Support design evaluation method for tunnel shotcrete steel fiber reinforced concrete

Abstract

The application discloses a kind of support design evaluation method of tunnel shotcrete steel fiber reinforced concrete, which comprises the following steps: determining the size of steel fiber reinforced concrete support structure;The tensile region of steel fiber reinforced concrete support structure is detected;The pre-crack height of tensile region is calculated;The tensile stress of tensile region after reduction is calculated;The position after the rise of neutral axis is solved;The actual bending moment value of cracking state of tensile region is calculated;The crack height of tensile region after correction is solved according to actual bending moment value;The actual crack width of tensile region is calculated according to the crack height of tensile region after correction;The actual crack width of tensile region and the limit crack width are compared to determine the support design evaluation result of tunnel shotcrete steel fiber reinforced concrete.The application reflects the characteristics of the rise of neutral axis when steel fiber reinforced concrete support structure is in flexural failure, and also considers the characteristics of tensile stress reduction after cracking of steel fiber reinforced concrete support structure, so that the evaluation result is more accurate and reasonable.

Description

Technical Field

[0001] This invention relates to the field of shotcrete support structures for tunnels, and more specifically to a method for evaluating the design of shotcrete steel fiber reinforced concrete support structures for tunnels. Background Technology

[0002] A tunnel is an engineering structure buried in the earth's strata. Its excavation disrupts the initial stress balance of the strata, leading to ground loosening, surrounding rock instability, and tunnel deformation. The quality of tunnel construction directly depends on the quality of the initial support. Ordinary shotcrete, used for initial tunnel support, has high compressive strength but low tensile strength. The problems with ordinary concrete highlight the advantages of steel fiber reinforced concrete, prompting further research. Steel fiber reinforced concrete is a novel multiphase composite material formed by incorporating randomly distributed steel fibers into ordinary concrete. These randomly distributed steel fibers effectively inhibit the propagation of microcracks and the formation of macrocracks within the concrete, significantly improving its tensile and crack resistance, thus resulting in better load-bearing capacity. Therefore, steel fiber reinforced concrete is increasingly widely used as an initial support structure for tunnels, especially those under high ground stress.

[0003] A survey of the current research status of steel fiber reinforced concrete both domestically and internationally reveals several shortcomings in existing methods for evaluating the support design of steel fiber reinforced concrete.

[0004] (1) It does not reflect the characteristic of the neutral axis rising when the steel fiber reinforced concrete support structure fails under bending;

[0005] (2) The design results are conservative because the characteristics of tensile stress reduction after cracking of steel fiber reinforced concrete support structure are not considered.

[0006] (3) The maximum crack height is 70% of the component thickness, which does not conform to the actual crack height. The actual crack height needs to be calculated.

[0007] Therefore, it is urgent to establish a comprehensive design and evaluation method for steel fiber reinforced concrete support. Summary of the Invention

[0008] To address the aforementioned shortcomings in existing technologies, this invention provides a method for evaluating the support design of shotcrete steel fiber reinforced concrete in tunnels. By considering the reduction of tensile stress in the tension zone and the rise of the neutral axis, the actual crack width is calculated, thereby making the evaluation results more accurate and reasonable.

[0009] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0010] A method for evaluating the support design of shotcrete steel fiber reinforced concrete tunnels includes the following steps:

[0011] S1. Determine the dimensions of the steel fiber reinforced concrete support structure;

[0012] S2. Based on the dimensions of the steel fiber reinforced concrete support structure in step S1, the tension zone of the steel fiber reinforced concrete support structure is tested.

[0013] S3. Calculate the predicted crack height in the tension zone;

[0014] S4. Calculate the reduced tensile stress in the tensile zone based on the predicted crack height in the tensile zone in step S3.

[0015] S5. Based on the tensile stress in the tension zone after reduction and the stress-strain relationship of the cross section in step S4, determine the position of the neutral axis after it rises.

[0016] S6. Calculate the actual bending moment value of the tensile zone cracking state based on the tensile stress reduced in step S4 and the position of the neutral axis after rising in step S5.

[0017] S7. Based on the actual bending moment value of the tensile zone cracking state in step S6, calculate the corrected crack height in the tensile zone.

[0018] S8. Calculate the actual crack width in the tensile zone based on the crack height corrected in step S7.

[0019] S9. Determine whether the actual crack width in the tension zone in step S8 is greater than the limit crack width; if so, increase the size of the steel fiber reinforced concrete support structure and jump to step S1; otherwise, determine that the size of the steel fiber reinforced concrete support structure in step S1 meets the safety specifications.

[0020] Furthermore, step S2 includes the following sub-steps:

[0021] S21. Calculate the uniformly distributed load acting on the steel fiber reinforced concrete beam, expressed as:

[0022] q = γ z h d Where: q is the uniformly distributed load acting on the steel fiber reinforced concrete beam, γ z For the surrounding rock density, h d This is the equivalent deformation pressure height value;

[0023] S22. Based on the uniformly distributed load acting on the steel fiber reinforced concrete beam in step S21, calculate the cross-sectional force in the tension zone of the steel fiber reinforced concrete support structure, expressed as:

[0024]

[0025] Where: M is the cross-sectional force in the tension zone of the steel fiber reinforced concrete support structure, and L is the span length of the steel fiber reinforced concrete beam;

[0026] S23. Calculate the flexural bearing capacity of the tension zone of a steel fiber reinforced concrete support structure, expressed as:

[0027]

[0028] Where: M max γ is the flexural bearing capacity of the tension zone of the steel fiber reinforced concrete support structure, γ is the plastic influence coefficient of the section modulus, and f is the bending capacity of the tension zone of the steel fiber reinforced concrete support structure. ftk , where b is the standard value of the axial tensile strength of steel fiber reinforced concrete, and h is the cross-sectional width and height.

[0029] S24. Determine whether the cross-sectional force in the tension zone of the steel fiber reinforced concrete support structure in step S22 is greater than the bending bearing capacity of the tension zone of the steel fiber reinforced concrete support structure in step S23. If so, determine that the steel fiber reinforced concrete support structure is cracked and proceed to step S3. Otherwise, determine that the dimensions of the steel fiber reinforced concrete support structure in step S1 meet the safety specifications.

[0030] Further, in step S3, the predicted crack height in the tension zone is calculated, expressed as:

[0031]

[0032] Where: x is the predicted crack height in the tension zone. denoted as , where is the distance between the neutral axis and the edge of the tension zone in the uncracking limit state, and z is the distance from the neutral axis at the crack tip in the cracked state.

[0033] Furthermore, step S4 includes the following sub-steps:

[0034] S41. Based on the fitting relationship between the mid-span deflection and the predicted crack height in the tension zone, the formula for calculating the mid-span deflection is determined, expressed as:

[0035]

[0036] Where: l is the mid-span deflection, x is the predicted crack height in the tension zone, and h is the section height;

[0037] S42. Based on the principle that the equivalent tensile force before and after cracking in the tension zone is equal, calculate the tensile stress in the tension zone under the ultimate limit state without cracking, expressed as:

[0038]

[0039] Where: σ max γ is the tensile stress in the tension zone under the uncracking limit state, γ is the plastic influence coefficient of the section modulus, and f is the tensile stress in the tension zone. ftk This refers to the standard value of the axial tensile strength of steel fiber reinforced concrete.

[0040] S43. Based on the formula for calculating the mid-span deflection in step S41 and the tensile stress in the tension zone under the uncracked limit state in step S42, calculate the reduced tensile stress in the tension zone, expressed as:

[0041]

[0042] Where: σ tf This represents the tensile stress after reduction in the tension zone.

[0043] Furthermore, step S5 includes the following sub-steps:

[0044] S51. Based on the similar triangle relationship, the relationship between the compressive stress in the compression zone and the position of the neutral axis after its ascent is determined by the following formula:

[0045]

[0046] Where: f c The stress is the compressive stress in the compression zone, h is the section height, h′ is the position of the neutral axis after it has risen, and f is the cross-sectional height. fc =γf ftk γ is the plastic influence coefficient of the section modulus, f ftk This refers to the standard value of the axial tensile strength of steel fiber reinforced concrete.

[0047] S52. Substituting the relationship between the compressive stress in the compression zone and the position of the neutral axis after its ascent in step S51 into the function of the compressive stress in the compression zone, it can be expressed as:

[0048]

[0049] Where: σ(y) is the function of compressive stress in the compression zone, and y is the distance of the compression zone from the neutral axis;

[0050] S53. Based on the tensile stress reduced in the tension zone in step S4, the stress-strain relationship of the cross section, and the functional expression of the compressive stress in the compression zone after substituting the relationship between the compressive stress in the compression zone and the position of the neutral axis after its rise in sub-step S52, solve for the position of the neutral axis after its rise, which is expressed as:

[0051]

[0052] Where: N k σ represents the actual axial force value in the tensile zone cracking state. tf denoted as σb, where σb is the cross-sectional width and σh is the cross-sectional height.

[0053] Further, in step S6, the actual bending moment value of the tensile zone crack state is calculated, expressed as:

[0054]

[0055] Where: M k σ is the actual bending moment value in the tension zone cracking state. tf σ is the tensile stress in the tension zone after reduction, h' is the position of the neutral axis after it rises, h is the section height, b is the section width, σ(y) is the function of the compressive stress in the compression zone, and y is the distance of the compression zone from the neutral axis.

[0056] Furthermore, step S7 includes the following sub-steps:

[0057] S71. Determine the relationship between the corrected crack height in the tension zone and the position of the neutral axis after it rises.

[0058] S72, the relationship between the actual bending moment value of the tensile zone in the cracked state in step S6 and the position of the neutral axis after the correction in step S71, and the solution for the corrected crack height are expressed as:

[0059]

[0060] Where: h' is the position of the neutral axis after elevation, x′ is the corrected crack height, b is the section width, h is the section height, γ is the plastic influence coefficient of the section modulus, and f ftk M is the standard value of the axial tensile strength of steel fiber reinforced concrete. k This represents the actual bending moment value in the cracked state of the tension zone.

[0061] Furthermore, step S8 includes the following sub-steps:

[0062] S81. Based on the fitting relationship between mid-span deflection and predicted crack height in the tension zone, determine the relationship between the actual crack width in the tension zone and the predicted crack height in the tension zone.

[0063] Furthermore, the actual crack width in the tension zone is calculated and expressed as:

[0064]

[0065] Where: w is the actual crack width in the tension zone, l is the mid-span deflection, L is the span length of the tension zone of the steel fiber reinforced concrete support structure, x′ is the corrected crack height, and h is the section height.

[0066] The beneficial effects of this invention are as follows:

[0067] (1) This invention reflects the characteristic of the neutral axis rising when the steel fiber reinforced concrete support structure fails under bending, and at the same time considers the characteristic of tensile stress reduction after the steel fiber reinforced concrete support structure cracks, so as to make the evaluation results more accurate and reasonable.

[0068] (2) The present invention calculates the actual crack height by taking into account the reduction of tensile stress in the tensile zone, which is more consistent with the actual cracking situation.

[0069] (3) The present invention can design the dimensions of the tunnel steel fiber shotcrete support structure based on the calculated actual crack width, which improves work efficiency, ensures the economic safety of the construction process, and has very important engineering significance. Attached Figure Description

[0070] Figure 1 A flowchart of a method for evaluating the support design of shotcrete steel fiber reinforced concrete in tunnels;

[0071] Figure 2 The diagrams show the stress distribution in the uncracked limit state and the predicted cracking state, where a is the stress distribution in the uncracked limit state and b is the predicted crack height in the tension zone.

[0072] Figure 3 The diagram shows the stress distribution and equivalent diagram of the uncracked limit state, where a is the stress distribution diagram of the uncracked limit state and b is the equivalent diagram of tensile stress in the uncracked limit state.

[0073] Figure 4 These are stress distribution diagrams, where a is the stress distribution diagram of the uncracking limit state and b is the stress distribution diagram of the cracked state.

[0074] Figure 5 Simplified stress and strain distribution diagrams for the cracked section. Detailed Implementation

[0075] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0076] like Figure 1 As shown, a method for evaluating the design of shotcrete support for tunnels includes steps S1-S9:

[0077] S1. Determine the dimensions of the steel fiber reinforced concrete support structure.

[0078] In an optional embodiment of the present invention, the present invention determines the dimensions of the steel fiber reinforced concrete support structure, namely the cross-sectional height h.

[0079] S2. Based on the dimensions of the steel fiber reinforced concrete support structure in step S1, the tension zone of the steel fiber reinforced concrete support structure is tested.

[0080] In an optional embodiment of the present invention, the present invention detects the tension zone of the steel fiber reinforced concrete support structure, that is, determines whether the tension zone of the steel fiber reinforced concrete support structure has cracked. First, the steel fiber reinforced concrete support structure is considered as a pure bending beam member, and the span of the tension zone of the steel fiber reinforced concrete support structure is calculated. Then, the uniformly distributed load acting on the steel fiber reinforced concrete beam is calculated, and then the cross-sectional force and bending bearing capacity of the tension zone of the steel fiber reinforced concrete support structure are calculated. Based on the cross-sectional force and bending bearing capacity of the tension zone of the steel fiber reinforced concrete support structure, it is determined whether the tension zone of the steel fiber reinforced concrete support structure has cracked.

[0081] Step S2 includes the following sub-steps:

[0082] S21. Calculate the uniformly distributed load acting on the steel fiber reinforced concrete beam, expressed as:

[0083] q = γ z h d

[0084] Where: q is the uniformly distributed load acting on the steel fiber reinforced concrete beam, γ z For the surrounding rock density, h d h is the equivalent deformation pressure height value. d =0.33w·e 0.6s w is the tunnel span correction factor, w = 0.2 + 0.1B, B is the tunnel span, s is the surrounding rock grade, and e is the natural constant, which is taken as 2.72.

[0085] S22. Based on the uniformly distributed load acting on the steel fiber reinforced concrete beam in step S21, calculate the cross-sectional force in the tension zone of the steel fiber reinforced concrete support structure, expressed as:

[0086]

[0087] Where: M is the cross-sectional force in the tension zone of the steel fiber reinforced concrete support structure, and L is the span length of the steel fiber reinforced concrete beam, with L taken as 1m.

[0088] S23. Calculate the flexural bearing capacity of the tension zone of a steel fiber reinforced concrete support structure, expressed as:

[0089]

[0090] Where: M max To determine the flexural capacity of the tension zone of a steel fiber reinforced concrete (SFR) supported structure, calculate the flexural capacity M of the tension zone of the SFR supported structure according to the "Code for Design of Concrete Structures" GB50010-2010. max γ is the plastic influence coefficient of the section modulus. γ mThe basic value of the plastic influence coefficient of the section modulus of the concrete support structure is γ, and for rectangular sections it is taken as γ. m =1.55, h is the section height. When h < 400mm, take h = 400mm; when h > 1600mm, take h = 1600mm, f ftk f is the standard value of the axial tensile strength of steel fiber reinforced concrete. ftk =f tk (1+a t λ f )×k tf f tk According to the standard value of axial tensile strength of concrete determined in the current "Code for Design of Concrete Structures" GB50010-2010, a t k is the influence coefficient of steel fiber on the axial tensile strength of steel fiber reinforced concrete. tf λ is the influence coefficient of the cross-sectional height of the steel fiber member on its tensile strength. f This represents the characteristic value of steel fiber content. ρ f For steel fiber volume fraction, l f d represents the length of the steel fiber. f denoted as the diameter or equivalent diameter of the steel fiber, and b as the cross-sectional width, where b is 1m.

[0091] S24. Determine whether the cross-sectional force in the tension zone of the steel fiber reinforced concrete support structure in step S22 is greater than the bending bearing capacity of the tension zone of the steel fiber reinforced concrete support structure in step S23. If so, determine that the steel fiber reinforced concrete support structure is cracked and proceed to step S3. Otherwise, determine that the dimensions of the steel fiber reinforced concrete support structure in step S1 meet the safety specifications.

[0092] S3. Calculate the predicted crack height in the tension zone.

[0093] In an optional embodiment of the present invention, if cracking of the steel fiber reinforced concrete support structure is determined through step-by-step detection, the present invention needs to calculate the predicted crack height in the tension zone.

[0094] Specifically, the distance from the neutral axis to the edge of the tension zone in the uncracking limit state of the steel fiber reinforced concrete support structure is: In the cracked state, the actual tensile stress at the crack incision end is equal to the ultimate bearing tensile stress, and the distance from the neutral axis is y. Figure 2 As shown.

[0095] This invention calculates the predicted crack height in the tension zone, expressed as:

[0096]

[0097] Where: x is the predicted crack height in the tension zone. denoted as , where is the distance between the neutral axis and the edge of the tension zone in the uncracking limit state, and z is the distance from the neutral axis at the crack tip in the cracked state.

[0098] S4. Calculate the reduced tensile stress in the tensile zone based on the predicted crack height in the tensile zone in step S3.

[0099] In an optional embodiment of the present invention, the present invention considers the characteristics of tensile stress reduction after cracking of steel fiber reinforced concrete support structures, and therefore calculates the reduced tensile stress in the tension zone to make the tensile stress in the tension zone more consistent with the actual situation. The present invention first needs to determine the fitting relationship between the mid-span deflection and the predicted crack height in the tension zone, and then determine the relationship between the tensile stress in the tension zone and the predicted crack height in the tension zone under the uncracking limit state, such as... Figure 3 As shown, based on the fact that the equivalent tensile force in the tension zone before and after the crack-free limit state of the steel fiber reinforced concrete support structure is equal, the relationship between the tensile stress in the tension zone and the predicted crack height in the tension zone under the crack-free limit state can be obtained. Finally, the reduced tensile stress in the tension zone can be calculated.

[0100] Step S4 includes the following sub-steps:

[0101] S41. Based on the fitting relationship between the mid-span deflection and the predicted crack height in the tension zone, the formula for calculating the mid-span deflection is determined, expressed as:

[0102]

[0103] Where: l is the mid-span deflection, x is the predicted crack height in the tension zone, and h is the section height.

[0104] S42. Based on the principle that the equivalent tensile force before and after cracking in the tension zone is equal, calculate the tensile stress in the tension zone under the ultimate limit state without cracking, expressed as:

[0105]

[0106] Where: σ max γ is the tensile stress in the tension zone under the uncracking limit state, γ is the plastic influence coefficient of the section modulus, and f is the tensile stress in the tension zone. ftk This is the standard value for the axial tensile strength of steel fiber reinforced concrete.

[0107] S43. Based on the formula for calculating the mid-span deflection in step S41 and the tensile stress in the tension zone under the uncracked limit state in step S42, calculate the reduced tensile stress in the tension zone, expressed as:

[0108]

[0109] Where: σ tf This represents the tensile stress after reduction in the tension zone.

[0110] S5. Based on the tensile stress and cross-sectional stress-strain relationship after the reduction in the tension zone in step S4, determine the position of the neutral axis after it rises.

[0111] In an optional embodiment of the present invention, in order to reflect the characteristic of the neutral axis rising when the steel fiber reinforced concrete support structure fails under bending, the present invention solves for the position of the neutral axis after it rises, so that the obtained position of the neutral axis is more accurate.

[0112] Step S5 includes the following sub-steps:

[0113] S51. Based on the similar triangle relationship, the relationship between the compressive stress in the compression zone and the position of the neutral axis after its ascent is determined by the following formula:

[0114]

[0115] Where: f c The stress is the compressive stress in the compression zone, h is the section height, h′ is the position of the neutral axis after it has risen, and f is the cross-sectional height. fc =γf ftk γ is the plastic influence coefficient of the section modulus, f ftk This is the standard value for the axial tensile strength of steel fiber reinforced concrete.

[0116] Specifically, in the uncracking limit state of a steel fiber reinforced concrete support structure, the compressive stress in the compression zone is equal to the tensile stress in the tension zone, i.e., f fc =γf ftk After cracking, the height of the compression zone and the compressive stress decrease, which can be obtained from similar triangles:

[0117] have to:

[0118] like Figure 4 As shown, by transforming this formula, the relationship between the compressive stress in the compression zone and the position of the neutral axis after it rises can be determined.

[0119] S52. Substituting the relationship between the compressive stress in the compression zone and the position of the neutral axis after its ascent in step S51 into the function of the compressive stress in the compression zone, it can be expressed as:

[0120]

[0121] Where: σ(y) is the function of compressive stress in the compression zone, and y is the distance of the compression zone from the neutral axis.

[0122] Specifically, in this step, the tensile stress in the tension zone of the cracked section of the steel fiber reinforced concrete support structure is equivalent to a uniformly distributed tensile stress, and the compressive stress in the compression zone is equivalent to a triangular distribution calculation. Figure 5 As shown.

[0123] S53. Based on the tensile stress reduced in the tension zone in step S4, the stress-strain relationship of the cross section, and the functional expression of the compressive stress in the compression zone after substituting the relationship between the compressive stress in the compression zone and the position of the neutral axis after its rise in sub-step S52, solve for the position of the neutral axis after its rise, which is expressed as:

[0124]

[0125] Where: N k σ represents the actual axial force value in the tensile zone cracking state. tf denoted as the tensile stress after reduction in the tension zone, b is the cross-sectional width (1m), and h is the cross-sectional height.

[0126] S6. Based on the tensile stress reduced in the tension zone in step S4 and the position of the neutral axis after rising in step S5, calculate the actual bending moment value of the tension zone cracking state.

[0127] In an optional embodiment of the present invention, the actual bending moment value of the tensile zone cracking state is calculated by the cross-sectional stress-strain relationship bending moment equation based on the tensile stress reduced in the tensile zone in step S4 and the position of the neutral axis after rising in step S5.

[0128] This invention calculates the actual bending moment value of the cracked state in the tension zone, expressed as:

[0129]

[0130] Where: M k σ is the actual bending moment value in the tension zone cracking state. tf Let σ(y) be the tensile stress after reduction in the tension zone, h' be the position of the neutral axis after it rises, h be the section height, b be the section width (b is taken as 1m), σ(y) be the function of the compressive stress in the compression zone, and y be the distance of the compression zone from the neutral axis.

[0131] S7. Based on the actual bending moment value of the tensile zone cracking state in step S6, calculate the corrected crack height in the tensile zone.

[0132] In an optional embodiment of the present invention, the present invention can solve for the corrected crack height in the tension zone based on the actual bending moment value of the cracked state in the tension zone in step S6 and based on the equilibrium state of cracking in the steel fiber reinforced concrete support structure.

[0133] Step S7 includes the following sub-steps:

[0134] S71. Determine the relationship between the corrected crack height in the tension zone and the position of the neutral axis after it rises.

[0135] Specifically, by combining the expression for calculating the reduced tensile stress in the tension zone in step S43 and the expression for solving the position of the neutral axis after its rise in step S53, the relationship between the corrected crack height in the tension zone and the position of the neutral axis after its rise can be determined.

[0136] S72, the relationship between the actual bending moment value of the tensile zone in the cracked state in step S6 and the position of the neutral axis after the correction in step S71, and the solution for the corrected crack height are expressed as:

[0137]

[0138] Where: h' is the position of the neutral axis after elevation, x′ is the corrected crack height, b is the cross-sectional width (b is 1m), h is the cross-sectional height, γ is the plastic influence coefficient of the section modulus, and f ftk M is the standard value of the axial tensile strength of steel fiber reinforced concrete. k This represents the actual bending moment value in the cracked state of the tension zone.

[0139] Specifically, the relationship between the corrected crack height in the tension zone and the position of the neutral axis after its ascent in step S71 of this invention, and the expression for solving the corrected crack height in this step, are as follows: Figure 5 As shown, the bending moment M can be obtained from the stress-strain relationship of the cross section. k and axial force N k Therefore, an equation containing only the corrected crack height can be determined, and solving this equation will yield the specific value of the corrected crack height.

[0140] S8. Calculate the actual crack width in the tensile zone based on the crack height corrected in step S7.

[0141] Step S8 includes the following sub-steps:

[0142] S81. Based on the fitting relationship between mid-span deflection and predicted crack height in the tension zone, determine the relationship between the actual crack width in the tension zone and the predicted crack height in the tension zone.

[0143] Specifically, based on the fitting relationship between mid-span deflection and the predicted crack height in the tension zone, i.e. the expression for calculating the reduced tensile stress in the tension zone in step S43, the present invention can determine the relationship between the actual crack width in the tension zone and the predicted crack height in the tension zone.

[0144] S82: Based on the corrected crack height in step S7 and the relationship between the actual crack width in the tension zone and the predicted crack height in the tension zone in sub-step S81, calculate the actual crack width in the tension zone, expressed as:

[0145]

[0146] Where: w is the actual crack width in the tension zone, l is the mid-span deflection, L is the span length of the steel fiber reinforced concrete supported beam (L is taken as 1m), x′ is the corrected crack height, and h is the section height.

[0147] S9. Determine whether the actual crack width in the tension zone in step S8 is greater than the limit crack width; if so, increase the size of the steel fiber reinforced concrete support structure and jump to step S1; otherwise, determine that the size of the steel fiber reinforced concrete support structure in step S1 meets the safety specifications.

[0148] In an optional embodiment of the invention, the limiting crack width w max According to the provisions of Table 3.4.5 in the "Code for Design of Concrete Structures" GB50010-2020, w is selected. max =0.2mm, the specific width can be adjusted and controlled according to the on-site design requirements. Then compare the actual crack width w in the tension zone with the ultimate crack width w in step S8. max If the actual crack width in the tension zone is less than or equal to the ultimate crack width, the dimensions of the steel fiber reinforced concrete support structure in step S1 are deemed to meet the safety specifications, and the tunnel shotcrete support design is considered reasonable. If the actual crack width in the tension zone is greater than the ultimate crack width, the dimensions of the steel fiber reinforced concrete support structure in step S1 are deemed not to meet the safety specifications, the tunnel shotcrete support design is considered unreasonable, and the dimensions of the steel fiber reinforced concrete support structure are increased. This invention considers the influence of the size effect of the steel fiber reinforced concrete support structure on the standard value of the axial tensile strength of steel fiber reinforced concrete by referring to the component size factor, as shown in Table 1.

[0149] Table 1. Influence coefficient of cross-sectional height of steel fiber members on tensile strength

[0150]

[0151] Then proceed to step S1 and repeat the above steps until the dimensions of the steel fiber reinforced concrete support structure meet the safety specifications.

[0152] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for evaluating the design of shotcrete-supported tunnels with steel fiber reinforced concrete, characterized in that, Includes the following steps: S1. Determine the dimensions of the steel fiber reinforced concrete support structure; S2. Based on the dimensions of the steel fiber reinforced concrete support structure in step S1, the tension zone of the steel fiber reinforced concrete support structure is tested. S3. Calculate the predicted crack height in the tension zone; S4. Calculate the reduced tensile stress in the tensile zone based on the predicted crack height in the tensile zone in step S3. S5. Based on the tensile stress in the tension zone after reduction and the stress-strain relationship of the cross section in step S4, determine the position of the neutral axis after it rises. S6. Calculate the actual bending moment value of the tensile zone cracking state based on the tensile stress reduced in step S4 and the position of the neutral axis after rising in step S5. S7. Based on the actual bending moment value of the tensile zone cracking state in step S6, calculate the corrected crack height in the tensile zone. S8. Calculate the actual crack width in the tensile zone based on the crack height corrected in step S7. S9. Determine whether the actual crack width in the tension zone in step S8 is greater than the limit crack width; if so, increase the size of the steel fiber concrete support structure and jump to step S1; otherwise, determine that the size of the steel fiber concrete support structure in step S1 meets the safety specifications. Step S7 includes the following sub-steps: S71. Determine the relationship between the corrected crack height in the tension zone and the position of the neutral axis after it rises. S72, the relationship between the actual bending moment value of the tensile zone in the cracked state in step S6 and the position of the neutral axis after the correction in step S71, and the solution for the corrected crack height are expressed as: in: This is the position after the neutral axis rises. The corrected crack height. b For the cross-sectional width, h For the cross-sectional height, The plastic influence coefficient of the section modulus. This refers to the standard value of the axial tensile strength of steel fiber reinforced concrete. This represents the actual bending moment value in the tension zone cracking state. Step S8 includes the following sub-steps: S81. Based on the fitting relationship between mid-span deflection and predicted crack height in the tension zone, determine the relationship between the actual crack width in the tension zone and the predicted crack height in the tension zone. S82. Based on the corrected crack height in step S7 and the relationship between the actual crack width in the tension zone and the predicted crack height in the tension zone in sub-step S81, calculate the actual crack width in the tension zone, expressed as: in: w This represents the actual crack width in the tension zone. l For mid-span deflection, L The span length of the tension zone of the steel fiber reinforced concrete support structure. The corrected crack height. h This represents the cross-sectional height.

2. The method for evaluating the support design of shotcrete steel fiber reinforced concrete tunnels according to claim 1, characterized in that, Step S2 includes the following sub-steps: S21. Calculate the uniformly distributed load acting on the steel fiber reinforced concrete beam, expressed as: in: q This refers to a uniformly distributed load acting on a steel fiber reinforced concrete beam. The surrounding rock is heavily soiled. This is the equivalent deformation pressure height value; S22. Based on the uniformly distributed load acting on the steel fiber reinforced concrete beam in step S21, calculate the cross-sectional force in the tension zone of the steel fiber reinforced concrete support structure, expressed as: in: M This refers to the cross-sectional force in the tension zone of the steel fiber reinforced concrete support structure. L The span length of the steel fiber reinforced concrete beam; S23. Calculate the flexural bearing capacity of the tension zone of a steel fiber reinforced concrete support structure, expressed as: in: This refers to the flexural bearing capacity of the tension zone in a steel fiber reinforced concrete support structure. The plastic influence coefficient of the section modulus. This refers to the standard value of the axial tensile strength of steel fiber reinforced concrete. b For the cross-sectional width, h The height of the cross section; S24. Determine whether the cross-sectional force in the tension zone of the steel fiber reinforced concrete support structure in step S22 is greater than the bending bearing capacity of the tension zone of the steel fiber reinforced concrete support structure in step S23. If so, determine that the steel fiber reinforced concrete support structure is cracked and proceed to step S3. Otherwise, determine that the dimensions of the steel fiber reinforced concrete support structure in step S1 meet the safety specifications.

3. The method for evaluating the support design of shotcrete steel fiber reinforced concrete tunnels according to claim 1, characterized in that, In step S3, the predicted crack height in the tension zone is calculated, expressed as: in: x To predict the crack height in the tension zone, This represents the distance between the neutral axis and the edge of the tension zone in the uncracking limit state. z This refers to the distance from the neutral axis at the crack tip in the cracked state.

4. The method for evaluating the support design of shotcrete steel fiber reinforced concrete tunnels according to claim 1, characterized in that, Step S4 includes the following sub-steps: S41. Based on the fitting relationship between the mid-span deflection and the predicted crack height in the tension zone, the formula for calculating the mid-span deflection is determined, expressed as: in: l For mid-span deflection, x To predict the crack height in the tension zone, h The height of the cross section; S42. Based on the principle that the equivalent tensile force before and after cracking in the tension zone is equal, calculate the tensile stress in the tension zone under the ultimate limit state without cracking, expressed as: in: This represents the tensile stress in the tension zone under the limit state before cracking. The plastic influence coefficient of the section modulus. This refers to the standard value of the axial tensile strength of steel fiber reinforced concrete. S43. Based on the formula for calculating the mid-span deflection in step S41 and the tensile stress in the tension zone under the uncracked limit state in step S42, calculate the reduced tensile stress in the tension zone, expressed as: in: This represents the tensile stress after reduction in the tension zone.

5. The method for evaluating the support design of shotcrete steel fiber reinforced concrete in tunnels according to claim 1, characterized in that, Step S5 includes the following sub-steps: S51. Based on the similar triangle relationship, the relationship between the compressive stress in the compression zone and the position of the neutral axis after its ascent is determined by the following formula: in: For compressive stress in the compression zone, h For the cross-sectional height, This is the position after the neutral axis rises. , The plastic influence coefficient of the section modulus. This refers to the standard value of the axial tensile strength of steel fiber reinforced concrete. S52. Substituting the relationship between the compressive stress in the compression zone and the position of the neutral axis after its ascent in step S51 into the function of the compressive stress in the compression zone, it can be expressed as: in: The expression for the compressive stress in the compression zone is given by the function of the expression for the compressive stress in the compression zone. y This represents the distance from the compressed region to the neutral axis. S53. Based on the tensile stress reduced in the tension zone in step S4, the stress-strain relationship of the cross section, and the functional expression of the compressive stress in the compression zone after substituting the relationship between the compressive stress in the compression zone and the position of the neutral axis after its rise in sub-step S52, solve for the position of the neutral axis after its rise, which is expressed as: in: This represents the actual axial force value in the tension zone cracking state. The tensile stress after reduction in the tension zone, b For the cross-sectional width, h This represents the cross-sectional height.

6. The method for evaluating the support design of shotcrete steel fiber reinforced concrete in tunnels according to claim 1, characterized in that, In step S6, the actual bending moment value of the tensile zone crack state is calculated, and expressed as: in: This represents the actual bending moment value in the tension zone cracking state. The tensile stress after reduction in the tension zone, This is the position after the neutral axis rises. h For the cross-sectional height, b For the cross-sectional width, The expression for the compressive stress in the compression zone is given by the function of the expression for the compressive stress in the compression zone. y This represents the distance from the compressed area to the neutral axis.

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