Method for determining non-uniform grouting reinforcement thickness of two-way unequal pressure circular tunnel

Abstract

The application provides a two-way unequal-pressure circular tunnel non-uniform grouting reinforcement thickness determination method, which comprises the following steps: S1. establishing a two-way unequal-pressure circular tunnel surrounding rock-grouting reinforcement ring model, wherein the model is composed of a tunnel, a grouting reinforcement ring and surrounding rock from inside to outside; S2. constructing a surrounding rock stress model under surrounding rock-grouting reinforcement ring coupling, a grouting reinforcement ring stress model under surrounding rock-grouting reinforcement ring coupling, a two-way unequal-pressure circular tunnel grouting thickness balance model and a surrounding rock-grouting reinforcement ring interface line model, and solving coefficient ε k based on the constructed models; S3. constructing a grouting thickness calculation model of a target grouting point, and solving the grouting reinforcement thickness of the target grouting point; the thickness of the grouting reinforcement ring at different positions of the tunnel can be accurately determined, thereby providing protection for engineering safety, and the whole process is simple, convenient and has strong universality.​​

Description

Technical Field

[0001] This invention relates to the field of tunnel engineering, and in particular to a method for determining the thickness of non-uniform grouting reinforcement in a circular tunnel with two-way unequal pressure. Background Technology

[0002] The stress in the surrounding rock at any point on the tunnel boundary varies with location, and the thickness of the grouting reinforcement ring should increase or decrease accordingly. Selecting an appropriate grouting reinforcement ring thickness can reduce construction costs and improve the overall safety of the project; therefore, the rational design of the reinforcement ring thickness is of great significance to the safety of underground engineering. Currently, the main design methods for the non-uniformly distributed grouting ring thickness in circular tunnels under biaxial unequal compressive stress fields include engineering analogy, field testing, and numerical simulation. Engineering analogy relies too heavily on the construction experience and subjective judgment of designers; field testing is time-consuming and labor-intensive, and the selected test sections cannot cover the entire geological conditions of the tunnel project; numerical simulation also suffers from drawbacks such as a large modeling workload and a lack of model universality.

[0003] Therefore, in order to solve the above-mentioned technical problems, it is urgent to propose new technical means. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a method for determining the thickness of non-uniform grouting reinforcement in a circular tunnel with two-way unequal pressure. This method can accurately determine the thickness of the grouting reinforcement ring at different locations in the tunnel, thereby ensuring engineering safety. Moreover, the whole process is simple, convenient, and highly versatile.

[0005] This invention provides a method for determining the thickness of non-uniform grouting reinforcement in a circular tunnel with biaxial unequal pressure, comprising the following steps:

[0006] S1. Establish a two-dimensional unequal pressure circular tunnel surrounding rock-grouting reinforcement ring model, wherein the model consists of the tunnel, the grouting reinforcement ring, and the surrounding rock, respectively, on the inner and outer sides;

[0007] S2. Construct a stress model of the surrounding rock under the coupled action of the surrounding rock and the grouting reinforcement ring, a stress model of the grouting reinforcement ring under the coupled action of the surrounding rock and the grouting reinforcement ring, a grouting thickness balance model of a circular tunnel with two-way unequal pressure, and a boundary model of the surrounding rock and the grouting reinforcement ring. Based on the constructed models, solve for the coefficient ε. k ;

[0008] S3. Construct a calculation model for the grouting thickness at the target grouting point, and determine the grouting reinforcement thickness at the target grouting point; wherein: the grouting thickness calculation model is:

[0009]

[0010] Where: t jThis represents the grouting reinforcement thickness at the j-th grouting point, where i is the imaginary unit, and θ j This represents the angle at the j-th grouting point, where R0 is the tunnel radius and a is the compensation value. This represents the boundary model between the surrounding rock and the grouting reinforcement zone.

[0011] Furthermore, the boundary model of the surrounding rock-grouting reinforcement zone is as follows:

[0012]

[0013] Where: R is the virtual radius of the boundary model between the surrounding rock and the grouting reinforcement zone; ξ=e iθ .

[0014] Furthermore, the stress model of the surrounding rock under the coupled action of the surrounding rock and the grouting reinforcement ring is as follows:

[0015]

[0016]

[0017]

[0018] Where: λ represents the lateral pressure coefficient of the surrounding rock, and p represents the vertical force of the surrounding rock. The derivative of the model representing the boundary between the surrounding rock and the grouting reinforcement zone is given. ζ represents the conjugate of the boundary model of the surrounding rock-grouting reinforcement zone. k Represents the coefficient. For the tangential stress of the surrounding rock, The radial stress of the surrounding rock. This represents the shear stress of the surrounding rock.

[0019] Furthermore, the stress model of the grouting reinforcement ring under the coupled action of surrounding rock and grouting reinforcement ring is as follows:

[0020]

[0021]

[0022]

[0023] in: represents the internal friction angle of the grouting reinforcement ring, and c represents the cohesion of the grouting reinforcement ring. For the tangential stress of the grouting reinforcement ring, For the radial stress of the grouting reinforcement ring, The shear stress of the grouting reinforcement ring.

[0024] Furthermore, the grouting thickness balance model for a circular tunnel with unequal pressure in both directions is as follows:

[0025]

[0026] The beneficial effects of this invention are: through this invention, the thickness of the grouting reinforcement ring at different locations in the tunnel can be accurately determined, thereby ensuring the safety of the project. Moreover, the whole process is simple, convenient, and has strong versatility. Attached Figure Description

[0027] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0028] Figure 1 This is a flowchart of the present invention.

[0029] Figure 2 This is a schematic diagram of the biaxially unequal pressure circular tunnel surrounding rock-grouting reinforcement ring model structure of the present invention.

[0030] Figure 3 This is a schematic diagram of the boundary between the surrounding rock and the grouting reinforcement ring, which is a specific example of the present invention.

[0031] Figure 4 This is a model diagram of the surrounding rock and grouting reinforcement ring of a circular tunnel with unequal pressure in two directions after grouting. Detailed Implementation

[0032] The present invention will be further described in detail below:

[0033] This invention provides a method for determining the thickness of non-uniform grouting reinforcement in a circular tunnel with biaxial unequal pressure, comprising the following steps:

[0034] S1. Establish a biaxially unequal-pressure circular tunnel surrounding rock-grouting reinforcement ring model, wherein the model consists of the tunnel, the grouting reinforcement ring, and the surrounding rock, respectively, with the inner tunnel and the outer tunnel being the tunnel itself; the biaxially unequal-pressure circular tunnel surrounding rock-grouting reinforcement ring model is as follows: Figure 2 As shown, 1-fractured surrounding rock; 2-tunnel excavation boundary; 3-undisturbed surrounding rock; Figure 4 In the diagram, 1-tunnel boundary; 2-grouting ring; 3-undisturbed surrounding rock; 4-grouting thickness.

[0035] S2. Construct a stress model of the surrounding rock under the coupled action of the surrounding rock and the grouting reinforcement ring, a stress model of the grouting reinforcement ring under the coupled action of the surrounding rock and the grouting reinforcement ring, a grouting thickness balance model of a circular tunnel with two-way unequal pressure, and a boundary model of the surrounding rock and the grouting reinforcement ring. Based on the constructed models, solve for the coefficient ε. k ;

[0036] S3. Construct a calculation model for the grouting thickness at the target grouting point, and determine the grouting reinforcement thickness at the target grouting point; wherein: the grouting thickness calculation model is:

[0037]

[0038] where: t j represents the grouting reinforcement thickness at the j-th grouting point, i is the imaginary unit, and θ j represents the angle at the j-th grouting point, R0 is the tunnel radius, a is the compensation value, and its value range is 0 < a < 1. Generally, the value is 0.5. represents the surrounding rock - grouting reinforcement circle boundary line model.

[0039] Specifically: The surrounding rock - grouting reinforcement circle boundary line model is:

[0040]

[0041] where: R is the virtual radius of the surrounding rock - grouting reinforcement circle boundary line model, ξ = e iθ .

[0042] The surrounding rock stress model under the coupling action of the surrounding rock - grouting reinforcement circle is:

[0043]

[0044]

[0045]

[0046] where: λ represents the lateral pressure coefficient of the surrounding rock, p represents the vertical force of the surrounding rock, represents the derivative of the surrounding rock - grouting reinforcement circle boundary line model, represents the conjugate of the surrounding rock - grouting reinforcement circle boundary line model, ζ k represents the coefficient, is the tangential stress of the surrounding rock, is the radial stress of the surrounding rock, is the shear stress of the surrounding rock.

[0047] The stress model of the grouting reinforcement circle under the coupling action of the surrounding rock - grouting reinforcement circle is:

[0048]

[0049]

[0050]

[0051] where: represents the internal friction angle of the grouting reinforcement circle, c represents the cohesion of the grouting reinforcement circle, is the tangential stress of the grouting reinforcement circle, is the radial stress of the grouting reinforcement circle, is the shear stress of the grouting reinforcement circle.

[0052] The grouting thickness balance model for a circular tunnel with unequal pressure in both directions is as follows:

[0053] In solving the problem, first solve equations (3)-(9) simultaneously to obtain the coefficient ε. k , with coefficient ε k Substituting these equations into formula (2), the boundary line equation is determined. Finally, substituting the boundary line equation into formula (1), the thickness of the grouting reinforcement ring at each point is calculated. The coefficient ε... k Let k be a series, and k represent the number of terms in the series. By using the above method, the thickness of the grouting reinforcement ring at different locations in the tunnel can be accurately determined, thereby ensuring the safety of the project. Moreover, the whole process is simple, convenient, and highly versatile.

[0054] The following specific example further illustrates this point:

[0055] A tunnel project is located in a Class IV surrounding rock area, primarily composed of silty shale and limestone. The rock mass is relatively fractured to broken, with a layered, fragmented structure. Karst development is prevalent in this area, making tunnel excavation prone to roof falls, water inrushes, and mudslides; therefore, grouting reinforcement is necessary. The known vertical ground stress in this area is p = 15 MPa, the lateral pressure coefficient is λ = 0.67, the equivalent excavation radius of the tunnel is R0 = 2.0 m, the rock mass cohesion is c = 2 MPa, and the internal friction angle is...

[0056]

[0057] The corresponding equation for the boundary between the surrounding rock and the grouting reinforcement ring can be obtained by using the theoretical thickness balance relationship (7) of the biaxial unequal pressure circular tunnel grouting:

[0058] It can be seen from this formula that for the coefficient ε k Using only the 5th order is sufficient to meet the engineering accuracy requirements;

[0059] In the formula, ξ=e iθ .

[0060] The grouting thickness t at the j-th grouting point can then be obtained. j The calculation formula is as follows:

[0061]

[0062] Based on the engineering considerations of grouting pressure and construction safety, a grouting point is set every 30 degrees. Therefore, the grouting thickness at the corresponding grouting point is:

[0063]

[0064]

[0065] The boundary between the surrounding rock and the grouting reinforcement zone is as follows: Figure 3 As shown.

[0066] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for determining the thickness of non-uniform grouting reinforcement in a circular tunnel with biaxial unequal pressure, characterized in that: Includes the following steps: S1. Establish a two-dimensional unequal pressure circular tunnel surrounding rock-grouting reinforcement ring model, wherein the model consists of the tunnel, the grouting reinforcement ring and the surrounding rock from the inside out; S2. Construct a stress model for the surrounding rock under the coupled action of the surrounding rock and the grouting reinforcement ring, a stress model for the grouting reinforcement ring under the coupled action of the surrounding rock and the grouting reinforcement ring, a grouting thickness balance model for a circular tunnel with two-way unequal pressure, and a boundary model for the surrounding rock and the grouting reinforcement ring. Solve for the coefficients based on the constructed models. ; S3. Construct a calculation model for the grouting thickness at the target grouting point, and determine the grouting reinforcement thickness at the target grouting point; wherein: the grouting thickness calculation model is: (1)； in: This represents the grouting reinforcement thickness at the j-th grouting point, where i is an imaginary unit. This represents the angle at the j-th grouting point. Where is the tunnel radius. As compensation value, This represents a model of the boundary between the surrounding rock and the grouting reinforcement zone. The model for the boundary between the surrounding rock and the grouting reinforcement zone is as follows: (2)； Where: R is the virtual radius of the boundary model between the surrounding rock and the grouting reinforcement zone. ; The stress model of the surrounding rock under the coupled action of the surrounding rock and the grouting reinforcement ring is as follows: (3) (4) (5) in: This represents the lateral pressure coefficient of the surrounding rock. This represents the vertical stress in the surrounding rock. The derivative of the model representing the boundary between the surrounding rock and the grouting reinforcement zone is given. This represents the conjugate of the model representing the boundary between the surrounding rock and the grouting reinforcement zone. For coefficients, For the tangential stress of the surrounding rock, The radial stress of the surrounding rock. The shear stress of the surrounding rock; The stress model of the grouting reinforced ring under the coupled action of surrounding rock and grouting reinforced ring is as follows: (6) (7) (8) in: Indicates the internal friction angle of the grouting reinforcement ring. This indicates the cohesion of the grouting reinforcement ring. For the tangential stress of the grouting reinforcement ring, For the radial stress of the grouting reinforcement ring, Shear stress in the grouting reinforcement ring; The grouting thickness balance model for a circular tunnel with unequal pressure in both directions is as follows: (9)； Solve the simultaneous equations (3)-(9) to obtain the coefficients. .

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