JP2555517B2 - Method and device for measuring the shape of a buried structure - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for measuring the shape of a buried structure, and in particular, the shape and size of a buried part such as a concrete foundation or a concrete pile after construction (hereinafter simply referred to as a shape as appropriate). ) By a non-drilling method.

[0002]

2. Description of the Related Art As a method of measuring the shape of cast-in-place concrete piles by the non-excavation method, "Development of non-destructive inspection technology for piles (part 1) of the 24th Geotechnical Research Conference (June 1989) 5) -Pile shape measurement technology "has been proposed. This method detects the reflected wave from each part of the pile of the pulse wave generated when the pile head is tapped with a hammer, expresses it as a velocity time waveform, and then displays that data for the pile in the ground. It is considered to be a rod, and it is applied to the wave equation derived from the force balance considering the interaction between the pile and the soil during wave propagation, and the shape including the cross-sectional area of each part of the pile is to be measured.

[0003]

By the way, the dimensions of each part of an inverted T-shaped independent foundation in which a base portion is formed at the lower end of a pillar portion for securing a supporting force, such as a concrete foundation of a transmission line tower, are described. Non-destructive measurement is required.

[0004] For example, when the equipment of an existing transmission line is to be strengthened, it is necessary to consider whether or not the concrete foundation of the transmission line tower can bear the load of the equipment after the reinforcement. However, there are cases where design drawings cannot be obtained for old concrete foundations, and it is necessary to measure the shape of the foundation by some method. In this case, there is also a method of measuring the shape by excavating around the foundation, but if excavating the foundation, the ground may be disturbed and the bearing capacity may decrease, so it is desirable to measure by non-excavation.

It is also conceivable to apply the wave theory method used for piles, that is, the pulse reflection method. However, the above wave theory is based on the wave equation assuming that the resistance action of the surrounding soil to the small portion of the pile consists of velocity components corresponding to the wave state of the small portion of the pile, and the velocity component of soil resistance The coefficient for is relevant. Since the estimated value of the soil resistance coefficient is affected by various soil characteristic factors such as soil density, water content, and unit volume weight, it often causes an error from the actual value. There is a problem that it is difficult to improve the accuracy of shape measurement.

Further, the reflected wave is used to measure the position of the tip of the pile or the expanded diameter part or the position of the defect, but the width of the waveform of the reflected wave is distorted and widened. In addition to the above error, a certain degree of skill is required to distinguish the reflected wave from any of the above parts.

Further, the pulse reflection method is effective for a long and simple pile shape, but it is clarified from where it is a reflected wave for a relatively wide width and a complicated shape. Is difficult to do.

An object of the present invention is to provide a method and apparatus for measuring the shape of an embedded structure, which can measure the dimensions of each part including the cross-sectional dimensions of concrete piles and foundations without being affected by the characteristics of soil.

[0009]

In order to achieve the above object, the present invention has been made in view of the fact that an elastic body such as a concrete pile or a foundation has a unique resonance frequency according to its material, size and shape. Exciting the embedded structure to be measured, measuring the resonant frequency of the embedded structure, based on the measured resonant frequency and the resonance conditional expression of the embedded structure assumed in advance,
The shape of the buried structure was calculated.

Resonance modes include longitudinal wave resonance, transverse wave resonance,
There are torsional wave resonance, surface wave resonance, etc., and in principle, any resonance mode can be used.

For example, in the case of utilizing the longitudinal wave resonance mode, the buried structure to be measured is excited in the vertical axis direction, and the propagation speed of the longitudinal wave propagating through the buried structure and the vibration in the exciting direction are measured. The resonance frequency is extracted from the measured vibration,
The shape of the embedded structure is obtained based on the extracted resonance frequency and the resonance condition expression of the embedded structure that is assumed in advance.

In the above, in the case of a concrete pile or foundation having a uniform cross-sectional diameter, or a concrete pile having a diameter-expanded portion at the lower end or a concrete foundation having a base portion, as the resonance conditional expression, the buried structure is It is set assuming that it has a column portion having a circular or rectangular cross section and a base portion having a circular or rectangular cross section having a cross-sectional area different from that of the column body portion.

Further, the number of resonance frequencies to be extracted is basically the same as the number of unknown dimensions, and a simultaneous equation consisting of the same number of resonance condition expressions obtained by substituting this is solved to obtain the unknown dimensions. be able to.

In the above, the resonance conditional expression is set by assuming that the pillar portion of the buried structure is a truncated cone or a truncated pyramid and the pillar portion is a part of a sphere. In this case, if the cross-sectional area of the upper end of the pillar is measured and the radius of the sphere is approximated by the height of the pillar according to the geometrical relationship, the unknown dimension is calculated as the height of the pillar and the cross-sectional area of the lower end. The height and cross-sectional area of the base can be reduced to four.

Further, if the cross-sectional area of the lower end of the pillar is geometrically approximated by the cross-sectional area of the upper end, the inclination angle, and the height of the pillar, unknown dimensions can be obtained by calculating the height of the pillar and the height of the base. Area 3
Can be reduced to individual pieces.

In this case, as the resonance condition expression, the first resonance condition expression (Equation 13) based on the first mode in which the embedded structure expands and contracts in the vertical direction, and the base portion of the embedded structure are perpendicular to the vertical axis. And a resonance condition expression (Expression 17) based on the second mode that expands and contracts in the direction is set, and the resonance frequency of the first mode, which is one less than the number of unknown dimensions, is extracted from the resonance frequency spectrum, By extracting one resonance frequency fB of the second mode and substituting these resonance frequencies into the respective resonance conditional expressions to obtain the unknown dimension, the measurement accuracy of the dimension of the base portion can be improved.

Further, as the resonance condition formula, the resonance condition formula (Formula 13) based on the first mode in which the buried structure expands and contracts in the vertical direction is used, and the resonance frequency spectrum has a number one less than the number of unknown dimensions. The resonance frequency of the first mode is extracted, and the resonance frequency fB of the second mode in which the base portion of the embedded structure expands and contracts in the direction perpendicular to the vertical axis is extracted from the resonance frequency spectrum. From the frequency fB and the propagation velocity v, the cross-sectional area S ₂ of the base portion is S ₂ = (v
It is possible to obtain the unknown dimension by approximating by a relationship of / 2fB) ² and substituting S ₂ and the extracted resonance frequency of the first mode into the respective resonance conditional expressions. The resonance frequency fB is a resonance frequency between the second-order and third-order resonance frequencies of the first mode.

When it is difficult to measure the resonance frequency fB, in addition to the first resonance conditional expression, the second longitudinal wave when the upper end of the embedded structure is excited in the direction perpendicular to the vertical axis is used. A resonance condition formula (equation 24, 24 ', 25, 25') is set, the propagation velocity of a longitudinal wave propagating in the embedded structure to be measured is measured, and the upper end of the embedded structure is applied in the vertical axis direction. The first frequency spectrum of the longitudinal wave is measured by shaking, and the second frequency spectrum of the longitudinal wave is measured by exciting the upper end in a direction perpendicular to the vertical axis. A resonance frequency that is one or two less than the number of unknown dimensions is extracted from the frequency spectrum, and the extracted resonance frequency, the known dimension of the embedded structure, and the propagation velocity are used as the first resonance conditional expression. Substituting and from the second frequency spectrum, 1
One or two resonance frequencies are extracted, and the extracted resonance frequencies, the known dimensions of the embedded structure, and the propagation velocity are substituted into the second resonance conditional expression to obtain the number of unknown dimensions. The shape of the buried structure can be obtained by solving the simultaneous equations.

On the other hand, the shape measuring apparatus of the present invention has input means for inputting frequency spectrum data including the resonance frequency of the buried structure to be measured, and a resonance conditional expression for the buried structure which is assumed in advance. This can be realized by including shape calculation means for calculating the shape of the buried structure based on a plurality of resonance frequencies analyzed by the frequency analysis means and the resonance condition expression.

Further, the frequency spectrum data is inputted with a vibrating means for vibrating the buried structure to be measured, a vibration detecting means for detecting the vibration of the buried structure, and an output signal of the vibration detecting means. Frequency analysis means for analyzing a frequency spectrum including the resonance frequency of the embedded structure.

[0021]

First, the principle of the method for measuring the shape of an embedded structure according to the present invention will be described. As mentioned above, a buried structure such as a concrete foundation is one of elastic bodies, and generally,
The elastic body has a unique resonance frequency according to its material, size, and shape. There are many natural frequencies of an elastic body. Further, there are a plurality of vibration modes of the elastic body, and there are a longitudinal wave vibrating in the propagation direction of the vibration wave, a transverse wave vibrating in a direction orthogonal to the propagation direction, a torsion wave having a rotation axis in the propagation direction, and a surface wave propagating on the surface. Further, for these vibration forms, there are innumerable modes having different resonance frequencies.

This mode will be described by taking the case of longitudinal waves of a prismatic elastic body as an example. When the vertical and horizontal lengths of the cross section of the prism are a ₁ and a ₂ , and the height (or length) is h, the resonance frequency f of the prism is given by the following equation (1).

[0023]

[Equation 1]

In the equation (1), v is the longitudinal wave propagation velocity, and l, m and n are non-negative integers.
Various combinations of (l, m, n) represent different modes and generally have different frequencies. For example (0,0,
As shown in FIG. 7A, the mode 1) is a stretching vibration in which the upper and lower ends in the h direction are antinodes and the center is a node, and the frequency f is given by f = v · 1 / 2h. . Also, (0,
The modes (0, 2) and (0, 0, 3) are as shown in FIGS. 7B and 7C, respectively. In general, (0,0,
The mode of n) is a vibration in which n nodes exist in the h direction,
The frequency f is given by f = vn / 2h. In addition, the (1, 0, 0) mode is a mode in which stretching vibration occurs in the direction of arrow 1 shown in FIG.
The 0) mode is a mode of stretching vibration in the direction of arrow 2 in the figure, and the (1, 1, 1) mode is a mode of stretching vibration in all directions of arrows 1, 2, 3 in the figure.

As described above, when the dimensions of each part of the prismatic elastic body and the propagation velocity of the longitudinal wave are given, the resonance frequency of the prism is determined. In addition, in the case other than the prism, and in the case other than the longitudinal wave, it cannot be expressed by a simple formula like the above formula (1). However, it is the same that the elastic body has a number of resonance frequencies of many modes that are unique to each elastic body.

Therefore, the present invention intends to measure the shape of an embedded structure, such as a concrete foundation, which is an elastic body, by measuring the resonant frequency of the structure by reversing the above relationship. .

Next, the principle of the method for measuring the shape of an embedded structure of the present invention will be described with reference to a concrete example. Here, since it has been found that it is possible to sufficiently measure the shape of the buried structure by utilizing only the longitudinal wave among the above-mentioned vibration forms, the method of measuring using the longitudinal wave will be described below. To do. However, the present invention is intended to measure the shape by utilizing the resonance phenomenon, and is not limited to the longitudinal wave.

(Basic method) As is well known, the vibration problem of an elastic body is similar to that of an electric circuit. Therefore, in the vibration analysis, we introduced the same concept of impedance as an electric circuit,
An embedded structure with a complicated shape is decomposed into blocks with a simple shape, the impedance of each block is obtained, this is assembled, and the overall impedance is constructed and analyzed. This makes it possible to analyze the vibration problem of an embedded structure having a complicated shape, as will be described below.

First, for the sake of simplicity, consider a truncated cone-shaped column. As shown in FIG. 9, the vertical axis direction of the column 5 is x
X, the axial stress in the cross section perpendicular to this axis
(X) and the displacement in the axial direction are ξ, they have the relationship of the following expression (2).

X (x) = k∂ξ / ∂x (2) where k is the elastic modulus, where Young's modulus is E and Poisson's ratio is σ and is expressed by the following equation (3).

K = (1−σ) E / (1 + σ) (1-2σ) (3) Correspondence with an electric circuit is represented by the cross-sectional area of the column 5 at the coordinate x of the x axis as S (x). Then, −X (x) · S (x) corresponds to the voltage, and the displacement speed, that is, ∂ξ / ∂t corresponds to the current. Therefore, the impedance Z at the coordinate x
(X) can be expressed by the following equation (4).

[0032]

[Equation 2]

Now, assuming that the columnar body 5 is vibrating at an angular frequency ω (= 2πf), ∂ξ / ∂t can be expressed by the following expression (5) by complex number expression. In the equation, ρ is the density of the elastic body.

∂ξ / ∂t = (1 / iωρ) (∂X / ∂x) (5) Here, assuming that the cross-sectional area S (x) = S (constant), the coordinate x
The impedance Z (x) at is given by the following equation (6).

[0035]

(Equation 3)

Here, β is a propagation constant, and if the wavelength is λ, then β = 2π / λ. Z ₀ is called characteristic impedance, and Z ₀ = S · ωρ / β = S · k / v. In the above equation (6), each term of the numerator and denominator having K ₁ as a coefficient is a traveling wave component, and similarly, the term having K ₂ as a coefficient is a reflected wave component. These K ₁ and K ₂ can be determined by the state of one end of the column 5. For example, when an elastic body of impedance Z ₁₀ is connected to the end portion of x = h, the above equation (6) becomes the following equation (7).

[0037]

[Equation 4]

When this is applied to a concrete foundation 6 such as a steel tower having a base portion as shown in FIG. 10, it becomes as follows.

In order to simplify the explanation, the concrete foundation 6 of this example has a prismatic columnar section 7 having a square cross section,
It is assumed that the base portion 8 has a square prismatic cross section. First, the steel tower portion 9, the pillar portion 7, and the base portion 8 are disassembled. Then, the impedance of the tower section 9 above x = 0 is Z
_11. Let Z ₁₂ be the impedance of the concrete foundation 6 consisting of the pillar 7 and the base 8 located below.

When the concrete foundation 6 is excited in the vertical axis direction by the force F at x = 0, the equivalent circuit of FIG. 11 is established.

In FIG. 11, the combined impedance Z becomes (Z ₁₁ + Z ₁₂ ). Assuming that the characteristic impedances of Z ₁₁ and Z ₁₂ are Z ₀₁ and Z ₀₂ , respectively, their ratio is given by the following equation (8).

[0042]

(Equation 5)

Here, S ₀₁ , k ₁ and v ₁ are the cross-sectional area, elastic modulus and longitudinal wave propagation velocity of the steel tower 9, respectively, and S ₀₂ , k 1
₂ and v ₂ are the cross-sectional area, elastic modulus, and longitudinal wave propagation velocity of the uppermost end of the concrete foundation 6.

By the way, in general, S ₀₁ / S ₀₂ ≈1 / 100, (k ₁ / v ₁ ) / (k ₂ / v ₂ ) ≈2,3, and Z ₀₁ / Z ₀₂ <0.05. Therefore, the resonance of Z = 0 is Z ₁₁ ≈0,
It can be approximated as Z≈Z ₁₂ . That is, the resonance of the entire concrete foundation 6 to which the steel tower part 9 is attached can be regarded as approximately equal to the resonance of only the concrete foundation 6. Therefore, only the concrete foundation will be treated below.

For the sake of calculation, the columnar portion 7 of the truncated pyramid of the concrete foundation 6 shown in FIG. 10 is considered as a part of a sphere as shown in FIG. Moreover, since the taper angle θ is small, the influence of the spherical portions on both end surfaces is neglected.

First, consider the fundamental wave of the column portion 7. The traveling wave component ξ (+) and the reflected wave component ξ (−) of the displacement ξ described in the equation (6) are given by the following equation, where r is the coordinate in the basic axis direction.

[0047]

(Equation 6)

Therefore, the impedance Z (r) at the coordinate position r is given by the following equation (9).

[0049]

(Equation 7)

Here, Z ₀ (r) is given by the following equation (10).

[0051]

(Equation 8)

Next, as shown in FIG. 10, the impedance Z (r ₁ ) seen from r = r ₁ when the base portion 8 of a regular prism is connected to the end of r = r ₂ is the impedance of the base portion 8. Z ₂ is given by the following equation (11). In addition,
h = r ₂ −r ₁ .

[0053]

[Equation 9]

The impedance Z ₂ of the base portion 8 is given by the following equation (12) from the equation (7), where t is the thickness of the base portion 8 and S ₂ (= B ² ) is the cross-sectional area of the regular prism. To be The cross-sectional area S ₂ of the base portion 8 is uniform, and the lower end is the free end in FIG.

Z ₂ = i (B ² kβ / ω) tan βt = i (S ₂ kβ / ω) tan βt (12) Here, the overall resonance of the concrete foundation 6 is Z ( It occurs when r ₁ ) is “0”. That is, it occurs when the numerator is "0". Therefore, by rearranging the numerator of Expression (11) as “0”, the resonance condition expression of Expression (13) below is obtained.

Βr ₂ (S ₁ sinβh · cosβt + S ₂ cosβh · sinβt) −S ₂ sinβh · sinβt = 0 (13) Here, S ₁ is the bottom area of the columnar portion 7 (in the case of a truncated pyramid,
b ² ). Further, the propagation constant β is given by the following equation (14) as described above.

Β = 2π / λ = 2πf / v (14) The propagation velocity v of the longitudinal wave is a unique value of the measurement object foundation and can be measured by a known method. The frequency f is the base 6 of FIG.
The upper end of is vibrated in the x-axis direction, and the resonance frequency of the foundation 6 generated thereby is measured. The resonance frequency of the longitudinal wave is measured by mounting an acceleration sensor on the upper end and analyzing the frequency spectrum from the output signal of the sensor.

Therefore, in the resonance condition expression of the equation (13), since the unknowns are S ₁ , S ₂ , h, t, and r ₂ , five resonance frequencies f of longitudinal waves are measured, and those resonance vibrations are measured. Number f
From the measured propagation velocity v, the five β's are obtained by the equation (14), and these are substituted into the equation (13) to obtain the five simultaneous equations. By solving the simultaneous equations, the unknown geometrical dimensions can be obtained.

Since the upper end of the column 7 is generally exposed on the ground, the dimension a is obtained by actual measurement.

If the base of the object to be measured does not have the base portion 8, as a result, S ₁ = S ₂ , t = 0 or S ₁ ≈
The solution is obtained with S ₂ , t≈0.

Similarly, when the columnar portion 7 is not a truncated pyramid but a prism having a uniform cross section, a solution is obtained with S ₁ = a ² or S ₁ ≈a ² .

Further, as shown in FIGS. 12 (a) and 12 (b), the equation (13) shows that the exposed ground portion of the columnar portion 7 has a circular (φ ₁ ) or rectangular (a ₁ × a ₂ ) cross section. Can also be applied if
The buried portion was estimated to have the shape shown in the figure, and the calculated S
It is possible to obtain (φ ₂ , B) and (b ₁ , b ₂ , B ₁ , B ₂ ) from ₁ and S ₂ , respectively.

Now, a simplified method for obtaining the unknown number r ₂ in the equation (13) will be described. When the taper angle θ is small, r ₂ ≈
Since r ₁ + h can be approximated, r ₂
Can be expressed by the following equation.

[0064]

[Equation 10]

Since the dimension a can be actually measured on the exposed part on the ground, the unknown r ₂ can be represented by the unknown h.

By substituting this into the equation (13), the unknowns to be obtained are reduced to four, S ₁ , S ₂ , h, and t. When a = b, the expression (15) is meaningless, but in this case, the expression (1
3) becomes the following expression (13 ').

S ₁ sin βh · cos βt + S ₂ cos βh · sin βt = 0 (13 ′) Furthermore, since the taper angle θ can also be measured at the exposed portion on the ground, when the columnar portion 7 is a regular pyramid, S ₁ = b ² . Therefore, b can be expressed by the following equation (16) from the geometrical relation.

B = 2htan θ + a (16) Therefore, the unknowns in the equation (13) are S ₂ , h, t.
Reduced to 3.

Therefore, the dimension a, the taper angle θ, the propagation velocity v, and the three resonance frequencies f ₁ , f ₂ , and f ₃ are measured, and the equation (1
The shape of the buried portion can be obtained by obtaining β ₁ , β ₂ , and β _{3 according} to 4) and substituting them in equation (13) to solve the simultaneous equations.

In the above description, an example of measuring the shape of the buried structure using longitudinal wave resonance has been described.
As described above, the present invention is not limited to the longitudinal wave resonance, and its purpose is to measure the shape by utilizing the resonance phenomenon. That is, as in the case of the longitudinal wave described above, the resonance conditional expression for the transverse wave, the torsional wave, or the surface wave is theoretically determined, and therefore, the necessary number of resonance frequencies corresponding to those vibration modes is measured according to the unknown number. , The size of each part can be obtained by solving the simultaneous equations.

(Modification Method 1) According to the previous expression (13), when the base portion 8 as shown in FIG. 10 is provided, the calculation accuracy of the bottom side dimension b of the columnar portion 7 and the square dimension B of the base portion 8 is very good. Turned out not. Therefore, in order to improve the accuracy of the dimensions b and B, it is preferable to use the resonance mode shown in FIG. That is, as shown by the arrow in FIG. 13, this is a resonance mode in which the columnar portion 7 is compressed and the base portion 8 is also compressed. The vibration method in this mode is the same as in the basic method.

In this mode, the resonance condition expression is
Given in 7).

Β′r ₂ (b ² sin β′h · cos β ″ t + B ² cos β′h · sin β ″ t) −B ² sin β′h · sin β ″ t = 0 (17) where β ″ = √ {Β ′ ² − (π / B) ² } (18) Resonant frequency fB (β ′ = 2πfB / corresponding to this mode
v) is obtained from the frequency spectrum obtained by the above-mentioned vibration method according to the following judgment. First, when the upper end surface of the foundation 6 is excited in the vertical foundation axis direction by a hammer or the like and the vibration wave in that direction is detected by the acceleration sensor, a spectrum of a large number of resonance frequencies is obtained. If f ₁ , f ₂ , f ₃ , ... from the lowest frequency of the spectrum are given,
fB was found that appearing between f ₂ and f _3. here,
f ₁ is a fundamental wave, and f ₂ , f ₃ ... Are second-order, third-order ... Components. Then, it was found that the following relationships exist among f ₁ , f ₂ , and f ₃ .

2f ₁ <f ₂ <3f ₁ 3f ₁ <f ₃ <5f ₁ : (19): As a result, fB can be easily detected.

Therefore, in the case of a concrete foundation expected to have the base portion 8, one of the three resonance frequencies f ₁ , f ₂ and f ₃ described above is replaced by fB, and the resonance condition formula is defined for fB. (17) is used. Then, the resonance condition expression (13) is used for two of the other resonance frequencies f ₁ , f ₂ , and f ₃ . As a result, the unknown number S ₂ (= B ² ),
It is possible to obtain the shape by solving three simultaneous equations of h and t and solving them.

(Modification method 2) Base portion 8 in the case of a regular prism
The dimension B can be approximated by the following equation (20) using the resonance frequency fB described in the modification method 1. The precision of the dimension B by this was less than 2%.

B = √S ₂ = v / 2fB (20) When two resonance frequencies corresponding to fB, fB ₁ and fB _2, can be recognized, the horizontal cross section of the base portion 8 is rectangular B ₁ × B ₂
It can be estimated that Equation (20) in this case is as follows.

B ₁ = v / 2fB ₁ (20a) B ₂ = v / 2fB ₂ (20b) Therefore, the formula (2) is replaced with the formula (17) of the modification method 1.
0) or equations (20a) and (20b) can be used to determine the dimensions of each part of the foundation 6.

(Modification Method 3) If the above fB spectrum does not appear clearly, Modification Method 1 or 2 cannot be used. In this case, the vibration mode shown in FIG. 14 is used. That is, this mode is due to resonance of a longitudinal wave generated in the lateral direction of the base portion 8 when the upper portion of the columnar portion 7 is vibrated in the direction perpendicular to the vertical axis (hereinafter referred to as lateral vibration).

Consider the impedance model of FIG. 15 for the resonance analysis of FIG. The impedance Z ₃ viewed from the upper end surface of FIG. 15 is given by the following equation (21), where the characteristic impedances of the respective portions are Z ₃₁ and Z ₃₂ .

[0081]

[Equation 11]

By modifying this, the following equation (22) is obtained.

[0083]

(Equation 12)

The relationship between Z ₃₁ and Z ₃₂ is given by the following equation (23).

Z ₃₂ / Z ₃₁ = (b ² + 2Bt) / 2Bt (23) Resonance occurs when either of the two factors of the numerator of formula (22) is “0”.

First, the following expression (24) is obtained from the condition that the first factor of the numerator of expression (22) is "0".

[0087]

(Equation 13)

Further, the following equation (25) is obtained from the condition that the second factor is "0".

[0089]

[Equation 14]

Dimension of each part is obtained by using one or both of these expressions (24) and (25) and the resonance condition expression (13). That is, the resonance frequency fB ₀ (β ₀ = 2πfB ₀ / v) in the base portion 8 at the time of lateral excitation is measured, and the expression (24) or (25) is applied as a resonance condition expression that satisfies this. Note that the order with the lowest frequency at fB ₀ is the vibration mode of FIG.
Follow 4). The next order follows the equation (25) in the vibration mode of FIG. The next order has a relationship that sequentially and alternately follows the equation (24).

Further, the lateral vibration of the base portion 8 is as shown in FIG.
There are vibration modes such as 6 (c). In this mode, the frequency in the basic mode according to equation (24) is as shown in FIG.
It is √2 times that in the case of (a).

The above equations (24) and (25) show the case where the base portion 8 is a regular prism, but when the horizontal cross section of the concrete foundation is rectangular, the equations (24 ') and (25') are obtained, respectively. . The vibration mode of each equation is shown in FIGS. 17 (a) and 17 (b).

[0093]

(Equation 15)

Now, in order to find the resonance frequency fB ₀ corresponding to this vibration mode from the lateral excitation spectrum, first, the above-mentioned equation (1) is calculated from the actual measurement dimension a and the approximate dimensions of the taper angles θ and h.
Using 6), determine the approximate size of b. The approximate dimension of h is experimentally given by the following equation (26) from the above resonance frequencies f ₁ and f ₂ .

H≈v / {2 (f ₂ −f ₁ )} (26) Generally, the dimension B of the base portion 8 and the dimension b of the column portion 7 are
Has a relationship of B≈2b. When the relationship between fB ₀ and B was experimentally obtained based on these, the following expression (27) was obtained.

FB ₀ ≈v / (2B × 0.9) (27) Therefore, from the above relation, approximately B, and further approximately fB ₀
Then, based on this, an accurate f is calculated from the lateral excitation spectrum.
Find B ₀ .

The basic principle of the method for measuring the shape of an embedded structure of the present invention and its modification method have been described above. Since equations (13), (17), (24), and (25) are transcendental equations, and solutions cannot be analytically obtained, they are actually obtained by numerical analysis using a computer.

The contents of each of the above methods are summarized as follows.

In the basic method, the upper surface of the concrete foundation is excited in the vertical direction, and the resonance frequencies f ₁ , f ₂ and f ₃ are extracted from the spectrum of the vibration waveform in that direction. Then, these are substituted into the equation (13) to calculate b, B, and t.

In the modification method 1, the upper surface of the concrete foundation is vertically excited, and the resonance frequencies f ₁ , f ₂ , f ₃ , fB are extracted from the spectrum of the vibration waveform in that direction. And
_Two of f ₁ , f ₂ , and f ₃ are substituted into the equation (13). Also, fB is substituted into the equation (17). By those formulas,
Calculate b, B, and t.

In the modification method 2, the upper surface of the concrete foundation is vertically excited, and the resonance frequencies f ₁ , f ₂ , f ₃ , and fB are extracted from the spectrum of the vibration waveform in that direction. And
_Two of f ₁ , f ₂ , and f ₃ are substituted into the equation (13). Next, fB is substituted into the equation (20) to determine B, and b and t are calculated based on the equation (13) into which fB is substituted.

When there are two resonance frequencies corresponding to fB, it is estimated that the base portion has a rectangular shape.
B ₁ and B ₂ are obtained from the above equations (20a) and (20b).

In the modification method 3, the upper surface of the concrete foundation is vertically excited, the resonance frequencies f ₁ , f ₂ and f ₃ are extracted from the spectrum of the vibration waveform in that direction, and the upper side surface of the concrete foundation is vertically extracted. Vibration is applied in the direction orthogonal to the axis, and the resonance frequency fB ₀ is extracted from the spectrum of the vibration waveform in that direction.
Then, _two of f ₁ , f ₂ , and f ₃ are substituted into the equation (13). Further, fB ₀ is substituted into the equation (24) or (25). B, B, and t are calculated based on these substitution formulas.

The horizontal section of the base portion is rectangular (B ₁ ×
In the case of B ₂ ), the formula (24 ′) or the formula (25 ′) is used.

[0105]

EXAMPLE An example in which the shape of the buried structure was measured by the method of the present invention will be described with reference to FIGS. FIG.
2 is a flowchart showing an embodiment of the processing procedure of the shape calculation means according to the characteristic part of the present invention, and FIG. 2 is a functional block diagram showing the overall shape measuring device of the present invention.

In this embodiment, the concrete foundation 10 for a power transmission line tower as shown in FIG. 2 is used as a measurement target, and the dimensions of each part of the buried portion are estimated. That is, it is estimated from the shape of the exposed portion on the ground that the pillar portion 11 has a regular truncated pyramid shape, and the base portion 1 has a regular prism shape at the lower end of the pillar portion 11.
Assuming that 2 exists, a resonance conditional expression is set and measurement is performed.

The configuration of the shape measuring apparatus of this embodiment will be described with reference to FIG. First, as a vibrating means for applying vibration to the concrete foundation 10, vibration is applied by an impulse method in which a predetermined portion of the foundation is hit with a hammer or the like, or a vibrator that generates sinusoidal vibration, and the frequency is swept. The sweep method can be applied. In this embodiment, the hammer 21 is used. The hammer 21 is provided with a vibrating force detecting means for detecting a vibrating force and outputting an electric signal, and this electric signal is amplified by the preamplifier 23 as a vibrating detection signal 22 and is fed to the FFT analyzer 24. It has been entered. As a vibration detecting means for detecting the vibration of the concrete foundation 10, an acceleration sensor 25 is attached to the upper end surface of the concrete foundation 10. The mounting position is on the upper surface of the foundation on the center side of the tower near the diagonal line facing the center direction of the tower (right side in the figure) .In order to improve the accuracy of vibration detection, use an adhesive such as an instant adhesive. Attach firmly via. If the upper surface of the foundation is tilted, insert an appropriate adapter so that the sensor surface becomes horizontal, and fix it firmly without backlash. This acceleration sensor 25
Is a piezoelectric accelerometer, which is capable of detecting vibration components in three directions of x, y, and z directions as shown by arrows, and converts the vibration in each direction into a vibration detection signal 26 of an electric signal. It is designed to output. This vibration detection signal 26 is amplified by the charge amplifier 27, and then FF
It is input to the T analyzer 24.

An FFT (fast fourier transform) analyzer 24 A / D-converts the input vibration detection signal 22 and vibration detection signal 26 respectively, and performs Fourier transform by computer processing to convert the vibration waveform into a frequency spectrum. It is designed to analyze. By the way, hammer 2
In the case of the impulse method in which the base 10 is hit with 1, the frequency spectrum of the vibration force is not flat, so the vibration frequency spectrum of the vibration detection signal 22 and the vibration detection signal 26 obtained by detecting the vibration force of the hammer 21. The frequency spectrum is standardized by taking a ratio with the frequency spectrum, and measured as a frequency response. The frequency response of the frequency spectrum analysis result of the vibration detection signal 26 thus measured is displayed on the display screen. In addition, the frequency spectrum data analyzed as necessary is recorded on the floppy disk (FD) 28.

The shape calculation device 29 is configured using a microcomputer including an input device, a calculation processing device, a storage device, an output device, and the like. In the storage device, a resonance condition formula (for example, formula 13,
17, 24, 25, etc.), related arithmetic expressions, the arithmetic processing program shown in FIG. 1, and the like, which are necessary for the arithmetic processing of the shape measurement are stored in advance. Further, the frequency response data of the concrete foundation 10 is read from the FD 28 via the input device into the storage device, and the actual measurement data of the upper end of the foundation and the actual measurement data such as the propagation velocity input from the input device are stored in the storage device. Then, along the flowchart of FIG. 1, the shape and dimensions of the concrete foundation 10 are calculated by using the measured data and the frequency response data, and the result is output via an output device such as a display or a printer. It has become.

Hereinafter, the concrete foundation 1 according to the present embodiment.
The procedure of 0 shape measurement will be described. First, at the upper end of the concrete foundation 10 exposed above the ground, the dimensions a ₁ and a ₂ of the upper end sides of the pillar 11 (in the case of this embodiment, a ₁ = a ₂
= A), the inclination angle (taper angle) θ ₁ of the side surface of the column body 11,
θ ₂ (θ ₁ = θ ₂ = θ in the case of this embodiment) and the propagation velocity v of the longitudinal wave propagating in the concrete foundation 10 are measured.

An example of the method of measuring the propagation velocity v will be described with reference to FIG. In this embodiment, an ultrasonic vibrator 31 and a sound wave detector 32 are opposed to and held in contact with both sides of the concrete foundation 10. A vibration signal 34 is applied from the propagation velocity measuring device 33 to the vibration exciter 31, an ultrasonic pulse is radiated into the foundation, and the ultrasonic pulse propagating through the concrete foundation 10 is detected by the acoustic wave detector 32. . This detection signal 35
Is received by the propagation velocity measuring device 33, the time from the output timing of the excitation signal 34 to the reception timing of the detection signal 35 is measured, and the sound wave propagation time is measured between the shaker 31 and the sound wave detector 32 in advance. Propagation velocity v by dividing distance d
Ask for. When the propagation velocity of the concrete foundation 10 was measured in this way, v = 4165 m / s was obtained.

Concrete foundation 10 with hammer 21
Tap the top end of x in either the x, y, or z direction. When the upper end surface is hit in the x direction, the frequency response of the vibration detection signal 26x of the acceleration sensor 25 in the x direction is measured. Similarly, the vibration frequency response of the vibration detection signal 26y in the y direction when hitting in the y direction or the opposite direction and the frequency response of the vibration detection signal 26z in the z direction when hitting in the z direction or the opposite direction are measured.

FIG. 4 shows the F of the upper end surface of the foundation.₁Point in x direction
Measurement of frequency response of ball striking ball in vertical axis direction
The results are shown. The horizontal axis of the figure represents the frequency kHz, and the vertical axis the vibration.
The ratio between the motion detection signal 26 and the vibration detection signal 22 is expressed in dB value.
are doing. The accuracy of this frequency response measurement result is 8Hz
is there. In the figure, the frequency showing a remarkable peak is
It is the resonance frequency that satisfies the condition of equation (13), and
The low frequency component is the resonance frequency f of the fundamental wave in the longitudinal vibration mode.
₁(624 Hz). Also, f₁Higher than the next peak value
Resonance frequency f of secondary frequency₂(1.472 kHz). resonance
Frequency f₂The peak frequency is higher than
Vibration frequency f₃(2.384 kHz). These f ₁, F₂,
f₃, ... is 2f₁<F₂<3f₁3f₁<F₃<5f
₁Since there is a relationship of ...₂, F₃.. is extracted
Can be

As for fB, it is sufficient to extract the frequency of the peak value appearing between f ₂ and f ₃ as described above.
B = 1.76 kHz can be extracted.

Similarly, in FIG. 5, the upper end side surface (in the figure,
The measurement result of the frequency response when the F ₂ point (on the opposite side surface) is tapped in the z direction, that is, when lateral vibration is applied is shown. As can be seen from the figure, it has a peak at a frequency of 2.752 kHz. This is considered to be the resonance frequency of the mode in which the base portion simultaneously vibrates horizontally and vertically as shown in FIG. 16 (c). Therefore, a value obtained by dividing this by √2 is the resonance frequency fB ₀ of the fundamental wave in the resonance condition expression of the expression (24). That is, fB ₀ = 1.946 kHz, and the corresponding peak is recognized in the frequency response of FIG.

Using the frequency response data thus obtained, the processing procedure in the shape calculation device 29 for obtaining the unknown dimensions of each part of the concrete foundation 10 will be described with reference to the flowchart of FIG. In the present embodiment, the case where the shape is calculated by using the equation (13) of the above-mentioned resonance condition equations as a basis and using the equations (17) and (18) together to improve the dimension estimation accuracy of the base portion 12 is shown. .

(Step 101) Measured data such as known dimensions are input through an input device. The actual measurement data of the present embodiment are three values of the propagation velocity v, the side dimension a of the upper end of the column portion, and the taper angle θ, and v = 4165 m / s and a =
Enter 40 cm and θ = 2.9 °.

(Step 102) The frequency response data is read from the FD 28 and stored in the storage device.

(Step 103) Expressions (15) and (16)
According to the relationship shown in, the radius r ₂ of the sphere and the lower end side dimension b of the column portion 11 among the unknown dimensions of the equation (13) are respectively set to the side dimension a as in the following equations (28) and (29). The taper angle θ is used to approximate other unknown dimensions.

R ₂ = bh / (b−a) (28) b = 2h · tan θ + a (29) (Step 104) The number N of unknown dimensions of the resonance condition expression (13) is calculated. In the case of the present embodiment, the height h of the column body portion 11,
Since the three sides B and the thickness t of the base 12 are unknown, N = 3.

(Step 105) From the resonance frequencies f ₁ , f ₂ , f ₃ , ... Of the frequency response spectrum data of FIG. 4, (N-1) or two resonance frequencies (for example,
f ₁ and f ₂ ) are extracted.

(Step 106) Here, the resonance frequency fB corresponding to the lateral vibration mode of the base portion 12 is extracted from the spectrum data of the frequency response of FIG.

(Step 107) Here, the propagation constants β ₁ , β ₂ , β ′ are respectively obtained from the extracted resonance frequencies f ₁ , f ₂ , fB by the following equations, and the propagation constants β ₁ , β ₂ , β ′ are obtained as corresponding resonance condition equations. Substitute and make simultaneous equations.

Β ₁ = 2πf ₁ / v (30) β ₂ = 2πf ₂ / v (31) β ′ = 2πfB / v (32) Further, β ″ is obtained according to the equation (18), and these are given by (1
Substituting into 3) and (17), the following equations are obtained respectively. Here, in the present embodiment, in view of the fact that the rigidity of the base portion 12 changes depending on the thickness t of the base portion 12 and the phenomenon of resonance vibration is different, the term including the side dimension B in the equations (13) and (17). The adjustment coefficient c of the rigidity is introduced into the. However, c ≦
1.0, and in this example, c = 0.95.

[0125] ^{_{β 1 r 2 (b 2 sinβ}} 1 h · cosβ 1 t + cB 2 β 1 r 2 cosβ 1 h · sinβ 1 t) -cB 2 sinβ 1 h · sinβ 1 t = 0 ...... (33) β 2 r _{^{2 (b 2 sinβ 2 h ·}} cosβ 2 t + cB 2 β 2 r 2 cosβ 2 h · sinβ 2 t) -cB 2 sinβ 2 h · sinβ 2 t = 0 ...... (34) β'r 2 (b 2 sinβ ' h · cosβ ″ t + cB ² cosβ′h · sinβ ″ t) −cB ² sinβ′h · sinβ ″ t = 0 (35) where β ″ = √ {β ′ ² − (π / B) ² } (36) (Step 108) The above equations (28) to (32), (3)
Substituting the measured data or the resonance frequency into 6),
The results are substituted into equations (33) to (35) and solved by a numerical calculation method to calculate unknown dimensions b, B, h, t. This numerical calculation is performed by iterative calculation using the Newton-Raphson method and the regular Falsi method. And
The value when the left side of the equations (33) to (35) converges to a minute value ε or less is taken as the solution. In addition, since the initial value of each unknown dimension is required for the calculation, the dimension generally used as a concrete foundation (h = 200 cm, t = 50 cm)
And B = v / 2fB, which is an approximate value of B.

(Step 109) The unknown dimensions b, B, h, and t obtained in the above step 108 are output, and the process ends.

The results of the above-mentioned shape measurement are shown in Table 1 below together with the measured dimensions.

[0128]

[Table 1]

As can be seen from Table 1, the dimensions of the buried portion of the concrete foundation 10 could be estimated with extremely high accuracy. The measurement result is output to the display of the output device as shown in FIG. 7 or from the printer.

Next, a modification in which the equations (13) and (24) are used as the resonance condition equations in the calculation of step 107 will be described. In this case, the equation (24) is applied using the resonance frequency fB ₀ (1.946 kHz) related to the lateral vibration of the base portion 12 extracted from the frequency response data of FIG. By substituting the relationship of Expression (29) into Expression (24) and rearranging, the following Expression (37) is obtained.

[0131] 2Bt · tanθ {(B-2h · tanθ-a) β 0/2} - {(2h · tanθ + a) 2 + 2Bt} cot {(2h · tanθ + a) β 0/2} = 0 ... (37) β ₀ = 2πfB ₀ / v (38) This equation (37), (38) and the above equations (33), (34)
The unknown dimensions b, B, h, and t are calculated by numerical analysis using. The results of this shape measurement are shown in Table 2 below.

[0132]

[Table 2]

The difference between the calculated values in Table 1 and Table 2 is 1 cm or less. Moreover, all the calculated values are within 5% of the measured values, and it can be said that both calculated values are in good agreement with the measured values.

As described above, according to the embodiment of FIG. 1 and its modification, the shape of the concrete foundation having the base portion can be measured with high accuracy without being affected by soil.

Further, in the above-mentioned embodiment, the method of measurement using the resonance condition formula assuming a concrete foundation having a base portion has been described, but it goes without saying that it can be applied as it is to an embedded structure such as a concrete pile. In this case, if there is no expanded diameter portion, an unknown dimension corresponding to the expanded diameter portion is obtained as "0". Alternatively, if the resonance frequency fB cannot be observed and if f ₂ ≈2f _1, it may be determined that the base portion or the enlarged diameter portion does not exist. Similarly, when the columnar portion has no taper, a solution is obtained with b = a.

Further, since the mounting state of the acceleration sensor 25 has a great influence on the measurement of the frequency response, it is desirable to firmly and surely mount it on the concrete foundation.
For example, when measuring a change in the shape of a concrete foundation over time, it is desirable to previously embed a sensor mounting screw or the like when installing the concrete foundation.

[0137]

As described above, according to the present invention,
Since the shape of the buried structure is measured using the resonance phenomenon, the dimensions of each part of the structure with a complicated shape can be measured accurately and nondestructively without being affected by the surrounding soil. it can.

Further, since the base portion and the expanded diameter portion are not estimated based on the time relationship of reflected waves and the like, the shape of the buried structure can be easily measured with high accuracy without requiring measurement skill.

[Brief description of drawings]

FIG. 1 is a flowchart showing an example of a processing procedure of a shape calculation means according to a characteristic part of the present invention.

FIG. 2 is a functional block diagram of an embodiment of the buried structure shape measuring apparatus according to the present invention.

FIG. 3 is a diagram illustrating an example of propagation velocity measurement.

FIG. 4 is a frequency response diagram when the upper end of a concrete foundation is vibrated in the vertical axis direction.

FIG. 5 is a frequency response diagram when the upper end of the concrete foundation is excited in a direction orthogonal to the vertical axis, in that direction.

FIG. 6 is a shape diagram based on a calculation result.

FIG. 7 is a diagram illustrating the types of longitudinal wave vibration modes of an elastic body for explaining the principle of the present invention.

FIG. 8 is a diagram illustrating a longitudinal wave vibration mode of an elastic body for explaining the principle of the present invention.

FIG. 9 is a view showing an elastic body model of a truncated cone for deriving a theoretical formula of a resonance condition of the present invention.

FIG. 10 is a diagram showing a model for deriving a theoretical formula of a resonance condition of the present invention regarding a concrete foundation having a base portion.

11 is an equivalent circuit diagram showing the model of FIG. 10 by introducing the concept of impedance of an electric circuit.

FIG. 12 is a diagram showing an example of the shape of a concrete foundation having a base portion.

FIG. 13 is a diagram for explaining a resonance conditional expression using one of the lateral vibration modes of the base portion.

FIG. 14 is a diagram for explaining a resonance conditional expression using another one of the lateral vibration modes of the base portion.

FIG. 15 is an impedance configuration diagram of the model of FIG.

FIG. 16 is a diagram illustrating types of lateral vibration modes of a base portion of a regular prism.

FIG. 17 is a diagram illustrating types of lateral vibration modes of a base portion of a rectangular prism.

[Explanation of symbols]

 10 Concrete Foundation 11 Pillar Part 12 Base Part 21 Hammer 22 Excitation Detection Signal 23 Preamplifier 24 FFT Analyzer 25 Acceleration Sensor 26 Vibration Detection Signal 27 Charge Amplifier 28 Floppy Disk 29 Shape Calculator 31 Exciter 32 Sound Wave Detector 33 Propagation velocity measuring device

Front Page Continuation (73) Patent Holder 592196754 Yoshio Akama 10-9-3 Minami Yagiyama, Taichiro-ku, Sendai City, Miyagi Prefecture (73) Patent Holder 000222015 Yu 1-1, Inc. 4-1-1, Enooka, Miyagino-ku, Sendai City ( 72) Inventor Yoshio Morii 2-28-27, Kuromatsu, Izumi-ku, Sendai-shi, Miyagi Prefecture (72) Yoshiyasu Matsumura 2-29, Yagiyamahonmachi, Taishiro-ku, Sendai City, Miyagi Prefecture (72) Inventor, Ishikawa Ai Miyagi Prefecture 6-23, Kamo, 1-23, Izumi-ku, Sendai-shi (72) Inventor Noriyuki Chiba 38-22 Yamada Jiyugaoka, Taihaku-ku, Sendai-shi, Miyagi Prefecture (72) Yoshio Akama 3--9, Yagiyamaminami, Taihaku-ku, Sendai-shi, Miyagi 10 (72) Inventor Hiroyuki Kuriki 6-21-3 Okino, Wakabayashi-ku, Sendai-shi, Miyagi (56) References JP-A-55-96408 (JP, A) JP-A-59-97002 (JP, A)

Claims (14)

(57) [Claims] 1. An embedded structure to be measured is vibrated, a resonance frequency of the embedded structure is measured, and based on the measured resonance frequency and a resonance conditional expression of the embedded structure which is assumed in advance, A method for measuring the shape of an embedded structure by calculating the shape of the embedded structure. 2. The embedded structure to be measured is excited in the vertical axis direction, the propagation velocity of a longitudinal wave propagating through the embedded structure and the vibration in the exciting direction are measured, and resonance vibration is obtained from the measured vibration. A method for measuring the shape of an embedded structure, in which the number of the embedded structure is extracted, and the shape of the embedded structure is obtained based on the extracted resonance frequency and a previously assumed resonance conditional expression of the embedded structure. 3. The buried structure according to any one of claims 1 and 2, wherein the embedded structure has a column portion having a circular or rectangular cross section and a base portion having a circular or rectangular cross section having a cross-sectional area different from that of the column body portion. A method for measuring the shape of an embedded structure, characterized in that the resonance condition expression is set assuming that there is. 4. The method according to claim 3, wherein the number of resonance frequencies to be extracted is the same as the number of unknown dimensions, and the same number of resonance conditional expressions obtained by substituting the same are solved to obtain the unknown dimensions. A method for measuring the shape of an embedded structure, characterized by: 5. The method for measuring the shape of an embedded structure according to claim 1, wherein the embedded structure is a concrete foundation or a concrete pile. 6. It is assumed that the embedded structure has a column portion having a circular or rectangular cross section and a base portion having a circular or rectangular cross section having a cross-sectional area different from that of the column portion, and the upper end of the embedded structure has a vertical axis. Set the longitudinal wave resonance condition expression when excited in the direction,
The propagation velocity of the longitudinal wave propagating through the buried structure to be measured is measured, and the upper end of the buried structure is excited in the vertical axis direction to measure the vibration of the longitudinal wave, and it is unknown from the measured frequency spectrum. The number of dimensions of resonance frequencies is extracted, and the simultaneous equations of the number of unknown dimensions obtained by substituting the extracted resonance frequencies, the known dimensions of the embedded structure, and the propagation velocity into the resonance condition equation are solved. And a method for measuring the shape of an embedded structure for determining the shape of the embedded structure. 7. The method according to claim 6, wherein the pillar portion of the buried structure is assumed to be a truncated cone or a truncated pyramid, and the pillar portion is approximated as a part of a sphere to set the resonance conditional expression. , The cross-sectional area of the upper end of the pillar is measured and the radius of the sphere is approximated by the height of the pillar according to the geometrical relationship, and the height of the pillar and the cross-sectional area of the lower end and the height of the base are A method for measuring the shape of an embedded structure, which comprises determining four cross-sectional areas as unknown dimensions. 8. The method according to claim 6, wherein the pillar of the buried structure is assumed to be a truncated cone or a truncated pyramid, and the pillar is approximated as a part of a sphere to set the resonance conditional expression. , Measuring the cross-sectional area of the upper end of the pillar portion and the inclination angle of the side surface of the pillar portion and approximating the radius of the sphere by the height of the pillar portion according to the geometrical relationship, and the cross-sectional area of the lower end of the pillar portion A buried structure characterized by geometrically approximating the upper end cross-sectional area, the inclination angle, and the column body height, and determining three of the column body height, the base portion height, and the cross-sectional area as unknown dimensions. Shape measurement method. 9. The resonance condition expression according to claim 7, wherein the resonance condition expression is a first resonance condition expression (Expression 13) based on a first mode in which the buried structure expands and contracts in a vertical direction, and the buried structure object. The second base part expands and contracts in the direction perpendicular to the vertical axis.
And a resonance condition expression (Expression 17) based on the mode of (1) is set, and the resonance frequency of the first mode, which is one less than the number of unknown dimensions, is extracted from the resonance frequency spectrum,
A method for measuring the shape of an embedded structure, which comprises extracting resonance frequencies fB of the second mode and substituting these resonance frequencies into respective resonance conditional expressions to obtain the unknown dimension. 10. The resonance condition expression according to claim 7, wherein the resonance condition expression is a resonance condition expression (Expression 13) based on a first mode in which the embedded structure expands and contracts in a vertical direction. The resonance frequency of the first mode, which is one less than the number of unknown dimensions, is extracted, and the base part of the embedded structure expands and contracts in the direction perpendicular to the vertical axis from the resonance frequency spectrum. Resonance frequency fB
From the resonance frequency fB and the propagation velocity v, the cross-sectional area S ₂ of the base portion is approximated by the relationship of S ₂ = (v / 2fB) ² , and this S ₂ and the extracted first A method for measuring the shape of an embedded structure, characterized in that the unknown frequency is obtained by substituting the resonance frequency of a mode into each resonance condition expression (expression 13). 11. The embedded structure according to claim 10, wherein the resonance frequency fB is a resonance frequency between a second-order resonance frequency and a third-order resonance frequency of the first mode. Shape measurement method. 12. It is assumed that the embedded structure has a column body having a circular or rectangular cross section and a base portion having a circular or rectangular cross section having an area different from that of the column body, and the upper end of the embedded structure is arranged in the vertical axis direction. The first resonance condition expression (equation 13) of the longitudinal wave when excited to the vertical axis is set, and the second resonance of the longitudinal wave when the upper end of the embedded structure is excited in the direction perpendicular to the vertical axis is set. A resonance condition formula (equation 24, 24 ', 25, 25') is set to measure the propagation velocity of a longitudinal wave propagating through the buried structure to be measured, and the upper end of the buried structure is applied in the vertical axis direction. The first frequency spectrum of the longitudinal wave is measured by shaking, and the upper end is excited in the direction perpendicular to the vertical axis to measure the second frequency of the longitudinal wave.
Frequency spectrum is measured, and one or two resonance frequencies less than the number of unknown dimensions are extracted from the measured first frequency spectrum, and the extracted resonance frequencies and the known dimensions of the embedded structure are extracted. And the propagation velocity are substituted into the first resonance conditional expression, one or two resonance frequencies are extracted from the second frequency spectrum, and the extracted resonance frequency and the embedded structure are extracted. The method for measuring the shape of an embedded structure by solving a simultaneous equation of the number of unknown dimensions obtained by substituting the known dimension and the propagation velocity into the second resonance conditional expression. 13. An input means for inputting frequency spectrum data including a resonance frequency of an embedded structure to be measured, and a resonance conditional expression of the embedded structure which is assumed in advance, and is analyzed by the frequency analyzing means. A shape measuring device for an embedded structure, comprising: a shape calculation means for calculating the shape of the embedded structure based on a plurality of resonance frequencies and the resonance condition expression. 14. A vibrating means for vibrating an embedded structure to be measured, a vibration detecting means for detecting vibration of the embedded structure, and an output signal of the vibration detecting means for inputting the embedded structure. A frequency analysis means for analyzing a frequency spectrum including a resonance frequency, and a resonance conditional expression of a presumed buried structure, and a plurality of resonance frequencies analyzed by the frequency analysis means and the resonance conditional expression. A shape measuring device for a buried structure, comprising: a shape calculation means for calculating the shape of the buried structure based on the above.