JP2013194367A - Estimation method of embedment depth from vibration characteristics of rigid body simulating boulder - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an estimation method of an embedment depth from vibration characteristics of a rigid body simulation a boulder with which the boulder on a slope is simulated into the rigid body having an embedment in the foundation.SOLUTION: A boulder on a slope is simulated into a rigid body having an embedment in the foundation, a test piece 1 is created having the dimension and weight different from the rigid body and while changing a foundation strength, the dimension and weight of the test piece 1 and a condition of the embedment of the test piece 1, the number of vibration intrinsic for the test piece 1 is measured.

Description

  The present invention relates to a method for estimating a penetration depth based on vibration characteristics of a rigid body that simulates a boulder.

Efficient and quantitative judgment of the risk of falling rocks on the slopes along the railroads and taking appropriate measures against high-risk rocks are important for safe and stable transportation of railways against rockfall disasters. Important for maintenance.
There are two types of rock fall occurrence types: a roll type (fall type) and a fall type. As for the former type, the name of falling type is used for railways and the type of falling type or rolling type is used for roads. In the present invention, the former type is called a rolling type.

  As shown in FIG. 17, the boulder-type rockfall is “a natural mountain in which the rock mass is buried in a softer material (matrix) than the rock mass, the matrix portion is selectively weathered and eroded, and the rock mass is raised, It falls ”(see Non-Patent Documents 1 and 2 below).

Railway Technical Research Institute: Falling Rock Countermeasure Technical Manual, pp. 2-4, 1999.3 Japan Road Association: Ochiishi Countermeasure Handbook, pp. 7-9, 2000.6 Kenji Ogata, Hiroyuki Matsuyama, Nobuyuki Amano: Judgment of rock fall risk using vibration characteristics, JSCE Proceedings, No. 749 / VI-61, pp. 123-135, 2003.12. Masaru Takemoto, Yu Fujiwara, Seiya Yokota, Takashi Mitsuka, Kuniomi Kai, Ei Okamoto: Development of a field survey and judgment system using the rock fall risk vibration survey method-Development of a system to judge the risk of rock fall on the field- Japan Society of Civil Engineers 65th Annual Academic Lecture, pp. 75-76, 2010.9 Hideki Saito, Yasunori Otsuka, Fumiaki Kamihan, Kenichi Kojima, Osamu Murata, Takaomi Ma, Kazuhide Sawada, Atsushi Yashima, Takahiro Fukada: Fundamental experiment on stability evaluation of rock slopes by remote non-contact vibration measurement, Japan Society of Civil Engineers 65th Annual Scientific Lecture, pp. 47-48, 2010.9 Hideki Saito, Yasunori Otsuka, Takaomi Ma, Kazuhide Sawada, Fumiaki Kamihan, Osamu Murata, Takahiro Fukada: Examination of rock mass stability evaluation by remote non-contact vibration measurement, 46th Geotechnical Research Conference, pp. 1845-1846, 20111.7 Takahiro Fukada, Ryoji Izuminami, Yasuki Mori: Consideration of system construction and measurement results for vibration measurement of rocks on slopes, Japan Society of Civil Engineers 65th Annual Lecture, pp. 77-78, 2010.9 Railway Technical Research Institute: Design standards for railway structures, etc., explanation (foundation structure, anti-earth pressure structure), pp. 128-129,2000.6 Railway Technical Research Institute: Design standards for railway structures, etc., explanation (foundation structure, anti-earth pressure structure), pp. 88-89,2000.6

Various countermeasures (see Non-Patent Documents 3 to 6 above) have been attempted for the above-mentioned high-risk boulders, but a practical estimation of the inset depth of the boulders greatly related to the rock-fall risk level. A method has not yet been proposed.
In view of the above situation, the present invention targets a boulder-type rock fall on a slope, simulates this boulder into a rigid body having a root in the ground, and estimates the depth of penetration related to the rock fall risk from its vibration characteristics. It is an object of the present invention to provide a method for estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder that is compact and can be used sufficiently even on an actual slope.

In order to achieve the above object, the present invention provides
[1] In the method of estimating the depth of penetration based on the vibration characteristics of a rigid body simulating a boulder, the specimens with different shapes and weights of the rigid body were prepared by simulating a boulder on the slope as a rigid body with a root in the ground. Then, the natural frequency of the specimen is measured by changing the ground strength, the shape and weight of the specimen, and the depth of penetration of the specimen.

[2] In the method for estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder according to [1] above, the natural frequency of the specimen is measured by hitting the specimen with a rubber hammer. It is characterized by that.
[3] In the method of estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder according to [2] above, an accelerometer is arranged on the upper surface of the specimen, and an AD converter is used to convert the waveform from the accelerometer to an AD converter. And recording with a personal computer.

  [4] In the method for estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder according to the above [1] or [2], the size and weight of the test specimen are 0. 3m, 0.4m in width, 0.5m in height, the second specimen A has a length of 0.3m, a width of 0.5m, a height of 0.4m, and a weight of 1.38kN, respectively. B is 0.3 m long, 0.4 m wide, 0.8 m high, and the second specimen B is 0.3 m long, 0.8 m wide, 0.4 m high, and has a weight of 2.21 kN, respectively. It is characterized by being.

[5] In the method for estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder according to [4] above, the target strength of the ground reaction force coefficient kv ₃₀ (MN / m ³ ) is 40 to 50, and the built ground strength The ground type with a 47.6 is “soft”, the target strength is 70-80, the ground type with the built ground strength of 79.1 is “medium”, the ground strength with the target strength of 100 or more and the built ground strength is 146 The type is “hard”, and each of the specimens is arranged on each of the “soft”, “medium”, and “hard” boards.

[6] In the estimation method of the penetration depth based on the vibration characteristics of a rigid body simulating a boulder according to [1] or [2] above, the specimen and the ground are modeled and eigenvalue analysis is performed by a three-dimensional finite element method. It is characterized by that.
[7] In the method of estimating the penetration depth based on the vibration characteristics of a rigid body simulating a boulder as described in [6] above, the ground density is set to 0 in order to eliminate the influence of the vibration of the ground itself, and further statically measured The actual result is analytically reproduced by evaluating the ground using a double equivalent value as a dynamic value considering the strain effect of the ground with respect to the flat plate loading test equivalent value.

[8] In the method for estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder according to [6] above, the dimensionless quantities Q ₁ and Q ₂ defined with respect to the ground strength and the dimensions of the specimen are variables. The natural frequency is calculated by the following estimation formula.
d = 0.3584 (f / f ₀ ^* ) − 0.351
Where d is the depth of penetration of the specimen, f is the natural frequency in the presence of the specimen, and f ₀ ^* is the natural frequency when the exposed part of the specimen is considered not to be incorporated. It is.

[9] In the method for estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder according to [8] above, the dimensionless amount Q ₁ is {E / (W / A)} ^1/2 , The dimensionless quantity Q ₂ is √ {(b / h ₀ ) ² / (b / h ₀ ) ² +1}.
Here, E is the modulus of deformation of the specimen, W is the weight of the specimen, and A is a bottom area of the specimen is in contact with the ground, b is specimen blow width, h ₀ is the specimen without embedment It is height.

[10] In the method of estimating the penetration depth based on the vibration characteristics of a rigid body simulating a boulder according to [8] above, the penetration ratio d / h _{0 of the} specimen and the natural frequency have a proportional relationship. Using the ratio of the natural frequency f in the presence of the specimen to the specimen and the natural frequency f ₀ ^* when the exposed portion of the specimen is considered to be not incorporated, the root of the specimen is used. The estimated length of the insertion depth is approximated by the estimation formula, and the correlation coefficient of this estimation formula is R ² = 0.926.

According to the present invention, the following effects can be achieved.
(1) Simulate a boulder into a rigid body with a root in the ground, create a specimen with a different size and weight in place of this rigid body, change the conditions such as ground strength, depth of penetration, etc. By conducting a measurement experiment, it is possible to provide a practical method for estimating the depth of intrusion of a boulder that has a great relationship with the rock fall risk. The natural frequency measurement method performed in this experiment is sufficiently usable even on an actual slope because the system configuration using a rubber hammer used for striking is compact.
(2) It was proposed to reproduce the experiment by modeling the rigid body and the ground and performing eigenvalue analysis using the three-dimensional finite element method. In that case, in order to eliminate the influence of the vibration of the ground itself, the density of the ground is set to 0, and further, a value equivalent to a dynamic double considering the strain effect of the ground with respect to the value equivalent to the statically measured flat plate loading test. It was proved that the suitability of the results of the experiment and the analysis was good by evaluating the ground using
(3) The vibration characteristics of a rigid body with roots in the ground are considered to exhibit highly nonlinear behavior, but have a high correlation with the dimensionless quantities Q ₁ and Q ₂ defined for the ground strength and the shape of the rigid body. The natural frequency could be calculated by the estimation formula using these as explanatory variables.
(4) In addition, since the purpose of the present invention is to estimate the depth of penetration, the natural frequency calculated by assuming that the exposed portion is not rooted and the measured natural frequency in the state where the root is rooted are used. An estimation formula for estimating the penetration depth is provided.

It is a figure which shows the shape and weight of the test body considered as the rigid body which concerns on this invention. It is a figure which shows the particle size accumulation curve of the ground material which concerns on this invention. It is a figure which shows the outline | summary of the vibration and vibration measurement of the test body which concern on this invention. It is a figure which shows the acceleration waveform which measured and recorded the vibration of the test body which concerns on this invention. It is a figure which shows the example of calculation of the natural frequency by the FFT process which concerns on this invention. It is a figure which shows the shape and arrangement | positioning of the test body which concern on this invention. It is a figure which shows the relationship (experimental result) of the penetration ratio of the test body which concerns on this invention, and a natural frequency. It is a figure which shows the analysis result of the penetration ratio of the test piece which concerns on this invention being 0 (eigenvalue). It is a figure which shows the relationship (analysis result) of the penetration ratio and natural frequency of the test body which concerns on this invention. It is a figure which shows the correlation of the natural frequency (analysis value) and natural frequency (experimental value) which concern on this invention. It is a figure which shows the relationship between the deformation coefficient of the ground based on this invention, and a natural frequency. Is a diagram showing the relationship between dimensionless quantity Q ₂ and natural frequency f ₀ relating to the aspect ratio of the present invention. It is a figure which shows the rigid body which has roots in the ground which concerns on this invention. It is a figure which shows the exposed part of the rigid body which concerns on this invention. It is a figure which shows the correlation (analysis value and estimation formula) of the natural frequency which concerns on this invention. It is a figure which shows the correlation (real length and estimated length) of the penetration depth which concerns on this invention. It is a schematic diagram which shows the example of a boulder type falling rock.

  The method of estimating the depth of penetration based on the vibration characteristics of a rigid body simulating a boulder according to the present invention simulates a boulder on a slope as a rigid body with a root in the ground, and produces specimens with different sizes and weights of this rigid body. Then, the natural frequency of the specimen is measured by changing the ground strength, the size and weight of the specimen, and the depth of penetration of the specimen.

Hereinafter, embodiments of the present invention will be described in detail.
The present invention proposes a method for estimating the depth of intrusion of a boulder that is greatly related to the risk of falling rock, targeting a boulder type rock fall. In this method, first, the stone is simulated as a “rigid body having a root in the ground”. As this rigid body, specimens with different weights and dimensions are prepared, and these specimens are embedded at different ground strengths and different penetration depths, and the natural frequency is calculated from the acceleration waveform measured by hitting with a hammer ( Experiment). Next, this experimental result is reproduced by eigenvalue analysis by a three-dimensional finite element method (analysis). Next, by using the vibration characteristics of the rigid body that has rooting in the ground, obtained by this experiment and analysis, the depth of rooting of the boulder is estimated. The method will be described below step by step.

  FIG. 1 is a diagram showing the shape and weight of a specimen considered as a rigid body according to the present invention. 1A shows a specimen A, and FIG. 1B shows a specimen B. The specimen A is 0.3 m (vertical) × 0.4 m (horizontal) × 0.5 m (height). The weight is 1.38 kN, and there are two types of specimen B: 0.3 m (length) × 0.4 m (width) × 0.8 m (height) and weight 2.21 kN. The specimen used in the experiment was made of concrete (nominal strength 24, W / C = 60%). The dimensions and weight of the specimen are rectangular parallelepiped because of the fact that there are many occurrences of up to 2kN weight due to the actual situation of rockfall disasters in railways, and that many cases can be tested by changing the dimensions in order to investigate the influence of the shape. And the above dimensions and weight.

On the other hand, the earth basin for embedding the specimen was set to a size that is 2 m long × 3 m wide × 2 m deep enough to allow the two specimens A and B to be placed side by side and to be tested without being affected by the boundary. After constructing the foundation ground to a height of 1 m, the specimen is installed horizontally, and the vibration is measured while constructing the ground of the base part in sequence.
In addition, the earth tub main body is made to produce strongly with the steel mountain stopper and the plywood.

Next, the characteristics of the ground material will be described.
The characteristics and particle size accumulation curves of the materials used as the foundation ground and the basement ground are as shown in Table 1 and FIG. 2, and the engineering classification is gravel-mixed fine-grained sand (SF-G). In FIG. 2, the horizontal axis indicates the particle size (mm), and the vertical axis indicates the passing mass percentage (%).

Hereinafter, experimental examples will be described.
The ground strength used in the experiment is managed by the ground reaction force coefficient corresponding to the flat plate loading test using a small FWD tester. The target ground reaction force coefficient is soft: 40-50MN / m ³ , medium: 70 ˜80 MN / m ³ , Hard: Three strengths of 100 MN / m ³ or more.
Preliminary compaction tests were conducted in advance to manufacture the ground having these predetermined strengths, and compaction conditions such as the ground material removal thickness of 100 to 150 mm and the number of rollings by the vibration plate 60 kg class were determined. As shown in Table 2, the actually measured ground reaction force coefficients after the construction of the ground are as follows: soft: 47.6 MN / m ³ , medium: 79.1 MN / m ³ , hard: 146 MN / m ³ .

In the experiment, there were three types of conditions for setting the rooting ratio d / h ₀ (d: rooting length, h ₀ : exposure height) to be 0, 1/3, and 1. By placing the specimen vertically or horizontally, it is possible to conduct experiments in cases where the penetration depth and exposure length are different without changing the penetration ratio.
The experiment will be conducted in order from the softness of the ground type, and the ground will be constructed while measuring and managing the ground reaction force coefficient for each stratum. Then, when the experiment of the human series with different rooting ratio was completed, the basement ground was removed, the base ground was removed by 0.1 m, and it was confirmed that the ground reaction force coefficient did not change significantly. Constructing ground for different ground types under consolidation conditions. In the case of experimental cases with different ground strengths, all of them were remade from the basic ground so as to have a predetermined strength.

As shown in Table 2, the experiment cases carried out by this repetitive procedure are 2 types of specimens A and B, 3 types of soft, medium, and hard types of ground, and 3 of the penetration ratio 0, 1/3, and 1 It is a combination of types.
Next, a measurement method (excitation and vibration measurement) in the experiment will be described.
FIG. 3 is a diagram showing an outline of vibration and vibration measurement of a specimen according to the present invention, FIG. 3 (a) is a schematic diagram of an experimental method, and FIG. 3 (b) is a drawing substitute showing an installation state of an accelerometer. FIG. 3C is a system configuration diagram of vibration and vibration measurement.

  As shown in FIG. 3, two accelerometers 2 are attached to the upper surface of the specimen 1, and the coordinates are always such that the short side direction of the bottom face of the specimen 1 is the x direction, the long side direction is the y direction, and the vertical direction is the z direction. The acceleration waveform when the rubber hammer 3 is hit about 10 times in each of the x and y directions is passed through the AD converter 4 and recorded in the personal computer (PC) 5. In addition, 6 is a laying ground and 7 is a foundation ground.

The specifications of the equipment used for vibration measurement are the accelerometer 2 is a piezoelectric type, a preamplifier built-in type, a 3-axis type, the frequency range is 3-5,000 Hz, and the AD converter 4 is a 16-channel simultaneous sampling type. The frequency is 88.2 kHz / ch (MAX), and the amplification degree is 1 to 100 times.
As for the systematization of vibration measurement, ICT (Information and Communication Technology) type equipment with built-in preamplifier is adopted in consideration of use on railway slopes where the roadway conditions and work conditions are not always good. It has a simple and compact system configuration that eliminates the need for a charge amplifier.

FIG. 4 is a diagram showing an acceleration waveform obtained by measuring and recording the vibration of the specimen according to the present invention, FIG. 4 (a) is the measured acceleration waveform, the horizontal axis represents the measurement time (minute: second), and the vertical axis. The axis indicates acceleration (m / s ² ), and FIG. 4B shows the acceleration waveform cut out for each waveform. FIG. 5 is a diagram showing the natural frequency after the FFT processing according to the present invention, and shows the result of the FFT processing of the acceleration waveform cut out for each waveform shown in FIG. 4B. In FIG. 5, the horizontal axis indicates the natural frequency (Hz), and the vertical axis indicates the Fourier amplitude.

As shown in FIG. 4 and FIG. 5 described above, the recorded acceleration waveform is subjected to fast Fourier transform (FFT) one wave at a time, and the dominant frequency that becomes the maximum value of the Fourier spectrum at that time is determined as the natural frequency of the specimen 1. And
The rubber hammer 3 was used for the vibration because the contact time with the rock mass was long when hitting compared to a steel hammer, and a relatively large impact force was obtained even with a small one, and the measurement target 10 This is because a stable impact force can be applied to the rock mass in a frequency range of about 80 Hz.

Next, the experimental results obtained as described above will be described.
The natural frequency of a rigid body having a root in the ground is related to the shape of the rigid body, the strength of the surrounding ground, the depth of root penetration, and the like. First, the natural frequency due to the difference in the penetration ratio according to the specimen and ground strength will be described.
FIG. 6 is a view showing the shape and arrangement of the specimen used in the experiment according to the present invention, and FIG. 6A is the first specimen A (A-H500), which is 0.3 m (longitudinal) × , 0.4 m (horizontal) y, 0.5 m (height), FIG. 6B is the first specimen B (B-H800), 0.3 m long, 0.4 m wide, 0 height .8m, FIG. 6 (c) is the second specimen A (A-H400), 0.3 m in length, 0.5 m in width, 0.4 m in height, and FIG. 6 (d) is the second specimen. B (B-H400), which is 0.3 m in length, 0.8 m in width, and 0.4 m in height. That is, the first specimen A is the specimen A shown in FIG. 1, the first specimen B is the specimen B shown in FIG. 1, and the second specimen A is the first specimen. The one in which the installation direction of A and the second specimen B are changed are those in which the installation direction of the first specimen B is changed. In addition to the three types of ground types and the three types of penetration ratios shown in Table 2, these specimens are further tested in two directions, x and y, so that 72 natural frequency data are obtained in total. can get.

  The first specimen A shown in FIG. 6 (a) was installed so as to have a height of 0.5 m (indicated as “A-H500” in the figure), and was hit in the short side direction (vertical) of 0.3 m. Time is assumed to be the natural frequency fx in the x direction, and the time when it is hit in the long side direction (horizontal) of 0.4 m is the natural frequency fy in the y direction. Similarly, the natural frequencies of the striking directions x and y when the first specimen B shown in FIG. 6B is set to a height of 0.8 m (denoted as “B-H800”) are also fx. And fy, and the experimental results are shown in FIG.

  FIG. 7 is a diagram showing the relationship between the penetration ratio and the natural frequency of the specimen according to the present invention. FIG. 7 (a) shows the first specimen A, height 0.5m (A-H500), ground. 7 is “soft”, FIG. 7B is the first specimen A, height 0.5 m (A-H500), and the ground is “medium”, FIG. 7C is the first specimen. B, height 0.8m (B-H800), if the ground is "soft", Fig. 7 (d) is the first specimen B, height 0.8m (B-H800), the ground is "medium" It is a figure which shows the experimental result in the case of. The ground types are as shown in Table 2.

Both are the results for the ground “soft” and “medium” cases. From this result, the natural frequency increases in proportion to the penetration ratio d / h ₀ and also increases with the ground strength. I understand.
Further, the difference between the specimens A and B is the weight and the height, but when the ground strength is the same, the natural frequency of the specimen A is larger overall.

In any result, when the penetration ratio increases, the natural frequency increases, and both can be approximated by a straight line.
The experimental results of the ground “hard” case and the cases of the second specimens A and B also showed the same tendency as in FIG.
Next, the natural frequency obtained in the above experiment is reproduced by eigenanalysis using a three-dimensional finite element method. Therefore, eigenanalysis by the three-dimensional finite element method will be described.

(1) Analytical model and calculation conditions First, in order to analytically determine the natural frequency of a rigid body with a root in the ground, the experimental specimen and the ground were modeled, and the eigenvalue obtained by the three-dimensional finite element method. Analyze.
The size of the specimen and ground model is assumed to be actual, and the ground is an isotropic elastic body. The boundary conditions in the analysis are fixed support for both the horizontal and vertical directions on the bottom and side surfaces. Further, the separation between the specimen and the ground was ignored, and perfect adhesion was assumed.

As another analysis device, the density of the ground is set to zero. This is because the vibration of the ground itself affects the vibration of the specimen, and it is difficult to specify the natural frequency of the specimen in order of the lower order modes. That is, the density of the ground was set to 0 in order to eliminate the influence of ground vibration.
The ground strength is evaluated as follows. That is, in the experiment, ground strength is managed by a small FWD, and k _V30 as a value corresponding to a flat plate loading test is measured. The ground reaction force coefficient with respect to the bottom surface of the rigid body having an arbitrary width, and the relationship between the ground reaction force coefficient and the ground deformation coefficient are expressed by the following equations (1) and (2), respectively (see Non-Patent Document 7).

k _V = k _V30 (B _V /0.3) ^-3/4 (1)
E ₀ = B (1−v ² ) k _V · I _P (2)
Where k _V : ground reaction force coefficient (MN / m ³ )
k _V30 : Ground reaction force coefficient with a loading plate diameter of 30 cm (MN / m ³ ) B _V : Rigid body conversion width [B _V = √ (a × b), m]
E ₀ : Ground deformation coefficient (MPa)
B: Loading width (MPa) v: Poisson's ratio (0.3)
I _P : Shape factor. Furthermore, the dynamic value in the case of a small strain region is evaluated by a value about twice the static deformation coefficient calculated from a relatively large strain region such as a flat plate loading test. (See Non-Patent Document 8 above).

E = 2E ₀ (3)
From the above formulas (1) to (3), when the ground strength under the experimental conditions is converted into the deformation coefficient, the “Poisson” ratio, “Medium”, and “Hard” of the ground type are respectively set as Poisson's ratio v = 0.3. E ₀ (soft) = 7.5 MPa, E ₀ (medium) = 12.5 MPa, and E ₀ (hard) = 23.1 MPa. Also, the double equivalent values are E (soft) = 15.0 MPa, E (medium) = 25.0 MPa, E (hard) = 46.2 MPa.

The eigenvalue analysis of each case is performed under the above calculation conditions. As an example, FIG. 8 shows the analysis result of the first specimen A (A-H500) and the penetration ratio dh ₀ = 0 in FIG. In FIG. 8, 11 is the ground, and 12 is a specimen (A-H500).
(2) Analysis Results Similar to the arrangement of the experimental results shown in FIG. 7, the relationship between the penetration ratio and the natural frequency is also shown in FIG. Similar to the experimental results of FIG. 7, it can be seen that the penetration ratio and the natural frequency are in a proportional relationship.
(3) Suitability between experiment and analysis FIG. 10 shows the correlation between the natural frequency obtained as a result of the eigenvalue analysis and the natural frequency measured in the experiment. In FIG. 10, the white circle is the first specimen A (A--H500), the white square is the first specimen B (B--H800), and the white rhombus is the second specimen A (A-H400, white). The triangle is the second specimen B (B-H400), and the plot is the case where the ground strength is 2E ₀ corresponding to double in the experimental case indicated by each legend (see FIG. 6 for the notation). The result at this time can be represented by an approximate line (thick line), but is not plotted in order to avoid the figure becoming complicated, but when the ground strength is E ₀ , the approximate line In this way, by evaluating the ground strength with 2E ₀ which is a double equivalent value, it can be seen that the eigenvalue analysis result and the experimental result are well matched.

As described above, the specimen and the ground are modeled with the same dimensions as the experimental conditions, and the density is set to 0 in order to eliminate the influence of the vibration of the ground itself. The actual phenomenon can be analytically reproduced by evaluating as a typical value equivalent to twice the static value.
However, some variation is seen in the experimental results, so the subsequent examination will be based on the analysis results.
(4) Relationship between Ground Strength and Natural Frequency FIG. 11 is a diagram showing the relationship between the deformation coefficient of the ground and the natural frequency of the rigid body according to the present invention. As a characteristic value related to the ground strength on the horizontal axis, a dimensionless amount {E / (W) composed of a deformation coefficient (E), a weight of the rigid body (W), and a bottom area (A = a × b) where the rigid body is in contact with the ground. / A)} ^1/2 and the vertical axis represents the natural frequency, and the analysis of the case of the first specimen A (A-H500) in FIG. It is an example of a result. In FIG. 11, the black circle is A-H500-0-x, the white circle is A-H500-0-y, the black triangle is A-H500-1 / 3-x, the white triangle is A-H500-1 / 3-y, The black square is A-H500-1-x, and the white square is A-H500-1-y. (The number after A-500 is the penetration ratio, and the subsequent x and y indicate the striking direction.)
Since the relationship between the characteristic value and the natural frequency is a straight line, the relationship between the characteristic value and the natural frequency can be expressed by the following equation (4) using the proportionality constant α.

f = α {√ (E / (W / A)} = αQ ₁ (4)
The dimensionless amount shown here is defined as Q ₁ = {E / (W / A)} ^1/2 .
The same relationship is obtained for analysis cases other than A-H500, and the proportionality constant α in each case at that time is a value shown in Table 3.

(5) Relationship between rigid body shape and natural frequency Next, the relationship between the rigid body shape and the natural frequency will be considered.
Consideration and research for estimating the ground motion acceleration from a case where a rigid body such as a tombstone falls down during an earthquake has been reported (see Non-Patent Document 9 above). This is based on the fact that the aspect ratio b / h ₀ obtained from the height h ₀ of the rigid body and the width b in the dominant direction of the ground motion is related to the static overturning condition of the rigid body. That is, since it is presumed that there is a high correlation between the aspect ratio representing the shape of the rigid body and the stability, the relationship between the aspect ratio and the natural frequency of the rigid body was examined.

As a result of examining characteristic values based on the aspect ratio such as b / h ₀ , (b / h ₀ ) ^1/2 , and (b / h ₀ ) ² , the dimensionless quantity Q shown in the following equation (5) is obtained. ₂ has a high correlation with the natural frequency of the rigid body without root.
Q ₂ = √ {(b / h ₀ ) ² / (b / h ₀ ) ² +1} (5)
Where b: width of the rigid body in the striking direction (m)
h ₀ : height of rigid body without root (m)
It is.

FIG. 12 is a diagram showing the relationship between the dimensionless quantity Q ₂ related to the aspect ratio and the natural frequency f _{0 according to} the present invention.
Here, it is necessary to consider the physical meaning of the dimensionless quantity Q ₂ related to the aspect ratio. Now, with respect to the rocking vibration of a rigid body on a semi-infinite elastic ground, the frequency equation in the case where there is no rooting is that the determinant of the coefficient of the homogeneous equation for Y and Θ shown in the following equation (6) is 0. Obtained as an equal expression (see Non-Patent Document 9 above) (however, symbols in the document are replaced with those in this specification, and other newly appearing items are M: mass, n: natural circular frequency) , k _s : horizontal ground coefficient, k _v : vertical ground coefficient, J: mass moment of inertia around the center of gravity).

(Abk _s −Mn ² ) Y− (abh ₀ ² k _s / 4) Θ = 0− (abh ₀ k _s / 2) Y + {(ab ³ k _v / 12) + (abh ₀ ² k _s / 4) −Jn ² } Θ = 0 (6)
In the above equation (6), if the horizontal ground coefficient k _s = 0 for simplification, the frequency equation is as follows.

_{^{MJn 4 - (Mab 3 k v}} / 12) n 2 = 0 ... (7)
When the above equation (7) is solved for n, the first natural frequency of the rocking vibration is rewritten using the relationship of n = 2πf to obtain the following equation (8), which is defined by the above equation (5). The value comes out as a coefficient.
f = √ {(b / h ₀ ) ² / (b / h ₀ ) ² +1} · 1 / 2π√ (k _v ab / M) (8)
f = 1 / 2π√ (K / M) (9)
Here, considering the fact that the natural frequency of the simple vibration of the mass system with the spring constant K and mass M can be expressed by the above equation (9), the aspect ratio b / h relating to the basic natural frequency as a coefficient _The dimensionless quantity Q ₂ related to ₀ is meaningful.

As described above, by setting the density to 0 in order to eliminate the influence of ground vibration, it becomes possible to analyze the eigenvalue of a rigid body having a penetration, and further, considering the strain of the ground, the deformation coefficient is set to a static value. By evaluating at a 2-fold equivalent, it was shown that the suitability of the experimental results and analysis was good.
It was also found that the natural frequency of a rigid body with a root has a relationship with the root ratio, the ground strength, the aspect ratio representing the shape of the rigid body, and the like.

In other words, although the behavior of a rigid body having a root in the ground is a complex nonlinear phenomenon, an estimation formula having a natural frequency as an objective variable can be created from several explanatory variables.
Therefore, an estimation formula for the penetration depth by multiple regression analysis is created as follows.
(1) Estimating Formula for Rooting Depth FIG. 13 is a diagram showing a rigid body having a root in the ground according to the present invention, and FIG. 14 is a diagram showing an exposed portion of the rigid body according to the present invention.

As shown in FIG. 13, the natural frequency of the rigid body 22 having a root in the ground 21 has been calculated. A procedure for estimating the penetration depth d using the measurement result of the natural frequency at this time is proposed.
First, as shown in FIG. 14, consideration is given to an exposed portion of the ground surface of the rigid body 22 having a root in the ground 21. About this exposed part, it is possible to grasp dimensions a, b, h ₀ [depth (vertical), width (horizontal), height of exposed part], weight W, strength of the ground 21 (deformation coefficient), etc. It is.

Then, it is considered that the exposed part is not embedded, and from the examination of the experiment and analysis results so far, the natural frequency f ₀ ^* of the rigid body 22 at that time is the dimensionless quantity Q ₁ related to the ground strength and the shape of the rigid body 22 Using the dimensionless quantity Q ₂ related to, the above-described analysis result is subjected to multiple regression analysis, and the natural frequency is approximated as an objective variable by the following equation.
f ₀ ^* = 0.745Q ₁ · Q ₂ +2.537 (10)
Here, f ₀ ^* is a natural frequency of a rigid body with zero root, and Q ₁ and Q ₂ are dimensionless quantities represented by the above formulas (4) and (9). The correlation coefficient of the multiple regression analysis of the above formula (10) is R ² = 0.980.

FIG. 15 shows the relationship between the analysis result of the natural frequency f _{0 in} the case where there is no rooting and the natural frequency f ₀ ^{* that} can be calculated from the above equation (10). Thus, it can be seen that there is a high correlation between the analysis result and the estimated value obtained by Equation (10).
Next, as shown in FIG. 7 and FIG. 9, since it is known that there is a proportional relationship between the rooting ratio d / h ₀ and the natural frequency, the natural frequency f in a state where there is rooting. And the estimated length of the penetration depth was approximated by the following equation (11) using the ratio of the natural frequency f ₀ ^* when it was assumed that the exposed portion was not embedded. Note that the correlation coefficient of the estimation formula (11) is R ² = 0.926.

d = 0.358 (f / f ₀ ^* ) − 0.351 (11)
Thus, by grasping the ground strength around the boulder and the dimensions of the exposed portion, the natural frequency f ₀ ^* of the exposed portion is calculated by the above equation (5), and the natural frequency f in the above equation (11) is calculated. Is obtained by actual measurement, and the penetration depth d can be estimated.
(2) Verification of estimation formula As a specific calculation example of the penetration depth estimation, the penetration ratio of the second specimen A (A-H400) in FIG. 6 is 1/3, the ground “middle”: E = 25 MPa. Consider the case of an x-direction strike. In this case, the penetration length d = 0.1 m, the exposure length h ₀ = 0.3 m, W = 1.38 kN, and the length in each direction is a = 0.5 m and b = 0.3 m. A = a × b = 0.15 m ² , b / h ₀ = 0.3 / 0.3 = 1.

Therefore, from the above formulas (4) and (5), Q ₁ = 52.129, Q ₂ = 0.707 is obtained, and the natural frequency of the rigid body that is considered to have no exposure portion is f ₀ ^* = Calculated as 30.0 Hz.
By substituting the natural frequency f ₀ ^* of the rigid body and the natural frequency f = 40.9 Hz in a state where there is a root into the above equation (11), the estimated length of the root is d = 0.137 m. And obtained. At this time, the difference between the depth of penetration and the actual length of 0.1 m is 0.037 m.

FIG. 16 shows the correlation between the actual length of the penetration depth calculated in this way and the estimated length according to the above equation (11).
The correlation coefficient is as high as 0.926, and it was shown that the depth of rooting can be accurately estimated with an error within ± 0.1 m at maximum with respect to the actual length.
As mentioned above, according to the present invention,
(1) Simulating a boulder into a rigid body with a root in the ground, creating specimens with different shapes and weights, and changing the conditions such as ground strength and depth of penetration, and measuring natural frequencies. . The natural frequency measurement method performed in the experiment is sufficiently usable even on an actual slope because the rubber hammer used for impact and the system configuration are compact.
(2) We tried to reproduce the experiment by modeling the rigid body and the ground and performing eigenvalue analysis using the three-dimensional finite element method. In order to eliminate the influence of the vibration of the ground itself, the density of the ground was set to 0, and the value equivalent to the static load of the plate loading test was set to a dynamic double equivalent value considering the strain effect of the ground. By using it to evaluate the ground, it was shown that the compatibility of the results of the experiment and analysis is good.
(3) The vibration characteristics of a rigid body with roots in the ground are considered to exhibit highly nonlinear behavior, but have a high correlation with the dimensionless quantities Q ₁ and Q ₂ defined for the ground strength and the shape of the rigid body. It was shown that the natural frequency can be calculated by an estimation formula using these as explanatory variables.
(4) In addition, since the purpose of the present invention is to estimate the depth of penetration, the natural frequency calculated by assuming that the exposed portion is not rooted and the measured natural frequency in the state where the root is rooted are used. An estimation formula for estimating the penetration depth was proposed.

  In addition, this invention is not limited to the said Example, Based on the meaning of this invention, a various deformation | transformation is possible and these are not excluded from the scope of the present invention.

  The method of estimating the depth of penetration based on the vibration characteristics of a rigid body simulating a boulder according to the present invention simulates a boulder on a slope as a rigid body with a root in the ground, and a depth of penetration based on the vibration characteristics of a rigid body simulating a boulder. It can be used as an estimation method.

1, A, B Specimen 2 Accelerometer 3 Rubber hammer 4 AD converter 5 Personal computer (PC)
6 Nesting ground 7 Foundation ground 11,21 Ground 12 Specimen (A-H500)
22 Rigid body

Claims (10)

  Simulating a boulder on a slope into a rigid body with a root in the ground, preparing specimens with different sizes and weights of the rigid body, ground strength, dimensions and weight of the specimen, and depth of penetration of the specimen A method for estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder, wherein the natural frequency of the specimen is measured under different conditions.   The method of estimating a penetration depth by vibration characteristics of a rigid body simulating a boulder according to claim 1, wherein the measurement of the natural frequency of the specimen is performed by hitting the specimen with a rubber hammer. Of the depth of penetration by the vibration characteristics of a rigid body simulating a rolling stone.   3. A method for estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder according to claim 2, wherein an accelerometer is arranged on the upper surface of the specimen, and a waveform from the accelerometer is converted into a personal computer via an AD converter. A method for estimating the depth of penetration based on the vibration characteristics of a rigid body simulating a boulder, which is recorded by   3. The method of estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder according to claim 1 or 2, wherein the dimension and weight of the specimen are 0.3 m in length and 0.4 m in width for the first specimen A. The second specimen A has a height of 0.3 m, a width of 0.5 m, a height of 0.4 m, and a weight of 1.38 kN. The first specimen B has a height of 0. 3 m, 0.4 m in width, 0.8 m in height, the second specimen B is 0.3 m in length, 0.8 m in width, 0.4 m in height, and each has a weight of 2.21 kN. A method for estimating the depth of penetration based on the vibration characteristics of a rigid body simulating a boulder. 5. The method for estimating a penetration depth by vibration characteristics of a rigid body simulating a boulder according to claim 4, wherein the target strength of the ground reaction force coefficient kv ₃₀ (MN / m ³ ) is 40-50 and the constructed ground strength is 47.6. The ground type is “soft”, the target strength is 70-80, the ground type with a built ground strength of 79.1 is “medium”, the ground strength with a target strength of 100 or more and the built ground strength is 146 is “hard”. , And placing each of the test specimens on the “soft”, “medium”, and “hard” local boards, and a method for estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder.   3. A method for estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder according to claim 1 or 2, wherein said specimen and ground are modeled and eigenvalue analysis is performed by a three-dimensional finite element method. Of the depth of penetration by the vibration characteristics of a rigid body simulating   7. A method for estimating a penetration depth by vibration characteristics of a rigid body simulating a boulder according to claim 6, wherein the ground density is 0 in order to eliminate the influence of the vibration of the ground itself, and further a statically measured flat plate loading test A rigid body simulating a boulder characterized by analytically reproducing the actual result by evaluating the ground using a value equivalent to twice the dynamic value considering the strain effect of the ground with respect to the equivalent value. Of estimating depth of penetration by vibration characteristics of In the method of estimating the embedment depth due to vibration characteristics of rigid simulating the boulder of claim 6, wherein, following the estimated equation the ground strength and the specimen dimensionless quantity Q ₁ defined for dimensions and Q ₂ as a variable A method for estimating the penetration depth based on the vibration characteristics of a rigid body simulating a boulder, characterized by calculating the natural frequency using
d = 0.358 (f / f ₀ ^* ) − 0.351
Where d is the depth of penetration of the specimen, f is the natural frequency in the presence of the specimen, and f ₀ ^* is the natural frequency when the exposed part of the specimen is considered not to be incorporated. It is. 9. The method of estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder according to claim 8, wherein the dimensionless quantity Q ₁ is {E / (W / A)} ^1/2 and the dimensionless quantity Q ₂ is √ {(b / h ₀ ) ² / (b / h ₀ ) ² +1}. A method for estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder.
Here, E is the modulus of deformation of the specimen, W is the weight of the specimen, and A is a bottom area of the specimen is in contact with the ground, b is specimen blow width, h ₀ is the specimen without embedment It is height. 9. The method of estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder according to claim 8, wherein the specimen has a proportional relationship between the penetration ratio d / h ₀ and the natural frequency. Using the ratio of the natural frequency f in the presence of the natural frequency and the natural frequency f ₀ ^* when the exposed portion of the specimen is considered not to be embedded, A method for estimating a penetration depth based on vibration characteristics of a rigid body simulating a boulder, characterized in that an estimated length is approximated by the estimation formula, and a correlation coefficient of the estimation formula is R ² = 0.926.