A method for predicting surface vibration waveforms during tunnel blasting

Abstract

This invention provides a method for predicting surface vibration waveforms during tunnel blasting, comprising: first, deriving the vibration waveform function of a short-charge explosive charge based on Heelan theory; then, constructing a vibration calculation form suitable for tunnel cut-out blasting based on this short-charge explosive charge vibration waveform function, and calculating the surface vibration waveform function of the cut-out holes using the superposition principle; next, simplifying and correcting the formula for the waveform function of multiple-hole blasting to obtain the surface vibration waveform function of multiple-hole blasting in the tunnel; finally, determining the specific parameters in the formula by comparing with field measured data, and obtaining a surface vibration waveform function curve suitable for field use. This method can comprehensively and accurately predict the waveform time history curve of the entire process of surface vibration during tunnel blasting, rather than just predicting a single blasting peak value. It can effectively promote the field application of surface vibration waveform prediction for tunnel blasting and is of great significance for optimizing blasting parameters and ensuring the safety of various facilities and personnel around the blasting area.

Description

Technical Field

[0001] This invention relates to the field of tunnel technology, and more specifically, to a method for predicting surface vibration waveforms during tunnel blasting. Background Technology

[0002] With the continuous advancement of urbanization, the urban population is increasing year by year, which has brought enormous pressure to urban traffic. To effectively alleviate urban congestion, many cities are constructing or about to construct subway tunnels that traverse downtown areas. Drill-and-blast method, as an economical, effective, and fast excavation method, has become one of the main methods for subway construction projects. However, when blasting is carried out in urban areas, it poses significant risks to buildings and underground pipelines due to their proximity to surrounding structures. Therefore, it is necessary to conduct relevant calculation and prediction studies on the surface vibrations caused by tunnel blasting to avoid the negative impacts of blasting vibrations.

[0003] Currently, the Sadovsky formula is commonly used to predict surface vibrations during tunnel blasting, as shown in the following equation. However, the Sadovsky formula only considers the effects of charge quantity and distance on blasting vibrations, neglecting the influence of surrounding rock elastic modulus, longitudinal wave velocity, and explosive parameters (explosive diameter, detonation velocity) on blasting vibrations. Since blasting velocity is highly sensitive to changes in these parameters, the blasting vibration results calculated using the Sadovsky formula will contain significant errors. Furthermore, the Sadovsky formula only reflects the peak value variation of blasting vibrations in a single blast, failing to reflect the frequency and duration of the blast, factors crucial for the study of blasting vibrations.

[0004]

[0005] The background description provided herein is for the purpose of generally presenting the context of this disclosure. Unless otherwise indicated herein, the material described in this section is not prior art to the claims of this application and should not be acknowledged as prior art by virtue of its inclusion in this section. Summary of the Invention

[0006] To address the aforementioned technical problems in related technologies, this invention proposes a method for predicting surface vibration waveforms during tunnel blasting, characterized by comprising the following steps:

[0007] S1. Based on Heelan theory, the vibration waveform function of a short-barreled explosive charge is derived, where the radial and axial velocities excited by the short-barreled explosive charge are:

[0008]

[0009] in,

[0010] ω=2πf

[0011]

[0012] Frequency f is generally considered to decrease with increasing charge and distance from the detonation point; k and α are coefficients and attenuation exponents related to the terrain, geological conditions, and vibration direction at the blast point; Q is the maximum charge per segment; R is the distance from the observation point to the center of the charge; V p and V s These are the longitudinal wave velocity and transverse wave velocity of the surrounding rock, respectively, where the subscripts r and z represent the directions, respectively;

[0013] S2. Construct the vibration waveform function of the short column charge to calculate the vibration of the actual tunnel slotting blasting, and divide the slotting hole into multiple short column charges for superposition calculation based on the superposition principle to obtain the surface vibration waveform function of the tunnel slotting hole blasting.

[0014] S3. The formula for the waveform function of multi-hole blasting is simplified and corrected to obtain the surface vibration waveform function of tunnel multi-hole blasting.

[0015] S4. Verify the waveform function of the multi-hole blasting based on the measured vibration time history curves on site, determine the relevant parameters in the formula, and construct a surface waveform function curve of tunnel blasting vibration suitable for the site.

[0016] Specifically, the calculation method for the short-column explosive charge blasting vibration waveform function in step S1 is as follows:

[0017] According to Heelan theory, the displacement solutions for P-waves and S-waves under lateral pressure loads in a short cylindrical cavity are:

[0018]

[0019]

[0020] in,

[0021]

[0022]

[0023]

[0024]

[0025] R p R s Z p and Z s These represent the R-direction displacement and Z-direction displacement of the P-wave and S-wave, respectively; V p and V s These represent the propagation velocities of the P-wave and S-wave, respectively; R is the distance from the observation point to the center of the medicine pack. The angle between the wave propagation direction and the negative z-axis; P(t) is the radial pressure exerted on the short cylindrical cavity; and denoted as the source function for P-waves and S-waves; Δ is the volume of the short column cavity; G is the shear modulus of the surrounding rock; E is the elastic modulus of the surrounding rock; ρ is the density of the surrounding rock; and μ is the Poisson's ratio of the surrounding rock.

[0026] Summing and differentiating equation (1), we obtain the formulas for calculating the radial and axial vibration velocities excited by the short column charge:

[0027]

[0028] The maximum peak velocities in the radial and axial directions at the measuring point are calculated using equation (2). Simultaneously, the test data shows that the vibration wave is a function that gradually decreases with time. To simplify the calculation of the vibration waveform's functional form, it is assumed that the on-site vibration waveform fluctuates in a sinusoidal form, and its vibration formula can be expressed as:

[0029]

[0030] Specifically, the radial pressure P(t) on the short column cavity is calculated as follows:

[0031] P(t)=P m e -at+b (4)

[0032] in,

[0033]

[0034] a and b are the detonation attenuation coefficients of the explosive, which are related to the explosive material, its properties, and the borehole axial decoupling coefficient; P m It is the maximum pressure considering the explosion stress wave and the expansion of the detonation gas; n is the factor that increases the detonation gas pressure; ρ e D represents the density of the explosive. e d is the detonation velocity of the explosive; c d is the diameter of the explosive; b The diameter of the borehole.

[0035] Specifically, the calculation method for the surface vibration waveform function of the tunnel cut hole blasting in step S2 is as follows:

[0036] Since the short-column explosive charge diffuses uniformly outward in the form of cylindrical waves, the vibration velocities in the radial (r) and axial (Z) directions at any point on the wavefront can be calculated using step S1. Then, by transforming between cylindrical and rectangular coordinates, the vibration velocity in the r direction is decomposed to obtain the triaxial vibration waveform function at any measuring point on the ground surface, as shown in the following formula:

[0037] X = r·sinθ

[0038] Y = r·cosθ

[0039] Z = Z(5)

[0040] Finally, the vibrations caused by multiple short explosive charges are superimposed to obtain the vibration caused by the actual explosive charge. The calculation process for surface vibration during slot hole blasting is as follows:

[0041] First, the long charge of medicine is divided into n short cylindrical charges of the same size, and the mass of each short cylindrical charge is the same. The axial distance from the i-th short cylindrical charge to the measuring point is:

[0042]

[0043] The distance from the center of explosion of the i-th short explosive charge to the measuring point is:

[0044]

[0045] Then, the time for the vibration wave of the i-th short column of the drug pack to reach the measuring point is:

[0046]

[0047]

[0048] Substituting equations (6) to (8) into equation (3) and superimposing them, we can obtain the vibration formulas for the columnar explosive charge measuring point B in the r and z directions as follows:

[0049]

[0050]

[0051] Finally, by decomposing the vibration velocity in the r direction along the x and y axes, the horizontal and vertical vibration velocities at measuring point B can be obtained as follows:

[0052] V x (t)=V r (t)·sinθ

[0053] V y (t)=V r (t)·cosθ (10)

[0054] Where θ is the angle between the line connecting the measuring point and the medicine bag and the vertical line to the ground.

[0055] Specifically, the simplified calculation method for the surface vibration waveform function of the tunnel group blasting in step S3 is as follows:

[0056] When the charge and volume of the blast holes are consistent, and the geological conditions experienced by the seismic waves generated by the explosion are also the same, the vibration function of each single-hole blasting is only related to the distance between the blast centers R. The distance between the blast centers from the surface measuring point to each blast hole is much larger than the distance between the slotting holes. The change in the blast center distance caused by the arrangement of the slotting holes is small and can be ignored. The vibration velocity waveforms formed by each blast hole are consistent, and the blasting function of the group of holes is only a temporal reproduction of the single-hole blasting. When the interval time between blast holes is the same, the simplified vibration waveform function of the tunnel group of holes with micro-delay blasting is as follows:

[0057]

[0058] In the formula, T is the borehole detonation interval; N is the total number of boreholes detonated in one operation; and m is the borehole detonation sequence.

[0059] Specifically, the method further includes: S5, predicting the peak value and frequency changes of blasting vibration of buildings around the tunnel based on the obtained surface vibration waveform function of tunnel blasting, and adjusting the blasting parameters and scheme.

[0060] The method for predicting surface vibration waveforms during tunnel blasting proposed in this invention has the following beneficial effects:

[0061] (1) More comprehensive consideration of factors

[0062] The method for predicting surface vibration waveforms during tunnel blasting in this invention fully considers factors such as the elastic modulus, shear modulus, explosive density, detonation velocity, and diameter of the surrounding rock, and can more accurately reflect the actual situation of blasting vibration.

[0063] (2) It can more realistically reflect the blasting vibration signal

[0064] The surface vibration waveform prediction method for tunnel blasting of the present invention can directly predict the time history curve of blasting vibration, rather than a single vibration peak prediction. It can more realistically assess the impact of blasting vibration on peak value, frequency and other factors, and minimize the harm of blasting vibration.

[0065] (3) The monitoring workload is small

[0066] When factors such as blasting cycle advance, surrounding rock grade, and distance change, the blasting vibration function can be obtained simply by adjusting the relevant parameters in the theoretical calculation formula, without the need for multiple field tests. Attached Figure Description

[0067] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0068] Figure 1 This is a flowchart of a method for predicting surface vibration waveforms during tunnel blasting, provided by an embodiment of the present invention.

[0069] Figure 2 This is a schematic diagram showing the relative positions of the measuring points to the tunnel;

[0070] Figure 3 This is a schematic diagram showing the relative positions of the tunnel explosive charges and measuring points;

[0071] Figure 4 This is a simplified diagram of the model calculation in this embodiment;

[0072] Figure 5 This is a comparison chart of the calculation and actual measurement of tunnel group blasting in this embodiment. Detailed Implementation

[0073] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the scope of protection of the present invention.

[0074] Example 1

[0075] refer to Figure 1 This embodiment discloses a method for predicting surface vibration waveforms during tunnel blasting, which includes the following steps:

[0076] S1. Derive the short-column explosive charge explosion vibration waveform function based on Heelan theory;

[0077] According to Heelan theory, the displacement solutions for P-waves and S-waves under lateral pressure loads in a short cylindrical cavity are:

[0078]

[0079]

[0080] in,

[0081]

[0082]

[0083]

[0084]

[0085] R p R s Z p and Zs These represent the R-direction displacement and Z-direction displacement of the P-wave and S-wave, respectively; V p and V s These represent the P-wave velocity and S-wave velocity of the surrounding rock, respectively; R is the distance from the observation point to the center of the explosive charge. The angle between the wave propagation direction and the negative z-axis; P(t) is the radial pressure exerted on the short cylindrical cavity; and denoted as the source function for P-waves and S-waves; Δ is the volume of the short column cavity; G is the shear modulus of the surrounding rock; E is the elastic modulus of the surrounding rock; ρ is the density of the surrounding rock; and μ is the Poisson's ratio of the surrounding rock.

[0086] Summing and differentiating equation (1), we obtain the formulas for calculating the radial and axial vibration velocities excited by the short column charge:

[0087]

[0088] The maximum peak vibration velocities in the radial and axial directions at the measuring point can be calculated from equation (2). Simultaneously, the test data shows that the vibration wave is a function that gradually decreases with time. To simplify the calculation of the vibration waveform's functional form, it is assumed that the on-site vibration waveform fluctuates in a sinusoidal form, and its vibration formula can be expressed as:

[0089]

[0090] in,

[0091] ω=2πf

[0092]

[0093] The frequency f is generally considered to decrease with the amount of explosive and the distance from the detonation point; k and α are coefficients and attenuation exponents related to the topography, geological conditions, and vibration direction of the blasting point. Generally, α is taken as 1 to 2, k is taken as 30 to 70 in rock, and k is taken as 150 to 250 in soil. The harder the rock mass, the smaller the values ​​of k and α. The subscripts r and z represent the r and z directions in the RTZ coordinate system, respectively, such as V. pr This represents the component of the longitudinal wave velocity of the surrounding rock in the r direction, and so on.

[0094] The radial pressure P(t) on the short cylindrical cavity is calculated as follows:

[0095] P(t)=P m e -at+b (4)

[0096] in,

[0097]

[0098] a and b are the detonation attenuation coefficients of the explosive, which are related to the explosive material, its properties, and the borehole axial decoupling coefficient; P m This considers the maximum pressure under the influence of explosion stress wave and the expansion of detonation gases; n is the factor that increases the detonation gas pressure, taken as 8 to 11; ρ e D represents the density of the explosive. e d is the detonation velocity of the explosive; c d is the diameter of the explosive; b The diameter of the borehole.

[0099] S2. Construct the vibration waveform function of the short column charge to calculate the vibration of the actual tunnel slotting blasting, and divide the slotting hole into multiple short column charges for superposition calculation based on the superposition principle to obtain the surface vibration waveform function of the tunnel slotting hole blasting.

[0100] Since the short-column explosive charge diffuses uniformly outward in the form of cylindrical waves, the vibration velocities in the radial (r) and axial (Z) directions at any point on the wavefront can be calculated using the methods described in step 1. Figure 1 As shown. By transforming between cylindrical and rectangular coordinate systems, the vibration velocity in the r-direction can be decomposed, thus obtaining the triaxial vibration waveform function at any measuring point on the ground surface, as shown in the following formula:

[0101] X = r·sinθ

[0102] Y = r·cosθ

[0103] Z = Z(5)

[0104] Since the actual detonation velocity of a cylindrical explosive charge in the field is often between 2000 and 7000 m / s, the lateral load P(t) cannot be applied to the borehole wall simultaneously. To account for the vibration velocity calculation deviation caused by the detonation velocity, the cylindrical explosive charge is decomposed into multiple short cylindrical explosive charges. It is assumed that the blasting vibration waveform of the long cylindrical explosive charge is formed by the successive detonation of multiple short cylindrical explosive charges. Finally, the vibrations caused by the multiple short cylindrical explosive charges are superimposed to obtain the vibration caused by the actual cylindrical explosive charge. The relative positions of the tunnel explosive charge and the measuring points are as follows: Figure 2 As shown. The calculation process for surface vibration during slotting blasting is as follows:

[0105] First, divide the long pouch of length l into n short pouches of the same size, each with the same mass. Figure 2 It can be seen that the axial distance from the i-th short column of the drug pack to the measuring point is:

[0106]

[0107] The distance from the center of explosion of the i-th short explosive charge to the measuring point is:

[0108]

[0109] Then, the time for the vibration wave of the i-th short column of the drug pack to reach the measuring point is:

[0110]

[0111]

[0112] Substituting equations (6) to (8) into equation (3) and superimposing them, we can obtain the vibration formulas for the columnar explosive charge measuring point B in the r and z directions as follows:

[0113]

[0114]

[0115] Finally, by decomposing the vibration velocity in the r direction along the x and y axes, the horizontal and vertical vibration velocities at measuring point B can be obtained as follows:

[0116] V x (t)=V r (t)·sinθ

[0117] V y (t)=V r (t)·cosθ(10)

[0118] S3. The formula for the waveform function of multi-hole blasting is simplified and corrected to obtain the surface vibration waveform function of tunnel multi-hole blasting.

[0119] When the charge and volume of the blast holes are consistent, and the geological conditions experienced by the seismic waves generated by the explosion are also the same, the vibration function of each single-hole blast is only related to the distance between the blast centers R. Under normal circumstances, the distance between the blast centers from the surface measuring point to each blast hole is much larger than the distance between the slotting holes. The change in the blast center distance caused by the arrangement of the slotting holes is small and can be ignored. Therefore, it can be assumed that the vibration velocity waveforms formed by each blast hole are consistent, and the blasting function of the group of holes is only a temporal reproduction of the single-hole blast. When the interval time between blast holes is the same, the simplified vibration waveform function of the tunnel group of holes with differential blasting is as follows:

[0120]

[0121] In the formula, T is the borehole detonation interval; N is the total number of boreholes detonated in one operation; and m is the borehole detonation sequence.

[0122] S4. Verify the waveform function of the multi-hole blasting based on the measured vibration time history curves on site, determine the relevant parameters in the formula, and construct a surface waveform function curve of tunnel blasting vibration suitable for the site.

[0123] Furthermore, this embodiment uses the obtained surface vibration waveform function of tunnel blasting to predict the peak value and frequency changes of blasting vibration of various buildings (structures) around the tunnel, so as to adjust the blasting parameters and scheme in a timely manner and reduce the damage caused by tunnel blasting to surrounding buildings (structures).

[0124] This also includes:

[0125] S5. Based on the obtained surface vibration waveform function of tunnel blasting, predict the peak value and frequency change of blasting vibration of buildings around the tunnel, and adjust the blasting parameters and scheme.

[0126] This experiment was conducted on a field test of a cut-and-cover tunnel section of an access line for a municipal rail transit line. Two boreholes were simultaneously detonated using No. 2 emulsion explosive. Explosive parameters are shown in Table 1: borehole diameter 42mm, explosive diameter 32mm, single-hole charge 0.6kg, borehole depth 1.0m, and borehole openings sealed with 0.4m of stemming material. Instruments were deployed at a distance of 12.1m from the tunnel face along the ground axis to monitor blasting vibrations. The surrounding rock mechanical parameters are shown in Table 2.

[0127] Table 1 Explosive Parameters

[0128]

[0129] Table 2. Rock Mechanical Parameters

[0130]

[0131] 1): The explosive charges for the tunnel cut holes are divided, and the simplified model calculation diagram is as follows: Figure 4 As shown. The horizontal axial distance from the measuring point to the blast center is 12.1m, i.e., z = 12.1. The height from the measuring point to the blast source is h = 10m, i.e., y = 10m. The measuring point is located on the tunnel axis, so x = 0m. According to the linear superposition principle, this columnar explosive charge is divided into a superposition of 8 short columnar explosive charges.

[0132] The P-wave velocity and S-wave velocity of the surrounding rock can be obtained using Heelan theory:

[0133]

[0134]

[0135] Taking the detonation gas pressure increase factor n = 8, the peak lateral pressure of each short column charge can be obtained from Equation 4 as follows:

[0136]

[0137] The axial distance from each short column of explosive to the measuring point can be obtained from equation (6):

[0138]

[0139] The detonation distance of each short-column explosive charge can be obtained from equation (7):

[0140]

[0141] The arrival time of the vibration wave from each short column of explosive charge at the measuring point can be obtained from equation (8):

[0142]

[0143]

[0144] The blasting site is classified as Class IV surrounding rock. Taking k = 60 and α = 1.39, the attenuation frequency at the measuring point is calculated as follows:

[0145]

[0146] Therefore, the angular frequency ω = 2πf = 269.3

[0147] Then, substitute the calculation results into equation (9) to solve for the surface vibration waveform function of single-hole blasting.

[0148] 2) Substitute the calculated surface vibration waveform function of single-hole blasting into equation (11) to obtain the surface vibration waveform function of multi-hole blasting. Since the two holes are blasted simultaneously, the differential time T = 0 ms.

[0149] 3) The calculated surface vibration waveforms from tunnel borehole blasting were compared with the measured data, and plotted as follows: Figure 4 As shown in the figure, the waveform function obtained from theoretical calculation is highly consistent with the measured function in terms of peak vibration velocity and vibration mode, thus verifying the correctness of the vibration waveform function of the cylindrical explosive charge in the tunnel group. The calculation results of this formula can more accurately predict the surface vibration waveform.

[0150] Compared with existing technologies, the surface vibration waveform prediction method for tunnel blasting proposed in this embodiment has the following advantages:

[0151] (1) More comprehensive consideration of factors

[0152] The method for predicting surface vibration waveforms during tunnel blasting proposed in this embodiment fully considers factors such as the elastic modulus and shear modulus of the surrounding rock, the density of the explosive, the detonation velocity, and the diameter, and can more accurately reflect the actual situation of blasting vibration.

[0153] (2) It can more realistically reflect the blasting vibration signal

[0154] The surface vibration waveform prediction method for tunnel blasting proposed in this embodiment can directly predict the time history curve of blasting vibration, rather than just the vibration peak value prediction. It can more realistically assess the impact of blasting vibration on peak value, frequency, etc., and minimize the harm of blasting vibration.

[0155] (3) The monitoring workload is small

[0156] When factors such as blasting cycle advance, surrounding rock grade, and distance change, the blasting vibration function can be obtained simply by adjusting the relevant parameters in the theoretical calculation formula, without the need for multiple field tests.

[0157] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting surface vibration waveforms during tunnel blasting, characterized in that, Includes the following steps: S1. Based on Heelan theory, the vibration waveform function of a short-barreled explosive charge is derived, where the radial and axial velocities excited by the short-barreled explosive charge are: ， in, ， The frequency f is generally considered to decrease with increasing charge and distance from the detonation point; k and α are coefficients and attenuation exponents related to the terrain, geological conditions, and vibration direction at the blast point. R represents the maximum single-segment drug quantity, and R is the distance from the observation point to the center of the drug pack. and These are the longitudinal wave velocity and transverse wave velocity of the surrounding rock, respectively, where the subscripts r and z represent the directions, respectively; S2. Construct the vibration waveform function of the short column charge to calculate the vibration of the actual tunnel slotting blasting, and divide the slotting hole into multiple short column charges for superposition calculation based on the superposition principle to obtain the surface vibration waveform function of the tunnel slotting hole blasting. S3. The formula for the waveform function of multi-hole blasting is simplified and corrected to obtain the surface vibration waveform function of tunnel multi-hole blasting. S4. Verify the waveform function of the multi-hole blasting based on the measured vibration time history curves on site, determine the relevant parameters in the formula, and construct a surface waveform function curve of tunnel blasting vibration suitable for the site.

2. The method for predicting surface vibration waveforms during tunnel blasting according to claim 1, characterized in that: The calculation method for the short-column explosive charge blasting vibration waveform function in step S1 is as follows: According to Heelan theory, the displacement solutions for P-waves and S-waves under lateral pressure loads in a short cylindrical cavity are: ， in, ， , , as well as These represent the R-direction displacement and Z-direction displacement of the P-wave and S-wave, respectively. and These represent the propagation velocities of the P-wave and S-wave, respectively; R is the distance from the observation point to the center of the medicine pack. The angle between the wave propagation direction and the negative z-axis direction; The radial pressure exerted on the short cylindrical cavity; and The source functions for P-waves and S-waves; Let G be the volume of the short column cavity; G be the shear modulus of the surrounding rock; E be the elastic modulus of the surrounding rock; ρ be the density of the surrounding rock; and μ be the Poisson's ratio of the surrounding rock. Summing and differentiating equation (1), we obtain the formulas for calculating the radial and axial vibration velocities excited by the short column charge: ， The maximum peak vibration velocities in the radial and axial directions at the measuring point are calculated using equation (2). Simultaneously, the test data shows that the vibration wave is a function that gradually decreases with time. To simplify the calculation of the vibration waveform's functional form, it is assumed that the on-site vibration waveform fluctuates in a sinusoidal form, and its vibration formula can be expressed as: 。 3. The method for predicting surface vibration waveforms during tunnel blasting according to claim 2, characterized in that: The radial pressure P(t) on the short cylindrical cavity is calculated as follows: ， in, ， a、b is the detonation attenuation coefficient of the explosive, which is related to the explosive material, property parameters, and the axial decoupling coefficient of the borehole. P m It is the maximum pressure considering the explosion stress wave and the expansion of the detonation gas; n is the factor that increases the detonation gas pressure. Density of the explosive; For the detonation velocity of the explosive; The diameter of the explosive; The diameter of the borehole.

4. The method for predicting surface vibration waveforms during tunnel blasting according to claim 1, characterized in that: The calculation method for the surface vibration waveform function of the tunnel cut hole blasting in step S2 is as follows: Since the short-column explosive charge diffuses uniformly outward in the form of cylindrical waves, the vibration velocities in the radial (r) and axial (Z) directions at any point on the wavefront can be calculated using step S1. Then, by transforming between cylindrical and rectangular coordinates, the vibration velocity in the r direction is decomposed to obtain the triaxial vibration waveform function at any measuring point on the ground surface, as shown in the following formula: ， Finally, the vibrations caused by multiple short explosive charges are superimposed to obtain the vibration caused by the actual explosive charge. The calculation process for surface vibration during slot hole blasting is as follows: First, the length is l The medicine packs are divided into n There are several short cylindrical drug packets of the same size, and each short cylindrical drug packet has the same mass. The first... i The axial distance from the short column charge to the measuring point is: ， No. i The distance from the short-barreled explosive charge to the measuring point is: ， Then, the first i The time it takes for the vibration wave from the short column of the explosive charge to reach the measuring point is: ， Substituting equations (6) to (8) into equation (3) and superimposing them, we can obtain the vibration formulas for the columnar explosive charge measuring point B in the r and z directions as follows: ， Finally, the vibration velocity in the r direction is along... x and y By decomposing the axis, the horizontal and vertical vibration velocities at measuring point B can be obtained as follows: ， in, θ The angle between the line connecting the measuring point and the medicine bag and the vertical line to the ground surface.

5. The method for predicting surface vibration waveforms during tunnel blasting according to claim 1, characterized in that: The simplified calculation method for the surface vibration waveform function of the tunnel group blasting in step S3 is as follows: When the charge and volume of explosives in each borehole are consistent, and the geological conditions experienced by the seismic waves generated by the explosion are also the same, the vibration function of each single-hole blasting is only related to the distance from the blast center. R Regarding the fact that the distance from the surface measuring point to each blast hole is much greater than the distance between the slotting holes, the change in the blast center distance caused by the arrangement of the slotting holes is small and can be ignored. The vibration velocity waveform formed by each blast hole is consistent, and the group blasting function is only a time reproduction of the single-hole blast. When the blast hole interval time is the same, the simplified vibration waveform function of the tunnel group blasting is as follows: ， In the formula, is the interval between borehole detonations; N is the total number of boreholes detonated in one operation; and m is the detonation sequence of the boreholes.

6. The method for predicting surface vibration waveforms during tunnel blasting according to claim 1, further comprising: S5. Based on the obtained surface vibration waveform function of tunnel blasting, predict the peak value and frequency change of blasting vibration of buildings around the tunnel, and adjust the blasting parameters and scheme.

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