Active support design method for tunnel early-high-strength rock anchoring and shotcreting synergistic effect bearing arch

Abstract

The invention relates to the technical field of civil engineering, and particularly discloses a tunnel early-high-strength rock anchoring and shotcreting synergistic effect bearing arch active support design method which comprises the following steps: determining a rock anchor bearing arch acting load and establishing a rock anchor bearing arch calculation model; calculating to obtain the most unfavorable section displacement and stress of the rock anchor bearing arch; verifying whether the displacement of the rock anchor bearing arch meets the requirement; a safety evaluation method of the pre-stressed anchor rods is provided, and the safety of the pre-stressed anchor rods is evaluated according to a rock anchor bearing arch calculation result; establishing a sprayed concrete calculation model; calculating to obtain the most unfavorable section displacement and stress of the sprayed concrete; a sprayed concrete safety and durability evaluation method is provided; active support parameters are determined according to the calculation result of the rock anchor bearing arch and the calculation result of the sprayed concrete. By means of the method, the safety and durability of rock-anchor-shotcrete active supporting under different supporting parameters can be simply, rapidly and accurately calculated, reference is provided for tunnel engineering design adopting active supporting, and good engineering value is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of civil engineering, and in particular to a tunnel early high-strength rock anchor-spraying synergistic bearing arch active support design method. Background Art

[0002] The New Austrian Tunneling Method (NATM) theory emphasizes taking measures to improve the mechanical properties of the surrounding rock, such as pre-reinforcement, shotcrete reinforcement, rock grouting, etc., so as to improve the self-bearing capacity and stability of the surrounding rock. However, in the current tunnel construction, the passive support of traditional support structures is often preferred. Traditional support has low passive bearing efficiency, numerous components and long time consumption, redundant parameters and poor economy, which makes it difficult to meet the "safety, efficiency and economy" requirements of tunnel construction. When adopting the New Austrian Tunneling Method (NATM) construction concept for tunnel construction, tunnel anchors and shotcrete are two important types of support. Among them, anchor-sprayed support is a key component of the initial support of the tunnel, and its support effect is crucial to the design of the initial support. At present, the deformation of early high-strength rock anchor-shotcrete bearing arch in tunnels has brought great challenges to engineering safety. Domestic and foreign scholars have provided some research basis through analogy design, model verification and field testing. However, the active support design method of early high-strength rock anchor-shotcrete bearing arch in tunnels is still not perfect. Therefore, it is of great significance to construct an active support design method for early high-strength rock anchor-shotcrete bearing arch in tunnels and realize the active support design of anchor-shotcrete bearing arch based on early high-strength rock anchor-shotcrete. Summary of the invention

[0003] In order to solve the problems existing in the prior art, the present invention provides a design method for active support of a tunnel early high-strength rock-anchor-spraying synergistic bearing arch, which can achieve simple, fast and accurate calculation of the safety and durability of rock-anchor-spraying active support under different support parameters, provide a reference for the design of tunnel engineering using active support, and solve the problems mentioned in the above background technology.

[0004] To achieve the above object, the present invention provides the following technical solution: a tunnel early high-strength rock bolt spraying synergistic bearing arch active support design method, comprising the following steps:

[0005] S1. Determine the load acting on the rock anchor bearing arch and establish a calculation model for the rock anchor bearing arch;

[0006] S2. Calculate the most unfavorable cross-sectional displacement and stress of the rock anchor bearing arch according to the calculation model of the rock anchor bearing arch;

[0007] S3. Propose deformation control standards to verify whether the displacement of the rock anchor bearing arch meets the requirements;

[0008] S4. Propose a method for evaluating the safety of prestressed anchor rods and evaluate the safety of prestressed anchor rods based on the calculation results of the rock anchor bearing arch;

[0009] S5. Determine the shotcrete load based on the calculated displacement of the rock anchor bearing arch;

[0010] S6. Establishing a shotcrete calculation model;

[0011] S7. Calculate the most unfavorable cross-sectional stress of shotcrete according to the shotcrete calculation model;

[0012] S8. Propose a method for evaluating the safety and durability of shotcrete;

[0013] S9. Determine the safety and durability of shotcrete based on the calculation results of the shotcrete calculation model;

[0014] S10. Determine active support parameters based on the calculation results of the rock anchor bearing arch and the shotcrete calculation results.

[0015] Preferably, the step S1 specifically includes:

[0016] S11. Establish the equilibrium equation according to the radial stress and strain and tangential stress and strain in the rock mass, bring in the boundary conditions, calculate the stress in the elastic zone of the surrounding rock according to the Lame stress formula, calculate the stress in the plastic zone of the surrounding rock according to the classical chamber theory, and calculate the control radius of the rock anchor bearing at the same time. Finally, obtain the thickness of the rock anchor bearing arch. The formula is as follows:

[0017] L s =F1(R s ,R) (1)

[0018] Where: F1(x) is the calculation function of the rock anchor bearing arch thickness; R s is the control radius of rock anchor bearing, (m); L s is the thickness of the rock anchor bearing arch, (m); R is the radius of the tunnel, m;

[0019] S12. The vertical load of the rock anchor bearing arch is calculated based on the thickness of the rock anchor bearing arch, and then the horizontal load of the rock anchor bearing arch is calculated based on the lateral pressure coefficient value provided in the specification. The formula is as follows:

[0020] q s =F2(L s ,γ) (2)

[0021] e s =F2(q s ,λ) (3);

[0022] Where: F2(x) is the load calculation function of the rock anchor bearing arch; q s is the vertical load of the rock anchor bearing arch, (kPa); e s is the horizontal load of the rock anchor bearing arch, (kPa); γ is the weight of the rock anchor bearing arch, kN / m3 ;λ is the lateral pressure coefficient;

[0023] S13. Determine the calculation model of the rock anchor bearing arch according to the stress state of the bottom of the rock anchor bearing arch. If the bottom of the rock anchor bearing arch is under tension, a tangential force will be generated at the contact surface of the shotcrete-surrounding rock, and the deformation and stress distribution of the rock anchor bearing arch model will change. At this time, the structure is subject to the combined effects of loosening pressure and the tangential force at the contact surface of the shotcrete-surrounding rock. In order to accurately evaluate the stability and safety of the project, it is necessary to establish a mechanical model that comprehensively considers the effects of these two loads. If the bottom of the rock anchor bearing arch is under compression, no tangential force will be generated at the contact surface of the shotcrete-surrounding rock. At this time, the structure is only subject to the loosening pressure.

[0024] Preferably, the step S2 specifically includes:

[0025] S21. According to the thickness of the rock anchor bearing arch, the vertical load and the horizontal load of the rock anchor bearing arch, a mechanical equation is established to obtain the stress and displacement of the most unfavorable section of the rock anchor bearing arch under the loosening pressure. The formula is as follows:

[0026] σ cs =G1(e s ,q s ,L s ) (4)

[0027] σ ts =G1(e s ,q s ,L s ) (5)

[0028] w Cs =G1(e s ,q s ,L s ) (6)

[0029] Where: G1(x) is the calculation function of the most unfavorable cross-sectional stress and displacement of the rock anchor bearing arch under loosening pressure; σ cs is the top stress of the most unfavorable section of the rock anchor bearing arch under loosening pressure, (kPa); σ ts is the bottom stress of the most unfavorable section of the rock anchor bearing arch under loosening pressure, (kPa); w Cs is the displacement of the most unfavorable section of the rock anchor bearing arch under loosening pressure, (m);

[0030] S22. According to the thickness of the rock anchor bearing arch and the tensile stress value at the bottom of the most unfavorable section of the rock anchor bearing arch, a mechanical equation is established to obtain the stress and displacement of the most unfavorable section of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface. The formula is as follows:

[0031] σ' cs =G2(qt ,L s ) (7)

[0032] σ' ts =G2(q t ,L s ) (8)

[0033] w' Cs =G2(q t ,L s ) (9)

[0034] Where: G2(x) is the calculation function of the most unfavorable cross-sectional stress and displacement of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface; q t is the bottom tensile stress of the most unfavorable section of the rock anchor bearing arch under loosening pressure, (kPa); σ′ cs is the top stress of the most unfavorable section of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface, (kPa); σ′ ts is the bottom stress of the most unfavorable section of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface, (kPa); w′ Cs is the displacement of the most unfavorable section of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface, (m);

[0035] S23. Determine the calculation model of the rock anchor bearing arch according to the stress state at the bottom of the rock anchor bearing arch. If the bottom of the rock anchor bearing arch is under tension, the structure is subjected to the combined effect of loosening pressure and the tangential force of the shotcrete-surrounding rock contact surface. The formula is as follows:

[0036] σ cs总 =G3(σ cs ,σ' cs ) (10)

[0037] σ ts总 =G3(σ ts ,σ' ts ) (11)

[0038] w Cs总 =G3(w Cs ,w' Cs ) (12)

[0039] Where: G3(x) is the stress and displacement calculation function of the rock anchor bearing arch when the most unfavorable section is under tension at the bottom; σ cs总 is the final top stress of the rock anchor bearing arch when the most unfavorable section is under tension at the bottom, (kPa); σ ts总 is the final bottom stress of the rock anchor bearing arch when the most unfavorable section is in the bottom tension state, (kPa); w Cs总is the final displacement of the rock anchor bearing arch when the most unfavorable section is under tension at the bottom, (m);

[0040] If the bottom of the rock anchor bearing arch is under pressure, no tangential force will be generated at the contact surface of shotcrete-surrounding rock. At this time, the structure is only affected by the loosening pressure. At this time, the final stress and displacement of the rock anchor bearing arch under the most unfavorable section with the bottom under pressure are equal to the stress and displacement under the loosening pressure.

[0041] Preferably, the step S3 specifically includes:

[0042] S31. Determine the surrounding rock deformation control value u according to the specification w ;

[0043] S32. Determine the surrounding rock deformation control value and the total displacement of the most unfavorable section of the rock anchor bearing arch according to the specifications to determine whether the active support parameters of the rock anchor bearing arch meet the requirements.

[0044] Preferably, the step S4 specifically includes:

[0045] S41. Determine the ultimate elongation of the prestressed anchor rod according to the specification, and combine the length of the prestressed anchor rod to obtain the deformation control value u of the prestressed anchor rod. m ;

[0046] S42. According to the deformation control value of the prestressed anchor rod and the deformation value of the surrounding rock, the safety factor of the prestressed anchor rod is determined and the safety of the prestressed anchor rod is evaluated. The formula is as follows:

[0047] k m =H1(u m ,w Cs总 ) (13)

[0048] Where: H1(x) is the calculation function of the safety factor of the prestressed anchor; k m It is the safety factor of the prestressed anchor rod. If it is greater than 1, it means it is safe, and if it is less than 1, it means it is unsafe.

[0049] Preferably, the step S5 is specifically as follows:

[0050] According to the final displacement value of the surrounding rock calculated by the rock anchor bearing arch calculation model, combined with the radial deformation stiffness and tangential deformation stiffness of the shotcrete, the vertical load and horizontal load on the shotcrete are calculated. The formula is as follows:

[0051] q p =I1(w Cs总 ,K s ,K l ) (14)

[0052] e p =I1(q p ,λ) (15)

[0053] Where: I1(x) is the calculation function of the load on shotcrete; q p is the vertical uniform load on shotcrete, (kPa); e p is the horizontal average load on shotcrete, (kPa); K s is the tangential deformation stiffness of shotcrete, (N / m); K l is the radial deformation stiffness of shotcrete (N / m).

[0054] Preferably, the step S6 is specifically:

[0055] The shotcrete calculation model is determined according to the stress state of the bottom of the rock anchor bearing arch. If the bottom of the rock anchor bearing arch is under tension, the shotcrete-surrounding rock contact surface generates a tangential force. Considering the coordinated deformation, the shotcrete model is subject to the combined effect of the deformation load and the tangential force of the shotcrete-surrounding rock contact surface. In order to accurately evaluate the stability and safety of the project, it is necessary to establish a mechanical model that comprehensively considers the effects of these two loads. If the bottom of the rock anchor bearing arch is under compression, the shotcrete-surrounding rock contact surface does not generate a tangential force, and the shotcrete model is only subject to the deformation load.

[0056] Preferably, the step S7 specifically includes:

[0057] S71. Based on the vertical uniformly distributed load and horizontal load of shotcrete and the thickness of shotcrete, a mechanical equation is established to obtain the stress of the most unfavorable section of shotcrete under the deformation load. The formula is as follows:

[0058] σ cp =J1(e p ,q p ,h) (16)

[0059] σ tp =J1(e p ,q p ,h) (17)

[0060] Where: J1(x) is the most unfavorable cross-sectional stress calculation function of shotcrete under deformation load; σ cp is the top stress of the most unfavorable section of shotcrete under deformation load, (kPa); σ tp is the bottom stress of the most unfavorable section of shotcrete under deformation load, (kPa); h is the thickness of shotcrete, (m);

[0061] S72. According to the thickness of shotcrete and the tensile stress value at the bottom of the most unfavorable section of the rock anchor bearing arch, a mechanical equation is established to obtain the stress of the most unfavorable section of shotcrete under the tangential force of the shotcrete-surrounding rock contact surface. The formula is as follows:

[0062] σ' cp =J2(q t ,h) (18)

[0063] σ' tp =J2(q t ,h) (19)

[0064] Where: J2(x) is the most unfavorable cross-sectional stress calculation function of shotcrete under the tangential force of the shotcrete-surrounding rock contact surface; σ′ cp is the top stress of the most unfavorable section of shotcrete under the tangential force of the shotcrete-surrounding rock contact surface, (kPa); σ′ tp is the bottom stress of the most unfavorable section of the shotcrete under the tangential force of the shotcrete-surrounding rock interface, (kPa);

[0065] S73. Determine the shotcrete calculation model according to the stress state of the bottom of the rock anchor bearing arch. If the bottom of the rock anchor bearing arch is under tension, the shotcrete model is subjected to the combined action of the deformation load and the tangential force of the shotcrete-surrounding rock contact surface. The formula is as follows:

[0066] σ cp总 =J3(σ cp ,σ' cp ) (20)

[0067] σ tp总 =J3(σ tp ,σ' tp ) (twenty one)

[0068] Where: J3(x) is the stress and displacement calculation function of shotcrete when the most unfavorable section is under tension at the bottom; σ cp总 is the final top stress of shotcrete when the most unfavorable section is under tension at the bottom, (kPa); σ tp总 is the final bottom stress of shotcrete when the most unfavorable section is under bottom tension, (kPa);

[0069] If the bottom of the rock anchor bearing arch is under compression, no tangential force will be generated at the contact surface of shotcrete-surrounding rock. At this time, the shotcrete model is only subjected to the deformation load. At this time, the final stress and displacement of the shotcrete under the most unfavorable section with the bottom under compression are equal to the stress and displacement under the deformation load.

[0070] Preferably, the step S8 specifically includes:

[0071] S81. According to the specification, the safety factor control value k of shotcrete is proposed;

[0072] S82. Determine the tangential safety factor of shotcrete based on the strength and thickness of shotcrete. The formula is as follows:

[0073] k q =K1(f t ,σ tp总 )(twenty two)

[0074] Where: K1(x) is the calculation function of the tangential safety factor of shotcrete; f t is the strength of shotcrete, (kPa); k q is the tangential safety factor of shotcrete;

[0075] S83. According to the specification, the calculation method of radial safety factor of shotcrete is proposed, and the formula is as follows:

[0076] k j压 =K2(f ck ,b,h)(23)

[0077] k j拉 =K2(f tk ,b,h)(24)

[0078] Where: K2(x) is the calculation function of radial safety factor of shotcrete; f ck is the ultimate compressive strength of shotcrete, (kPa); f tk is the ultimate tensile strength of shotcrete, (kPa); k j压 k is the radial safety factor of shotcrete under pressure; j拉 is the radial safety factor of shotcrete under tension;

[0079] S84. A durability evaluation method for shotcrete is proposed. The ultimate bearing capacity of shotcrete is calculated based on the weight of shotcrete and the ultimate tensile strength of shotcrete. The cracking load of shotcrete is calculated based on the bending moment and axial force of shotcrete. The formula is as follows:

[0080] σ tk =K3(f tk ,γ)(25)

[0081] σ 裂 =K3(M,N,b,h)(26)

[0082] Where: K3(x) is the calculation function of the bearing capacity and cracking load of shotcrete; σ tk is the bearing capacity of shotcrete, (kPa); σ 裂is the cracking load of shotcrete, (kPa); M is the bending moment of shotcrete; N is the axial force of shotcrete; if the bearing capacity of shotcrete is greater than the cracking load, it means that the shotcrete has not cracked, otherwise it means that it has cracked.

[0083] The beneficial effects of the present invention are as follows: based on the rock-anchor bearing arch calculation model and the shotcrete calculation model, the present invention obtains a tunnel early high-strength rock-anchor-shotcrete synergistic bearing arch active support design method through deformation control standards and shotcrete safety and durability evaluation methods. The calculation process of the obtained method is clear and rigorous, the calculation formula is simple and easy to understand, the calculation process is simple and efficient, and the calculation results are accurate and highly reliable. Ordinary designers can simply, quickly and accurately reproduce the research ideas and processes according to the active fault zone dislocation stratum deformation calculation method obtained by the present invention, thereby calculating the safety and durability of rock-anchor-shotcrete active support under different support parameters, providing a reference for the design of tunnel engineering using active support, and having good engineering value. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 Schematic diagram of the steps of the method of the present invention;

[0085] Figure 2 It is a schematic diagram of a calculation model of a rock anchor bearing arch under loosening pressure provided by an embodiment of the present invention;

[0086] Figure 3 It is a schematic diagram of a calculation model of a rock anchor bearing arch under the action of a tangential force on the shotcrete-surrounding rock contact surface provided by an embodiment of the present invention;

[0087] Figure 4 is a schematic diagram of a shotcrete calculation model under deformation load provided by an embodiment of the present invention;

[0088] Figure 5 It is a schematic diagram of a shotcrete calculation model under the action of tangential force on the shotcrete-surrounding rock contact surface provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0089] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions 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 are within the scope of protection of the present invention.

[0090] See also Figure 1-Figure 5 The present invention provides a technical solution: a tunnel early high-strength rock bolt spraying synergistic bearing arch active support design method, such as Figure 1 As shown, the following steps are included:

[0091] Step 1: Determine the load acting on the rock anchor bearing arch and establish a rock anchor bearing arch calculation model.

[0092] The specific steps include:

[0093] 1) According to the radial stress-strain and tangential stress-strain in the rock mass, the equilibrium equation is established, the boundary conditions are brought in, and then the stress in the elastic zone of the surrounding rock is calculated according to the Lame stress formula, and the stress in the plastic zone of the surrounding rock is calculated according to the classical chamber theory. At the same time, the control radius of the rock anchor bearing is calculated, and finally the thickness of the rock anchor bearing arch is obtained. The formula is as follows:

[0094] L s =R s -R (27)

[0095]

[0096] Where: R s is the control radius of rock anchor bearing, (m); L s is the thickness of the rock anchor bearing arch, (m); R is the radius of the tunnel, m; is the friction angle of the rock anchor bearing arch, °; c is the cohesion of the rock anchor bearing arch, kPa; P0 is the original rock stress of the rock anchor bearing arch, kPa.

[0097] 2) The vertical load of the rock anchor bearing arch is calculated according to the thickness of the rock anchor bearing arch, and then the horizontal load of the rock anchor bearing arch is calculated according to the lateral pressure coefficient value provided by the specification. The formula is as follows:

[0098] q s =γL s (29)

[0099] e s =λq s (30);

[0100] Where: q s is the vertical load of the rock anchor bearing arch, (kPa); e s is the horizontal load of the rock anchor bearing arch, (kPa); γ is the weight of the rock anchor bearing arch, kN / m 3 ;λ is the lateral pressure coefficient;

[0101] 3) Determine the calculation model of the rock anchor bearing arch according to the stress state at the bottom of the rock anchor bearing arch. If the bottom of the rock anchor bearing arch is under tension, a tangential force will be generated at the contact surface of the shotcrete-surrounding rock, and the deformation and stress distribution of the rock anchor bearing arch model will change. At this time, the structure is subject to the combined effects of loosening pressure and the tangential force at the contact surface of the shotcrete-surrounding rock. In order to accurately evaluate the stability and safety of the project, it is necessary to establish a mechanical model that comprehensively considers the effects of these two loads; if the bottom of the rock anchor bearing arch is under compression, no tangential force will be generated at the contact surface of the shotcrete-surrounding rock. At this time, the structure is only subject to the loosening pressure. The calculation model of the rock anchor bearing arch under the action of loosening pressure is shown in the attached figure. Figure 2 The calculation model of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface is shown in the attached figure. Figure 3 shown.

[0102] Step 2: Calculate the most unfavorable cross-sectional displacement and stress of the rock anchor bearing arch according to the rock anchor bearing arch calculation model.

[0103] The specific steps include:

[0104] 1) According to the thickness of the rock anchor bearing arch, the vertical load and the horizontal load of the rock anchor bearing arch, a mechanical equation is established to obtain the stress and displacement of the most unfavorable section of the rock anchor bearing arch under the loosening pressure. The formula is as follows:

[0105]

[0106] Where: cs is the top stress of the most unfavorable section of the rock anchor bearing arch under loosening pressure, (kPa); σ ts is the bottom stress of the most unfavorable section of the rock anchor bearing arch under loosening pressure, (kPa); w Cs is the displacement of the most unfavorable section of the rock anchor bearing arch under loosening pressure, (m); q s is the vertical uniformly distributed load on the rock anchor bearing arch, (kPa); L is the vertical distance from point O to the lowest point of the rock anchor bearing arch, m; H is the distance from the tunnel radius R minus L, m; X1, and M p (θ) is the calculation coefficient; b is taken as 1m; E s is the equivalent elastic modulus of the rock anchor bearing arch, kPa; I s is the equivalent moment of inertia of the rock anchor bearing arch, Nm.

[0107] 2) According to the thickness of the rock anchor bearing arch and the tensile stress value at the bottom of the most unfavorable section of the rock anchor bearing arch, a mechanical equation is established to obtain the stress and displacement of the most unfavorable section of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface. The formula is as follows:

[0108]

[0109]

[0110] Where: q t is the bottom tensile stress of the most unfavorable section of the rock anchor bearing arch under loosening pressure, (kPa); σ′ cs is the top stress of the most unfavorable section of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface, (kPa); σ′ ts is the bottom stress of the most unfavorable section of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface, (kPa); w′ Cs is the displacement of the most unfavorable section of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface, (m); β is the angle of half of the shotcrete calculation model, °; X1, and M p (θ') is the calculation coefficient.

[0111] 3) According to the stress state of the bottom of the rock anchor bearing arch, the calculation model of the rock anchor bearing arch is determined. If the bottom of the rock anchor bearing arch is under tension, the structure is subjected to the combined action of loosening pressure and the tangential force of the shotcrete-surrounding rock contact surface. The formula is as follows:

[0112] σ cs总 =σ cs +σ′ cs (37)

[0113] σ ts总 =σ ts +σ′ ts (38)

[0114] w Cs总 =w Cs +w′ Cs (39)

[0115] Where: cs总 is the final top stress of the rock anchor bearing arch when the most unfavorable section is under tension at the bottom, (kPa); σ ts总 is the final bottom stress of the rock anchor bearing arch when the most unfavorable section is in the bottom tension state, (kPa); w Cs总 is the final displacement of the rock anchor bearing arch when the most unfavorable section is under tension at the bottom, (m);

[0116] If the bottom of the rock anchor bearing arch is under pressure, no tangential force will be generated at the contact surface of shotcrete-surrounding rock. At this time, the structure is only affected by the loosening pressure. At this time, the final stress and displacement of the rock anchor bearing arch under the most unfavorable section with the bottom under pressure are equal to the stress and displacement under the loosening pressure.

[0117] Step 3: Propose deformation control standards to verify whether the displacement of the rock anchor bearing arch meets the requirements.

[0118] The specific steps include:

[0119] 1) Determine the surrounding rock deformation control value u according to the specification w ;

[0120] 2) Determine the surrounding rock deformation control value and the total displacement of the most unfavorable section of the rock anchor bearing arch according to the specifications to judge whether the active support parameters of the rock anchor bearing arch meet the requirements.

[0121] Step 4: Propose a method for evaluating the safety of prestressed anchor rods and evaluate the safety of prestressed anchor rods based on the calculation results of the rock anchor bearing arch.

[0122] The specific steps include:

[0123] 1) Determine the ultimate elongation of the prestressed anchor according to the specification, and combine the length of the prestressed anchor to obtain the deformation control value u of the prestressed anchor m , the formula is as follows:

[0124] u m =δL (40)

[0125] Where: u m is the deformation control value of the prestressed anchor rod, (m); δ is the ultimate elongation of the prestressed anchor rod; L is the length of the prestressed anchor rod, (m);

[0126] 2) According to the deformation control value of the prestressed anchor and the deformation value of the surrounding rock, the safety factor of the prestressed anchor is determined and the safety of the prestressed anchor is evaluated. The formula is as follows:

[0127]

[0128] Where: k m It is the safety factor of the prestressed anchor rod. If it is greater than 1, it means it is safe, and if it is less than 1, it means it is unsafe.

[0129] Step 5: Determine the shotcrete load based on the calculated displacement of the rock anchor bearing arch.

[0130] The specific steps include:

[0131] According to the final displacement value of the surrounding rock calculated by the rock anchor bearing arch calculation model, combined with the radial deformation stiffness and tangential deformation stiffness of the shotcrete, the vertical load and horizontal load on the shotcrete are calculated. The formula is as follows:

[0132]

[0133] e p =λq p (43)

[0134] Where: q pis the vertical uniform load on shotcrete, (kPa); e p is the horizontal average load on shotcrete, (kPa); K s is the tangential deformation stiffness of shotcrete, (N / m); K l is the radial deformation stiffness of shotcrete (N / m); λ is the lateral pressure coefficient.

[0135] Step 6: Establish a shotcrete calculation model.

[0136] The specific steps include:

[0137] The calculation model of shotcrete is determined according to the stress state of the bottom of the rock anchor bearing arch. If the bottom of the rock anchor bearing arch is under tension, the shotcrete-surrounding rock contact surface generates a tangential force. Considering the coordinated deformation, the shotcrete model is subject to the combined effect of deformation load and the tangential force of the shotcrete-surrounding rock contact surface. In order to accurately evaluate the stability and safety of the project, it is necessary to establish a mechanical model that comprehensively considers the effects of these two loads; if the bottom of the rock anchor bearing arch is under compression, the shotcrete-surrounding rock contact surface does not generate a tangential force, and the shotcrete model is only subject to the deformation load. The calculation model of shotcrete under deformation load is shown in the attached figure. Figure 4 The calculation model of shotcrete under the tangential force of the shotcrete-surrounding rock contact surface is shown in the attached figure. Figure 5 shown.

[0138] Step 7: Calculate the most unfavorable cross-sectional stress of shotcrete according to the shotcrete calculation model.

[0139] The specific steps include:

[0140] 1) According to the vertical uniformly distributed load and horizontal load of shotcrete and the thickness of shotcrete, a mechanical equation is established to obtain the stress of the most unfavorable section of shotcrete under deformation load. The formula is as follows:

[0141]

[0142] Where: cp is the top stress of the most unfavorable section of shotcrete under deformation load, (kPa); σ tp is the bottom stress of the most unfavorable section of shotcrete under deformation load, (kPa); h is the thickness of shotcrete, (m).

[0143] 2) According to the thickness of shotcrete and the tensile stress value at the bottom of the most unfavorable section of the rock anchor bearing arch, a mechanical equation is established to obtain the stress of the most unfavorable section of shotcrete under the tangential force of the shotcrete-surrounding rock contact surface. The formula is as follows:

[0144]

[0145] Where: σ' cp is the top stress of the most unfavorable section of shotcrete under the tangential force of the shotcrete-surrounding rock contact surface, (kPa); σ' tp is the bottom stress of the most unfavorable section of the shotcrete under the tangential force of the shotcrete-surrounding rock interface, (kPa);

[0146] 3) Determine the shotcrete calculation model according to the stress state of the bottom of the rock anchor bearing arch. If the bottom of the rock anchor bearing arch is under tension, the shotcrete model is subjected to the combined action of deformation load and tangential force of the shotcrete-surrounding rock contact surface. The formula is as follows:

[0147] σ cp总 =σ cp +σ′ cp (48)

[0148] σ tp总 =σ tp +σ′ tp (49)

[0149] Where: cp总 is the final top stress of shotcrete when the most unfavorable section is under tension at the bottom, (kPa); σ tp总 is the final bottom stress of shotcrete when the most unfavorable section is under bottom tension, (kPa);

[0150] If the bottom of the rock anchor bearing arch is under compression, no tangential force will be generated at the contact surface of shotcrete-surrounding rock. At this time, the shotcrete model is only subjected to the deformation load. At this time, the final stress and displacement of the shotcrete under the most unfavorable section with the bottom under compression are equal to the stress and displacement under the deformation load.

[0151] Step 8. Propose a method for evaluating the safety and durability of shotcrete.

[0152] The specific steps include:

[0153] 1) According to the specification, the safety factor control value k of shotcrete is proposed;

[0154] 2) Determine the tangential safety factor of shotcrete based on the strength and thickness of shotcrete. The formula is as follows:

[0155]

[0156] Where: τ is the tangential force of the shotcrete-surrounding rock contact surface, (kPa); k q is the tangential safety factor of shotcrete;

[0157] 3) According to the specification, the calculation method of radial safety factor of shotcrete is proposed, and the formula is as follows:

[0158]

[0159] Where: f ck is the ultimate compressive strength of shotcrete, (kPa); f tk is the ultimate tensile strength of shotcrete, (kPa); k j压 k is the radial safety factor of shotcrete under pressure; j拉 is the radial safety factor of shotcrete under tension; N is the axial force of shotcrete, kN; e0 is the section eccentricity; α is the eccentricity influence number of the axial force; is the longitudinal bending coefficient of the component; b is the section width, (m); h is the section height, (m);

[0160] 4) A durability evaluation method for shotcrete is proposed. The ultimate bearing capacity of shotcrete is calculated based on the weight of shotcrete and the ultimate tensile strength of shotcrete. The cracking load of shotcrete is calculated based on the bending moment and axial force of shotcrete. The formula is as follows:

[0161] σ tk =γf tk (53)

[0162]

[0163] Where: tk is the bearing capacity of shotcrete, (kPa); σ 裂 is the cracking load of shotcrete, (kPa); M is the bending moment of shotcrete; N is the axial force of shotcrete; if the bearing capacity of shotcrete is greater than the cracking load, it means that the shotcrete has not cracked, otherwise it means that it has cracked.

[0164] Step 9: Determine the safety and durability of shotcrete based on the calculation results of the shotcrete calculation model.

[0165] Step 10: Determine active support parameters based on the calculation results of the rock anchor bearing arch and the shotcrete calculation results.

[0166] The embodiment of the present invention is based on the rock-anchor bearing arch calculation model and the shotcrete calculation model, and through the deformation control standard and the shotcrete safety and durability evaluation method, a tunnel early high-strength rock-anchor-shotcrete synergistic bearing arch active support design method is obtained. The safety and durability of the rock-anchor-shotcrete active support under different support parameters can be simply, quickly and accurately calculated. Ordinary designers can use this method to design tunnel projects using active support, which has good engineering value.

[0167] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A tunnel early high-strength rock bolt spraying synergistic bearing arch active support design method, characterized in that: The steps include: S1. Determine the load acting on the rock anchor bearing arch and establish a calculation model for the rock anchor bearing arch; S2. Calculate the most unfavorable cross-sectional displacement and stress of the rock anchor bearing arch according to the calculation model of the rock anchor bearing arch; S3. Propose deformation control standards to verify whether the displacement of the rock anchor bearing arch meets the requirements; S4. Propose a method for evaluating the safety of prestressed anchor rods and evaluate the safety of prestressed anchor rods based on the calculation results of the rock anchor bearing arch; S5. Determine the shotcrete load based on the calculated displacement of the rock anchor bearing arch; S6. Establishing a shotcrete calculation model; S7. Calculate the most unfavorable cross-sectional stress of shotcrete according to the shotcrete calculation model; S8. Propose a method for evaluating the safety and durability of shotcrete; S9. Determine the safety and durability of shotcrete based on the calculation results of the shotcrete calculation model; S10. Determine active support parameters based on the calculation results of the rock anchor bearing arch and the shotcrete calculation results.

2. The tunnel early high-strength rock bolt spraying synergistic bearing arch active support design method according to claim 1 is characterized by: The step S1 specifically includes: S11. Establish the equilibrium equation according to the radial stress and strain and tangential stress and strain in the rock mass, bring in the boundary conditions, calculate the stress in the elastic zone of the surrounding rock according to the Lame stress formula, calculate the stress in the plastic zone of the surrounding rock according to the classical chamber theory, and calculate the control radius of the rock anchor bearing at the same time. Finally, obtain the thickness of the rock anchor bearing arch. The formula is as follows: L s =F1(R s ,R) (1) Where: F1(x) is the calculation function of the rock anchor bearing arch thickness; R s L is the control radius of rock anchor bearing; s is the thickness of the rock anchor bearing arch; R is the radius of the tunnel; S12. The vertical load of the rock anchor bearing arch is calculated based on the thickness of the rock anchor bearing arch, and then the horizontal load of the rock anchor bearing arch is calculated based on the lateral pressure coefficient value provided in the specification. The formula is as follows: q s =F2(L s ,γ) (2) e s =F2(q s ,λ) (3); Where: F2(x) is the load calculation function of the rock anchor bearing arch; q s is the vertical load of the rock anchor bearing arch; e s is the horizontal load of the rock anchor bearing arch; γ is the weight of the rock anchor bearing arch; λ is the lateral pressure coefficient; S13. Determine the calculation model of the rock anchor bearing arch according to the stress state of the bottom of the rock anchor bearing arch. If the bottom of the rock anchor bearing arch is under tension, a tangential force will be generated at the contact surface of the shotcrete-surrounding rock, and the deformation and stress distribution of the rock anchor bearing arch model will change. At this time, the structure is subject to the combined effects of loosening pressure and the tangential force at the contact surface of the shotcrete-surrounding rock. Therefore, a mechanical model that comprehensively considers the effects of these two loads must be established. If the bottom of the rock anchor bearing arch is under compression, no tangential force will be generated at the contact surface of the shotcrete-surrounding rock. At this time, the structure is only subject to the loosening pressure.

3. The tunnel early high-strength rock bolt spraying synergistic bearing arch active support design method according to claim 1 is characterized by: The step S2 specifically includes: S21. According to the thickness of the rock anchor bearing arch, the vertical load and the horizontal load of the rock anchor bearing arch, a mechanical equation is established to obtain the stress and displacement of the most unfavorable section of the rock anchor bearing arch under the loosening pressure. The formula is as follows: σ cs =G1(e s ,q s ,L s ) (4) σ ts =G1(e s ,q s ,L s ) (5) w Cs =G1(e s ,q s ,L s ) (6) Where: G1(x) is the calculation function of the most unfavorable cross-sectional stress and displacement of the rock anchor bearing arch under loosening pressure; σ cs is the top stress of the most unfavorable section of the rock anchor bearing arch under loosening pressure; ts is the bottom stress of the most unfavorable section of the rock anchor bearing arch under loosening pressure; w Cs is the displacement of the most unfavorable section of the rock anchor bearing arch under loosening pressure; S22. According to the thickness of the rock anchor bearing arch and the tensile stress value at the bottom of the most unfavorable section of the rock anchor bearing arch, a mechanical equation is established to obtain the stress and displacement of the most unfavorable section of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface. The formula is as follows: σ' cs =G2(q t ,L s ) (7) σ' ts =G2(q t ,L s ) (8) w' Cs =G2(q t ,L s ) (9) Where: G2(x) is the calculation function of the most unfavorable cross-sectional stress and displacement of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface; q t is the bottom tensile stress of the most unfavorable section of the rock anchor bearing arch under loosening pressure; σ′ cs is the top stress of the most unfavorable section of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface; σ′ ts w′ is the bottom stress of the most unfavorable section of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface; Cs is the displacement of the most unfavorable section of the rock anchor bearing arch under the tangential force of the shotcrete-surrounding rock contact surface; S23. Determine the calculation model of the rock anchor bearing arch according to the stress state at the bottom of the rock anchor bearing arch. If the bottom of the rock anchor bearing arch is under tension, the structure is subjected to the combined effect of loosening pressure and the tangential force of the shotcrete-surrounding rock contact surface. The formula is as follows: s cs总 =G3(σ cs ,in cs ) (10) s ts总 =G3(σ ts ,in ts ) (11) In Cs总 =G3(in Cs ,In' Cs ) (12) Where: G3(x) is the stress and displacement calculation function of the rock anchor bearing arch when the most unfavorable section is under tension at the bottom; σ cs总 is the final top stress of the rock anchor bearing arch when the most unfavorable section is in the bottom tension state; σ ts总 is the final bottom stress of the rock anchor bearing arch when the most unfavorable section is in the bottom tension state; w Cs总 is the final displacement of the rock anchor bearing arch when the most unfavorable section is under tension at the bottom; If the bottom of the rock anchor bearing arch is under pressure, no tangential force will be generated at the contact surface of shotcrete-surrounding rock. At this time, the structure is only affected by the loosening pressure. At this time, the final stress and displacement of the rock anchor bearing arch under the most unfavorable section with the bottom under pressure are equal to the stress and displacement under the loosening pressure.

4. The tunnel early high-strength rock bolt spraying synergistic bearing arch active support design method according to claim 1 is characterized by: The step S3 specifically includes: S31. Determine the surrounding rock deformation control value u according to the specification w ; S32. Determine the surrounding rock deformation control value and the total displacement of the most unfavorable section of the rock anchor bearing arch according to the specifications to determine whether the active support parameters of the rock anchor bearing arch meet the requirements.

5. The tunnel early high-strength rock bolt-spraying synergistic bearing arch active support design method according to claim 1 is characterized by: The step S4 specifically includes: S41. Determine the ultimate elongation of the prestressed anchor rod according to the specification, and combine the length of the prestressed anchor rod to obtain the deformation control value u of the prestressed anchor rod. m ; S42. According to the deformation control value of the prestressed anchor rod and the deformation value of the surrounding rock, the safety factor of the prestressed anchor rod is determined and the safety of the prestressed anchor rod is evaluated. The formula is as follows: k m =H1(u m ,In Cs总 ) (13) Where: H1(x) is the calculation function of the safety factor of the prestressed anchor; k m It is the safety factor of the prestressed anchor rod. If it is greater than 1, it means it is safe, and if it is less than 1, it means it is unsafe.

6. The tunnel early high-strength rock bolt spraying synergistic bearing arch active support design method according to claim 1 is characterized by: The step S5 specifically includes: calculating the vertical load and horizontal load on the shotcrete according to the final displacement value of the surrounding rock calculated by the rock anchor bearing arch calculation model and the radial deformation stiffness and tangential deformation stiffness of the shotcrete, and the formula is as follows: q p =I1(w Cs总 ,K s ,K l ) (14) and p =I1(q p ,λ) (15) Where: I1(x) is the calculation function of the load on shotcrete; q p is the vertical uniformly distributed load on the shotcrete; p K is the horizontally distributed load on the shotcrete; s is the tangential deformation stiffness of shotcrete; K l is the radial deformation stiffness of shotcrete.

7. The tunnel early high-strength rock bolt spraying synergistic bearing arch active support design method according to claim 1 is characterized by: The step S6 specifically includes: determining the shotcrete calculation model according to the stress state of the bottom of the rock anchor bearing arch; if the bottom of the rock anchor bearing arch is under tension, the shotcrete-surrounding rock contact surface generates a tangential force, and considering the coordinated deformation, the shotcrete model is subjected to the combined effect of the deformation load and the tangential force of the shotcrete-surrounding rock contact surface, and a mechanical model that comprehensively considers the effects of these two loads is established; if the bottom of the rock anchor bearing arch is under compression, the shotcrete-surrounding rock contact surface does not generate a tangential force, and the shotcrete model is only subjected to the effect of the deformation load.

8. The tunnel early high-strength rock bolt-spraying synergistic bearing arch active support design method according to claim 1 is characterized by: The step S7 specifically includes: S71. Based on the vertical uniformly distributed load and horizontal load of shotcrete and the thickness of shotcrete, a mechanical equation is established to obtain the stress of the most unfavorable section of shotcrete under the deformation load. The formula is as follows: σ cp =J1(e p ,q p ,h) (16) σ tp =J1(e p ,q p ,h) (17) Where: J1(x) is the most unfavorable cross-sectional stress calculation function of shotcrete under deformation load; σ cp is the top stress of the most unfavorable section of shotcrete under deformation load; tp is the bottom stress of the most unfavorable section of shotcrete under deformation load; h is the thickness of shotcrete; S72. According to the thickness of shotcrete and the tensile stress value at the bottom of the most unfavorable section of the rock anchor bearing arch, a mechanical equation is established to obtain the stress of the most unfavorable section of shotcrete under the tangential force of the shotcrete-surrounding rock contact surface. The formula is as follows: σ' cp =J2(q t ,h) (18) σ' tp =J2(q t ,h) (19) Where: J2(x) is the most unfavorable cross-sectional stress calculation function of shotcrete under the tangential force of the shotcrete-surrounding rock contact surface; σ′ cp is the top stress of the most unfavorable section of shotcrete under the tangential force of the shotcrete-surrounding rock contact surface; σ′ tp is the bottom stress of the most unfavorable section of shotcrete under the tangential force of the shotcrete-surrounding rock contact surface; S73. Determine the shotcrete calculation model according to the stress state of the bottom of the rock anchor bearing arch. If the bottom of the rock anchor bearing arch is under tension, the shotcrete model is subjected to the combined action of the deformation load and the tangential force of the shotcrete-surrounding rock contact surface. The formula is as follows: s cp总 =J3(σ cp ,in cp ) (20) s tp总 =J3(σ tp ,in tp ) (21) Where: J3(x) is the stress and displacement calculation function of shotcrete when the most unfavorable section is under tension at the bottom; σ cp总 is the final top stress of shotcrete when the most unfavorable section is in the bottom tension state; σ tp总 It is the final bottom stress of shotcrete when the most unfavorable section is under bottom tension; If the bottom of the rock anchor bearing arch is under compression, no tangential force will be generated at the contact surface of shotcrete-surrounding rock. At this time, the shotcrete model is only subjected to the deformation load. At this time, the final stress and displacement of the shotcrete under the most unfavorable section with the bottom under compression are equal to the stress and displacement under the deformation load.

9. The tunnel early high-strength rock bolt-spraying synergistic bearing arch active support design method according to claim 1 is characterized by: The step S8 specifically includes: S81. According to the specification, the safety factor control value k of shotcrete is proposed; S82. Determine the tangential safety factor of shotcrete based on the strength and thickness of shotcrete. The formula is as follows: k q =K1(f t ,s tp总 ) (22) Where: K1(x) is the calculation function of the tangential safety factor of shotcrete; f t is the strength of shotcrete; k q is the tangential safety factor of shotcrete; S83. According to the specification, the calculation method of radial safety factor of shotcrete is proposed, and the formula is as follows: k j压 =K2(f ck ,b,h) (23) k j拉 =K2(f tk ,b,h) (24) Where: K2(x) is the calculation function of radial safety factor of shotcrete; f ck is the ultimate compressive strength of shotcrete; f tk k is the ultimate tensile strength of shotcrete; j压 k is the radial safety factor of shotcrete under pressure; j拉 is the radial safety factor of shotcrete under tension; S84. A durability evaluation method for shotcrete is proposed. The ultimate bearing capacity of shotcrete is calculated based on the weight of shotcrete and the ultimate tensile strength of shotcrete. The cracking load of shotcrete is calculated based on the bending moment and axial force of shotcrete. The formula is as follows: σ tk =K3(f tk ,γ) (25) σ 裂 =K3(M,N,b,h) (26) Where: K3(x) is the calculation function of the bearing capacity and cracking load of shotcrete; σ tk is the bearing capacity of shotcrete; 裂 is the cracking load of shotcrete; M is the bending moment of shotcrete; N is the axial force of shotcrete; if the bearing capacity of shotcrete is greater than the cracking load, it means that the shotcrete has not cracked, otherwise it means that it has cracked.

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