Consideration of convergence-confinement curve calculation method for initial stress of tunnel primary support

Abstract

The application relates to the technical field of tunnel construction, in particular to a supporting characteristic curve calculation method of a tunnel steel frame based on a convergence-constraint method. A tunnel steel frame system considering prestress is constructed through a steel frame, an anchor rod and a cushion block, and then structural parameters and prestress constants of the tunnel steel frame system are obtained, the interaction among the steel frame, the anchor rod and the cushion block is fully considered, then the displacement characteristics of the tunnel steel frame system are obtained by using the structural parameters and the prestress constants, the tunnel displacement is obtained according to the displacement characteristics, and finally the supporting characteristic curve is obtained according to the displacement characteristics and the tunnel displacement, so that the supporting characteristic curve is more in line with the current tunnel construction condition, thereby improving the calculation accuracy, so that the optimal balance condition of the supporting system can be more accurately calculated when the convergence-constraint method is used.

Description

Technical Field

[0001] This invention relates to the field of tunnel construction technology, and specifically to a method for calculating the convergence-constraint curve considering the initial support prestress of a tunnel. Background Technology

[0002] Currently, tunnels are widely used in transportation construction due to their important role in improving highway technical conditions, shortening travel distances, increasing transport capacity, and reducing accidents. During tunnel construction, prestressed anchors, although relatively complex in construction technology and relatively expensive, are frequently used due to their high load-bearing capacity and strong ability to control pit deformation. Anchors are generally classified into prestressed anchors and non-prestressed anchors based on whether they are prestressed. Prestressed anchors consist of a free section and an anchoring section, typically using steel strands as the anchor rod body. The construction process involves first drilling the hole, then placing the anchor rod body, followed by the application of anchor grout. After the grout has reached the designed strength, the steel strands are tensioned to apply prestress. Because prestressed anchors require tensioning, they can provide support and anchoring force before the excavation of the lower soil layer. Therefore, this type of anchor has a strong ability to control deformation, and the early tensioning process allows for pre-testing of the anchor's load-bearing capacity, making quality assurance easier.

[0003] The emergence and application of new support systems such as rock bolts and shotcrete have promoted the development of the New Austrian Tunneling Method (NATM) for tunnels, and have also led to the formation of several calculation and design methods applicable to rock bolt and shotcrete support. These calculation methods no longer employ traditional load assumptions, but instead analyze the stability characteristics of the surrounding rock by analyzing the interaction between the structure and the rock mass. Among these methods, the convergence-constraint method (also known as the characteristic curve method) is frequently used. The convergence-constraint method assumes that the tunnel support system consists of the support structure and the surrounding rock mass. The surrounding rock, as the main load-bearing unit, forms a common load-bearing body with the support. They are interdependent and coordinate their deformation. Its basic principle is to determine the optimal equilibrium conditions of the support system by using the intersection of the characteristic curves of the surrounding rock and the characteristic curves of the support structure.

[0004] As the requirements for deformation control during tunnel excavation become increasingly stringent, steel frame support combined with prestressed anchor bolts is being used in tunnel construction. However, the traditional convergence-constraint method does not take into account the situation where steel frame support and prestressed anchor bolts are used together. This makes it difficult to obtain the optimal equilibrium conditions of the support system by using the traditional convergence-constraint method to obtain the support characteristic curve and then intersecting the support characteristic curve with the surrounding rock characteristic curve.

[0005] Therefore, there is an urgent need for a method to calculate the support characteristic curve that takes into account the coordination between steel frame support and prestressed anchor bolts, so that the support characteristic curve is more in line with the current tunnel construction conditions, thereby improving the accuracy of the calculation and enabling more accurate calculation of the optimal equilibrium conditions of the support system when using the convergence-constraint method. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a convergence-constraint curve calculation method that considers the initial support prestress of tunnels, thereby improving the accuracy of support characteristic curve calculation.

[0007] The technical solution adopted in this invention is a method for calculating the convergence-constraint curve considering the initial support prestress of a tunnel.

[0008] In the first feasible approach, a method for calculating the convergence-constraint curve of the tunnel's initial support prestress is considered, including:

[0009] Construct a prestressed tunnel steel frame system, which includes a steel frame, anchor bolts, and pads;

[0010] Obtain the structural parameters and prestress constant of the tunnel steel frame system considering prestress; the structural parameters include tunnel parameters, steel frame parameters, pad block parameters, and anchor bolt parameters;

[0011] The displacement characteristics of the tunnel steel frame system are obtained based on structural parameters and prestress constant.

[0012] The tunnel displacement is obtained based on the displacement characteristics;

[0013] The support characteristic curve of the tunnel steel frame is obtained based on the displacement characteristics and the amount of tunnel displacement.

[0014] In the second feasible method, in conjunction with the first feasible method, the prestress constant includes the prestress value and the stress-deformation characteristic quantity, which is obtained through the following method:

[0015] In the anchor pull-out test, multiple different tensile forces were applied, and the measured elongation of the anchor corresponding to each tensile force was measured.

[0016] Calculate the calculated elongation of the anchor bolt corresponding to each tension force;

[0017] The stress-deformation characteristic quantities are obtained based on each tensile force and the corresponding measured elongation value of the anchor rod and the calculated elongation value of the anchor rod.

[0018] In the third feasible method, in conjunction with the first feasible method, the displacement characteristics of the tunnel steel frame system are obtained based on structural parameters and prestress constants, including:

[0019] The first alternative displacement characteristics are obtained based on tunnel parameters, steel frame parameters, and pad block parameters;

[0020] The second alternative displacement characteristics are obtained based on the anchor bolt parameters and the prestress constant.

[0021] The final displacement characteristics are determined based on the first and second alternative displacement characteristics.

[0022] In combination with the third feasible method, in the fourth feasible method, the first alternative displacement characteristic is obtained through the following formula:

[0023]

[0024] In the above formula, K s For the first alternative displacement characteristic, a is the tunnel radius, s is the support spacing along the tunnel length, θ is half the angle between the wedges, w is the support flange width, and A s I is the cross-sectional area of ​​the steel frame. s Let E be the moment of inertia of the steel frame section. s t represents the elastic modulus of steel. B E represents the thickness of the pad. B This is the elastic modulus of the pad material.

[0025] Combining the third feasible method, in the fifth feasible method, the second alternative displacement characteristic is obtained through the following formula:

[0026]

[0027] In the above formula, K b As the second alternative displacement characteristic, s c s1 is the circumferential spacing of the anchor bolts, d is the longitudinal spacing of the anchor bolts. b l is the diameter of the anchor rod. b E is the net length of the anchor bolt. b f is the elastic modulus of the anchor bolt. pre Let Q be the prestress value to be applied, and let Q be the characteristic quantity of deformation under stress.

[0028] In the sixth possible implementation method, combining the third implementation method, the final displacement characteristics are determined based on the first and second alternative displacement characteristics, including:

[0029] The first alternative displacement characteristic and the second alternative displacement characteristic are added together to obtain the third alternative displacement characteristic; the final displacement characteristic includes the first alternative displacement characteristic, the second alternative displacement characteristic and the third alternative displacement characteristic.

[0030] Combining the sixth feasible method, the seventh feasible method obtains the tunnel displacement based on displacement characteristics, including:

[0031] The first maximum support resistance is obtained based on tunnel parameters, steel frame parameters, and pad block parameters;

[0032] The second maximum support resistance is obtained based on the anchor bolt parameters and prestress variables;

[0033] The tunnel displacement is obtained based on the first maximum support resistance, the second maximum support resistance, and the displacement characteristics.

[0034] Combining the seventh feasible method, in the eighth feasible method, the first maximum support resistance is obtained through the following formula:

[0035]

[0036] In the above formula, p amsx For the first maximum support resistance, σ ys Let be the yield strength of the steel, x be the thickness of the steel frame section, a be the tunnel radius, s be the support spacing along the tunnel length, θ be half the angle between the wedges, and A be the yield strength of the steel. s I is the cross-sectional area of ​​the steel frame. s Let t be the moment of inertia of the steel frame section. B This refers to the thickness of the pad block.

[0037] Combining the seventh feasible method, in the ninth feasible method, the tunnel displacement is obtained based on the first maximum support resistance, the second maximum support resistance, and displacement characteristics, including:

[0038] The first tunnel displacement is obtained based on the first maximum support resistance and the first alternative displacement characteristics.

[0039] The second tunnel displacement is obtained based on the second maximum support resistance and the second alternative displacement characteristics.

[0040] In conjunction with the ninth feasible method, the tenth feasible method obtains the support characteristic curve of the tunnel steel frame based on displacement characteristics and tunnel displacement, including:

[0041] Obtain the initial displacement of the tunnel;

[0042] The characteristic curves of the first-stage support are drawn based on the initial displacement of the tunnel and the characteristics of the first alternative displacement.

[0043] The second-stage support characteristic curve is drawn based on the initial tunnel displacement, the first tunnel displacement, and the characteristics of the third alternative displacement.

[0044] The third-stage support characteristic curve is plotted based on the initial tunnel displacement, the first tunnel displacement, the second tunnel displacement, the first maximum support resistance, and the second maximum support resistance.

[0045] As can be seen from the above technical solution, the beneficial technical effects of the present invention are as follows:

[0046] A prestressed tunnel steel frame system is constructed using steel frames, anchor bolts, and pads. The structural parameters and prestress constant of this system are then obtained, fully considering the interactions between the steel frame, anchor bolts, and pads. The displacement characteristics of the tunnel steel frame system are then obtained using the structural parameters and prestress constant, followed by the tunnel displacement. Finally, the support characteristic curve is derived from the displacement characteristics and tunnel displacement, making the curve more consistent with current tunnel construction conditions and improving calculation accuracy. This allows for more accurate calculation of the optimal equilibrium conditions of the support system when using the convergence-constraint method. Attached Figure Description

[0047] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0048] Figure 1 This is a schematic diagram illustrating a method for calculating the convergence-constraint curve considering the initial support prestress of a tunnel, as provided in this embodiment.

[0049] Figure 2 This is a structural schematic diagram of a tunnel steel frame system considering prestress, provided in this embodiment;

[0050] Figure 3 The support characteristic curve of the tunnel steel frame based on the convergence-constraint method is provided in this embodiment;

[0051] Figure label:

[0052] 1-Steel frame, 2-Anchor bolt, 3-Padded block. Detailed Implementation

[0053] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are merely illustrative of the technical solution of the present invention and are therefore intended to limit the scope of protection of the present invention.

[0054] It should be noted that, unless otherwise stated, the technical or scientific terms used in this application should have the ordinary meaning understood by those skilled in the art. The terms "first," "second," etc., in the specification, claims, and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for implementation of the embodiments of this disclosure described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. Unless otherwise stated, the term "a plurality of" means two or more. In this disclosure, the character " / " indicates an "or" relationship between the preceding and following objects. For example, A / B means: A or B. The term "and / or" describes an association relationship between objects, indicating that three relationships can exist. For example, A and / or B means: A or B, or, A and B. The term "corresponding" can refer to an association or binding relationship; A corresponding to B means that there is an association or binding relationship between A and B.

[0055] Combination Figure 2 As shown, in some embodiments, the steel frame 1, as an important component of the permanent support, is often used in conjunction with shotcrete anchors and other components. Generally, the steel frame is prefabricated in the factory. During on-site installation, wooden blocks of varying thicknesses must be used to ensure close contact between the steel frame and the surrounding rock, and even a certain preload may be applied. Therefore, in prestressed tunnel steel frame systems, not only the steel frame 1 and anchors 2 must be considered, but also the pads 3. The displacement caused by the steel frame, pads, etc., is expressed by formula μ. p =μ 1p +μ 2p +μ 3p , where μ 1p For the displacement of the steel frame itself, μ 2p The displacement caused by the wooden block, μ 3p Let L be the displacement caused by the expansion and contraction of the steel frame. When the expansion and contraction of the support is determined to be ΔL, the radial displacement generated by L is...

[0056] Combination Figure 1 As shown, this embodiment provides a method for calculating the convergence-constraint curve considering the initial support prestress of a tunnel, including:

[0057] Step S01: Construct a prestressed tunnel steel frame system, which includes a steel frame, anchor bolts, and pads.

[0058] Step S02: Obtain the structural parameters and prestress constant of the tunnel steel frame system considering prestress; the structural parameters include tunnel parameters, steel frame parameters, pad block parameters, and anchor bolt parameters;

[0059] Step S03: Obtain the displacement characteristics of the tunnel steel frame system based on the structural parameters and prestress constant;

[0060] Step S04: Obtain the tunnel displacement based on the displacement characteristics;

[0061] Step S05: Obtain the support characteristic curve of the tunnel steel frame based on the displacement characteristics and tunnel displacement.

[0062] In some embodiments, a tunnel steel frame system that takes prestress into account is constructed, such as Figure 2 As shown, the prestressed tunnel steel frame system includes a steel frame 1, anchor bolts 2, and pads 3. The structural parameters of this tunnel steel frame system are obtained, including tunnel parameters, steel frame parameters, pad parameters, and anchor bolt parameters. Tunnel parameters include the tunnel radius *a* and the support spacing *s* along the tunnel length. Steel frame parameters include half the angle between wedges *θ*, the support flange width *w*, and the steel frame cross-sectional area *A*. s Moment of inertia I of steel frame section s Steel frame cross-section thickness x, steel elastic modulus E s The parameters of the pad block include the pad block thickness t. B The elastic modulus E of the pad material B Anchor bolt parameters include the circumferential spacing s of the anchor bolts. c The longitudinal spacing s1 of the anchor bolts, and the diameter d of the anchor bolts. b The net length l of the anchor bolt b The elastic modulus E of the anchor bolt b .

[0063] Optionally, the prestress constant includes the prestress value and the stress-deformation characteristic quantity. The prestress value to be applied to the tunnel steel frame system is f. pre The stress-deformation characteristic quantity is Q, which is a constant related to the stress-deformation characteristics of the anchor rod, pad, and anchor head.

[0064] Optionally, obtaining the stress-deformation characteristic quantity includes: in the anchor pull-out test, applying multiple different tensile forces and measuring the measured elongation value of the anchor corresponding to each tensile force; calculating the calculated elongation value of the anchor corresponding to each tensile force; and obtaining the stress-deformation characteristic quantity based on each tensile force and the measured and calculated elongation values ​​of the anchor corresponding to each tensile force.

[0065] Alternatively, the theoretical elongation u of the prestressed anchor can be calculated using the following formula:

[0066]

[0067] In the above formula, f py Let A be the tensile stress of the prestressed anchor rod, L be the length of the prestressed anchor rod, and A be the tensile stress of the prestressed anchor rod. P E represents the cross-sectional area of ​​the prestressed anchor rod. PThis is the elastic modulus of the prestressed anchor rod.

[0068] Optionally, the characteristic quantity of stress-deformation is obtained by the following formula:

[0069]

[0070] In the above formula, Q is the characteristic quantity of deformation under force; T1 is the first tensile force in the anchor pull-out test, T2 is the second tensile force in the anchor pull-out test, u1 is the calculated elongation value of the anchor corresponding to the first tensile force, u2 is the calculated elongation value of the anchor corresponding to the second tensile force, u'1 is the measured elongation value of the anchor corresponding to the first tensile force, and u'2 is the measured elongation value of the anchor corresponding to the second tensile force.

[0071] In some embodiments, the magnitudes of the first pulling force and the second pulling force are different.

[0072] Optionally, the displacement characteristics of the tunnel steel frame system are obtained based on structural parameters and prestress constant, including: obtaining a first alternative displacement characteristic based on tunnel parameters, steel frame parameters, and pad block parameters; obtaining a second alternative displacement characteristic based on anchor bolt parameters and prestress constant; and determining the final displacement characteristics based on the first and second alternative displacement characteristics.

[0073] Optionally, the first alternative displacement characteristic is obtained by the following formula:

[0074]

[0075] In the above formula, K s For the first alternative displacement characteristic, a is the tunnel radius, s is the support spacing along the tunnel length, θ is half the angle between the wedges, w is the support flange width, and A s I is the cross-sectional area of ​​the steel frame. s Let E be the moment of inertia of the steel frame section. s t represents the elastic modulus of steel. B E represents the thickness of the pad. B This is the elastic modulus of the pad material.

[0076] Alternatively, the second alternative displacement characteristic is obtained by the following formula:

[0077]

[0078] In the above formula, K b As the second alternative displacement characteristic, s c s1 is the circumferential spacing of the anchor bolts, d is the longitudinal spacing of the anchor bolts. b l is the diameter of the anchor rod. b E is the net length of the anchor bolt. b f is the elastic modulus of the anchor bolt. preLet Q be the prestress value to be applied, and let Q be the characteristic quantity of deformation under stress.

[0079] Optionally, determining the final displacement characteristic based on the first alternative displacement characteristic and the second alternative displacement characteristic includes: adding the first alternative displacement characteristic and the second alternative displacement characteristic to obtain a third alternative displacement characteristic; the final displacement characteristic includes the first alternative displacement characteristic, the second alternative displacement characteristic, and the third alternative displacement characteristic.

[0080] Alternatively, the third alternative displacement characteristic is obtained by the following formula:

[0081] K sb =K s +K b

[0082] In the above formula, K sb K is the third alternative displacement characteristic. s K is the first alternative displacement characteristic. b This is the second alternative displacement characteristic.

[0083] Optionally, the tunnel displacement is obtained based on displacement characteristics, including: obtaining the first maximum support resistance based on tunnel parameters, steel frame parameters, and pad block parameters; obtaining the second maximum support resistance based on anchor bolt parameters and prestress variables; and obtaining the tunnel displacement based on the first maximum support resistance, the second maximum support resistance, and displacement characteristics.

[0084] Optionally, the first maximum support resistance is obtained by the following formula:

[0085]

[0086] In the above formula, p amsx For the first maximum support resistance, σ ys Let be the yield strength of the steel, x be the thickness of the steel frame section, a be the tunnel radius, s be the support spacing along the tunnel length, θ be half the angle between the wedges, and A be the yield strength of the steel. s I is the cross-sectional area of ​​the steel frame. s Let t be the moment of inertia of the steel frame section. B This refers to the thickness of the pad block.

[0087] In some embodiments, when the wedge plane is rectangular, the side is equal to w, that is, the flange width of the steel frame is w, then p amax This represents the maximum support resistance acting on the steel frame.

[0088] Optionally, the second maximum support resistance is obtained by the following formula:

[0089]

[0090] In the above formula, P bmaxFor the second maximum support resistance, f py This represents the design value for the tensile strength of the prestressed anchor bolt.

[0091] In some embodiments, one end of the end-anchored anchor rod is an anchor head, and the other end is an anchoring section connected to the surrounding rock. Tightening the nut brings the washer into close contact with the steel frame, causing the anchor rod to function. The end-anchored anchor rod then fully functions, p bmax The maximum radial pressure that prestressed anchor bolts provide to the surrounding rock.

[0092] Optionally, the tunnel displacement is obtained based on the first maximum support resistance, the second maximum support resistance, and the displacement characteristics, including: obtaining the first tunnel displacement based on the first maximum support resistance and the first alternative displacement characteristics; and obtaining the second tunnel displacement based on the second maximum support resistance and the second alternative displacement characteristics.

[0093] Optionally, the first tunnel displacement is obtained using the following formula:

[0094]

[0095] In the above formula, u smax p is the displacement of the first tunnel. amax For the first maximum support resistance, K s denoted as the first alternative displacement characteristic, where a is the tunnel radius.

[0096] Optionally, the displacement of the second tunnel is obtained using the following formula:

[0097]

[0098] In the above formula, u bmax p is the displacement of the second tunnel. bmax For the second maximum support resistance, K b This is the second alternative displacement characteristic, where a is the tunnel radius.

[0099] Optionally, the support characteristic curve of the tunnel steel frame is obtained based on the displacement characteristics and the tunnel displacement, including: obtaining the initial displacement of the tunnel; drawing the first-stage support characteristic curve based on the initial displacement of the tunnel and the first alternative displacement characteristics; drawing the second-stage support characteristic curve based on the initial displacement of the tunnel, the first tunnel displacement, and the third alternative displacement characteristics; and drawing the third-stage support characteristic curve based on the initial displacement of the tunnel, the first tunnel displacement, the second tunnel displacement, the first maximum support resistance, and the second maximum support resistance.

[0100] Optionally, the formula for the support characteristic curve is as follows: [Formula for support characteristic curve is shown below]. Figure 3 As shown:

[0101]

[0102] Optionally, the formula for the support characteristic curve is as follows: [Formula for support characteristic curve is shown below]. Figure 3 As shown:

[0103]

[0104] In the above formula, u0 is the initial displacement of the tunnel, and K s As the first alternative displacement characteristic, u smax K represents the displacement of the first tunnel. sb As the third alternative displacement characteristic, u c u represents the x-coordinate of the starting point of the characteristic curve of the third-stage support system. bmax K represents the displacement of the second tunnel. c This represents the slope of the characteristic curve for the third-stage support system.

[0105] In some embodiments, point (u0+u smax p amax Substitute into the formula By calculating b1, the support characteristic curve function for the second stage can be obtained. smax The maximum support resistance design value of the steel frame is given by substituting the maximum support resistance design value of the steel frame into the formula. That is, to obtain the starting x-coordinate u of the characteristic curve of the third stage support. c Set the starting x-coordinate u c Substitute into the formula The starting point ordinate P of the characteristic curve of the third-stage support was calculated. c The slope of the characteristic curve of the third-stage support is... Among them, u sbmax =u smax +u bmax p sbmax =p smax +p bmax Point (u) c P c Substitute The support characteristic curve function for the third stage can then be obtained.

[0106] In some embodiments, the steel frame and prestressed anchor bolts are installed at different times, resulting in different steel frame support characteristic curves considering prestress. Figure 3 This is a schematic diagram of a support characteristic curve, combined with... Figure 3 It can be seen that before the steel frame support reaches its maximum deformation p smax Previously, prestressed anchor bolts were installed, and when the steel frame support reached u smax Even at that time, it still plays a role because the prestressed anchor support strengthens the steel frame support, until it reaches u bmax The entire support system was only in a state of failure at that time.

[0107] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A convergence-confinement curve calculation method considering the initial support prestress of a tunnel, characterized in that, include: Construct a prestressed tunnel steel frame system, which includes a steel frame, anchor bolts, and pads; Obtain the structural parameters and prestress constant of the tunnel steel frame system considering prestress; the structural parameters include tunnel parameters, steel frame parameters, pad block parameters, and anchor bolt parameters; The displacement characteristics of the tunnel steel frame system are obtained based on structural parameters and prestress constant. The tunnel displacement is obtained based on the displacement characteristics; The support characteristic curve of the tunnel steel frame is obtained based on the displacement characteristics and the amount of tunnel displacement.

2. The method of claim 1, wherein, The prestress constant includes the prestress value and the stress-deformation characteristic quantity. The stress-deformation characteristic quantity is obtained in the following way: In the anchor pull-out test, multiple different tensile forces were applied, and the measured elongation of the anchor corresponding to each tensile force was measured. Calculate the calculated elongation of the anchor bolt corresponding to each tension force; The stress-deformation characteristic quantities are obtained based on each tensile force and the corresponding measured elongation value of the anchor rod and the calculated elongation value of the anchor rod.

3. The method of claim 1, wherein, The displacement characteristics of the tunnel steel frame system are obtained based on structural parameters and prestress constants, including: The first alternative displacement characteristics are obtained based on tunnel parameters, steel frame parameters, and pad block parameters; The second alternative displacement characteristics are obtained based on the anchor bolt parameters and the prestress constant. The final displacement characteristics are determined based on the first and second alternative displacement characteristics.

4. The method of claim 3, wherein, The first alternative displacement characteristic is obtained through the following formula: In the above formula, K s For the first alternative displacement characteristic, a is the tunnel radius, s is the support spacing along the tunnel length, θ is half the angle between the wedges, w is the support flange width, and A s I is the cross-sectional area of ​​the steel frame. s Let E be the moment of inertia of the steel frame section. s t represents the elastic modulus of steel. B E represents the thickness of the pad. B This is the elastic modulus of the pad material.

5. The method of claim 3, wherein, The second alternative displacement characteristic is obtained through the following formula: In the above formula, K b As the second alternative displacement characteristic, s c s1 is the circumferential spacing of the anchor bolts, d is the longitudinal spacing of the anchor bolts. b l is the diameter of the anchor rod. b E is the net length of the anchor bolt. b f is the elastic modulus of the anchor bolt. pre Let Q be the prestress value to be applied, and let Q be the characteristic quantity of deformation under stress.

6. The method of claim 3, wherein, The final displacement characteristics are determined based on the first and second alternative displacement characteristics, including: The first alternative displacement characteristic and the second alternative displacement characteristic are added together to obtain the third alternative displacement characteristic; the final displacement characteristic includes the first alternative displacement characteristic, the second alternative displacement characteristic and the third alternative displacement characteristic.

7. The method of claim 6, wherein, The tunnel displacement is obtained based on displacement characteristics, including: The first maximum support resistance is obtained based on tunnel parameters, steel frame parameters, and pad block parameters; The second maximum support resistance is obtained based on the anchor bolt parameters and prestress variables; The tunnel displacement is obtained based on the first maximum support resistance, the second maximum support resistance, and the displacement characteristics.

8. The method of claim 7, wherein, The first maximum support resistance is obtained by the following formula: In the above formula, p amax For the first maximum support resistance, σ ys Let be the yield strength of the steel, x be the thickness of the steel frame section, a be the tunnel radius, s be the support spacing along the tunnel length, θ be half the angle between the wedges, and A be the yield strength of the steel. s I is the cross-sectional area of ​​the steel frame. s Let t be the moment of inertia of the steel frame section. B This refers to the thickness of the pad block.

9. The method of claim 7, wherein, The tunnel displacement is obtained based on the first maximum support resistance, the second maximum support resistance, and displacement characteristics, including: The first tunnel displacement is obtained based on the first maximum support resistance and the first alternative displacement characteristics. The second tunnel displacement is obtained based on the second maximum support resistance and the second alternative displacement characteristics.

10. The method of claim 9, wherein, The support characteristic curves of the tunnel steel frame are obtained based on displacement characteristics and tunnel displacement, including: Obtain the initial displacement of the tunnel; The characteristic curves of the first-stage support are drawn based on the initial displacement of the tunnel and the characteristics of the first alternative displacement. The second-stage support characteristic curve is drawn based on the initial tunnel displacement, the first tunnel displacement, and the characteristics of the third alternative displacement. The third-stage support characteristic curve is plotted based on the initial tunnel displacement, the first tunnel displacement, the second tunnel displacement, the first maximum support resistance, and the second maximum support resistance.

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