Supporting structure of shield close-to-underpass civil air defense channel and construction method
Through the composite structure of a segmented inflatable airbag and a detachable inner support frame, combined with distributed monitoring, the dynamic adjustment and monitoring difficulties of traditional rigid support structures in shield construction are solved, and the rapid movement and reuse of the support structure are achieved, and construction safety and monitoring accuracy are improved.
Patent Information
- Application Number
- CN202510913432.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-03
- Publication Date
- 2025-08-15
AI Technical Summary
When the shield structure is penetrated under the civil defense passage, the traditional rigid support structure cannot be dynamically adjusted, which is prone to collapse, and is difficult to monitor, difficult to install and disassemble, high cost, and limited space, so it cannot effectively support the old brick arched structure.
The composite structure of a segmented inflatable airbag and a removable internal support frame is adopted, combined with distributed monitoring components, and the rapid movement and adaptive support of the support structure are realized, and deformation is monitored through the total station to ensure safety.
The rapid movement and reuse of the support structure is realized, the construction cost is reduced, the safety and monitoring accuracy is improved, the risk of collapse is avoided, and the construction needs of narrow spaces is adapted.
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Figure CN120487126A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of shield construction, and in particular to a support structure and a construction method for a shield tunnel passing under a civil air defense passage. Background Art
[0002] During shield construction, tunneling often involves crossing under and alongside various pipelines and buildings, necessitating reinforcement solutions tailored to the hydrogeology and actual building conditions. Civil air defense facilities still exist in the old city, but many are dilapidated and date back to their construction. They typically feature brick arched roofs, brick rectangular bases, and either brick or concrete semicircular arches. These semicircular arches are composed of two quarter-circle structures joined together, with the seam located at the very top. These old structures are prone to collapse when the ground they sit on is disturbed, causing road subsidence, which can disrupt ground traffic at best and cause casualties at worst.
[0003] In the existing technology, when a shield tunnel passes under such a building, it is generally necessary to support and reinforce the structure with steel plates, steel structures or full-height frames, and supplemented by certain grouting measures to reinforce the stratum. However, this type of reinforcement method has a certain risk of collapse, especially for brick-built arched civil air defense passages. Ground disturbance can easily cause collapse, and traditional rigid supports cannot adapt to structural deformation and it is difficult to dynamically adjust the support range. In addition, in confined space conditions, the support structure is difficult to install and disassemble, the size of the materials in and out is affected by the space, and the splicing time is long, the cost is high, and the efficiency is low. In addition, existing monitoring methods make it difficult to effectively obtain deformation data of civil air defense structures under the obstruction of support structures. Civil air defense passages may undergo gradual deformation under the disturbance of shield excavation. When the crack width of the arch waist or arch exceeds the critical value of the brickwork and is not detected by monitoring, it may suddenly trigger a chain collapse. Summary of the Invention
[0004] In response to the problems existing in the existing technology, the present invention provides a support structure and construction method for a shield tunnel passing under a civil air defense passage, which can realize the rapid movement of the support structure and solve the industry problem of the immovable traditional rigid support. At the same time, the inflatable airbags and detachable internal support frames in the support structure can be reused multiple times, reducing construction costs.
[0005] The technical solutions of the present invention are as follows: In a first aspect of the present invention, a support structure for a shield tunnel passing through a civil air defense passage is provided, comprising: The segmented airbag assembly is composed of multiple independent inflatable airbags spliced longitudinally along the civil air defense passage. The inflatable airbag includes a hollow annular capsule with an inflation and deflation interface provided on the hollow annular capsule; The detachable inner support frame is assembled from multiple steel plates into a frame structure, and the outer contour of the inner support frame fits the inner periphery of the bottom of the inflatable airbag; The distributed monitoring component includes a threaded sleeve pre-buried at the joints of adjacent inflatable airbags and a threaded rod installed in the threaded sleeve. The position of the threaded rod is used as a leakage monitoring point, and the threaded rod is monitored by a total station. In some embodiments of the present invention, the curved surface shape of the outer periphery of the hollow annular sac matches the arched cross-sectional shape of the inner wall of the civil air defense passage, and the contact pressure between the inflated airbag and the inner wall of the civil air defense passage is 0.1-0.3Mpa after inflation. In some embodiments of the present invention, a positioning mortise and tenon structure is provided between adjacent steel plates of the detachable inner support frame, and the adjacent steel plates are connected by bolts. In some embodiments of the present invention, the threaded rod is screwed into the sleeve through a thread and extends 10-15 cm beyond the inner surface of the inflatable airbag. In some embodiments of the present invention, the axis of the threaded rod is consistent with the deformation-sensitive direction of the civil air defense passage, and the deformation-sensitive direction of the civil air defense passage includes the vertical direction of the arch crown and the 45° direction of the arch waist of the civil air defense passage.
[0006] In some embodiments of the present invention, at least three detachable inner support frames are correspondingly provided in each of the inflatable airbags. The three detachable inner support frames are evenly distributed along the longitudinal direction of the inflatable airbag, and a plate is laid on the bottom frame of the detachable inner support frame. In some embodiments of the present invention, an airbag end plate is provided at each end of the independent inflatable airbag, and the shape of the airbag end plate matches the cross-sectional shape of the inflatable airbag. In a second aspect of the present invention, a construction method for a shield tunnel approaching a support structure for passing under a civil air defense passage is provided, comprising the following steps: When the shield cutterhead reaches the set position of the civil air defense passage, after cleaning the inner wall of the civil air defense passage, at least three sections of inflatable air bags are continuously laid in the civil air defense passage, and the inflatable air bags are inflated to form an advanced support section; Installing a detachable inner support frame so that the detachable inner support frame supports the inner periphery of the bottom of the inflatable airbag; When the shield machine is about to pass through the last section of the inflatable airbag in the advance support section, the deformation data of the leakage monitoring point of the first section of the inflatable airbag in the advance support section is monitored by a total station. If the monitored deformation data is normal, the first section of the inflatable airbag is deflated, folded, and transported to the front of the tunnel through the civil air defense passage for re-inflation; Repeat the above steps until the shield has completely passed through the civil air defense passage, and finally remove the inner support frame and recover the inflatable airbag. In some embodiments of the present invention, after the detachable inner support frame is installed, panels are laid on the bottom frame of the detachable inner support frame to ensure normal use of the civil air defense passage.
[0007] In some embodiments of the present invention, if the monitored deformation data is abnormal, the deformed position is first reinforced and repaired, and the monitoring is continued. The inflatable airbag is deflated after the deformation data meets the requirements.
[0008] One or more technical solutions of the present invention have the following beneficial effects: (1) The present invention adopts an inflatable airbag to support the interior of the civil air defense passage. The inflatable airbag is simple to manufacture, light in weight, easy to use, and convenient to transport in a narrow space. The hollow structure solves the problem of reverse transportation of the inflatable airbag in a narrow space. The inflatable airbag is arranged in front, middle and back of the shield cutter head, that is, 10-15m in front and back of the cutter head. As the shield advances, the inflatable airbag moves from back to front. The inflatable airbag is deflated before moving. The airbag is moved to the front through the annular space in the middle of the inflatable airbag, and is arranged in close contact with the existing airbag and then quickly inflated to support the civil air defense structure. It can realize the rapid movement of the support structure and solve the industry problem that the traditional rigid support cannot be moved.
[0009] (2) The support structure of the present invention adopts a composite structure of an inflatable airbag and a detachable inner support frame, wherein the segmented airbag group forms an adaptive support surface through a controllable air pressure of 0.1-0.3MPa, and its equivalent stiffness can be intelligently adjusted with the deformation of the stratum, thereby reducing the amount of material used compared to a full-chamber support; the detachable inner support frame is connected by mortise and tenon bolts, which can quickly complete the assembly and provide the node bending resistance, thereby improving the anti-collapse safety factor of the civil air defense passage vault, and the inflatable airbag and the detachable inner support frame can be reused many times.
[0010] (3) The present invention solves the problem of traditional support structures blocking the measurement line of sight by adopting embedded monitoring points. The axis of the monitoring point is oriented in the deformation-sensitive direction of the civil air defense passage (vertical direction of the arch crown and 45° direction of the arch waist). In conjunction with the total station, high-precision monitoring is achieved. When the width of the cracks in the arch waist or arch crown exceeds the critical value of the brickwork, it can be detected in time to avoid sudden chain collapse.
[0011] (4) The construction method provided by the present invention always maintains a set length of the advance support section (three sections of inflatable airbags) during the construction process to ensure that the front and rear of the shield cutterhead are in the protection zone; the airbag usage can be reduced by moving the rear airbag forward, and the front section area is monitored before the shift. The inflatable airbag is allowed to shift only when the monitoring data is qualified, which can prevent accidents from happening. BRIEF DESCRIPTION OF THE DRAWINGS
[0012] Figure 1 Schematic diagram of the longitudinal section of the support structure of the shield tunnel approaching and passing under the civil air defense passage of the present invention; Figure 2 It is a structural schematic diagram of the longitudinal section of the inflatable airbag of the present invention; Figure 3Schematic diagram of the cross-section of the inflatable airbag of the present invention; Figure 4 This is a schematic diagram of the civil air defense passage; Figure 5 A schematic diagram of the structure of the monitoring component installation of the present invention; Figure 6 It is a structural schematic diagram of the detachable inner support frame of the present invention; In the figure: 1. Civil air defense passage and ground layer; 2. Inflatable airbag; 3. Interface; 4. Outer periphery of airbag; 5. Inner periphery of airbag; 6. End plate of airbag; 7. Removable inner support frame; 8. Bolt; 9. Monitoring component; 10. Threaded sleeve; 11. Threaded rod. DETAILED DESCRIPTION
[0013] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0014] Example 1 In a typical embodiment of the present invention, a support structure for a shield tunnel passing through a civil air defense passage is proposed, such as Figures 1 to 6 Shown, including: The segmented airbag assembly is composed of multiple independent inflatable airbags 2 spliced longitudinally along the civil air defense passage. The inflatable airbag 2 includes a hollow annular capsule body, and the hollow annular capsule body is provided with an inflation and deflation interface 3; The detachable inner support frame 7 is assembled into a frame structure by multiple steel plates, and the outer contour of the inner support frame fits the inner periphery of the bottom of the inflatable airbag 2; The distributed monitoring assembly 9 includes a threaded sleeve 10 embedded in the joint of adjacent inflatable airbags 2 and a threaded rod 11 installed in the threaded sleeve 10. The position of the threaded rod 11 is used as a leakage monitoring point, and the threaded rod 11 is monitored by a total station.
[0015] The above-mentioned support structure realizes modular expansion of the support range through the longitudinal splicing of the segmented airbag groups. The hollow annular airbag design greatly reduces the weight of a single-section airbag compared with the traditional steel support structure, greatly alleviating the transportation pressure in the narrow civil air defense passage; the detachable inner support frame 7 is fitted with the inner periphery 5 of the airbag to form a rigid-flexible composite structure, which can improve the local bending stiffness of the civil air defense passage and effectively suppress the risk of vault cracking; the distributed monitoring component 9 breaks through the obstruction of the traditional support body to the measurement line of sight, and the pre-embedded technology of the threaded sleeve 10 ensures that the monitoring point is directly fixed to the civil air defense structure, which can effectively reduce the measurement error.
[0016] like Figure 2 and Figure 3As shown, the outer periphery 4 of the airbag and the inner periphery 5 of the airbag form a hollow annular sac. An interface 3 is set at 45 degrees to the left of the top of the inner periphery 5 of the airbag. The interface 3 serves as the inflation port and the deflation port. To facilitate the movement of the inflatable airbag 2 during construction, the length of each section of the inflatable airbag 2 is positioned at 10m. The curved surface shape of the outer periphery of the hollow annular sac matches the arched cross-sectional shape of the inner wall of the civil air defense passage. The contact pressure between the inflated airbag 2 and the inner wall of the civil air defense passage is 0.1-0.3Mpa. Within this pressure range, a buffer layer is formed on the contact surface between the inflatable airbag 2 and the inner wall of the civil air defense passage, preventing the civil air defense passage from unevenly settling due to the shield tunneling process. In addition, the curved surface matching design of the hollow annular sac makes the effective contact area between the airbag and the inner wall of the civil air defense passage reach more than 95%, significantly improving the support efficiency.
[0017] Furthermore, the airbag 2 is made of a highly ductile rubber material. To enhance support for the airbag 2, an airbag end plate 6 is provided at each end of the independent airbag 2. The shape of the airbag end plate 6 matches the cross-sectional shape of the airbag. Specifically, the airbag 2 and the airbag end plate 6 can be configured as an integral structure, or an airbag end plate 6 can be fixed to each end of the airbag 2 using adhesive.
[0018] In this embodiment, a positioning mortise and tenon structure is provided between adjacent steel plates of the detachable inner support frame 7, and the adjacent steel plates are connected by bolts 8. Specifically, considering that the arc-shaped top of the inflatable airbag 2 can fit with the inner wall surface of the civil air defense passage in the inflated state, the detachable inner support frame 7 is configured to be composed of four detachable steel plates, which are connected by bolts 8, as shown in FIG. Figure 6 As shown, when reinforcing the airbag 2, four detachable steel plates are assembled by bolts 8. After the airbag reinforcement is completed, the steel plates are removed by removing the bolts 8. The frame structure composed of the four detachable steel plates supports the bottom position of the airbag 2 and the civil air defense passage to ensure the overall fit of the airbag 2 and the civil air defense passage.
[0019] Furthermore, at least three detachable inner support frames 7 are provided in each inflatable airbag 2, and the three detachable inner support frames 7 are evenly distributed along the longitudinal direction of the inflatable airbag 2. Panels are laid on the bottom edges of the detachable inner support frames 7, and the provided panels enable normal walking above the bottom of the inflatable airbag 2, thereby ensuring normal use of the civil air defense passage.
[0020] like Figure 5 As shown, the threaded rod 11 is screwed into the sleeve and extends 10-15 cm from the inner surface of the inflatable airbag 2. After the measurement is completed, the leakage monitoring point can be screwed into the sleeve and retracted 15 cm to prevent collision when the inflatable airbag 2 moves forward. The total station uses the existing structure to monitor the displacement data of the threaded rod 11 during the shield tunneling process, which is used to represent the deformation data at the leakage monitoring point on the inner wall of the civil air defense tunnel.
[0021] Furthermore, the axis of the leakage monitoring point aligns with the deformation-sensitive direction of the civil air defense passage. Sensitive locations for deformation in civil air defense passages include the base, crown, and haunch. The primary sensitive directions are vertically along the crown and at 45° to the haunch. Among brick-built civil air defense passage failure modes, crown settlement and haunch intrusion account for a significant proportion. Directional monitoring can improve the accuracy of early warnings.
[0022] In the actual application process, through on-site inspection of the structure of the civil air defense passage and stratum 1, such as Figure 4 As shown, the position of the shield machine underpass is determined, and the position of the civil air defense structure with large deformation is reinforced. During reinforcement, an inflatable hollow airbag is used to support the civil air defense passage. The cross-section of the inflatable airbag 2 is customized according to the cross-section of the civil air defense passage. Its length is 10m per section, and 3 sections form a cycle. The hollow cross-section structure of the inflatable airbag 2 can reduce gas consumption. The inflatable airbag 2 is arranged in front, middle and back of the shield cutter head, specifically 10-15m in front and behind the cutter head. As the shield advances, the inflatable airbag 2 moves from back to front. The inflatable airbag 2 is deflated before moving. The deflated airbag is moved to the front from the middle of the inflatable airbag 2, arranged in close contact with the existing airbag and quickly inflated to support the civil air defense structure. The inflation pressure is based on the set support pressure. The inflatable airbag is then reinforced by setting a detachable internal support frame. After the inflatable airbag support is completed, the internal support frame is disassembled for easy recycling.
[0023] In this embodiment, the monitoring points at the bottom, arch and waist of the civil air defense passage should be arranged at the joints of the two inflatable air bags according to the length of the air bags, and the exposed length of the threaded rod 11 should not be less than the thickness of the air bags, so as to facilitate the monitoring of the civil air defense structure; the shield tunneling should strictly follow the tunneling requirements, do a good job of synchronous grouting and secondary grouting, strictly control the tunnel deformation and ground settlement according to the monitoring data, and carry out deep hole grouting when necessary; the segments of the shield tunneling under the civil air defense structure section should use segments with increased grouting holes to facilitate subsequent grouting to control the deformation of the stratum.
[0024] Example 2 In a typical embodiment of the present invention, a construction method for a shield tunnel approaching a support structure of an air defense passage is provided, comprising the following steps: Step 1: When the shield cutterhead reaches the set position of the civil air defense passage, after cleaning the inner wall of the civil air defense passage, at least three sections of inflatable airbags are continuously laid in the civil air defense passage, and the inflatable airbags are inflated to form an advanced support section; Step 2: Install the detachable inner support frame so that the detachable inner support frame supports the inner periphery of the bottom of the inflatable airbag; Step 3: When the shield machine is about to pass through the last section of the inflatable airbag in the advance support section, the deformation data of the leakage monitoring point of the first section of the inflatable airbag in the advance support section is monitored by a total station. If the monitoring data is normal, the first section of the inflatable airbag is deflated, folded, and transported to the front of the tunnel through the civil air defense passage for re-inflation; Step 4: Repeat the above steps until the shield machine completely passes through the civil air defense passage, and finally remove the inner support frame and recover the inflatable airbag.
[0025] In this embodiment, after the detachable inner support frame is installed, panels are laid on the bottom edge of the detachable inner support frame, and people can walk normally on the panels to ensure the normal use of the civil air defense passage.
[0026] In this embodiment, if the monitored deformation data is abnormal, the deformed position is first reinforced and repaired, and the monitoring is continued. The inflatable airbag is deflated after the deformation data meets the requirements.
[0027] In the above construction method, the set length of the advance support section (three sections of inflatable airbags) is always maintained to ensure that the front and rear of the shield cutterhead are in the protection zone; by moving the rear airbag forward, the airbag usage can be reduced, and the front section area is monitored before shifting. Only when the monitoring data is qualified is the inflatable airbag allowed to shift, which can prevent accidents from happening.
[0028] In this embodiment, the cross-sectional type of the inflatable airbag, the cross-sectional dimensions of the inflatable airbag, and the dimensions of the inflatable airbag in the uninflated state are designed according to the cross-sectional shape of the civil air defense passage, and the hollow cross-sectional dimensions of the inflatable airbag are designed according to construction-related requirements to complete the cross-sectional design of the inflatable airbag.
[0029] Specifically, the following steps are included: 1. Surveying and mapping the cross-section of the civil air defense passage: Determine the cross-sectional form of the inflatable airbag by accurately surveying and mapping the geometric parameters of the inner wall of the civil air defense passage, such as the arch height, span, and arch waist angle.
[0030] 2. Determine the outer size of the airbag: The outer radius of the airbag must be equal to or slightly larger than the inner wall curvature radius of the channel. The cross-sectional perimeter of the airbag is Lairbag = Lchannel + δ ( δ The compensation for material compression deformation is usually 1% to 3% of the channel circumference).
[0031] Check the contact pressure using the material mechanics formula: P=F / A∈[0.1,0.3]MPa; where F is the force exerted by the internal air pressure of the airbag on the channel wall; A is the effective contact area (needs to be ≥95% of the channel inner wall area).
[0032] 3. Calculate the size of the hollow section: hollow ratio η = AHollow / A Total × 100%; of which, A Hollow refers to the cross-sectional area of the hollow part. A Total refers to the overall cross-sectional area of the airbag, which is determined by the size of the civil air defense passage. η Too high will reduce the hoop stiffness, and the anti-collapse ability needs to be verified through finite element analysis; η It is recommended to control it within 40%~60% (if it is too small, inflation will take a long time, and if it is too large, the support force will be insufficient).
[0033] 4. Design the dimensions of the uninflated state, and design the folded thickness and curled diameter based on the material compression rate and transportation space limitations.
[0034] Furthermore, after the inflatable airbag enters the civil air defense passage, it must first be inflated according to design requirements and used only after it meets the design requirements. Specifically, the inflation test must verify: 1. The pressure decay within 30 minutes is ≤5%; 2. The gap between the inflated contour and the passage is ≤2cm.
[0035] The construction method provided in this embodiment always maintains a set length of the advance support section (three-section inflatable airbags) during the construction process to ensure that the front and rear of the shield cutterhead are in the protection zone; the airbag usage can be reduced by moving the rear airbag forward, and the front section area is monitored before shifting. The inflatable airbag is allowed to shift only if the monitoring data is qualified, which can prevent accidents from occurring.
[0036] Although the above describes the specific embodiments of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without any creative work are still within the scope of protection of the present invention.
Claims
1. A support structure for a shield tunnel passing under a civil air defense passage, characterized in that: include: The segmented airbag assembly is composed of multiple independent inflatable airbags spliced longitudinally along the civil air defense passage. The inflatable airbag includes a hollow annular capsule with an inflation and deflation interface provided on the hollow annular capsule; The detachable inner support frame is assembled from multiple steel plates into a frame structure, and the outer contour of the inner support frame fits the inner periphery of the bottom of the inflatable airbag; The distributed monitoring component includes a threaded sleeve pre-buried at the joints of adjacent inflatable airbags and a threaded rod installed in the threaded sleeve. The position of the threaded rod is used as a leakage monitoring point, and the threaded rod is monitored by a total station.
2. The support structure for the shield tunnel under the civil air defense passage according to claim 1 is characterized in that: The curved surface shape of the outer periphery of the hollow annular sac matches the arched cross-sectional shape of the inner wall of the civil air defense passage, and the contact pressure between the inflated air bag and the inner wall of the civil air defense passage is 0.1-0.3Mpa after inflation.
3. The support structure for the shield tunnel under the civil air defense passage according to claim 1 is characterized in that: Positioning mortise and tenon structures are provided between adjacent steel plates of the detachable inner support frame, and the adjacent steel plates are connected by bolts.
4. The support structure for the shield tunnel under the civil air defense passage according to claim 1 is characterized in that: The threaded rod is screwed into the sleeve through a thread and then extends out of the inner surface of the inflatable airbag by 10-15 cm.
5. The support structure for the shield tunnel passing under the civil air defense passage according to claim 1 is characterized in that: The axis of the threaded rod is consistent with the deformation-sensitive direction of the civil air defense passage, and the deformation-sensitive direction of the civil air defense passage includes the vertical direction of the arch crown and the 45° direction of the arch waist of the civil air defense passage.
6. The support structure for the shield tunnel under the civil air defense passage according to claim 1, characterized in that: At least three detachable inner support frames are correspondingly arranged in each of the inflatable airbags. The three detachable inner support frames are evenly distributed along the longitudinal direction of the inflatable airbag, and a plate is laid on the bottom frame of the detachable inner support frame.
7. The support structure for the shield tunnel passing under the civil air defense passage according to claim 1, characterized in that: An airbag end plate is respectively provided at both ends of the independent inflatable airbag, and the shape of the airbag end plate matches the cross-sectional shape of the inflatable airbag.
8. A construction method for a shield tunnel underpass supporting structure of a civil air defense passage according to any one of claims 1 to 7, characterized in that: The following steps are involved: When the shield cutterhead reaches the set position of the civil air defense passage, after cleaning the inner wall of the civil air defense passage, at least three sections of inflatable air bags are continuously laid in the civil air defense passage, and the inflatable air bags are inflated to form an advanced support section; Installing a detachable inner support frame so that the detachable inner support frame supports the inner periphery of the bottom of the inflatable airbag; When the shield machine is about to pass through the last section of the inflatable airbag in the advance support section, the deformation data of the leakage monitoring point of the first section of the inflatable airbag in the advance support section is monitored by a total station. If the monitored deformation data is normal, the first section of the inflatable airbag is deflated, folded, and transported to the front of the tunnel through the civil air defense passage for re-inflation; Repeat the above steps until the shield has completely passed through the civil air defense passage, and finally remove the inner support frame and recover the inflatable airbag.
9. The construction method of the shield tunnel underpass supporting structure of the civil air defense passage according to claim 8, characterized in that: After installing the removable inner support frame, lay panels on the bottom edge of the removable inner support frame to ensure the normal use of the civil air defense passage.
10. The construction method of the shield tunnel underpass of the support structure of the civil air defense passage according to claim 8, characterized in that: If the monitored deformation data is abnormal, the deformed position will be reinforced and repaired first, and continuous monitoring will be carried out. The inflatable airbag will be deflated after the deformation data meets the requirements.
Citation Information
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