A method for analyzing and evaluating the safety of a frame structure in terms of collapse vibration propagation

Abstract

The application discloses a kind of frame structure collapse vibration propagation law analysis and safety evaluation method, analysis includes: obtaining frame structure, site soil layer and initial state parameter of collapse body ground contact;The continuous ground contact process of frame structure directional collapse is decoupled into multiple single collapse body according to time sequence impact load sequence;Based on the peak value of each impact load is calculated, and according to half-sine wave hypothesis and impulse theorem, load duration is determined;The dynamic stiffness matrix of layered ground is constructed, and the three-dimensional dynamic Green function considering impact load sequence is established;In frequency domain-wave number domain, ground surface vibration velocity is obtained by solving and inverse transformation.Safety evaluation includes: predicting the spatial distribution of peak vibration velocity of ground surface particle caused by frame structure directional collapse;Assess the safety of adjacent buildings or determine the safety distance.The application can accurately predict the spatial directional effect and attenuation law of collapse vibration, and provide a reliable theoretical tool for safety evaluation of blasting demolition engineering.

Description

Technical Field

[0001] This invention belongs to the field of engineering blasting vibration assessment technology, specifically relating to an analysis of the propagation law of vibration during the collapse of a frame structure and a method for safety evaluation. Background Technology

[0002] The collapse vibrations generated by blasting demolition are characterized by low frequency, large amplitude, long duration, and long propagation distance, posing a serious threat to nearby buildings, underground pipelines, and infrastructure such as subway tunnels. Accurately predicting the propagation law of collapse vibrations, especially the spatial distribution of peak particle velocity (PPV), is a core aspect of the safety assessment of blasting demolition projects.

[0003] Existing methods for predicting collapse vibrations have the following shortcomings: 1) Empirical formulas lack theoretical support: Currently, power-law models (such as Zhou Jiahan's formula) based on fitting field monitoring data are widely used in engineering. However, their coefficients and exponents have large variability and lack a solid mechanical theoretical basis; 2) Vibration directionality cannot be predicted: Traditional empirical formulas only express PPV as a function of distance, which cannot reflect the spatial directionality effect of directional collapse vibration of frame structures, which is significantly greater in the collapse direction than in the opposite direction; 3) Ignoring the characteristics of the ground contact process: Existing methods simplify the collapsed body into a single rigid body, ignoring the "segmented and progressive" ground contact disintegration characteristics of frame structures (inter-layer lateral displacement, layer-by-layer ground contact), resulting in large deviations in prediction results; 4) Lack of a frequency-time domain analytical framework: Existing methods mostly perform empirical fitting in the time domain and have not established a frequency-wavenumber domain analytical model based on elastic wave dynamics, making it difficult to consider soil layering, material damping, and wave field interference effects.

[0004] Therefore, there is an urgent need for an analytical method for the propagation law of collapse vibration of frame structures with a solid theoretical foundation, which can take into account the mechanism of structural disintegration upon contact with the ground, the characteristics of soil layering, and the dispersion and interference effects of wave propagation, so as to achieve accurate prediction of the spatial distribution of collapse vibration. Summary of the Invention

[0005] The problem to be solved by this invention is to provide an analysis and safety evaluation method for the propagation law of vibration during the collapse of a frame structure, so as to solve the technical problem that the existing empirical formulas lack theoretical basis and cannot predict the spatial directionality of vibration, and to achieve accurate prediction of the spatial distribution of the peak velocity of the vibration particles during the directional collapse of the frame structure.

[0006] This invention adopts the following technical solution: a method for analyzing the propagation law of collapse vibration in a frame structure, comprising the following steps:

[0007] S1. Obtain the geometric parameters of the frame structure, the soil layer parameters of the site, and the initial state parameters of the collapsed body upon contact with the ground.

[0008] S2. Decouple the continuous ground contact process of the directional collapse of the frame structure into a sequence of impact loads in which multiple individual collapsed bodies hit the ground in a time sequence.

[0009] S3. Calculate the peak load and load time history of each individual collapsed body impact in the impact load sequence.

[0010] S4. Construct the dynamic stiffness matrix of the layered foundation, and based on the theory of elastic wave dynamics, establish a three-dimensional dynamic Green's function considering the impact load sequence.

[0011] S5. Solve the three-dimensional dynamic Green's function in the frequency domain-wavenumber domain, and obtain the time-domain vibration velocity of the ground observation point through multiple inverse transformations to characterize the propagation law of collapse vibration.

[0012] Further, in step S2, the impact load sequence includes corner-end single-unit collapse impact loads corresponding to the closure of the blast cut and flat-end single-unit collapse impact loads corresponding to the sequential ground contact of each floor; the initial application time of each impact load is determined according to the timing of the ground contact of each floor of the frame structure.

[0013] Furthermore, in step S3, the peak load is calculated based on the theory of ultimate bearing capacity of the foundation:

[0014] The dynamic intrusion process of a single collapsed object at the flat end is equivalent to the foundation failure problem of a continuously variable depth foundation.

[0015] The dynamic intrusion process of the corner collapse is equivalent to the foundation failure problem of a continuously variable width foundation.

[0016] Furthermore, the ultimate bearing capacity of the foundation is calculated using the following formula:

[0017] ;

[0018] in, γ represents the ultimate bearing capacity of the foundation, c represents the soil cohesion, and γ represents the soil unit weight. Basic depth; Base width; , , This is the bearing capacity coefficient. , , For shape factor, , , For depth factor:

[0019] Specifically, the expressions for the shape factor and depth factor are as follows:

[0020] ;

[0021] ;

[0022] in, Based on length, Let be the internal friction angle of the soil. ,but .

[0023] The final penetration depth of a single collapsed body can be obtained by solving the following formula:

[0024] ;

[0025] In the formula, The mass of a single collapsed body. The velocity of a single collapsing object upon impact with the ground. This represents the final depth of penetration.

[0026] For a single collapse at a corner, substitute B=2D into the calculation and set D to 0; for a single collapse at a flat end, B is a constant equal to the width of the collapse.

[0027] Solve for the final intrusion depth Then, substitute it into The calculation formula is used to obtain the peak load of qu, which is the result of the calculation of the single collapsed body's impact on the ground.

[0028] Furthermore, in step S3, the load time history is represented in half-sine wave form:

[0029] ;

[0030] in, For time indexing, duration T is given by the momentum theorem. Sure, This represents the peak impact force.

[0031] Further, in step S4, the dynamic stiffness matrix of the layered foundation is constructed, including the following methods:

[0032] The site is discretized into multiple layers of horizontally isotropic linear elastic media and a bottom half-space;

[0033] The wave equation is decoupled into P-wave, SV-wave and SH-wave by Helmholtz decomposition;

[0034] Derive the frequency domain dynamic stiffness matrix of a single-layer soil;

[0035] The overall dynamic stiffness matrix is ​​formed by assembling using the direct stiffness method;

[0036] A hysteresis damping model is introduced to characterize the damping of soil materials.

[0037] Further, in step S5, the solution in the frequency domain-wavenumber domain includes:

[0038] The impact load sequence is converted to the frequency-wavenumber domain by performing a space-time Fourier transform.

[0039] Substituting into the global dynamic equilibrium equations, the displacement response in the frequency domain and wavenumber domain is obtained by solving.

[0040] The vibration velocity in the time-space domain is obtained by using the two-dimensional wavenumber domain inverse Fourier transform and the one-dimensional frequency domain inverse Fourier transform.

[0041] The present invention also provides: a method for evaluating the safety of frame structure collapse vibration based on the aforementioned analysis method, comprising:

[0042] A1. Based on the results obtained in step S5, predict the spatial distribution of peak vibration velocity of surface particles caused by the directional collapse of the frame structure.

[0043] A2. Compare the predicted peak particle velocity with the preset safe vibration threshold to assess the safety of nearby buildings or determine the safe distance.

[0044] Furthermore, in step A2, the safe vibration threshold is determined based on the structural type, natural frequency, and relevant national standards of the protected building.

[0045] Furthermore, in step A2, the safe distance refers to the minimum radial distance when the predicted peak velocity of the mass point is less than the safe vibration threshold; when the actual distance is less than the safe distance, vibration reduction measures are taken or the blasting demolition plan is adjusted.

[0046] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0047] 1. Based on elastic wave dynamics and layered medium wave theory, this invention establishes an analytical solution framework in the frequency domain and wavenumber domain, overcoming the deficiency of empirical formulas lacking theoretical support, and successfully predicts the spatial directionality effect of directional collapse vibration of frame structures, which is significantly greater in the collapse direction than in the opposite direction, thus solving the problem that traditional methods cannot reflect the vibration directionality.

[0048] 2. This invention decouples the "segmented progressive" ground contact of the frame structure into a multi-load sequence, taking into account the different characteristics of impact loads at the corner ends and flat ends, which is more in line with the actual physical process; through the layered foundation dynamic stiffness matrix and hysteresis damping model, it can take into account soil layering, material damping and wave field interference effects, and can be directly used to predict the spatial distribution of PPV, providing a basis for determining the safety distance and designing vibration reduction measures. Attached Figure Description

[0049] Figure 1 This is a flowchart illustrating the overall analytical method of the present invention.

[0050] Figure 2 This is a three-dimensional layered ground-based wave field propagation and mechanical model in an embodiment of the present invention;

[0051] Figure 3 This is a simplified equivalent strategy for the impact load of a collapsed body on the ground in this embodiment of the invention;

[0052] Figure 4 The figure shows a comparison between the theoretical analysis results of collapse vibration in this embodiment of the invention and the finite element simulation and Zhou Jiahan's formula. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the application will be further described in detail below with reference to the accompanying drawings. The described embodiments are only a part of the embodiments involved in this invention. All non-innovative embodiments based on these embodiments by other researchers in the art are within the protection scope of this invention. Furthermore, the step numbers in the embodiments of this invention are only set for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0054] Example 1

[0055] This embodiment provides an analysis method for the propagation law of collapse vibration in a frame structure. The overall process is as follows: Figure 1 As shown, it includes the following steps:

[0056] S1. Obtain the geometric parameters of the frame structure, the soil layer parameters of the site, and the initial state parameters of the collapsed body upon contact with the ground.

[0057] S2. Decouple the continuous ground contact process of the directional collapse of the frame structure into a sequence of impact loads in which multiple individual collapsed bodies hit the ground in a time sequence.

[0058] S3. Calculate the peak load and load time history of each individual collapsed body impact in the impact load sequence.

[0059] S4. Construct the dynamic stiffness matrix of the layered foundation, and based on the theory of elastic wave dynamics, establish a three-dimensional dynamic Green's function considering the impact load sequence.

[0060] S5. Solve for the dynamic Green's function in the frequency domain-wavenumber domain, and obtain the time-domain vibration velocity of the ground observation point through multiple inverse transformations to characterize the propagation law of collapse vibration.

[0061] Furthermore, in step S2, the impact load sequence includes corner impact loads corresponding to the closure of the blast cut and flat impact loads corresponding to the sequential ground contact of each floor; the initial application time of each impact load is determined according to the timing of the ground contact of each floor of the frame structure.

[0062] Furthermore, in step S3, the calculation of the peak load is based on the theory of ultimate bearing capacity of the foundation.

[0063] In this embodiment, the simplified equivalent strategy for the ground impact load of the collapsed body is as follows: Figure 3 As shown, it is divided into flat-end single-unit impact and corner-end single-unit impact.

[0064] Specifically, the dynamic intrusion process of a single collapse body at a flat end is equivalent to the foundation failure problem of a continuously variable depth foundation; the dynamic intrusion process of a single collapse body at a corner end is equivalent to the foundation failure problem of a continuously variable width foundation.

[0065] Furthermore, the ultimate bearing capacity of the foundation is expressed by the following formula:

[0066] ;

[0067] in, γ represents the ultimate bearing capacity of the foundation, c represents the soil cohesion, and γ represents the soil unit weight. Basic depth; Base width; , , This is the bearing capacity coefficient. , , For shape factor, , , For depth factors.

[0068] The final penetration depth of a single collapsed body can be obtained by solving the following formula:

[0069] ;

[0070] In the formula, The mass of a single collapsed body. The velocity of a single collapsing object upon impact with the ground. This represents the final depth of penetration.

[0071] For a single collapsed body at a corner, substitute B=2D into the calculation and set D to 0; for a single collapsed body at a flat end, B is a constant equal to the width of the collapsed body. Solve for... Then, substitute it into The calculation formula yields The calculation result is the peak load of the single collapsed body impact.

[0072] Furthermore, in step S3, the load time history is represented in half-sine wave form:

[0073] ;

[0074] in, For time indexing, duration T is given by the momentum theorem. Sure, This represents the peak impact force.

[0075] In this embodiment, the three-dimensional layered ground wavefield propagation and mechanical model is as follows: Figure 2 As shown in the figure, consider a layered foundation system consisting of n horizontally isotropic linear elastic media, with a semi-infinite space rock mass at its bottom. Establish a global Cartesian coordinate system, defining the z-axis vertically downwards as positive. In the layered foundation, stress waves propagate downwards and are reflected and transmitted at the interfaces between layers, thus forming a superimposed wave field of descending and ascending waves within any single layer.

[0076] Furthermore, in step S4, constructing the dynamic stiffness matrix of the layered foundation includes:

[0077] The site is discretized into multiple layers of horizontally isotropic linear elastic media and a bottom half-space; the wave equation is decoupled into P-wave, SV-wave and SH-wave through Helmholtz decomposition.

[0078] The frequency domain dynamic stiffness matrix of a single-layer soil is derived; the overall dynamic stiffness matrix is ​​assembled by the direct stiffness method; and a hysteresis damping model is introduced to characterize the damping of the soil material.

[0079] Further, in step S5, the solution in the frequency domain-wavenumber domain includes:

[0080] The impact load sequence is transformed into the frequency-wavenumber domain by performing a time-space Fourier transform, and then substituted into the global dynamic equilibrium equation to obtain the displacement response in the frequency-wavenumber domain.

[0081] The vibration velocity in the time-space domain is then obtained through two-dimensional wavenumber domain inverse Fourier transform and one-dimensional frequency domain inverse Fourier transform.

[0082] To verify the effectiveness of the analytical method of this invention, the analytical results of the collapse vibration theory of this invention are compared with the results of finite element simulation and Zhou Jiahan's formula method, such as... Figure 4 As shown, Figure 4 In the figure, 'a' represents the curve of the measurement line 1. Figure 4 In the figure, b represents the curve of the test line 2.

[0083] It is evident that the method proposed in this invention can accurately reflect the macroscopic trend of collapse vibration attenuation with increasing radial distance; more importantly, it successfully reflects the spatial directional effect of the vibration velocity in the collapse direction being greater than that in the opposite direction. In terms of vibration velocity magnitude, the overall attenuation trend of theoretical predictions and numerical simulation results agrees well, fully verifying the accuracy of this analytical method in evaluating the directional collapse vibration response of frame structures. Furthermore, the predicted value of Zhou Jiahan's formula is in excellent agreement with the prediction results of the proposed method on the opposite side of the collapse. However, on the other hand, Zhou Jiahan's formula cannot reflect the directional effect of vibration propagation caused by the ground contact mechanism of the collapsed body.

[0084] Example 2

[0085] This embodiment provides a method for evaluating the safety of frame structure collapse vibration based on the analysis method of Embodiment 1, including:

[0086] A1. Vibration prediction: Using the analysis method described above, predict the spatial distribution of peak vibration velocity of surface particles caused by the directional collapse of the frame structure;

[0087] A2. Safety Assessment: The predicted peak particle velocity is compared with a preset safe vibration threshold to assess the safety of nearby buildings or determine a safe distance.

[0088] Furthermore, in step A2, the safe vibration threshold is determined based on the structural type, natural frequency, and relevant national standards of the protected building.

[0089] Furthermore, in step A2, the safe distance refers to the minimum radial distance when the predicted peak velocity of the mass point is less than the safe vibration threshold; when the actual distance is less than this safe distance, it is recommended to take vibration reduction measures or adjust the blasting demolition plan.

[0090] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for analyzing the propagation law of collapse vibration in a frame structure, characterized in that, Includes the following steps: S1. Obtain the geometric parameters of the frame structure, the soil layer parameters of the site, and the initial state parameters of the collapsed body upon contact with the ground. S2. Decouple the continuous ground contact process of the directional collapse of the frame structure into a sequence of impact loads in which multiple individual collapsed bodies hit the ground in a time sequence. S3. Calculate the peak load and load time history of each individual collapsed body impact in the impact load sequence. S4. Construct the dynamic stiffness matrix of the layered foundation, and based on the theory of elastic wave dynamics, establish a three-dimensional dynamic Green's function considering the impact load sequence. S5. Solve the three-dimensional dynamic Green's function in the frequency domain-wavenumber domain, and obtain the time-domain vibration velocity of the ground observation point through multiple inverse transformations to characterize the propagation law of collapse vibration.

2. The analytical method according to claim 1, characterized in that, In step S2, the impact load sequence includes corner-end single-unit collapse impact loads corresponding to the closure of the blast cut and flat-end single-unit collapse impact loads corresponding to the sequential ground contact of each floor; the initial application time of each impact load is determined according to the timing of the ground contact of each floor of the frame structure.

3. The analytical method according to claim 1, characterized in that, In step S3, the peak load is calculated based on the theory of ultimate bearing capacity of the foundation: The dynamic intrusion process of a single collapsed object at the flat end is equivalent to the foundation failure problem of a continuously variable depth foundation. The dynamic intrusion process of the corner collapse is equivalent to the foundation failure problem of a continuously variable width foundation.

4. The analytical method according to claim 3, characterized in that, The ultimate bearing capacity of the foundation is calculated using the following formula: ； in, γ represents the ultimate bearing capacity of the foundation, c represents the soil cohesion, and γ represents the soil unit weight. Basic depth; Base width; , , This is the bearing capacity coefficient. , , For shape factor, , , For depth factor: The final penetration depth of a single collapsed body can be obtained by solving the following formula: ； In the formula, The mass of a single collapsed body. The velocity of a single collapsing object upon impact with the ground. This represents the final depth of penetration. For a single collapse at a corner, substitute B=2D into the calculation and set D to 0; for a single collapse at a flat end, B is a constant equal to the width of the collapse; solve for the final intrusion depth. Then, substitute The calculation formula will yield the results. The calculation results are used as the peak load of the single collapsed body impact.

5. The analytical method according to claim 4, characterized in that, The shape factor and depth factor are calculated as follows: ； ； in, Based on length, Let be the internal friction angle of the soil. ,but .

6. The analytical method according to claim 4, characterized in that, In step S3, the load time history is represented in half-sine wave form: ； in, For time indexing, duration T is given by the momentum theorem. Sure, This represents the peak impact force.

7. The analytical method according to claim 1, characterized in that, In step S4, the dynamic stiffness matrix of the layered foundation is constructed, and the method includes: The site is discretized into multiple layers of horizontally isotropic linear elastic media and a bottom half-space; The wave equation is decoupled into P-wave, SV-wave and SH-wave by Helmholtz decomposition; Derive the frequency domain dynamic stiffness matrix of a single-layer soil; The overall dynamic stiffness matrix is ​​formed by assembling using the direct stiffness method; A hysteresis damping model is introduced to characterize the damping of soil materials.

8. The analytical method according to claim 1, characterized in that, In step S5, the solution in the frequency domain-wavenumber domain includes: The impact load sequence is converted to the frequency-wavenumber domain by performing a space-time Fourier transform. Substituting into the global dynamic equilibrium equations, the displacement response in the frequency domain and wavenumber domain is obtained by solving. The vibration velocity in the time-space domain is obtained by using the two-dimensional wavenumber domain inverse Fourier transform and the one-dimensional frequency domain inverse Fourier transform.

9. A method for evaluating the safety of frame structure collapse vibration based on the analysis method described in any one of claims 1 to 8, characterized in that, include: A1. Based on the results obtained in step S5, predict the spatial distribution of peak vibration velocity of surface particles caused by the directional collapse of the frame structure. A2. Compare the predicted peak particle velocity with the preset safe vibration threshold to assess the safety of nearby buildings or determine the safe distance.

10. The safety evaluation method according to claim 9, characterized in that, In step A2, the safe vibration threshold is determined based on the structural type, natural frequency, and relevant national standards of the protected building; the safe distance refers to the minimum radial distance when the predicted peak velocity of the mass point is less than the safe vibration threshold; when the actual distance is less than the safe distance, vibration reduction measures are taken or the demolition plan is adjusted.

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