resists passage of the wave 114, and seismic
power can be deflected, reflected, diffracted, or otherwise
dissipated before it enters the protection zone 112 as the
attenuated wave 114 with attenuated seismic power. Moreover, given
the tapered shape of the structural arrangement 100, which can also
be considered to be angles of the elements 102a and 102b with
respect to the z-axis, seismic power can be directed downward, away
from any structures or objects desired to be protected within the
structural protection zone 112.
[0112] 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
FIGS. 4B and 5-7, a grouping of elements, such as the element 102a,
may still be advantageously used on an incident side of the
structural protection zone 112 in order to limit seismic power
reaching the protection zone. Thus, while the element 102b on the
side of the protection zone opposite the incident side causes the
structural arrangement 100 to be much more effective, embodiments
can nevertheless employ an array of elements 102b on the incident
side of the protection zone, where the elastic wave 114 is expected
to be incident, with some helpful attenuation and deflection of
seismic power reaching the protection zone.
[0113] 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.
[0114] FIG. 2A is a top-view of the structural arrangement 100
illustrated in FIG. 1B, viewing the X-Y plane, down along a line of
sight following the Z-axis illustrated in FIG. 1B. As illustrated
in FIG. 2A, a length 222 of the upper aperture 104 can be
considered to extend the entire length between the upper end of the
element 102a and the upper end of the element 102b. This is
because, between the elements 102a and 102b, there is some degree
of attenuation of the incident wave 114 at all points, even though
the attenuation can vary. Although the cross-sectional profiles of
the elements 102a and 102b are round, it should be understand that
cross-sectional profiles of elements in other embodiments may have
any shape, such as oval, rectangular, or any other shape. However,
if drilling is used to form the elements, it is likely most
convenient to bore out elements with circular cross sections.
[0115] 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.
[0116] FIG. 2B illustrates that a structural arrangement can have
more than just two elements, such as the elements 102a and 102b in
FIG. 1B and FIG. 2A. In particular, four elements 102a are oriented
along a line (element row) 226, in the direction of the y-axis,
between the incident wave 114 and the protection zone 112. The four
elements 102a form a structural grouping 232 of elements. Because
these elements are on a side of the production zone 112 that is
expected to receive the incident seismic wave 114, the structural
grouping 232 can be referred to as an "incident" structural
grouping of elements.
[0117] FIG. 2C is a top view of two elements 202a and 202b. The
element 202a is formed of a plurality of discrete sub-elements
208a. The discrete set of elements 208a can be smaller than the
element 102a in FIG. 1B, or they may be of the same size as element
102a. The element 202a forms a cluster with the sub-elements
situated to increase structural strength. In particular, in FIG.
2C, the sub-elements 228a are located such that cross-sections of
the respective sub-elements 208a corresponding to the element 202a
are located at points collectively defining a hexagon 230.
Similarly, the element 202b is formed of discrete sub-elements 208b
located at points defining the hexagon 230. The cross sections
illustrated in FIG. 2C are located in a cross-sectional plane that
is the X-Y plane shown in FIG. 2C. However, another example
cross-sectional plane in which the elements can be located at
points forming a hexagon is a plane perpendicular to the elements
202a, which do not extend downward along the Z axis.
[0118] 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.
[0119] 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.
[0120] 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
FIG. 1B.
[0121] 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.
[0122] 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 FIG. 1B.
[0123] FIG. 2E is a top-view illustration of a superstructure 240b
that includes two structural arrangements. In particular, one
structural arrangement is formed by a first of the elements 102a
and a first of the elements 102b, while a second structural
arrangement similar to that shown in FIG. 1B is formed by a second
of each of the groupings 102a and 102b of elements.
[0124] FIG. 2F is a top-view illustration of a superstructure 240c
that includes trench elements 203a and 203b. In particular, the top
view in FIG. 2F shows that the trenches 203a and 203b are not
boreholes, but instead are substantially rectangular in their
cross-sectional profiles. Each of the trench elements 203a-b
defines an inner volume in the earth, filled with a medium that
resists transmission of the seismic wave 114 toward the protection
zone 112. Furthermore, one pair of the trench elements 203a-b forms
a structural arrangement similar to the arrangement 100 in FIG. 1B,
while a second pair of the elements 203a and 203b forms a second
structural arrangement. The trench elements 203a and 203b form two
separate structural arrangements, with respective upper and lower
apertures, similar to the upper and lower apertures, 104 and 106,
respectively, in FIG. 1B, for example.
[0125] FIG. 3 is a cross-sectional side-view diagram showing how
embodiments can be advantageously used to protect structures in the
sea, such as a sea platform structure 336. The platform 336 stands
above a surface 338 of the sea, while legs of the platform are
anchored into the earth 118 below the seafloor 337. It is desirable
to protect the sea platform 336, which can include an oil rig or
other structure in the sea, by forming a protection zone 312 around
the platform.
[0126] In FIG. 3, the protection zone 312 is formed at the upper
aperture of elements 302a and 302b. The elements 302a-b are
anchored into the earth 118 at their respective lower ends 110,
while their upper ends 108 extend above the sea surface 338. In
other embodiments, the lower ends 110 of the elements 302a-b are
not anchored into the earth, but instead, the elements 302a-b are
suspended mechanically, such that they extend only a certain
distance below the surface 338 of the sea. In either case, the
elements 302a-b redirect power from an incident elastic, water wave
that would otherwise be expected to be incident at the sea platform
336 in its full strength.
[0127] 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.
[0128] 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 FIG. 3. In other embodiments, any one of the groupings of
arrangements or discrete sub-elements that are illustrated in FIGS.
2B-2F may be used to protect against water waves, for example.
Furthermore, in some embodiment wave damping structures, only a
plurality of elements 302a on the incident side of the protection
zone are used, such that they form an incident structural grouping.
Furthermore, as described hereinafter in connection with FIG. 4B,
for example, structural groupings of elements can be used to
protect against damaging water waves expected to be incident on
land, such as tsunami waves.
[0129] FIG. 4A is a cross-sectional, side-view illustration of
incident and transmission structural groupings 434a and 434b,
respectively, of elements on either side of a protection zone 112.
The incident structural grouping 434 includes three elements 102a
on the incident side of the protection zone 112. Each of the
elements 102a has the upper end 108 and the lower end 110, similar
to the elements described in connection with FIG. 1B. Each element
102a defines a line 438a extending from the upper end 108 to the
lower end 110. This line forms an acute angle 440a (less than
90.degree.) with a line 436 that defines a travel direction of the
wave 114 toward the protection zone.
[0130] 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 FIG. 1B) is sufficiently
large, and where the elements extend sufficiently below and toward
the protection zone 112, the elements can attenuate power from the
wave 114 that reaches the protection zone. Preferred dimensions and
orientation of the elements 102a-b can be understood, in part, by
reference to an acoustic "muffler" described hereinafter in
connection with FIG. 12.
[0131] 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.
[0132] 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 FIGS.
2B and 2D-F provide further advantages, including wider protection
zones.
[0133] While a superstructure is not specifically annotated in FIG.
4A, it should be understood that the incident grouping 434a and
transmission grouping 434b together can be considered to form a
superstructure 435. Such a superstructure is particularly well
suited to preventing power from incident waves from entering the
protection zone 112. Combinations of incident and transmission
groupings of elements can significantly reduce a depth to which
borehole or other elements need to be drilled in order to reduce
seismic power by a given amount. This has significant cost
advantages, as increasing bore depths are significantly expensive.
In many embodiments, significant attenuation, such as 34 dB of
attenuation, is expected, even where depths of lower apertures in
the earth, or below the surface of water, are only on the order of
100 m, for example. The incident structural grouping 434a and
optional transmission grouping 434b together form a superstructure
435.
[0134] FIG. 4B is a cross-sectional side-view illustration of an
incident structural grouping 437 of elements 402 that can be
employed to protect against incident elastic water waves 314, such
as a tsunami wave. The elements 402 are anchored into the earth 118
near a shore of the sea expected to receive an incident wave. The
elements 402 can be solid, similar to the elements 302a and 302b
illustrated in FIG. 3, for example.
[0135] FIGS. 5-7 are top-view illustrations of additional incident
structural groupings of elements with different configurations and
functions. It should be understood that optional transmission-side
structural groupings of elements can have similar configurations
and may form part of other embodiment elastic wave damping
structures, even though transmission groupings are not illustrated
in FIGS. 5-7.
[0136] FIG. 5 is a top-view illustration of an arrangement of
elements 102a forming an incident structural grouping 534 of the
elements in a sawtooth pattern 542. The incident structural
grouping 534 is arranged between the incoming, expected incident
seismic wave 114 and the protection zone 112. As described
hereinafter in connection with FIG. 9E, for example, substantially
sawtooth-type groupings of elements can be situated on both the
incident side of the protection zone at which the anticipated
seismic wave is expected to the incident, and also on the
transmission side of the protection zone, the side of the
protection zone opposite the incident side. Thus, with
sawtooth-type grouping of elements on both sides of the protection
zone, elements from respective groupings can form one or more
structural arrangements similar to the arrangement 100 in FIG. 1B.
Therefore, superstructures including sawtooth-type groupings, just
as superstructures including element rows or element array-type
groupings, can also have the significant advantage of providing
relatively broadband protection against incident seismic waves.
[0137] FIG. 6 is a top-view illustration of a substantially
sawtooth periodic pattern 642 of elements 102a that form an
incident structural grouping 634 of elements.
[0138] 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.
[0139] FIG. 7 is a top-view illustration of an additional incident
structural grouping of elements 102a that illustrates interference
of reflected wavelets from the elements of a grouping. In
particular, the seismic wave 114 impinges on the incident grouping
of elements 102a with an incident seismic wavefront 746. As is
understood in the art of wave mechanics, the respective elements
102a will reflect some of the seismic power incident on them in the
form of seismic wavelets 748. The reflected seismic wavelet 748
from the respective elements 102a will interfere with each other,
either constructively or destructively in various positions that
depend on separation of the elements 102a, as well as the
wavelength of the incident seismic wave.
[0140] 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.
[0141] Interference effects can also be exploited advantageously to
generate electrical power electro-mechanically. In particular, as
illustrated in FIG. 7, an electromechanical power generator 744 is
located at a position of expected constructive interference between
the incident and reflected waves, such that the magnified
mechanical power from the waves is converted into electrical power
in order to provide power during a power outage due to an
earthquake causing the seismic wave, for example.
[0142] Finite element modeling has been employed to predict
attenuation of waves of various embodiments seismic wave damping
structures. FIGS. 8A-8C, 9A-9B, and 9C-9D illustrate some of these
methods and results.
[0143] FIG. 8A is a top-view illustration of a protection zone 112
formed between model borehole elements 802a and 802b. The model
borehole elements 802a are arranged in element rows and include an
incident grouping of elements 834a. Similarly, the modeled elements
802b are arranged in rows on the opposite side of the protection
zone from the incident grouping to form a transmission grouping
834b. As also illustrated in FIG. 8A, a 3D section of earth with a
array of the borehole elements 802a therein is an example of a
"metamaterial" as used herein.
[0144] FIG. 8B is a three-dimensional (3D) illustration of what is
shown in FIG. 8A. In particular, it is noted that the incident
grouping 834a of elements 802a, together with the transmission
grouping of elements 802b, form a superstructure 840, with the
protection zone 112 there between. Individual locations in the 3D
meshing represent points used for the finite element analysis.
[0145] FIG. 8C is a 3D view of trench elements 803a and 803b in a
3D finite element meshing. The modeled trench element 803a is
similar to one or more of the trench elements 203a illustrated in
FIG. 2F. Likewise, the modeled trench element 803b is similar to
one or more of the trench elements 203b illustrated in FIG. 2F.
[0146] The finite element analysis performed on the analytical
models illustrated in FIGS. 8A-8C indicate that the borehole based
seismic wave damping structure of FIGS. 8A-8B, and the trench-based
seismic wave damping structure illustrated in FIG. 8C reduce direct
seismic wave power reaching the protection zone by more than 40 dB.
It is noted that a diffractive component upwelling through the
V-shaped structure has been calculated to be 22 dB lower than the
peak seismic wave power observed for the same location in the
protection zone without the implementation of the damping
structures.
[0147] FIG. 9B is a 3D representation of the finite element
analysis, with the direction of the incident wave 114 shown.
[0148] FIG. 9C is a graph showing a source time function for
rupture velocity of an earthquake measured in California in 1991.
This source time function was used as input to the finite element
analysis. The seismic event is modeled for the response of the
source function estimated for the Hector Mine earthquake in 1991
(Magnitude 7.1-USGS). Typical seismic frequencies are less than 1
Hz with minimal power above 1 Hz.
[0149] FIG. 9D is a graph showing power reduction calculated in a
foundation 912, both with and without the borehole cloak
(substantially sawtooth periodic pattern superstructure illustrated
in FIG. 9E formed of elements 903a in a substantially sawtooth 942a
grouping and elements 903b in a substantially sawtooth 942b
grouping).
[0150] FIG. 9E is collection of areal and depth view seismic wave
snapshots calculated with and without embodiment seismic wave
damping (cloaking) structures, providing a finite difference model
of the effects on seismic wave propagation from seismic cloaking.
In particular, the top row shows an areal view of seismic wave
snapshots, with and without cloaking structures. The bottom row
shows a depth view of seismic wave snapshots, with and without
cloaking structures.
[0151] FIG. 9E illustrates that using a single vertical borehole
array or trench may significantly reduce the surface wave power
reaching a protected region. However, seismic power is able to be
directed by diffraction around the barrier. Using a V-shaped
muffler (sawtooth) design is, therefore, much more effective in
blocking surface waves in the 3D extent.
[0152] FIG. 10 is a table showing various high-value assets that
may be protected, as examples, using embodiment elastic wave
damping structures. FIG. 10 also shows an expected upper aperture
widths (see, e.g., upper aperture 804 in FIG. 8B) and lateral
extents (see, e.g., lateral extent 805 in FIG. 8A) of a damping
structure for each example asset, with a corresponding, example
number of boreholes that is expected to be effective in
significantly attenuating seismic power within a protection zone,
such as the protection zone 112 in FIGS. 8A-8B, including the
asset.
[0153] Superstructures as described herein, and as exemplified by
the superstructure 840 in FIG. 8B, can divert, attenuate, and
create destructive interference of hazardous seismic waves that
would otherwise reach a high valued asset such as the assets listed
in FIG. 10. Example superstructures, also referred to herein a
cloaking arrays, may be 50-200 meters wide (in upper aperture), and
hundreds of meters to a few kilometers in lateral extent depending
on protected asset size and risk. An example, single borehole
diameter can be 1 meter for the structures listed in FIG. 10, where
400 boreholes can populate an example 100 square meter region. For
most applications, borehole depths can be an estimated 150 meters
or less. These depths can be particularly relevant where surface
seismic waves are of greatest concern.
[0154] FIG. 11 is a series of diagrams 1160-1162, and a graph 1163,
showing the comparative effects of seismic cloaking generally on
seismic wave propagation for a single, vertical barrier element
compared with an embodiment structural element, as calculated using
a finite difference 2D model of the barrier structures. The seismic
event is modeled for the response of the source function estimated
for the Hector Mine earthquake in 1991 (Mag. 7.1-USGS), as
illustrated in FIG. 9C. Typical seismic frequencies are less than 1
Hz, with minimal power above 1 Hz.
[0155] 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 FIG.
1B.
[0156] 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.
[0157] FIGS. 12A- 12 B are a diagram and equations illustrating
semi-analytical simulation of acoustic propagation through a
"tapered muffler" 1200 geometry. The tapered muffler 1200 and
associated equations can be found in Easwaran and Munjal, J. Sound
and Vibration 152 (1992), 73-93 and can be used as part of
understanding the efficacy of embodiment structural arrangements,
such as the arrangement 100 illustrated in FIG. 1B, in proving a
barrier against seismic waves.
[0158] 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 FIG. 12B provide a simple,
analytical, transfer matrix approach to evaluating energy
attenuation as a function of the entrance 1206, an exit (upper
aperture) 1204, a depth 1219, and related angle dimensions.
[0159] FIGS. 13A and 13B are graphs showing transmission loss as a
function of frequency for various acoustic "muffler" parameters
assuming a wave speed of 1500 meters per second (m/s). The
calculations were performed using the analytical tools shown in
FIGS. 12A-12B in order to at least begin to understand optimization
of parameters for structural arrangements such as the arrangement
100 in FIG. 1B.
[0160] 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
FIGS. 13A-13B include: (i) Increasing the depth at constant angle
increases attenuation at the lower frequencies, but reduces
attenuation at the higher frequency due to multiple nodes; (ii)
Increasing the depth at constant top & bottom aperture
dimensions (i.e., while reducing the angle) reduces attenuation
across the entire frequency range; and (iii) Increasing the bottom
aperture opening reduces attenuation across the entire frequency
range. These trends can be applied advantageously to design of
structural apertures for seismic wave attenuation in embodiment
elastic wave damping structures in order to maximize seismic wave
attenuation.
[0161] FIG. 14 is a collage of photographs showing apparatus used
to study, on a model scale, non-naturally occurring, man-made
structures such as borehole arrays and trenches embedded in elastic
media analogous to rock and compact soil using a machined table-top
scaled physical model. The effort focused on examining the effects
of borehole arrays and trenches (metamaterials) on seismic wave
propagation, diversion, scattering, and attenuation through spatial
measurements from controlled seismic sources. The time series
measurements were then compared and analyzed with computer model
simulations.
[0162] The solid model was composed of Delrin.RTM. 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.RTM. blocks were machined to contain
boreholes in prescribed patterns or trenches defining a V-shaped
muffler and compared with homogeneous solid blocks. The Delrin.RTM.
blocks contained boreholes in prescribed patterns or trenches
defining a V-shaped muffler.
[0163] 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.RTM. 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.
[0164] Similarly, a V-trench barrier structure was machined in a
separate Delrin.RTM. block where the 3 mm diameter boreholes were
in contact, forming continuous hollow walls on both sides of the
barrier structure. A Modal-Shop.RTM. variable transducer 1462 was
used to vertically load on the Delrin.RTM. 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.RTM. blocks. PCB.RTM. model 352C33
accelerometers 1460 were used to measure the temporal and spatial
vibration distributions observed on the Delrin.RTM. surface. An
IOTECH.RTM. wavebook 516E was used to record each time series trace
using a synchronized 70 kHz sample rate per channel.
[0165] FIGS. 15A-15C show measured results that illustrate the
effects of a model V-trench machined in Delrin.RTM. block table-top
experimental configuration. FIG. 15A shows four accelerometer time
series traces measured in a center line across a homogeneous solid
Delrin.RTM. block relative to the transducer source location.
Receivers 1, 3, 4, and 7 were 1, 3, 4, and 7 inches from the
source, respectively. Particle velocities were computed by
integrating the measured accelerations and then applying a
high-pass filter to remove low frequency drift. A single 10 kHz
Ricker vertical load burst was recorded as it traveled from its
source. Each trace records a similar time series, showing a direct
surface wave arrival (circled outline) followed by later reflection
arrival interference from the Delrin.RTM. block side and bottom
boundaries. The first break of the direct arrivals shows a wave
speed of 1693 m/s. Spherical spreading and Delrin.RTM. attenuation
losses are not compensated in the measurement plots. At the
observed wave speed, the P-wavelength was estimated at 17 mm.
[0166] FIG. 15B shows four accelerometer time series traces
measured in the center line across the Delrin.RTM. block that
contains a V-trench barrier structure perpendicularly oriented to
the direction of elastic wave propagation relative to the
transducer source location. Receivers 1, 3, 4, and 7 were 1, 3, 4,
and 7 inches from the source, respectively, where receivers 3 and 4
were between the near and far trench walls.
[0167] FIG. 15C shows the trench barrier structure in schematic
form. The times series traces show that the direct surface wave is
reflected off the near trench wall, where very little direct wave
is observed inside the keep out zone between the near and far
trench walls. The reflected arrival interference from the bottom
surface is observed at the surface between the trench walls. In
this geometry, elastic waves were able to leak through the aperture
at the trench bottom and travel to the surface. These amplitudes,
however, are lower than those of the peak surface wave that would
be observed in the same locations if the barrier cloaking structure
were not present.
[0168] FIG. 16 shows earthquake magnitude reduction expected due to
subsurface barrier structures, based on extrapolation from the
measured and modelled results. In this simple analysis, the power
drop observed in the measurement and model studies are presented in
terms of Mw reduction. The V-trench structure shows that a
magnitude 7.0 earthquake energy intensity can be reduced to 5.4-5.0
for the peak power of the direct destructive surface wave. The
leakage through the aperture is measured to show a modest
reduction. However, when modeling the earth, where the boundaries
are infinite, diffraction leakage through the aperture is small,
and the structure would be expected provide a significant reduction
in wave energy. Notably, modeled and measured Delrin.RTM. block
waveforms and amplitudes agreed within 3 dB.
Seismic Wave Damping Systems and Corresponding Methods
[0169] 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.
[0170] 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.
[0171] 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
[0172] 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.
[0173] 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.
[0174] 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.
[0175] 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 FIG. 1A, this seismic wave power is
referred to as "attenuated surface waves 60'," as opposed to the
incident surface waves 60 that are initially incident at the
elements 30a-b of the seismic damping structure. Hereinafter, this
residual seismic wave power propagating within the protection zone
may be referred to as "residual waves," which may be residual
surface waves or other types residual seismic wave power that enter
the protection zone. The residual wave power that propagates within
a protection zone, such as the protection zone 40 illustrated in
for FIG. 1A, will propagate most strongly at seismic wave
frequencies that are resonant in the seismic damping structure.
[0176] FIG. 17A is similar to FIG. 1A in some respects, but also
illustrates a seismic wave damping system, in its environment of
use, the benefits of which extend beyond those described above for
seismic damping structures alone. FIG. 17A also includes
terminology specific to seismic damping systems disclosed herein,
as further described hereinafter. In FIG. 17A, in addition to the
elements 30a and 30b, which constitute a seismic damping structure,
there is illustrated an anti-resonance damping structure 1770 that
dampens residual wave 1760' that propagate within the protection
zone at resonance frequencies at a resonance frequency defined by
the seismic damping structure. As seismic waves 1760 travel from
the earthquake center 50 in a distal medium 1719, the seismic wave
1760 are incident at the element 30a, which forms a border of the
protection zone 40 together with the element 30b. The
anti-resonance damping structure 1770 is positioned within the
protection zone 40 and is configured to dampen the residual wave
1760 from 1760' propagating within the protection zone at the
resonance frequency. Example resonance frequencies are illustrated
hereinafter in connection with FIG. 24E, for example.
[0177] Example anti-resonance damping structures 1770 may include a
Helmholtz resonator or array of Helmholtz resonators, as
illustrated in FIG. 23A and FIG. 23D, an array of trees planted in
the protection zone, or an array of towers placed on the protection
zone, as illustrated in FIGS. 24A and 24D, and array of buried
cylinders, such as the meta-concrete array illustrated in FIGS. 25A
and 25C, among other structures that are described herein or are
otherwise or are known to those of skill in the art.
[0178] FIG. 17B is a schematic diagram illustrating the elements
30a and 30b, which form a seismic damping structure 1700, together
with the anti-resonance damping structure 1770, as illustrated in
FIG. 17A. Together, the structure 1770 and the seismic damping
structure 1700 form an embodiment seismic wave damping system 1772.
It should be understood that seismic damping structures (also
referred to herein by "seismic wave damping structures," "elastic
wave damping structures," "superstructures," "arrangements" of
elements, and similar terms) that are described throughout the
application may be used in an embodiment seismic wave damping
systems. These structures include structural arrangements, such as
the arrangement 100 in FIG. 1B, superstructures, such as the
superstructure 240a illustrated in FIG. 2D, incident and
transmission groupings of elements as described in connection with
FIGS. 6 and 8A-8C, for example, and any other structures described
herein. For each of these structures, in view of the disclosure
herein, a person of skill will understand how to calculate
resonance frequencies from a property of the host medium and from
one or more properties of the elements embedded within the host
medium, such as depth or length thereof. A depth 119 of an element
102b, for example, is illustrated in FIG. 1B. A further property of
an element may include a length thereof, such as a length from the
upper and 108 to the lower and 110 of the element 102a illustrated
in FIG. 1B.
[0179] The host medium 1718 shown in FIG. 17A can include earth,
such as the earth 118 illustrated in FIG. 4A. Furthermore, any
natural or man-made host medium, such as rock, sand, gravel, etc.
or concrete, bricks, or other building materials may form part of
the host medium 1718. Furthermore, it should be understood that the
distal medium 1719 may be of the seven of the same material as the
host medium 1718, forming one continuous medium. The distal medium
and host medium are delineated only by the seismic damping
structure, comprising the elements 30a and 30b in FIGS. 17A-17B,
which form the boundary of the protection zone.
[0180] 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.
[0181] FIG. 18A illustrates general "seismic muffler" geometry for
disclosed seismic damping structures described hereinabove. In the
example of FIG. 18A, a borehole array muffler, also referred to
herein as a seismic damping structure 1800, is configured to dampen
seismic waves and form a protection zone around a structure asset
20, in this case a nuclear power plant, to be protected. Also
illustrated in FIG. 18A is the anti-resonance damping structure
1770 of FIG. 17A, which can further enhance seismic protection in
the system formed by the combination of the structure 1800 and the
anti-resonance damping structure 1770 by damping resonance
frequencies defined by the seismic damping structure 1800. The
structure 1800 is a V-shaped seismic muffler that diverse,
dissipates, and reduces ground motion from hazardous seismic waves
prior to reaching the critical infrastructure 20. Seismic wave
types caused by earthquakes can include surface and body waves.
Surface seismic waves, such as Rayleigh and Love waves, commonly
cause significant damage and destruction to buildings and
structures.
[0182] 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 TL.sub.ent (Kinsler et al., 2000) and the loss
through the conical muffler TL.sub.con (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.sub.con+TL.sub.ent (1)
[0183] 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).
T L ent = - 10 log ( 1 - 0.25 ( k 0 b ) 2 + 0.6 i ( k 0 b ) - 1
0.25 ( k 0 b ) 2 + 0.6 i ( k 0 b ) + 1 2 ) ( 2 ) ##EQU00001##
[0184] 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).
[ p 1 v 1 ] = [ T 11 T 12 T 21 T 22 ] [ p 2 v 2 ] . ( 3 )
##EQU00002##
[0185] Using the above transfer matrix, we can describe the
TL.sub.con term in Eqn. (1) for a conical muffler as follows
(Easwaran and Munjal, 1992):
T L con = 20 log ( 0.5 b t .times. T 11 + 4 vT 12 .pi. t 2 + T 21 4
v .pi. b 2 + ( t b ) 2 T 22 ) , ( 4 ) ##EQU00003##
in which the terms in the Eqn. (4) are in turn defined below:
T 11 = z 2 z 1 cos ( k 0 l ) - sin ( k 0 l ) k 0 z 1 , ( 5 ) T 12 =
i 4 vz 1 .pi. b 2 z 2 sin ( k 0 l ) , ( 6 ) T 21 = i .pi. b 2 sin (
k 0 l ) 4 v ( z 2 z 1 + 1 ( k 0 z 1 ) 2 ) - i .pi. b 2 cos ( k 0 l
) 4 vk 0 z 1 2 , ( 7 ) T 22 = z 1 z 2 cos ( k 0 l ) + sin ( k 0 l )
k 0 z 2 , ( 8 ) z 1 = bl t - b , ( 9 ) z 2 = z 1 + l , ( 10 ) k 0 =
2 .pi. f v . ( 11 ) ##EQU00004##
[0186] Term definitions for the muffler characteristics specified
in Eqns. (1)-(11) are described in Table 1.
TABLE-US-00001 TABLE 1 Term Definitions for Muffler Characteristics
in Equations (1) to (11) Equation Term Definition TL Total
transmission loss through muffler structure TL.sub.ent Transmission
loss across muffler inlet TL.sub.con Transmission loss through the
conical muffler P.sub.i(1, 2) Pressure at muffler inlet (entrance)
and outlet (exit) v.sub.i(1, 2) Elastic wave velocity at the
muffler inlet (entrance) and outlet (exit) k.sub.0 Wavevector in
free space, defined in equation (11) B Muffler inlet (entrance)
diameter T.sub.11, T.sub.12, T.sub.21, T.sub.22 Transfer matrix
elements, defined in equations (5-8) T Muffler outlet (exit)
diameter L Muffler length z.sub.i(1, 2) Geometrical muffler
quantities, defined in equations (9-10) v Elastic wavespeed in
medium F Elastic wave frequency
[0187] 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 FIGS. 19A-21C. From the performance results, resonance
frequencies characterizing seismic wave damping structures may be
determined, as will be illustrated in examples described
hereinafter.
[0188] 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 FIG. 19B). The one or more resonance frequencies
may further be determined as a function a physical property of the
host medium such as wavespeed in the host medium, which is v in
Table. 1. A particular manner in which the equations and parameters
noted above lead to a determination of resonance frequencies will
become further apparent to one of skill in the art in view of the
examples provided hereinafter.
[0189] 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.
[0190] 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.
[0191] FIG. 18B is a color-coded or shaded, side-view graphical
drawing that illustrates particle velocity, in unit length per
second, over a cross-sectional area showing the seismic damping
structure 1800 in cross section.
[0192] FIGS. 19A-19D are cross-sectional diagrams and graphs,
respectively, illustrating the effect of a muffler inlet diameter
and wall slope on seismic wave transmission loss behavior through
conical shaped mufflers (seismic damping structures for different
wall slope inlet diameters. FIG. 19A specifically is a
cross-sectional diagram of a seismic damping structure illustrating
muffler geometry and parameters situated in a homogenous,
isotropic, solid host medium. FIG. 19A illustrates the same basic
geometry shown in FIG. 12A, wherein the terms entrance (lower
aperture), exit (upper aperature), and length, among other terms,
are defined.
[0193] FIG. 19B is a diagram illustrating four different muffler
geometries and their respective dimensions. These structural
geometries are contrasted where the outlet diameter is 0.5 km and
the muffler length (also referred to herein as muffler "depth" or
as a "depth" of elements forming a seismic wave damping structure
is 0.25 km for all cases a-d. The inlet diameter is varied from 0.1
km, to 0.25 km, to 0.35 km, to 0.5 km.
[0194] FIG. 19C is a graph illustrating elastic wave transmission
loss as a function of seismic wavelength corresponding to seismic
frequencies spanning from 0.1-10 Hz. These calculations treat
seismic waves as elastic, which is a helpful approximation. This is
shown for all four cases a-d corresponding to FIG. 19B.
[0195] FIG. 19D is a graph illustrating P and S wave transmission
loss (spectral ratio of muffler outlet and inlet) behavior for the
four muffler examples of FIG. 19B as a function of seismic
frequency. The solid lines in FIG. 19B represent P-wave
transmission losses with a P wave velocity of 1550 m/s, while the
dotted lines represent S wave losses with an S wave velocity of
17th of 700 m/s.
[0196] FIGS. 20A-20C illustrate the effect of muffler length and
output diameter for various damping structure seismic damping
structure geometries. In particular, seismic wave transmission
losses through proportional conical mufflers for different muffler
length and output and outlet diameters are illustrated, where wall
slope and inlet diameter are constant. FIG. 20A illustrates four
different muffler geometries that are contrasted, where the inlet
diameter is 0.1 km and the muffler wall slope is constant for all
cases. The outlet diameters are 0.1 km, 0.2 km, 0.4 km, and 0.6 km,
where the corresponding muffler length are 0.18 km, 0.55 km, and
0.9 km, respectively. A vertical wall muffler is shown for
comparison purposes.
[0197] FIG. 20B is a graph showing elastic wave (approximate for a
seismic wave) transmission loss as a function of seismic wavelength
corresponding to seismic frequencies spanning 0.1-10 Hz.
[0198] FIG. 20C is a graph illustrating P and S wave transmission
loss (spectral ratio of muffler outlet and inlet) behavior for the
four muffler examples illustrated in FIG. 20A as a function of
seismic wave incident frequency. Solid lines represent P-wave
transmission losses with a P velocity of 1500 m/s, while dotted
lines represent the S wave losses with an S velocity of 700
m/s.
[0199] FIGS. 21A-21C illustrate a comparison of the analytical
calculations to 2D numerical finite difference models for two
muffler examples, namely a shallow sloping muffler model (a) having
a wall slope and a vertical wall muffler model (d) (also shown in
FIG. 19B). FIG. 21A illustrates cross-sectional muffler geometry
for these examples. FIG. 21B is a cross-sectional illustration of
the example structures (a) and (d). FIG. 21C shows calculated P and
S wave transmission loss (spectral ratio of muffler outlet and
inlet) behavior for the two muffler examples of FIG. 21A as a
function of seismic frequency. Solid lines represent P-wave
transmission losses with a P-velocity of 1500 m/s, while dotted
lines represent S-wave losses with an S-velocity of 700 m/s. The
symbol markings correspond to the numerical model computations for
single frequency--continuous wave (CW) seismic tones.
[0200] FIG. 22A illustrates a source time function from the Hector
Mine 1999 earthquake (Mag. 7.1-USGS), which was estimated from the
slip velocity distribution. The 2D vertical-depth view and 2D
aerial-plan view simulations described hereinafter use a source
time function proportional to the normalized slip velocity
illustrated in FIG. 22A. FIG. 22B is a graph showing a frequency
distribution for the Hector Mine earthquake. The source time
function exhibits its peak amplitude at 0.3 Hz with minimal
amplitudes above 3 Hz.
[0201] FIG. 23A is a color-coded or shaded vertical depth view of
the seismic wave field after nine seconds for the up-going shear
waves, where a protection zone is formed by elements 30a-30b,
combined with a Helmholtz resonator array 2370, which together form
a seismic wave damping system 2372.
[0202] FIG. 23B is a graph showing the source function for the
Hector Mine earthquake, which was injected by simulation at the
bottom boundary shown in the graph, over time, into the horizontal
component as a source as a line source.
[0203] FIG. 23C is an equation showing a transmission factor T for
a finite number N of resonators. In this manner, a net effect on
residual wave damping for a Helmholtz resonator array may be
calculated.
[0204] FIG. 23D is a schematic diagram illustrating the Helmholtz
resonator array, anti-resonance damping structure 2370 that is
pictorially illustrated in FIG. 23A.
[0205] The following are two examples for how to use the equations
in FIG. 23C in order to configure a Helmholtz resonator array to
address a particular resonance frequency of a seismic damping
structure. When the Helmholtz resonator array, or another
anti-resonance damping structure within the scope of embodiments,
is built or otherwise configured to address a particular seismic
wave frequency, as used herein, it is considered to be configured
to dampen residual waves having the frequency by being
"mechanically tuned" to the resonance frequency. "Mechanical
tuning" in some embodiments may be accomplished by virtue of
construction with particular mechanical dimensions, properties, or
parameters. In other embodiments, "mechanical tuning" may be
accomplished in whole or in part by adjustments that follow actual
construction of the anti-resonance damping structure.
[0206] 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.
[0207] 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.
[0208] FIG. 23E is a graph illustrating the benefits of using the
Helmholtz resonator array (anti-resonance damping structure) 2370
in the seismic wave damping system 2372. A curve 2373 shows seismic
amplitude as a function of frequency where there is no seismic wave
damping structure provided to create a protection zone.
Correspondingly, where only a seismic wave damping structure is
used without an anti-resonance damping structure, a curve 2376
shows a greatly reduced seismic amplitude as a function of
frequency. However, as will be noted, the curve 2376 shows several
resonances 2374 (also referred to herein as "resonance frequencies"
or "resonant frequencies"), that are present in the spectrum 2376.
By contrast with the curve 2376 and the curve 2373, a dashed curve
2378 shows the effect of a full seismic wave damping system the
full seismic wave damping system 2372 including the Helmholtz
resonator array 2370. As illustrated, the resonances 2374 are
dramatically damped at the higher frequencies associated with the
seismic wave damping structure alone. This illustrates the
significant damping benefit that can be obtained by embodiments
herein when a system includes an anti-resonance damping structure
that is configured specifically to dampen the one or more resonance
frequencies of the seismic wave damping structure.
[0209] FIG. 24A is a color-coded or shaded, vertical depth view
graphs of a seismic wave field after nine seconds for the up going
shear wave, where the source function for the Hector Mine
earthquake, as illustrated in FIG. 24B, was injected at the bottom
boundary over time into the horizontal component as a line source.
A representative above ground tower or tree anti-resonance damping
structure 2470 is illustrated, which, together with the seismic
wave damping structure formed by the combination of elements 30a
and 30b, forms a seismic wave damping system 2472.
[0210] FIG. 24C illustrates an equation that can be used to
calculate a frequency that can be damped by the array 2470 of
resonators (in FIG. 24A, towers or trees, for example) illustrated
in FIG. 24A.
[0211] FIG. 24D is a more detailed illustration of the array of
resonators 2470, which have a lattice constant L and height H above
the ground. L may have various values in different embodiments,
depending on the number of resonators desired, the resonant
frequency to be addressed, the diameter or other cross-sectional
dimension of the elements, and other factors. At the right of FIG.
24D is shown a cross-sectional view of a single one of the
resonators 2469, which can be a tower or tree, for example. The
resonator 2469 has a cross-sectional area A and a diameter D. The
diameter D, for a cylindrical tower or tree, is an example of a
cross-sectional dimension. In general, embodiments may include
cross-sectional dimensions, such as diameters, on the order or 1 m,
on the order of 5 m, on the order of 10 m, for example. Using the
information of FIGS. 24C-24D, a person of skill can readily
calculate a resonance frequency that may be addressed by a given
array of tower towers or trees, and a person of skill may configure
the tower or tree array 2470 to dampen a residual wave propagating
within a protection zone at one or more given resonance
frequencies. It will be understood that while the equation in FIG.
24C is for the infinite array of resonators 2470, similar results
may be obtained for a large array, or calculated, or numerically
obtained via numerical modeling to address particular resonance
frequencies of associated seismic damping structures. An array of
trees may be an array that does not naturally occur, such as an
array of trees that are periodically spaced, for example.
[0212] 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.
[0213] For exemplary wood towers, example parameters can include
v.sub.p=2200 m/s, p.sub.r=450 kg/m3, vs=1200 m/s, and A=0.071
m.sup.2. Example ground host medium parameters can include
v.sub.p=900 m/s, p.sub.g=1200 kg/m.sup.3, and v.sub.s=500 m/s, with
r=v.sub.s/v.sub.p, L=50, .mu..sub.g=1.times.10.sup.8 for a shear
modulus of soil, and E.sub.r=1.times.10.sup.9 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.
[0214] FIG. 24E is a graph showing seismic amplitude as a function
of frequency in connection with the infinite array of resonators
2470 illustrated in FIGS. 24A and 24D. The curve 2373 shows a case
where no seismic wave protection is provided. The curve 2376, as in
FIG. 23E, illustrates a case where only the seismic wave damping
structure formed by the elements 30a and 30b is provided, wherein
the structure is characterized by resonances the resonances 2374.
However, where the muffler (seismic wave damping structure) is
combined with the array of tower resonance absorbers 2470, the
resonances 2374 are significantly damped.
[0215] FIG. 25A is a color-coded or shaded, vertical depth view
graph showing seismic power in the form of particle velocity as a
function of depth and cross range for a seismic wave damping system
2572. In this case, similarly, the Hector Mine earthquake source
function, as illustrated in FIG. 25B, was injected at the bottom
border over time into the horizontal component as a line source the
system 2572 includes the seismic wave damping structure formed by
the elements 30a-30b and also a meta-concrete array 2582. The
meta-concrete array 2582 is an example of buried cylinders, and
geometry of the buried cylinders, particularly because the
meta-concrete array 2582, is illustrated further in FIG. 25C.
[0216] FIG. 25C is a cross-sectional view of the meta-concrete
array 2582 that is illustrated in FIG. 25A. A particular cylinder
2580 of the array 2582 is also shown in greater detail.
[0217] FIG. 25D illustrates how resonance frequency may be obtained
in terms of any lost an elastic modulus E.sub.S of a soft coating
of the cylinders 2580 and in terms of a core size R1 of a heavy
core in the cylindrical elements 2580. This equation permits the
person of ordinary skill in the art to configure an array of buried
cylinders to dampen resonance frequencies predicted for a
particular seismic wave damping structure. In addition, further
information regarding these example structures, which may be termed
"meta-concrete arrays," may be found in "Meta-concrete: designed
aggregates to enhance dynamic performance," Journal of the
Mechanics and Physics of Solids 65 (2014) 69-81, which is hereby
incorporated herein by reference in its entirety.
[0218] FIG. 25E is a graph illustrating seismic amplitude as a
function of frequency that can be reduced using the meta-concrete
array 2582 as part of the seismic wave damping system 2572
illustrated in FIG. 25A. The curves 2373 and 2376 that were
previously described are shown, together with the route of the
resonance the resonance frequencies 2374. A curve 2578 (dashed)
illustrates that in the case of the meta-concrete array
anti-resonance damping structure, similar benefits may be obtained
by specifically addressing the resonance frequencies 2374 of the
seismic wave damping structure by appropriate configuration of the
anti-resonance damping structure meta-concrete array 2582.
[0219] FIG. 26 is a flow diagram illustrating a procedure 2600
seismic wave for constructing a seismic wave protection zone,
according to an embodiment herein. At 2684, elements are embedded
within a host medium, thus defining a seismic wave damping
structure that is characterized by a resonance frequency, and also
thereby forming a border of a protection zone. The seismic wave
damping structure is particularly configured to attenuate power of
a seismic wave traveling from a distal medium to the host medium
and which is incident at the protection zone formed by the
elements.
[0220] 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.
[0221] 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.
[0222] 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.
[0223] The teachings of all patents, published applications and
references cited herein are incorporated by reference in their
entirety.
[0224] 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.
* * * * *