Measurement method of viscosity coefficient of rock mass Maxwell viscoelastic model

Abstract

The invention discloses a method for measuring the viscosity coefficient of the Maxwell viscoelastic model of rock mass, comprising the following steps: based on the blasting design, determining the borehole diameter, explosive density, detonation velocity and rock wave impedance; according to the blasting design, determining the position of the last detonation blast hole, and arranging 5 to 8 large-range vibration velocity testers within a range of 1.0m to 3.0m from the blast hole behind the blasting area; recording the data collected by the vibration meter during the blasting process, and extracting the radial vibration velocity peak value; based on the law of conservation of momentum of shock wave propagation, calculating the radial stress at each vibration velocity measurement point; analyzing and determining the radial stress attenuation characteristics of the Maxwell viscoelastic model of rock mass; based on the measured radial stress at different positions, fitting and determining the viscosity coefficient of the Maxwell viscoelastic model of rock mass. The method has the advantages of simple operation, fast measurement speed, low cost, etc.

Description

Technical Field

[0001] The invention relates to the technical field of geotechnical engineering, and in particular to a method for measuring the viscosity coefficient of a rock mass Maxwell viscoelastic model. Background Art

[0002] Drilling and blasting technology is widely used in geotechnical engineering fields such as water conservancy and hydropower, transportation, and railways due to its high efficiency and economic advantages. Explosion shock waves are one of the main factors that cause damage to rock mass and protective structures caused by the explosion of explosives in the blasthole. It has important reference and application value for blasting construction and explosion protection design. Therefore, it is very important and necessary to study the propagation and attenuation law of shock waves in the rock mass. When studying the attenuation law of shock waves in the rock mass, the viscoelastic medium model is closer to the actual situation than the elastic medium model. For this reason, many researchers have proposed many mathematical models, such as Maxwell model, Kelvin model, three-parameter solid model, Burgers model, etc. In the vicinity of the blasthole, the rock mass is strongly compressed by the shock wave and exhibits the properties of a fluid. It is reasonable to use the Maxwell viscoelastic model to describe the propagation of shock waves in the rock mass near the blasthole. The Maxwell viscoelastic model contains two important rock mass parameters, one is the rock mass elastic modulus, and the other is the rock mass viscosity coefficient. The rock mass elastic modulus is easy to measure through triaxial compression tests, while the rock mass viscosity coefficient is relatively difficult to measure.

[0003] At present, the viscosity coefficient of the Maxwell viscoelastic model of rock mass is mostly determined by conducting dynamic impact tests. For example, Deng Ketao et al., in the article "Determination of Several Material Functions of Viscoelastic Materials", used the periodic triangular load loading form to test the viscosity coefficient of rock mass based on the energy dissipation characteristics of viscoelastic materials. In the article "Testing Method of Rock Viscosity Coefficient", Wang Guanshi et al. calculated the viscosity coefficient of the Kelvin viscoelastic model of rock mass based on the attenuation coefficient of the characteristic waveform amplitude of the measuring point over time according to the spectrum change law during the propagation of stress waves. Obviously, the existing test method is relatively complicated to operate, the test cost is also relatively expensive, and the subsequent data processing also requires professional researchers to carry out, and it does not use engineering applications. Summary of the invention

[0004] The technical problem to be solved by the present invention is how to provide a method for measuring the viscosity coefficient of the rock mass Maxwell viscoelastic model which is simple to operate, fast to measure and economical.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for measuring the viscosity coefficient of the Maxwell viscoelastic model of rock mass, characterized by comprising the following steps:

[0006] Based on the blasting design, determine the borehole diameter, explosive density, detonation velocity and rock wave impedance;

[0007] According to the blasting design, determine the location of the last blast hole, and arrange 5 to 8 large-range vibration velocity testers within 1.0m to 3.0m from the blast hole behind the blasting area;

[0008] Record the data collected by the vibration meter during the blasting process and extract the peak value of the radial vibration velocity;

[0009] Based on the law of conservation of momentum of shock wave propagation, the radial stress at each vibration velocity measurement point is calculated;

[0010] Based on the motion equation and displacement equation of shock wave, and combined with the symmetry of shock wave propagation in the rock mass around the blast hole, the radial stress attenuation characteristics of the rock mass Maxwell viscoelastic model are analyzed and determined;

[0011] Based on the measured radial stress at different positions, the viscosity coefficient of the Maxwell viscoelastic model of the rock mass is determined by fitting.

[0012] Preferably, the detonation interval between the last detonation hole and the penultimate detonation hole is greater than 150ms.

[0013] Preferably, the measuring range of the large-range vibration velocity tester is greater than 70 cm / s.

[0014] A further technical solution is that the large-range vibration velocity tester is arranged into a measuring line, the distance between adjacent measuring points in the area close to the blasthole is 20cm-40cm, and the distance between adjacent measuring points in the area far from the blasthole is 40cm-60cm.

[0015] A further technical solution is that the method for determining the radial stress attenuation characteristics of the rock mass Maxwell viscoelastic model comprises the following steps:

[0016] The rock mass around the blasthole is divided into n parts evenly, and it is assumed that the propagation process of the shock wave in each part of the rock mass does not affect each other;

[0017] The propagation problem of shock wave in each delineated rock mass is regarded as the propagation problem of shock wave in a variable cross-section rod;

[0018] By combining the displacement and motion equations of shock wave propagation, and combining the constitutive equation of the Maxwell viscoelastic model of rock mass and the area of ​​each rock mass at the end face of the blasthole wall, the radial stress attenuation formula of the Maxwell viscoelastic model of rock mass is obtained as formula (1):

[0019]

[0020] Where: p s is the radial stress; p maxis the peak value of the hole wall pressure; r is the radius of the blasthole; ρ is the rock density; C is the rock longitudinal wave velocity; η is the rock viscosity coefficient; x is the distance from the center of the blasthole; and e is a natural constant.

[0021] A further technical solution is that the fitting and determination of the viscosity coefficient of the rock mass Maxwell viscoelastic model specifically comprises the following steps:

[0022] According to the radial stress attenuation formula of the rock mass Maxwell viscoelastic model, that is, formula (1), the radial stress data obtained by the test are preliminarily processed to obtain multiple groups of data combinations (x1, y1), where x1 and y1 are calculated by formula (2) and formula (3) respectively.

[0023] x1=rx (2)

[0024]

[0025] According to the data combination (x1, y1), an exponential fitting function is used to fit the coefficients A and B. The fitting function is shown in formula (4).

[0026]

[0027] According to the fitting coefficient B, the viscosity coefficient η of the rock mass Maxwell viscoelastic model is determined as shown in formula (5):

[0028]

[0029] The beneficial effect of adopting the above technical solution is that the measurement method of the present invention can be combined with blasting construction for testing, without the need to design a special test plan, and the required test instrument is a commonly used blasting vibration tester, which is simple to operate, fast and economical. The measurement method only needs to perform simple processing on the vibration velocity peak data obtained by the test, which is conducive to wide-scale promotion and application. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0031] Figure 1 A flowchart of the method according to an embodiment of the present invention;

[0032] Figure 2 A schematic diagram of a detonation network in the method according to an embodiment of the present invention;

[0033] Figure 3 A planar layout diagram of measuring points in the method described in an embodiment of the present invention;

[0034] Figure 4 It is a test data fitting diagram in the method described in the embodiment of the present invention;

[0035] In the picture: 1. The last blast hole; 2. Vibration velocity tester. DETAILED DESCRIPTION

[0036] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0037] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0038] The deep hole step blasting technology was used to excavate the slope rock mass of a hydropower project. The rectangular hole arrangement was adopted, the spacing between the blast holes was 3.0m×2.5m, the blast hole diameter was 90mm, the blast hole depth was 10m, and the blocking length was 3.0m. The rock mass was mainly granite with a density of 2600kg / m 3 The rock mass longitudinal wave velocity is 4800m / s and the elastic modulus is 60GPa. Ammonium nitrate explosive is used for blasting construction, and the density of explosive is 900kg / m 3 The explosion velocity is 3000 m / s. In combination with blasting construction, the viscosity coefficient of the granite Maxwell viscoelastic model is measured by the method of the present invention.

[0039] like Figure 1 As shown, the embodiment of the present invention discloses a method for measuring the viscosity coefficient of the Maxwell viscoelastic model of a rock mass, comprising the following steps:

[0040] S1. Based on the blasting design, determine the parameters such as borehole diameter, explosive density, detonation velocity and rock wave impedance;

[0041] S2. According to the blasting design, determine the position of the last blast hole 1, such as Figure 2 As shown, the interval between the detonation of the second to last blast hole is 200ms, and six vibration velocity testers with a range of 100cm / s are arranged in the range of 1.0m to 4.0m from the blast hole behind the blast area. The vibration velocity tester 2 is arranged in a measuring line, as shown in FIG. Figure 3 As shown;

[0042] S3, record the data collected by the vibration instrument during the blasting process, and extract the radial vibration velocity peak value, as shown in Table 1;

[0043] S4. Based on the law of conservation of momentum of shock wave propagation, the radial stress at each vibration velocity measuring point is calculated;

[0044] S5. Based on the motion equation and displacement equation of the shock wave, and combined with the symmetry of the shock wave propagation in the rock mass around the blast hole, the radial stress attenuation characteristics of the rock mass Maxwell viscoelastic model are analyzed and determined, which specifically includes the following steps:

[0045] Step S5-1, the rock mass around the blast hole is evenly divided into n parts, and it is assumed that the propagation process of the shock wave in each of the divided rock mass does not affect each other;

[0046] Step S5-2, treating the propagation problem of the shock wave in each defined rock mass as the propagation problem of the shock wave in a variable cross-section rod;

[0047] Step S5-3, the displacement and motion equations of shock wave propagation are combined, and the constitutive equation of the rock mass Maxwell viscoelastic model and the area of ​​each rock mass at the end face of the blasthole wall are combined to obtain the radial stress attenuation formula of the rock mass Maxwell viscoelastic model as formula (1),

[0048]

[0049] Where: p s is the radial stress; p max is the peak value of the hole wall pressure; r is the radius of the blasthole; ρ is the rock density; C is the rock longitudinal wave velocity; η is the rock viscosity coefficient; x is the distance from the center of the blasthole; and e is a natural constant.

[0050] S6. Based on the measured radial stress at different positions, the viscosity coefficient of the Maxwell viscoelastic model of the rock mass is determined by fitting, which specifically includes the following steps:

[0051] Step S6-1, according to the radial stress attenuation formula of the rock mass Maxwell viscoelastic model, that is, formula (1), the radial stress data obtained by the test is preliminarily processed to obtain multiple groups of data combinations (x1, y1), where x1 and y1 are calculated by formula (2) and formula (3) respectively, as shown in Table 1;

[0052] x1=rx (2)

[0053]

[0054] Step S6-2: According to the data combination (x1, y1), an exponential fitting function is used to fit the coefficients A and B. The fitting function is shown in formula (4). The fitting curve is as follows: Figure 4 As shown, the fitting determination coefficients are A = 1.0 and B = 2.71:

[0055]

[0056] Step S6-3: Determine the viscosity coefficient η of the Maxwell viscoelastic model of the rock mass according to the fitting coefficient B, as shown in formula (5). The viscosity coefficient of the rock mass calculated by formula (5) is 2.3 MPa·s.

[0057]

[0058] Table 1 Measured data

[0059]

[0060] The method of the present invention is combined with blasting construction, and a conventional blasting vibration tester can be used to quickly and easily test the viscosity coefficient of the rock mass Maxwell viscoelastic model. It is a simple, fast and economical measurement method and can provide a reference for engineering applications.

Claims

1. A method for measuring the viscosity coefficient of a rock mass Maxwell viscoelastic model, characterized in that The steps include: Based on the blasting design, determine the borehole diameter, explosive density, detonation velocity and rock wave impedance; According to the blasting design, determine the location of the last blast hole, and arrange 5 to 8 large-range vibration velocity testers within 1.0m to 3.0m from the blast hole behind the blasting area; Record the data collected by the vibration meter during the blasting process and extract the peak value of the radial vibration velocity; Based on the law of conservation of momentum of shock wave propagation, the radial stress at each vibration velocity measurement point is calculated; Based on the motion equation and displacement equation of shock wave, and combined with the symmetry of shock wave propagation in the rock mass around the blast hole, the radial stress attenuation characteristics of the rock mass Maxwell viscoelastic model are analyzed and determined; Based on the measured radial stress at different positions, the viscosity coefficient of the Maxwell viscoelastic model of the rock mass is determined by fitting; The method for determining the radial stress attenuation characteristics of the rock mass Maxwell viscoelastic model comprises the following steps: The rock mass around the blasthole is divided into n parts evenly, and it is assumed that the propagation process of the shock wave in each part of the rock mass does not affect each other; The propagation problem of shock wave in each delineated rock mass is regarded as the propagation problem of shock wave in a variable cross-section rod; By combining the displacement and motion equations of shock wave propagation, and combining the constitutive equation of the Maxwell viscoelastic model of rock mass and the area of ​​each rock mass at the end face of the blasthole wall, the radial stress attenuation formula of the Maxwell viscoelastic model of rock mass is obtained as formula (1): （1） Where: p s is the radial stress; p max is the peak value of the pore wall pressure; r is the radius of the blast hole; ρ is the rock mass density; is the rock mass longitudinal wave velocity; η is the viscosity coefficient; is the distance from the center of the blast hole; e is a natural constant; The fitting and determination of the viscosity coefficient of the rock mass Maxwell viscoelastic model specifically comprises the following steps: According to the radial stress attenuation formula of the rock mass Maxwell viscoelastic model, that is, formula (1), the radial stress data obtained by the test are preliminarily processed to obtain multiple sets of data combinations: , in , Calculated by formula (2) and formula (3) respectively, （2） （3） According to the data combination , using exponential fitting function, fitting determination coefficient A , B , the function determined by fitting is shown in formula (4), （4） According to the fitting coefficient B , determine the viscosity coefficient of the Maxwell viscoelastic model of rock mass η , as shown in formula (5), （5）。 2. The method for measuring viscosity coefficient of rock mass Maxwell viscoelastic model according to claim 1, characterized in that: The detonation interval between the last detonation hole and the second to last detonation hole is greater than 150ms.

3. The method for measuring viscosity coefficient of rock mass Maxwell viscoelastic model according to claim 1, characterized in that: The measuring range of the large-range vibration velocity tester is greater than 70 cm / s.

4. The method for measuring viscosity coefficient of rock mass Maxwell viscoelastic model according to claim 1, characterized in that: The large-range vibration velocity tester is arranged in a measuring line, the distance between adjacent measuring points in the area close to the blasthole is 20cm-40cm, and the distance between adjacent measuring points in the area far from the blasthole is 40cm-60cm.

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