CN114417610A - Method for acquiring rock mass joint stiffness - Google Patents

Method for acquiring rock mass joint stiffness Download PDF

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CN114417610A
CN114417610A CN202210060116.9A CN202210060116A CN114417610A CN 114417610 A CN114417610 A CN 114417610A CN 202210060116 A CN202210060116 A CN 202210060116A CN 114417610 A CN114417610 A CN 114417610A
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incident
wave
harmonic
transmission
gamma
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范立峰
卫秀文
江枫
王梦
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Beijing University of Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/15—Correlation function computation including computation of convolution operations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Abstract

The invention discloses a method for acquiring joint stiffness of a rock mass, which is characterized in that a function expression of a transmission coefficient T is deduced according to a method for discontinuously deforming displacement in a linear deformation joint rock mass by stress waves: establishing a function relation of incident harmonic and transmission harmonic with respect to joint stiffness at a frequency domain angle; carrying out discrete Fourier transform on incident waves and transmitted waves in a time domain to obtain a series of incident harmonics and a series of transmitted harmonics; fitting a section which enables the incident harmonic and the transmission harmonic data to meet the transmission coefficient function expression by combining a series of incident harmonic and transmission harmonic data according to the function expression of the transmission coefficient TPhysical stiffness kn. According to the method, the rock mass is knocked once, and strain change curves of two positions before and after the joint are measured: the time domain strain-time diagram of incident waves and transmitted waves can determine the joint stiffness of the internal joints of the rock rod in an input procedure, so that the experimental procedures are simplified, and secondary pollution caused by drilling coring measurement of the rock mass is avoided.

Description

Method for acquiring rock mass joint stiffness
Technical Field
The invention belongs to the technical field of rock mass measurement, and particularly relates to a method for inverting the linear macroscopic joint stiffness of a rock rod.
Background
The rock body is composed of complete rocks and discontinuous surfaces such as joint cracks and faults, stress waves are incident into the rock body, emission and transmission phenomena can occur at joints, and obtained incident wave and transmitted wave signals can carry mechanical parameters related to the joints, such as joint rigidity, so that the internal structural characteristics of the rock body and the change rule of the stress can be known. With the construction of underground engineering and mining engineering in China, joint structures in rocks have important influence on the overall strength and stability of rock masses in the process of mining and excavating, and are also important for 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 by incident waves and transmitted waves.
At present, the method for acquiring the joint rigidity in the rock mass mainly comprises a drilling coring method, wherein a rock core containing joints inside is taken out by destroying an external rock mass. And measuring and calculating the core to obtain the required joint rigidity. However, the traditional drilling method has a large damage degree to the rock, can expose the interior to the air, causes secondary pollution, and is greatly influenced by the hardness degree of the rock and human factors.
With the gradual maturity of wave method testing technology, it becomes possible to obtain the joint rigidity in the rock by using incident wave and transmitted wave signals obtained by a strain gauge by using waves (mechanical waves or electromagnetic waves) as information carriers, and an important basis can be provided for researching the propagation of stress waves in the rock containing joints.
According to the invention, an incident wave strain signal and a jointed transmission wave strain signal in a time domain are obtained through a super-dynamic strain gauge, and the linear joint stiffness in the measured rock mass is researched by means of a concept of introducing a transmission coefficient in a frequency domain through discrete Fourier transform, so that an accurate and reliable calculation method is provided.
Disclosure of Invention
According to the invention, an incident wave strain signal and a jointed transmission wave strain signal in a time domain are obtained through a super-dynamic strain gauge, and the linear joint stiffness in the measured rock mass is researched by means of a concept of introducing a transmission coefficient in a frequency domain through discrete Fourier transform, so that an accurate and reliable calculation method is provided.
Technical scheme of the invention
The invention relates to a function expression of a transmission coefficient T derived according to a displacement discontinuity method of stress waves in a linear deformation jointed rock mass: establishing incident harmonic gamma in frequency domain angle(1)(f) And transmission harmonic gamma(2)(f) About joint stiffness knThe functional relation of (1); passing the time domain down incident wave xi1(t) and transmitted wave ξ2(t) performing a discrete Fourier transform to obtain: a series of incident harmonics gamma(1)(f) And a series of transmission harmonics gamma(2)(f) (ii) a Fitting joint stiffness k enabling the incident harmonic and transmission harmonic data to meet the transmission coefficient function expression by combining a series of incident harmonic and transmission harmonic data according to the transmission coefficient function expressionn,。
The measurement section includes: for density rho, elastic modulus E and incident wave xi under time domain of granite rod1(t) and transmitted wave ξ2(t) and measuring the incident wave xi1(t) and transmitted wave ξ2(t) performing discrete Fourier transform to obtain a series of corresponding incident harmonics gamma in the frequency domain(1)(f) The numerical value of (A): the method comprises the following steps of (1) including a real part and an imaginary part; a series of reflection harmonics gamma(2)(f) The numerical value of (A): including both real and imaginary components. Fitting the joint stiffness k through which the incident wave passes by using 1stopt software according to a function expression formula of the transmission coefficient T derived by the method for linear deformation of displacement discontinuity in the jointed rock mass according to the stress wave by using the measurement and calculation resultsn。
The detailed description is as follows:
the first step is as follows: method for solving incident harmonic wave in frequency domain through discrete Fourier transform by time domain incident wave
When the knocking device is used as shown in figure 2, two one-dimensional even granite rock rod samples are selected, and the middle parts of the two rock rods are densely formed by vibrating gypsum to form 5cIn a gypsum joint model with the thickness of m, strain gauges are adhered to the left side l/4 and the right side l/4 of the joint, as shown in figure 1, after the left end of a rock rod is knocked, dynamic load is transmitted in a rock body in the form of stress waves, and incident wave pulse xi is measured through the strain gauge at the left end l/41(t), as shown in FIG. 3, is a strain-time curve of a set of incident waves measured by experiment, and t is the change time of the incident waves.
Passing incident wave xi1(t) obtaining incident harmonics γ at a range of frequencies by discrete Fourier transform(1)(f) Wherein f is the harmonic frequency in the frequency domain after the Fourier transform of the time domain incident wave, the frequency interval and the frequency range can be determined according to the actual incident wave condition, and the incident harmonic gamma is(1)(f) Calculated as complex number: consists of real and imaginary parts.
The second step is that: and solving transmission harmonic waves in a frequency domain through discrete Fourier transform by the time-domain transmission waves.
When the pendulum bob impacts the left end of the granite rock rod, the stress wave generated therewith is transmitted to the right, and when the stress wave passes through the first strain gauge, the stress wave is recorded as an incident wave xi1(t) when the incident wave passes through the middle gypsum joint, the incident wave is transmitted, the generated transmitted wave continues to propagate to the right, and when the incident wave passes through the second strain gauge, the transmitted wave is recorded as a transmitted wave xi2(t), as shown in FIG. 4, is a set of experimentally measured strain-time curves of the transmitted waves. t is the time of change of the transmitted wave.
Measuring the transmission wave pulse xi2(t) performing discrete Fourier transform to obtain transmission harmonics gamma corresponding to each other under a series of frequencies(2)(f) Wherein f is the harmonic frequency in the frequency domain after the Fourier transform of the time domain transmission wave, the frequency interval and the frequency range can be determined according to the actual transmission wave condition, and the transmission harmonic gamma is(2)(f) Calculated as complex number: the method is composed of real numbers and imaginary numbers.
The third step: establishing incident harmonic gamma in frequency domain angle(1)(f) And transmission harmonic gamma(2)(f) About knIs used for the functional expression of (1).
According to a series of incident harmonics gamma(1)(f) And transmission harmonic gamma(2)(f) Inversion of joint stiffness k in rocknThe derivation process of (1) is as follows: with a single incident harmonic gamma(1)(f0) And a single transmission harmonic gamma(2)(f0) For example, we introduce a transmission coefficient T, then
γ(2)(f)＝Tγ(1)(f) (1)
According to the continuous equation, Hooke's law and the condition that the stress wave is not continuous when passing through the linear deformation joint, the transmission coefficient when the normal incidence of the stress wave passes through the single linear deformation joint can be obtained
Figure BDA0003477916290000031
In the formula: k is a radical ofnJoint stiffness; f is the harmonic frequency in the frequency domain after Fourier transformation of the incident wave and the transmitted wave in the time domain; w is the harmonic angular velocity, w ═ 2 π f; z is rho0V0(ii) a T is divided into a real part expression R (f) and an imaginary part expression I (f):
Figure BDA0003477916290000032
Figure BDA0003477916290000033
the actually measured transmission harmonic gamma(2)(f) Corresponding to the incident harmonic y divided by this frequency(1)(f) Obtaining: t is1、 T2、T3、T4、……TnAre all plural.
The fourth step: so that T is calculated from the test waveform1、T2、T3、T4、……TnFitting the discrete data with the continuous function curves of the formula 3 and the formula 4 to obtain an unknown parameter knThe size of (2).
The real part function expression R (f), T of the transmission coefficient T1、T2、T3、T4、……TnThe real part value and the imaginary part function of (A) are expressed as I (f), T1、T2、T3、T4、……TnThe imaginary part value, the frequency f, the elastic modulus E and the wave impedance z are input into a 1stopt program, and k is adjusted through continuous iterationnA value of such that knThe function curves taken into the real part function expression R (f) and the imaginary part function expression I (f) are respectively combined with the T obtained by the test1、T2、T3、…… TnThe distance between the real part data curve and the imaginary part data curve is closest, the sum of squares of data deviation is minimum, the goodness of fit is optimal, and k is obtained at the momentnI.e. joint stiffness in the rock.
Compared with the prior art, the method provided by the invention can realize that the strain change curves of two positions before and after the joint are measured by only knocking the rock mass once: the joint stiffness of the joint inside the rock rod can be determined by inputting the time domain strain-time diagrams of incident waves and transmitted waves into a program, so that the experimental procedure is simplified, and the problems that the joint stiffness obtaining step is complex in the existing experimental method and secondary pollution is caused to the drilling coring measurement of the rock body are solved.
Drawings
FIG. 1 is a one-dimensional homogeneous rock sample.
Fig. 2 is a schematic diagram of a stress wave propagation process.
FIG. 3 is an incident wave xi1(t)。
FIG. 4 is a transmission wave ξ2(t)。
Fig. 5 is a pendulum impact test apparatus.
FIG. 6 is a schematic view of the structure of the device of the present invention.
Detailed Description
The invention is implemented using a rapping device, as described in further detail below:
the first step is as follows: selecting the same granite rock rod samples 5 and 7, and measuring the length of the granite rock rod 5 for 3 times by using a graduated scale to obtain l1、l2、l3Taking the average value of three measurements as the length of the rock rod
Figure BDA0003477916290000041
Measuring the end diameter of the rock rod 5 with a vernier caliper 3 times to obtain d1、d2、d3Taking the average value of three measurement results as the section diameter of the rock rod
Figure BDA0003477916290000042
Using formulas
Figure BDA0003477916290000043
Calculating the cross section area A of the rock rod; finally, measuring the mass M of the rock rod by an electronic scale; using formulas
Figure BDA0003477916290000044
Calculating to obtain the density rho of the rock mass rod0(ii) a Measuring wave velocity V by wave velocity instrumentpRho is given by the formula E0Vp 2Obtaining an elastic modulus E; using the formula z ═ ρ0VpThe wave impedance z is obtained.
The second step is that: fig. 5 shows a pendulum impact test apparatus. The test device comprises pendulum bob 1, a scale adjusting ruler 2, a pendulum bob fixing rod 3, a rock rod fixing wheel 4 and a baffle 8, wherein one end of the pendulum bob can freely swing, the mass of the pendulum bob can be automatically replaced, and the amplitude and the wavelength of incident waves are controlled by adjusting the mass and the amplitude angle of the pendulum bob 1. The strain gauge 9 is attached to the left side l/4 of the joint 6, the other end of the strain gauge is connected with the ultra-dynamic strain gauge 12, the strain gauge 11 is attached to the right side l/4 of the joint 6, the other end of the strain gauge is connected with the ultra-dynamic strain gauge 12, the ultra-dynamic collection frequency is 100ksps, when the pendulum bob 1 knocks the left end of the rock rod 5, stress waves generated along with the strain gauge propagate rightwards, and when the strain gage passes through the first strain gauge 10, the stress waves are recorded as incident waves xi1(t), mixing xi1(t) performing discrete Fourier transform to obtain a series of incident harmonics gamma of frequency domain angle(1)(f)。
The second step is that: when the incident wave passes through the middle gypsum joint 6, transmission occurs, and the resulting transmitted wave continues to travel to the right, passing through the second strain gauge 11, and is recorded as transmitted wave ξ2(t), mixing xi2(t) performing discrete Fourier transform to obtain a series of incident harmonics gamma of frequency domain angle(2)(f)。
The third step: establishing incident harmonic gamma in frequency domain angle(1)(f) And transmission harmonic gamma(2)(f) About knThe functional expression of (1) is T. According to the continuous equation and Hooke's law and the discontinuous boundary condition of linear displacement when the stress wave is in linear deformation joint, the function expression of the transmission coefficient T can be obtained and comprises a real part function expression R (f) and an imaginary part function expression I (f). And the actually measured transmission harmonic gamma(2)(f) Corresponding to the incident harmonic y divided by this frequency(1)(f) Obtaining: t is1、T2、T3、T4、……TnAre all plural.
The fourth step: inputting a real part function expression R (f), a real part numerical value, an imaginary part function expression I (f), an imaginary part numerical value, a frequency f, an elastic modulus E and a wave impedance z of the transmission coefficient T into a 1stopt program, and carrying out a common parameter k of the real part function and the imaginary part functionnBy continuously iteratively adjusting knA value of such that knThe function curves of the real part function expression R (f) and the imaginary part function expression I (f) are respectively substituted with the T obtained by the experiment1、T2、T3、 T4、……TnThe distance between the real part data curve and the imaginary part data curve is closest, the square sum of the data deviation reaches the minimum, the goodness of fit is optimal, and k is obtained at the momentnI.e. joint stiffness in the rock.

Claims (3)

1. A method for acquiring rock mass joint stiffness is characterized by comprising the following steps: according to the displacement discontinuity method of the stress wave in the linear deformation jointed rock mass, a function expression of the transmission coefficient T is deduced: establishing incident harmonic gamma in frequency domain angle(1)(f) And transmission harmonic gamma(2)(f) About joint stiffness knThe functional relation of (1); passing the time domain down incident wave xi1(t) and transmitted wave ξ2(t) performing a discrete Fourier transform to obtain: a series of incident harmonics gamma(1)(f) And a series of transmission harmonics gamma(2)(f) (ii) a According to the penetrationFitting a function expression of the transmission coefficient T by combining a series of data of incident harmonic and transmission harmonic to enable the data of the incident harmonic and the transmission harmonic to meet the joint stiffness k of the transmission coefficient function expressionn。
2. The method for acquiring the rock mass joint stiffness according to claim 1, characterized by comprising the following steps: the measurement section includes: for density rho, elastic modulus E and incident wave xi under time domain of granite rod1(t) and transmitted wave ξ2(t) and measuring the incident wave xi1(t) and transmitted wave ξ2(t) performing discrete Fourier transform to obtain a series of incident harmonics gamma corresponding to the frequency domain(1)(f) The numerical value of (A): the method comprises the following steps of (1) including a real part and an imaginary part; a series of reflection harmonics gamma(2)(f) The numerical value of (A): the method comprises the following steps of (1) including a real part and an imaginary part; fitting joint stiffness k through which the incident wave passes by using 1stopt software according to a function expression of a transmission coefficient T derived by a method for realizing the linear deformation of the stress wave according to the measurement and calculation results and according to the displacement discontinuity method in the jointed rock bodyn。
3. The method for acquiring the rock mass joint stiffness according to claim 1, characterized by comprising the following steps: the technical implementation steps of the method are as follows:
the first step is as follows: method for solving incident harmonic wave in frequency domain through discrete Fourier transform by time domain incident wave
Selecting two one-dimensional uniform granite rock rod samples, vibrating and compacting the gypsum to form a gypsum joint model with the thickness of 5cm in the middle of the two rock rods, pasting strain gauges at the left side l/4 and the right side l/4 of the joint, after knocking the left end of the rock rod, dynamically loading the rock body in a stress wave mode, and measuring an incident wave pulse xi through the strain gauge at the left end l/41(t) is a set of experimentally measured strain-time curves of the incident waves, and t is the change time of the incident waves;
passing incident wave xi1(t) obtaining incident harmonics γ at a range of frequencies by discrete Fourier transform(1)(f) Wherein f is the harmonic frequency in the frequency domain of the time domain incident wave after Fourier transformationThe interval and frequency range depend on the actual incident wave, the incident harmonic gamma(1)(f) Calculated as complex number: the device consists of a real number part and an imaginary number part;
the second step is that: solving transmission harmonic waves in a frequency domain through discrete Fourier transform by time-domain transmission waves;
when the pendulum bob impacts the left end of the granite rock rod, the stress wave generated therewith is transmitted to the right, and when the stress wave passes through the first strain gauge, the stress wave is recorded as an incident wave xi1(t) when the incident wave passes through the middle gypsum joint, the incident wave is transmitted, the generated transmitted wave continues to propagate to the right, and when the incident wave passes through the second strain gauge, the transmitted wave is recorded as a transmitted wave xi2(t) is a set of experimentally measured strain-time curves of the transmitted waves; t is the change time of the transmitted wave;
measuring the transmission wave pulse xi2(t) performing discrete Fourier transform to obtain transmission harmonics gamma corresponding to each other under a series of frequencies(2)(f) Wherein f is the harmonic frequency in the frequency domain after the Fourier transform of the time domain transmission wave, the frequency interval and the frequency range are determined according to the actual transmission wave condition, and the transmission harmonic gamma is(2)(f) Calculated as complex number: the device consists of a real number part and an imaginary number part;
the third step: establishing incident harmonic gamma in frequency domain angle(1)(f) And transmission harmonic gamma(2)(f) About knThe functional expression of (a);
according to a series of incident harmonics gamma(1)(f) And transmission harmonic gamma(2)(f) Inversion of joint stiffness k in rocknThe derivation process of (1) is as follows: single incident harmonic gamma(1)(f0) And a single transmission harmonic gamma(2)(f0) Introduction of the transmission coefficient T, then
γ(2)(f)＝Tγ(1)(f) (1)
Obtaining the transmission coefficient when the normal incidence of the stress wave passes through the single linear deformation joint according to a continuous equation, Hooke's law and the condition of the discontinuous boundary of the linear displacement when the stress wave passes through the linear deformation joint
Figure FDA0003477916280000021
In the formula: k is a radical ofnJoint stiffness; f is the harmonic frequency in the frequency domain after Fourier transformation of the incident wave and the transmitted wave in the time domain; w is the harmonic angular velocity, w ═ 2 π f; z is rho0V0(ii) a T is divided into a real part expression R (f) and an imaginary part expression I (f):
Figure FDA0003477916280000022
Figure FDA0003477916280000023
the actually measured transmission harmonic gamma(2)(f) Corresponding to the incident harmonic y divided by this frequency(1)(f) Obtaining: t is1、T2、T3、T4、……TnAre all plural;
the fourth step: so that T is calculated from the test waveform1、T2、T3、T4、……TnFitting a plurality of discrete data of the real part and the imaginary part with two continuous function curves of a formula (3) and a formula (4) respectively to obtain an unknown parameter knThe size of (d);
the real part function expression R (f), T of the transmission coefficient T1、T2、T3、T4、……TnThe real part value and the imaginary part function of (A) are expressed as I (f), T1、T2、T3、T4、……TnThe imaginary part value, the frequency f, the elastic modulus E and the wave impedance z are input into a 1stopt program, and k is adjusted through continuous iterationnA value of such that knThe function curves of the real part function expression R (f) and the imaginary part function expression I (f) are respectively substituted with the T obtained by the test1、T2、T3、……TnThe distance between the real part data curve and the imaginary part data curve is closest, the square sum of the data deviation reaches minimum, and fitting is carried outGoodness is best when k isnI.e. joint stiffness in the rock.
CN202210060116.9A 2022-01-19 2022-01-19 Method for acquiring rock mass joint stiffness Pending CN114417610A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115561313A (en) * 2022-10-09 2023-01-03 四川大学 Method for predicting static shear stiffness of rock joint based on sound wave test

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115561313A (en) * 2022-10-09 2023-01-03 四川大学 Method for predicting static shear stiffness of rock joint based on sound wave test
CN115561313B (en) * 2022-10-09 2024-01-26 四川大学 Method for predicting static shear stiffness of rock joint based on acoustic wave test

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