A method for obtaining rock mass joint stiffness

Abstract

The present invention discloses a method for obtaining rock joint stiffness. According to the displacement discontinuity method of stress wave in linearly deformed jointed rock mass, a function expression of transmission coefficient T is derived: a function relationship between incident harmonic and transmitted harmonic about joint stiffness is established in frequency domain; incident wave and transmitted wave are subjected to discrete Fourier transform in time domain to obtain a series of incident harmonic and a series of transmitted harmonic; according to the function expression of transmission coefficient T, a series of incident harmonic and transmitted harmonic data are combined to fit the joint stiffness k that makes the incident harmonic and transmitted harmonic data satisfy the transmission coefficient function expression. n This method only requires one tap on the rock mass to measure the strain change curves at two locations before and after the joint: the time-domain strain-time diagram of the incident wave and the transmitted wave. The joint stiffness of the joint inside the rock rod can be determined by inputting it into the program, which simplifies the experimental process and avoids secondary contamination of the core drilling measurement of the rock mass.

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 discontinuous surfaces such as joints, fissures, and faults. When stress waves are incident into the rock mass, emission and transmission phenomena will occur at the joints. The incident and transmitted wave signals obtained will carry mechanical parameters related to the joints, such as joint stiffness, and thus the internal structural characteristics of the rock mass and the law of stress changes can be understood. With the construction of underground engineering and mining engineering in my country, the joint structure in the rock has an important influence on the overall strength and stability of the rock mass during mining and excavation, and is also crucial to the design and construction of engineering structures. Therefore, in order to obtain the internal joint parameters of the rock mass, it is necessary to design a method for inverting the internal joint stiffness of the rock mass from the incident and transmitted waves.

[0003] At present, the main method for obtaining the internal joint stiffness of rock mass is the core drilling method, which destroys the external rock mass and takes out the rock core containing internal joints. The required joint stiffness can be obtained by measuring and calculating the rock core. However, 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.

[0004] With the gradual maturity of wave testing technology, it has become possible to use waves (mechanical waves or electromagnetic waves) as information carriers and obtain the incident wave and transmitted wave signals using strain gauges to obtain the stiffness of internal joints in rocks. This can provide an important basis for studying the propagation of stress waves in jointed rocks.

[0005] The invention obtains the incident wave strain signal in the time domain and the transmission wave strain signal through the joints by means of the ultra-dynamic strain meter, introduces the concept of transmission coefficient in the frequency domain by means of discrete Fourier transform, and provides an accurate and reliable calculation method to study the stiffness of linear joints inside the measured rock mass. Summary of the invention

[0006] The invention obtains the incident wave strain signal in the time domain and the transmission wave strain signal through the joints by means of the ultra-dynamic strain meter, introduces the concept of transmission coefficient in the frequency domain by means of discrete Fourier transform, and provides an accurate and reliable calculation method to study the stiffness of linear joints inside the measured rock mass.

[0007] Technical solution of the present invention

[0008] The present invention is based on the displacement discontinuity method of stress wave in linear deformation jointed rock mass, and derives the functional expression of transmission coefficient T: the incident harmonic γ is established in the frequency domain angle (1)(f) and the transmitted harmonic γ (2) (f) about the joint stiffness k n Functional relationship; discrete Fourier transform of the incident wave ξ1(t) and the transmitted wave ξ2(t) in the time domain can be obtained: a series of incident harmonics γ (1) (f) and a series of transmitted harmonics γ (2) (f) Based on the functional expression of the transmission coefficient T, a series of incident harmonic and transmitted harmonic data can be combined to fit the joint stiffness k that makes the incident harmonic and transmitted harmonic data satisfy the transmission coefficient functional expression. n ,.

[0009] The measurement part includes: the granite rod density ρ, elastic modulus E, the incident wave ξ1(t) and the transmitted wave ξ2(t) in the time domain, and the discrete Fourier transform of the incident wave ξ1(t) and the transmitted wave ξ2(t) to obtain a series of corresponding incident harmonics γ in the frequency domain. (1) (f) value: including real and imaginary parts; a series of reflected harmonics γ (2) The value of (f): includes two parts, real and imaginary. Based on the above measurement and calculation results, the function expression of the transmission coefficient T derived by the displacement discontinuity method of stress waves in linear deformation jointed rock mass is used to fit the joint stiffness k through which the incident wave passes using 1stopt software. n .

[0010] The detailed description is as follows:

[0011] Step 1: Obtain the incident harmonics in the frequency domain from the incident wave in the time domain by discrete Fourier transform

[0012] When Figure 2 The striking device shown in the figure is used to select two one-dimensional uniform granite rock rod samples. The middle of the two rock rods are compacted by gypsum vibration to form a 5 cm thick gypsum joint model. Strain gauges are glued at the left 1 / 4 and right 1 / 4 of the joints, as shown in the figure. Figure 1 As shown in the figure, after striking the left end of the rock rod, the dynamic load propagates in the rock mass in the form of a stress wave, and the incident wave pulse ξ1(t) is measured by the strain gauge at the 1 / 4 position of the left end, as shown in the figure. Figure 3 As shown, a set of strain-time curves of incident waves measured in the experiment are shown, and t is the changing time of the incident wave.

[0013] The incident wave ξ1(t) is transformed by discrete Fourier transform to obtain the incident harmonics γ at a series of frequencies (1) (f) where f is the harmonic frequency in the frequency domain after Fourier transform of the incident wave in the time domain. The frequency interval and frequency range can be determined according to the actual incident wave. The incident harmonic γ (1) (f) After calculation, it is a complex number: it consists of two parts: a real number and an imaginary number.

[0014] Step 2: Obtain the transmitted harmonics in the frequency domain from the time domain transmitted wave through discrete Fourier transform.

[0015] When the pendulum strikes the left end of the granite rock rod, the stress wave generated propagates to the right and is recorded when it passes through the first strain gauge, which is recorded as the incident wave ξ1(t). When the incident wave passes through the middle gypsum joint, it is transmitted, and the generated transmission wave continues to propagate to the right. When it passes through the second strain gauge, it is recorded as the transmission wave ξ2(t), as shown in Figure 4 The figure shows a set of strain-time curves of the transmission wave measured in the experiment. t is the change time of the transmission wave.

[0016] The measured transmission wave pulse ξ2(t) is subjected to discrete Fourier transform to obtain a series of corresponding transmission harmonics γ (2) (f), where f is the harmonic frequency in the frequency domain after Fourier transform of the time domain transmission wave. The frequency interval and frequency range can be determined according to the actual transmission wave situation. The transmission harmonic γ (2) (f) After calculation, it is a complex number: It consists of two parts: a real number and an imaginary number.

[0017] Step 3: Establish the incident harmonic γ in the frequency domain (1) (f) and the transmitted harmonic γ (2) (f) about k n The function expression of .

[0018] According to a series of incident harmonics γ (1) (f) and the transmitted harmonic γ (2) (f) Inverse calculation of rock joint stiffness k n The derivation process is as follows: Taking a single incident harmonic γ (1) (f0) and a single transmitted harmonic γ (2) (f0) as an example, we introduce the transmission coefficient T, then

[0019] γ (2) (f) = Tγ (1) (f) (1)

[0020] According to 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 transmission coefficient when the stress wave passes through a single linear deformation joint at normal incidence can be obtained:

[0021]

[0022] Where: k nis 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; w is the harmonic angular velocity, w = 2πf; z = ρ0V0; T is divided into two parts: the real part expression R(f) and the imaginary part expression I(f):

[0023]

[0024]

[0025] The actual measured transmission harmonic γ (2) (f) corresponds to the incident harmonic γ divided by the frequency (1) (f) We obtain: T1, T2, T3, T4, ... T n All are plural.

[0026] Step 4: Make T1, T2, T3, T4, ... T calculated according to the test waveform n The real and imaginary discrete data of are matched with the two continuous function curves of equation 3 and equation 4 respectively, and the unknown parameter k is fitted. n size.

[0027] The real function expression of the transmission coefficient T is R(f), T1, T2, T3, T4, ... T n The real part value and imaginary part function expression I(f), T1, T2, T3, T4, ... T n The imaginary value, frequency f, elastic modulus E, and wave impedance z are input into the 1stopt program, and k is adjusted through continuous iteration. n The value of k n The function curves of the real part function expression R(f) and the imaginary part function expression I(f) are respectively consistent with the experimentally obtained T1, T2, T3, ... T n The distance between the real data curve and the imaginary data curve is the closest. At this time, the sum of the squares of the data deviations is minimized, and the goodness of fit is optimal. At this time, k n This is the joint stiffness in the rock.

[0028] Compared with the prior art, the method provided by the present invention can achieve the goal of only tapping the rock mass once and measuring the strain change curves at two locations before and after the joints: the time domain strain-time diagram of the incident wave and the transmitted wave. By inputting it into the program, the joint stiffness of the joints inside the rock rod can be determined, which simplifies the experimental process and solves the complex steps of obtaining the joint stiffness in the existing test methods, avoiding the problem of secondary pollution caused by drilling and coring measurements of the rock mass. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a one-dimensional homogeneous rock sample.

[0030] Figure 2 Schematic diagram of stress wave propagation process.

[0031] Figure 3 is the incident wave ξ1(t).

[0032] Figure 4 is the transmitted wave ξ2(t).

[0033] Figure 5 It is a pendulum impact test device.

[0034] Figure 6 It is a schematic diagram of the structure of the device of the present invention. DETAILED DESCRIPTION

[0035] The present invention is implemented by using a knocking device, which is further described in detail below:

[0036] Step 1: Select the same granite rock rod samples 5 and 7, use a ruler to measure the length of granite rock rod 5 three times to obtain l1, l2, and l3, and take the average of the three measurement results as the length of the rock rod Use a vernier caliper to measure the end diameter of the rock rod 5 three times to obtain d1, d2, and d3, and take the average of the three measurement results as the cross-sectional diameter of the rock rod. Using the formula Calculate the cross-sectional area A of the rock rod; finally, measure the mass M of the rock rod using an electronic scale; use the formula The rock mass rod density ρ0 is calculated; the wave velocity V is measured using a wave velocity meter p , using the formula E = ρ0V p 2 Get the elastic modulus E; use the formula z = ρ0V p Get the wave impedance z.

[0037] Step 2: If Figure 5 The figure shows a pendulum impact test device. The test device consists of a pendulum 1 with one end that can swing freely, a scale adjustment ruler 2, a pendulum fixing rod 3, a rock rod fixing wheel 4, and a baffle 8. The mass of the pendulum can be replaced by itself, and the amplitude and wavelength of the incident wave can be controlled by adjusting the mass and phase angle of the pendulum 1. The strain gauge 9 is attached to the left side of the joint 6 at 1 / 4, and the other end is connected to the ultra-dynamic strain gauge 12. The strain gauge 11 is attached to the right side of the joint 6 at 1 / 4, and the other end is connected to the ultra-dynamic strain gauge 12. The ultra-dynamic acquisition frequency is 100ksps. When the pendulum 1 hits the left end of the rock rod 5, the stress wave generated propagates to the right and is recorded when it passes through the first strain gauge 10. It is recorded as the incident wave ξ1(t). ξ1(t) is subjected to discrete Fourier transform to obtain a series of incident harmonics γ in the frequency domain angle. (1) (f).

[0038] Step 2: When the incident wave passes through the middle gypsum joint 6, transmission occurs. The generated transmission wave continues to propagate to the right. When it passes through the second strain gauge 11, it is recorded as the transmission wave ξ2(t). ξ2(t) is discretely Fourier transformed to obtain a series of incident harmonics γ in the frequency domain. (2) (f).

[0039] Step 3: Establish the incident harmonic γ in the frequency domain (1) (f) and the transmitted harmonic γ (2) (f) about k n The function expression T. According to the continuity equation and Hooke's law, as well as the linear displacement discontinuous boundary condition when the stress wave passes through the linear deformation joint, the function expression of the transmission coefficient T can be obtained, including the real part function expression R(f) and the imaginary part function expression I(f). The actual measured transmission harmonic γ (2) (f) corresponds to the incident harmonic γ divided by the frequency (1) (f) We obtain: T1, T2, T3, T4, ... T n All are plural.

[0040] Step 4: Input the real function expression R(f), real part value, imaginary function expression I(f), imaginary part value, frequency f, elastic modulus E, and wave impedance z of the transmission coefficient T into the 1stopt program to calculate the parameter k of the real and imaginary functions. n The fitting of k is adjusted by continuous iteration n The value of k n The function curves of the real part function expression R(f) and the imaginary part function expression I(f) are respectively related to the experimentally obtained T1, T2, T3, T4, ... T n The distance between the real data curve and the imaginary data curve is the closest. At this time, the sum of the squares of the data deviations is minimized and the goodness of fit is optimal. At this time, k n This is the joint stiffness in the rock.

Claims

1. A method for obtaining rock mass joint stiffness, characterized in that: According to the displacement discontinuity method of stress wave in linear deformation jointed rock mass, the functional expression of transmission coefficient T is derived: the incident harmonic γ is established in the frequency domain (1) (f) and the transmitted harmonic γ (2) (f) about the joint stiffness k n Functional relationship; discrete Fourier transform of the incident wave ξ1(t) and the transmitted wave ξ2(t) in the time domain can be obtained: a series of incident harmonics γ (1) (f) and a series of transmitted harmonics γ (2) (f) According to the function expression of the transmission coefficient T, combined with a series of incident harmonic and transmitted harmonic data, the joint stiffness k that makes the incident harmonic and transmitted harmonic data satisfy the transmission coefficient function expression is fitted. n ; The technical implementation steps of this method are as follows: Step 1: Obtain the incident harmonics in the frequency domain from the incident wave in the time domain by discrete Fourier transform; Two one-dimensional uniform granite rock rod samples were selected. A 5-cm thick gypsum joint model was formed by compacting the middle of the two rock rods with gypsum vibration. Strain gauges were attached at the 1 / 4 position on the left and the 1 / 4 position on the right of the joint. After the left end of the rock rod was struck, the dynamic load propagated in the rock mass in the form of a stress wave. The incident wave pulse ξ1(t) was measured by the strain gauge at the 1 / 4 position on the left end. This is a set of strain-time curves of the incident wave measured in the experiment, and t is the change time of the incident wave. The incident wave ξ1(t) is transformed by discrete Fourier transform to obtain the incident harmonics γ at a series of frequencies (1) (f) where f is the harmonic frequency in the frequency domain after Fourier transform of the incident wave in the time domain. The frequency interval and frequency range are determined according to the actual incident wave. The incident harmonic γ (1) (f) after calculation, it is a complex number: it consists of two parts: a real number and an imaginary number; Step 2: Obtain the transmitted harmonics in the frequency domain from the time domain transmitted wave through discrete Fourier transform; When the pendulum hits the left end of the granite rock rod, the stress wave generated propagates to the right and is recorded when passing through the first strain gauge, which is recorded as the incident wave ξ1(t). When the incident wave passes through the middle gypsum joint, it is transmitted, and the generated transmission wave continues to propagate to the right. When passing through the second strain gauge, it is recorded as the transmission wave ξ2(t). This is a set of strain-time curves of the transmission wave measured in the experiment; t is the change time of the transmission wave; The measured transmission wave pulse ξ2(t) is subjected to discrete Fourier transform to obtain a series of corresponding transmission harmonics γ (2) (f), where f is the harmonic frequency in the frequency domain after Fourier transform of the time domain transmission wave. The frequency interval and frequency range are determined according to the actual transmission wave situation. The transmission harmonic γ (2) (f) after calculation, it is a complex number: it consists of two parts: a real number and an imaginary number; Step 3: Establish the incident harmonic γ in the frequency domain (1) (f) and the transmitted harmonic γ (2) (f) about k n Function expression of ; According to a series of incident harmonics γ (1) (f) and the transmitted harmonic γ (2) (f) Inversion of rock joint stiffness k n The derivation process is as follows: a single incident harmonic γ (1) (f0) and a single transmitted harmonic γ (2) (f0), introducing the transmission coefficient T, then γ (2) (f)=Tγ (1) (f) (1) According to the continuity equation and Hooke's law, as well as the linear displacement discontinuity boundary condition when the stress wave passes through the linear deformation joint, the transmission coefficient when the stress wave is normally incident through a single linear deformation joint is obtained: Where: 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; w is the harmonic angular velocity, w = 2πf; z = ρ0V0; T is divided into two parts: the real part expression R(f) and the imaginary part expression I(f): The actual measured transmission harmonic γ (2) (f) corresponds to the incident harmonic γ divided by the frequency (1) (f) We obtain: T1, T2, T3, T4, ... T n All are plural; Step 4: Make T1, T2, T3, T4, ... T calculated according to the test waveform n The real and imaginary discrete data of are matched with the two continuous function curves of formula (3) and formula (4) respectively, and the unknown parameter k is fitted. n size; The real function expression of the transmission coefficient T is R(f), T1, T2, T3, T4, ... T n The real part value and imaginary part function expression I(f), T1, T2, T3, T4, ... T n The imaginary value, frequency f, elastic modulus E, and wave impedance z are input into the 1stopt program, and k is adjusted through continuous iteration. n The value of k n The function curves of the real part function expression R(f) and the imaginary part function expression I(f) are respectively related to the experimentally obtained T1, T2, T3, ... T n The distance between the real data curve and the imaginary data curve is the closest. At this time, the sum of the squares of the data deviations is minimized and the goodness of fit is optimal. At this time, k n This is the joint stiffness in the rock.

2. The method for obtaining rock mass joint stiffness according to claim 1, characterized in that: The measurement part includes: the granite rod density ρ, elastic modulus E, the incident wave ξ1(t) and the transmitted wave ξ2(t) in the time domain, and the discrete Fourier transform of the incident wave ξ1(t) and the transmitted wave ξ2(t) to obtain a series of corresponding incident harmonics γ in the frequency domain. (1) (f) value: including real and imaginary parts; a series of reflected harmonics γ (2) The value of (f) includes two parts: real and imaginary. Based on the above measurement and calculation results, the functional expression of the transmission coefficient T derived by the displacement discontinuity method of stress waves in linear deformation jointed rock mass is used to fit the joint stiffness k through which the incident wave passes using 1stopt software. n .

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