Yield determination method for confined concrete box steel arch in soft rock tunnel

Abstract

The present invention provides a yield determination method for a soft rock tunnel confined concrete box steel arch frame. Under the limit state, the axial compressive ultimate bearing capacity N is obtained according to the stress distribution for the confined concrete box steel arch frame section. u and pure bending ultimate bearing capacity M u ; According to the stress state of the section, the expressions of the section axial force N and bending moment M are derived; through the axial compression ultimate bearing capacity N u , Pure bending ultimate bearing capacity M u , the cross-section axial force N and bending moment M are dimensionless, and the compression-bending yield criterion of the confined concrete box steel arch section is obtained; for the confined concrete box steel arch to be measured, the structural mechanics force method is used to decompose it and the current axial force F is obtained. Nφ and the current bending moment M φ The calculation formula is: the current axial force F Nφ and the current bending moment M φ Substitute the compression-bending yield criterion and, based on the generalized cross-sectional yield function, determine the yield condition of the confined concrete box-section steel arch to be measured. Clarify the yield condition of the support structure to avoid overly conservative or risky designs.

Description

Technical Field

[0001] The invention relates to the technical field of steel arch structure performance testing, and in particular to a yield determination method for a soft rock tunnel confined concrete box-shaped steel arch. Background Art

[0002] As a new form of support, constrained concrete arches have attracted considerable attention for their practicality and economic benefits. Although the technology is still in its early stages of development, its enormous potential and research value are already evident. For example, in tunnels facing fault zones, where surrounding rock is difficult to support, the use of constrained concrete arches instead of traditional H-steel supports successfully resolved the issue of insufficient support strength, effectively preventing tunnel collapse and enabling smooth passage through the fault zone. The use of constrained concrete arches saves steel compared to traditional steel arches, bringing significant economic and social benefits. The use of constrained concrete arches has also significantly reduced costs in subway tunnel construction.

[0003] As a new type of support, a method for determining the bearing yield of confined concrete box steel arches is urgently needed to ensure construction safety and quality. Summary of the Invention

[0004] The present invention proposes a yield determination method for a soft rock tunnel confined concrete box steel arch frame, so as to solve the technical problem that there is no corresponding yield determination method for the new support form of the confined concrete box steel arch frame in the prior art.

[0005] To solve the above technical problems, the present invention provides a yield determination method for a confined concrete box steel arch in a soft rock tunnel, comprising the following steps:

[0006] Step S1: Under the ultimate limit state, for the confined concrete box steel arch section, calculate the ultimate axial compressive bearing capacity N according to the stress distribution u and pure bending ultimate bearing capacity M u ;

[0007] Step S2: derive the expressions of the cross-sectional axial force N and bending moment M according to the cross-sectional stress state;

[0008] Step S3: The axial compression limit bearing capacity N u , Pure bending ultimate bearing capacity M u , the cross-sectional axial force N and bending moment M are dimensionless to obtain the compression-bending yield criterion of the confined concrete box steel arch cross-section;

[0009] Step S4: Decompose the confined concrete box steel arch frame to be measured using the structural mechanics force method to obtain the current axial force F Nφ and the current bending moment M φ Calculation formula:

[0010] Step S5: The current axial force F Nφ and the current bending moment M φ The compression-bending yield criterion is introduced, and the yield condition of the confined concrete box steel arch to be measured is obtained according to the generalized yield function of the section.

[0011] Preferably, in step S1, the axial compressive ultimate bearing capacity N u and pure bending ultimate bearing capacity M u The expression is:

[0012]

[0013] Where b is the width of the confined concrete box steel arch frame; t1 is the thickness of the upper and lower steel plates; h is the height of the confined concrete box steel arch frame; t2 is the thickness of the left and right steel plates; t3 is the thickness of the middle steel plate; σ s and σ c are the tensile and compressive yield limits of steel and the compressive yield limit of concrete respectively; h1 represents the position of the neutral axis in the pure bending state without axial force.

[0014] Preferably, in step S2, the expressions of the cross-sectional axial force N and the bending moment M are:

[0015]

[0016] Where h0 represents the position moved between -h1 and h / 2.

[0017] Preferably, step S3 includes:

[0018] Step S31: non-dimensionalizing the cross-sectional axial force N and bending moment M to obtain a dimensionless implicit function of the cross-sectional area of ​​the confined concrete box steel arch frame;

[0019] Step S32: collecting steel parameters and concrete parameters of the confined concrete box steel arch to be measured;

[0020] Step S33: Substitute the steel material parameters and concrete parameters into the dimensionless expressions of the cross-sectional axial force N and the bending moment M to obtain the compression-bending yield criterion.

[0021] Preferably, the expression of the dimensionless implicit function in step S31 is:

[0022]

[0023]

[0024] Where n and m are the dimensionless axial force and dimensionless bending moment, respectively; b represents the width of the confined concrete box steel arch; t1 represents the thickness of the upper and lower steel plates; h represents the height of the confined concrete box steel arch; t2 represents the thickness of the left and right steel plates; t3 represents the thickness of the middle steel plate; σ s and σ c They are the tensile and compressive yield limits of steel and the compressive yield limit of concrete respectively; h1 represents the position of the neutral axis in the pure bending state without axial force; h0 represents the position moving between -h1 and h / 2.

[0025] Preferably, the compressive yield limit of concrete in the dimensionless expressions of the cross-sectional axial force N and the bending moment M in step S33 is set to zero to obtain the compression-bending yield criterion of the box section.

[0026] Preferably, the compressive yield limit of concrete and the cross-sectional parameter t2 in the dimensionless expressions of the cross-sectional axial force N and the bending moment M in step S33 are set to zero, thereby obtaining the compression-bending criterion of the H-shaped steel cross-section.

[0027] Preferably, in step S4, the current axial force F Nφ and the current bending moment M φ The calculation formula is:

[0028] F Nφ =q1R(sin 2 φ+λcos 2 φ);

[0029]

[0030] Where, It is the clockwise angle with the vertical diameter, with a value range of 0 to π; R represents the arch radius; q1 represents the vertical load borne by the arch; q2 represents the horizontal load; λ = q1 / q2 represents the lateral pressure coefficient.

[0031] Preferably, step S5 includes:

[0032] Step S51: Obtain the current axial force F Nφ and the current bending moment M φ The dimensionless expression of ;

[0033] Step S52: The current axial force F Nφ and the current bending moment M φ The dimensionless expression of is brought into the yield criterion;

[0034] Step S53: determining the yield condition of the confined concrete box steel arch to be measured according to the cross-section generalized yield function.

[0035] The beneficial effects of the present invention include at least: by deriving the compression-bending yield criterion formula of the constrained concrete box section, the present invention theoretically analyzes the ultimate strength bearing capacity and structural stability ultimate bearing capacity of this type of arch frame, and can clarify the yield condition of the support structure, so that the designer can accurately judge the safety and bearing capacity of the support structure during the design stage, and avoid overly conservative or high-risk designs. Through yield judgment, the material selection and configuration of the support structure can be optimized, material waste can be reduced, and cost-effectiveness can be improved. The yield judgment method of the support form can provide a clear bearing capacity boundary, which helps to predict support failure modes and potential risks, enhance the anti-destruction ability of the overall structure, and improve engineering safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Schematic diagram of a method flow in an embodiment of the present invention;

[0037] Figure 2 This is a schematic diagram of a confined concrete box section according to an embodiment of the present invention;

[0038] Figure 3 Schematic diagram of mn curves of different cross sections and parameters according to an embodiment of the present invention;

[0039] Figure 4 Schematic diagram of a confined concrete box steel arch frame for a soft rock tunnel according to an embodiment of the present invention;

[0040] Figure 5 Schematic diagram of mechanical analysis of a confined concrete box steel arch in a soft rock tunnel according to an embodiment of the present invention. DETAILED DESCRIPTION

[0041] The following is a clear and complete description of the technical solutions in the embodiments of the present invention, in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0042] like Figure 1 As shown, an embodiment of the present invention provides a yield determination method for a confined concrete box steel arch in a soft rock tunnel, comprising the following steps:

[0043] Step S1: Under the ultimate limit state, for the confined concrete box steel arch section, calculate the ultimate axial compressive bearing capacity N according to the stress distribution u and pure bending ultimate bearing capacity M u .

[0044] Specifically, the tunnel steel arch section is primarily in a compression-bending state. Based on this result, the yield criterion for the confined concrete box section is derived. Because the section is composed of both steel and concrete, the following specific assumptions are made in the derivation:

[0045] (1) The neutral axis position of the compression-bending member under the elastic limit load is the same as the neutral axis position when the plastic hinge is formed, and the plane section assumption is satisfied;

[0046] (2) The full-section plasticity criterion is adopted, that is, it is assumed that in the limit state, both steel and concrete have reached the maximum material strength value, the compressive strength is borne by both concrete and steel, the tensile strength is borne only by steel, and the stress is distributed in a rectangular shape along the cross section.

[0047] Confined concrete box sections such as Figure 2 As shown in the figure, when only axial force or bending moment acts on the cross section, under the limit state, the axial compressive ultimate bearing capacity N can be obtained according to its stress distribution. u and pure bending ultimate bearing capacity M u .

[0048]

[0049] Where b is the width of the confined concrete box steel arch frame; t1 is the thickness of the upper and lower steel plates; h is the height of the confined concrete box steel arch frame; t2 is the thickness of the left and right steel plates; t3 is the thickness of the middle steel plate; σ s and σ c are the tensile and compressive yield limits of steel and the compressive yield limit of concrete respectively; h1 represents the position of the neutral axis in the pure bending state without axial force.

[0050] Step S2: Derive expressions for the section axial force N and bending moment M based on the section stress state.

[0051] Specifically, for Figure 2 For the confined concrete box section shown, it is assumed that the neutral axis is at y = h0 and h0 moves between -h1 and h / 2. By making the entire section reach the plastic yield limit, the relationship between the axial force and the section geometric parameters and material strength parameters is established by the equilibrium condition of the section forces:

[0052]

[0053] The relationship between bending moment and geometric parameters and strength parameters is:

[0054]

[0055] Step S3: Through the axial compression limit bearing capacity N u , Pure bending ultimate bearing capacity M u, the section axial force N and bending moment M are dimensionless, and the compression-bending yield criterion of the confined concrete box steel arch section is obtained.

[0056] Specifically, when axial force and bending moment act on the cross section, the expressions of the cross section axial force N and bending moment M are derived according to the cross section stress state, and the axial force and bending moment are dimensionlessly processed to obtain the cross section compression-bending yield criterion:

[0057] f(n,m)≤1(5)

[0058] Where n = N / N u , m=M / M u , f is the generalized yield function of the section; n and m are the dimensionless axial force and dimensionless bending moment respectively; N and M are the axial force and bending moment of the section respectively, N u and M u are the ultimate compressive bearing capacity and the ultimate bending bearing capacity of the section, respectively, and the dimensionless expression is:

[0059]

[0060]

[0061] From equations (6) and (7), it can be seen that the dimensionless internal force formula of the confined concrete box section is an implicit function and is difficult to be transformed into the generalized yield function form of equation (5). Therefore, it is necessary to substitute the specific parameters of the confined concrete box section and simplify the above formula to obtain the compression-bending yield criterion of the confined concrete box steel arch section:

[0062] When this type of section is not filled with concrete, that is, the compressive yield limit of concrete in the above formula is set to zero, the compression-flexural yield criterion for the box section can be obtained. Simultaneously, by setting the section parameter t2 to zero, the compression-flexural yield criterion for the H-beam section can also be obtained. This embodiment statistically analyzes the compression-flexural yield criteria for different types of sections based on different structures and parameters, as shown in Table 1.

[0063] Table 1: Yield criterion for concrete C40 and steel Q235

[0064]

[0065]

[0066] Draw the mn curve of each section, such as Figure 3As shown. The physical meaning of the m-n curve is that the dimensionless axial force n and dimensionless bending moment m calculated from the axial force N and bending moment M of the component are within the positive envelope range of the m-n curve and the coordinate axes, the component is in a safe state and there is no risk of strength failure; otherwise, it reaches the ultimate state of compression and bending and strength failure occurs. For the arch frame, the m-n curve can judge the ultimate state of the compression and bending combination of any section, and thus become the overall yield criterion of the arch frame.

[0067] Step S4: Decompose the measured restrained concrete box steel arch frame by using the force method of structural mechanics to obtain the current axial force F Nφ and the current bending moment M φ calculation formula.

[0068] Specifically, the restrained concrete box steel arch frame is a new type of restrained concrete arch frame formed by pouring fine aggregate concrete or cement mortar inside the closed "day" - shaped box section, as Figure 4 shown.

[0069] At the nodes of the restrained concrete box steel arch frame, high-strength bolts are used for connection, so it can be regarded as an equal-rigidity arch frame as a whole. The mechanical analysis model of the equal-rigidity arch frame is as Figure 5 shown, where the radius of the arch frame is R, the arch frame bears the vertical load q1, the horizontal load q2, the lateral pressure coefficient λ = q1 / q2, and the section flexural rigidity of the arch frame member is EI.

[0070] The equal-rigidity steel arch frame structure is a once indeterminate structure, as Figure 5 shown. In this embodiment, the force method of structural mechanics is used for solution. Among them, the calculation formula of the axial force:

[0071] F Nφ = q1R(sin 2 φ + λcos 2 φ)(8)

[0072] The calculation formula of the bending moment: [[ID=​​​​​​​​​​​​​​​​Specifically, the ultimate bearing capacity of the arch frame refers to the maximum load value that the arch frame can withstand when it is subjected to load. When the load reaches this limit, the material of the arch frame will undergo damage such as yielding and breaking, causing the arch frame to lose its bearing capacity. Therefore, in the theoretical calculation, when the axial force and bending moment combination of the most unfavorable section of the arch frame just reaches the compression-bending yield criterion corresponding to the mn curve, the corresponding arch frame force q1 is considered to be the ultimate bearing capacity of the arch frame q lcr Combining the calculation formula of the arch internal force and the section bending yield criterion as follows, the current axial force and the current bending moment are dimensionless, and the yield condition can be determined by determining whether they are within the bending yield criterion curve obtained in step S3.

[0077]

[0078] f(n,m)≤1 (b)

[0079] By comparing the point formed by n1 and m1 with the compression-bending yield criterion, the yield condition of the current soft rock tunnel confined concrete box steel arch can be obtained.

[0080] The technical features of the above embodiments may be combined in any manner. To simplify the description, not all possible combinations of the technical features in the above embodiments are described. Only preferred embodiments of the present invention are presented. While the description is relatively specific and detailed, it should not be construed as limiting the scope of the present invention. As long as there are no conflicts in the combination of these technical features, they should be considered to be within the scope of this specification.

[0081] It should be noted that, for those skilled in the art, various modifications and improvements can be made without departing from the scope of the present invention, and these modifications and improvements fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A yield determination method for a confined concrete box steel arch in a soft rock tunnel, characterized by: The following steps are involved: Step S1: Under the ultimate limit state, for the confined concrete box steel arch section, calculate the ultimate axial compressive bearing capacity N according to the stress distribution u and pure bending ultimate bearing capacity M u ; Step S2: derive the expressions of the cross-sectional axial force N and bending moment M according to the cross-sectional stress state; Step S3: The axial compression limit bearing capacity N u , Pure bending ultimate bearing capacity M u , the cross-sectional axial force N and bending moment M are dimensionless to obtain the compression-bending yield criterion of the confined concrete box steel arch cross-section; Step S4: Decompose the confined concrete box steel arch frame to be measured using the structural mechanics force method to obtain the current axial force F Nφ and the current bending moment M φ Calculation formula: Step S5: The current axial force F Nφ and the current bending moment M φ Substitute the compression-bending yield criterion into the criterion, and obtain the yield condition of the confined concrete box steel arch to be measured according to the generalized yield function of the section; In step S1, the axial compressive ultimate bearing capacity N u and pure bending ultimate bearing capacity M u The expression is: Where b is the width of the confined concrete box steel arch frame; t1 is the thickness of the upper and lower steel plates; h is the height of the confined concrete box steel arch frame; t2 is the thickness of the left and right steel plates; t3 is the thickness of the middle steel plate; σ s and σ c are the tensile and compressive yield limits of steel and the compressive yield limit of concrete, respectively; h1 represents the position of the neutral axis in the pure bending state without axial force; Step S3 includes: Step S31: non-dimensionalizing the cross-sectional axial force N and bending moment M to obtain a dimensionless implicit function of the cross-sectional area of ​​the confined concrete box steel arch frame; Step S32: collecting steel parameters and concrete parameters of the confined concrete box steel arch to be measured; Step S33: Substitute the steel material parameters and concrete parameters into the dimensionless expressions of the cross-sectional axial force N and the bending moment M to obtain the compression-bending yield criterion.

2. The yield determination method for a confined concrete box steel arch in a soft rock tunnel according to claim 1 is characterized by: In step S2, the expressions of the cross-sectional axial force N and bending moment M are: Where h0 represents the position moved between -h1 and h / 2.

3. The yield determination method for a confined concrete box steel arch in a soft rock tunnel according to claim 1, characterized in that: The expression of the dimensionless implicit function in step S31 is: Where n and m are the dimensionless axial force and dimensionless bending moment, respectively; b represents the width of the confined concrete box steel arch; t1 represents the thickness of the upper and lower steel plates; h represents the height of the confined concrete box steel arch; t2 represents the thickness of the left and right steel plates; t3 represents the thickness of the middle steel plate; σ s and σ c They are the tensile and compressive yield limits of steel and the compressive yield limit of concrete respectively; h1 represents the position of the neutral axis in the pure bending state without axial force; h0 represents the position moving between -h1 and h / 2.

4. The yield determination method for a confined concrete box steel arch in a soft rock tunnel according to claim 1 is characterized in that: The compressive yield limit of concrete in the dimensionless expressions of the cross-sectional axial force N and the bending moment M in step S33 is set to zero to obtain the compression-bending yield criterion of the box section.

5. The yield determination method for a confined concrete box steel arch in a soft rock tunnel according to claim 1 is characterized in that: The concrete compressive yield limit and the section parameter t2 in the dimensionless expressions of the section axial force N and the bending moment M in step S33 are set to zero, and the compression-bending criterion of the H-shaped steel section is obtained.

6. The yield determination method for a confined concrete box steel arch in a soft rock tunnel according to claim 1, characterized in that: In step S4, the current axial force F Nφ and the current bending moment M φ The calculation formula is: F Nφ =q1R(sin 2 φ+λcos 2 f); Where, It is the clockwise angle with the vertical diameter, with a value range of 0 to π; R represents the arch radius; q1 represents the vertical load borne by the arch; q2 represents the horizontal load; λ = q1 / q2 represents the lateral pressure coefficient.

7. The yield determination method for a confined concrete box steel arch in a soft rock tunnel according to claim 1, characterized in that: Step S5 includes: Step S51: Obtain the current axial force F Nφ and the current bending moment M φ The dimensionless expression of ; Step S52: The current axial force F Nφ and the current bending moment M φ The dimensionless expression of is brought into the yield criterion; Step S53: determining the yield condition of the confined concrete box steel arch to be measured according to the cross-section generalized yield function.

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