A quick and accurate method for determining safe allowable distance of blasting vibration

Abstract

The application discloses a kind of fast and accurate discrimination methods of blasting vibration safety allowable distance, belong to the field of geotechnical engineering blasting technology.It is specifically disclosed to establish the simplified mathematical model of explosion wave propagation and explosion wave propagation control equation;Obtain the basic mechanical parameters of the rock where the blasting engineering is located;Get the time history curve of blasthole wall stress wave action;Solve the explosion wave propagation control equation, get the radial stress complex variable function and particle displacement complex variable function at any time around the explosion source;Get radial stress time domain variable function and particle vibration velocity function;The characteristic function relationship between the peak value of radial stress and the peak value of particle vibration velocity is constructed, and the peak stress wave propagation attenuation function is introduced at the same time, and finally the particle peak vibration velocity is obtained.The particle peak vibration velocity distribution curve is drawn;Get blasting vibration safety allowable distance.The application can quickly and accurately calculate the blasting vibration safety allowable distance conforming to the specification, with high calculation efficiency and accurate prediction results.

Description

Technical Field

[0001] The invention belongs to the technical field of geotechnical engineering blasting, and in particular relates to a method for quickly and accurately judging a safe allowable distance of blasting vibration. Background Art

[0002] With the rapid development of infrastructure and engineering construction in my country, blasting technology has been widely used in mineral mining, earthwork excavation, structure demolition, and tunneling. For buildings or other objects requiring protection near the blast source, damage is inevitable when the blasting vibration exceeds their inherent dynamic response limit. The greater the blasting vibration amplitude, the more pronounced this damage. Therefore, the negative effects induced by blasting vibration are a critical safety issue that cannot be ignored during blasting. When designing and constructing blasting operations, the first and most critical consideration is determining whether surrounding buildings are safe under blasting vibration conditions. In engineering practice, peak particle vibration velocity is generally used as a safety criterion for blasting vibration. The distance between the location of the maximum particle peak vibration velocity that a building can withstand and the blast source is referred to as the safe allowable distance for blasting vibration. Currently, the main methods for determining the safe allowable distance for blasting vibration include empirical formulas, numerical simulations, and field monitoring.

[0003] Empirical formula method: For example, in Chinese patent publication number CN107990798B, the inventors proposed a method for determining the safe permissible distance for blasting vibrations from civil buildings in mountainous areas. This method calculates the safe permissible distance for blasting vibrations using an empirical formula. The parameters K and α involved in the formula are empirically determined based on the topographic and geological conditions between the blasting point and the protected object. In actual use, the values ​​of the formula parameters are highly subjective and arbitrary, and reasonable calculation results cannot be guaranteed.

[0004] Numerical simulation methods: For example, Yang Guang et al. proposed an analysis of the impact of cutting slope excavation on an adjacent existing railway tunnel. They used the finite element method to study the effect of blasting vibrations generated by blasting on the existing tunnel structure. However, this method suffers from the limitations of the meshing scheme. Using a finer mesh results in low computational efficiency and a longer computational time; using a coarser mesh results in inaccurate computational accuracy.

[0005] Actual monitoring method: For example, in Chinese patent publication number CN110514377B, the inventors proposed a method that uses actual monitoring data to evaluate the impact of blasting vibration on buildings. However, this method suffers from the cumbersome arrangement of blasting monitoring points, the lengthy monitoring process, and the significant human and material resources involved, making it neither economical nor convenient. Summary of the Invention

[0006] In view of the problems existing in the existing judgment of the safe allowable distance of blasting vibration, such as strong subjectivity of parameter values, low calculation efficiency, long time required, and high consumption of manpower and material resources, the present invention provides a method for quickly and accurately judging the safe allowable distance of blasting vibration.

[0007] The present invention adopts the following technical solutions:

[0008] A method for quickly and accurately determining the safe allowable distance of blasting vibration includes the following steps:

[0009] Step 1: Based on the relative geographic information of the blasting project and the surrounding buildings to be protected, a simplified mathematical model of blast wave propagation and the blast wave propagation control equation are established.

[0010] Step 2: Obtain the basic mechanical parameters of the rock at the blasting project site. The basic mechanical parameters of the rock include rock density ρ, Young's elastic modulus E, and rock Poisson's ratio ν.

[0011] Step 3: Assume that the inner wall of the blasthole is subjected to a uniformly distributed explosion impact load at a certain moment. The time history curve of the stress wave on the blasthole wall is represented by the function F(t). For different explosives, F(t) has different function expressions, which depends on the actual situation.

[0012] Step 4: Solve the explosion wave propagation control equation established in step 1 to obtain the complex variable function of radial stress and the complex variable function of particle displacement at any time around the explosion source.

[0013] Step 5: Using the Laplace numerical inverse transform method, the radial stress complex function is converted into the radial stress time domain variable function, and the particle displacement complex function is converted into the particle displacement time domain variable function. Then, the particle displacement time domain variable function is differentiated with respect to time to obtain the particle vibration velocity function.

[0014] Step 6: Construct the characteristic function relationship between the radial stress peak and the particle vibration velocity peak, and introduce the peak stress wave propagation attenuation function. Finally, obtain the particle peak vibration velocity and draw the particle peak vibration velocity distribution curve.

[0015] Step 7: Based on the safe allowable particle peak vibration velocity at the location of the object to be protected and the particle peak vibration velocity distribution curve obtained in step 6, the safe allowable distance for blasting vibration can be quickly and accurately inferred.

[0016] Preferably, the explosion wave propagation control equation is:

[0017]

[0018] Among them, ψ(r,t) is the displacement potential function, t is the time after detonation, a is the radius of the blast hole, r is the distance from any point around the blast hole to the center of the blast hole, c p is the longitudinal wave velocity, σ r (a, t) is the radial stress of the blasthole wall; F(t) is the time history curve of the stress wave on the blasthole wall.

[0019] Preferably, the time history curve F(t) of the stress wave action on the blasthole wall is expressed as:

[0020] F(t)=P d (eγ / n) n t n e -γt (2);

[0021] Among them, P d is the peak pressure of detonation wave, n and γ are stress wave parameters.

[0022] Preferably, the Laplace transform method is used to solve the explosion wave propagation control equation, and the radial stress complex variable function of any point around the explosion source is obtained as follows:

[0023]

[0024] The complex variable function of particle displacement is:

[0025]

[0026] Where H(t-t') is the Heaviside step function, η = κ / c p , t'=(ra) / c p , m=(λ+2μ) / μ, κ is the Laplace operator, λ and μ are Lame constants, which can be calculated from Young's elastic modulus E and Poisson's ratio ν, that is, λ=νE / [(1+ν)(1-2ν)], μ=E / [2(1+ν)], K0 and K1 are the derivatives of the zero-order and first-order modified Bessel function of the second kind, respectively.

[0027] Preferably, the radial stress complex variable function is solved by using the Laplace numerical inverse transform method, and the radial stress time domain variable function of any point around the explosion source is obtained as follows:

[0028]

[0029] Where α is an arbitrary real number and 0≤α≤Re(κ), T is a specific parameter and αT=5~10, and n is the number of calculations;

[0030] The particle displacement complex variable function is solved by the Laplace numerical inverse transform method and then differentiated with respect to time to obtain the particle vibration velocity function, as follows:

[0031]

[0032] Preferably, assuming that the time when the radial stress reaches its peak value is t1 and the time when the particle vibration velocity reaches its peak value is t2, the characteristic function relationship g(r) between the peak value of the particle vibration velocity and the radial stress peak value at any point around the blasthole is obtained according to the following formula:

[0033]

[0034] σ(r,t1) is the peak value of radial stress, v(r,t2) is the peak value of particle vibration velocity;

[0035] The peak stress wave propagation attenuation function is:

[0036]

[0037] Where, P r is the peak pressure of the explosion wave at a distance r from the center of the blasthole, θ is the stress wave attenuation parameter, which is θ = 2-ν / (1+ν), and ν is the Poisson's ratio of the rock;

[0038] The calculation formula for the peak vibration velocity of the particle is:

[0039] V max (r) = g(r)P r (9).

[0040] The present invention has the following beneficial effects:

[0041] (1) Based on rigorous mathematical derivation, the present invention comprehensively considers the influence of factors such as explosive type, geological conditions and the propagation attenuation process of blast waves on the peak velocity of blasting vibration particles, and can quickly and accurately calculate the safe allowable distance of blasting vibration that meets the standards. The calculation efficiency is high and the prediction results are accurate.

[0042] (2) Compared with traditional empirical formulas, the various parameters in the present invention have clear physical definitions, and there is no problem of uncertainty in the results caused by artificial determination of parameter values ​​in traditional empirical formulas.

[0043] (3) Compared with numerical calculation or actual monitoring methods, the present invention can quickly and accurately give the judgment result of the safe allowable distance of blasting vibration while ensuring the prediction accuracy. It takes a short time and consumes less manpower and material resources, and has good economy and applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a simplified mathematical model of the blast wave propagation in Example 1.

[0045] Figure 2 This is the particle peak vibration velocity distribution curve of Example 1. DETAILED DESCRIPTION

[0046] The specific implementation of the present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0047] Example 1

[0048] Combine Figure 1 and Figure 2 A method for quickly and accurately determining the safe allowable distance of blasting vibration includes the following steps:

[0049] Step 1: Based on the relative geographical information of the blasting project and the surrounding buildings to be protected, a simplified mathematical model of blast wave propagation and the blast wave propagation control equation are established. The simplified mathematical model of blast wave propagation is as follows: Figure 1 shown.

[0050] The governing equation for blast wave propagation is:

[0051]

[0052] Where ψ(r,t) is the displacement potential function, t is the time after detonation, a is the radius of the blasthole, which is set to 100 mm in this embodiment; r is the distance from any point around the blasthole to the center of the blasthole, c is the distance from any point around the blasthole to the center of the blasthole, and p is the longitudinal wave velocity, σ r (a, t) is the radial stress of the blasthole wall; F(t) is the time history curve of the stress wave on the blasthole wall.

[0053] Step 2: Obtain the basic mechanical parameters of the rock at the blasting project site. The basic mechanical parameters of the rock include rock density ρ, Young's elastic modulus E, and rock Poisson's ratio ν. In this embodiment, the rock at the blasting project site is mainly Indiana limestone, and the rock density ρ of Indiana limestone is 2320 kg / m 3 , Young's elastic modulus E is 23.5 GPa, and the Poisson's ratio ν of the rock is 0.26.

[0054] Step 3: Assume that the inner wall of the blasthole is subjected to a uniformly distributed explosion impact load at a certain moment. The time history curve of the stress wave on the blasthole wall is represented by the function F(t). For different explosives, F(t) has different function expressions, which depends on the actual situation.

[0055] In this embodiment, the stress wave action time history curve F(t) of the blasthole wall is expressed as:

[0056] F(t)=P d (eγ / n) n t n e -γt (2);

[0057] Among them, P dis the peak pressure of the detonation wave, which is 20 GPa in this embodiment, and n and γ are stress wave parameters.

[0058] Step 4: Solve the explosion wave propagation control equation established in step 1 to obtain the complex variable function of radial stress and the complex variable function of particle displacement at any time around the explosion source.

[0059] The Laplace transform method is used to solve the explosion wave propagation control equation, and the radial stress complex variable function of any point around the explosion source is obtained as follows:

[0060]

[0061] The complex variable function of particle displacement is:

[0062]

[0063] Where H(t-t') is the Heaviside step function, η = κ / c p , t'=(ra) / c p , m=(λ+2μ) / μ, κ is the Laplace operator, λ and μ are Lame constants, which can be calculated from Young's elastic modulus E and Poisson's ratio ν, that is, λ=νE / [(1+ν)(1-2ν)], μ=E / [2(1+ν)], K0 and K1 are the derivatives of the zero-order and first-order modified Bessel function of the second kind, respectively.

[0064] Step 5: Using the Laplace numerical inverse transform method, the radial stress complex function is converted into the radial stress time domain variable function, and the particle displacement complex function is converted into the particle displacement time domain variable function. Then, the particle displacement time domain variable function is differentiated with respect to time to obtain the particle vibration velocity function.

[0065] The radial stress complex variable function is solved by using the Laplace numerical inverse transform method, and the radial stress time domain variable function at any point around the explosion source is obtained as follows:

[0066]

[0067] Wherein, α is an arbitrary real number and 0≤α≤Re(κ), T is a specific parameter and αT=5-10. In this embodiment, α=0.2, T=50, and n is the number of calculations, which is 2000.

[0068] The particle displacement complex variable function is solved by the Laplace numerical inverse transform method and then differentiated with respect to time to obtain the particle vibration velocity function, as follows:

[0069]

[0070] Step 6: Construct the characteristic function relationship between the radial stress peak and the particle vibration velocity peak, and introduce the peak stress wave propagation attenuation function. Finally, the particle peak vibration velocity is obtained and the particle peak vibration velocity distribution curve is drawn. The particle peak vibration velocity distribution curve of this embodiment is as follows: Figure 2 shown.

[0071] Assuming that the time when the radial stress reaches its peak value is t1 and the time when the particle vibration velocity reaches its peak value is t2, the characteristic function relationship g(r) between the peak value of the particle vibration velocity and the radial stress peak value at any point around the blasthole is obtained according to the following formula:

[0072]

[0073] σ(r,t1) is the peak value of radial stress, v(r,t2) is the peak value of particle vibration velocity;

[0074] The peak stress wave propagation attenuation function is:

[0075]

[0076] Where, P r is the peak pressure of the explosion wave at a distance r from the center of the blasthole, θ is the stress wave attenuation parameter, which is θ = 2-ν / (1+ν), and ν is the Poisson's ratio of the rock;

[0077] The calculation formula for the peak vibration velocity of the particle is:

[0078] V max (r) = g(r)P r (9).

[0079] Step 7: Based on the safe allowable particle peak vibration velocity at the location of the object to be protected and the particle peak vibration velocity distribution curve obtained in step 6, the safe allowable distance for blasting vibration can be quickly and accurately inferred.

[0080] This embodiment assumes that the safety-allowed peak vibration velocity of the particle point at the location of the object to be protected is 1 cm / s. Figure 2 It can be quickly and accurately deduced that the safe allowable distance for blasting vibration is about 98m.

[0081] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A method for quickly and accurately determining the safe allowable distance of blasting vibration, characterized in that: The following steps are involved: Step 1: Based on the relative geographic information of the blasting project and the surrounding buildings to be protected, a simplified mathematical model of blast wave propagation and the blast wave propagation control equation are established; Step 2: Obtain the basic mechanical parameters of the rock at the blasting project site, including rock density ρ, Young's elastic modulus E, and rock Poisson's ratio ν; Step 3: Assume that the inner wall of the blasthole is subjected to a uniformly distributed explosion impact load at a certain moment, and the time history curve of the stress wave on the blasthole wall is represented by the function F(t); Step 4: Solve the explosion wave propagation control equation established in step 1 to obtain the complex variable function of radial stress and the complex variable function of particle displacement at any point around the explosion source; Step 5: Using the Laplace numerical inverse transform method, the radial stress complex function is converted into the radial stress time domain variable function, and the particle displacement complex function is converted into the particle displacement time domain variable function. Then, the particle displacement time domain variable function is differentiated with respect to time to obtain the particle vibration velocity function. Step 6: Construct the characteristic function relationship between the radial stress peak and the particle vibration velocity peak, and introduce the peak stress wave propagation attenuation function. Finally, the particle peak vibration velocity is obtained and the particle peak vibration velocity distribution curve is drawn. Step 7: Based on the safe allowable particle peak vibration velocity at the location of the object to be protected and the particle peak vibration velocity distribution curve obtained in step 6, the safe allowable distance for blasting vibration can be quickly and accurately inferred.

2. A method for quickly and accurately determining the safe allowable distance of blasting vibration according to claim 1, characterized in that: The governing equation for blast wave propagation is: Among them, ψ(r,t) is the displacement potential function, t is the time after detonation, a is the radius of the blast hole, r is the distance from any point around the blast hole to the center of the blast hole, c p is the longitudinal wave velocity, σ r (a, t) is the radial stress of the blasthole wall; F(t) is the time history curve of the stress wave on the blasthole wall.

3. The method for quickly and accurately determining the safe allowable distance of blasting vibration according to claim 1 is characterized in that: The time history curve of stress wave on the blasthole wall F(t) is expressed as: F(t)=P d (eγ / n) n t n e -γt (2); Among them, P d is the peak pressure of detonation wave, n and γ are stress wave parameters.

4. A method for quickly and accurately determining the safe allowable distance of blasting vibration according to claim 2, characterized in that: The Laplace transform method is used to solve the explosion wave propagation control equation, and the radial stress complex variable function of any point around the explosion source is obtained as follows: The complex variable function of particle displacement is: Where H(t-t') is the Heaviside step function, η = κ / c p , t'=(ra) / c p , m = (λ + 2μ) / μ, κ is the Laplace operator, λ and μ are the Lamé constants, K0 and K1 are the derivatives of the zero-order and first-order modified Bessel function of the second kind, respectively.

5. A method for quickly and accurately determining the safe allowable distance of blasting vibration according to claim 4, characterized in that: The radial stress complex variable function is solved by using the Laplace numerical inverse transform method, and the radial stress time domain variable function at any point around the explosion source is obtained as follows: Where α is an arbitrary real number and 0≤α≤Re(κ), T is a specific parameter and αT=5~10, and n is the number of calculations; The particle displacement complex variable function is solved by the Laplace numerical inverse transform method and then differentiated with respect to time to obtain the particle vibration velocity function, as follows:

6. A method for quickly and accurately determining the safe allowable distance of blasting vibration according to claim 5, characterized in that The time when the radial stress reaches its peak is t1, and the time when the particle vibration velocity reaches its peak is t2. The characteristic function relationship g(r) between the peak value of the particle vibration velocity and the peak value of the radial stress at any point around the blasthole is obtained according to the following formula: σ(r,t1) is the peak value of radial stress, v(r,t2) is the peak value of particle vibration velocity; The peak stress wave propagation attenuation function is: Where, P r is the peak pressure of the explosion wave at a distance r from the center of the blasthole, θ is the stress wave attenuation parameter, which is θ = 2-ν / (1+ν), and ν is the Poisson's ratio of the rock; The calculation formula for the peak vibration velocity of the particle is: V max (r)=g(r)P r (9)。

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