A method for inverting joint stiffness in rock mass based on reflected waves
Through the hyperdynamic strain meter, the reflection coefficient function expression is derived, which solves the damage and pollution problems of rocks by traditional drilling methods, and realizes accurate measurement and accurate calculation of rock joint stiffness.
Patent Information
- Application Number
- CN202210059617.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-01-19
- Publication Date
- 2025-01-03
- Estimated Expiration
- 2042-01-19
AI Technical Summary
Traditional drilling methods have great damage to rocks, causing secondary pollution, and are greatly affected by the hardness of the rocks and human factors, making it difficult to accurately determine the internal joint stiffness of the rock body.
The strain-time curve of incident and reflected waves is measured by a hyperdynamic strain meter, discrete Fourier transform is performed, the functional expression of the reflection coefficient is derived, and the stiffness of a single linear macroscopic joint is fitted with the continuous equation and Hook's law. .
Non-contact measurement is realized, operating steps are simplified, calculation accuracy is improved, damage to rocks and secondary pollution is avoided, and the internal joint stiffness of the rock poles is accurately determined.
Smart Images
Figure CN114417609B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of rock mass measurement, and in particular relates to a method for inverting the stiffness of a single linear macro joint in a rock rod. Background Art
[0002] Rock mass is composed of intact rock and discontinuities such as joints, fissures, and faults. The properties of joints have an important influence on the strength and stability of the rock mass, and the degree of influence is related to the joint stiffness. How to accurately determine the joint stiffness has always been an important research topic. In order to obtain the mechanical parameters of the internal joints of the rock mass, the drilling method is often used to drill and coring the rock. By measuring the core, the required mechanical parameters can be obtained. The traditional drilling method has a large degree of damage to the rock, which will expose the interior to the air, causing secondary pollution, and is greatly affected by the hardness of the rock and human factors. With the gradual maturity of wave method testing technology, it is possible to use waves (mechanical waves or electromagnetic waves) as information carriers, and to obtain the incident wave and reflected wave signals obtained by non-contact measurement to obtain the internal joint stiffness of the rock. This can provide an important basis for studying the propagation of stress waves in jointed rocks. Summary of the invention
[0003] The present invention obtains the strain-time curve of the incident wave ε1(t) and the strain-time curve of the reflected wave ε2(t) passing through the left side of the joint through the ultra-dynamic strain gauge, and converts them into a series of incident harmonics of frequency domain angles through discrete Fourier transform: (0) (f), a series of reflected harmonics u (1) (f) Divide the reflected harmonic corresponding to each frequency by the incident harmonic one by one to obtain: R1, R2, R3, ... R n According to the continuity equation and Hooke's law, as well as the linear displacement discontinuous boundary condition when the stress wave passes through a linear deformation joint, the functional expression of the reflection coefficient R when the stress wave passes through a single linear deformation joint with normal incidence can be derived. n The corresponding discrete data curve is consistent with the function curve of the reflection coefficient R, and the unknown joint stiffness k can be fitted. n size.
[0004] The technical solution adopted by the present invention is a method for inverting the joint stiffness in the rock mass based on reflected waves, which is described in detail as follows:
[0005] Step 1: Derive the functional expression of the reflection coefficient R.
[0006] The rock mass in the initial undisturbed state has a single linear macro joint at x1. At any position on the left side of the joint, there is an incident harmonic u perpendicular to the joint and propagating along the positive direction of the x-axis. (0) , the reflected harmonic is represented by u (1), define R as the reflection coefficient, and describe the boundary conditions of the joint according to the linear displacement discontinuity boundary conditions when the stress wave passes through the linear deformation joint according to the continuity equation and Hooke's law. The reflection coefficient when the stress wave passes through a single linear deformation joint with normal incidence is obtained
[0007]
[0008] k n is the joint stiffness; f is the harmonic frequency in the frequency domain after Fourier transform of the incident wave and the transmitted wave in the time domain; R is divided into two parts: the real function expression Re(f) and the imaginary function expression Im(f). The real function expression Re(f) and the imaginary function expression Im(f) have a common parameter k n .
[0009] Step 2: Determine the incident wave and reflected wave in the time domain.
[0010] The pendulum impact test device is used to dynamically load the free end of the specimen on the left side. The propagation process of the stress wave generated by the pendulum impact in the specimen is as follows: Figure 2 As shown. When a dynamic load is applied, stress waves are generated in the specimen. The stress wave pulse propagates to the right in the specimen. When it passes through the strain gauge position for the first time, it is recorded by the strain gauge, which is ε1(t) shown in the figure, and is called the incident wave; it continues to propagate to the right. When it propagates to the joint, the stress wave is reflected and propagates to the left. When the reflected stress wave pulse passes through the strain gauge position again, it is recorded by the strain gauge for the second time, which is ε2(t) shown in the figure, and is called the reflected wave; t is the change time of the incident wave and the reflected wave, Figure 3 A set of strain-time curves of incident wave and reflected wave measured in the experiment.
[0011] Step 3: Perform discrete Fourier transform on the incident and reflected waves in the time domain.
[0012] The time domain incident wave ε1(t) and the time domain reflected wave ε2(t) in the strain-time curve are expressed by the formula After discrete Fourier transform, we can obtain: a series of incident harmonics u of the time domain incident wave ε1(t) in the frequency domain (0) (f) A series of reflected harmonics u of the time domain reflected wave ε2(t) in the frequency domain (1) (f), the frequency interval and the total frequency range can be determined according to the specific situation. (1) (f) corresponds to the incident harmonic u divided by the frequency (0) (f), we get: R1, R2, R3, ... R n All are plural.
[0013] Step 4: From the known R1, R2, R3...R nFitting unknown parameter k with a series of discrete data and R function expression n .
[0014] The real function expression of R Re(f) and R1, R2, R3...R n The real part of R, the imaginary part of R, the function expression Im(f), and R1, R2, R3, ... R n The imaginary part, frequency range, and wave impedance are input into the 1stopt program to calculate the common parameter k of the real function Re(f) and the imaginary function Im(f). n By continuously iteratively adjusting k n When k n Substitute the real part function curve of Re(f) and R1, R2, R3...R n The distance between the real value curves is closest, and k n Substitute the imaginary function curve of Im(f) and R1, R2, R3...R n The distance between the imaginary value curve is the closest, at this time the sum of the squares of the data deviations is minimized, the goodness of fit is optimal, and the k n This is the joint stiffness in the rock.
[0015] Compared with the prior art, the present invention has the following technical advantages:
[0016] The present invention can determine the joint stiffness of the joint inside the rock rod only through the strain change curve at a certain point before the joint: the time domain waveform diagram of the incident wave and the reflected wave, thereby avoiding the drilling and coring measurement of the rock rod.
[0017] The present invention uses an ultra-dynamic strain gauge to measure the strain variation law at a certain point on the left end of the joint. Only one strain gauge needs to be pasted, which overcomes the shortcomings of the traditional drilling and coring method, which causes great damage to the rock, exposes the interior to the air, causes secondary pollution, and is greatly affected by the hardness of the rock and human factors. The operation steps are simplified and the calculation accuracy is improved. BRIEF DESCRIPTION OF THE DRAWINGS
[0018] Figure 1 One-dimensional homogeneous rock sample.
[0019] Figure 2 Schematic diagram of the stress wave propagation process.
[0020] Figure 3 Strain-time curves of incident wave and reflected wave (a) incident wave ε1(t); (b) incident wave ε2(t).
[0021] Figure 4 Figure 2 is a diagram of the pendulum impact test device.
[0022] Figure 5 Flowchart for implementation of this method. DETAILED DESCRIPTION
[0023] The present invention is described in detail below with reference to the accompanying drawings and embodiments.
[0024] Step 1: Use a steel ruler to measure the length of the rock rod 3, measure three times, and take the average value l; use a vernier caliper to measure the cross-sectional diameter of the end of the rock rod, measure three times, and take the average value d. Use the formula Calculate the cross-sectional area of the rock rod; finally, measure the mass M of the rock rod using an electronic scale, and use the formula The rock rod density ρ is calculated; based on the measured rock rod density ρ, the wave velocity V is measured using a wave velocity meter p , using the formula E = ρ0V p 2 The elastic modulus E is obtained; according to the measured rock rod density ρ and wave velocity V p , using the formula z = ρV p Get the wave impedance z.
[0025] Step 2: Based on the continuity equation and Hooke's law, as well as the linear displacement discontinuous boundary condition when the stress wave passes through a linear deformation joint, the functional expression of the reflection coefficient R when the stress wave is normally incident through a single linear deformation joint can be obtained:
[0026] Step 3: If Figure 4 The pendulum impact test device is shown in the figure. Take two one-dimensional uniform rock samples, compact them by gypsum vibration to form a 3cm thick joint 4, squeeze and compact the gypsum joint model at the connection position of the two rock rods 3 and 5, and stick the strain gauge 8 at the 1 / 4 position on the left side of the joint. The loading device consists of a pendulum 1 with a rotatable end, a measuring rod 2, a fixed wheel 6 and a baffle 7. The pendulum hammer head can be designed and replaced by itself. The stress wave waveform, wavelength and amplitude can be controlled by changing the shape, length and material of the hammer head, and the impact energy can be controlled by adjusting the swing angle. The strain gauge 8 is connected to the ultra-dynamic strain gauge 9 to collect the strain at the 1 / 4 position of the left part of the joint under the action of the impact load. The ultra-dynamic acquisition frequency is 100ksps, and the trigger mode used is single trigger. The measurement results: incident wave ε1(t) and reflected wave ε2(t) are output to the computer.
[0027] Step 4: Based on the time-strain data obtained by the ultra-dynamic strain gauge 8, Fourier transform is performed to obtain a series of incident harmonics u in the frequency domain (0) , reflected harmonic u (1) .
[0028] Step 5: From the known R1, R2, R3...R n Fitting unknown parameter k with a series of discrete data and R function expression n. The real function expression Re(f) of R and R1, R2, R3...R n The real part of R, the imaginary part of R, the function expression Im(f), and R1, R2, R3, ... R n The imaginary part, frequency range, and wave impedance are input into the 1stopt program to calculate the common parameter k of the real function Re(f) and the imaginary function Im(f). n By continuously iteratively adjusting k n When k n Substitute the real part function curve of Re(f) and R1, R2, R3...R n The distance between the real value curves is closest, and k n Substitute the imaginary function curve of Im(f) and R1, R2, R3...R n The distance between the imaginary value curve is the closest, at this time the sum of the squares of the data deviations is minimized, the goodness of fit is optimal, and the k n This is the joint stiffness in the rock.
Claims
1. A method for inverting joint stiffness in rock mass based on reflected waves, characterized in that: The implementation steps of this method are as follows: Step 1: Derive the functional expression of the reflection coefficient R; The rock mass in the initial undisturbed state has a single linear macro joint at x1. At any position on the left side of the joint, there is an incident harmonic u perpendicular to the joint and propagating along the positive direction of the x-axis. (0) , the reflected harmonic is represented by u (1) , define R as the reflection coefficient, and describe the boundary conditions of the joints according to the linear displacement discontinuous boundary conditions when the stress wave passes through the linear deformation joint according to the continuity equation and Hooke's law; obtain the reflection coefficient when the stress wave passes through a single linear deformation joint with normal incidence k n is the joint stiffness; f is the harmonic frequency in the frequency domain after Fourier transform of the incident wave and the transmitted wave in the time domain; R is divided into two parts: the real function expression Re(f) and the imaginary function expression Im(f). The real function expression Re(f) and the imaginary function expression Im(f) have a common parameter k n ; Step 2: Determine the incident wave and reflected wave in the time domain; The pendulum impact test device is used to dynamically load the specimen at the free end on the left side of the specimen. The stress wave generated by the pendulum impact propagates in the specimen. When the dynamic load is applied, a stress wave is generated in the specimen. The stress wave pulse propagates to the right in the specimen. When it passes through the strain gauge position for the first time, it is recorded by the strain gauge, i.e., ε1(t), which is called the incident wave. When it continues to propagate to the right and reaches the joint, the stress wave is reflected and propagates to the left. When the reflected stress wave pulse passes through the strain gauge position again, it is recorded by the strain gauge for the second time, i.e., ε2(t), which is called the reflected wave. t is the change time of the incident wave and the reflected wave. Step 3: Perform discrete Fourier transform on the incident and reflected waves in the time domain; The time domain incident wave ε1(t) and the time domain reflected wave ε2(t) in the strain-time curve are expressed by the formula After discrete Fourier transform, we can obtain: a series of incident harmonics u of the time domain incident wave ε1(t) in the frequency domain (0) (f) A series of reflected harmonics u of the time domain reflected wave ε2(t) in the frequency domain (1) (f), the frequency interval and the total frequency range can be determined according to the specific situation; each group of reflected harmonics u (1) (f) corresponds to the incident harmonic u divided by the frequency (0) (f), we get: R1, R2, R3, ... R n All are plural; Step 4: From the known R1, R2, R3...R n Fitting unknown parameter k with a series of discrete data and R function expression n ; The real function expression Re(f) of R and R1, R2, R3...R n The real part of R, the imaginary part of R, the function expression Im(f), and R1, R2, R3, ... R n The imaginary part, frequency range, and wave impedance are input into the 1stopt program to calculate the common parameter k of the real function Re(f) and the imaginary function Im(f). n The fitting of k n When k n Substitute the real part function curve of Re(f) and R1, R2, R3...R n The distance between the real value curves is closest, and k n Substitute the imaginary function curve of Im(f) and R1, R2, R3...R n The distance between the imaginary value curve is the closest, at this time the sum of the squares of the data deviations is minimized, the goodness of fit is optimal, and the k n It is the joint stiffness in the rock; In the second step of the pendulum impact test device, two one-dimensional uniform rock samples are taken and compacted by gypsum vibration to form a 3cm thick joint. The gypsum joint model is squeezed and compacted at the connection position of the two rock rods, and a strain gauge is pasted at the 1 / 4 position on the left side of the joint. The loading device consists of a pendulum rotating at one end, a measuring rod, a fixed wheel and a baffle; the pendulum hammer head can be designed and replaced, and the stress wave waveform, wavelength and amplitude can be controlled by changing the hammer head shape, hammer head length and hammer head material respectively, and the impact energy can be controlled by adjusting the swing angle; the strain gauge is connected to the ultra-dynamic strain gauge to collect the strain at the 1 / 4 position of the left part of the joint under the action of the impact load, where the ultra-dynamic acquisition frequency is 100ksps, and the trigger mode adopted is single trigger; the measurement results: incident wave ε1(t) and reflected wave ε2(t) are output to the computer.
2. A method for inverting joint stiffness in rock mass based on reflected waves according to claim 1, characterized in that: In the first step, the length of the rock rod is measured three times with a steel ruler, and the average value l is taken; the cross-sectional diameter of the end of the rock rod is measured three times with a vernier caliper, and the average value d is taken. The formula Calculate the cross-sectional area of the rock rod; finally, measure the mass M of the rock rod using an electronic scale, and use the formula The rock rod density ρ is calculated; based on the measured rock rod density ρ, the wave velocity V is measured using a wave velocity meter p , using the formula E = ρV p 2 The elastic modulus E is obtained; according to the measured rock rod density ρ and wave velocity V p , using the formula z = ρV p Get the wave impedance z.
3. The method for inverting joint stiffness in rock mass based on reflected waves according to claim 1, characterized in that: In the first step, based on the continuity equation and Hooke's law, as well as the linear displacement discontinuity boundary condition when the stress wave passes through a linear deformation joint, the functional expression of the reflection coefficient R when the stress wave is normally incident through a single linear deformation joint is obtained.
4. The method for inverting joint stiffness in rock mass based on reflected waves according to claim 1, characterized in that: According to the time-strain data obtained by the ultra-dynamic strain gauge, a series of incident harmonics u in the frequency domain are obtained by Fourier transform. (0) , reflected harmonic u (1) .