Rock-soil mass mechanical detection method and system

Abstract

The invention provides a rock-soil mass mechanical detection method and system, and the method comprises the steps: determining the contribution degree of a friction angle in a rock-soil body to the change of the shear strength of the rock-soil body according to a frequency sequence in the free vibration process of each hollow cylinder sample, and determining the critical point of the rock-soil body from elastic deformation to plastic deformation through the contribution degree; determining the maximum lag caused by the cohesion among the soil particles on the memory effect of the rock-soil body according to the vibration response of each cylinder sample under the forced vibration of different excitation frequencies, and determining the response coefficient of the dynamic shear in the linear viscoelastic area of the rock-soil body and the energy dissipation amount of the nonlinear viscoelastic area according to the maximum lag; and according to the critical point, the response coefficient and the energy dissipation amount, constructing a relation curve of the maximum dynamic shear modulus ratio and the shear strain amplitude of the rock-soil body. By means of the scheme, the conversion process of the rock-soil body between the dynamic characteristics of different mechanical behaviors can be predicted, and then the accuracy of the rock-soil body resonance column test result is improved.

Description

Technical Field

[0001] The present application relates to the field of geotechnical engineering technology, and more specifically, to a method and system for detecting geotechnical body mechanics. Background Art

[0002] Geotechnical engineering is an important branch of civil engineering, which mainly involves the study of soil, rock and their interaction with structures. Geotechnical engineering involves the physical and mechanical properties of soil and rock, engineering properties and their application in engineering projects, such as foundation design, underground structure, tunnel construction, etc. Geotechnical testing of rock and soil is the process of studying and analyzing the mechanical properties of geotechnical materials such as soil and rock through various experimental and testing methods. These tests are aimed at understanding the physical characteristics, mechanical behavior and response of rock and soil under different engineering conditions, and then provide data support for geotechnical engineering design, construction and stability assessment. Existing geotechnical testing includes: rebound modulus test, consolidation test, triaxial compression test, vibration triaxial test and resonant column test.

[0003] The resonant column test obtains the dynamic characteristics of the soil by studying the resonance phenomenon of the rock and soil under different frequency excitations. The existing resonant column test usually forces the cylindrical specimen or hollow cylindrical specimen of the rock and soil to vibrate, and fits the relationship curve between the maximum dynamic shear modulus ratio and the shear strain amplitude of the rock and soil through the data collected during the test. However, in practical applications, the dynamic characteristics of the mechanical behavior of the rock and soil are not constant, that is, when the strain amplitude is small in the resonant column test, the rock and soil has a certain recovery ability for deformation, and the shear modulus ratio of the rock and soil changes linearly and slowly at this time. When the strain amplitude is large, the deformation of the rock and soil is difficult to recover. At this time, the attenuation rate of the shear modulus ratio of the rock and soil increases suddenly and presents complex nonlinear characteristics. The existing technology lacks accurate characterization of the transformation process of the dynamic characteristics of the rock and soil under different mechanical behaviors, resulting in a large error in the curve fitting of the resonant column test. Therefore, how to predict the transformation process between the dynamic characteristics of different mechanical behaviors of the rock and soil, and then improve the accuracy of the resonant column test results of the rock and soil has become a difficult problem faced by the industry. Summary of the invention

[0004] The present application provides a rock and soil mechanical testing method and system, which can predict the transition process between the dynamic characteristics of different mechanical behaviors of the rock and soil, thereby improving the accuracy of the rock and soil resonant column test results.

[0005] In a first aspect, the present application provides a resonant column testing method, which is used in a rock and soil mechanics testing system to perform a resonant column test on a rock and soil body. The method comprises: Prepare multiple hollow cylindrical specimens of rock and soil, perform torsional free vibration tests on all hollow cylindrical specimens using a resonant column instrument, and collect frequency sequences during the vibration of each hollow cylindrical specimen using an intelligent sensor; Based on the attenuation characteristics of each frequency series, the critical point where the rock mass changes from elastic deformation to plastic deformation is determined; Prepare multiple cylindrical samples of different densities of rock and soil, perform axial forced vibration tests on all cylindrical samples of different densities using a resonant column instrument, and collect the vibration response of each cylindrical sample at different excitation frequencies using an intelligent sensor; Determine the maximum hysteresis caused by the cohesion between soil particles on the memory effect of the rock and soil mass according to the relevant characteristics of all vibration responses, and then determine the dynamic shear characteristics of the linear viscoelastic zone of the rock and soil mass and the energy dissipation in the nonlinear viscoelastic zone through the maximum hysteresis; The dynamic mechanical response of the rock mass under different shear strain amplitude changes is predicted according to the critical point, the response coefficient and the energy dissipation, and the relationship curve is filled in the resonant column test report of the rock mass.

[0006] In some embodiments, the torsional free vibration test of all prepared hollow cylindrical specimens by a resonance column instrument specifically includes: Preset multiple torsional exciting forces, wherein each torsional exciting force corresponds to a hollow cylindrical specimen; A hollow cylindrical sample is selected as a selected hollow cylindrical sample, and the selected hollow cylindrical sample is wrapped with a rubber film and then installed in a sample column of a resonance column instrument; Starting the resonance column instrument, applying an exciting force corresponding to the torsional direction of the selected hollow cylindrical sample, and immediately cutting off the power supply of the resonance column instrument, so that the selected hollow cylindrical sample can vibrate freely, until the selected hollow cylindrical sample stops vibrating, thereby completing the free vibration test of the selected hollow cylindrical sample; Continue to complete the free vibration test of the remaining hollow cylindrical specimens.

[0007] In some embodiments, collecting the frequency sequence of each hollow cylindrical specimen during the free vibration test by the intelligent sensor specifically includes: For each hollow cylindrical specimen, the displacement data of each hollow cylindrical specimen during free vibration is collected by the intelligent sensor; The frequency sequence during the test of each hollow cylindrical specimen is determined according to the displacement data.

[0008] In some embodiments, determining the critical point at which the rock mass changes from elastic deformation to plastic deformation based on the attenuation characteristics of each frequency sequence specifically includes: determining the attenuation characteristics of each frequency sequence; Determine a decay sequence based on all decay characteristics; The critical point at which the rock mass changes from elastic deformation to plastic deformation is determined according to the attenuation sequence.

[0009] In some embodiments, performing axial forced vibration tests on all cylindrical samples of different densities by using a resonant column instrument specifically includes: Preset multiple axial stable exciting forces; A cylindrical sample is selected as a selected cylindrical sample, and the selected cylindrical sample is wrapped with a rubber film and installed in the sample column of the resonance column instrument; Starting the resonant column instrument, applying a plurality of axially stable exciting forces, so that the selected cylindrical sample is forced to vibrate under the action of each axially stable exciting force, wherein each axially stable exciting force corresponds to an exciting frequency, and completing a steady-state forced vibration test of the selected cylindrical sample; Continue to complete the steady-state forced vibration test of the remaining cylindrical specimens.

[0010] In some embodiments, dividing the excitation frequency of the rock mass into viscoelastic zones by the maximum hysteresis, and then determining the response coefficient of dynamic shear in the linear viscoelastic zone and the energy dissipation in the nonlinear viscoelastic zone specifically includes: According to the maximum hysteresis, the excitation frequency of the rock-soil body is divided into a linear viscoelastic region and a nonlinear viscoelastic region; Get the vibration response sequence; Determining a response coefficient of dynamic shear in the linear viscoelastic region according to a data segment corresponding to the vibration response sequence in the linear viscoelastic region; The energy dissipation in the nonlinear viscoelastic region is determined according to the data segments corresponding to the vibration response sequence in the nonlinear viscoelastic region.

[0011] In some embodiments, predicting the dynamic mechanical response of the rock mass under different shear strain amplitude changes according to the critical point, the response coefficient and the energy dissipation specifically includes: Determine the linear response curve of the rock and soil body in the linear viscoelastic region according to the response coefficient; Determining a nonlinear response curve of the rock and soil body in a nonlinear viscoelastic region according to the energy dissipation; Determine the mutation point of the shear strain amplitude of the rock and soil body according to the critical point; The dynamic mechanical response of the rock-soil mass under different shear strain amplitude changes is predicted according to the linear response curve, the nonlinear response curve and the mutation point.

[0012] In a second aspect, the present application provides a rock and soil mechanics detection system, the rock and soil mechanics detection system includes a resonant column test unit, and the resonant column test unit includes: The first test module is used to instruct the resonant column instrument to perform a torsional free vibration test on all prepared hollow cylindrical specimens, and collect the frequency sequence of each hollow cylindrical specimen during the free vibration test through an intelligent sensor, wherein the hollow cylindrical specimens are prepared from rock and soil; A first processing module is used to determine the critical point where the rock and soil body changes from elastic deformation to plastic deformation based on the attenuation characteristics of each frequency sequence; The second test module is used to instruct the resonant cylinder instrument to perform axial forced vibration tests on all cylindrical samples of different densities, and collect the vibration response of each cylindrical sample at different excitation frequencies through the intelligent sensor, wherein the cylindrical sample is prepared from rock and soil; The second processing module is used to determine the maximum hysteresis caused by the cohesion between soil particles on the memory effect of the rock and soil body according to the frequency correlation of all vibration responses, and divide the excitation frequency of the rock and soil body into viscoelastic zones according to the maximum hysteresis, so as to determine the response coefficient of dynamic shear in the linear viscoelastic zone and the energy dissipation in the nonlinear viscoelastic zone; The result generation module is used to predict the dynamic mechanical response of the rock mass under different shear strain amplitude changes according to the critical point, the response coefficient and the energy dissipation, and to generate the resonant column test results of the rock mass based on all the dynamic mechanical responses.

[0013] In a third aspect, the present application provides a computer device, comprising a memory and a processor, wherein the memory stores codes, and the processor is configured to obtain the codes and execute the above-mentioned resonant column testing method.

[0014] In a fourth aspect, the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the above-mentioned resonant column testing method is implemented.

[0015] The technical solution provided by the embodiments disclosed in this application has the following beneficial effects: In the rock and soil mechanics testing method and system provided in the present application, firstly, a torsional free vibration test is performed on all prepared hollow cylindrical specimens by a resonant column instrument, and the frequency sequence of each hollow cylindrical specimen during the free vibration test is collected by an intelligent sensor, wherein the hollow cylindrical specimen is prepared from rock and soil; the critical point at which the rock and soil transforms from elastic deformation to plastic deformation is determined based on the attenuation characteristics of each frequency sequence; an axial forced vibration test is performed on all cylindrical specimens of different densities by a resonant column instrument, and the frequency sequence of each cylindrical specimen under different excitations is collected by an intelligent sensor. The invention discloses a method for preparing a vibration response of a rock-soil body under a certain frequency, wherein a cylindrical specimen is prepared from a rock-soil body; determining a maximum hysteresis caused by the cohesion between soil particles on the memory effect of the rock-soil body according to the frequency correlation of all vibration responses, dividing the excitation frequency of the rock-soil body into viscoelastic zones according to the maximum hysteresis, and then determining the response coefficient of dynamic shear in the linear viscoelastic zone and the energy dissipation in the nonlinear viscoelastic zone; predicting the dynamic mechanical response of the rock-soil body under different shear strain amplitude changes according to the critical point, the response coefficient and the energy dissipation, and generating a resonant column test result of the rock-soil body based on all dynamic mechanical responses.

[0016] It can be seen that the present application first performs a torsional free vibration test on a hollow cylindrical specimen of the rock mass, and extracts the transition point of the dynamic characteristics of the rock mass through the attenuation characteristics of the test results, that is, the critical point where the rock mass changes from elastic deformation to plastic deformation. Then, an axial forced vibration test is performed on the cylindrical specimen of the rock mass to extract the important mechanical characteristics of the rock mass in different characteristic ranges (that is, the linear viscoelastic region and the nonlinear viscoelastic region) (that is, the response coefficient of dynamic shear and the energy dissipation). Finally, the critical point, the response coefficient and the energy dissipation are used to fit the test results (that is, the relationship curve between the maximum dynamic shear modulus ratio and the shear strain amplitude). In summary, the present application can predict the transition process between the dynamic characteristics of different mechanical behaviors of the rock mass, thereby improving the accuracy of the test results of the resonant column of the rock mass. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is an exemplary flow chart of a resonant column testing method according to some embodiments of the present application; Figure 2 is an exemplary flow chart for implementing a free vibration test according to some embodiments of the present application; Figure 3 is a schematic structural diagram of a resonance column instrument according to some embodiments of the present application; Figure 4 is a schematic structural diagram of a resonant column test unit according to some embodiments of the present application; Figure 5 It is a schematic diagram of the structure of a computer device for implementing a resonant column testing method according to some embodiments of the present application. DETAILED DESCRIPTION

[0018] In order to better understand the technical solution of the present application, the technical solution of the present application will be described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0019] refer to Figure 1 , which is an exemplary flow chart of a resonant column testing method according to some embodiments of the present application, wherein the resonant column testing method 100 mainly comprises the following steps: In step 101, a torsional free vibration test is performed on all prepared hollow cylindrical specimens by using a resonant column instrument, and a frequency sequence of each hollow cylindrical specimen during the free vibration test is collected by an intelligent sensor, wherein the hollow cylindrical specimens are prepared from rock and soil.

[0020] In some embodiments, before performing a torsional free vibration test on all prepared hollow cylindrical specimens by using a resonant column instrument, the method further includes: preparing a plurality of hollow cylindrical specimens of the rock and soil body.

[0021] In specific implementation, the preparation of multiple hollow cylindrical specimens of rock and soil can be achieved in the following manner, namely: first, collect samples of the rock and soil in the test area, sieve the samples, and prepare twenty hollow cylindrical specimens using the disturbed soil specimen preparation method in the "GBT50123-2019 Geotechnical Test Method Standard", wherein the consolidation confining pressure and moisture content are the same each time the specimen is prepared. For example, in this application, the consolidation confining pressure is set to 200 kPa and the moisture content is set to 14% each time the specimen is prepared.

[0022] In some embodiments, reference Figure 2 , which is an exemplary flow chart of implementing free vibration testing according to some embodiments of the present application. In the present application, the free vibration test in torsional direction of all prepared hollow cylindrical specimens by a resonance column instrument can be implemented by the following steps: In step 1011, a plurality of torsional exciting forces are preset, wherein each torsional exciting force corresponds to a hollow cylindrical specimen; In step 1012, a hollow cylindrical sample is selected as a selected hollow cylindrical sample, and the selected hollow cylindrical sample is wrapped with a rubber film and installed in a sample column of a resonance column instrument; In step 1013, the resonance column instrument is started, an exciting force corresponding to the torsional direction of the selected hollow cylindrical sample is applied, and the power supply of the resonance column instrument is immediately cut off to allow the selected hollow cylindrical sample to vibrate freely until the selected hollow cylindrical sample stops vibrating, thereby completing the free vibration test of the selected hollow cylindrical sample; In step 1014, the free vibration test of the remaining hollow cylindrical specimens is continued to be completed.

[0023] In specific implementation, the torsional exciting force in this application can be preset according to actual needs. For example, if there are 20 hollow cylindrical specimens in this application, the torsional exciting force is preset to 20 values ​​starting from 0.1N and increasing by 0.5N each time, that is, preset to 0.1N, 0.6N, 1.1N,...10.1N.

[0024] In some embodiments, the frequency sequence of each hollow cylindrical specimen collected during the free vibration test by the intelligent sensor can be implemented by the following steps: For each hollow cylindrical specimen, the displacement data of each hollow cylindrical specimen during free vibration is collected by the intelligent sensor; The frequency sequence during the test of each hollow cylindrical specimen is determined according to the displacement data.

[0025] In specific implementation, the displacement data of each hollow cylindrical sample during the free vibration process can be collected by the intelligent sensor in the following manner, namely: after cutting off the power supply of the resonance column instrument, the displacement value of each hollow cylindrical sample during the free vibration process is collected by the intelligent sensor at preset intervals, and all the collected displacement values ​​are sorted in the order of collection, and the obtained sequence is used as the displacement data of each hollow cylindrical sample during the free vibration process.

[0026] In specific implementation, the frequency sequence during the test of each hollow cylindrical specimen can be determined based on the displacement data in the following manner, namely: for the displacement data of each hollow cylindrical specimen, the instantaneous frequency corresponding to each displacement value in the displacement data can be calculated by the Hilbert transform in the prior art, and then all the instantaneous frequencies are arranged in order, and the obtained sequence is used as the frequency sequence during the test of the hollow cylindrical specimen.

[0027] In some embodiments, reference Figure 3 , which is a schematic diagram of the structure of a resonance column instrument according to some embodiments of the present application, and is specifically described as follows: Passive end cover plate 1, used to fix one end face of the sample and ensure that the sample does not move during the test; A sample column 2, used for containing a sample; The active end seat plate 3 is used to transmit the external exciting force to drive the sample to vibrate; Torsional vibration spring 4, providing torsional stiffness, used to control and adjust the exciting force in the torsional direction; Torsional vibration damper 5, used to control and reduce the vibration amplitude of the instrument in the torsional direction to avoid damage to the instrument; Axial spring 6, providing axial stiffness, used to control and adjust the axial exciting force; The axial damper 7 is used to control and reduce the axial vibration amplitude of the instrument to avoid damage to the instrument.

[0028] It should be noted that the smart sensor in this application refers to an integrated sensor that collects displacement, vibration frequency and vibration amplitude, which will not be described in detail here.

[0029] In step 102, a critical point at which the soil mass changes from elastic deformation to plastic deformation is determined based on the attenuation characteristics of each frequency sequence.

[0030] In some embodiments, determining the critical point at which the rock mass changes from elastic deformation to plastic deformation based on the attenuation characteristics of each frequency sequence can be achieved by using the following steps: determining the attenuation characteristics of each frequency sequence; Determine a decay sequence based on all decay characteristics; The critical point at which the rock mass changes from elastic deformation to plastic deformation is determined according to the attenuation sequence.

[0031] In specific implementation, the attenuation characteristics of each frequency sequence can be determined in the following manner, namely: the damping ratio of each frequency sequence can be calculated by the formula mentioned in Chapter 10.4.5 (Resonant Column Test-Data Processing-Torsional Damping Ratio) of "GBT50269-2015 Foundation Dynamic Characteristics Test Specification", and each damping ratio is used as the attenuation characteristic of the corresponding frequency sequence. In other embodiments, the attenuation characteristics of each frequency sequence can also be determined by other existing technologies, which is not limited here.

[0032] It should be noted that the attenuation characteristic in the present application is a parameter value indicating how fast the energy of the hollow cylindrical specimen decays during the vibration process. The larger the attenuation characteristic, the faster the energy of the hollow cylindrical specimen decays during the vibration process. The smaller the attenuation characteristic, the slower the energy of the hollow cylindrical specimen decays during the vibration process. Generally speaking, the larger the attenuation characteristic, the greater the material strength of the rock and soil body, that is, the less likely it is to deform.

[0033] In specific implementation, determining the attenuation sequence according to all attenuation characteristics can be achieved in the following manner: first, obtaining the torsional exciting force corresponding to each attenuation characteristic in the free vibration test, and then arranging all the attenuation characteristics from small to large according to the size of the corresponding torsional exciting force, and using the obtained sequence as the attenuation sequence.

[0034] It should be noted that the attenuation sequence in the present application is a sequence that describes the change in the material strength of the rock and soil mass with the applied exciting force.

[0035] In specific implementation, determining the critical point at which the rock and soil body changes from elastic deformation to plastic deformation according to the attenuation sequence can be achieved in the following manner, namely: first, subtracting the average value of the attenuation sequence from each attenuation characteristic in the attenuation sequence to obtain a zero-mean attenuation sequence k, then adding the products between every two values ​​with the same interval in the sequence k, arranging the absolute values ​​of the obtained sums from small to large according to the size of the interval to obtain a sequence f, comparing each value in the sequence f with a preset threshold in turn, and recording the interval corresponding to the first value less than the threshold as a parameter p, and finally, using the pth torsional excitation force after arranging the torsional excitation forces from small to large as the critical point at which the rock and soil body changes from elastic deformation to plastic deformation according to the attenuation sequence, wherein every two values ​​with the same interval refer to two values ​​with the same interval in the attenuation sequence, for example, the interval between the first value and the third value in the attenuation sequence is 2 (i.e., 3-1=2), and the interval between the fifth value and the third value in the attenuation sequence is 2, then the interval between the first value and the third value is the same as the interval between the fifth value and the third value.

[0036] It should be noted that the threshold value preset in the step of determining the critical point in the present application is a smaller value greater than zero. For example, the threshold value is preset to 0.05 in the present application. In other embodiments, the threshold value can also be preset to other smaller values ​​greater than zero.

[0037] It should be noted that the critical point in the present application refers to the critical exciting force for the rock and soil to transform from elastic deformation to plastic deformation. When an exciting force below the critical point is applied to the rock and soil, the rock and soil exhibits elastic deformation during the vibration process. When an exciting force above the critical point is applied to the rock and soil, the rock and soil exhibits plastic deformation during the vibration process.

[0038] In step 103, an axial forced vibration test is performed on all cylindrical samples of different densities by using a resonant column instrument, and the vibration response of each cylindrical sample at different excitation frequencies is collected by an intelligent sensor, wherein the cylindrical samples are prepared from rock and soil.

[0039] In some embodiments, before performing axial forced vibration tests on all cylindrical samples of different densities by using a resonant column instrument, the method further includes: preparing a plurality of cylindrical samples of different densities of the rock and soil body.

[0040] In specific implementation, the preparation of multiple cylindrical specimens of different densities of rock and soil can be achieved in the following manner, namely: first, collect samples of the rock and soil in the test area, sieve the samples, and then use the disturbed soil sample preparation method in the "GBT50123-2019 Geotechnical Test Method Standard" to prepare multiple cylindrical specimens under different consolidation confining pressures (each consolidation confining pressure corresponds to a density), wherein the moisture content is the same each time the sample is prepared. For example, in this application, the moisture content is set to 14% each time the sample is prepared. Furthermore, different densities are multiple densities preset according to actual needs. For example, 10 different consolidation confining pressures can be arbitrarily selected from the range of 200 to 600 kPa.

[0041] In some embodiments, the axial forced vibration test of all cylindrical specimens of different densities by a resonant column instrument can be implemented by the following steps: Preset multiple axial stable exciting forces; A cylindrical sample is selected as a selected cylindrical sample, and the selected cylindrical sample is wrapped with a rubber film and installed in the sample column of the resonance column instrument; The resonant column instrument is started, and a plurality of axially stable exciting forces are applied to force the selected cylindrical sample to vibrate under the action of each axially stable exciting force, wherein each axially stable exciting force corresponds to an exciting frequency, and a steady-state forced vibration test of the selected cylindrical sample is completed; Continue to complete the steady-state forced vibration test of the remaining cylindrical specimens.

[0042] It should be noted that the axially stable exciting force in the present application is preset according to actual needs. For example, in the present application, the axially stable exciting force can be preset to 20 values ​​starting from 0.1N and increasing by 0.5N each time, that is, preset to 0.1N, 0.6N, 1.1N,...10.1N.

[0043] In specific implementation, the vibration response of each cylindrical sample at different excitation frequencies can be collected by an intelligent sensor in the following manner, namely: for each excitation frequency of each cylindrical sample, when the cylindrical sample and the resonance column instrument are in a resonant state, the vibration frequency of the cylindrical sample at the excitation frequency is collected by the intelligent sensor, and the vibration frequency is used as the vibration response of the cylindrical sample at the excitation frequency, thereby obtaining the vibration response of each cylindrical sample at different excitation frequencies.

[0044] In step 104, the maximum hysteresis caused by the cohesion between soil particles on the memory effect of the rock and soil body is determined based on the frequency correlation of all vibration responses, and the excitation frequency of the rock and soil body is divided into viscoelastic zones according to the maximum hysteresis, thereby determining the response coefficient of dynamic shear in the linear viscoelastic zone and the energy dissipation in the nonlinear viscoelastic zone.

[0045] In some embodiments, determining the maximum hysteresis caused by the cohesion between soil particles on the memory effect of the rock and soil mass based on the frequency correlation of all vibration responses can be achieved in the following manner, namely: converting all vibration responses into vibration response sequences; Determining the frequency correlation of the rock-soil body's response between every two adjacent excitation frequencies according to the vibration response sequence; The maximum hysteresis caused by the cohesion between soil particles on the memory effect of the rock mass is determined based on all frequency dependencies.

[0046] In specific implementation, converting all vibration responses into vibration response sequences can be achieved in the following manner, namely: first, for each cylindrical specimen, all vibration responses of each cylindrical specimen can be arranged from small to large according to the corresponding excitation frequency, and the obtained sequence is used as the response subsequence of each cylindrical specimen, and then, the response subsequence of each cylindrical specimen is multiplied by the square root of the consolidation confining pressure when each cylindrical specimen is prepared, and all the multiplied sequences are added together, and then, the added sequence is divided by the total number of cylindrical specimens, and finally, the sequence obtained by dividing by the total number of cylindrical specimens is used as the vibration response sequence.

[0047] It should be noted that the vibration response sequence in this application is a sequence that describes the change of the resonant frequency of the rock and soil body under external excitation.

[0048] In specific implementation, determining the frequency correlation of the response of the rock and soil body between every two adjacent excitation frequencies according to the vibration response sequence can be achieved in the following manner, namely: for the i-th data in the vibration response sequence, calculating the partial autocorrelation coefficient of the vibration response sequence at lag i, using the partial autocorrelation coefficient as the frequency correlation of the response between the i-th excitation frequency and the i-1-th excitation frequency, and then obtaining the frequency correlation of the response of the rock and soil body between every two adjacent excitation frequencies.

[0049] It should be noted that the frequency correlation in the present application is a parameter that represents the dependence of the dynamic behavior of the rock and soil body on different excitation frequencies. The greater the frequency correlation, the greater the dependence of the dynamic behavior of the rock and soil body on different excitation frequencies, that is, the more correlated the change in the resonant frequency of the rock and soil body is with the change in the excitation frequency. The smaller the frequency correlation, the smaller the dependence of the dynamic behavior of the rock and soil body on different excitation frequencies, that is, the less correlated the change in the resonant frequency of the rock and soil body is with the change in the excitation frequency.

[0050] In specific implementation, the maximum hysteresis caused by the memory effect of the cohesion between soil particles on the rock and soil body can be determined according to all frequency correlations. That is, first, all frequency correlations are arranged in the order of corresponding hysteresis from small to large, and then, each frequency correlation in the arranged sequence is compared with a preset coupling threshold, and the hysteresis corresponding to the frequency correlation that is first less than the coupling threshold is taken as the maximum hysteresis caused by the memory effect of the cohesion between soil particles on the rock and soil body.

[0051] It should be noted that the maximum lag in the present application is a parameter value that measures the maximum lag time of the response of the rock and soil body when subjected to external vibration. The larger the maximum lag, the longer the maximum lag time of the response of the rock and soil body when subjected to external vibration. The smaller the maximum lag, the shorter the maximum lag time of the response of the rock and soil body when subjected to external vibration. After being subjected to external vibration, due to the cohesion between the soil particles of the rock and soil body, the deformation or mechanical properties of the rock and soil body will delay the response.

[0052] In some embodiments, the viscoelastic division of the excitation frequency of the rock mass by the maximum hysteresis, and then determining the response coefficient of dynamic shear in the linear viscoelastic zone and the energy dissipation in the nonlinear viscoelastic zone can be achieved by the following steps, namely: According to the maximum hysteresis, the excitation frequency of the rock-soil body is divided into a linear viscoelastic region and a nonlinear viscoelastic region; Get the vibration response sequence; Determining a response coefficient of dynamic shear in the linear viscoelastic region according to a data segment corresponding to the vibration response sequence in the linear viscoelastic region; The energy dissipation in the nonlinear viscoelastic region is determined according to the data segments corresponding to the vibration response sequence in the nonlinear viscoelastic region.

[0053] It should be noted that the linear viscoelastic zone in the present application refers to the interval in which the stress-strain relationship of the rock and soil body follows a linear law, and the nonlinear viscoelastic zone refers to the interval in which the stress-strain relationship of the rock and soil body does not follow a linear law. As a preferred embodiment, the present application divides the excitation frequency of the rock and soil body into a linear viscoelastic zone and a nonlinear viscoelastic zone according to the maximum hysteresis, which can be achieved in the following manner, namely: the interval from zero to the maximum hysteresis is used as a linear viscoelastic zone, and the interval greater than the maximum hysteresis is used as a nonlinear viscoelastic zone.

[0054] In specific implementation, determining the response coefficient of dynamic shear in the linear viscoelastic region according to the data segment corresponding to the vibration response sequence in the linear viscoelastic region can be achieved in the following manner, namely: first, obtaining the resonance amplitude corresponding to each excitation frequency in the forced vibration test, and then taking the reciprocal of the square of all excitation frequencies in the linear viscoelastic region as the dependent variable, and taking the resonance amplitude corresponding to each excitation frequency as the independent variable, fitting to a curve with a maximum term of quadratic through the least squares method in the prior art, and then taking the coefficient of the quadratic term in the fitting curve as the response coefficient of dynamic shear in the linear viscoelastic region.

[0055] It should be noted that the response coefficient in this application is a parameter value that measures the sensitivity of the change of the dynamic shear characteristics of the rock and soil in the linear viscoelastic zone to the external excitation response. The larger the response coefficient, the more sensitive the change of the dynamic shear characteristics of the rock and soil in the linear viscoelastic zone to the external excitation response. The smaller the response coefficient, the less sensitive the change of the dynamic shear characteristics of the rock and soil in the linear viscoelastic zone to the external excitation response.

[0056] In a specific implementation, determining the energy dissipation in the nonlinear viscoelastic zone according to the data segment corresponding to the vibration response sequence in the nonlinear viscoelastic zone can be achieved in the following manner, namely: first, obtaining the resonance amplitude corresponding to each excitation frequency in the forced vibration test, and then taking the reciprocal of the square of all excitation frequencies in the nonlinear viscoelastic zone as the dependent variable, and taking the resonance amplitude corresponding to each excitation frequency as the independent variable, fitting to a curve with a maximum term of quadratic through the least squares method in the prior art, and then taking the coefficient of the linear term in the fitting curve as the energy dissipation in the nonlinear viscoelastic zone.

[0057] It should be noted that the energy dissipation in the present application is a parameter value that measures the degree of energy loss caused by external excitation due to changes in mechanical properties of the rock and soil in the nonlinear viscoelastic zone. The greater the energy dissipation, the more energy loss caused by external excitation due to changes in mechanical properties of the rock and soil in the nonlinear viscoelastic zone. The smaller the energy dissipation, the less energy loss caused by external excitation due to changes in mechanical properties of the rock and soil in the nonlinear viscoelastic zone. In the nonlinear viscoelastic zone, part of the external excitation force is used to destroy the rock and soil structure, and at this time the internal structure of the rock and soil is loose, and losses will occur when the excitation force is transmitted between the particles of the rock and soil.

[0058] In addition, it should be noted that the resonance amplitude corresponding to each excitation frequency in the forced vibration test in the present application can be achieved in the following manner, namely: for each excitation frequency of each cylindrical specimen, when the cylindrical specimen and the resonance column instrument are in a resonant state, the vibration amplitude of the cylindrical specimen at the excitation frequency is collected by the intelligent sensor, and then, the average value of the vibration amplitudes of all cylindrical specimens at the same excitation frequency is taken as the resonance amplitude corresponding to the corresponding excitation frequency, thereby obtaining the resonance amplitude corresponding to each excitation frequency in the forced vibration test.

[0059] In step 105, the dynamic mechanical response of the rock mass under different shear strain amplitude changes is predicted according to the critical point, the response coefficient and the energy dissipation, and the resonant column test result of the rock mass is generated based on all the dynamic mechanical responses.

[0060] In some embodiments, the prediction of the dynamic mechanical response of the rock mass under different shear strain amplitude changes according to the critical point, the response coefficient and the energy dissipation can be achieved in the following manner, namely: Determine the linear response curve of the rock and soil body in the linear viscoelastic region according to the response coefficient; Determining a nonlinear response curve of the rock and soil body in a nonlinear viscoelastic region according to the energy dissipation; Determine the mutation point of the shear strain amplitude of the rock and soil body according to the critical point; The dynamic mechanical response of the rock-soil mass under different shear strain amplitude changes is predicted according to the linear response curve, the nonlinear response curve and the mutation point.

[0061] In specific implementation, the linear response curve of the rock and soil body in the linear viscoelastic zone can be determined according to the response coefficient in the following manner, namely: first, the first-order coefficient of the curve in the process of determining the response coefficient is obtained, and the response coefficient is divided by the first-order coefficient to obtain the parameter v. Finally, y=1 / (1+vx) is used as the linear response curve of the rock and soil body in the linear viscoelastic zone, wherein y is the maximum dynamic shear modulus ratio of the rock and soil body, and x is the shear strain amplitude.

[0062] It should be noted that the linear response curve in this application is a curve that describes the mechanical properties of rock and soil in the linear viscoelastic region.

[0063] In a specific implementation, the nonlinear response curve of the rock and soil body in the nonlinear viscoelastic zone is determined according to the energy dissipation. First, the quadratic term coefficient of the curve in the process of determining the energy dissipation is obtained, and the quadratic term coefficient is divided by the energy dissipation to obtain the parameter u. Finally, y=1 / (1+ux) is used as the linear response curve of the rock and soil body in the linear viscoelastic zone, wherein y is the maximum dynamic shear modulus ratio of the rock and soil body, and x is the shear strain amplitude.

[0064] It should be noted that the nonlinear response curve in this application is a curve that describes the mechanical properties of rock and soil in the non-linear viscoelastic region.

[0065] In specific implementation, determining the mutation point of the shear strain amplitude of the rock and soil body according to the critical point can be achieved in the following manner, namely: first, obtaining the magnitude of the torsional exciting force corresponding to the critical point, and then preparing a cylindrical rock and soil sample with a consolidation confining pressure of 200 kPa, a water content of 14%, and a length of 10 cm, and performing a forced vibration test on the cylindrical sample using a resonance column instrument, wherein the magnitude of the axial exciting force applied in the forced vibration test is the same as the magnitude of the torsional exciting force corresponding to the critical point, and then collecting the resonance amplitude when the cylindrical sample resonates with the resonance column instrument, dividing the resonance amplitude by the length of the cylindrical sample, and using the obtained value as the mutation point of the shear strain amplitude of the rock and soil body.

[0066] It should be noted that the mutation point in this application refers to the critical shear strain amplitude at which the rock and soil mass changes from elastic deformation to plastic deformation.

[0067] In specific implementation, the following method can be used to predict the dynamic mechanical response of the rock-soil mass under different shear strain amplitude changes according to the linear response curve, the nonlinear response curve and the mutation point, namely: the curve with the abscissa before the mutation point in the linear response curve is connected with the curve with the abscissa after the mutation point in the nonlinear response curve, and the obtained curve is used as the relationship curve between the maximum dynamic shear modulus ratio of the rock-soil mass and the shear strain amplitude. Finally, any shear strain amplitude is used as the abscissa of the relationship curve, and the ordinate corresponding to the abscissa in the relationship curve is the dynamic mechanical response of the rock-soil mass, thereby obtaining the dynamic mechanical response of the rock-soil mass under different shear strain amplitude changes.

[0068] It should be noted that the dynamic mechanical response in this application refers to the maximum dynamic shear modulus ratio of the rock and soil mass.

[0069] In specific implementation, the resonant column test results of the rock and soil mass can be generated based on all dynamic mechanical responses in the following manner, namely: taking all dynamic mechanical responses as dependent variables and all shear strain amplitudes as independent variables, drawing a test curve of the resonant column test of the rock and soil mass, and taking the test curve as the resonant column test result of the rock and soil mass.

[0070] In addition, in another aspect of the present application, in some embodiments, the present application provides a rock and soil mechanics detection system, the rock and soil mechanics detection system includes a resonant column test unit, referring to Figure 2 , which is a schematic diagram of the structure of a resonant column test unit according to some embodiments of the present application, the resonant column test unit 400 includes: a first test module 401, a first processing module 402, a second test module 403, a second processing module 404 and a result generation module 405, which are respectively described as follows: The first test module 401, in the present application, is mainly used to instruct the resonant column instrument to perform a torsional free vibration test on all prepared hollow cylindrical samples, and to collect the frequency sequence of each hollow cylindrical sample during the free vibration test through an intelligent sensor, wherein the hollow cylindrical sample is prepared from a rock and soil body; A first processing module 402, in the present application, the first processing module 402 is mainly used to determine the critical point at which the rock and soil body changes from elastic deformation to plastic deformation based on the attenuation characteristics of each frequency sequence; The second test module 403, in the present application, is mainly used to instruct the resonant cylinder instrument to perform axial forced vibration tests on all cylindrical samples of different densities, and collect the vibration response of each cylindrical sample at different excitation frequencies through the intelligent sensor, wherein the cylindrical sample is prepared from rock and soil; The second processing module 404, in the present application, is mainly used to determine the maximum hysteresis caused by the cohesion between soil particles on the memory effect of the rock and soil body according to the frequency correlation of all vibration responses, and to divide the excitation frequency of the rock and soil body into viscoelastic zones according to the maximum hysteresis, so as to determine the response coefficient of dynamic shear in the linear viscoelastic zone and the energy dissipation in the nonlinear viscoelastic zone; The result generation module 405 in the present application is mainly used to predict the dynamic mechanical response of the rock mass under different shear strain amplitude changes according to the critical point, the response coefficient and the energy dissipation, and to generate the resonant column test results of the rock mass based on all the dynamic mechanical responses.

[0071] In addition, the present application also provides a computer device, which includes a memory and a processor, wherein the memory stores codes, and the processor is configured to obtain the codes and execute the above-mentioned resonant column testing method.

[0072] In some embodiments, reference Figure 5 , which is a schematic diagram of the structure of a computer device for implementing a resonant column testing method according to some embodiments of the present application. The resonant column testing method in the above embodiment can be Figure 5 The computer device 500 shown in the figure is implemented, and the computer device 500 includes at least one processor 501, a communication bus 502, a memory 503 and at least one communication interface 504.

[0073] The processor 501 may be a general-purpose central processing unit (CPU) or an application specific integrated circuit (ASIC).

[0074] The communication bus 502 may be used to transmit information between the above-mentioned components.

[0075] The memory 503 may be a read-only memory (ROM) or other types of static storage devices that can store static information and instructions, a random access memory (RAM) or other types of dynamic storage devices that can store information and instructions, or an electrically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CDROM) or other optical disc storage, optical disc storage (including compressed optical disc, laser disc, optical disc, digital versatile disc, Blu-ray disc, etc.), a magnetic disk or other magnetic storage device, or any other medium that can be used to carry or store the desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto. The memory 503 may exist independently and be connected to the processor 501 through the communication bus 502. The memory 503 may also be integrated with the processor 501.

[0076] The memory 503 is used to store the program code for executing the solution of the present application, and the execution is controlled by the processor 501. The processor 501 is used to execute the program code stored in the memory 503. The program code may include one or more software modules. The resonant column testing method in the above embodiment can be implemented by the processor 501 and one or more software modules in the program code in the memory 503.

[0077] The communication interface 504 uses any transceiver or other device for communicating with other devices or communication networks, such as Ethernet, radio access network (RAN), wireless local area networks (WLAN), etc.

[0078] In a specific implementation, as an embodiment, a computer device may include multiple processors, each of which may be a single-core (singleCPU) processor or a multi-core (multiCPU) processor. The processor here may refer to one or more devices, circuits, and / or processing cores for processing data (such as computer program instructions).

[0079] The above-mentioned computer device may be a general-purpose computer device or a special-purpose computer device. In a specific implementation, the computer device may be a desktop computer, a portable computer, a network server, a personal digital assistant (PDA), a mobile phone, a tablet computer, a wireless terminal device, a communication device or an embedded device. The embodiment of the present application does not limit the type of computer device.

[0080] In addition, the present application also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the above-mentioned resonant column testing method is implemented.

[0081] In summary, in the rock and soil mechanics detection method and system disclosed in the embodiment of the present application, first, a torsional free vibration test is performed on all prepared hollow cylindrical specimens by a resonant column instrument, and the frequency sequence of each hollow cylindrical specimen during the free vibration test is collected by an intelligent sensor, wherein the hollow cylindrical specimen is prepared from rock and soil; the critical point at which the rock and soil transforms from elastic deformation to plastic deformation is determined based on the attenuation characteristics of each frequency sequence; an axial forced vibration test is performed on all cylindrical specimens of different densities by a resonant column instrument, and the frequency sequence of each cylindrical specimen during the free vibration test is collected by an intelligent sensor. Vibration response under different excitation frequencies, wherein a cylindrical specimen is prepared from rock and soil; the maximum hysteresis caused by the cohesion between soil particles on the memory effect of the rock and soil is determined based on the frequency correlation of all vibration responses, and the excitation frequency of the rock and soil is divided into viscoelastic zones according to the maximum hysteresis, thereby determining the response coefficient of dynamic shear in the linear viscoelastic zone and the energy dissipation in the nonlinear viscoelastic zone; the dynamic mechanical response of the rock and soil under different shear strain amplitude changes is predicted based on the critical point, the response coefficient and the energy dissipation, and the resonant column test results of the rock and soil are generated based on all the dynamic mechanical responses.

[0082] It can be seen that the present application first performs a torsional free vibration test on a hollow cylindrical specimen of the rock mass, and extracts the transition point of the dynamic characteristics of the rock mass through the attenuation characteristics of the test results, that is, the critical point where the rock mass changes from elastic deformation to plastic deformation. Then, an axial forced vibration test is performed on the cylindrical specimen of the rock mass to extract the important mechanical characteristics of the rock mass in different characteristic ranges (that is, the linear viscoelastic region and the nonlinear viscoelastic region) (that is, the response coefficient of dynamic shear and the energy dissipation). Finally, the critical point, the response coefficient and the energy dissipation are used to fit the test results (that is, the relationship curve between the maximum dynamic shear modulus ratio and the shear strain amplitude). In summary, the present application can predict the transition process between the dynamic characteristics of different mechanical behaviors of the rock mass, thereby improving the accuracy of the test results of the resonant column of the rock mass.

[0083] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0084] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A resonant column test method, used in a rock and soil mechanics detection system to perform a resonant column test on a rock and soil body, characterized in that: The method includes: A resonant column instrument is used to perform a torsional free vibration test on all prepared hollow cylindrical specimens, and an intelligent sensor is used to collect the frequency sequence of each hollow cylindrical specimen during the free vibration test, wherein the hollow cylindrical specimens are prepared from rock and soil; Based on the attenuation characteristics of each frequency series, the critical point where the rock mass changes from elastic deformation to plastic deformation is determined; Axial forced vibration tests are performed on all cylindrical specimens of different densities by using a resonant cylinder instrument, and the vibration responses of each cylindrical specimen at different excitation frequencies are collected by using an intelligent sensor, wherein the cylindrical specimens are prepared from rock and soil. The maximum hysteresis caused by the cohesion between soil particles on the memory effect of the rock and soil mass is determined according to the frequency correlation of all vibration responses, and the excitation frequency of the rock and soil mass is divided into viscoelastic zones according to the maximum hysteresis, so as to determine the response coefficient of dynamic shear in the linear viscoelastic zone and the energy dissipation in the nonlinear viscoelastic zone; The dynamic mechanical response of the rock mass under different shear strain amplitude changes is predicted according to the critical point, the response coefficient and the energy dissipation, and the resonant column test result of the rock mass is generated based on all the dynamic mechanical responses.

2. The method according to claim 1, characterized in that The torsional free vibration test of all prepared hollow cylindrical specimens by resonance column instrument includes: Preset multiple torsional exciting forces, wherein each torsional exciting force corresponds to a hollow cylindrical specimen; A hollow cylindrical sample is selected as a selected hollow cylindrical sample, and the selected hollow cylindrical sample is wrapped with a rubber film and then installed in a sample column of a resonance column instrument; Starting the resonance column instrument, applying an exciting force corresponding to the torsional direction of the selected hollow cylindrical sample, and immediately cutting off the power supply of the resonance column instrument, so that the selected hollow cylindrical sample can vibrate freely, until the selected hollow cylindrical sample stops vibrating, thereby completing the free vibration test of the selected hollow cylindrical sample; Continue to complete the free vibration test of the remaining hollow cylindrical specimens.

3. The method according to claim 1, characterized in that The frequency sequence collected by intelligent sensors during the free vibration test of each hollow cylindrical specimen specifically includes: For each hollow cylindrical specimen, the displacement data of each hollow cylindrical specimen during free vibration is collected by the intelligent sensor; The frequency sequence during the test of each hollow cylindrical specimen is determined according to the displacement data.

4. The method according to claim 1, characterized in that Based on the attenuation characteristics of each frequency sequence, the critical point of the transition from elastic deformation to plastic deformation of the rock and soil mass is determined, including: determining the attenuation characteristics of each frequency sequence; Determine a decay sequence based on all decay characteristics; The critical point at which the rock mass changes from elastic deformation to plastic deformation is determined according to the attenuation sequence.

5. The method according to claim 1, characterized in that The axial forced vibration test of all cylindrical specimens of different densities by resonance column instrument includes: Preset multiple axial stable exciting forces; A cylindrical sample is selected as a selected cylindrical sample, and the selected cylindrical sample is wrapped with a rubber film and installed in the sample column of the resonance column instrument; The resonant column instrument is started, and a plurality of axially stable exciting forces are applied to force the selected cylindrical sample to vibrate under the action of each axially stable exciting force, wherein each axially stable exciting force corresponds to an exciting frequency, and a steady-state forced vibration test of the selected cylindrical sample is completed; Continue to complete the steady-state forced vibration test of the remaining cylindrical specimens.

6. The method according to claim 1, characterized in that The maximum hysteresis is used to divide the excitation frequency of the rock and soil into viscoelastic zones, and then the response coefficient of dynamic shear in the linear viscoelastic zone and the energy dissipation in the nonlinear viscoelastic zone are determined, which specifically includes: According to the maximum hysteresis, the excitation frequency of the rock-soil body is divided into a linear viscoelastic region and a nonlinear viscoelastic region; Get the vibration response sequence; Determining a response coefficient of dynamic shear in the linear viscoelastic region according to a data segment corresponding to the vibration response sequence in the linear viscoelastic region; The energy dissipation in the nonlinear viscoelastic region is determined according to the data segments corresponding to the vibration response sequence in the nonlinear viscoelastic region.

7. The method according to claim 1, characterized in that Predicting the dynamic mechanical response of the rock mass under different shear strain amplitude changes according to the critical point, the response coefficient and the energy dissipation specifically includes: Determine the linear response curve of the rock and soil body in the linear viscoelastic region according to the response coefficient; Determining a nonlinear response curve of the rock and soil body in a nonlinear viscoelastic region according to the energy dissipation; Determine the mutation point of the shear strain amplitude of the rock and soil body according to the critical point; The dynamic mechanical response of the rock-soil mass under different shear strain amplitude changes is predicted according to the linear response curve, the nonlinear response curve and the mutation point.

8. A rock and soil mechanics detection system, the rock and soil mechanics detection system comprising a resonant column test unit, characterized in that: The resonant column testing unit comprises: The first test module is used to instruct the resonant column instrument to perform a torsional free vibration test on all prepared hollow cylindrical specimens, and collect the frequency sequence of each hollow cylindrical specimen during the free vibration test through an intelligent sensor, wherein the hollow cylindrical specimens are prepared from rock and soil; A first processing module is used to determine the critical point where the rock and soil body changes from elastic deformation to plastic deformation based on the attenuation characteristics of each frequency sequence; The second test module is used to instruct the resonant cylinder instrument to perform axial forced vibration tests on all cylindrical samples of different densities, and collect the vibration response of each cylindrical sample at different excitation frequencies through the intelligent sensor, wherein the cylindrical sample is prepared from rock and soil; The second processing module is used to determine the maximum hysteresis caused by the cohesion between soil particles on the memory effect of the rock and soil body according to the frequency correlation of all vibration responses, and divide the excitation frequency of the rock and soil body into viscoelastic zones according to the maximum hysteresis, so as to determine the response coefficient of dynamic shear in the linear viscoelastic zone and the energy dissipation in the nonlinear viscoelastic zone; The result generation module is used to predict the dynamic mechanical response of the rock mass under different shear strain amplitude changes according to the critical point, the response coefficient and the energy dissipation, and to generate the resonant column test results of the rock mass based on all the dynamic mechanical responses.

9. A computer device, characterized in that: The computer device comprises a memory and a processor, wherein the memory stores codes, and the processor is configured to obtain the codes and execute the resonant column testing method according to any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the resonant column testing method according to any one of claims 1 to 7 is implemented.

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