JP6523945B2 - Vibration reduction method in ground environment and its weight for vibration reduction - Google Patents

Description

  The present invention relates to a method of reducing vibration in a ground environment and a weight for reducing the vibration.

  Conventionally, as a method of reducing ground vibration due to vibration or the like of construction heavy machinery accompanying construction work, for example, as conventional example 1: as shown in FIG. 8A, houses etc. that are vibration source 1 and vibration reduction target 2 There is known a method of forming the vibration isolation wall 4 between the vibration receiving building and the building. As in the construction method of the ground vibration propagation suppressing structure described in Patent Document 1, this is the inside of a groove in which a solidifying material is mixed in a predetermined range of the ground between the vibration source and the affected facility. A plurality of bag-like bodies supported by the support member in a row, supplying a fluid into the bag-like body to expand it before the solidifying material hardens, and then curing the solidifying material to form a hollow portion Is to form a hollow wall body having the above structure (see Patent Document 1).

  Also, as Conventional Example 2: The rigidity of the ground immediately below the vibration source is, for example, improved by mixing with cement, or, as shown in FIG. There is known a method of reducing the response of the ground to reduce the vibration by enhancing the pressure (see Patent Document 2).

JP, 2009-121085, A JP, 2009-287165, A

  However, in the conventional method of reducing vibrations in the ground environment, in the above-mentioned conventional example 1, the wraparound from the lower part of the wall is large, and a large reduction in vibrations can not be expected for the scale of construction. Furthermore, there is a problem that the cost associated with the construction is large both in cost and construction period.

  Moreover, in the prior art example 2, when implemented in a wide range, cost increases more than a vibration-proof wall, conversely, when the range of ground improvement is narrowed, there is a problem that a construction plan will be restricted. The vibration reduction method in the ground environment and the weight thereof for vibration reduction according to the present invention have been proposed to solve such problems.

The gist for solving the above-mentioned subject of the vibration reduction method in the ground environment concerning the present invention and achieving the object is to reduce the vibration on the ground surface between the vibration source on the ground surface and the object of vibration reduction. In laying weights in a row direction orthogonal to a straight line connecting the centers of gravity of the vibration source and the object,
The mass m _w (the mass of the weight per 1 m in the row direction in the width B) of the weight is
m _w = (1 / (1+ (α / R))) m _s ,
In addition, m _s = ((1 + π) / π ² ) _{s s} · √ (Bλ ³ ),
Here, R represents the vibration reduction rate of the target (reduced amount / original vibration amplitude of the vibration amplitude), alpha is the surface wave contribution (0 <α <1), m s interaction with the weight of the unit length Is the density of the ground mass, _{s s} is the density of the ground, B is the width of the weight (m), λ is the wavelength of the surface wave to be subjected to vibration reduction (m), ν is the Poisson's ratio of the ground,
Setting the vibration reduction rate R and the surface wave contribution rate α, and laying in the orthogonal direction according to the mass m _{w of the} weight determined thereby, to reduce the vibration of the vibration source .

  The length Lw of the weight in the column direction includes Lw> 2 · dt (where d is the distance between the weight and the center of gravity of the object, (m)).

The gist for solving the above-mentioned subject of a weight for vibration reduction in the ground environment concerning the present invention and attaining an object is the above-mentioned vibration source and the object between the vibration source on the ground surface and the object of vibration reduction. The weight of the weight laid in the row direction orthogonal to the straight line connecting the respective centers of gravity with
As a mass m _w of a weight per meter in the row direction with a width B,
m _w = (1 / (1+ (α / R))) · m _s
In addition, m _s = ((1 + π) / π ² ) _{s s} · √ (Bλ ³ ),
Here, R represents the vibration reduction rate of the target (reduced amount / original vibration amplitude of the vibration amplitude), alpha is the surface wave contribution (0 <α <1), m s interaction with the weight of the unit length Is the density of the ground mass, _{s s} is the density of the ground, B is the width of the weight (m), λ is the wavelength of the surface wave to be subjected to vibration reduction (m), ν is the Poisson's ratio of the ground,
It is possible to set the expected vibration reduction rate R and the surface wave contribution rate α to determine the mass m _w and thereby determine the required weight of the weight.

According to the vibration reduction method in the ground environment of the present invention and the weight for vibration reduction thereof, a desired vibration reduction rate is exhibited simply by installing the weight on the ground surface, and excavation work and earth work are unnecessary. In addition, installation of the weight is also low vibration, and furthermore, removal is easy.
Furthermore, the excellent effect that the effect of vibration reduction can be predicted easily and accurately can be obtained.

It is a schematic plan view which shows the outline | summary of the vibration reduction method in the ground environment which concerns on this invention. It is a perspective view which shows the relationship between the weight and the stress of the ground surface in the vibration reduction method in the ground environment of the same invention. It is a figure of stress distribution which shows the influence on the ground assuming that stress will deform | transform linearly by the stress of the ground surface. FIG. 6 is a characteristic curve diagram showing the relationship between vibration damping and frequency. FIG. 6 is a characteristic curve diagram showing that the relationship between vibration damping and frequency is defined as a solid line. It is a characteristic curve figure which shows the result of the excitation experiment by heavy equipment travel. It is a characteristic curve figure which shows the result of the excitation experiment by impact excitation. It is schematic block diagram (A), (B) which shows the vibration reduction method described in patent document 1, 2 as a prior art example.

  The vibration reduction method in the ground environment according to the present invention and the weight for vibration reduction thereof damp the vibration of the vibration source 1 when being transmitted to a vibration reduction target (target) 2 such as a building as shown in FIG. It is a method of determining the weight (or mass) of the weight 3 for achieving a desired vibration reduction rate R (reduction amount of vibration amplitude / original vibration amplitude, the same applies hereinafter).

The vibration reduction rate R and the surface wave contribution rate α are arbitrarily set, and the mass m _w (kg) or weight of the weight 3 that achieves the numerical value is determined. As shown in FIG. 2, the specifications of the weight 3 laid in the direction orthogonal to the line a connecting the respective centers of gravity of the target 2 for vibration reduction and the vibration source 1 have a width B (m), unit length 1 m, as the height H (optionally, alternate with stress), the inertial force F _{= m} w · g per unit length of the weight 3 (g is the gravitational: unit kg · f) is set to.

The stress q (kg · f / m ² ) on the ground surface under the inertial force F is q = F / (B × 1) = F / B. And if the balance equation of this inertia force F and the spring constant K of a ground spring is shown by a simple equation,
m _w ω ² u−K (u−u _o ) = 0 (attenuation is ignored) (1)
here,
m _w : Weight of weight 3 per unit length (in the depth direction in FIG. 2) as width B,
ω: excitation frequency,
u _o : displacement when there is no weight (vibration amplitude),
u: displacement when there is a weight (vibration amplitude),
K: The spring constant of the ground spring at the bottom of the weight.

Then, in the vibration amplitude (u), if the rate of change of the amplitude is (u _o −u) / u _o and the equation (1) is modified, u / u _o = −K / (m _w ω ² − K), where the rate of change is
(U _o −u) / u _o =
m _w ω ² / (m _w ω ² −K) = 1 / (1−K / (m _w ω ² )) Formula (2)

  In order to obtain the spring constant K of the ground spring, as shown in FIG. 3, assuming that the effect of the stress q on the ground surface changes linearly, the influence of the ground surface on the ground is: As shown in the figure, let √ (Bλ) be a coordinate axis z downward. λ: The wavelength (m) of the surface wave to be subjected to vibration reduction.

The stress q is, as shown in FIG. 3, from the position of z directed downward in the ground to 0 to √ (Bλ),
q = (F / B) · (1−z / (BBλ)), and when z is further down, q = 0.

Vertical strain of the ground due to the stress q, ε _v = q / E,
E: Young's modulus of the ground (= 2 (1 +)) G),
G: Shear rigidity of the ground (= _{s s} Vs ² ),
ν: Poisson's ratio of the ground,
_{s s} : density of ground (kg / m ³ ),
Vs: Shear wave velocity of the ground (average value to the depth of the ground considered: m / s),
It is.
By integrating the strain ε _v , the displacement u of the ground surface is
u = ∫ε _v dz = (F / EB) · (√ (Bλ) / 2) = (F / 2E) · (√ (λ / B))
It can be obtained from the spring constant K = F / u of the ground spring.

Therefore, the spring constant of the ground spring K = F / u = 2E · (((B / λ)) = 4 (1 + ν) G · (√ (B / λ)) = 4 (1 + ν) (ρ _s Vs ² ) (((B / λ))

Here, assuming that the Vs relating to the ground depth is C: velocity of a surface wave to be subjected to vibration reduction (= λ · ω / (2π)), the spring constant K of the ground spring is
K = 4 (1 ++) _s C ² ( ² (B / λ)) = 4 (1 + 1) _s (λ ² · ω ² / 4π ² )) = ((1 + ν) / π ² ) _{s s} · ((( Bλ ³ ) · ω ² Equation (3)

Here, the mass m _s (kg) of the soil mass interacting with the weight 3,
If we define m _s = ((1 + ν) / π ² ) ρ _s · √ (Bλ ³ ),
Since the above equation (3) is K = m _s ω ² , the rate of change of the above equation (2) is
(U _o −u) / u _o = 1 / (1−K / (m _w ω ² )) = 1 / (1−m _s / m _w ) equation (4)
It becomes.

  The general properties of the equations (2) and (4) can be interpreted as the transfer function of a single mass system, as shown in FIG. Then, assuming that the damping is sufficiently large (the damping wall is scraped as the damping is large (FIG. 4), the damping is so large that the peak can be ignored) for simplicity, the relationship shown in FIG. 5 holds Suppose. λ c is a corner wavelength.

Then, if FIG. 5 is shown by a formula,
0 <| (u _o −u) / u _o | = 1 / | (1−m _s / m _w ) | ≦ 1, provided that λ ≦ λ c
Furthermore, when 0 <λ <λc, | (u _o −u) / u _o | = 1. When λ = λs, m _s = 2m _w .

The vibration reduction rate R is R = | (u _o −u) / u _o | from the above equation (4), but the force acting on the ground from the weight 3 is a component transmitted along the ground surface (surface (Waves) and components that dissipate into the ground (body waves), of which only the components of surface waves that travel along the ground surface contribute to vibration reduction.

Therefore, assuming that the surface wave contribution factor contributing to the reduction of the surface wave vibration is α (0 <α <1 and standard 0.5 <α <0.7),
R = α · | (u _o −u) / u _o | Equation (5).

Therefore, by setting the desired desired vibration reduction rate R ′ and the surface wave contribution rate α in advance,
The mass m _w of the weight 3 at that time is
m _w ′ = (1 / (1+ (α / R ′))) · m _s where R ′ <α, equation (6).
In the case of the condition of R ′ <α, it is always m _s > 2m _w . In the case of 0 <λ <λc, as shown in FIG. 5, | (u _o −u) / u _o | = 1, but in reality, 0 <| (u _o −u) / u _o Since <1 and the surface wave contribution factor α is the upper limit of the physical effect, the target vibration reduction factor R ′ must be R ′ <α, whereby R> α Expressions become unnecessary.

As described above, the mass m _w ′ per unit length of the weight 3 is determined in the case where the desired vibration reduction rate R ′ is to be obtained. Verification by the prediction formula is confirmed by an excitation experiment. For example, when the vibration amplitude u _o at the time of no countermeasure (when there is no weight) is obtained, assuming that the weight 3 is the measured value u of the vibration amplitude after installation and the predicted value u ′, u ′ = (1− R) u _o formula (7).

The vibration reduction rate R is determined from the above equation (5) as the vibration amplitude u _o and u obtained from the excitation test on a real ground, and the surface wave contribution factor α = 0.6, and the measured vibration amplitude u, Comparison with vibration amplitude u 'obtained by said Formula (7) is shown to FIG. 6, FIG. In FIG. 6, weights 3 of 0.6 t / m ² and 1.2 t / m ² are laid, and a construction heavy machine is run and vibrated as a vibration source, and in FIG. The actual ground was hit and oscillated by m ² and measured.

  Since the compared vibration amplitude u and the predicted vibration amplitude u 'are substantially matched, the validity of the prediction equation (7) can be confirmed.

Thus, by the mass m _w of the weight 3 obtained by the equation (6), as shown in FIG. 1, it is orthogonal to the straight line a connecting the respective centers of gravity of the vibration source 1 and the object 2 of vibration reduction. Lay in the row direction. In addition, since the vibration wraps around from the end of the row of weights 3, in order to prevent this, the length Lw of the weights 3 in the row direction is Lw> 2.dt (where dt is the center of gravity between the weight and the object Set the distance, m).

  By doing as described above, even if the vibration comes inward from the end of the weight 3, the vibration propagates by avoiding the vibration reduction target 2, which is a preferable method for reducing the vibration.

  The vibration reducing method in the ground environment according to the present invention and the weight thereof for vibration reduction can be widely applied to vibration reduction measures that can easily estimate the vibration from the vibration source of the ground and obtain a desired reduction effect. It is a thing.

1 Vibration source,
2 vibration reduction object (building etc.),
Three weight,
4 anti-vibration wall,
5 sandbag guide frame.

Claims (3)

On the ground surface between the vibration source on the ground surface and the object of vibration reduction,
In laying a weight for reducing vibration, in a row direction orthogonal to a straight line connecting the respective centers of gravity of the vibration source and the object,
The mass m _w (the mass of the weight per 1 m in the row direction in the width B) of the weight is
m _w = (1 / (1+ (α / R))) m _s ,
In addition, m _s = ((1 + π) / π ² ) _{s s} · √ (Bλ ³ ),
Here, R represents the vibration reduction rate of the target (reduced amount / original vibration amplitude of the vibration amplitude), alpha is the surface wave contribution (0 <α <1), m s interaction with the weight of the unit length Is the density of the ground mass, _{s s} is the density of the ground, B is the width of the weight (m), λ is the wavelength of the surface wave to be subjected to vibration reduction (m), ν is the Poisson's ratio of the ground,
Setting the vibration reduction rate R and the surface wave contribution rate α, and laying in the orthogonal direction according to the weight m _{w of the} weight determined thereby, to reduce the vibration of the vibration source,
Vibration reduction method in the ground environment characterized by The length Lw in the column direction of the weight is such that Lw> 2 · dt, where dt is the distance between the center of gravity of the weight and the object, m)
The vibration reduction method in ground environment according to claim 1 characterized by the above. The weight to be laid in a row direction orthogonal to a straight line connecting the respective centers of gravity of the vibration source and the object between the vibration source on the ground surface and the object of vibration reduction is:
As a mass m _w of a weight per meter in the row direction with a width B,
m _w = (1 / (1+ (α / R))) m _s ,
In addition, m _s = ((1 + π) / π ² ) _{s s} · √ (Bλ ³ ),
Here, R represents the vibration reduction rate of the target (reduced amount / original vibration amplitude of the vibration amplitude), alpha is the surface wave contribution (0 <α <1), m s interaction with the weight of the unit length Is the density of the ground mass, _{s s} is the density of the ground, B is the width of the weight (m), λ is the wavelength of the surface wave to be subjected to vibration reduction (m), ν is the Poisson's ratio of the ground,
Setting the predicted vibration reduction rate R and the surface wave contribution rate α to determine the mass m _w , whereby the required weight of the weight is determined;
Weight for vibration reduction characterized by

Images