Method for quickly and accurately judging safe allowable distance of blasting vibration

Abstract

The invention discloses a method for rapidly and accurately judging a blasting vibration safety allowable distance, and belongs to the technical field of geotechnical engineering blasting. The method specifically comprises the steps of establishing a simplified mathematical model of explosive wave propagation and an explosive wave propagation control equation; basic mechanical parameters of rocks of the blasting engineering are obtained; obtaining a blast hole wall stress wave action time history curve; solving the explosion wave propagation control equation to obtain a radial stress complex variable function and a mass point displacement complex variable function at any moment around an explosion source; obtaining a radial stress time domain variable function and a mass point vibration velocity function; constructing a characteristic function relationship between a radial stress peak value and a mass point vibration velocity peak value, introducing a peak value stress wave propagation attenuation function, finally obtaining a mass point peak value vibration velocity, and drawing a mass point peak value vibration velocity distribution curve; and the blasting vibration safety allowable distance is obtained. According to the method, the blasting vibration safety allowable distance conforming to the specification can be rapidly and accurately calculated, the calculation efficiency is high, and the prediction result is accurate.

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 determining 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, cavern tunnel excavation, etc. For buildings near the blast source or other objects that need to be protected, when the blasting vibration they are subjected to exceeds the dynamic response limit they can bear, certain damage will inevitably occur, and the greater the blasting vibration amplitude, the more obvious the damage effect. Therefore, in the blasting process, the negative effects induced by blasting vibration are an important safety issue that cannot be ignored. When designing and constructing blasting operations, the first and most critical point is to determine whether the surrounding buildings are in a safe state under the conditions of blasting vibration. In engineering practice, the peak vibration velocity of the particle point is generally used as the safety criterion for blasting vibration. At the same time, the distance between the location of the maximum particle peak vibration velocity that the building can withstand and the blast source is called the safe allowable distance of blasting vibration. At present, there are mainly empirical formula methods, numerical simulation methods and actual monitoring methods to determine the safe allowable distance of blasting vibration.

[0003] Empirical formula method: For example, in the Chinese patent with announcement number CN107990798B, the inventor proposed a method for determining the safe allowable distance of blasting vibration for civil buildings in mountainous areas. This method calculates the safe allowable distance of blasting vibration according to an empirical formula. The parameters K and α involved in the formula are empirical parameters determined according to the terrain 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 it is impossible to ensure that a reasonable calculation result is obtained.

[0004] Numerical simulation method: For example, Yang Guang et al. proposed an analysis of the impact of road cutting slope excavation on the adjacent existing railway tunnel, and used the finite element method to study the impact of blasting vibration generated by blasting construction on the existing tunnel structure. The disadvantage of this method is that numerical calculations are usually limited by the grid division method. If a fine grid is divided, the calculation efficiency is low and the time required is long; if a coarse grid is divided, the calculation accuracy cannot be effectively guaranteed.

[0005] Actual monitoring method: For example, in the Chinese patent with the announcement number CN110514377B, the inventor proposed a method of using actual monitoring data to evaluate the impact of blasting vibration on buildings. The disadvantage of this method is that the arrangement of blasting monitoring points is relatively cumbersome, the entire monitoring process takes a long time, and it consumes a lot of manpower and material resources, which is not economical and convenient. Summary of the invention

[0006] In view of the problems existing in the existing determination of the safe allowable distance of blasting vibration, such as strong subjectivity in parameter selection, low calculation efficiency, long time required, and large consumption of manpower and material resources, the present invention provides a method for quickly and accurately determining 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 comprises 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 location of the blasting project. 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 blast hole is subjected to a uniformly distributed explosion impact load at a certain moment, then the time history curve of the stress wave action on the blast hole 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 around the explosion source at any time.

[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, 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 of 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 blasthole wall stress wave action time history curve F(t) 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 Laplace numerical inverse transform method is used to solve the complex variable function of the particle displacement and then to differentiate it 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 the peak value is t1, and the time when the particle vibration velocity reaches the peak value is t2, the characteristic function relationship g(r) between the peak value of the particle vibration velocity at any point around the blasthole and the peak value of the radial stress 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 a particle is:

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

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

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

[0042] (2) Compared with traditional empirical formulas, all parameters in the present invention have clear physical definitions, and there is no problem of result uncertainty caused by artificially determining 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 little 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 explosion wave propagation of 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 is further described below in conjunction with the accompanying drawings and specific embodiments:

[0047] Example 1

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

[0049] Step 1: According to 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. Figure 1 shown.

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

[0051]

[0052] Wherein, 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 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 location of the blasting project, which include rock density ρ, Young's elastic modulus E, and rock Poisson's ratio ν. In this embodiment, the rock at the location of the blasting project 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 rock is 0.26.

[0054] Step 3: Assume that the inner wall of the blast hole is subjected to a uniformly distributed explosion impact load at a certain moment, then the time history curve of the stress wave action on the blast hole 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 around the explosion source at any time.

[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, and in this embodiment, α=0.2, T=50, and n is the number of calculations, which is 2000.

[0068] The Laplace numerical inverse transform method is used to solve the complex variable function of the particle displacement and then to differentiate it 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 value and the particle vibration velocity peak value, and introduce the peak stress wave propagation attenuation function, and finally obtain the particle peak vibration velocity and draw the particle peak vibration velocity distribution curve. 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 the peak value is t1, and the time when the particle vibration velocity reaches the peak value is t2, the characteristic function relationship g(r) between the peak value of the particle vibration velocity at any point around the blasthole and the peak value of the radial stress 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 a 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 of 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 protection scope 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: According to the relative geographic information position of the blasting project and the surrounding buildings to be protected, a simplified mathematical model of blast wave propagation and blast wave propagation control equation are established; Step 2: Obtain the basic mechanical parameters of the rock at the location of the blasting project. The basic mechanical parameters of the rock include 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 action 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 radial stress complex variable function and the particle displacement complex variable function of any point around the explosion source; Step 5: Using the Laplace numerical inverse transformation 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, and 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, introduce the peak stress wave propagation attenuation function, finally obtain the particle peak vibration velocity, and draw the particle peak vibration velocity distribution curve; 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 of 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. A method for quickly and accurately determining the safe allowable distance of blasting vibration according to claim 1, 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 Laplace numerical inverse transform method is used to solve the complex variable function of the particle displacement and then to differentiate it 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 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 at any point around the blasthole and the peak value of the radial stress 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 a particle is: V max (r)=g(r)P r (9)。

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