Design and verification method and system for critical width of arch foot beam in arch cap tunnel

Abstract

The present invention provides a design and verification method and system for the critical width of an arch foot support beam of an arch cover method tunnel, comprising the following steps: obtaining rock mass parameters below the arch foot support beam; obtaining cross-section design parameters of the arch cover method tunnel; judging whether the tunnel is deeply buried or shallowly buried; calculating the vertical pressure load of the corresponding tunnel; calculating the vertical load acting on the single-side support beam; respectively obtaining the critical width of the support beam under plastic conditions and the critical width of the support beam under brittle conditions, and selecting the larger value of the two as the critical width of the support beam b The critical width design and verification method and system of the arch foot support beam of the arch cover method tunnel provided by the present invention not only considers the possibility of traditional plastic failure but also considers the possibility of brittle failure, thereby achieving the purpose of reducing the engineering cost of the large-span dark-cut station of the arch cover and support beam method while ensuring safety.

Description

Technical Field

[0001] The invention belongs to the technical field of tunnel engineering, and more specifically, relates to a design and verification method and system for the critical width of an arch foot support beam of an arch cap method tunnel. Background Art

[0002] With the rapid development of urban rail transit networks, large-span underground excavation stations are gradually increasing in bustling urban areas. Compared with other traditional large-span underground excavation station construction methods such as double-side wall pilot pit method, CD method, CRD method, middle hole method, etc., the arch cover and beam method is a safe and efficient construction method proposed in the past decade.

[0003] The characteristic of the arch cover joist method is that after the arch is excavated, the joist is constructed at the arch foot. The joist needs to be arranged on a rock mass with a certain self-stabilizing ability, that is, bearing capacity. If necessary, the joist and the rock mass are connected by anchor rods. The joist is mostly a right-angled trapezoid, with the slope facing inward and upward. The outside and bottom of the joist are both rock mass, and the slope is in contact with the arch cover. The design indicator of the joist is mainly the width of the joist. Since the excavation span generally depends on the formation conditions and is a fixed value, if the joist width is too large, the actual width of the station will be reduced, squeezing the usable space of the building. If the joist width is too small, the structure will become unstable and cause accidents.

[0004] At present, the arch cap joist method still uses the foundation bearing capacity method to calculate the joist at the arch foot of the secondary lining structure. However, the foundation bearing capacity characteristic value provided by the geological survey is based on the statistical results of standard tests, which does not conform to the situation that after the lower half of the station is excavated, the foundation is transformed from a semi-infinite body to a vertical rock slope. The existing joist design method lacks theoretical support and does not conform to the actual working conditions. Summary of the invention

[0005] The purpose of the present invention is to provide a design and calculation method and system for the critical width of an arch foot support beam of an arch cap method tunnel, aiming to solve the technical problem that the existing support beam calculation method is inconsistent with the actual situation.

[0006] To achieve the above object, the technical solution adopted by the present invention is: to provide a design and verification method for the critical width of the arch foot support beam of the arch cover method tunnel, comprising the following steps:

[0007] Obtain the rock mass parameters below the arch foot support beam; obtain the design parameters of the arch cover tunnel section; determine whether the tunnel is deep buried or shallow buried; calculate the corresponding tunnel vertical pressure load;

[0008] Among them, if the tunnel is deeply buried, the calculation formula of the vertical pressure load q of the deeply buried tunnel is;

[0009]

[0010] If the tunnel is shallow, the vertical pressure load The calculation formula is:

[0011]

[0012] in, To calculate the side pressure coefficient; is the rupture angle; is the friction angle on both sides of the top soil column; The depth of the tunnel; It is the surrounding rock level; is the influence coefficient of tunnel width; B is the tunnel width;

[0013] Calculate the vertical load acting on the single-sided joist;

[0014] Obtain the critical width of the joist under plastic conditions and the critical width of the joist under brittle conditions respectively, and select the larger value of the two as the critical width of the joist b The value of .

[0015] Preferably, the rock mass parameters include: surrounding rock weight , surrounding rock level , Calculation of friction angle of surrounding rock 、Friction angle of rock and soil , rock and soil cohesion c, rock tensile strength , Rock Poisson's ratio One or more of .

[0016] Preferably, the tunnel section design parameters include: section span , Height of unsupported vertical wall below joist h 、Tunnel depth One or more of .

[0017] Preferably, the calculation formula used in the calculation of the vertical load acting on the single-sided joist is:

[0018] in, is the magnitude of the vertical load acting on the single-side joist; is the size of the corresponding tunnel vertical pressure load; is the tunnel width.

[0019] Preferably, the critical width of the joist under plastic conditions is The calculation formula is:

[0020]

[0021] in, is the magnitude of the vertical load acting on the single-side joist; is the cohesion of rock and soil; is the internal friction angle of rock and soil; The surrounding rock is heavy; is the height of the unsupported vertical wall below the joist. Preferably, the critical width of the joist under brittle conditions is The calculation formula is:

[0022] in, is the magnitude of the vertical load acting on the single-side joist; The surrounding rock is heavy; is the height of the unsupported vertical wall below the joist; is the tensile strength of rock; is the Poisson's ratio of rock.

[0023] Preferably, the determining whether the tunnel is deeply buried or shallowly buried comprises:

[0024] Determining tunnel width The rate of increase or decrease of surrounding rock pressure for every increase or decrease of 1m;

[0025] Determine the tunnel width influence factor

[0026] Calculate the vertical load of the tunnel and calculate the height ;

[0027] according to and The relationship between them determines whether the tunnel load model should be calculated as deep or shallow burial.

[0028] Preferably, the height is calculated according to the tunnel burial depth H and the tunnel vertical load. The relationship between the tunnel load model and the tunnel load model is used to determine whether the tunnel load model is calculated as deep or shallow. For the surrounding rock of grade IV to VI, if , then it is shallow buried, otherwise it is deep buried; for the surrounding rock of grade I~III, if , it is shallow burial, otherwise it is deep burial.

[0029] Preferably, the calculation side pressure coefficient The calculation formula is: in, is the friction angle on both sides of the top soil column; is the rupture angle when the maximum thrust is generated; Calculate the friction angle for the surrounding rock.

[0030] The critical width design and calculation system of the arch foot support beam of the arch cover method tunnel is characterized in that it is used to execute the steps described in the critical width design and calculation method of the arch foot support beam of the arch cover method tunnel as described in any one of the above items, including:

[0031] A rock mass parameter acquisition module is used to obtain the rock mass parameters below the arch foot support beam;

[0032] Section parameter acquisition module, used to obtain the design parameters of the arch-cover tunnel section;

[0033] The judgment module is used to judge whether the tunnel is deep buried or shallow buried; the vertical pressure load module is used to calculate the vertical pressure load of the corresponding tunnel;

[0034] Vertical load module, used to calculate the vertical load acting on the single-side joist;

[0035] The critical width verification module is used to obtain the critical width of the joist under plastic conditions and the critical width of the joist under brittle conditions, and select the larger value of the two as the value of the critical width of the joist.

[0036] The beneficial effect of the method and system for designing and verifying the critical width of the arch foot support beam of the arch cover method tunnel provided by the present invention is that: compared with the prior art, the method and system for designing and verifying the critical width of the arch foot support beam of the arch cover method tunnel provided by the present invention not only considers the possibility of traditional plastic failure but also considers the possibility of brittle failure, thereby achieving the purpose of reducing the engineering cost of the large-span dark-cut station of the arch cover and support beam method while ensuring safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0038] Figure 1 A flowchart of a method for designing and calculating the critical width of an arch foot support beam of an arch cap method tunnel provided by an embodiment of the present invention;

[0039] Figure 2 It is a schematic diagram of rock stress analysis below the arch cover joist after excavation by the arch cover method in the present invention;

[0040] Figure 3 is the limit equilibrium state stress circle of a stress unit at the free boundary of the vertical slope after excavation by the arch cover method in the present invention;

[0041] Figure 4 The load model diagram for shallow tunnels with the ground level basically level;

[0042] Figure 5 A flowchart of a critical width design and calculation system for an arch foot support beam of an arch cap method tunnel provided in an embodiment of the present invention.

[0043] In the figure: 1. Rock mass parameter acquisition module; 2. Section parameter acquisition module; 3. Judgment module; 4. Vertical pressure load module; 5. Vertical direction load module; 6. Critical width verification module. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0045] In the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific direction, be constructed and operated in a specific direction, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0046] It should be noted that the design and verification method for the critical width of the arch foot support beam of the arch cover method tunnel provided by the present invention is subject to the following conditional restrictions: the working condition considered by the present invention is that the arch cover is completely excavated by grooving and slope cutting, and no initial support such as spraying and mixing is performed to close the surrounding rock, and the rock mass below the arch foot support beam is transformed from a three-way compressive stress state to a two-way stress state. The present invention does not consider the shape of the sliding surface when verifying the plastic failure stability, and performs stability verification according to the Mohr-Coulomb strength criterion. When verifying the plastic / brittle failure stability of the working condition studied by the present invention, a plane strain problem is used for solution, that is, the strain in the out-of-plane direction is 0.

[0047] The present invention aims to solve the problem of the lack of existing joist size design methods and conservative design, and avoid waste caused by over-design or safety problems caused by under-design. The present invention provides methods for plastic failure stability verification and brittle failure stability verification, and takes the larger value calculated by the two as the critical joist width.

[0048] From the perspective of plastic failure, when the lower section of the station is excavated, the relationship between the single-side support beam and the rock mass is as follows: Figure 2As shown in the figure, is the pressure transmitted from the arch cover to the joist, is the horizontal pressure transmitted from the joist to the bedrock, and is the numerical pressure transmitted from the joist to the bedrock. Obviously, this model is very similar to the traditional vertical slope. For a simplified homogeneous rock slope without a fracture surface, it can be regarded as a plane problem. Regardless of the shape of the sliding surface, in order to have a sliding space, the sliding surface and the free surface (i.e., the free surface after excavation) must have an intersection. Therefore, from the perspective of stress, the stability is verified according to the Moore-Coulomb strength criterion.

[0049] From the perspective of brittle failure, rock is a typical brittle material, which is quite different from soil. Therefore, there is a certain inapplicability when using the Mohr-Coulomb strength criterion, and its shear strength parameters are difficult to accurately measure, which has a great impact on the results. Therefore, it is necessary to consider the possibility of its brittle failure. Among the four major strength theories, the first and second strength theories are applicable to brittle failure. The first strength theory is the maximum tensile stress theory, and the second strength theory is the maximum tensile strain theory. For the working conditions studied in this invention, the rock mass under the arch foot support beam changes from a three-way compressive stress state to a two-way stress state, but there is still no problem of tensile stress. Therefore, it is impossible for the maximum tensile stress to be greater than or equal to the maximum compressive stress (absolute value), so the first strength theory is not applicable. Therefore, the second strength theory is used for analysis.

[0050] Please also read Figures 1 to 4 The design and calculation method for the critical width of the arch foot support beam of the arch cover tunnel provided by the present invention is now described. The design and calculation method for the critical width of the arch foot support beam of the arch cover tunnel provided by the present invention comprises the following steps:

[0051] S1. Obtain the rock mass parameters below the arch foot support beam.

[0052] Rock mass parameters include: surrounding rock weight , surrounding rock level , Calculation of friction angle of surrounding rock 、Friction angle of rock and soil , rock and soil cohesion , rock tensile strength , Rock Poisson's ratio One or more of .

[0053] The above rock mass parameters can usually be obtained through geological survey reports. If some parameters are not provided, refer to the Engineering Geology Manual. The rock mass mechanical parameters can be obtained by referring to the following table:

[0054] Table 1 Physical parameters of rock mass

[0055]

[0056] The tensile strength of rock is generally not provided in geological survey reports. According to the Engineering Geology Manual, the empirical relationship between the ultimate tensile strength, ultimate shear strength, ultimate bending strength and ultimate compressive strength of rock can be obtained by referring to the following table:

[0057] Table 2 Empirical ratios of tensile strength to compressive strength of common rocks

[0058]

[0059] If the compressive strength of the rock is not provided in the geological survey report, the value can be obtained by referring to the following table:

[0060] Table 3 Empirical data of mechanical properties of common rocks

[0061]

[0062] S2. Obtain the design parameters of the arch-cover tunnel section.

[0063] Tunnel section design parameters include: section span B, i.e. tunnel width, height of unsupported vertical wall below the joist h 、Tunnel depth One or more of .

[0064] S3. Determine whether the tunnel is deeply buried or shallowly buried.

[0065] In this step, the deep or shallow buried tunnel is determined based on the geological survey data in accordance with TB 10003-2016 "Railway Tunnel Design Code".

[0066] The specific implementation process of step S3 may be:

[0067] S3.1. Determine tunnel width The rate of increase or decrease of surrounding rock pressure for every increase or decrease of 1m ,by =5m surrounding rock vertical uniform pressure, the values ​​are as follows:

[0068] Table 4 Surrounding rock pressure increase and decrease rate Value table

[0069]

[0070] S3.2: Determine the tunnel width effect factor :

[0071] S3.3: Calculation of vertical loads in tunnels Calculation height , the formula is as follows:

[0072]

[0073] S3.4: According to the tunnel depth H and height The relationship between the two determines whether the tunnel load model is calculated as deep or shallow. Specifically, the division boundary is: for the surrounding rock of grade IV to VI, if , then it is shallow buried, otherwise it is deep buried; for the surrounding rock of grade I~III, if , it is shallow burial, otherwise it is deep burial.

[0074] S4. Calculate the corresponding tunnel vertical pressure load .

[0075] In this step, the corresponding tunnel vertical pressure load is calculated according to TB 10003-2016 "Railway Tunnel Design Code" .

[0076] The specific implementation process of step S4 may be:

[0077] S4.1. Calculate the vertical pressure loads according to the judgment result of step S3.

[0078] If the tunnel is deeply buried, the calculation formula for the vertical pressure load q of the deeply buried tunnel is:

[0079]

[0080] If the tunnel is shallowly buried, its model is as follows Figure 4 , vertical pressure load The calculation formula is:

[0081] In the calculation formula, the side pressure coefficient is calculated The calculation formula is:

[0082]

[0083] The rupture angle at which the maximum thrust is generated :

[0084]

[0085] The friction angle on both sides of the top soil column It is an empirical value, obtained by referring to the following table:

[0086] Table 5 Friction angle The value of

[0087]

[0088] S5. Calculate the vertical load acting on the single-sided joist .

[0089] In this step, the load Q is calculated as:

[0090] S6. Obtain the critical width of the joist under plastic conditions and the critical width of the joist under brittle conditions , select , The larger value of b The value of .

[0091] In this step, The calculation formula is:

[0092] The calculation formula is:

[0093] Critical Width of Joists Under Plastic Conditions The specific acquisition process is:

[0094] For ease of understanding, the symbols to be used are explained as follows: is the minimum principal stress, is the maximum principal stress, is the internal friction angle, For cohesion, is the maximum allowable principal stress, The vertical pressure transmitted by the joist. is the vertical load acting on the single-side joist. is the critical width of the joist, is the weight of the rock mass, is the distance between the stress unit and the bottom of the joist, It is the unsupported height after excavation of the lower rock mass. is the strain in the coordinate axis direction, , , is the stress in the coordinate axis direction, is Young's modulus, is Poisson's ratio, is the lateral pressure coefficient, is the lateral pressure coefficient after excavation of the lower rock mass, To allow for elongation strain, is the tensile strength of rock.

[0095] Please also read Figure 2 and Figure 3 , known , the maximum allowable principal stress when the rock mass is in the limit equilibrium state can be obtained :

[0096]

[0097] In order to ensure the safety of the project, the maximum principal stress required in the limit equilibrium state should be greater than the actual maximum principal stress, that is, the rock and soil mass will not be damaged and meet the requirements. , more specifically, should satisfy:

[0098]

[0099] in is the vertical pressure transmitted by the joist. For the convenience of calculation, the value can be obtained by the following formula:

[0100]

[0101] Since this inequality should be satisfied within the entire cross-section excavation depth range, then:

[0102]

[0103] Critical width of joists under brittle conditions The specific acquisition process is:

[0104] For the convenience of description, set the coordinate axis, the vertical direction is z Direction, the horizontal direction in the plane is x direction, and the horizontal direction outside the plane is y Direction, such as Figure 2 As shown; According to the generalized Hooke's law:

[0105]

[0106]

[0107]

[0108] In the absence of any engineering disturbance, only geostress exists, and the rock and soil body is a semi-infinite body,

[0109]

[0110]

[0111]

[0112] So there is

[0113]

[0114] For the working condition described in the present invention, after the lower rock mass is excavated, the rock mass at the excavation boundary below the arch foot changes from three-way compression to two-way compression. , the horizontal stress in the plane at the boundary is 0, and the strain in the vertical plane direction is 0 (plane strain problem), then

[0115]

[0116]

[0117] Therefore, there is

[0118] because z Towards, y Therefore, according to the characteristics of the second strength theory, x A positive strain (elongation) will occur in the direction, which should satisfy:

[0119]

[0120] Here the negative sign indicates the direction of tensile strain. Allowable elongation strain

[0121]

[0122] therefore

[0123]

[0124] The maximum vertical stress should satisfy

[0125]

[0126] Then there is

[0127]

[0128] Example 1

[0129] Taking Shuiqinggou Station as an example, the design and verification method of the critical width of the arch foot support beam of the arch cover method tunnel described in the present invention includes the following steps:

[0130] Step 1: According to the engineering geological data and the Engineering Geology Manual, obtain the rock mass parameters below the arch foot support beam. This example is in the IV grade surrounding rock type, and the surrounding rock weight is taken =26.1kN / m3, friction angle of surrounding rock =65°, , cohesion =1.2MPa, internal friction angle =48°.

[0131] Step 2: According to the engineering geological data, the design parameters of the arch-cover tunnel section are obtained. The actual buried depth of the main body of the water-clearing tunnel is about 16.6m~20.4m, and the span (including the thickness of the secondary lining) is 22.5m. Therefore, the height of the tunnel top from the ground is taken as =20m, =22.5m

[0132] Step 3: Determine whether the tunnel is deep buried or shallow buried according to the parameters in Step 1 and Step 2. Calculation height of tunnel vertical load:

[0133]

[0134] Therefore, the actual burial depth H of Shuiqinggou Station satisfies

[0135]

[0136] That is, the tunnel load is calculated according to the shallow buried model, such as Figure 4 shown.

[0137] Step 4: Calculate the corresponding tunnel vertical pressure load :

[0138]

[0139] Step 5: Calculate the vertical load acting on the single-sided joist :

[0140]

[0141] Step 6: Perform plastic failure stability check and brittle failure stability check respectively, and take the larger value of the two calculated widths as the critical joist width b , and take the maximum value of the two as the critical width of the joist The numerical value of .

[0142] In the plastic failure stability verification, there should be:

[0143]

[0144] In the brittle failure stability calculation, according to the geological survey report in the embodiment, the surrounding rock is granite, the natural compressive strength is 53.79 MPa, and the saturated compressive strength is 51.64 MPa. The tensile strength / compressive strength coefficient is 0.028, and the tensile strength is taken from Table 2. , Poisson's ratio is 0.2. Calculation:

[0145]

[0146] The critical width of the joist .

[0147] The present invention also provides a system for calculating the critical width of the arch foot support beam of the arch cover method tunnel, which is used to execute the steps described in the method for calculating the critical width of the arch foot support beam of the arch cover method tunnel described in any of the above items. Figures 1 to 5The system includes: a rock mass parameter acquisition module 1, a section parameter acquisition module 2, a judgment module 3, a vertical pressure load module 4, a vertical direction load module 5 and a critical width verification module 6; the rock mass parameter acquisition module 1 is used to obtain the rock mass parameters below the arch foot support beam; the section parameter acquisition module 2 is used to obtain the section design parameters of the arch cover method tunnel; the judgment module 3 is used to judge whether the tunnel is deeply buried or shallowly buried; the vertical pressure load module 4 is used to calculate the vertical pressure load of the corresponding tunnel; the vertical direction load module 5 is used to calculate the vertical load acting on the single-side support beam; the critical width verification module 6 is used to respectively obtain the critical width of the support beam under plastic conditions and the critical width of the support beam under brittle conditions, and select the larger value of the two as the value of the critical width of the support beam.

[0148] The present invention provides a method and system for designing and verifying the critical width of an arch foot support beam of a tunnel using the arch cover method. The arch cover method is often used in soil-rock combined strata, and rock is a typical brittle material. In the present invention, not only the possibility of traditional plastic failure but also the possibility of brittle failure is considered, thereby achieving the purpose of reducing the engineering cost of a large-span underground excavation station using the arch cover and support beam method while ensuring safety.

[0149] The present invention aims at the problem that the existing joist design method in the prior art lacks theoretical support and is inconsistent with the actual working conditions. Starting from the instability form and mechanical mechanism of the rock mass under the unfavorable working conditions, the present invention obtains new control conditions, improves the joist verification method through theoretical deduction and numerical analysis methods, and thus obtains the design method of the joist critical width. The construction cost of the large-span dark excavation station using the arch cover joist method is reduced while ensuring safety.

[0150] 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 and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. The design and verification method of the critical width of the arch foot beam of the arch cover tunnel is characterized by: The following steps are involved: Obtain the rock mass parameters below the arch foot joist; Obtain the design parameters of the arch-cover tunnel section; determine whether the tunnel is deep buried or shallow buried; Calculate the corresponding tunnel vertical pressure load; Among them, if the tunnel is deeply buried, the calculation formula of the vertical pressure load q of the deeply buried tunnel is; q=λ×0.45×2 s-1 oh If the tunnel is shallowly buried, the calculation formula for the vertical pressure load q is: Among them, λ is the calculated side pressure coefficient; β is the rupture angle; θ is the friction angle on both sides of the top soil column; H is the tunnel burial depth; s is the surrounding rock grade; ω is the tunnel width influence coefficient; B is the tunnel width; γ is the surrounding rock weight; Calculate the vertical load acting on the single-sided joist; The critical width of the joist under plastic conditions and the critical width of the joist under brittle conditions are obtained respectively, and the larger value of the two is selected as the value of the critical width b of the joist.

2. The design and verification method for the critical width of the arch foot beam of the arch cap tunnel as claimed in claim 1 is characterized in that: Rock mass parameters include: surrounding rock density γ, surrounding rock grade s, surrounding rock calculated friction angle Internal friction angle of rock and soil Rock and soil cohesion c, rock tensile strength [σ t ], one or more of the rock Poisson’s ratio μ.

3. The design and verification method for the critical width of the arch foot beam of the arch cover tunnel as claimed in claim 2 is characterized in that: The tunnel section design parameters include: one or more of the following: tunnel width B, unsupported vertical wall height h below the joist, and tunnel burial depth H.

4. The design and verification method for the critical width of the arch foot beam of the arch cap tunnel as claimed in claim 3 is characterized in that: The calculation formula used in the vertical load acting on the single-sided joist is: Q=q×B / 2 Among them, Q is the magnitude of the vertical load acting on the single-side support beam; q is the magnitude of the corresponding vertical pressure load of the tunnel; and B is the width of the tunnel.

5. The design and verification method for the critical width of the arch foot beam of the arch cap tunnel as claimed in claim 4 is characterized in that: Determining whether the tunnel is deeply buried or shallowly buried includes: Determine the rate of increase or decrease of surrounding rock pressure when the tunnel width B increases or decreases by 1m; Determine the tunnel width influence coefficient ω Calculate the vertical load of the tunnel at the calculation height h a ; Calculate the height h based on the tunnel depth H and the tunnel vertical load a The relationship between them determines whether the tunnel load model should be calculated as deep or shallow burial.

6. The design and calculation method for the critical width of the arch foot beam of the arch cap tunnel as claimed in claim 5 is characterized in that: The height h is calculated based on the tunnel depth H and the tunnel vertical load a The relationship between the tunnel load model and the tunnel load model is used to determine whether the tunnel load model is calculated as deep or shallow. For the surrounding rock of grade IV to VI, if H < 2.5h a , then it is shallow buried, otherwise it is deep buried; for the surrounding rock of grade I to III, if H<2h a , it is shallow burial, otherwise it is deep burial.

7. The design and verification method for the critical width of the arch foot support beam of the arch cap tunnel according to claim 6, wherein the calculation formula for calculating the lateral pressure coefficient λ is: in, θ is the friction angle on both sides of the top soil column; β is the rupture angle when the maximum thrust is generated; Calculate the friction angle for the surrounding rock.

8. The design and verification method for the critical width of the arch foot support beam of the arch cover tunnel according to any one of claims 1 to 7, characterized in that: Critical width b of joist under plastic conditions p The calculation formula is: Among them, Q is the magnitude of the vertical load acting on the single-side joist; c is the cohesion of the rock and soil; is the internal friction angle of rock and soil; γ is the weight of surrounding rock; h is the height of the unsupported vertical wall under the joist.

9. The design and calculation method for the critical width of the arch foot beam of the arch cap tunnel as claimed in claim 8 is characterized in that: Critical width of joist under brittle conditions b f The calculation formula is: Where Q is the vertical load acting on the single-sided joist; γ is the weight of the surrounding rock; h is the height of the unsupported vertical wall below the joist; [σ t ] is the tensile strength of rock; μ is the Poisson’s ratio of rock.

10. A system for designing and verifying the critical width of an arch foot support beam of an arch capping tunnel, characterized in that it is used to execute the steps described in the method for designing and verifying the critical width of an arch foot support beam of an arch capping tunnel as claimed in any one of claims 1 to 9, comprising: A rock mass parameter acquisition module is used to obtain the rock mass parameters below the arch foot support beam; Section parameter acquisition module, used to obtain the design parameters of the arch-cover tunnel section; A judgment module, used to judge whether the tunnel is deeply buried or shallowly buried; Vertical pressure load module, used to calculate the vertical pressure load of the corresponding tunnel; Vertical load module, used to calculate the vertical load acting on the single-side joist; The critical width verification module is used to obtain the critical width of the joist under plastic conditions and the critical width of the joist under brittle conditions, and select the larger value of the two as the value of the critical width of the joist.

Images