Rock stress wave attenuation characteristic analysis method based on split Hopkinson pressure bar device

Abstract

The invention discloses a rock stress wave attenuation characteristic analysis method based on a split Hopkinson pressure bar device. Comprising the following steps: 1, preparing a test device; step 2, test design and execution; step 3, data acquisition; step 4, data analysis; 5, attenuation characteristic analysis; step 6, calibrating constitutive parameters; step 7, verifying the method; according to SHPB test data analysis of rock rod samples with different lengths and the same length, the attenuation characteristics of stress waves in rocks are obtained. Based on a Maxwell model and a standard linear solid (SLS) model, a quantitative mapping relation between time domain and frequency domain attenuation characteristics of rock stress waves is established, and a time-frequency determination method of constitutive parameters of the Maxwell model based on SHPB test data and a univariate step-by-step solving method of constitutive parameters of the standard linear solid (SLS) model are provided.

Description

Technical Field

[0001] The invention belongs to the technical field of rock mechanics and relates to a rock stress wave attenuation characteristic analysis method based on a separated Hopkinson pressure bar device. Background Art

[0002] The attenuation mechanism of stress wave propagation in rock mass is a core scientific issue in the field of rock mechanics, and has important engineering value for deep resource exploitation, underground space development and geological disaster prevention and control. Natural rock mass is composed of a variety of minerals, and complex geological tectonic actions form multi-scale discontinuous structural surfaces, such as micro-defects and macro-joints. These structural surfaces will significantly affect the propagation characteristics of stress waves. The viscoelastic constitutive model provides a quantitative characterization method for the propagation attenuation of stress waves in rock mass. In order to achieve accurate identification of model parameters, researchers have developed a variety of dynamic loading test methods. According to different loading methods, they can be divided into pendulum tests, light gas gun tests, lead breaking tests and separated Hopkinson pressure bar tests. Among them, the pendulum impact test based on large aspect ratio rock bar specimens has become the main means of analyzing the attenuation characteristics of traditional rock wave propagation because of its clear principle and simple and controllable stress wave propagation path.

[0003] The traditional pendulum test method is simple in principle and can better analyze the propagation process of one-dimensional stress waves in rock rods, but it has certain limitations: First, the loading rate is insufficient: limited by the impact speed of the pendulum, the frequency of the stress wave generated is low, it is difficult to consider the high-frequency attenuation characteristics of the stress wave, and it is difficult to accurately analyze the dynamic mechanical response of the rock under high strain rate; Second, the sample size limit: this method requires a long rod sample with an aspect ratio greater than 10 and a length greater than 1m. The sample preparation process is difficult and the mechanical properties of the sample often have large non-uniformity, which restricts the applicability and accuracy of the method. Summary of the invention

[0004] The present invention provides a rock stress wave attenuation characteristic analysis method based on a Hopkinson pressure bar device to solve the problems raised in the above background technology.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The rock stress wave attenuation characteristic analysis method based on the separated Hopkinson pressure bar device includes:

[0007] Step 1: Preparation of test equipment;

[0008] Step 2: Experimental design and execution;

[0009] Step 3: data collection;

[0010] Step 4: data processing;

[0011] Step 5: attenuation characteristic analysis;

[0012] Step six, constitutive parameter calibration;

[0013] Step 7: Method validation;

[0014] In step one, a split Hopkinson pressure bar (SHPB) device is used for the test. The SHPB device consists of a striking bar, an incident bar, a transmission bar, and a velocimeter. Strain gauges are attached to the incident bar and the transmission bar to record the strain signals of the incident wave, reflected wave, and transmitted wave.

[0015] In step 2, rock samples of different lengths are designed to meet the needs of stress wave attenuation characteristic analysis to observe the attenuation of stress waves in samples of different lengths. By adjusting the speed of the striking rod, incident stress waves of different intensities are generated to ensure the diversity of test data.

[0016] In step three, a tachometer is used to measure the speed of the striking rod to ensure the accuracy of the test conditions, and the strain gauge data on the incident rod and the transmission rod are recorded to obtain the waveform information of the incident wave, reflected wave and transmitted wave.

[0017] In step 4, the recorded waveform data is processed to extract the strain amplitudes of the incident wave, reflected wave, and transmitted wave. Through normalization processing, the influence of input waveform differences on the results is reduced, thereby improving the accuracy of data analysis.

[0018] In step 5, the time domain attenuation coefficient and the frequency domain attenuation coefficient are determined based on the SHPB test. For rock samples of different lengths, the relationship between the amplitude of the transmitted wave and the length of the sample is analyzed to obtain the frequency domain and time domain attenuation coefficients. For rock samples of the same length, the superposition of multiple reflected waves inside the rock mass is ignored, the Fourier amplitude attenuation from the incident wave signal to the transmitted wave signal is analyzed, and the lower limit of the frequency domain attenuation coefficient is calculated. The transmitted wave signal is superimposed with the reflected wave inside the rock, the Fourier amplitude attenuation from the incident wave signal to the superimposed signal is analyzed, and the upper limit of the frequency domain attenuation coefficient is calculated.

[0019] In step 6, the time domain and frequency domain attenuation coefficients of step 5 are used to calibrate the parameters of the Maxwell model and the standard linear solid (SLS) model, and the attenuation characteristics of stress waves in rocks are quantified to more comprehensively describe the attenuation characteristics of stress waves in rocks and facilitate numerical simulation analysis and engineering applications. Based on the time domain and frequency domain attenuation coefficients of rock samples of different lengths in step 5, the constitutive parameters of the Maxwell model are calibrated, and the mapping relationship between the time domain attenuation coefficient and the frequency domain attenuation coefficient is proposed. Based on the frequency domain attenuation coefficients of rock samples of the same length in step 5, the constitutive parameters of the standard linear solid (SLS) model are calibrated, and a single variable step-by-step solution method for the constitutive parameters of the SLS model is proposed to simplify the solution process of the constitutive parameters.

[0020] In the above step seven, the effectiveness of the analysis method is fully verified through various means such as theoretical analysis, experimental verification and numerical simulation.

[0021] As a further technical solution of the present invention, in the step 3, a split Hopkinson pressure bar test device (SHPB) can be used to achieve high strain rate loading of a short rock bar. The basic principle is that a striking bar (i.e., a bullet) hits an incident bar at a certain speed to generate an incident stress wave, which is transmitted to the specimen through the elastic incident bar, and a reflected wave and a transmitted wave are generated at the same time. The speed of the bullet is measured by a velocimeter, and the strain signals of the incident wave, reflected wave and transmitted wave are obtained based on the strain gauges attached to the incident bar and the transmission bar. The average strain rate of the specimen can be obtained based on the one-dimensional stress wave theory. Mean strain ε and mean stress σ:

[0022]

[0023] Where I, R and T represent the incident, reflected and transmitted waves recorded in the test, respectively, C is the elastic longitudinal wave velocity, l 0 is the original length of the sample, E is the elastic modulus of the compression rod, A is the cross-sectional area of ​​the compression rod, and A 0 is the cross-sectional area of ​​the specimen.

[0024] In the above step 4, in actual operation, it is usually difficult to ensure that the incident waves are completely consistent, but the bullet speed can be adjusted to make the incident wave waveform as close as possible, and then the transmitted wave is divided by the peak value of the incident wave for normalization processing through formula (4) to reduce the influence of the input waveform difference on the result:

[0025]

[0026] where ε T is the transmission rod strain record, ε I is the incident rod strain record.

[0027] As a further technical solution of the present invention, in step 5, the time domain attenuation characteristics of rock samples of different lengths are analyzed by measuring the normalized transmission wave peak value ε′ of rock samples of different lengths. Ti , and then perform linear fitting in the logarithmic domain to calculate the time domain attenuation coefficient β. The linear fitting expression for calculating the time domain attenuation coefficient based on rock samples of different lengths is as follows:

[0028] ln(ε′ Ti )=-βl i +ln(ε 0 ) (5)

[0029] In the formula, ε′ Ti represents the peak value of the normalized transmission wave in the time domain, li is the length of the rock sample.

[0030] As a further technical solution of the present invention, in step 5, for rock samples of different lengths, longer samples will experience more significant attenuation than shorter samples. Assuming that the incident wave remains consistent, the frequency domain attenuation coefficient calculation formula based on rock samples of different lengths is as follows:

[0031]

[0032] Where α(ω) is the frequency domain attenuation coefficient and ω is the circular frequency. and The lengths are l 2 Specimen and length l 1 Fourier amplitude of the sample strain (l 2 > 1 ).

[0033] In step 5, the propagation of stress waves in the Hopkinson bar can be approximated as the propagation of one-dimensional plane stress waves. Unlike a one-dimensional rock bar, when the stress wave passes through an interface with different wave impedances, reflection and transmission phenomena will occur. The calculation formulas for the reflection coefficient F and the transmission coefficient T are as follows:

[0034]

[0035] Where n is the dimensionless wave impedance ratio, ρ is the density, C is the elastic wave velocity, A is the cross-sectional area, and 1 and 2 below represent media 1 and 2.

[0036] As a further technical solution of the present invention, in step 5, in order to simplify the complexity of the test, an attenuation characteristic analysis method based on a single length rock rod is proposed. In the Hopkinson pressure rod test, for a single length rock rod, the propagation of the incident wave to the transmitted wave undergoes three main processes: interface transmission, rock medium attenuation, and superposition of interface reflection waves. To simplify the analysis, the superposition of reflection waves at interface 1 and interface 2 is first ignored, and the transmission coefficients at interface 1 and interface 2 are respectively T 1 and T 2 , then the lower limit estimate of the frequency domain attenuation coefficient based on the same length of rock sample can be calculated by the following formula:

[0037]

[0038] Where α(ω) is the frequency domain attenuation coefficient. and are the Fourier amplitudes of the transmitted wave and the incident wave, respectively, and l is the length of the sample. Further considering the influence of the superposition of multiple reflected waves on the transmitted wave, the reflection coefficients at interface 1 and interface 2 are respectively F 1 and F 2, then the upper limit estimate of the frequency domain attenuation coefficient based on the same length of rock sample can be calculated by the following formula:

[0039]

[0040] E=F 2 F 1 exp[-α(ω)×2l] (10)

[0041] Where α(ω) is the frequency domain attenuation coefficient. E reflects the superposition effect of the reflected wave and its attenuation, l is the length of the sample, and n represents the number of reflections at interfaces 1 and 2. Compared with equation (8), equation (9) has an additional series term generated by the superposition of multiple reflected waves. In practical applications, since the number of reflections is difficult to determine accurately, the specific number of series terms is also difficult to give accurately. However, for the case of a short stress equilibrium time, it can be considered that the stress wave has experienced multiple reflections in a short time, and an approximate estimate can be made by superposition of infinite reflected waves. At this time, equation (9) can be simplified to:

[0042]

[0043] Based on the test results, the upper and lower limit estimates of the attenuation coefficient can be measured by equations (8) and (11), respectively. When the propagation time of the stress wave in the sample is greater than the wavelength, the transmitted wave signal does not undergo the reflection wave superposition process. In this case, the lower limit estimate is more accurate. Conversely, the upper limit estimate is more accurate. There is a time difference between the superimposed reflection wave and the transmitted wave. This time difference can be estimated by the stress equilibrium time. When the stress equilibrium time is small, the influence of the time difference can usually be ignored.

[0044] As a further technical solution of the present invention, in step 6, in order to more comprehensively quantify the attenuation characteristics of rock stress waves, the Maxwell constitutive model and the standard linear solid (SLS) model are calibrated using test data. The impact velocity of the Hopkinson pressure bar test is relatively high, and the high-frequency components of the stress wave are rich. The Maxwell model can be used to quantify the attenuation characteristics of the high-frequency components of the stress wave. Based on the frequency domain attenuation coefficient obtained from rock samples of different lengths in step 5, the constitutive parameters of the Maxwell model are calibrated using the following formula:

[0045]

[0046] Among them, C M is the propagation speed of stress waves in the Maxwell constitutive model, which is equal to the rock wave speed C s , so there is only one viscosity coefficient to be solved: η M (θ M =η M / E M), the test results can be fitted by global optimization method to determine the viscosity coefficient.

[0047] The time domain peak value of the SHPB test is mainly determined by the high-frequency component. The high frequency waves are:

[0048]

[0049] At this time, the frequency domain attenuation coefficient α remains stable and equal to the time domain attenuation coefficient β, thereby obtaining the mapping relationship between the frequency domain attenuation coefficient and the time domain attenuation coefficient. Based on the time domain attenuation coefficient obtained from rock samples of different lengths in step 5, the constitutive parameters of the Maxwell model are calibrated using the following formula:

[0050]

[0051] Since the constitutive parameters obtained by frequency domain and time domain analysis are consistent, the accuracy of the constitutive model can be evaluated by mutual verification of the attenuation characteristics in the time domain and frequency domain.

[0052] As a further technical solution of the present invention, in step six, since the stress of the Maxwell model will be close to complete relaxation when loaded at low frequency, its analysis of the low-frequency attenuation characteristics is not accurate enough, and the standard linear solid (SLS) model combines the advantages of the Maxwell model and the Kelvin-Voigt model, and can more comprehensively describe the attenuation characteristics of stress waves in various frequency bands. Therefore, the standard linear solid (SLS) model is further used to analyze the attenuation characteristics of stress waves in various frequency bands. The simplest standard linear solid (SLS) model includes a double unit body formed by connecting a Maxwell unit in parallel with a spring element, and its frequency domain attenuation coefficient is determined by the following formula:

[0053]

[0054] Consistent with the Maxwell constitutive model, when the stress wave frequency is high, the attenuation coefficient of the SLS model remains stable and equal to the time domain attenuation coefficient:

[0055]

[0056] Where E 0 It is the elastic modulus of the parallel spring, which mainly controls the propagation behavior of low-frequency stress waves. M is the relaxation modulus. Since the propagation of high-frequency waves maintains a constant phase velocity, it can be considered to be equal to the rock elastic wave velocity. At this time, E M Equal to the elastic modulus of rock. θ M is the relaxation time, θ M From the viscosity constant η M Divided by the relaxation modulus E M Get, EM and θ M Mainly controls the propagation behavior of high-frequency stress waves.

[0057] As a further technical solution of the present invention, in step 6, the constitutive parameters of the standard linear solid (SLS) model are calibrated based on the test results of the rock sample of the same length in step 5. In order to simplify the calibration process of the constitutive parameters, a single variable step-by-step solution method for the constitutive parameters of the standard linear solid (SLS) is proposed:

[0058] (1) Based on the high-frequency attenuation coefficient obtained from the rock test of the same length in step 5, the constitutive parameters of the Maxwell model are calibrated using equation (14), and the time domain attenuation coefficient β is determined.

[0059] (2) According to the time domain attenuation coefficient β, the constraint conditions of the constitutive parameters of the SLS model are given using equation (16). At this time, the parameters E of the standard linear solid (SLS) constitutive model are 0 and η M The variable to be solved will be constrained by equation (16) and become 1 E 0 .

[0060] (3) Based on the low-frequency attenuation coefficient obtained from the rock test of the same length in step 5, the variable E to be solved is determined by global optimization analysis using equation (15): 0 .

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] The present invention proposes a method for obtaining the attenuation characteristics of stress waves in rocks based on the SHPB test data analysis of rock rod specimens of different lengths and single length. Based on the Maxwell model and the standard linear solid (SLS) model, a quantitative mapping relationship between the time domain and frequency domain attenuation characteristics of rock stress waves is established. A time-frequency determination method for the constitutive parameters of the Maxwell model based on SHPB test data and a single variable step-by-step solution method for the constitutive parameters of the standard linear solid (SLS) model are proposed to more comprehensively quantify the attenuation characteristics of stress waves in rocks and facilitate numerical simulation analysis and engineering applications. This method overcomes the loading rate and sample size limitations of traditional pendulum tests through high strain rate loading and short rock rod test design, reduces the complexity and cost of the test, and provides a more efficient and accurate test and theoretical framework for the analysis of rock mass propagation attenuation characteristics. At the same time, it provides a scientific basis for the prediction of stress wave propagation in the fields of deep resource exploitation, underground space utilization, and extreme disaster prevention and control. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is a flow chart of the method of the present invention;

[0064] Figure 2This is a diagram of the split Hopkinson pressure bar test apparatus;

[0065] Figure 3 Schematic diagram of stress wave propagation in SHPB test;

[0066] Figure 4 This is the Maxwell model diagram;

[0067] Figure 5 is the Maxwell type standard linear solid (SLS) diagram;

[0068] Figure 6 This is the normalized measurement result diagram of the transmission rod strain gauge;

[0069] Figure 7 This is the SHPB finite element model diagram;

[0070] Figure 8 The incident, transmitted and reflected wave shapes of working conditions 1-3;

[0071] Fig. 9 Comparison between the calculated and measured values ​​of the Fourier amplitude of the transmission rod strain;

[0072] Fig.10 Comparison of attenuation coefficients between the Maxwell constitutive and standard linear solid (SLS) models;

[0073] Figure 11(a) is a comparison of the Fourier amplitude results of the 80 mm sample;

[0074] Figure 11(b) is a comparison of the Fourier amplitude results of the 140 mm sample;

[0075] Figure 11(c) is a comparison of the Fourier amplitude results of the 200 mm sample;

[0076] Fig.12 is the variation of the estimated error with respect to the strain rate;

[0077] Figure 13(a) is a comparison of the waveforms of the transmission rod of the 80mm sample;

[0078] Figure 13(b) is a comparison of the waveforms of the transmission rod of the 140mm sample;

[0079] Figure 13(c) is a comparison of the waveforms of the transmission rod of the 200mm sample;

[0080] Figure 14(a) is a comparison of the numerical simulation results and the measured results of the spectrum of the 80mm sample;

[0081] Figure 14(b) is a comparison between the numerical simulation results and the measured results of the spectrum of the 140 mm sample;

[0082] Figure 14(c) is a comparison between the numerical simulation results and the measured results of the spectrum of the 200 mm sample. DETAILED DESCRIPTION

[0083] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0084] Please refer to the attached Figure 1 - Figure 14, an embodiment provided by the present invention:

[0085] Test equipment

[0086] In order to verify the effectiveness of the rock stress wave attenuation characteristic analysis method, a series of SHPB tests on granite specimens were carried out on a 74.4mm split Hopkinson pressure bar (SHPB) device in the laboratory of Ningbo University. The rod used was high-strength steel, with an elastic modulus of 214GPa, a wave velocity of 5236.8m / s, a bullet length of 398mm, an incident rod length of 2745mm, a transmission rod length of 1792mm, an incident rod strain gauge recording point 1727mm from the specimen end face, a transmission rod strain gauge recording point 892mm from the specimen end face, a strain gauge sensitivity of 2252E-6, and a strain signal sampling frequency of 1MHz. In the test, a paper sheet with a diameter of 60mm and a thickness of 5mm was used as a pulse shaper. In order to reduce the friction effect between the compression rod and the contact surface of the specimen, a thin layer of vaseline was evenly applied on the contact surface of the specimen and the pressure bar. The results of the empty rod impact test showed that the coaxiality of the compression rod was good and the stress wave propagated in the compression rod in a one-dimensional manner.

[0087] Rock samples

[0088] The rock samples are sesame gray granite from Rizhao, Shandong. The samples are cut from a large rock wall to ensure that the sample has a small discreteness. The results of the previous static load test show that the basic physical parameters of the rock are as follows: density is 2730kg / m 3 , wave velocity is 4573m / s, elastic modulus is 5.71GPa, Poisson's ratio is 0.28, and compressive strength is 113MPa. The rock samples were processed into four cylindrical specimens of different lengths, namely 40mm, 80mm, 140mm and 200mm, and the diameter of the specimens was 69mm.

[0089] Test conditions

[0090] By measuring the strain waveforms at both ends of the specimen, the attenuation characteristics of stress waves in specimens of different lengths are analyzed. The specific test conditions are shown in Table 1, where conditions 1 to 3 use specimens with an aspect ratio greater than 1, and the specimen lengths are 80 mm, 140 mm, and 200 mm, respectively. The traditional Hopkinson bar test usually uses specimens with an aspect ratio less than 1 to achieve stress balance more quickly, while the embodiment selects specimens with a larger aspect ratio to better reflect the propagation of one-dimensional stress waves. The influence of stress balance will be discussed later. Conditions 1 to 3 use similar bullet velocities to ensure the consistency of the incident wave waveform. Taking conditions 1 to 3 as examples, see Appendix. Figure 8 The typical incident wave and transmitted wave waveforms are shown. To ensure the integrity of the experimental data, the original waveforms are not filtered in this invention to retain the complete frequency components of the actual waveforms. Figure 8 It can be seen that under similar bullet velocities, the incident wave waveforms corresponding to 80mm, 140mm and 200mm rock rods are highly consistent, while the transmitted wave waveforms show significant attenuation characteristics. Working conditions 4 to 9 use 40mm specimens and different bullet velocities to study the effects of aspect ratio and different strain rates on the test results.

[0091] Table 1 Test conditions

[0092]

[0093] Analysis of attenuation characteristics based on rock rods of different lengths

[0094] Time domain attenuation coefficient calculation

[0095] For the test results of rock rods of different lengths, it is relatively simple to first analyze the time domain attenuation characteristics. The transmission rod strain is normalized using equation (4), and then the normalized transmission rod peak value is linearly fitted using equation (5) to calculate the time domain attenuation coefficient. The results are shown in the attached figure. Figure 6 As shown in the figure, the normalized peak values ​​at 80mm, 140mm and 200mm are 0.8420, 0.7526 and 0.6423 respectively. The calculated time domain attenuation coefficient is 2.2571 and the determination coefficient of the linear fit is 0.9953, indicating a high goodness of fit and reliable results. However, since only three samples were used, the uncertainty of the experiment has a greater impact on the fitting results, and the calculated results may not be robust. Therefore, they need to be verified with the frequency domain attenuation characteristics.

[0096] Frequency domain attenuation coefficient calculation

[0097] Based on the corresponding relationship between the time domain attenuation coefficient and the frequency domain attenuation coefficient of the high-frequency stress wave, the viscosity coefficient of the Maxwell constitutive model can be calculated as 4.8472e-05 by substituting the time domain attenuation coefficient (2.2571) into formula (14), and then the corresponding frequency domain attenuation coefficient can be obtained. Substituting the frequency domain attenuation coefficient into formula (6), combined with the transmission wave data of 80mm and 140mm rock rods, the theoretical prediction values ​​of the Fourier amplitude of the transmission wave of 140mm and 200mm rock rods can be calculated respectively. The results are shown in the attached figure. Fig. 9 As shown. Fig. 9 It can be seen that when the frequency exceeds 4000Hz, the corresponding transmission wave spectrum curves of rock rods of different lengths show significant overlap characteristics, indicating that the effective component of the signal in this frequency band accounts for a relatively low proportion and is greatly interfered by high-frequency noise. Based on this, 4000Hz is set as the high-frequency cutoff frequency. Figure 6 The bandwidth of the transmission wave is about 0.5ms, while the sampling frequency of the experiment is 1MHz. The resolution of the Fourier spectrum is calculated to be 2000Hz. Although the spectrum resolution can be improved by zero padding or period extension, the frequency band less than 2000Hz will contain numerical errors because the effective components of the signal have not increased substantially, and the closer to 0, the greater the error. Based on the above analysis, 2000Hz-4000Hz is defined as the effective high-frequency component, and 1000-2000Hz is selected as the effective low-frequency band to reduce the interference of errors. In the high-frequency effective frequency band, the spectrum curves of the predicted value and the measured value show a high degree of consistency. The mean absolute percentage error (MAPE) of each frequency band is calculated. The results show that the error in the 3000-4000Hz interval is the largest, which is 9.6%, while the average error of the entire frequency band is 5.81%. In general, the errors in each frequency band are small, which verifies the correspondence between the attenuation characteristics in the time domain and the frequency domain, and the effectiveness of the attenuation characteristic analysis using the Maxwell constitutive method. It is worth noting that since equation (6) ignores the attenuation of the left-running interface reflection wave, the theoretical prediction value of the Maxwell model is slightly higher than the measured value. However, the measured results show that the overall error is within the acceptable range for engineering, which proves the validity of the Maxwell constitutive model and the corresponding relationship between the time-frequency attenuation characteristics, and provides a reliable basis for the subsequent attenuation characteristic analysis based on a single-size rock rod specimen.

[0098] Analysis of attenuation characteristics based on rock rods of the same length

[0099] High frequency attenuation characteristics analysis

[0100] The method based on rock samples of different lengths requires obtaining high-precision test results through rock samples of multiple sizes, which significantly increases the complexity of the test. In order to break through this limitation, the feasibility of attenuation characteristic analysis based on rock samples of the same length is explored. The effectiveness of the Maxwell constitutive model and the corresponding relationship between the time-frequency attenuation characteristics have been verified. Therefore, the Maxwell constitutive model can be used to first determine the time domain attenuation coefficient and the corresponding high-frequency attenuation characteristics. The lower and upper limits of the frequency domain attenuation coefficient can be estimated using equations (8) and (11), respectively. For the present invention, the longest sample length is 200 mm, the rock wave velocity is 4573 m / s, and the corresponding stress wave passes through the sample for 4.37e-5s, which is much smaller than the stress wave wavelength (0.5e-3s). Therefore, the time difference of the superposition of the reflected waves can be ignored, so it is more reasonable to use the upper limit value for estimation. The upper limit formula (11) is used to perform spectrum fitting on the attenuation characteristics of the high frequency band of 2000-4000 Hz, and the corresponding time domain attenuation coefficient is calculated. The average time domain attenuation coefficient of 80 mm, 140 mm and 200 mm rock rods is 2.1565, and the error (MAPE) with the results of rock rods of different lengths is only 4.40%. This result shows that it is feasible to use a single rock rod sample for attenuation characteristic analysis. This method only requires fewer tests to obtain more accurate results.

[0101] Low frequency attenuation characteristics analysis

[0102] Although the Maxwell constitutive model can effectively characterize the attenuation characteristics of the high-frequency band, there is a certain error in its prediction of the attenuation of the low-frequency component. Therefore, the standard linear solid (SLS) model is used to improve the accuracy of the prediction of the low-frequency attenuation characteristics. Based on the theoretical framework, the mean value of the time domain attenuation coefficient (2.1565) is taken for further calculation and analysis. At this time, the constitutive parameters of the standard linear solid (SLS) model will satisfy the constraints of formula (16). The constitutive parameters E of the standard linear solid (SLS) model are solved using the global optimization method. 0 is 12.34Gpa. Its corresponding frequency domain attenuation characteristics are shown in the attached Fig.10 As shown. Fig.10It can be seen that the frequency domain attenuation coefficient increases monotonically with the increase of frequency, and then gradually stabilizes. Its stable value is basically consistent with the time domain attenuation coefficient (2.1565). The high-frequency attenuation characteristics of the Maxwell constitutive and the standard linear solid (SLS) constitutive are basically the same, but there are significant differences in the low-frequency band. Based on the frequency domain attenuation coefficient, the transmission wave spectrum is predicted using equation (11). The comparison of the transmission wave frequency domain distribution calculated by the Maxwell constitutive and the standard linear solid (SLS) constitutive and the measured results is shown in Figure 11. The results show that the prediction results of the two are basically consistent in the high frequency band, while for the low frequency band less than 2000Hz, the estimated value of the Maxwell constitutive is smaller, and the estimated result of the standard linear solid (SLS) constitutive is more accurate. Comparing the prediction errors (MAPE) of each frequency band, the prediction error of the Maxwell model in the low frequency band (1000-2000Hz) is as high as 15.84%, while the standard linear solid (SLS) model reduces the maximum low-frequency error to 2.16% by introducing a low-frequency spring, but correspondingly, its prediction accuracy for the high frequency band (3000-4000Hz) is slightly reduced. However, for the full frequency band error, the prediction error of the standard linear solid (SLS) constitutive model is 6.38%, which is smaller than the Maxwell model (8.29%), and the overall prediction is more accurate. This model can significantly improve the prediction accuracy of low-frequency attenuation characteristics while maintaining a high high-frequency prediction accuracy, providing a more universal theoretical tool for multi-band stress wave propagation analysis.

[0103] A large number of experimental studies have shown that the mechanical response of rock specimens is significantly dependent on their geometric dimensions. Therefore, the size effect also needs to be considered when conducting error analysis. Based on the standard linear solid (SLS) constitutive model, the prediction errors of specimens of different sizes are analyzed. For 80 mm, 140 mm, and 200 mm specimens, the prediction error shows a significant increasing trend from 6.38% to 16.84% with the increase of specimen length. This phenomenon may be due to the fact that the stress equilibrium time increases with the increase of specimen length, resulting in an increase in the error caused by the time difference. In addition, the superposition effect of the actual reflected wave is not the superposition of infinite terms. The stress wave is significantly dispersed after a finite number of reflections, making the upper limit estimate higher than the measured result, and the deviation increases with the increase of the sample length. However, the smaller the sample size, the better. According to the SHPB test specification of the International Society for Rock Mechanics (ISRM), the sample diameter should be no less than 50 mm, and the aspect ratio should be controlled between 0.5 and 1. The experimental data show that under similar strain rate conditions, the error of the 40 mm specimen is as high as 19.15%, while the error of the 80 mm specimen is only 6.38%, which is significantly lower than the former. This difference may be due to the significant lateral inertia effect and geometric attenuation effect in the small aspect ratio specimen, which leads to the reduced applicability of the one-dimensional stress wave hypothesis, thereby affecting the accuracy of the test results. Based on the above analysis, it is recommended to select a specimen with an aspect ratio close to 1 (i.e., the 80 mm specimen in the present invention) in the attenuation relationship analysis to obtain better test accuracy. The mechanical behavior of rock mass will change under different strain rates, so it is necessary to further study the influence of strain rate on the prediction results. The analysis shows that the 40mm specimen has some defects in the basic physical assumptions, resulting in a certain benchmark error. This section mainly discusses the influence of strain rate on the trend of error change, focusing on the fluctuation of error. Fig.12 The trend of the overall error of the 40mm specimen with strain rate is shown. The results show that the error decreases first and then increases with the increase of strain rate. The overall error fluctuates between 12.5% ​​and 22.5%. The error is basically stable and has no obvious linear trend. This shows that the prediction based on the average constitutive parameters of the 80mm, 140mm and 200mm specimens can maintain a high robustness, verifying the applicability of the constitutive model. The adaptability of the model can be attributed to the effective control ability of the Maxwell unit in a wide strain rate range.

[0104] Numerical simulation verification

[0105] Numerical model design

[0106] LS-DYNA software was used for numerical simulation, and working conditions 1-3 were simulated and analyzed to verify the accuracy and applicability of the constitutive parameters. Based on the actual size of the Hopkinson pressure bar, a three-dimensional solid unit model was established, in which the bar and the specimen were both three-dimensional solid units, and the incident bar and the transmission bar were linear elastic constitutive models, and their material parameters were consistent with the test. The rock specimen adopted the standard linear solid (SLS) constitutive model, and material No. 76 (General-Viscoelastic constitutive) was selected in the LS-DYNA software, and the material parameters adopted the calculated average value. Since a shaper was set in the actual test, in order to completely retain the waveform of the incident wave in the numerical simulation, the numerical simulation adopted the loading method of converting the incident bar strain into the equivalent pressure at the bar end. The equivalent pressure P is the product of the incident bar strain and the input bar elastic modulus. The contact between the input rod and the rock adopts a frictionless contact model. To ensure the simulation accuracy, it is necessary to determine the appropriate grid size. According to the wave field propagation theory, a grid size that is too large will lead to a high-pass filtering effect. To better retain the wave field components, the grid size should be 1 / 8 to 1 / 16 of the minimum wavelength. Considering that the high-frequency components greater than 15000Hz are mainly test noise, this embodiment uses this frequency as the high-pass cutoff frequency. The grid size corresponding to 1 / 16 of the minimum wavelength is 1.9cm. This embodiment selects a grid size of 1cm, which can take into account both calculation accuracy and calculation efficiency. The model adopts uniform grid division, and its finite element model is shown in the attached figure. Figure 7 shown.

[0107] Simulation results and analysis

[0108] Figure 13 shows the comparison between the numerical simulation results of the standard linear solid (SLS) constitutive model and the linear elastic constitutive model and the measured transmission wave waveform. The results show that the standard linear solid (SLS) constitutive model can accurately reproduce the time domain waveform characteristics of the transmission wave, and its prediction curve is highly consistent with the measured data. The maximum prediction error of the transmission wave peak value of the standard linear solid (SLS) constitutive model is 4.58%, while the linear elastic constitutive model does not consider the attenuation effect of the medium, resulting in a gradual increase in the error, with the maximum error reaching 22.44%. This result illustrates the necessity of attenuation feature analysis in simulation.

[0109] Further analysis of the time domain attenuation coefficient shows that the simulation result of the standard linear solid (SLS) constitutive model is 2.1084, with an error of 2.23% from the theoretical value (2.1565) and a 6.53% error from the measured value (2.2571) of different rock rod tests, proving the simulation accuracy of the standard linear solid (SLS) constitutive model. Waveform difference analysis shows that the waveform of the simulation result is relatively smooth, which may be due to the high-frequency filtering effect of the finite element model suppressing the noise component in the measured signal. In addition, the wavelength of the simulated combination is slightly smaller than the measured value, and the difference mainly occurs in the unloading section. This may be because the present invention does not consider the influence of macroscopic joints, which will cause the waveform to lag, and its influence on the loading stage is small, but the influence on the unloading stage is large. Since the characteristics of the loading stage are the main focus in actual engineering situations, the impact of this deviation is relatively small. Comparing the spectrum differences between the simulation results and the measured results, Figure 14 compares the spectrum differences between the simulation results and the measured results. The results show that the numerical simulation results are highly consistent with the measured data in the main frequency bands. The error of each frequency band is calculated, and the maximum overall error is 9.63%, which is better than the upper limit estimate of the theoretical results (16.84%). This may be due to the fact that the theoretical model makes simplified assumptions about the number of reflection wave superpositions and the time difference effect, while the numerical simulation can more realistically reflect the wave field evolution process. It is worth noting that the error growth rate of the standard linear solid (SLS) constitutive model is significantly lower than that of the linear elastic model, and its error growth rate is less than 1 / 3 of that of the linear elastic model, highlighting the advantages of the viscoelastic constitutive model. The results of the numerical simulation further verify the applicability of the constitutive model and the effectiveness of the calculation method.

[0110] The present invention obtains the attenuation characteristics of stress waves in rocks by analyzing the SHPB test data of rock samples of different lengths and rock rod samples of the same length. A quantitative mapping relationship between the attenuation characteristics of rock stress waves in the time domain and frequency domain is established. A method for determining the parameters of the constitutive model that characterizes the dynamic mechanical properties of rocks is given. The effectiveness of this method is fully verified through theoretical analysis, experimental verification and numerical simulation. The specific conclusions are as follows: A method is proposed to obtain the attenuation characteristics of stress waves in rocks based on the SHPB test data analysis of rock samples with different lengths and rock rod samples with the same length. This method overcomes the loading rate and sample size limitations of traditional pendulum tests through high strain rate loading and short rock rod test design, reducing the complexity and cost of the test; based on the Maxwell model and the standard linear solid (SLS) model, a quantitative mapping relationship between the time domain and frequency domain attenuation characteristics of rock stress waves is established, and a time-frequency determination method for the constitutive parameters of the Maxwell model based on SHPB test data and a single variable step-by-step solution method for the constitutive parameters of the standard linear solid (SLS) model are proposed; a series of SHPB tests on rock media with different sample lengths and strain rates are designed and carried out, and the constitutive parameters of the Maxwell model and the standard linear solid (SLS) model are determined based on the proposed method. Combined with the test data, the accuracy of the corresponding relationship between the time-frequency attenuation characteristics and the applicability of the Maxwell model and the standard linear solid (SLS) model to different frequency components are verified, revealing the influence of aspect ratio and strain rate on the calculation accuracy of the method of the present invention.

Claims

1. A rock stress wave attenuation characteristic analysis method based on a split Hopkinson pressure bar device is characterized in that: include: Step 1, using a split Hopkinson pressure bar device to conduct the test; Step 2: Experimental design and execution; Design rock samples of different lengths to meet the needs of stress wave attenuation characteristic analysis, observe the attenuation of stress waves in samples of different lengths, and generate incident stress waves of different intensities by adjusting the speed of the striking rod to ensure the diversity of test data; Step 3: Data collection; Use a tachometer to measure the speed of the striking rod, record the strain gauge data on the incident rod and the transmission rod, and obtain the waveform information of the incident wave, reflected wave and transmitted wave; Step 4, processing the recorded waveform data; Step 5: attenuation characteristic analysis; Based on the SHPB test, the time domain attenuation coefficient and the frequency domain attenuation coefficient are determined respectively; for rock samples of different lengths, the relationship between the amplitude of the transmitted wave and the length of the sample is analyzed to obtain the frequency domain and time domain attenuation coefficients; for rock samples of the same length, the superposition of multiple reflected waves inside the rock mass is ignored, the Fourier amplitude attenuation from the incident wave signal to the transmitted wave signal is analyzed, and the lower limit of the frequency domain attenuation coefficient is calculated; the transmitted wave signal is superimposed with the reflected wave inside the rock, the Fourier amplitude attenuation from the incident wave signal to the superimposed signal is analyzed, and the upper limit of the frequency domain attenuation coefficient is calculated; Step six, constitutive parameter calibration; In step six, based on the time domain and frequency domain attenuation coefficients of rock samples of different lengths in step 5, the constitutive parameters of the Maxwell model are calibrated, and a mapping relationship between the time domain attenuation coefficient and the frequency domain attenuation coefficient is proposed; based on the frequency domain attenuation coefficients of rock samples of the same length in step 5, the constitutive parameters of the standard linear solid (SLS) model are calibrated, and a single variable step-by-step solution method for the constitutive parameters of the SLS model is proposed to simplify the solution process of the constitutive parameters.

2. The rock stress wave attenuation characteristic analysis method based on the Hopkinson pressure bar device according to claim 1 is characterized in that: In step 4, the transmitted wave is divided by the peak value of the incident wave to perform normalization processing to reduce the influence of the input waveform difference on the result: where ε T is the transmission rod strain record, ε I is the incident rod strain record.

3. The rock stress wave attenuation characteristic analysis method based on the Hopkinson pressure bar device according to claim 1 is characterized in that: In step 5, the time domain attenuation characteristics of rock samples of different lengths are analyzed by measuring the normalized transmission wave peak ε′ of rock samples of different lengths. Ti , and then a linear fitting is performed in the logarithmic domain to calculate the time domain attenuation coefficient β; the linear fitting expression for calculating the time domain attenuation coefficient based on rock samples of different lengths is shown in formula (5): ln(e′ Ti )=-βl i +ln(ε0) (5) In the formula, ε′ Ti represents the peak value of the normalized transmission wave in the time domain, l i is the length of the rock sample; Assuming that the incident wave remains the same, the frequency domain attenuation coefficient calculation formula based on rock samples of different lengths is shown in formula (6): Where α(ω) is the frequency domain attenuation coefficient, and ω is the circular frequency; and are the Fourier amplitudes of strain of the specimen with length l2 and the specimen with length l1 (l2>l1); Let the transmission coefficients at interface 1 and interface 2 be T1 and T2 respectively, then the lower limit estimate of the frequency domain attenuation coefficient based on the same length of rock sample can be calculated by formula (8): Where α(ω) is the frequency domain attenuation coefficient; and are the Fourier amplitudes of the transmitted wave and the incident wave, respectively, and l is the length of the sample; Let the reflection coefficients at interface 1 and interface 2 be F1 and F2 respectively, then the upper limit estimate of the frequency domain attenuation coefficient based on the same length of rock sample can be calculated by formula (11): Based on the experimental results, the upper and lower limit estimates of the attenuation coefficient are obtained by equations (8) and (11), respectively.

4. The rock stress wave attenuation characteristic analysis method based on the Hopkinson pressure bar device according to claim 1 is characterized in that: In step 6, the constitutive parameters of the Maxwell model are calibrated by formula (12) based on the frequency domain attenuation coefficients obtained from the rock samples of different lengths in step 5: Among them, C M is the propagation speed of stress waves in the Maxwell constitutive model, which is equal to the rock wave speed C s , so there is only one viscosity coefficient to be solved: η M (θ M =η M / E M ), the test results can be fitted by global optimization method to determine the viscosity coefficient; Based on the time domain attenuation coefficient of rock samples of different lengths obtained in step 5, the constitutive parameters of the Maxwell model are calibrated using formula (14): Since the constitutive parameters obtained by frequency domain and time domain analysis are consistent, the accuracy of the constitutive model can be evaluated by mutual verification of the attenuation characteristics of the time domain and frequency domain; Consistent with the Maxwell constitutive model, when the stress wave frequency is high, the attenuation coefficient of the SLS model remains stable and equal to the time domain attenuation coefficient β: Where E0 is the elastic modulus of the parallel spring, E M is the relaxation modulus, θ M For relaxation time.

5. The rock stress wave attenuation characteristic analysis method based on the Hopkinson pressure bar device according to claim 4 is characterized in that: In step 6, in order to simplify the calibration process of constitutive parameters, a single variable step-by-step solution method for standard linear solid constitutive parameters is proposed: (1) Based on the high-frequency attenuation coefficient obtained from the rock test of the same length in step 5, the constitutive parameters of the Maxwell model are calibrated using equation (14), and the time domain attenuation coefficient β is determined; (2) According to the time domain attenuation coefficient β, the constraints of the constitutive parameters of the SLS model are given using equation (16); at this time, the parameters E0 and η of the standard linear solid (SLS) constitutive M It will be constrained by equation (16), and the variable to be solved becomes 1 E0; (3) According to the low-frequency attenuation coefficient obtained from the rock test of the same length in step 5, the variable E0 to be solved is determined by global optimization analysis using equation (15); 6. The rock stress wave attenuation characteristic analysis method based on the Hopkinson pressure bar device according to claim 1 is characterized in that: It also includes step seven, method verification; through theoretical analysis, experimental verification and numerical simulation, the effectiveness of the analysis method is fully verified.

7. The rock stress wave attenuation characteristic analysis method based on the Hopkinson pressure bar device according to claim 1 is characterized in that: In the step 4, the specific operations are as follows: The recorded waveform data are processed to extract the strain amplitudes of the incident wave, reflected wave and transmitted wave, and then normalized.

8. The rock stress wave attenuation characteristic analysis method based on the Hopkinson pressure bar device according to claim 1 is characterized in that: In the step 1, the specific operations are as follows: The split Hopkinson pressure bar device includes a striking bar, an incident bar, a transmission bar and a tachometer. Strain gauges are attached to the incident bar and the transmission bar to record strain signals of incident waves, reflected waves and transmitted waves.

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