An active support design method for a load-bearing arch with the synergistic effect of early high-strength rock bolts and shotcrete in tunnels

Abstract

The present invention relates to the technical field of civil engineering, and specifically discloses a design method for the active support of a bearing arch with the synergistic effect of early high-strength rock anchors and shotcrete in tunnels, including: determining the load acting on the rock anchor bearing arch and establishing a calculation model for the rock anchor bearing arch; calculating the displacement and stress of the most unfavorable section of the rock anchor bearing arch; verifying whether the displacement of the rock anchor bearing arch meets the requirements; proposing a safety evaluation method for prestressed anchor rods and evaluating the safety of prestressed anchor rods according to the calculation results of the rock anchor bearing arch; establishing a calculation model for shotcrete; calculating the displacement and stress of the most unfavorable section of the shotcrete; proposing a safety and durability evaluation method for shotcrete; and determining the active support parameters according to the calculation results of the rock anchor bearing arch and the calculation results of the shotcrete. Through the method of the present invention, the safety and durability of the rock-anchor-shotcrete active support under different support parameters can be calculated simply, quickly and accurately, providing a reference for the design of tunnel projects using active support, and having good engineering value.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering, and particularly relates to a design method for the active support of a load-bearing arch through the synergistic effect of early high-strength rock bolts, rock bolts, and shotcrete in tunnels. Background Technique

[0002] The New Austrian Tunneling Method theory emphasizes taking measures to improve the mechanical properties of surrounding rocks, such as pre-reinforcement, shotcrete and bolt reinforcement, rock mass grouting and other means, so as to improve the self-bearing capacity and stability of surrounding rocks. However, in current tunnel construction, there is often a tendency towards the passive support effect of traditional support structures. Traditional support has low passive bearing efficiency, a large number of components, long construction time, redundant parameters, and poor economy, making it difficult to meet the requirements of "safety, efficiency, and economy" in tunnel construction. When constructing tunnels using the New Austrian Tunneling Method concept, tunnel rock bolts and shotcrete are two important types of support. Among them, the shotcrete and bolt support, as a key part of the initial support of tunnels, its support effect is crucial for the design of the initial support. At present, the deformation of the early high-strength rock bolt, rock bolt, and shotcrete load-bearing arch in tunnels has posed a huge challenge to engineering safety. Domestic and foreign scholars have provided some research bases through methods such as analogy design, model verification, and field testing. However, the active support design method for the early high-strength rock bolt, rock bolt, and shotcrete load-bearing arch in tunnels is still not perfect. Therefore, constructing a design method for the active support of a load-bearing arch through the synergistic effect of early high-strength rock bolts, rock bolts, and shotcrete in tunnels and realizing the active support design of shotcrete and bolts based on the early high-strength rock bolt, rock bolt, and shotcrete load-bearing arch is of great significance. Summary of the Invention

[0003] To solve the problems existing in the prior art, the present invention provides a design method for the active support of a load-bearing arch through the synergistic effect of early high-strength rock bolts, rock bolts, and shotcrete in tunnels, which realizes simple, fast, and accurate calculation of the safety and durability of the active support of rock - bolt - shotcrete under different support parameters, provides a reference for the design of tunnel projects using active support, and solves the problems mentioned in the above background technique.

[0004] To achieve the above object, the present invention provides the following technical solution: A design method for the active support of a load-bearing arch through the synergistic effect of early high-strength rock bolts, rock bolts, and shotcrete in tunnels, including the following steps:

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

[0006] S2. Calculate the displacement and stress of the most unfavorable section of the rock bolt load-bearing arch according to the calculation model of the rock bolt load-bearing arch;

[0007] S3. Propose a deformation control standard to verify whether the displacement of the rock bolt load-bearing arch meets the requirements;

[0008] S4. Propose a safety evaluation method for prestressed rock bolts and evaluate the safety of prestressed rock bolts according to the calculation results of the rock bolt load-bearing arch;

[0009] S5. Determine the acting load of shotcrete according to the calculated displacement of the rock anchor bearing arch;

[0010] S6. Establish a calculation model for shotcrete;

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

[0012] S8. Propose an evaluation method for the safety and durability of shotcrete;

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

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

[0015] Preferably, the specific steps of step S1 include:

[0016] S11. Establish a balance equation based on the radial stress-strain and tangential stress-strain in the rock mass, substitute the boundary conditions, then 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, calculate the control radius of the rock anchor bearing at the same time, and finally obtain the thickness of the rock anchor bearing arch. The formula is as follows:

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

[0018] Where: F 1 (x) is the calculation function of the thickness of the rock anchor bearing arch; R s is the control radius of the rock anchor bearing, (m); L s is the thickness of the rock anchor bearing arch, (m); R is the tunnel radius, m;

[0019] S12. Calculate the vertical load of the rock anchor bearing arch according to the thickness of the rock anchor bearing arch, and then obtain the horizontal load of the rock anchor bearing arch according to the lateral pressure coefficient value provided by the specification. The formula is as follows:

[0020] q s =F 2 (L s ,γ) (2)

[0021] e s =F 2 (q s ,λ) (3);

[0022] Where: F 2 (x) is the load calculation function of the rock anchor bearing arch; q sis the vertical load on the rock anchor bearing arch, (kPa); e s is the horizontal load on the rock anchor bearing arch, (kPa); γ is the unit weight of the rock anchor bearing arch, kN / m 3 ; λ is the coefficient of lateral pressure;

[0023] S13. 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 in tension, tangential force will be generated at the shotcrete-rock mass contact surface, and the deformation and stress distribution of the rock anchor bearing arch model will change. At this time, the structure is under the combined action of loosening pressure and tangential force at the shotcrete-rock mass 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 action of these two loads; if the bottom of the rock anchor bearing arch is in compression, no tangential force will be generated at the shotcrete-rock mass contact surface. At this time, the structure is only under the action of 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, establish a mechanical equation to obtain the stress and displacement of the most unfavorable section of the rock anchor bearing arch under the action of loosening pressure. The formula is as follows:

[0026] σ cs = G 1 (e s , q s , L s ) (4)

[0027] σ ts = G 1 (e s , q s , L s ) (5)

[0028] w Cs = G 1 (e s , q s , L s ) (6)

[0029] Where: G 1 (x) is the calculation function of the stress and displacement of the most unfavorable section of the rock anchor bearing arch under the action of loosening pressure; σ cs is the top stress of the most unfavorable section of the rock anchor bearing arch under the action of loosening pressure, (kPa); σ ts is the bottom stress of the most unfavorable section of the rock anchor bearing arch under the action of loosening pressure, (kPa); w Cs is the displacement of the most unfavorable section of the rock anchor bearing arch under the action of loosening pressure, (m);

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

[0031] σ' cs =G 2 (q t ,L s ) (7)

[0032] σ' ts =G 2 (q t ,L s ) (8)

[0033] w' Cs =G 2 (q t ,L s ) (9)

[0034] Where: G 2 (x) is the calculation function of the stress and displacement of the most unfavorable section of the rock anchor bearing arch under the tangential force of the shotcrete-rock mass contact surface; q t is the bottom tensile stress of the most unfavorable section of the rock anchor bearing arch under the action of 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-rock mass 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-rock mass 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-rock mass 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 in tension, the structure is under the combined action of loosening pressure and the tangential force of the shotcrete-rock mass contact surface. The formula is as follows:

[0036] σ cs总 =G 3 (σ cs ,σ' cs ) (10)

[0037] σ ts总 =G 3 (σ ts ,σ' ts ) (11)

[0038] w Cs总 =G 3 (w Cs, w' Cs ) (12)

[0039] Where: G 3 (x) is the stress and displacement calculation function of the rock anchor bearing arch in the state of tension at the bottom of the most unfavorable section; σ cs总 is the final top stress of the rock anchor bearing arch in the state of tension at the bottom of the most unfavorable section, (kPa); σ ts总 is the final bottom stress of the rock anchor bearing arch in the state of tension at the bottom of the most unfavorable section, (kPa); w Cs总 is the final displacement of the rock anchor bearing arch in the state of tension at the bottom of the most unfavorable section, (m);

[0040] If the bottom of the rock anchor bearing arch is under compression, no tangential force will be generated at the shotcrete - surrounding rock contact surface. 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 in the state of compression at the bottom of the most unfavorable section are equal to the stress and displacement under the action of the loosening pressure.

[0041] Preferably, the step S3 specifically includes:

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

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

[0044] Preferably, the step S4 specifically includes:

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

[0046] S42. Determine the safety factor of the prestressed anchor bolt and evaluate the safety of the prestressed anchor bolt according to the deformation control value of the prestressed anchor bolt and the surrounding rock deformation value. The formula is as follows:

[0047] k m = H 1 (u m , w Cs总 ) (13)

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

[0049] Preferably, the step S5 is specifically:

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

[0051] q p =I 1 (w Cs总 ,K s ,K l ) (14)

[0052] e p =I 1 (q p ,λ) (15)

[0053] Where: I 1 (x) is the calculation function of the load on the shotcrete; q p is the vertical uniform load on the shotcrete, (kPa); e p is the horizontal uniform load on the shotcrete, (kPa); K s is the tangential deformation stiffness of the shotcrete, (N / m); K l is the radial deformation stiffness of the shotcrete, (N / m).

[0054] Preferably, the step S6 is specifically as follows:

[0055] Determine the calculation model of the shotcrete according to the stress state at the bottom of the rock anchor bearing arch. If the bottom of the rock anchor bearing arch is in tension, tangential force is generated at the shotcrete-rock mass contact surface. Considering the coordinated deformation, the shotcrete model is under the combined action of the deformation load and the tangential force at the shotcrete-rock mass contact surface. In order to accurately evaluate the stability and safety of the project, a mechanical model considering the combined action of these two loads needs to be established; if the bottom of the rock anchor bearing arch is in compression, no tangential force is generated at the shotcrete-rock mass contact surface, and the shotcrete model is only under the action of the deformation load.

[0056] Preferably, the step S7 specifically includes:

[0057] S71. According to the vertical uniform load and horizontal load of the shotcrete and the thickness of the shotcrete, establish a mechanical equation to obtain the stress of the most unfavorable section of the shotcrete under the action of the deformation load. The formula is as follows:

[0058] σ cp =J 1 (e p ,q p ,h) (16)

[0059] σ tp =J 1 (e p ,qp , h) (17)

[0060] In the formula: J 1 (x) is the calculation function of the most unfavorable cross-section stress of shotcrete under the action of deformation load; σ cp is the top stress of the most unfavorable cross-section of shotcrete under the action of deformation load, (kPa); σ tp is the bottom stress of the most unfavorable cross-section of shotcrete under the action of deformation load, (kPa); h is the thickness of shotcrete, (m);

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

[0062] σ' cp = J 2 (q t , h) (18)

[0063] σ' tp = J 2 (q t , h) (19)

[0064] In the formula: J 2 (x) is the calculation function of the most unfavorable cross-section stress of shotcrete under the action of the tangential force at the shotcrete-rock mass contact surface; σ′ cp is the top stress of the most unfavorable cross-section of shotcrete under the action of the tangential force at the shotcrete-rock mass contact surface, (kPa); σ′ tp is the bottom stress of the most unfavorable cross-section of shotcrete under the action of the tangential force at the shotcrete-rock mass contact surface, (kPa);

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

[0066] σ cp总 = J 3 (σ cp , σ' cp ) (20)

[0067] σ tp总 = J 3 (σ tp , σ' tp ) (21)

[0068] In the formula: J 3(x) is the stress and displacement calculation function of shotcrete under the most unfavorable section with tension at the bottom; σ cp总 is the final top stress of shotcrete under the most unfavorable section with tension at the bottom, (kPa); σ tp总 is the final bottom stress of shotcrete under the most unfavorable section with tension at the bottom, (kPa);

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

[0070] Preferably, the step S8 specifically includes:

[0071] S81. Propose the safety factor control value k of shotcrete according to the specification;

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

[0073] k q = K 1 (f t , σ tp总 )(22)

[0074] In the formula: K 1 (x) is the tangential safety factor calculation function of shotcrete; f t is the strength of shotcrete, (kPa); k q is the tangential safety factor of shotcrete;

[0075] S83. Propose the calculation method of the radial safety factor of shotcrete according to the specification. The formula is as follows:

[0076] k j压 = K 2 (f ck , b, h)(23)

[0077] k j拉 = K 2 (f tk , b, h)(24)

[0078] In the formula: K 2 (x) is the radial safety factor calculation function 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 is the radial safety factor of shotcrete when it is under compression;j拉 is the radial safety factor when shotcrete is in tension;

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

[0080] σ tk = K 3 (f tk ,γ)(25)

[0081] σ 裂 = K 3 (M,N,b,h)(26)

[0082] In the formulas: K 3 (x) is the calculation function for 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 indicates that the shotcrete is not cracked, otherwise it indicates cracking.

[0083] The beneficial effects of the present invention are as follows: Based on the calculation models of rock anchor bearing arch and shotcrete, through the deformation control criteria and the evaluation methods for the safety and durability of shotcrete, the active support design method for the tunnel early high-strength rock anchor shotcrete synergistic action bearing arch is obtained. The calculation process of the obtained method is clear and rigorous, the calculation formulas are 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 deformation calculation method for the fault displacement strata under active faults obtained by the present invention, so as to calculate the safety and durability of the rock-anchor-shotcrete active support under different support parameters, providing a reference for the design of tunnel projects using active support, and having good engineering value. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 is the schematic diagram of the step flow of the method of the present invention;

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

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

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

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

[0089] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts belong to the scope of protection of the present invention.

[0090] Please refer to Figures 1 - 5 , the present invention provides a technical solution: a design method for the active support of the bearing arch of early - high - strength rock bolts and shotcrete in tunnels. As Figure 1 shown, it includes the following steps:

[0091] Step 1: Determine the loads acting on the rock - bolt bearing arch and establish a calculation model of the rock - bolt bearing arch.

[0092] Specifically, it includes the following steps:

[0093] 1) Establish an equilibrium equation based on the radial stress - strain and tangential stress - strain in the rock mass, substitute the boundary conditions, then calculate the stress in the elastic zone of the surrounding rock according to the Lame stress formula and the stress in the plastic zone of the surrounding rock according to the classical chamber theory. At the same time, calculate the control radius of the rock - bolt bearing and finally obtain the thickness of the rock - bolt bearing arch. The formula is as follows:

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

[0095]

[0096] In the formula: R s is the control radius of the rock - bolt bearing, (m); L s is the thickness of the rock - bolt bearing arch, (m); R is the tunnel radius, m; is the friction angle of the rock - bolt bearing arch, °; c is the cohesion of the rock - bolt bearing arch, kPa; P 0 is the in - situ stress of the rock - bolt bearing arch, kPa.

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

[0098] qs =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 unit weight of the rock anchor bearing arch, kN / m 3 ; λ is the coefficient of lateral pressure;

[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 in tension, a tangential force will be generated at the shotcrete-rock mass contact surface, and the deformation and stress distribution of the rock anchor bearing arch model will change. At this time, the structure is under the combined action of the loosening pressure and the tangential force at the shotcrete-rock mass contact surface. To accurately evaluate the stability and safety of the project, a mechanical model considering the combined action of these two loads needs to be established; if the bottom of the rock anchor bearing arch is in compression, no tangential force will be generated at the shotcrete-rock mass contact surface. At this time, the structure is only under the action of the loosening pressure. The calculation model of the rock anchor bearing arch under the action of the loosening pressure is shown in Appendix Figure 2 as shown, and the calculation model of the rock anchor bearing arch under the action of the tangential force at the shotcrete-rock mass contact surface is shown in Appendix Figure 3 as shown.

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

[0103] Specifically, it includes the following steps:

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

[0105]

[0106] Where: σ cs is the top stress of the most unfavorable section of the rock anchor bearing arch under the action of the loosening pressure, (kPa); σ ts is the bottom stress of the most unfavorable section of the rock anchor bearing arch under the action of the loosening pressure, (kPa); w Cs is the displacement of the most unfavorable section of the rock anchor bearing arch under the action of the loosening pressure, (m); q s is the uniformly distributed vertical load borne by 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 obtained by subtracting L from the tunnel radius R, m; X 1 , and M p (θ) is the calculation coefficient; b is taken as 1 m; 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, N·m.

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

[0108]

[0109]

[0110] In the formula: q t is the bottom tensile stress of the most unfavorable section of the rock anchor bearing arch under the action of the loosening pressure, (kPa); σ′ cs is the top stress of the most unfavorable section of the rock anchor bearing arch under the action of the tangential force on 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 action of the tangential force on 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 action of the tangential force on the shotcrete-surrounding rock contact surface, (m); β is the included angle of half of the shotcrete calculation model, °; X 1 、 and M p (θ') is the calculation coefficient.

[0111] 3) Determine the calculation model of the rock anchor bearing arch according to the force state at the bottom of the rock anchor bearing arch. If the bottom of the rock anchor bearing arch is in tension, the structure is under the combined action of the loosening pressure and the tangential force on 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] In the formula: σ cs总 is the final top stress of the rock anchor bearing arch in the state of tension at the bottom of the most unfavorable section, (kPa); σts总 is the ultimate bottom stress of the rock-anchored load-bearing arch in the state of tensile stress at the bottom of the most unfavorable section, (kPa); w Cs总 is the ultimate displacement of the rock-anchored load-bearing arch in the state of tensile stress at the bottom of the most unfavorable section, (m);

[0116] If the bottom of the rock-anchored load-bearing arch is under compression, no tangential force is generated at the contact surface between the shotcrete and the surrounding rock. At this time, the structure is only affected by the loosening pressure. At this time, the ultimate stress and displacement of the rock-anchored load-bearing arch in the state of compressive stress at the bottom of the most unfavorable section are equal to the stress and displacement under the action of the loosening pressure.

[0117] Step 3: Propose a deformation control standard to verify whether the displacement of the rock-anchored load-bearing arch meets the requirements.

[0118] Specifically, it includes the following steps:

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

[0120] 2) Determine whether the active support parameters of the rock-anchored load-bearing arch meet the requirements according to the surrounding rock deformation control value determined by the specification and the total displacement of the most unfavorable section of the rock-anchored load-bearing arch.

[0121] Step 4: Propose a safety evaluation method for prestressed anchor bolts and evaluate the safety of prestressed anchor bolts according to the calculation results of the rock-anchored load-bearing arch.

[0122] Specifically, it includes the following steps:

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

[0124] u m = δL (40)

[0125] In the formula: u m is the deformation control value of the prestressed anchor bolt, (m); δ is the ultimate elongation rate of the prestressed anchor bolt; L is the length of the prestressed anchor bolt, (m);

[0126] 2) Determine the safety factor of the prestressed anchor bolt according to the deformation control value of the prestressed anchor bolt and the surrounding rock deformation value, and evaluate the safety of the prestressed anchor bolt. The formula is as follows:

[0127]

[0128] In the formula: k m is the safety factor of the prestressed anchor bolt. If it is greater than 1, it means safe; if it is less than 1, it means unsafe.

[0129] Step 5: Determine the load acting on the shotcrete according to the calculated displacement of the rock-anchored load-bearing arch.

[0130] Specifically, it includes the following steps:

[0131] Based on the final displacement value of the surrounding rock obtained from the calculation model of the rock anchor bearing arch, combined with the radial deformation stiffness and tangential deformation stiffness of the shotcrete, calculate the vertical load and horizontal load on the shotcrete. The formula is as follows:

[0132]

[0133] e p = λq p (43)

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

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

[0136] Specifically, it includes the following steps:

[0137] Determine the calculation model of the shotcrete according to the stress state at the bottom of the rock anchor bearing arch. If the bottom of the rock anchor bearing arch is in tension, a tangential force is generated at the shotcrete - surrounding rock contact surface. Considering the coordinated deformation, the shotcrete model is under the combined action of the deformation load and the tangential force at 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 action of these two loads; if the bottom of the rock anchor bearing arch is in compression, no tangential force is generated at the shotcrete - surrounding rock contact surface, and the shotcrete model is only under the action of the deformation load. The calculation model of the shotcrete under the action of the deformation load is as shown in Appendix Figure 4 shown, and the calculation model of the shotcrete under the action of the tangential force at the shotcrete - surrounding rock contact surface is as shown in Appendix Figure 5 shown.

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

[0139] Specifically, it includes the following steps:

[0140] 1) Based on the vertical uniform load, horizontal load and thickness of the shotcrete, establish a mechanical equation to obtain the stress of the most unfavorable section of the shotcrete under the action of the deformation load. The formula is as follows:

[0141]

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

[0143] 2) Based on the thickness of the shotcrete and the bottom tensile stress value of the most unfavorable section of the rock bolt supporting arch, establish a mechanical equation to obtain the stress of the most unfavorable section of the shotcrete under the action of the tangential force at the shotcrete-rock mass contact surface. The formula is as follows:

[0144]

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

[0146] 3) Determine the calculation model of the shotcrete according to the stress state at the bottom of the rock bolt supporting arch. If the bottom of the rock bolt supporting arch is in tension, the shotcrete model is under the combined action of the deformation load and the tangential force at the shotcrete-rock mass 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: σ cp总 is the final top stress of the shotcrete in the state where the bottom of the most unfavorable section is in tension, (kPa); σ tp总 is the final bottom stress of the shotcrete in the state where the bottom of the most unfavorable section is in tension, (kPa);

[0150] If the bottom of the rock bolt supporting arch is in compression, no tangential force is generated at the shotcrete-rock mass contact surface. At this time, the shotcrete model is only under the action of the deformation load. At this time, the final stress and displacement of the shotcrete in the state where the bottom of the most unfavorable section is in compression are equal to the stress and displacement under the action of the deformation load.

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

[0152] Specifically, it includes the following steps:

[0153] 1) Propose the control value k of the safety factor of shotcrete according to the specification;

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

[0155]

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

[0157] 3) Propose the calculation method of the radial safety factor of shotcrete according to the specification. The formula is as follows:

[0158]

[0159] In the formula: f ck is the ultimate compressive strength of shotcrete, (kPa); f tk is the ultimate tensile strength of shotcrete, (kPa); k j压 is the radial safety factor of shotcrete under compression; k j拉 is the radial safety factor of shotcrete under tension; N is the axial force of shotcrete, kN; e 0 is the eccentricity of the section; α is the eccentricity influence number of the axial force; is the longitudinal bending coefficient of the member; b is the section width, (m); h is the section height, (m);

[0160] 4) Propose the durability evaluation method of shotcrete. Calculate the ultimate bearing capacity of shotcrete according to the unit weight of shotcrete and the ultimate tensile strength of shotcrete, and calculate the cracking load of shotcrete according to the bending moment and axial force of shotcrete. The formula is as follows:

[0161] σ tk =γf tk (53)

[0162]

[0163] In the formula: 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 is not cracked, otherwise it means it is cracked.

[0164] Step 9. Determine the safety and durability of shotcrete according to the calculation results of the shotcrete calculation model.

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

[0166] Based on the rock anchor bearing arch calculation model and the shotcrete calculation model, the embodiment of the present invention obtains the active support design method for the bearing arch of the early high-strength rock anchor shotcrete synergy in the tunnel through the deformation control standard and the evaluation method for the safety and durability of the shotcrete. It can simply, quickly, and accurately calculate the safety and durability of the rock-anchor-shotcrete active support under different support parameters. Ordinary designers can use this method to design tunnel projects with active support, which has good engineering value.

[0167] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within 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 of the rock anchor bearing arch and establish a calculation model for the rock anchor bearing arch; specifically include the following: 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 is the control radius of rock anchor bearing; L 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 effect of loosening pressure and the tangential force of the shotcrete-surrounding rock contact surface. Therefore, a mechanical model that comprehensively considers the effects of these two loads should 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 effect of loosening pressure. 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 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.

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 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.

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 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.

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 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.

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 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 to be 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.

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 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.

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 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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