Explosion overpressure calculation method suitable for end-blocked tunnel

Abstract

The invention discloses an explosion overpressure calculation method suitable for an end plugging tunnel. The explosion overpressure calculation method comprises the steps that 1, the position LD of an end effect demarcation point is determined; step 2, calculating a first overpressure peak value PF; 3, according to the distance LBC from the target to the explosion center, the distance Lmax from the tunnel blocking end to the explosion center and the reflected wave overpressure PF, r on the tunnel blocking face, the end reflection overpressure peak PER is calculated; and step 4, comparing the LBC with the LD, and calculating the maximum overpressure Pmax borne by the target. The method comprises the following steps: determining an end reflection effect demarcation point LD and an end reflection overpressure PER; when the explosion center distance LBC does not exceed the LD, the maximum overpressure in the tunnel is determined by a first overpressure peak value; and when the explosion center distance is greater than LD, the maximum overpressure in the tunnel is determined by an end reflection overpressure peak value, so that the target maximum overpressure of the shock waves in the blocked tunnel can be accurately calculated, and the calculation error does not exceed 10%.

Description

Technical Field

[0001] This invention relates to the field of tunnel construction, and in particular to a method for calculating explosive overpressure applicable to end-sealing tunnels. Background Technology

[0002] Tunnels, as typical underground structures, play a vital role in transportation, mining production, and safety engineering. Due to their enclosed nature, explosions within tunnels can easily cause numerous casualties and enormous economic losses. Tunnels sealed at one end are common in construction tunnels, mining roadways, and tunnels with protective doors. Existing research mainly focuses on load calculations for tunnels connected at both ends, lacking effective methods for calculating shock wave overpressure in tunnels with sealed ends.

[0003] Unlike tunnels open at both ends, the propagation of shock waves in a tunnel sealed at one end is affected by the constraint of the sealed end, resulting in significant end-reflection overpressure (P). ER Near the sealing end, the end-reflected overpressure can even be higher than the initial shock wave overpressure (P). F The maximum overpressure load is controlled by the shock wave. Existing internal explosion calculation models lack methods for calculating the overpressure of shock waves in sealed tunnels, which greatly limits the rapid assessment of explosion hazards within tunnels and hinders the development of tunnel protection technology. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for calculating explosive overpressure suitable for end-sealed tunnels, which addresses the shortcomings of the prior art. This method can accurately calculate the target maximum overpressure of the shock wave in the sealed tunnel, and the calculation error does not exceed 10%.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] A method for calculating explosive overpressure applicable to end-sealed tunnels includes the following steps.

[0007] Step 1: Based on the explosive mass m, the tunnel cross-sectional area S, and the distance L from the tunnel sealing end to the blast center. max Determine the location L of the end effect boundary. D .

[0008] Step 2: Calculate the initial overpressure peak value P F .

[0009] Step 3: Based on the distance L from the target to the explosion center BC Distance L from the tunnel sealing end to the blast center max and the overpressure P of the reflected wave on the tunnel sealing surface F,r Calculate the peak overpressure P reflected at the end.ER .

[0010] Step 4, place L BC With L D Compare the values ​​and calculate the maximum overpressure P on the target. max The specific calculation method is as follows:

[0011] A, when L BC ≤L D At that time, P max = P F .

[0012] B, when L BC >L D At that time, P max = P ER .

[0013] In step 1, the location of the end effect boundary point The calculation formula is:

[0014] (1)

[0015] In the formula, a and b are the locations of the end effect boundary points. The experimental fit coefficient of the calculation formula.

[0016] When m is taken as the unit of kg, the specific value of the explosive mass is given; when S is taken as the unit of m... 2 The specific value of the tunnel cross-sectional area, L max The specific value of the distance from the tunnel sealing end to the blast center is taken in meters;

[0017] The unit is m; L max The unit is m.

[0018] In step 1, by conducting a target explosion simulation test and fitting the corresponding data on the internal explosion overpressure of the end-sealed tunnel, we obtained: a = -0.453, b = 0.761.

[0019] In step 2, the initial overpressure peak P F The calculation formula is:

[0020] (2)

[0021] In the formula, c, d, and e represent the initial overpressure peak value P, respectively. F The experimental fit coefficient of the calculation formula.

[0022] When m is taken as the unit of kg, the specific value of the explosive mass is given; when S is taken as the unit of m... 2The specific value of the tunnel cross-sectional area, L BC The specific value of the distance between the target and the explosion center is taken in meters.

[0023] In step 2, by conducting a target explosion simulation test and fitting the corresponding data on the internal explosion overpressure of the end-sealed tunnel, we obtained: c=-0.2226, d=1.675, e=-0.1464.

[0024] In step 3, the overpressure P of the reflected wave on the tunnel sealing surface F,r The calculation formula is:

[0025] (3)

[0026] In the formula, P F,i The overpressure of the incident wave on the tunnel sealing surface is expressed in MPa.

[0027] In step 3, the peak value of the end-reflected overpressure P ER The calculation formula is:

[0028] (4)

[0029] in:

[0030] L CE =L max -L BC

[0031] In the formula, L CE To test the distance from the target to the blocking end, specific values ​​in meters are used.

[0032] f, g, and h represent the peak overpressure values ​​Pend of the reflected end pressure. ER The experimental fit coefficient of the calculation formula.

[0033] In step 3, by conducting target explosion simulation tests and corresponding data fitting on straight-walled arch tunnels, circular tunnels and square tunnels with end sealing, we obtained: f=0.4158, g=-0.8276, h=1.368.

[0034] Step 5: Experimental Verification: By conducting wall overpressure simulation tests on target explosions under different tunnel conditions or different explosion scenarios, the maximum simulated overpressure experienced by the target is obtained. Then all the maximum overpressure errors If none of the values ​​exceed the average overpressure error threshold, then the maximum overpressure P experienced by the target calculated in step 4 is determined to be the overpressure P. max If the result is satisfactory, repeat steps 1 to 4 to correct the corresponding experimental fit coefficients in the formula.

[0035] In step 5, the average overpressure error threshold is 10%.

[0036] The present invention has the following beneficial effects: The present invention determines the boundary point L of the end reflection effect. D and end-reflection overpressure P ER When the distance from the center of the explosion to L BC No more than L D At that time, the maximum overpressure inside the tunnel is determined by the initial overpressure peak value; when the distance between the burst centers is greater than L... D At that time, the maximum overpressure inside the tunnel is determined by the peak value of the overpressure reflected at the end, thus enabling accurate calculation of the target maximum overpressure of the shock wave in the sealed tunnel, with a calculation error of no more than 10%. Attached Figure Description

[0037] Figure 1 This diagram illustrates the propagation process of shock waves within a tunnel under internal explosion conditions, as described in this invention.

[0038] Figure 2 The first peak overpressure P was displayed. F and the peak overpressure of the end reflection P ER A graph showing the change in distance from the explosion center.

[0039] Figure 3 The waveforms showing the overpressure variation over time near the plugging end at different burst center distances are displayed.

[0040] Figure 4 The flowchart shows a method for calculating explosive overpressure applicable to end-sealed tunnels according to the present invention.

[0041] Figure 5 The predicted value P obtained using formula (2) is shown. F，P With test value P F Error curves under different parameters.

[0042] Figure 6 The predicted value P obtained using formula (4) is shown. ER，P With test value P ER Error curves under different parameters.

[0043] Figure 7 The predicted value L obtained using formula (1) is shown. D，P With test value L D Error curves under different parameters.

[0044] Figure 8 The graph shows the peak overpressure as a function of the distance from the blast center under different tunnel cross sections. Detailed Implementation

[0045] The present invention will now be described in further detail with reference to the accompanying drawings and specific preferred embodiments.

[0046] like Figure 1 As shown, the propagation process of the shock wave in the tunnel under the action of an internal explosion can be divided into the following four stages: free air explosion—wall reflection superposition—plane wave formation—reflection at the sealing end and propagation back. The first three stages (the first 16ms) are the same as the shock wave propagation process of a conventional tunnel explosion, while in the fourth stage (after 16ms), the shock wave will form a significant end reflection overpressure (P) upon reaching the sealing surface. ER ), thus forming such Figure 3 The secondary overpressure peak value is shown.

[0047] As the distance between the burst centers increases, two types of overpressure peaks are detected inside the tunnel: the end-reflected overpressure peak (P0). ER ) and the first peak overpressure (P F The trends of these two overpressure peak values ​​are opposite. As the distance from the burst center increases (closer to the sealing end), the initial overpressure peak gradually decreases, while the end-reflected overpressure gradually increases. The time interval between the two peak overpressures also gradually decreases, eventually merging into the wall-reflected overpressure (P) at the sealing surface. F,r During the propagation of the shock wave, a P wave will appear at a certain location near the sealing end. F =P ER The dividing point is defined as the end reflection effect dividing point (L). D Therefore, as Figure 2 As shown, when the distance from the explosion center to LBC does not exceed L D At that time, the maximum overpressure inside the tunnel is determined by the initial overpressure peak value; when the distance between the burst centers is greater than L... D At that time, the maximum overpressure inside the tunnel is determined by the peak value of the end-reflection overpressure. The boundary point of the end-reflection effect (L) needs to be determined. D ) and end-reflection overpressure (P ER The calculation method for this is crucial for determining the safety protection against explosions inside tunnels.

[0048] like Figure 4 As shown, a method for calculating explosive overpressure applicable to end-sealed tunnels includes the following steps.

[0049] Step 1: Based on the explosive mass m, the tunnel cross-sectional area S, and the distance L from the tunnel sealing end to the blast center. max Determine the location L of the end effect boundary. D The specific calculation formula is as follows:

[0050] (1)

[0051] In the formula, When m is taken as the unit of kg, the specific value of the explosive mass is given; when S is taken as the unit of m... 2 The specific value of the tunnel cross-sectional area, Lmax The specific value of the distance from the tunnel closure end to the blast center is taken in meters. That is, the values ​​of m, S, and L in this formula. max All data used are dimensionless, with units not involved in the calculations, and were obtained by the applicant through experimental fitting.

[0052] The unit is m; L max The unit is m.

[0053] a and b are the locations of the boundary points of the end effect. The experimental fitting coefficients of the calculation formula are obtained in this embodiment by conducting a target explosion simulation test on the internal explosion overpressure of the end-sealed tunnel and fitting the corresponding data: a=-0.453, b=0.761. Therefore, the expression of formula (1) can also be written as:

[0054] (1)

[0055] Step 2: Calculate the initial overpressure peak value P F The specific calculation formula is as follows:

[0056] (2)

[0057] When m is taken as the unit of kg, the specific value of the explosive mass is given; when S is taken as the unit of m... 2 The specific value of the tunnel cross-sectional area, L BC The specific numerical values ​​of the distance from the target to the explosion center are taken in meters. That is, m, S, and L. BC Dimensionless data are used, and units are not involved in the calculations.

[0058] c, d, and e represent the initial overpressure peak value P, respectively. F The experimental fitting coefficients of the calculation formula are obtained in this embodiment by conducting a target explosion simulation test and fitting the corresponding data on the internal explosion overpressure of the end-sealed tunnel. The results are: c=-0.2226, d=1.675, e=-0.1464. Therefore, the expression of formula (2) can also be written as:

[0059] (2)

[0060] Step 3: Based on the distance L from the target to the explosion center BC Distance L from the tunnel sealing end to the blast center max and the overpressure P of the reflected wave on the tunnel sealing surface F,r Calculate the peak overpressure P reflected at the end. ER .

[0061] The reflected wave overpressure P on the aforementioned tunnel sealing surface F,rThe preferred calculation formula is:

[0062] (3)

[0063] In the formula, P F,i The overpressure of the incident wave on the tunnel sealing surface is expressed in MPa.

[0064] The aforementioned end-reflected overpressure peak value P ER The calculation formula is:

[0065] (4)

[0066] in:

[0067] L CE =L max -L BC

[0068] In the formula, L CE To test the distance from the target to the blocking end, specific values ​​in meters are used.

[0069] f, g, and h represent the peak overpressure values ​​Pend of the reflected end pressure. ER The experimental fitting coefficients of the calculation formula are obtained in this embodiment by conducting a target explosion simulation test and fitting the corresponding data on the internal explosion overpressure of the end-sealed tunnel. The results are: f=0.4158, g=-0.8276, h=1.368. Therefore, the expression of formula (4) can also be written as:

[0070] (4)

[0071] To ensure L CE A positive value is defined as L when the target is located between the explosion center and the sealing end. BC It is a positive value if it is positive, otherwise it is a negative value.

[0072] Step 4, place L BC With L D Compare the values ​​and calculate the maximum overpressure P on the target. max The specific calculation method is as follows:

[0073] A, when L BC ≤L D At that time, P max = P F .

[0074] B, when L BC >L D At that time, P max = P ER .

[0075] Step 5: Experimental Verification: By conducting wall overpressure simulation tests on target explosions under different tunnel conditions or different explosion scenarios, the maximum simulated overpressure experienced by the target is obtained. Then all the maximum overpressure errors If none of the values ​​exceed the maximum overpressure error threshold, then the maximum overpressure P experienced by the target calculated in step 4 is determined to be the maximum overpressure P. max If reliable; otherwise, repeat steps 1 to 4 to correct the corresponding experimental fitting coefficients in the formula. In this embodiment, the wall overpressure of different tunnel sections was tested, and the comparison showed that the prediction error of the internal explosion shock wave of the proposed calculation method for different tunnel sections was within 10% of the average overpressure error threshold, proving the accuracy and wide applicability of the calculation method proposed in this invention.

[0076] Formulas (3) and (4) above have certain limitations, requiring the shock wave reaching the sealing end to be in plane wave form. If L max If the value is too small, the explosion center will be too close to the sealing end, and the shock wave reaching the sealing surface will deviate from the conditions for using formulas (3) and (4), and the prediction effect will gradually deteriorate.

[0077] like Figure 5 As shown, the predicted value P F，P With test value P F The average error is 1.0%, confirming that the proposed model is effective in estimating the first peak overpressure P of the end-sealed tunnel. F Accuracy in this regard.

[0078] Figure 6 The prediction of P using formula (4) under different tunnel lengths and explosive masses was evaluated. ER The performance of [the tunnel]. For longer tunnels (L... max = 14.2m and 20m), the prediction remains reliable, and the predicted value P ER，P With test value P ER The average error is 3.0%. When the tunnel length is reduced to 10m and 5m, the corresponding errors increase to 49.6% and 119.3%, respectively. This trend indicates that when the shock wave reaching the sealing surface deviates from the assumed planar form in the formula, the prediction accuracy of formula (4) gradually decreases.

[0079] Figure 7 The L predicted by formula (1) is shown. D ,from Figure 8 It can be seen that the prediction result of formula (1) is reliable, L D The average error is 3.3%.

[0080] Furthermore, Figure 8The results show the prediction of the overpressure of explosion in different tunnel cross sections (straight wall arch, circular and square) using the prediction method proposed in this invention. It can be seen that formulas (2) and (4) still obtain reliable prediction results in tunnels with different cross sections, and the average error of overpressure prediction is less than 2.5%.

[0081] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for calculating explosive overpressure applicable to end-sealed tunnels, characterized in that: Includes the following steps: Step 1: Based on the explosive mass m, the tunnel cross-sectional area S, and the distance L from the tunnel sealing end to the blast center. max Determine the location L of the end effect boundary. D ; Step 2: Calculate the initial overpressure peak value P F ; Step 3: Based on the distance L from the target to the explosion center BC Distance L from the tunnel sealing end to the blast center max and the overpressure P of the reflected wave on the tunnel sealing surface F,r Calculate the peak overpressure P reflected at the end. ER ; Step 4, place L BC With L D Compare the values ​​and calculate the maximum overpressure P on the target. max The specific calculation method is as follows: A, when L BC ≤L D At that time, P max = P F ; B, when L BC >L D At that time, P max = P ER .

2. The method for calculating explosive overpressure applicable to end-sealed tunnels according to claim 1, characterized in that: In step 1, the end effect boundary point location L D The calculation formula is: (1) In the formula, a and b are the positions of the end effect boundary points L. D The experimental fit coefficient is calculated using the formula. When m is taken as the unit of kg, the specific value of the explosive mass is given; when S is taken as the unit of m... 2 The specific value of the tunnel cross-sectional area, L max The specific value of the distance from the tunnel sealing end to the blast center is taken in meters; L D The unit is m; L max The unit is m.

3. The method for calculating explosive overpressure applicable to end-sealed tunnels according to claim 2, characterized in that: In step 1, by conducting a target explosion simulation test and fitting the corresponding data on the internal explosion overpressure of the end-sealed tunnel, we obtained: a = -0.453, b = 0.

761.

4. The method for calculating explosive overpressure applicable to end-sealed tunnels according to claim 1, characterized in that: In step 2, the initial overpressure peak P F The calculation formula is: (2) In the formula, c, d, and e represent the initial overpressure peak value P, respectively. F The experimental fit coefficient is calculated using the formula. When m is taken as the unit of kg, the specific value of the explosive mass is given; when S is taken as the unit of m... 2 The specific value of the tunnel cross-sectional area, L BC The specific value of the distance between the target and the explosion center is taken in meters.

5. The method for calculating explosive overpressure applicable to end-sealed tunnels according to claim 4, characterized in that: In step 2, by conducting a target explosion simulation test and fitting the corresponding data on the internal explosion overpressure of the end-sealed tunnel, we obtained: c = -0.2226, d = 1.675, e = -0.1464.

6. The method for calculating explosive overpressure applicable to end-sealed tunnels according to claim 1, characterized in that: In step 3, the overpressure P of the reflected wave on the tunnel sealing surface F,r The calculation formula is: (3) In the formula, P F,i The overpressure of the incident wave on the tunnel sealing surface is expressed in MPa.

7. The method for calculating explosive overpressure applicable to end-sealed tunnels according to claim 1, characterized in that: In step 3, the peak value of the end-reflected overpressure P ER The calculation formula is: (4) in: L CE =L max -L BC In the formula, L CE To test the distance from the target to the blocking end, specific values ​​in meters are used; f, g, and h represent the peak overpressure values ​​Pend of the reflected end pressure. ER The experimental fit coefficient of the calculation formula.

8. The method for calculating explosive overpressure applicable to end-sealed tunnels according to claim 7, characterized in that: In step 3, By conducting a target explosion simulation test on the internal explosion overpressure of the end-sealed tunnel and fitting the corresponding data, we obtained: f = 0.4158, g = -0.8276, h = 1.

368.

9. The method for calculating explosive overpressure applicable to end-sealed tunnels according to claim 1, characterized in that: It also includes step 5, experimental verification: by conducting wall overpressure simulation tests on target explosions under different tunnels or different explosion conditions, the maximum simulated overpressure experienced by the target is obtained. Then all the maximum overpressure errors If none of the values ​​exceed the average overpressure error threshold, then the maximum overpressure P experienced by the target calculated in step 4 is determined to be the overpressure P. max If the result is satisfactory, repeat steps 1 to 4 to correct the corresponding experimental fit coefficients in the formula.

10. The method for calculating explosive overpressure applicable to end-sealed tunnels according to claim 9, characterized in that: In step 5, the average overpressure error threshold is 10%.

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