Method for determining yield of confined concrete box-type steel arch of soft rock tunnel

Abstract

The invention provides a yield judgment method for a confined concrete box-type steel arch of a soft rock tunnel, which comprises the following steps: in a limit state, for the cross section of the confined concrete box-type steel arch, obtaining an axial pressure limit bearing capacity Nu and a pure bending limit bearing capacity Mu according to stress distribution; deriving expressions of section axial force N and bending moment M according to the section stress state; according to the axial pressure ultimate bearing capacity Nu and the pure bending ultimate bearing capacity Mu, the section axial force N and the bending moment M are nondimensionalized, and the bending yield criterion of the confined concrete box type steel arch section is obtained; the method comprises the following steps: decomposing a confined concrete box-type steel arch to be measured by adopting a structural mechanical force method to obtain a calculation formula of a current axial force FN phi and a current bending moment M phi; the current axial force FN phi and the current bending moment M phi are substituted into a bending yield criterion, and the yield condition of the confined concrete box type steel arch to be measured is obtained according to a cross section generalized yield function. The yield condition of the supporting structure is clear, and the design which is too conservative or too high in risk is avoided.

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-type steel arch. Background Art

[0002] As a new type of support, constrained concrete arches have attracted much attention due to their practicality and economic benefits. Although the technology is still in the initial stage of development, its great potential and research value have already emerged. For example, when facing a fault zone, the surrounding rock of the tunnel is difficult to support. By using constrained concrete arches to replace traditional H-shaped steel supports, the problem of insufficient support strength has been successfully solved, effectively preventing the collapse of the tunnel and passing through the fault zone smoothly. The application of constrained concrete arches saves steel compared to traditional steel arches, bringing significant economic and social benefits. In the construction of subway tunnels, the use of constrained concrete arches has also greatly reduced costs.

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

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

[0007] Step S2: derive expressions of section axial force N and bending moment M according to the section 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 the bending moment M are dimensionless, and the compression-bending yield criterion of the cross-sectional area of ​​the restrained concrete box-shaped steel arch is obtained;

[0009] Step S4: Decompose the constrained 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 of

[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 constrained concrete box steel arch frame to be measured is obtained according to the generalized yield function of the section.

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

[0012]

[0013] Where b represents the width of the confined concrete box steel arch frame; t1 represents the thickness of the upper and lower steel plates; h represents the height of the confined concrete box steel arch frame; 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.

[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 comprises:

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

[0019] Step S32: collecting steel material parameters and concrete parameters of the constrained concrete box steel arch frame 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 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 expression of the dimensionless section axial force N and bending moment M in step S33 is set to zero to obtain the compression-bending yield criterion of the box section.

[0026] Preferably, the concrete compressive yield limit and the cross-sectional parameter t2 in the expressions of the dimensionless cross-sectional axial force N and bending moment M in step S33 are taken as zero, so as to obtain 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] In the formula, It is the clockwise angle with the vertical diameter, and its value range is 0~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 comprises:

[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 introduced 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 in 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, help 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 A schematic diagram of a method flow of an embodiment of the present invention;

[0037] Figure 2 It 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 of an embodiment of the present invention;

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

[0040] Figure 5 It is a schematic diagram of mechanical analysis of a soft rock tunnel confined concrete box steel arch frame 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 in the embodiments of the present invention. Obviously, the described embodiments are only 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 ordinary technicians in this field without creative work belong to the protection scope of the present invention.

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

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

[0044] Specifically, the tunnel steel arch section is mainly in a compression-bending state. Based on this result, the yield criterion for the confined concrete box section is derived. Since the section contains two materials, steel and concrete, the specific assumptions in the derivation are as follows:

[0045] (1) The position of the neutral axis of the compression-bending member under the elastic limit load is the same as the position of the neutral axis 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 compression is borne by both concrete and steel, the tension is borne only by steel, and the stress is distributed in a rectangular shape along the cross section.

[0047] Confined concrete box section 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 represents the width of the confined concrete box steel arch frame; t1 represents the thickness of the upper and lower steel plates; h represents the height of the confined concrete box steel arch frame; 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.

[0050] Step S2: Derive expressions of section axial force N and bending moment M according to the section stress state.

[0051] Specifically, for Figure 2 For the confined concrete box section shown in the figure, 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 the material strength parameters is established by the equilibrium condition of the section force:

[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 there are axial force and bending moment 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 compression-bending yield criterion of the cross section:

[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] It can be seen from equations (6) and (7) 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, the concrete compression yield limit in the above formula is set to zero, and the compression and bending yield criterion of the box section can be obtained. At the same time, on this basis, the section parameter t2 is set to zero, and the compression and bending criterion of the H-shaped steel section can also be obtained. In this embodiment, according to different structures and parameters, the compression and bending yield criterion of different types of sections is statistically analyzed 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 in the figure. The physical meaning of the m-n curve is that for the dimensionless axial force n and dimensionless bending moment m calculated from the axial force N and bending moment M of the component, if they are within the positive envelope range of the m-n curve and the coordinate axes, the component is in a safe state without the risk of strength failure; otherwise, it reaches the ultimate state of combined compression and bending and strength failure occurs. For the arch frame, the m-n curve can determine the ultimate state of combined compression and bending of any cross-section, and thus become the overall yield criterion of the arch frame.

[0067] Step S4: Decompose the measured confined 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 confined concrete box steel arch frame is a new type of confined 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 joints of the confined concrete box steel arch frame, high-strength bolts are used for connection, so it can be regarded as an arch frame with equal stiffness as a whole. The mechanical analysis model of the equal-stiffness 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 sectional flexural stiffness of the arch frame member is EI.

[0070] The equal-stiffness steel arch frame structure is a once statically 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:

[0073]

[0074] In the formula, is the angle clockwise from the vertical diameter direction, and the value range is 0 to π.

[0075] Step S5: Substitute the current axial force F Nφ and the current bending moment M φ into the combined compression and bending yield criterion, and obtain the yield situation of the measured confined concrete box steel arch frame according to the sectional generalized yield function.

[0076] 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 value, the material of the arch frame will yield, break, and other damage phenomena, 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 The calculation formula of the internal force of the arch frame and the section bending yield criterion are as follows. The current axial force and the current bending moment are dimensionless. After determining whether they are within the bending yield criterion curve obtained in step S3, the yield condition can be determined.

[0077]

[0078] f(n,m)≤1 (b)

[0079] By comparing the points 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 can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. Only the preferred embodiments of the present invention are expressed. The description is more specific and detailed, but it cannot be understood as limiting the scope of the present invention. As long as there is no contradiction in the combination of these technical features, they should be considered as within the scope of this specification.

[0081] It should be noted that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these modifications and improvements all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A yield determination method for a soft rock tunnel confined concrete box steel arch frame, characterized in that: The following steps are involved: Step S1: Under the limit state, for the confined concrete box steel arch section, the axial compressive ultimate bearing capacity N is calculated according to the stress distribution. u and pure bending ultimate bearing capacity M u ; Step S2: derive expressions of section axial force N and bending moment M according to the section 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 the bending moment M are dimensionless, and the compression-bending yield criterion of the cross-sectional area of ​​the restrained concrete box-shaped steel arch is obtained; Step S4: Decompose the constrained 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 of 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 constrained concrete box steel arch frame to be measured is obtained according to the generalized yield function of the section.

2. The yield determination method of a soft rock tunnel confined concrete box steel arch according to claim 1 is characterized by: In step S1, the axial compression limit bearing capacity N u and pure bending ultimate bearing capacity M u The expression is: Where b represents the width of the confined concrete box steel arch frame; t1 represents the thickness of the upper and lower steel plates; h represents the height of the confined concrete box steel arch frame; 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.

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

4. The yield determination method of a soft rock tunnel confined concrete box steel arch according to claim 1 is characterized in that: Step S3 includes: Step S31: non-dimensionalizing the cross-sectional axial force N and the bending moment M to obtain a dimensionless implicit function of the cross-sectional area of ​​the constrained concrete box-shaped steel arch frame; Step S32: collecting steel material parameters and concrete parameters of the constrained concrete box steel arch frame 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.

5. The yield determination method of a soft rock tunnel confined concrete box steel arch according to claim 4 is characterized in that: The expression of the dimensionless implicit function in step S31 is: Where n and m are 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.

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

7. The yield determination method of a soft rock tunnel confined concrete box steel arch according to claim 4 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.

8. The yield determination method of a soft rock tunnel confined concrete box steel arch according to claim 1 is 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); In the formula, It is the clockwise angle with the vertical diameter, and its value range is 0~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.

9. The yield determination method of a soft rock tunnel confined concrete box steel arch 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 introduced 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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