A load loading device for a deep-buried tunnel simulation test section and a test method

Abstract

The present application relates to a kind of deep-buried tunnel simulation test section load loading device and test method, loading device includes model box and hydraulic loading device, model box is overall square structure, through the cylindrical cavity is set in the center position, and the center of cylindrical cavity coincides with model box body center;Tunnel lining model is laid in cylindrical cavity, and hydraulic loading device is installed between the cavity wall of cylindrical cavity and tunnel lining model;Hydraulic loading device is communicated with the hydraulic equipment located in the outside of model box, and hydraulic equipment and hydraulic loading device are simultaneously communicated with control system;The present application can realize the surrounding rock pressure applied in the mode of complete contact to model lining, and more realistically reflects the stress deformation under the interaction of surrounding rock and lining.

Description

Technical Field

[0001] This invention relates to a load loading device and test method for a deep-buried tunnel simulation test section, belonging to the technical field of indoor model simulation test equipment for tunnel lining. Background Technology

[0002] Deeply buried tunnels are a key engineering focus in the geotechnical field. Due to the complex geological conditions in deep-buried tunnels, the tunnel lining is subjected to equally complex pressures from the surrounding rock. Indoor model tests are often used to study the stress and deformation of the lining under complex confining pressures. With the continuous advancement of indoor model test research, many problems related to deep-buried tunnels have been solved through these experiments.

[0003] Currently, the main equipment used in indoor model tests is the model test loading device. However, the loading method for the lining mostly involves directly applying loads (such as jacks) to a local area of ​​the lining, neglecting the complete contact between the surrounding rock and the lining. This results in limited agreement between the obtained test data and the actual situation. Therefore, it is urgent to study a model test loading device that allows for complete contact between the surrounding rock and the lining. To better develop tunnel technology, it is necessary to continuously improve the accuracy of the test data in indoor model tests in reflecting the actual situation, thereby enhancing the reference value of indoor model tests. Summary of the Invention

[0004] This invention provides a load loading device and test method for a deep-buried tunnel simulation test section, which can realize the application of surrounding rock pressure to the model lining in a fully contact manner, and more realistically reflects the stress and deformation under the interaction between the surrounding rock and the lining.

[0005] The technical solution adopted by this invention to solve its technical problem is:

[0006] A load loading device for a deep-buried tunnel simulation test section includes a model box and a hydraulic loading device. The model box is generally square in shape, with a through cylindrical cavity at its center, and the center of the cylindrical cavity coincides with the center of the model box.

[0007] The tunnel lining model is placed inside a cylindrical cavity, and a hydraulic loading device is installed between the cavity wall of the cylindrical cavity and the tunnel lining model.

[0008] The hydraulic loading device is connected to a hydraulic device located outside the model box, and both the hydraulic device and the hydraulic loading device are connected to the control system.

[0009] The hydraulic loading device applies pressure to the tunnel lining model by filling it with liquid;

[0010] As a further preferred embodiment of the present invention, the hydraulic loading device includes a rubber bladder and an internal frame. The rubber bladder is in the shape of a cylindrical ring and its interior is a closed hollow space for filling with liquid.

[0011] An internal frame is set inside the rubber bladder, and the internal frame supports the formed rubber bladder to match the cylindrical cavity at the center of the model box.

[0012] Symmetrical connecting pipes are pre-embedded in the wall of the rubber bladder, and the two connecting pipes extend out of the model box at the same time and are connected to the hydraulic equipment through the liquid delivery pipe;

[0013] As a further preferred embodiment of the present invention, several waterproof pressure sensors are installed on the inner wall of the rubber bladder, and a wire connecting tube is pre-embedded in the wall of the rubber bladder. The several waterproof pressure sensors are connected to an external control system through wires passing through the wire connecting tube.

[0014] Stress gauges and strain gauges are installed on the inner surface of the tunnel lining model. The stress gauges and strain gauges are also connected to the external control system via wires.

[0015] The connecting pipe is adjacent to the connecting pipe located above it;

[0016] As a further preferred embodiment of the present invention, the internal frame is arranged in a cylindrical structure, including a plurality of annular components and a plurality of transverse components, wherein the plurality of annular components are coaxially stacked sequentially, and there is a gap between adjacent annular components in the axial direction.

[0017] Several transverse members are welded along the axial direction of the inner frame to fix several ring members into shape, and the adjacent transverse members are spaced at the same distance in the radial direction of the inner frame.

[0018] As a further preferred embodiment of the present invention, when the internal frame is arranged inside the rubber bladder, the transverse members are bonded to the bladder wall of the rubber bladder.

[0019] As a further preferred embodiment of the present invention, the annular component is provided with a joint structure. The annular component is a hollow circular ring structure. The ring is not closed, and the connection is made through the joint structure within the unclosed end of the circular ring structure.

[0020] As a further preferred embodiment of the present invention, the model box is a metal structure with small holes opened on the top and side walls of the metal structure. Two small holes are opened on the top and one small hole is opened on the side wall. The two small holes on the top are respectively matched with a connecting pipe and a wire connecting pipe arranged adjacent to each other on the rubber bladder. The small hole on the side wall is matched with another connecting pipe arranged on the rubber bladder. That is, the two small holes on the top are respectively connected to the connecting pipe and the wire connecting pipe, and the small hole on the side wall is connected to another connecting pipe.

[0021] As a further preferred embodiment of the present invention, the position of the connecting tube or wire connecting tube on the rubber bladder is connected to the small hole of the matching model box by a waterproof connector tube.

[0022] The outer layer of the conductor is wrapped with waterproof material, and a rubber rod is wrapped around the conductor wrapped with waterproof material and the position where the rubber bladder is inserted before it is embedded in the connecting tube.

[0023] A test method based on the load loading device of the deep-buried tunnel simulation test section specifically includes the following steps:

[0024] Step S1: Calculate the stiffness of the rubber bladder required for the test according to similarity theory, prepare a rubber bladder with matching stiffness, stretch the annular component to the required size to form an internal frame, embed the internal frame into the rubber bladder for support, install the tunnel lining model in the annular column of the rubber bladder, and align the circumferential side of the tunnel lining model with the circumferential side of the rubber bladder to ensure that the surface of the rubber bladder is in close contact with the surface of the tunnel lining model.

[0025] Step S2: Start the control system and hydraulic equipment, and deliver liquid to the rubber bladder through the liquid delivery pipe to the two connecting pipes. The rubber bladder expands continuously under liquid pressure, generating pressure on the surface of the tunnel lining model and applying load.

[0026] Step S3: Several waterproof pressure sensors monitor the load applied by the rubber bladder to the surface of the tunnel lining model in real time and transmit the monitoring information to the control system.

[0027] Step S4: During the test, multiple loads are set, and the control system controls the hydraulic equipment to adjust the hydraulic pressure to match the set load sizes;

[0028] Step S5: After each set of required loads is applied to the tunnel lining model, the stress gauges and strain gauges on the inner surface of the tunnel lining model record the stress and deformation of the tunnel lining model in real time, and transmit the data to the control system for analysis.

[0029] As a further preferred embodiment of the present invention, in step S1, the stiffness of the rubber bladder is selected based on the stiffness of the tunnel lining prototype, the surrounding rock, and the stiffness of the model tunnel lining, using the similarity theory calculation formula as follows:

[0030]

[0031] In formula (1), E cp E represents the elastic modulus of the prototype tunnel lining. wp E represents the elastic modulus of the surrounding rock of the prototype tunnel. cm E represents the elastic modulus of the tunnel lining model. rm Let A be the elastic modulus of the rubber bladder. cp A is the cross-sectional area of ​​the prototype tunnel lining. wpA is the cross-sectional area of ​​the surrounding rock of the prototype tunnel. cm Let A be the cross-sectional area of ​​the tunnel lining model. rm Let be the cross-sectional area of ​​the rubber bladder.

[0032] By employing the above technical solutions, the present invention has the following beneficial effects compared to the prior art:

[0033] 1. The load loading device for the deep-buried tunnel simulation test section provided by the present invention fully considers the interaction between the surrounding rock and the lining in the actual tunnel. It simulates the confining pressure of the surrounding rock on the lining in the actual working condition by using a rubber bladder and a tunnel lining model, which is more in line with the real stress condition of the lining.

[0034] 2. This invention uses similarity theory as the basis for calculation to determine the stiffness of the rubber bladder under different conditions, and obtains a rubber bladder model with stiffness that conforms to the actual working conditions, thereby more accurately and realistically simulating the interaction between the surrounding rock and the lining, as well as the stress on the lining.

[0035] 3. The load loading device for the deep-buried tunnel simulation test section provided by the present invention is highly feasible, easy to operate, and has good applicability. It can provide more accurate and reliable test data and effectively improve the reference value of indoor model tests for tunnel lining. Attached Figure Description

[0036] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0037] Figure 1 This is a schematic diagram of the overall structure of a preferred embodiment provided by the present invention;

[0038] Figure 2 yes Figure 1 Sectional view of the structure at point AA;

[0039] Figure 3 yes Figure 1 Structural cross-section view at point BB;

[0040] Figure 4 This is a schematic diagram of the internal frame structure provided by the present invention;

[0041] Figure 5 This is a schematic diagram of the ring-shaped component provided by the present invention.

[0042] In the diagram: 1 is the model box, 2 is the tunnel lining model, 3 is the rubber bladder, 4 is the internal frame, 5 is the connecting pipe, 6 is the wire, 7 is the waterproof pressure sensor, 8 is the hydraulic equipment, 9 is the control system, 10 is the liquid delivery pipe, 11 is the transverse component, 12 is the ring component, and 13 is the wire connecting pipe. Detailed Implementation

[0043] The present invention will now be described in further detail with reference to the accompanying drawings. In the description of this application, it should be understood that the terms "left side," "right side," "upper part," "lower part," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. "First," "second," etc., do not indicate the importance of the components, and therefore should not be construed as a limitation of the present invention. The specific dimensions used in this embodiment are only for illustrating the technical solution and do not limit the scope of protection of the present invention.

[0044] As described in the background section, existing indoor simulation tests often neglect the interaction between the surrounding rock and the lining, especially the load applied by the surrounding rock to the lining, which leads to differences between the test data and the actual situation. Therefore, this application aims to provide a load loading device for a deep-buried tunnel simulation test section that can realistically reflect the actual situation, thereby improving the reference value of indoor model tests.

[0045] The overall structure provided in this application is as follows: Figure 1 As shown, the system includes a model box 1 and a hydraulic loading device. The model box is generally square in shape, with a through cylindrical cavity at its center, the center of which coincides with the center of the model box. This cylindrical cavity matches the shape of an actual tunnel. The tunnel lining model 2 is placed inside the cylindrical cavity. A hydraulic loading device is installed between the cavity wall and the tunnel lining model. This device simulates the surrounding rock, closely resembling real-world conditions. The hydraulic loading device applies loads to the tunnel lining model. Since different loads need to be applied, the hydraulic loading device is connected to a hydraulic device 8 located outside the model box. Adjusting the hydraulic device allows for the application of different pressures. The hydraulic device is controlled by a control system 9, which sends commands accordingly. Figure 1 As shown, the control system is a computer system.

[0046] A notable innovation of this application is that the hydraulic loading device applies pressure to the tunnel lining model by filling it with liquid. Liquid is chosen instead of gas because liquid is not easily compressed and its density remains relatively constant, making it more stable during the pressure application process on the tunnel lining model. In contrast, gas is very easily compressed, causing its density to change and resulting in instability during the pressure application process.

[0047] Specific hydraulic loading devices such as Figure 2As shown, the device includes a rubber bladder 3 and an internal frame 4. The rubber bladder is cylindrical in shape and has a closed hollow interior for filling with liquid. Before filling the rubber bladder with liquid, its structure needs to be maintained; therefore, an internal frame is provided inside the rubber bladder to support the formed rubber bladder and match the cylindrical cavity at the center of the model box. In the preferred embodiment provided in this application, the structure of the internal frame is as follows: Figure 4 As shown, the structure is cylindrical and includes several annular members 12 and several transverse members 11. The annular members are coaxially stacked sequentially, with a gap between adjacent annular members in the axial direction. Several transverse members are welded along the axial direction of the inner frame to fix the annular members in place. The adjacent transverse members are spaced equally in the radial direction of the inner frame. When the inner frame is placed inside the rubber bladder, the transverse members are bonded to the wall of the rubber bladder.

[0048] Since different internal frames are required to match different rubber bladders, in order to reduce production costs, the provided annular component needs to be expandable, such as... Figure 5 As shown, the annular component is equipped with a joint structure. The annular component is a hollow circular ring structure, which is not closed. The joint structure connects the two ends of the ring structure. Of course... Figure 5 This is only a preferred example provided in this application; the end of the annular component can also be directly connected via a connecting pipe with threads at both ends.

[0049] Symmetrical connecting pipes 5 are pre-embedded in the wall of the rubber bladder. Both connecting pipes extend simultaneously from the model box and connect to the hydraulic equipment via a liquid delivery pipe 10. Activating the hydraulic equipment allows liquid to be input into and output into the rubber bladder via the liquid delivery pipe. Of course, to better achieve liquid input and output, a pressure difference needs to be created within the rubber bladder to facilitate liquid output. Therefore… Figure 2 From the viewing angle, it can be seen that the two connecting tubes are respectively set at the top and bottom of the rubber bladder, and are arranged symmetrically.

[0050] Figure 3 As shown, several waterproof pressure sensors 7 are installed on the inner wall of the rubber bladder. A connecting pipe 6 is pre-embedded in the wall of the rubber bladder, and the waterproof pressure sensors are connected to an external control system via wires passing through the connecting pipe 13. Stress gauges and strain gauges are installed on the inner surface of the tunnel lining model, and these are also connected to the external control system via wires. The connecting pipe is adjacent to the connecting pipe located above. The waterproof pressure sensors, stress gauges, and strain gauges are all designed to facilitate real-time monitoring of the stress on the rubber bladder and the tunnel lining model.

[0051] In a preferred embodiment, the model box is a metal structure with outermost dimensions of 1000mm × 1000mm × 1000mm, a small hole radius of 200mm, a cylindrical cavity radius of 350mm, and a length of 800mm. Small holes are formed at the top and sidewalls of the metal structure, with two holes at the top and one hole at the sidewall. The two holes at the top are respectively matched with a connecting pipe and a wire connecting pipe adjacent to each other on the rubber bladder, while the hole at the sidewall is matched with another connecting pipe on the rubber bladder. That is, the two holes at the top are respectively pierced by the connecting pipe and the wire connecting pipe, and the hole at the sidewall is pierced by the other connecting pipe. The connecting pipe has an outer diameter of 20mm and a thickness of 3mm. In this application, the outermost layer of the rubber bladder has the same shape as the outline of the cylindrical cavity of the model box; therefore, the rubber bladder thickness is 10mm, and the outermost cross-sectional radius is 350mm. The innermost surface of the rubber bladder is in close contact with the outer surface of the lining, and the innermost cross-sectional radius is 200mm.

[0052] To ensure the tightness of each part and prevent water seepage at the joints, a connecting tube or wire is inserted through the rubber bladder and connected to the small hole of the matching model box through a waterproof connector tube; the outer layer of the wire is wrapped with waterproof material, and a rubber rod is wrapped around the wire wrapped with waterproof material and inserted into the connecting tube at the position where the rubber bladder is inserted.

[0053] Finally, this application also provides a test method based on a load loading device for a deep-buried tunnel simulation test section, which specifically includes the following steps:

[0054] Step S1: Calculate the stiffness of the rubber bladder required for the test according to similarity theory, prepare a rubber bladder with matching stiffness, stretch the annular component to the required size to form an internal frame, embed the internal frame into the rubber bladder for support, install the tunnel lining model in the annular column of the rubber bladder, and align the circumferential side of the tunnel lining model with the circumferential side of the rubber bladder to ensure that the surface of the rubber bladder is in close contact with the surface of the tunnel lining model.

[0055] Here, the installation steps need to be explained in detail. When installing the tunnel lining model into the rubber bladder, the telescopic part of the annular component is fully stretched from its initial size until the inner diameter of the rubber bladder is larger than the outer diameter of the tunnel lining model, so that the tunnel lining model can be installed into the rubber bladder more easily. After the tunnel lining model is installed, the telescopic part of the annular component is retracted to its initial position, so that the surface of the rubber bladder is in close contact with the outer surface of the tunnel lining model.

[0056] Step S2: Start the control system and hydraulic equipment, and deliver liquid to the rubber bladder through the liquid delivery pipe to the two connecting pipes. The rubber bladder expands continuously under liquid pressure, generating pressure on the surface of the tunnel lining model and applying load.

[0057] Step S3: Several waterproof pressure sensors monitor the load applied by the rubber bladder to the surface of the tunnel lining model in real time and transmit the monitoring information to the control system.

[0058] Step S4: During the test, multiple loads are set, and the control system controls the hydraulic equipment to adjust the hydraulic pressure to match the set load sizes;

[0059] Step S5: After each set of required loads is applied to the tunnel lining model, the stress gauges and strain gauges on the inner surface of the tunnel lining model record the stress and deformation of the tunnel lining model in real time, and transmit the data to the control system for analysis.

[0060] In step S1, the stiffness of the rubber bladder is selected based on the stiffness of the prototype tunnel lining, the surrounding rock, and the stiffness of the model tunnel lining, using the similarity theory calculation formula.

[0061]

[0062] In formula (1), E cp E represents the elastic modulus of the prototype tunnel lining. wp E represents the elastic modulus of the surrounding rock of the prototype tunnel. cm E represents the elastic modulus of the tunnel lining model. rm Let A be the elastic modulus of the rubber bladder. cp A is the cross-sectional area of ​​the prototype tunnel lining. wp A is the cross-sectional area of ​​the surrounding rock of the prototype tunnel. cm Let A be the cross-sectional area of ​​the tunnel lining model. rm Let be the cross-sectional area of ​​the rubber bladder; where, before the similarity theory calculation, the tensile stiffness E of the prototype tunnel lining needs to be calculated separately. cp A cp And the tensile stiffness E of the surrounding rock wp A wp And the tensile stiffness E of the tunnel lining model cm A cm .

[0063] In summary, the test device provided in this application can achieve the application of surrounding rock pressure to the tunnel model lining in a fully contact manner, which is highly feasible and has the characteristics of simple structure, economy and efficiency.

[0064] Those skilled in the art will understand that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the meaning consistent with their meaning in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0065] The meaning of "and / or" as used in this application includes situations where each exists alone or both exist simultaneously.

[0066] The term "connection" as used in this application can mean a direct connection between components or an indirect connection between components through other components.

[0067] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A load loading device for a deep-buried tunnel simulation test section, characterized in that: The utility model relates to a tunnel lining model test device, including model box (1) and hydraulic loading device, model box (1) is overall square structure, and the through -going cylindrical cavity is set up in the central position, and the center of cylindrical cavity coincides with model box (1) body center, Tunnel lining model (2) is arranged in cylindrical cavity, and hydraulic loading device is installed between the cavity wall of cylindrical cavity and tunnel lining model (2), The hydraulic loading device includes rubber capsule (3) and internal frame (4), and the inside of rubber capsule (3) is closed hollow space for filling liquid, Internal frame (4) is arranged in rubber capsule (3), and the rubber capsule (3) supported by internal frame (4) is matched with the inner cavity of cylindrical cavity in the central position of model box (1), Symmetrically preburied communication pipe (5) on the capsule wall of rubber capsule (3), two communication pipes (5) are simultaneously stretched out model box (1) through liquid delivery pipe (10) and are communicated with hydraulic equipment (8), Install several waterproof pressure sensors (7) on the inner cavity wall of rubber capsule (3), and preburied lead wire communication pipe (13) on the capsule wall of rubber capsule (3), and several waterproof pressure sensors (7) are connected with the control system (9) outside through the lead wire (6) of lead wire communication pipe (13) threaded, Install stress meter and strain meter on the inner surface of tunnel lining model (2), and stress meter and strain meter are also connected with the control system (9) outside through lead wire (6), The lead wire communication pipe (13) is adjacent to the communication pipe (5) located above, The hydraulic loading device is communicated with the hydraulic equipment (8) located outside model box (1), and the hydraulic equipment (8) and the hydraulic loading device are simultaneously communicated with the control system (9), Wherein, the hydraulic loading device applies pressure to tunnel lining model (2) through filling liquid, The internal frame (4) is arranged in cylindrical structure, including several annular members (12) and several transverse members (11), several annular members (12) are coaxially sequentially stacked, and there is spacing between adjacent annular members (12) in the axial direction, Several transverse members (11) are welded along the axial direction of internal frame (4), and several annular members (12) are fixed and formed, and adjacent transverse members (11) have the same spacing in the radial direction of internal frame (4), When internal frame (4) is arranged in rubber capsule (3), the transverse member (11) is cemented with the capsule wall of rubber capsule (3), The annular member (12) is provided with a joint structure, and the annular member (12) is a hollow ring structure, the ring of the annular member (12) is not closed, and the joint structure is connected in the non-closed end ring structure.

2. The load loading device for deep-buried tunnel simulation test section according to claim 1, characterized in that: The model box (1) is a metal structure, and a small hole is formed in the top and side wall of the metal structure, respectively, wherein two small holes are formed in the top, and one small hole is formed in the side wall, the two small holes in the top are matched with the adjacent communication pipes (5) and lead wire communication pipes (13) on the rubber capsule (3), and the small hole in the side wall is matched with another communication pipe (5) on the rubber capsule (3), that is, the two small holes in the top are threaded with the communication pipes (5) and the lead wire communication pipes (13), and the small hole in the side wall is threaded with another communication pipe (5).

3. The load loading device for deep-buried tunnel simulation test section according to claim 2, characterized in that: The position where the communicating pipe (5) or the wire communicating pipe (13) is arranged on the rubber capsule (3) is connected with the small hole of the matching model box (1) through a waterproof joint pipe; The wire (6) is wrapped with waterproof material, and after the wire (6) wrapped with waterproof material is arranged on the rubber capsule (3) and wrapped with a rubber rod, the wire (6) is embedded into the communicating pipe (5).

4. A test method based on the load loading device of the simulation test section of the deep-buried tunnel according to claim 1, characterized in that: Specifically, the following steps are included: Step S1: According to the similarity theory, the stiffness of the rubber capsule (3) required for the test is calculated, the rubber capsule (3) with matching stiffness is prepared, the annular member (12) is stretched to the required size to form an internal frame (4), the internal frame (4) is embedded in the rubber capsule (3) for support, the tunnel lining model (2) is installed in the rubber capsule (3), and the circumference side of the tunnel lining model (2) is aligned with the circumference side of the rubber capsule (3), so as to ensure that the rubber capsule (3) is tightly attached to the surface of the tunnel lining model (2); Step S2: Start the control system (9) and the hydraulic equipment (8), and deliver liquid to the two communicating pipes (5) through the liquid delivery pipe (10) into the rubber capsule (3), so that the rubber capsule (3) continuously expands under the pressure of the liquid, and the pressure on the surface of the tunnel lining model (2) is generated to apply load; Step S3: The waterproof pressure sensor (7) monitors the load applied by the rubber capsule (3) on the surface of the tunnel lining model (2) in real time, and transmits the monitoring information to the control system (9); Step S4: A plurality of loads are set during the test, and the control system (9) controls the hydraulic equipment (8) to adjust the hydraulic pressure to match the size of the plurality of loads set; Step S5: When each required load is applied to the tunnel lining model (2), the stress meter and strain meter on the inner surface of the tunnel lining model (2) record the stress and deformation of the tunnel lining model (2) in real time, and transmit the information to the control system (9) for analysis.

5. The method according to claim 4, wherein the load loading device is characterized in that: In step S1, the stiffness of the rubber capsule (3) is selected according to the stiffness of the tunnel lining prototype, the surrounding rock and the model tunnel lining, and the similarity theory calculation formula is （1） In formula (1), The elastic modulus of the prototype tunnel lining. The elastic modulus of the surrounding rock of the prototype tunnel. The elastic modulus of the tunnel lining model (2) is given. The elastic modulus of the rubber bladder (3) is... This refers to the cross-sectional area of ​​the prototype tunnel lining. This refers to the cross-sectional area of ​​the surrounding rock of the prototype tunnel. The cross-sectional area of ​​the tunnel lining model (2) is given by... Let be the cross-sectional area of ​​the rubber bladder (3).

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