Rock mass structural surface rigidity calculation method based on spectrum similarity evaluation

Abstract

The invention relates to a rock mass structural plane rigidity calculation method based on spectrum similarity evaluation, and the method comprises the following steps: 1, arranging a field test, 2, collecting data, 3, assuming a structural plane rigidity initial value, and calculating a waveform, 4, calculating spectrum similarity, and 5, assuming different structural plane rigidity initial values according to step length, and calculating the rigidity of a rock mass structural plane. And step 6, searching a maximum similarity value, and extracting a stiffness value corresponding to the maximum similarity value as a calculation stiffness value of the structural surface.

Description

Technical Field

[0001] The invention relates to a method for calculating rock mass structural surface stiffness, in particular to a method for calculating rock mass structural surface stiffness based on frequency spectrum similarity evaluation, and belongs to the technical field of rock mass structural surface stiffness. Background Art

[0002] In projects related to rock mass, how to analyze and evaluate the stability of rock mass in the project mainly depends on the mechanical properties of structural surfaces such as structural surfaces, cracks, soft and hard interlayers in the rock mass. Structural surface stiffness is an important rock mass deformation parameter and an important basis for analyzing and evaluating the stability of projects in actual projects. At present, in the measurement and calculation of structural surface stiffness, some scholars calculate the shear stiffness of the structural surface at the excitation position based on the amplitude of the transmitted wave and the amplitude of the reflected wave; some scholars use pulse reflection technology to measure the normal stiffness and shear stiffness of the structural surface, etc. The above methods all have certain limitations, so how to accurately obtain the structural surface stiffness is particularly important. Based on one-dimensional time series, the present invention uses stress wave testing technology, uses the results of Euclidean distance normalization to evaluate the similarity of the spectrum, and uses the overall waveform information to accurately reflect the complex mechanical characteristics of the structural surface, thereby accurately calculating the structural surface stiffness. Summary of the invention

[0003] The present invention aims at the technical problems existing in the prior art and provides a method for calculating the stiffness of rock structural surfaces based on spectrum similarity evaluation. The technical solution uses the result of Euclidean distance normalization to evaluate the degree of spectrum similarity, thereby replacing the method in previous studies that the equal area enclosed by the spectrum is equivalent to the equal spectrum, and solves the problems of inability to accurately determine the mechanical parameters of the structural surface, inability to fully utilize the waveform, and high sensitivity between variable parameters and single or multiple test targets.

[0004] In order to achieve the above object, the technical solution of the present invention is as follows: a method for calculating the stiffness of a rock mass structural surface based on spectrum similarity evaluation, the method comprising the following steps:

[0005] Step 1: Arrange field test,

[0006] In the normal direction of the structural surface, measuring points A and B are arranged at equidistant positions on both sides of the structural surface. On the extended measuring line formed by the two points, a point at a distance x from measuring point A is selected as the vibration source point, that is, as the point of action for implementing the impact load. It is stipulated that the structural surface is the center, the side where the vibration source point is located is the incident side, and the other side is the transmission side. The distance between the vibration source point and measuring point A is recorded as x, the distance between the structural surface and measuring point A is recorded as y, and the distance between measuring point B and the structural surface is recorded as z.

[0007] Step 2: Collect data,

[0008] An impact load is generated by knocking at the vibration source point. The vibration waveforms picked up by the acceleration sensor in the x and y directions at the measuring points A and B on both sides of the structural surface are transformed by Fourier transform to obtain the corresponding frequency spectra, which are u P1 、u S1 、u P2 and u S2 ;

[0009] Step 3: Assuming the initial value of the structural surface stiffness, calculate the waveform,

[0010] Assuming an initial value of the structural surface stiffness, the spectrum of the measuring point A is calculated from the spectrum of the transmitted wave at the measuring point B.

[0011] Based on the spherical diffusion theory of stress waves and the spectrum of transmitted longitudinal waves, the calculated spectra of the incident longitudinal wave and the reflected longitudinal wave at measuring point A can be calculated respectively:

[0012]

[0013] in,

[0014]

[0015] Where s1 and s2 are parameters that consider the stress wave propagation process in the rock mass, the stress wave amplitude attenuation caused by the spherical diffusion effect, and the stress wave waveform phase change caused by the propagation distance, respectively. P1 、v P2 is the propagation speed of longitudinal waves in the rock mass; is the circular frequency; are the calculated spectra of the reflected longitudinal wave and the incident longitudinal wave at the measuring point A, respectively; where T P and R P The calculation formula is:

[0016]

[0017] In the formula, K n is the normal stiffness of the structural surface; Z P1 , Z P2 is the wave impedance of the P wave at the incident and transmission sides. The calculated spectrum of the longitudinal wave at the measuring point A can be obtained for:

[0018]

[0019] Step 4: Calculate the spectrum similarity,

[0020] In order to evaluate the difference between the calculated spectrum and the measured spectrum at measuring point A, the Euclidean distance is used to judge the similarity between the measured spectrum and the calculated spectrum at measuring point A. The structural surface stiffness values ​​corresponding to the highest similarity or the smallest difference between the spectra are selected for comparison, and the evaluation methods are compared in terms of sensitivity and accuracy. Euclidean distance formula:

[0021]

[0022] In the formula and are the measured spectrum and the calculated spectrum respectively, d is the Euclidean distance between the two spectra, which evaluates the similarity of the spectra, A x is the amplitude of the measured spectrum.

[0023] Step 5: According to the step length, assuming different initial values ​​of structural surface stiffness, repeat steps 3-4 and calculate their spectral similarity.

[0024] Step 6: Find the maximum similarity value and extract the stiffness value corresponding to the maximum similarity value as the calculated stiffness value of the structural surface.

[0025] Compared with the prior art, the present invention has the following advantages: ① A spectrum similarity evaluation method based on Euclidean distance is established to intuitively evaluate the similarity between spectra, and the stiffness value is calculated using the two columns of spectra with the highest similarity;

[0026] ②Solve the problem that when the spectrum areas are equal, the difference between the spectra is large, which leads to large errors in the calculation of structural surface stiffness;

[0027] ③ Improve the stability of structural surface stiffness calculation results and the accuracy of structural surface stiffness values;

[0028] ④ The requirement on the subjective experience of the calculators can be reduced, and different calculators can obtain the same calculated values ​​according to this scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 The schematic diagram of measuring point arrangement is shown in Figure 2.

[0030] Figure 2 This is a schematic diagram of the measured waveform at the first test point. DETAILED DESCRIPTION

[0031] In order to deepen the understanding of the present invention, the present embodiment is described in detail below with reference to the accompanying drawings.

[0032] Example 1: See Figure 1 , Figure 2 , a method for calculating rock mass structural surface stiffness based on spectrum similarity evaluation, the method comprising the following steps:

[0033] Step 1: Arrange field test. Select a macroscopic structural surface with intact rock mass and flat slope surface on the mining slope of a certain mine for test. The length of the structural surface is measured to be 8.31m and the thickness is 0.28m. Arrange a measuring line in the normal direction of the structural surface, select a measuring point on both sides of the structural surface along the measuring line, arrange the three-axis acceleration sensor at the measuring point, and set the sensor's x direction to be consistent with the measuring line direction, and the sensor's y direction is perpendicular to the x direction. Then the stress wave measured in the x direction is a longitudinal wave, and the stress wave measured in the y direction is a transverse wave.

[0034] Step 2: Collect data, arrange the vibration source point on one side of the structural surface, set measuring point A between the two, and measuring point B on the other side of the structural surface, and set the distances between the vibration source point, measuring point A and measuring point B and the structural surface to 0.39, 0.11 and 0.08m respectively. The vibration waveforms picked up by the acceleration sensors in the x and y directions at measuring points A and B on both sides of the structural surface are Fourier transformed to obtain the corresponding spectrum.

[0035] Step 3: Assuming the initial value of the structural surface stiffness, calculate the waveform,

[0036] Assuming an initial value of the structural surface stiffness, the spectrum of the measuring point A is calculated from the spectrum of the transmitted wave at the measuring point B. The figure shows the measured waveform of the measuring point in the first test.

[0037] Step 4: Calculate the spectrum similarity,

[0038] Step 5: According to the step length, assuming different initial values ​​of structural surface stiffness, repeat steps 3-4 and calculate their spectral similarity.

[0039] Step 6: Find the maximum similarity value, and use the stiffness value corresponding to the maximum similarity value as the calculated stiffness value of the structural surface. The stiffness value of the structural surface is obtained by the calculation method of the present invention, and the results are shown in Table 1:

[0040] Table 1 Field test results

[0041]

[0042] It can be seen from the on-site experimental results of the structural surface stiffness test using the improved algorithm that the stability of the stiffness value calculation results has been greatly improved, and for different groups of experiments, the structural surface stiffness calculation results are roughly the same. At the same time, according to the test results, the variance of the normal stiffness test values ​​of each group of experiments is 0.63, and the variance of the tangential stiffness test values ​​is 0.44.

[0043] The average value of the real and imaginary stiffness of the 9 experiments was taken as the test value of the structural surface stiffness, and the normal stiffness of the structural surface was calculated to be 9.66 GPa·m -1 , the tangential stiffness is 7.04GPa·m -1 .

[0044] It should be noted that the above embodiments are not intended to limit the protection scope of the present invention, and equivalent changes or substitutions made on the basis of the above technical solutions all fall within the protection scope of the claims of the present invention.

Claims

1. A method for calculating rock mass structural surface stiffness based on spectrum similarity evaluation, characterized in that: The method comprises the following steps: Step 1: Arrange field test, Step 2: Collect data, Step 3: Assuming the initial value of the structural surface stiffness, calculate the waveform, Step 4: Calculate the spectrum similarity, Step 5: According to the step length, assuming different initial values ​​of structural surface stiffness, repeat steps 3-4 and calculate their spectral similarity. Step 6: Find the maximum similarity value and extract the stiffness value corresponding to the maximum similarity value as the calculated stiffness value of the structural surface.

2. The method for calculating rock mass structural surface stiffness based on spectrum similarity evaluation according to claim 1, characterized in that: Step 1: Arrange the field test as follows: In the normal direction of the structural surface, measuring points A and B are arranged at equidistant positions on both sides of the structural surface. On the extended measuring line formed by the two points, a point at a distance x from measuring point A is selected as the vibration source point, that is, as the point of action for implementing the impact load. It is stipulated that the structural surface is the center, the side where the vibration source point is located is the incident side, and the other side is the transmission side. The distance between the vibration source point and measuring point A is recorded as x, the distance between the structural surface and measuring point A is recorded as y, and the distance between measuring point B and the structural surface is recorded as z.

3. The method for calculating rock mass structural surface stiffness based on spectrum similarity evaluation according to claim 2 is characterized in that: Step 2: Collect data, as follows: knock at the vibration source point to generate an impact load, and the vibration waveforms picked up by the acceleration sensor in the x and y directions at the measuring points A and B on both sides of the structural surface are transformed by Fourier transform to obtain the corresponding frequency spectra, which are u P1 、u S1 、u P2 and u S2 .

4. The method for calculating rock mass structural surface stiffness based on spectrum similarity evaluation according to claim 3 is characterized in that: Step 3: Assuming the initial value of the structural surface stiffness, calculate the waveform, Assuming an initial value of the structural surface stiffness, the spectrum of the measuring point A is calculated from the spectrum of the transmitted wave at the measuring point B. Based on the spherical diffusion theory of stress waves and the spectrum of the transmitted longitudinal wave, the calculated spectrum of the incident longitudinal wave and the reflected longitudinal wave in the measuring point A are calculated respectively: in, Where s1 and s2 are parameters that consider the stress wave propagation process in the rock mass, the stress wave amplitude attenuation caused by the spherical diffusion effect, and the stress wave waveform phase change caused by the propagation distance, respectively. P1 、v P2 is the propagation speed of longitudinal waves in the rock mass; is the circular frequency; are the calculated spectra of the reflected longitudinal wave and the incident longitudinal wave at the measuring point A, respectively; where T P and R P The calculation formula is: In the formula, K n is the normal stiffness of the structural surface; Z P1 , Z P2 is the wave impedance of the P wave at the incident and transmission sides, and the calculated spectrum of the longitudinal wave at the measuring point A can be obtained for:

5. The method for calculating rock mass structural surface stiffness based on spectrum similarity evaluation according to claim 3, characterized in that: Step 4: Calculate the spectrum similarity as follows: In order to evaluate the difference between the calculated spectrum and the measured spectrum at measuring point A, the Euclidean distance is used to judge the similarity between the measured spectrum and the calculated spectrum at measuring point A. The structural surface stiffness values ​​corresponding to the highest similarity or the smallest difference between the spectra are selected for comparison. The evaluation methods are compared from the aspects of sensitivity and accuracy. The Euclidean distance formula is: In the formula and are the measured spectrum and the calculated spectrum respectively, d is the Euclidean distance between the two spectra, which evaluates the similarity of the spectra, A x is the amplitude of the measured spectrum.

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