JP2009030994A - Shape measurement method for buried concrete foundation, and device thereof - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reduce a noise by clarifying the distinction between the vibration mode used for measuring the shape and the size of a buried concrete foundation and other vibration modes generated in the buried concrete foundation, and to improve the measurement accuracy. <P>SOLUTION: An acceleration of a torsional vibration is detected by causing excitation to take place so that the torsional vibration is generated around the axis of the concrete foundation 2, and a plurality of resonance frequencies f of the acceleration detection value are extracted, and the size of the concrete foundation 2 is determined, based on the plurality of extracted resonance frequencies f, and a resonance condition formula that represents the relation between the resonance frequency f of the torsional vibration and the size of each part of the concrete foundation 2. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a method and an apparatus for measuring the shape and size of an embedded concrete foundation by non-excavation, and more particularly to a method for analyzing the shape and size of an embedded concrete foundation by torsional vibration.

  As a conventional method for measuring the shape and size of an embedded structure by non-excavation, there is a method of using resonance vibration of the embedded structure as described in Patent Document 1. In the method of Patent Document 1, a plurality of resonance frequencies are extracted by exciting a buried structure to be measured, and the relationship between the plurality of resonance frequencies and the dimensions of each part of the buried structure is represented. This is a method for obtaining the shape dimension of the embedded structure by calculation based on the resonance condition formula.

  For example, Patent Document 1 measures the shape and dimension of an inverted T-shaped concrete foundation, which is a steel tower foundation formed by connecting a truncated pyramid or truncated cone body portion and a floor portion having a rectangular or circular cross section. In order to do so, a resonance condition formula expressing the relationship between the resonance frequency and the dimensions of each part of the concrete foundation is set. Then, the width a of the top of the column body, the inclination angle θ of the side surface of the column body, the propagation velocity V of the longitudinal wave, etc. are measured, and the resonance vibration obtained by exciting the top of the column body in the vertical axis direction. Extract three numbers. A simultaneous equation is established by applying it to the resonance condition equation in which the three extracted resonance frequencies are set, and the height h of the column body portion embedded in the ground by solving the simultaneous equation, The width b, the width B of the floor board portion, the thickness t of the floor board portion, and the like are obtained.

Japanese Patent No. 2555517

  By the way, patent document 1 uses the resonance vibration of the longitudinal wave which is the expansion-contraction vibration which arises by vibrating the top part of an inverted T-shaped concrete foundation to a vertical-axis direction. However, the expansion and contraction vibration of the buried concrete foundation is greatly damped, and the resonance peak of the vibration spectrum may be buried in noise. Moreover, it is difficult to distinguish between bending vibration and other vibration modes, and it may be difficult to specify the resonance frequency of expansion and contraction from the vibration spectrum. As a result, the resonance frequency may be erroneously selected from the vibration spectrum, and the error of the analysis value may increase.

  Further, in Patent Document 1, since the propagation speed of the lateral vibration of the ground portion of the buried concrete foundation is measured by an ultrasonic propagation speed measuring device, the propagation speed of the stretching vibration used for the analysis does not exactly match. . In general, the propagation speed varies depending on the wave form such as longitudinal wave and transverse wave, and the resonance modes of various objects. Therefore, in the method of Patent Document 1 in which the resonance frequency and the propagation speed are separately measured, the propagation speed may be greatly different from the actual numerical value. Therefore, it is desired to improve the accuracy of measurement of the resonance frequency and the propagation speed of the vibration.

  The problem to be solved by the present invention is to clarify the distinction between the vibration mode used for measuring the geometric dimensions of the buried concrete foundation and other vibration modes generated in the buried concrete foundation, to reduce noise, and to improve the measurement accuracy. There is.

  In order to solve the above problems, the present invention relates to a method for measuring the shape of a buried concrete foundation formed by connecting a columnar part of a truncated pyramid or a truncated cone and a floor board part having a rectangular or circular cross section. The acceleration of the torsional vibration is detected by exciting the torsional vibration around the foundation axis, and a plurality of resonance frequencies of the detected acceleration value are extracted, and the extracted resonance frequencies and the torsional vibration are detected. It is characterized in that the dimensions of the buried concrete foundation are obtained on the basis of a resonance condition expression expressing the relationship between the resonance frequency and the dimensions of each part of the buried concrete foundation.

  According to the present invention, since the torsional vibration that occurs most strongly in the buried concrete foundation is used as the vibration mode used for measurement, the resonance peak of the vibration spectrum appears sharply and clearly. For this reason, it becomes easy to distinguish from other vibration modes, and the resonance peak is not buried in noise. As a result, the resonance frequency can be accurately extracted, and the measurement accuracy of the dimensions of the buried concrete foundation obtained based on the resonance frequency and the resonance condition formula is improved.

  The propagation speed of the torsional vibration is the propagation speed of the transverse wave, and the propagation speed of the transverse wave does not vary depending on the vibration mode. Therefore, if the ground portion and the buried portion of the concrete foundation are uniform in terms of the vibration medium, the propagation speed of the transverse wave measured by the ultrasonic propagation velocity measuring device on the side surface of the concrete foundation can be used for the analysis.

  In this case, some or all of the values of the top width or diameter, height, bottom width or diameter, and torsional vibration propagation speed of the column portion of the buried concrete foundation can be applied to the resonance conditional expression. . In addition, the value of the width | variety or diameter of a bottom part can be made into the estimated value based on the value of the width | variety or diameter of the top part of a pillar part, and the inclination-angle and height of a side surface. In this way, if the number of actually measured dimensions of each part of the buried concrete foundation is increased, the number of unknowns in the resonance condition formula is reduced accordingly, so that the error is reduced and the accuracy is increased.

  Moreover, in order to solve the above-mentioned problems, the buried concrete foundation is based on the resonance condition formula of torsional vibration that expresses the relationship between the resonance frequency of torsional vibration around the axis of the buried concrete foundation and the dimensions of each part of the buried concrete foundation. Setting for a specific combination of unknown dimensions in the buried part Finding the ratio of the propagation constant in the combination of unknown dimensions in other buried parts based on the following propagation constant, and describing the correspondence between the combination of dimensions and the ratio of the propagation constant The table is stored in advance in the database, and the acceleration of the torsional vibration is detected by exciting the torsional vibration around the axis of the buried concrete foundation, and a plurality of resonance frequencies of the acceleration detection value are extracted, Of the extracted resonance frequencies, the ratio of the other resonance frequencies based on the set resonance frequency is obtained, and the error between the ratio and the ratio of the propagation constant is The combination of dimensions to be smaller by searching from the data base, it is also possible to employ a method which is characterized in that to determine the dimensions of the buried concrete foundation.

  According to this, it is possible to measure the shape of the buried concrete foundation only by measuring the resonance frequency by creating a database storing a table in which the correspondence relationship between the combination of unknown dimensions and the ratio of the propagation constant is previously described. . In other words, in general, the shape and dimensions of the buried concrete foundation are determined, so that it can be classified for each foundation, and if a database for each classification is created in advance, the shape can be measured only by measuring the resonant frequency. become. Therefore, the trouble of actually measuring the dimensions of the buried concrete foundation can be saved. Further, since the value of the propagation velocity is not used for the measurement, the accuracy is improved, it is not necessary to measure the propagation velocity, and further labor is saved.

  In this case, two actual measured values of the width or diameter and height of the top of the column part of the buried concrete foundation, or three actual measured values of the width or diameter and height and the width or diameter of the bottom of the column part. Can also be applied to the resonance condition equation. The value of the width or diameter of the bottom portion is an estimated value based on the width or diameter of the top portion of the column body portion, the inclination angle of the side surface, and the height value. In this way, if the actual number of dimensions of each part of the buried concrete foundation is increased, the number of unknown resonance condition equations is reduced accordingly, so that creation and retrieval of the database is facilitated.

  Further, in this case, when the rotation axis of the column body part is inclined from the central axis about the middle of the column body part, the column body part has two column bodies of the first column body part and the second column body part. It is considered that they are connected, and the top width or diameter of the first column body portion, the bottom width or diameter of the second column body portion, and the height of the entire column body portion are measured and applied to the resonance condition equation. Further, it is possible to adopt a shape measuring method characterized in that a table is created by obtaining a ratio between a combination of dimensions of each part of the buried concrete foundation and a propagation constant based on the resonance condition formula.

  According to this, even when the rotation axis is inclined from the vertical axis about the middle of the column body portion, the column body portion is configured by connecting the two first column body portions and the second second column body portion. This makes it possible to create a database and determine the dimensions of each part of the buried concrete foundation.

  According to the present invention, it is possible to clarify the distinction between the vibration mode used for measuring the shape and dimension of the buried concrete foundation and other vibration modes generated in the buried concrete foundation, to reduce noise, and to improve the measurement accuracy.

  Embodiments of the present invention will be described below with reference to mathematical expressions and drawings.

  In this embodiment, an inverted T-shaped concrete foundation 2 as shown in FIG. The inverted T-shaped concrete foundation 2 is a foundation for a steel tower 4 as shown in FIG. Here, it is considered that the inverted T-shaped concrete foundation 2 is composed of the column body portion 6 and the floor base portion 8. The derivation of the torsional resonance conditional expression used in all the embodiments will be described with reference to FIG. In order to simplify the description in the derivation of the torsional resonance conditional expression, the cross sections of the columnar body portion 6 and the floor base portion 8 are assumed to be squares or circles.

  First, the torsional resonance conditional expression derived here will be briefly described. The width or diameter of the top portion of the column body portion 6 of the concrete foundation 2 in FIG. 1 is a, the width or diameter of the bottom portion of the column body portion 6 is b, the height of the column body portion 6 is h, the width of the floor portion 8 or The diameter is B, the thickness of the floor base 8 is t, and the torsional vibration propagation constant is β. Since the derived torsional resonance conditional expression is a function of a, b, t, B, h, and β, it can be expressed as F (a, b, t, B, h, β) = 0. Further, β can be expressed by the torsional resonance frequency f and the torsional vibration propagation velocity Vs by the following equation (6), so the torsional resonance conditional expression is also a function of f and Vs, and F (a, b, t, B, h, f, Vs) = 0. Note that the propagation velocity Vs is ideally a constant, but in actuality, there is some variation from base to base, so it is a variable here. From now on, this torsional resonance conditional expression will be derived.

  The distributed circuit theory of electrical circuits is used for vibration analysis of elastic bodies. Therefore, a matrix corresponding to the four terminals of each electric circuit of the columnar section 6 and the floor board section 8 is obtained and cascaded. Here, considering the torsional vibration around the axis (steel frame 10), the correspondence with the distributed circuit theory of the electric circuit is that the torque T around the axis corresponds to the voltage, and the rotational angular velocity ω = dφ / dt corresponds to the current.

  It is assumed that the four-terminal matrix of the column part 6 is represented by the formula (1).

式（１）の、Ａｈ、Ｂｈ、Ｃｈ、Ｄｈは、それぞれ次式（２）、（３）、（４）、（５）で表される。

Ah, Bh, Ch, and Dh in the formula (1) are represented by the following formulas (2), (3), (4), and (5), respectively.

ここで、波長をλ、振動数をｆ、剛性率をＧ、密度をρとする。また、伝播定数βは次式（６）で表される。

Here, the wavelength is λ, the frequency is f, the rigidity is G, and the density is ρ. The propagation constant β is expressed by the following equation (6).

柱体部６の特性インピーダンスは錐体台であるため一定ではなく、式（２）、式（３）のαａｂが平均化された特性インピーダンスに相当する。αは、柱体部６の断面が円の場合は次式（７）、断面が正方形の場合は次式（８）で表される。

The characteristic impedance of the columnar portion 6 is not constant because it is a truncated cone, and corresponds to the characteristic impedance obtained by averaging αab in the equations (2) and (3). α is expressed by the following formula (7) when the cross section of the columnar body 6 is a circle, and is expressed by the following formula (8) when the cross section is a square.

捩れ振動の波長が骨材の大きさ、鉄骨・鉄筋の太さよりかなり大きい１次乃至５次ぐらい迄の低次の共振モードでは、骨材や鉄骨・鉄筋はコンクリート内で一様分布と見なしてよく、剛性率Ｇや密度ρ等の共振振動数ｆに関わる物理量を、均一な弾性体のものとして扱うことができる。ただし、それらの値はコンクリートのみのときより増加する。骨材や鉄骨・鉄筋は軸に垂直方向の断面積がコンクリートの断面積に比べてかなり小さいので、伝播速度Ｖｓに関しては、コンクリートだけに比べて数パーセント増加したものとして扱えばよい。

In the first-order to fifth-order resonance modes where the torsional vibration wavelength is much larger than the size of the aggregate and the thickness of the steel frame / rebar, the aggregate, steel frame / rebar are considered to be uniformly distributed in the concrete. The physical quantity related to the resonance frequency f such as the rigidity G and density ρ can be handled as a uniform elastic body. However, those values increase compared to concrete alone. Aggregates, steel frames, and reinforcing bars have a cross-sectional area perpendicular to the axis that is considerably smaller than the cross-sectional area of concrete. Therefore, the propagation velocity Vs may be treated as an increase of several percent compared to concrete.

  The 4-terminal matrix of the floor unit 8 is expressed by the following equation (9).

ここで、ＺＢは特性インピーダンスであり、床盤部８の断面が円の場合は、Ｂを直径として次式（１０）で表され、床盤部８の断面が正方形の場合は、Ｂを幅として次式（１１）で表される。

Here, ZB is a characteristic impedance. When the cross section of the floor base 8 is a circle, it is expressed by the following formula (10) with B as the diameter. When the cross section of the floor base 8 is a square, B is the width. Is expressed by the following equation (11).

柱体部６と床盤部８とを縦続接続したコンクリート基礎２の４端子マトリックスは積を計算をして、次式（１２）となる。

The 4-terminal matrix of the concrete foundation 2 in which the column body portion 6 and the floor base portion 8 are connected in cascade, calculates the product and becomes the following equation (12).

ここで、柱体部６の上面と床盤部８の底面のトルク−回転角速度の縦ベクトルをそれぞれ次式（１３）、次式（１４）で表す。

Here, the vertical vectors of the torque-rotational angular velocity of the top surface of the column body portion 6 and the bottom surface of the floor base portion 8 are represented by the following equations (13) and (14), respectively.

式（１３）と（１４）の間の関係式は次式（１５）で表される。

The relational expression between the expressions (13) and (14) is expressed by the following expression (15).

ここで、柱体部６の上面から見たインピーダンスＺ（１）は、前述したトルクＴ、捩れ角の回転角速度ωと電圧、電流との対応関係から次式（１６）で表される。

Here, the impedance Z (1) viewed from the upper surface of the columnar portion 6 is expressed by the following equation (16) from the correspondence relationship between the torque T, the rotational angular velocity ω of the torsion angle, the voltage, and the current.

図１のように、コンクリート基礎２の周囲が空気や土である場合は、Ｔ（３）≒０としてよい。したがって、Ｚ（１）＝ＢＴ１／ＤＴ１と与えられる。共振はインピーダンスが０のときに起こるので、式（１６）の分子ＢＴ１を式（１７）で表し、これを０とおいた式を式（１８）とすると、式（１８）が捩れ振動の共振条件式である。

As shown in FIG. 1, when the surroundings of the concrete foundation 2 is air or soil, T (3) ≈0 may be set. Therefore, Z (1) = BT1 / DT1 is given. Since the resonance occurs when the impedance is 0, the numerator BT1 of the equation (16) is expressed by the equation (17), and when this is set to the equation (18), the equation (18) is the resonance condition of the torsional vibration. It is a formula.

また、図３のように、床盤部８の下にさらに栗石とコンクリート（捨てコンクリート１２）がある場合には、コンクリート基礎２全体の４端子マトリックスは、柱体部６、床盤部８、捨てコンクリート１２の３段の４端子マトリックスを縦続接続する。説明を簡単にするために、捨てコンクリート１２の断面は正方形であるとする。

In addition, as shown in FIG. 3, when there is a chestnut stone and concrete (discarded concrete 12) below the floor part 8, the four-terminal matrix of the entire concrete foundation 2 is composed of the column part 6, the floor part 8, Cascade connection of three-stage 4-terminal matrix of discarded concrete 12 is made. In order to simplify the explanation, it is assumed that the section of the discarded concrete 12 is square.

  The 4-terminal matrix of the discarded concrete 12 is expressed by the following equation (19).

ここで、ＺＢｓは特性インピーダンスで、捨てコンクリート１２の断面が正方形の場合はＢｓを幅として次式（２０）で表される。

Here, ZBs is a characteristic impedance. When the cross section of the discarded concrete 12 is a square, it is expressed by the following equation (20) with Bs as the width.

柱体部６と床盤部８と捨てコンクリート１２を縦続接続したコンクリート基礎２の４端子マトリックスは、積を計算して次式（２１）となる。

The 4-terminal matrix of the concrete foundation 2 in which the column body portion 6, the floor base portion 8, and the discarded concrete 12 are connected in cascade is calculated by the following equation (21).

ここで、柱体部６の上面と捨てコンクリート１２の底面のトルク−回転角速度の縦ベクトルをそれぞれ次式（２２）、次式（２３）で表す。

Here, the longitudinal vectors of the torque-rotational angular velocity of the upper surface of the columnar section 6 and the bottom surface of the discarded concrete 12 are expressed by the following equations (22) and (23), respectively.

すると、この間の関係式は次式（２４）で表される。

Then, the relational expression between them is expressed by the following expression (24).

ここで、柱体部６の上面から見たインピーダンスＺ（１）は、前述したトルクＴ、捩れ角の回転角速度ωと電圧、電流との対応関係から次式（２５）で表される。

Here, the impedance Z (1) viewed from the upper surface of the columnar section 6 is expressed by the following equation (25) from the correspondence relationship between the torque T, the rotational angular velocity ω of the torsion angle, the voltage, and the current.

図１の場合と同様に、Ｔ（４）≒０としてよい。したがって、Ｚ（１）＝ＢＴ２／ＤＴ２と与えられる。共振はインピーダンスが０のときに起こるので、式（２５）の分子ＢＴ２を式（２６）で表し、これを０とおいた式を式（２７）とすると、式（２７）が捩れ振動の共振条件式である。

As in the case of FIG. 1, T (4) ≈0 may be set. Therefore, Z (1) = BT2 / DT2. Since the resonance occurs when the impedance is 0, the numerator BT2 of the equation (25) is expressed by the equation (26), and when this is set to the equation (27), the equation (27) is the torsional vibration resonance condition. It is a formula.

式（１８）や式（２７）から分かるように伝播定数βに振動数ｆが含まれているので、コンクリート基礎２の各部寸法や伝播速度Ｖｓが与えられると、この式から多数の０点、即ち共振振動数が求められる。逆に、共振振動数が既知の場合は、未知のコンクリート基礎２の各部寸法や伝播速度Ｖｓを求めることもできる。

As can be seen from the equations (18) and (27), the frequency f is included in the propagation constant β. Therefore, given the dimensions of each part of the concrete foundation 2 and the propagation velocity Vs, a large number of 0 points from this equation, That is, the resonance frequency is obtained. On the contrary, when the resonance frequency is known, the dimensions and propagation speed Vs of each part of the unknown concrete foundation 2 can be obtained.

  Next, the configuration of the shape measuring device for the concrete foundation 2 will be described with reference to FIG. A dotted line 14 of the column body portion 6 is a ground position, and a portion below the dotted line 14 is buried in the ground. As an excitation method for applying vibration to the concrete foundation 2, a method of hitting a specific part with a hammer or the like, and a method of applying vibration by a vibrator generating sine wave vibration and sweeping the frequency can be applied. In this embodiment, an exciter 16 that sweeps a sine wave signal is used. A force sensor 18 is provided between the concrete foundation 2 and the vibrator 16 in order to detect the vibration force of the vibrator 16. The excitation force detected by the force sensor 18 is converted into an electric signal and input to the signal processing device 20. Further, the oscillator 21 generates a sine wave signal for sweeping to the vibrator 16. This sine wave signal is amplified via the amplifier 22 and input to the vibrator 16. An acceleration sensor 24 is used as means for detecting vibration. The acceleration detected by the acceleration sensor 24 is converted into an electrical signal and input to the signal processing device 20. The excitation force signal and the acceleration signal input to the signal processing device 20 are A / D converted, respectively, and converted into a frequency spectrum by arithmetic processing. The frequency spectrum is input from the signal processing device 20 to the computer 26 and displayed on a display or the like.

  The computer 26 includes an input device, a storage device, an arithmetic processing device, an output device, and the like. The storage device stores in advance items necessary for the shape measurement calculation process, such as the above-described resonance condition formula and related calculation formula, and stores actual measurement data, frequency spectrum, and the like input from the input device. . Then, calculation processing is performed based on the actually measured data and the resonance condition formula, the shape dimension of the concrete foundation 2 is obtained, and the result is output via an output device such as a display.

  Next, the procedure for measuring the shape of the concrete foundation 2 will be described. First, the width a of the top portion of the column body portion 6 of the concrete foundation 2, the inclination angle θ of the side surface of the column body portion 6, and the height h of the column body portion 6 are measured as necessary. The width a of the top of the columnar part 6 and the inclination angle θ of the side surface of the columnar part 6 can be measured from the fact that the top of the columnar part 6 is exposed to the ground. The height h of the column body portion 6 is measured by penetrating a steel bar or the like into the ground. In addition, the value measured beforehand is used for the propagation velocity Vs of the torsional vibration propagating through the concrete foundation 2 (refer to the method described in Patent Document 1 for the method of measuring the propagation velocity).

  Next, with reference to FIGS. 5A and 5B, how to attach the vibrator 16, the force sensor 18, and the acceleration sensor 24 to the column body portion 6 will be described. FIGS. 5A and 5B are plan views of the column body portion 6. First, the vibrator 16 and the force sensor 18 are attached to a jig 28 used for causing torsional vibration. Note that the jig 28 has a triangular prism shape whose cross section is a right-angled isosceles triangle. The jig 28 and the jig 30 for the acceleration sensor 24 are attached to the column body portion 6 using an adhesive or the like. The attachment position of the jig 28 may be anywhere on the top side surface of the column body portion 6 as long as it can cause torsional vibration. In this embodiment, the jig 28 is attached to the corner of the top side surface of the column body portion 6. The attachment position of the jig 30 may be anywhere as long as the torsional vibration can be detected, but in this embodiment, the jig 30 is attached to a corner of the top side surface of the column body part 6. When the column body portion 6 is a cylinder, a triangular prism-shaped jig 32 is attached as shown in FIG. 5B as a jig used for causing torsional vibration.

  Next, the force sensor 18 is attached to the jig 28, and the vibrator 16 is attached onto the force sensor 18 by tightening with a wing nut or the like. Further, the acceleration sensor 24 is attached to the jig 30 with a wing nut or the like. In order to confirm the torsional vibration, it is necessary to measure the torsional vibration at the two locations shown in FIG. 6, so another jig 34 and an acceleration sensor 36 are attached. In order to measure the acceleration in a plurality of directions at one place, a tripolar x, y, z direction acceleration sensor may be used.

  Then, the sine wave signal amplified by the amplifier 22 is input to the vibrator 16, and the excitation force in the direction of the arrow in FIG. 7 is applied to the concrete foundation 2 while sweeping the frequency of the sine wave signal. Apply torsional vibration around the axis and measure the frequency of torsional vibration. Next, the torsional resonance frequency is identified from the frequency spectrum converted from the excitation force and the acceleration signal.

  Here, a method for identifying the torsional resonance frequency will be described. The torsional resonance frequency is identified by the sign of the signal of the frequency spectrum and the peak of the signal based on the positional relationship between the vibrator 16 and the acceleration sensor 24 attached to the column portion 6. The torsional resonance frequency is identified from a reference vibration with one vibration node to a vibration frequency with n nodes, where n is a natural number, and is approximately 1 to 5 here. The frequency with n vibration nodes is referred to as the n-th resonance frequency, the primary resonance frequency is represented as f1, and the second resonance frequency is represented as f2, as shown in FIG. The torsional frequency is determined by the direction of excitation, and the direction of vibration can be detected by the acceleration sensor 24, and the direction appears in the sign of the signal. Therefore, the sign of the signal detected by the acceleration sensor 24 is confirmed from the position where the acceleration sensor 24 is attached and the position where the vibrator 16 is attached, and the direction of torsional vibration is confirmed. Table 1 shows the directions of torsional vibration when the vibration of the concrete foundation 2 at the position shown in FIG.

測定した振動数スペクトルをコンピュータ２６のディスプレイに表示させ、捩れ振動が起きる方向と振動数スペクトルのピークより、共振振動数を読み取る。図７に示した位置でのコンクリート基礎２の振動を測定した場合の振動数スペクトルの例を図８に示す。なお、図８に示すように、一般に１次共振振動数ｆ１はノイズに埋もれてピークが明瞭でないことが多い。

The measured frequency spectrum is displayed on the display of the computer 26, and the resonance frequency is read from the direction of the torsional vibration and the peak of the frequency spectrum. An example of the frequency spectrum when the vibration of the concrete foundation 2 at the position shown in FIG. 7 is measured is shown in FIG. As shown in FIG. 8, generally, the primary resonance frequency f1 is often buried in noise and the peak is often not clear.

  An unknown dimension of the concrete foundation 2 is obtained by substituting the actually measured dimension and the resonance frequency of the concrete foundation 2 obtained as described above into the resonance condition (18) or (27). Hereinafter, the methods 1 to 3 will be described in accordance with the difference in numerical values used for the calculation. Hereinafter, it is assumed that the cross sections of the columnar section 6 and the floor board section 8 are square.

  (Method 1) The width a of the top part of the columnar part 6, the inclination angle θ of the side surface, and the value of the propagation velocity Vs are used. These values are substituted into the resonance conditional expression (18) or (27). Then, three resonance frequencies are selected from the aforementioned torsional resonance frequencies f1, f2,... Fn, and simultaneous equations are established. If f1, f2, and f3 are selected, the following simultaneous equations (28) are established.

式（２８）を解いて、柱体部６の高さｈ、床盤部８の幅Ｂと厚さｔを未知数として求めることができる。

Equation (28) can be solved to obtain the height h of the columnar section 6 and the width B and thickness t of the floor board section 8 as unknowns.

  (Method 2) Measured values of the width a at the top of the columnar portion 6, the inclination angle θ of the side surface, and the height h are used. Note that the width b of the bottom portion of the column body portion 6 needs to be approximated by geometrically calculating with a, θ, and h to obtain a value. From these values and the resonance frequency fn of the torsion at three points, the width B and the thickness t of the floor board 8 are obtained as unknowns in the same manner as in the method 1. Further, unlike the method 1, the value of the propagation velocity Vs is not necessary.

  (Method 3) The propagation velocity Vs is added to the value used for the calculation in Method 2. As a result, the number of unknowns is reduced by 1, so that the torsional resonance frequency fn required for the calculation is reduced to two points, and the simultaneous equations become two. By solving these, the width B and the thickness t of the floor board 8 are obtained as unknowns.

  As described above, according to the present embodiment, the torsional vibration that occurs most strongly in the buried concrete foundation is used as the vibration mode used for measurement, so that the resonance peak of the vibration spectrum appears sharply and clearly. For this reason, it becomes easy to distinguish from other vibration modes, and the resonance peak is not buried in noise. Therefore, the resonance frequency fn can be accurately identified, and the measurement accuracy of the dimension of the embedded portion of the concrete foundation 2 obtained based on the resonance frequency fn and the resonance conditional expression (18) or (27) is improved. .

  Further, as described in the methods 1 to 3, if the actual number of dimensions of each part of the concrete foundation 2 is increased, the number of unknowns in the resonance condition equation is reduced accordingly, so that the error is reduced and the accuracy can be improved.

  In Example 1, the dimensions of each part of the concrete foundation 2 were obtained from the resonance frequency and the resonance condition formula using the measured values of the measurable part of the concrete foundation 2. The propagation constant (or resonance frequency) can be obtained from the resonance condition equation. Therefore, in this embodiment, using this, a database showing the relationship between the dimensions of each part of the concrete foundation 2 and the propagation constant (or resonance frequency) is created in advance, and the database is created based on the actually measured resonance frequency. The dimensions of each part of the concrete foundation 2 are obtained by collation. This method will be described separately in the present embodiment and the third and fourth embodiments depending on the database to be created. As described above, in the measurement, the primary resonance frequency is often buried in noise and the peak is not clear. Therefore, in this example and Examples 3 and 4, the propagation constant corresponding to the primary resonance frequency and the primary resonance frequency are not used.

  First, the width “a” and the height “h” of the top of the columnar body 6 are measured. Then, the values of a and h are substituted into formula (18) or formula (27). Next, a plurality of propagation constants β are obtained by changing numerical values of the width b of the bottom portion 6 of the column body portion 6, the width B of the floor base portion 8, and the thickness t within an appropriate range by an appropriate step size. At this time, with respect to one set of values (b, B, t), the value of β is obtained innumerably like β = βi (i = 2, 3,...), Similarly to the number of resonance frequencies. Βi indicates a propagation constant corresponding to the i-th resonance frequency. The numerical value is β2 <β3 <β4 <.

  A propagation constant ratio ki such as ki = βi / β2 (i = 3, 4,...) Is obtained based on one of βi thus obtained, for example, β2. In other words, ki is a ratio of propagation constants of theoretical values obtained by calculation. Then, a three-dimensional matrix database for ki (b, B, t) is created. For example, the database is as shown in Table 2. Note that k3 (1, 1, 1) in Table 2 indicates k3 obtained from β2 and β3 when (b, B, t) = (b1, B1, t1). Incidentally, for example, β2 when (b, B, t) = (b1, B1, t1) and β2 when (b, B, t) = (b1, B2, t2) are different values. Needless to say. A database as shown in Table 2 exists for each case of b = b2, b3,..., And further exists for each case of i = 4, 5,.

次に、上記のデータベースを寸法推定に用いる手順について説明する。まず、捩れの共振振動数ｆｍｉ（ｉ＝２、３…）を測定する。測定する共振振動数ｆｍｉの数は多ければ精度はよいが、２点でもよい。次に、伝播定数の比ｋｉを求める際に第２次共振振動数に対応するβ２を基準としたので、ここでは共振振動数ｆｍ２を基準にしてｋｍｉ＝ｆｍｉ／ｆｍ２（ｉ＝３、４…）のような共振振動数の比ｋｍｉを求める。ｋｍｉはすなわち、実測値の共振振動数の比である。

Next, a procedure for using the above database for size estimation will be described. First, the torsional resonance frequency fmi (i = 2, 3,...) Is measured. If the number of resonance frequencies fmi to be measured is large, the accuracy is good, but it may be two points. Next, since β2 corresponding to the secondary resonance frequency is used as a reference when obtaining the propagation constant ratio ki, here, kmi = fmi / fm2 (i = 3, 4,..., With reference to the resonance frequency fm2. The resonance frequency ratio kmi as shown in FIG. In other words, kmi is the ratio of the actually measured resonance frequency.

  Here, as can be seen from Equation (6), the ratio of propagation constants is equal to the ratio of resonance frequencies. Therefore, ki is equal to the ratio of the resonance frequency of the theoretical value, and comparing ki and kmi is a comparison of the ratio of the resonance frequency of the theoretical value and the ratio of the resonance frequency of the actual measurement value. Thus, by obtaining an error and selecting a combination (b, B, t) having a smaller error, (b, B, t) can be estimated with high accuracy. The error is calculated by the following equation (29).

ここで、ｐは誤差である。ｐが最小になるｋｉ（ｉ＝３、４…）を求め、この時の（ｂ、Ｂ、ｔ）を柱体部６の底部の幅ｂ、床盤部８の幅Ｂ、床盤部８の厚さｔとして求める。

Here, p is an error. ki (i = 3, 4...) that minimizes p is obtained, and (b, B, t) at this time is determined as the width b of the bottom part of the columnar part 6, the width B of the floor part 8, and the floor part 8. It is calculated | required as thickness t.

  Here, an analysis method using an analysis program using the above theory will be described. There are two analysis methods for shape analysis of a steel tower foundation, depending on the method of expressing the analysis results: a method in which the basic type of the standard steel tower foundation is used as the analysis result, and a method in which the dimensions of each part of the steel tower foundation are used as the analysis results. The method of using the foundation type as the analysis result is applied when the steel tower foundation to be analyzed is clearly known as the standard steel tower foundation, and the method of using the dimensions of each part as the analysis result is the steel tower foundation to be analyzed. Applicable when there is no information.

First, a method of using the basic type of the standard steel tower foundation as an analysis result will be described with reference to the flowchart of FIG.
(Step 101) The actually measured width a of the column body portion 6 of the concrete foundation 2 and the height h of the column body portion 6 and a plurality of torsional resonance frequencies, here, f2, f3, and f4 are input to the analysis program.
(Step 102) Using the inputted values of a and h as search conditions, a tower foundation type that meets conditions such as the shape and dimensions of the concrete foundation 2 is selected from the standard tower foundation table stored in the analysis program. In addition, in the standard steel tower foundation table, the shape and dimensions of a general standard steel tower foundation are described.
(Step 103) The minimum value and the maximum value of the width b of the column body portion 6, the width B of the floor base portion 8, and the thickness t are determined from the dimensions of the selected steel tower foundation mold.
(Step 104) A three-dimensional matrix (b, B, t) is created within the range between the minimum value and the maximum value in Step 103. Here, the step size of each dimension is Δb = 0.01 (m), ΔB = 0.1 (m), and Δt = 0.05 (m).
(Step 105) Substituting the actually measured values a and h and the values (b, B, t) of the three-dimensional matrix into the equation (18) or the equation (27), and the ratio ki of the theoretical propagation constant (resonance frequency). calculate.
(Step 106) The ratio kmi of the actually measured resonance frequency is calculated.
(Step 107) The ratio k i of the propagation constant (resonance frequency) of the theoretical value and the ratio k mi of the resonance frequency of the actual measurement value are compared, and an error is calculated by the equation (29). The combination with the smallest error (b, B, t) is selected.
(Step 108) The error is calculated by comparing the obtained combination of (a, h, b, B, t) with the combination of the dimensions of each part of the standard tower basic table.
(Step 109) The standard tower foundation type with the smallest error is output as the analysis result, and the process is terminated.

  FIG. 10 shows an example of the three-dimensional matrix data obtained by the above method, and Table 3 shows an example of the analysis result. Note that the numerical values of the analysis results of a and h in Table 3 are actually measured values. As can be seen from Table 3, the size of the buried portion of the concrete foundation 2 could be estimated with high accuracy.

次に、図１１のフローチャートに沿って鉄塔基礎の各部寸法を解析結果とする方法について説明する。
（ステップ２０１）解析プログラムに、実測したコンクリート基礎２の柱体部６の幅ａ、柱体部６の高さｈ、柱体部６の側面の傾斜角度θと複数の捩れ共振振動数ｆ２、ｆ３、ｆ４を入力する。
（ステップ２０２）ａ、ｈ、θより柱体部６の底部の幅ｂを計算し推定する。
（ステップ２０３）推定したｂを基に、計算用マトリックスの範囲を計算する。ここでは、ｂの範囲は０．８ｂ（ｍ）〜１．２b（ｍ）、Ｂの範囲は０．８８ｂ（ｍ）〜２．４ｂ（ｍ）、ｔの範囲は０．３（ｍ）〜０．８（ｍ）である。
（ステップ２０４）ステップ２０３の最小値と最大値の範囲内において、（ｂ、Ｂ、ｔ）の３次元マトリックスを作成する。なお、各寸法の刻み幅は、Δb＝０．０１（ｍ）、ΔＢ＝０．１（ｍ）、Δｔ＝０．０５（ｍ）である。
（ステップ２０５）実測したａ、ｈと３次元マトリックスの値（ｂ、Ｂ、ｔ）を式（１８）又は式（２７）に代入し、理論値の伝播定数（共振振動数）の比ｋｉを算出する。
（ステップ２０６）実測値の共振振動数の比ｋｍｉを算出する。
（ステップ２０７）理論値の伝播定数（共振振動数）の比ｋｉと実測値の共振振動数の比ｋｍｉを比較し、式（２９）により誤差を算出する。誤差が最も小さくなる（ｂ、Ｂ、ｔ）の組合せを選択する。
（ステップ２０８）上記ステップで求めた（ａ、ｈ、ｂ、Ｂ、ｔ）の組合せを解析結果として出力して処理を終了する。

Next, a method of using the dimensions of each part of the steel tower foundation as an analysis result will be described with reference to the flowchart of FIG.
(Step 201) In the analysis program, the actually measured width a of the column body portion 6 of the concrete foundation 2, the height h of the column body portion 6, the inclination angle θ of the side surface of the column body portion 6, and a plurality of torsional resonance frequencies f2, Input f3 and f4.
(Step 202) The width b of the bottom part of the columnar part 6 is calculated and estimated from a, h, and θ.
(Step 203) The range of the calculation matrix is calculated based on the estimated b. Here, the range of b is 0.8b (m) to 1.2b (m), the range of B is 0.88b (m) to 2.4b (m), and the range of t is 0.3 (m) to 0.8 (m).
(Step 204) Within the range of the minimum value and the maximum value in Step 203, a three-dimensional matrix of (b, B, t) is created. The step size of each dimension is Δb = 0.01 (m), ΔB = 0.1 (m), and Δt = 0.05 (m).
(Step 205) The actually measured values a and h and the values (b, B, t) of the three-dimensional matrix are substituted into Equation (18) or Equation (27), and the ratio ki of the theoretical propagation constant (resonance frequency) is obtained. calculate.
(Step 206) The resonance frequency ratio kmi of the actually measured values is calculated.
(Step 207) The ratio k i of the propagation constant (resonance frequency) of the theoretical value and the ratio k mi of the resonance frequency of the actual measurement value are compared, and the error is calculated by the equation (29). The combination with the smallest error (b, B, t) is selected.
(Step 208) The combination of (a, h, b, B, t) obtained in the above step is output as an analysis result, and the process is terminated.

  As described above, by creating a database of the ratio ki between the dimensions of the concrete foundation 2 and the propagation constant (resonance frequency) of the theoretical value in advance as in the present embodiment, the shape dimension can be determined only by the measured resonance frequency ratio. It becomes possible to measure. Further, since the value of the propagation velocity is not used for the measurement, the accuracy is improved, it is not necessary to measure the propagation velocity, and further labor is saved. It should be noted that if the step size of each part at the time of creating the database is reduced, the dimension can be measured with higher accuracy.

  In the second embodiment, the width a and the height h of the top of the column body 6 are substituted into the formula (18) or the formula (27), but in addition to these, the width b of the bottom of the column body 6 is substituted. . This b is obtained by geometrically calculating the side inclination angle θ and a and h. The subsequent steps are the same as in the second embodiment. Note that the database created in this embodiment is a two-dimensional matrix of ki and (B, t), and the required dimensions are the width B of the floor base 8 and the thickness t of the floor base 8.

  According to the present embodiment, the database to be created is a two-dimensional matrix (B, t), and the creation and retrieval of the database is facilitated.

  In addition, although a dimension can also be calculated | required in a present Example, since the width | variety b of the bottom part of the columnar part 6 calculated | required from the inclination | tilt angle (theta) of the side surface of the columnar part 6 is not flatness of the side surface of the columnar part 6. Since the error may be large and the analysis result of the width B and the thickness t of the floor board portion 8 may be deteriorated, the measurement of Example 2 is more desirable.

  In the second and third embodiments, the propagation velocity Vs is added as a value to be substituted into the equation (18) or the equation (27). In Examples 2 and 3, the ratio of the propagation constants k i of the theoretical values and the ratio k m of the propagation constants of the actual measurement values were compared. However, in this example, there is a propagation velocity Vs, so The value of the resonance frequency fi can be derived. Therefore, the theoretical resonance frequency fi and the actually measured resonance frequency fmi can be directly compared without using a ratio. For this reason, the database created in this embodiment is a three-dimensional or two-dimensional matrix database of the resonance frequency fi and the dimensions of each part. Further, the number of actually measured resonance frequencies fmi is good if it is large, but may be two. Other methods are the same as those in the second and third embodiments. The error is calculated by the following equation (30).

ｐが最小になるｆｉ（ｉ＝３、４…）を求め、この時の（ｂ、Ｂ、ｔ）又は（Ｂ、ｔ）の組み合わせを求める。

Fi (i = 3, 4,...) that minimizes p is obtained, and a combination of (b, B, t) or (B, t) at this time is obtained.

  According to the present embodiment, since the comparison can be made with the resonance frequency without using the ratio of the propagation constants, the database to be created may have the resonance frequency fi and the size of each part. Therefore, creation of a database becomes easy.

  In this embodiment, a case is considered in which the rotation axis (twisting axis) 38 is tilted around a point P on the vertical axis 40 of the columnar section 6 as shown in FIG. In this case, as shown in FIG. 12b, the columnar section 6 has two first columnar sections 44 and a second second columnar section 46, with a plane 42 parallel to the floor base section 8 passing through the point P as a boundary. Think of it as being connected. A basic four-terminal matrix formed by connecting the first column body portion 44, the second column body portion 46, and the floor base portion 8 is expressed by the following equation (31).

また、図１３のように床盤部８の下に捨てコンクリート１２が接続されてなる基礎の４端子マトリックスは次式（３２）になる。

Further, as shown in FIG. 13, the basic four-terminal matrix in which the discarded concrete 12 is connected under the floor board portion 8 is expressed by the following equation (32).

式（３１）、式（３２）から実施例１で述べたように共振条件式を求める。なお、式（３１）のＡｈ１、Ｂｈ１、Ｃｈ１、Ｄｈ１は、式（２）のＡｈ、式（３）のＢｈ、式（４）のＣｈ、式（５）のＤｈ中のｂがｃに、ｈがｈ１となった式であり、式（３２）のＡｈ２、Ｂｈ２、Ｃｈ２、Ｄｈ２は、式（２）のＡｈ、式（３）のＢｈ、式（４）のＣｈ、式（５）のＤｈ中のａがｃに、ｈがｈ２となった式である。なお、ｈ１は第１柱体部４４の高さ、ｈ２は第２柱体部４６の高さ、ｃは第１柱体部４４の底部の幅（第２柱体部４６の頂部の幅）である。以下この場合の形状測定方法を、方法４、５に分けて説明する。

As described in the first embodiment, the resonance condition equation is obtained from the equations (31) and (32). In Formula (31), Ah1, Bh1, Ch1, and Dh1 are Ah in Formula (2), Bh in Formula (3), Ch in Formula (4), and b in Dh in Formula (5) are c, h is an expression of h1, and Ah2, Bh2, Ch2, and Dh2 in Expression (32) are Ah in Expression (2), Bh in Expression (3), Ch in Expression (4), and Expression (5) In Dh, a is c and h is h2. In addition, h1 is the height of the 1st column body part 44, h2 is the height of the 2nd column body part 46, c is the width | variety of the bottom part of the 1st column body part 44 (width | variety of the top part of the 2nd column body part 46). It is. Hereinafter, the shape measuring method in this case will be described by dividing into methods 4 and 5.

(Method 4) The same method as in Example 2 is used. The width a of the top part of the first columnar part 44, the total height h of the first columnar part 44 and the second columnar part 46, and the width b of the bottom part of the second columnar part 46 are measured. Next, based on the resonance condition equation obtained from the equation (31) or (32), a four-dimensional matrix database relating to the ratio of the propagation constant β to a, b, B, and t is created within an appropriate range. Here, c can be obtained from h1 / h, a, and b using a similar relationship. Therefore, the value of c is fixed, and the database is created by changing the numerical values of (a, b, B, t). Thereafter, the same process as in the second embodiment is performed.
(Method 5) Although the value of c is fixed in Method 4, the value of h1 / h is fixed here. The width a of the top part of the first columnar part 44, the total height h of the first columnar part 44 and the second columnar part 46, and the width b of the bottom part of the second columnar part 46 are measured. Next, a database of a three-dimensional matrix relating to the ratio of the propagation constant β to B, t, and c is created within an appropriate range based on the resonance condition equation obtained from the equation (31) or (32). Thereafter, the same process as in the second embodiment is performed.

  As described above, according to the present embodiment, even when the rotation shaft 38 is inclined from the vertical axis 40 around the point P of the column body portion 6, the two first column body portions 44 and the second second column body portions 44 are arranged. The dimension of the concrete foundation 2 can be calculated | required now by thinking that the 2 pillar part 46 is connected.

  As described above, according to Examples 1 to 5, by using the torsional resonance conditional expression and the resonance frequency, the dimensions of each part of the buried concrete foundation can be obtained with high accuracy.

  Further, when it is assumed that there is a structure further below the discarded concrete 12 in FIG. 3 of Example 1, a four-terminal matrix such as Expression (19) for the structure is obtained. This can be dealt with by obtaining an equation in the same manner as the method of obtaining 27). In the analysis program of the second embodiment, the analysis is performed using the ratio of the propagation constants. However, an analysis program using the resonance frequency as in the fourth embodiment can be applied. In that case, the value of propagation velocity is required.

  In addition, although the present Example demonstrated the case where the cross section of the pillar part 6, the floor base part 8, and the discarded concrete 12 was a square or a circle, also in the case of a rectangle, although unknown amount increases, a resonance conditional expression is set. It can respond. That is, it is possible to measure the shape by the method of the present invention other than the buried concrete foundation as shown in FIG. 1 if the torsional resonance conditional expression corresponding to the shape of the foundation can be set.

It is a side view of a concrete foundation. It is a steel tower using a concrete foundation. It is a side view in case there is discarded concrete under a floor board part. It is a block diagram of the shape measuring apparatus of the concrete foundation 2. FIG. It is a top view of the column body part at the time of attaching each sensor which measures a torsional resonance frequency. It is a top view of the pillar part at the time of attaching two acceleration sensors. It is a reference figure for identifying a torsional resonance frequency. It is an example of the frequency spectrum at the time of measuring the vibration of a concrete foundation. It is a flowchart of the analysis program which makes the analysis result the basic | foundation type of the standard steel tower foundation of Example 2. FIG. It is an example of the three-dimensional matrix data of (b, B, t) of Example 2. It is a flowchart of the analysis program which makes each part dimension of the steel tower foundation of Example 2 an analysis result. It is a side view in case the rotating shaft of Example 5 inclines from a vertical axis centering on the middle of a column part. It is a side view in case there is discarded concrete under the floor board part of Example 5. FIG.

Explanation of symbols

2 Concrete foundation 6 Column body portion 8 Floor base portion 12 Discarded concrete 16 Exciter 18 Force sensor 20 Signal processing device 24 Acceleration sensor 44 First column body portion 46 Second column body portion

Claims (11)

In the method of measuring the shape of the buried concrete foundation formed by connecting the columnar part of the truncated pyramid or truncated cone and the floor part having a rectangular or circular cross section,
Detecting acceleration of torsional vibration by exciting so that torsional vibration occurs around the axis of the buried concrete foundation, extracting a plurality of resonance frequencies of the acceleration detection value, and extracting the plurality of resonance frequencies, A method for measuring the shape of a buried concrete foundation, wherein the dimensions of the buried concrete foundation are obtained based on a resonance condition expression representing a relationship between a resonance frequency of the torsional vibration and a dimension of each part of the buried concrete foundation.   The shape of a buried concrete foundation according to claim 1, wherein the width or diameter of the top portion of the pillar portion of the buried concrete foundation is actually measured and applied to the resonance condition formula to determine the size of the buried concrete foundation. Measuring method.   The shape measurement of the buried concrete foundation according to claim 1 or 2, wherein the height of the column body portion of the buried concrete foundation is actually measured and applied to the resonance condition formula to determine the size of the buried concrete foundation. Method.   In any 1 item | term of Claim 1 thru | or 3, it measures the width | variety or diameter of the top part of the said column body part of the said embedded concrete foundation, and the inclination angle and height of a side surface, Based on this measured value, the said column body part's A method for measuring the shape of a buried concrete foundation, wherein a width or a diameter of a bottom portion is estimated and applied to the resonance condition formula to determine a dimension of the buried concrete foundation.   5. The buried concrete according to claim 1, wherein a propagation speed of the torsional vibration of the buried concrete foundation is actually measured and applied to the resonance condition formula to determine a dimension of the buried concrete foundation. Basic shape measurement method. In the method of measuring the shape of the buried concrete foundation formed by connecting the columnar part of the truncated pyramid or truncated cone and the floor part having a rectangular or circular cross section,
Based on the resonance condition equation of the torsional vibration representing the relationship between the resonance frequency of the torsional vibration around the axis of the buried concrete foundation and the size of each part of the buried concrete foundation, the unknown dimension of the buried part of the buried concrete foundation is The ratio of the propagation constant in the combination of unknown dimensions of other embedded parts based on the next propagation constant set in a specific combination is obtained, and a table in which the correspondence between the combination of dimensions and the ratio of the propagation constant is described in a database in advance And detecting the acceleration of the torsional vibration so that the torsional vibration occurs around the axis of the buried concrete foundation, extracting a plurality of resonance frequencies of the detected acceleration value, The ratio of the other resonance frequencies with respect to the set resonance frequency as a reference is obtained, and the error between the ratio and the ratio of the propagation constant is minimized. The combination of dimensions by searching from the database, the shape measuring method of the buried concrete foundation, characterized in that to determine the dimensions of the buried concrete foundation.   In Claim 6, the width or diameter and height of the top portion of the pillar portion of the buried concrete foundation are measured and applied to the resonance condition formula, and the dimensions of each part of the buried concrete foundation are determined based on the resonance condition formula. A method for measuring the shape of a buried concrete foundation, wherein the ratio of the combination of the two and the propagation constant is obtained, the table is created, and the dimensions of the buried concrete foundation are obtained.   7. The width or diameter and height of the top portion of the column body portion of the buried concrete foundation and the inclination angle of the side surface are measured, and the width or diameter of the bottom portion of the column body portion is estimated based on the measured values. Then, it is applied to the resonance condition equation, and the ratio of the combination of the dimensions of each part of the buried concrete foundation and the propagation constant is obtained based on the resonance condition equation, and the table is prepared to obtain the dimension of the buried concrete foundation. A method for measuring the shape of a buried concrete foundation.   In Claim 6, when the rotation axis of the column body part is inclined from the central axis about the middle of the column body part, the column body part includes two columns, a first column body part and a second column body part. It is considered that the column bodies are connected, and the top width or diameter of the first column body portion, the width or diameter of the bottom portion of the second column body portion, and the height of the entire column body portion are measured and measured. Applying a resonance condition formula, obtaining a ratio of the combination of dimensions of each part of the buried concrete foundation and the propagation constant based on the resonance condition formula, creating the table and obtaining the dimension of the buried concrete foundation Method for measuring the shape of buried concrete foundation.   Vibration means for exciting the torsional vibration around the axis of the buried concrete foundation, acceleration detecting means for detecting acceleration of the torsional vibration, and torsional resonance of the buried concrete foundation from the output signal of the acceleration detecting means A frequency analysis means for analyzing a frequency spectrum including the frequency, and a resonance conditional expression representing a relationship between the resonance frequency and dimensions of each part of the buried concrete foundation, and is analyzed by the frequency analysis means. An embedded concrete foundation shape measuring device comprising: a computing means for computing the dimensions of the buried concrete foundation based on a plurality of resonance frequencies and the resonance condition formula.   Based on the resonance condition equation that expresses the relationship between the resonant frequency of torsion and the dimensions of each part of the buried concrete foundation, and based on the set propagation constants for a specific combination of unknown dimensions of the buried part of the buried concrete foundation. A ratio of other propagation constants is obtained, and a storage means for storing a table describing a correspondence relationship between a combination of dimensions and the ratio of the propagation constants, and excitation is performed so that torsional vibration occurs around the axis of the buried concrete foundation. Vibration means; acceleration detection means for detecting acceleration of the torsional vibration; and frequency analysis means for analyzing a frequency spectrum including a resonance frequency of torsion of the buried concrete foundation from an output signal of the acceleration detection means; Ratio of other resonance frequencies based on the set resonance frequency among the plurality of resonance frequencies analyzed by the frequency analysis means and the propagation Calculating means for calculating an error between the ratio of the amount, shape-measuring apparatus of the buried concrete foundation comprising a retrieval means for retrieving the storage means on the basis of the calculation result of the calculating means.

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