Non-blasting demolition method based on artificially generated stress concentration

Abstract

The invention discloses a non-blasting demolition method based on artificially generated stress concentration, which can realize efficient directional destruction and effectively avoid unnecessary structural damage and secondary disasters. According to the technical scheme, the method comprises the following steps: firstly, measuring the Lame constant of a bounded region by using a physical instrument; then, through a given operation frequency, the density of the virtual elastic material ball is selected, and the elastic displacement of the corresponding transmission partial differential equation set is calculated; thirdly, a density function of Hergrotz elastic displacement is calculated through a Tikhonov regularization method, and an expression of the elastic stress load is obtained; and finally, the elastic stress acts on the local boundary of the bounded area, so that the stress is concentrated on the local surface of the elastic inclusion.

Description

Technical Field

[0001] The present invention can be used in the fields of civil engineering, mechanical engineering, etc. Background Art

[0002] The stress - concentration blasting technology has crucial applications in many fields such as civil engineering, water conservancy projects, and oil and gas extraction. For example, in river regulation projects, this technology can be used to clear reefs and obstacles in the river, thereby widening the river and significantly improving the navigation capacity and flood - control capacity of the river; in dam regulation projects, the technology can effectively control the vibration and flying stones generated by blasting, greatly reducing the adverse effects on the main structure of the dam and the surrounding environment; in the field of oilfield engineering, applying the stress - concentration blasting technology to transform the reservoir has successfully increased the permeability of the reservoir and significantly increased the oil and gas production.

[0003] In view of the requirements for blasting safety and efficiency, people expect to minimize unnecessary damage and the impact on the surrounding environment. Therefore, during the implementation of the project, it is necessary to achieve the goal of precise blasting to reduce the adverse effects on the surrounding environment and lower the project cost.

[0004] Currently, traditional blasting technologies often rely on the energy release of a large amount of explosives and are difficult to accurately control the blasting range and effect, especially in situations with complex structures and sensitive surrounding environments. The destructive power of traditional blasting outside the target area is difficult to predict and is extremely likely to cause unnecessary structural damage, secondary disasters, and safety hazards. In engineering structural mechanics, stress concentration refers to the phenomenon of local stress concentration caused by geometric discontinuities or uneven load distributions in the material structure. The parts with stress concentration are usually more prone to fracture or damage. Based on this theory, this patent can, without knowing the elastic medium coefficient, accurately and efficiently concentrate energy on the key area to be blasted through reasonable design of the blasting plan, thereby achieving efficient directional destruction. Summary of the Invention

[0005] The object of the present invention is to provide a non - blasting demolition method based on artificially generated stress concentration, which can accurately control the blasting range according to the blasting requirements in engineering, thereby avoiding unnecessary structural damage and secondary disasters.

[0006] The above object of the present invention is achieved according to the following technical solutions:

[0007] A mathematical model is established for the area A where stress concentration is to be generated. Under the assumptions of linear elasticity, A is inside a bounded elastic material Ω and can be divided into two different cases for discussion. In the first case, there is a pre-existing elastic inclusion D near the boundary of area A, and the material properties of this object are different from those of area Ω. In the second case, there is no elastic inclusion near the boundary of area A. In order to generate a blast in area A, an artificially designed elastic inclusion D is placed near A. After that, we no longer distinguish whether the elastic inclusion D is pre-existing or artificially designed.

[0008] Select some elastic material samples of Ω and use high-precision instruments to measure the corresponding Young's modulus and Poisson's ratio, and use these two physical parameters to calculate the Lamé constants of the elastic material parameters of Ω.

[0009] Under the assumption of linear elastic displacement, the elastic displacement in the time domain can be described by the time-dependent Navier wave equation. Under Fourier transform, with the operating frequency ω fixed, use the Navier equation to establish an elastic displacement equation to describe the change of elastic displacement of Ω. On the boundary of Ω, it is divided into a stress load application area and an elastic displacement disappearance area. According to the Herglotz approximation theory, design the stress load on the load application area for the operating frequency ω so that the stress concentration in area A exceeds the safety factor of the elastic inclusion D, thereby causing the elastic inclusion D to blast. Use the inverse Fourier transform to superimpose the stress loads obtained in the frequency domain to obtain the time-domain Navier wave equation with initial and boundary values describing the elastic displacement field inside Ω. According to the theoretical analysis in mathematics, we can prove that under the action of the proposed stress load, the elastic inclusion D can be blasted. Description of the Drawings

[0010] Figure 1 Flowchart for extracting elastic medium parameters

[0011] Figure 2 Flowchart for stress concentration. Detailed Implementation Manner

[0012] The present invention will be further described below in conjunction with the accompanying drawings.

[0013] Under the assumptions of linear elasticity, we consider that Ω is a homogeneous, isotropic bounded region, and A is inside a bounded elastic material Ω and can be divided into two different cases for discussion. In the first case, there is a pre-existing elastic inclusion D near the boundary of area A, and the material properties of this object are different from those of area Ω. In the second case, there is no elastic inclusion near the boundary of area A. In order to generate a blast on area A, an artificially designed elastic inclusion D is placed near A. As Figure 1As shown, the Young's modulus \(E\) and Poisson's ratio \(v\) of the bounded region \(\Omega\) are obtained from the experimental equipment, and then the related Lamé constants \(\lambda\) and \(\mu\) are calculated. First, a material sample with a cross-sectional area of \(S\) and a length of \(L\) is selected, a tensile force of magnitude \(F\) is applied to the cross-section of the material, and the corresponding length change \(\Delta L\) is measured. Then the Young's modulus of the region Measure the propagation time of ultrasonic waves in the material, and calculate the longitudinal wave velocity \(v\) in combination with the known propagation distance l and the shear wave velocity \(v\) t , then the Poisson's ratio of the region Finally, we calculate the Lamé constants based on the known Young's modulus and Poisson's ratio and

[0014] As Figure 2 shown, for an isotropic material, the independent elastic constants are expressed in terms of the Lamé constants \(\lambda\) and \(\mu\), and its constitutive relation follows the generalized Hooke's law, which is expressed by the following equation:

[0015] \(\sigma\) ij =\(\lambda\varepsilon\) kk \(\delta\) ij + 2\(\mu\varepsilon\) ij (1)

[0016] In the formula: \(\sigma\) ij is the component of the stress tensor, \(\varepsilon\) ij is the component of the strain tensor, \(\varepsilon\) kk =\(\varepsilon\) 11 +\(\varepsilon\) 22 +\(\varepsilon\) 33 is the trace of the strain tensor, \(\sigma\) ij is the Kronecker symbol. Based on the constitutive relation and the motion equation of the isotropic material, we obtain the elastic wave equation in the time domain

[0017]

[0018] Perform a Fourier transform on the wave equation in the time domain, fix the operating frequency \(\omega\), and obtain the Navier equation to describe the elastic displacement change of the bounded elastic material \(\Omega\). In the boundary region of the bounded elastic material \(\Omega\), it can be clearly divided into the stress load application region and the elastic displacement vanishing region, and its specific form is expressed as follows

[0019]

[0020] where \(u\) represents the elastic displacement in the region \(\Omega\setminus D\), \(\Gamma\) 1 represents the displacement vanishing region, \(\Gamma\) 2 represents the stress load application region, and \(v\) is the region \(\Gamma\) 2The unit normal vector on it. It should be noted that the elastic displacement field within the inclusion D is denoted by w. This inclusion could be a material following isotropic properties, showing the same physical properties in all directions, resulting in a relatively uniform and regular distribution of the elastic displacement field; or it could be an anisotropic material, where the physical properties vary in different directions, leading to a more complex and diverse variation in its elastic displacement field. Next, for the operating frequency ω, we set the relevant stress load g to cause the elastic inclusion D to burst.

[0021] Near the local boundary of the elastic inclusion D, we establish a virtual elastic material sphere B r . For the operating frequency ω, we select B r 's false density q m , such that the frequency ω satisfies the following system of transmission partial differential equations

[0022]

[0023] m is a natural number selected a posteriori, and the false density q m is an increasing function of m, and its explicit expression can be modulated according to the bursting requirements. Using harmonic analysis and the theory of partial differential equations, the elastic displacement corresponding to the mathematical solution of this system of transmission partial differential equations has the following form:

[0024]

[0025] Here represents the spherical harmonic function on the unit sphere, and j m represents the spherical Bessel function. On the surface of the virtual sphere B r , this elastic displacement shows an obvious stress concentration phenomenon, and the strain corresponding to the elastic displacement is an increasing function of m, where B r0 is a sub-region of the virtual sphere B r . Thus, it can be seen that the strain tensor will continuously increase as the variable m gradually increases. When such a changing trend continues to develop, once it exceeds the limit range that the material can withstand, the resulting stress will show a sharp and rapid upward trend, leading to the damage or failure of the material.

[0026] Subsequently, using the Herglotz approximation theory, based on the elastic displacement of the system of equations (3), we construct the elastic displacement on the region D. By solving the equation with Tikhonov regularization,

[0027]

[0028] The Tikhonov regularization formula is where k p represents the wavenumber of the lateral displacement, and k s represents the wavenumber of the longitudinal displacement. Then the regularization kernel function g α can be expressed as Extend the elastic displacement solution on the local region to Ω, and then the elastic displacement field u = H 1 on the region Γ ω g α can be determined. Since the strain tensor can be expressed in terms of the displacement field:

[0029]

[0030] Combined with formula (1), the magnitude of the stress load g, σ(H ω g α (x)), is obtained. According to the Herglotz approximation theory, we know that applying the stress load g on the boundary Γ 1 will cause an elastic displacement u = H ω g α inside. This elastic displacement satisfies the transmission partial differential equation system (2) and shows stress concentration on the surface of the virtual sphere B r .

[0031] Next, we explain how to achieve the blasting of the elastic inclusion D. The key to the blasting of the elastic inclusion D lies in whether its safety factor can be reduced below the critical threshold. The safety factor of an elastic material is determined by the ratio of the ultimate stress to the working stress. Taking the widely used C30 concrete as a typical example, its compressive ultimate stress is generally at about 30 MPa. Based on the established calculation rule of the concrete safety factor, by applying a force of 4×10 6 Newtons per unit square area, after conversion, a working stress of 40 MPa can be generated, so that the working stress exceeds the compressive ultimate stress value of C30 concrete. In this case, the original stable stress state inside the concrete is broken, and the stress concentration region starts from the surface and gradually spreads inward. With the continuous action of the stress, cracks begin to form and expand continuously, and finally the blasting effect of the concrete structure is achieved.

[0032] Applying the stress load g on the region Γ 1 in the frequency domain increases the working stress in the region A and reduces the safety factor F D , thereby triggering the blasting of the elastic inclusion D. At a certain operating frequency band, using the inverse Fourier transform, we can obtain the magnitude of the stress load in the time domain, which is the superposition of multiple time-harmonic elastic displacement fields. Since the frequency-domain blasting is effective, the blasting effect of the elastic inclusion D can also be achieved in the time domain.

Claims

1. A non-explosive demolition method based on artificially generated stress concentration, comprising the following steps a. Under the assumption of linear elasticity, we consider Ω to be a uniform, isotropic bounded region, and A is inside a bounded elastic material Ω. We can divide it into two different cases for discussion. In the first case, there is an elastic inclusion D near the boundary of region A, and the material properties of this object are different from those of region Ω. In the second case, there is no elastic inclusion near the boundary of region A. In order to produce a blast on region A, we place an artificially designed elastic inclusion D near A. As shown in Figure 1, the Young's modulus E and Poisson's ratio v of the bounded area Ω are obtained according to the experimental equipment, and then the related Lamé constants λ and μ are calculated. First, a material sample with a cross-sectional area of ​​S and a length of L is selected, and a tensile force of magnitude , is applied to the cross-sectional area of ​​the material, and the corresponding length change ΔL is measured. Then the Young's modulus E of the area = FL / SΔL. The propagation time of the ultrasonic wave in the material is measured, and the velocity v of the longitudinal wave is calculated in combination with the known propagation distance. l and the velocity v of the shear wave t , then the Poisson's ratio of the region v = -v l / v t Finally, we calculated the Lame constant λ = vE / [(1+v)(1-2v)] and μ = E / [2(1+v)] based on the known Young's modulus and Poisson's ratio. b. For isotropic materials, the independent elastic constants are represented by Lame constants λ and μ, and their constitutive relations obey the generalized Hooke's law, which is expressed as follows: s ij =le kk d ij +2with ij (1.1) Where: ij are the components of the stress tensor, ε ij are the components of the strain tensor, ε kk =ε 11 +ε 22 +ε 33 is the trace of the strain tensor, σ ij is the Kronecker symbol. Based on the constitutive relations and motion equations of isotropic materials, we obtain the elastic wave equation in the time domain: Perform Fourier transform on the wave equation in the time domain, set the operating frequency ω, and obtain the Navier equation to describe the elastic displacement change of the bounded elastic material Ω. The boundary area of ​​the bounded elastic material Ω can be clearly divided into the stress load application area and the elastic displacement disappearance area, which can be expressed in the following specific form: Where u represents the elastic displacement in the region Ω\D, Γ1 represents the displacement vanishing region, Γ2 represents the stress load application region, and v is the unit normal vector on the region Γ2. It is worth noting that the elastic displacement field in the inclusion D is represented by w. Next, we set the relevant stress load g for the operating frequency ω to make the elastic inclusion D explode. c. Near the local boundary of the elastic inclusion D, we create a virtual elastic material ball B r For the operating frequency ω, select B r The false density q m , so that the frequency ω satisfies the following transmission partial differential equations m is a natural number selected afterwards, and the false density q m is an increasing function of m, and its display expression can be modulated according to the needs of the blow-up. Using harmonic analysis and partial differential equation theory, the elastic displacement corresponding to the mathematical solution of the transmission partial differential equation group is There are the following forms: here represents the spherical harmonics on the unit sphere, j m represents the spherical Bessel function. On the virtual sphere B r On the surface, the elastic displacement shows obvious stress concentration phenomenon. d. According to the elastic displacement corresponding to the mathematical solution of the partial differential equations in the previous step We construct region B r Elastic displacement on Solving the equation with the help of Tikhonov regularization, The Tikhonov regularization formula is: where k p The wave number representing the lateral displacement, k s represents the wave number of longitudinal displacement, then the regularized kernel function g α It can be expressed as The elastic displacement solution on the local area is extended to Ω, and then the elastic displacement field u=H on the area Γ1 can be determined ω g α Since the strain tensor can be expressed with the help of the displacement field: Combined with formula (1.1), we can get the magnitude of stress load gσ(H ω g α (x)). According to the Herglotz approximation theory, we know that applying a stress load g on the boundary Γ1 will cause an elastic displacement u=H inside ω g α The elastic displacement satisfies the transmission partial differential equations (1.2), and on the virtual sphere B r The surface shows stress concentration phenomenon. e. Apply stress load g to region Γ1 in the frequency domain, so that the working stress in region A increases and the safety factor F decreases D , which in turn triggers the elastic inclusion D explosion. In a certain operating frequency band, using the inverse Fourier transform, we can obtain the magnitude of the stress load in the time domain, which is the superposition of multiple time-harmonic elastic displacement fields. Because the frequency domain explosion is effective, the elastic inclusion D explosion effect can also be achieved in the time domain.

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