Tunnel portal slope anchor design method and device based on generalized logarithmic spiral failure model

Abstract

This invention discloses a design method and device for tunnel entrance slope anchor bolts based on a generalized logarithmic spiral failure model. The method includes: introducing a friction weight coefficient to characterize the contribution of the internal friction angle to the strength of the soil and rock mass; constructing a generalized logarithmic spiral failure model to uniformly characterize the spatial morphological features of fracture surfaces in various soil and rock masses; based on the generalized logarithmic spiral failure model, using the limit equilibrium analysis method with the center point of the generalized logarithmic spiral slip surface as the moment center, establishing a mechanical expression for the tunnel slope safety factor; using a gridded search analytical optimization method to solve for the most unfavorable slip surface and the safety factor; incorporating the end wall anchor bolts into the limit equilibrium system, calculating the safety factor increment and converting it into a total additional resistance moment, and distributing it to each slope anchor bolt and end wall anchor bolt to determine the design bearing capacity of a single anchor bolt, thus completing the anchor bolt parameter design; this invention unifies the spatial morphological description of fracture surfaces in various soil and rock masses, comprehensively considers slope sliding and end wall treatment in anchor bolt design, and improves the overall integrity and reliability of the reinforcement design.

Description

Technical Field

[0001] This invention relates to the field of tunnel engineering technology, and more specifically to a design method and device for tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model. Background Technology

[0002] The stability of the tunnel portal slope is a key factor determining the safety of tunnel construction and its long-term service performance. Currently, as transportation infrastructure continues to extend into mountainous areas with complex geological conditions, the engineering geological environment faced by tunnel construction and operation is becoming increasingly complex. During the construction phase, the excavation of the tunnel portal slope significantly disrupts the original stress balance of the rock mass. During the operation period, the mechanical properties of the soil and rock mass continue to deteriorate under long-term weathering and rainwater infiltration. Coupled with the frequent occurrence of extreme weather, earthquakes, and other sudden natural disasters, sudden slope slippage is highly likely.

[0003] Currently, the stability analysis of tunnel portal slopes mainly adopts the limit analysis method and the limit equilibrium method. Among them, the limit equilibrium method is the most widely used in engineering practice because of its relatively simple calculation. This method simplifies the rupture surface into a single circular arc or logarithmic spiral curve and calculates the slope safety factor based on static equilibrium conditions. In addition, in the field of slope anchor design, there is currently a lack of overall consideration, and conventional slope anchors have limited effect on improving the stability of the end wall.

[0004] However, existing slope safety factor calculation models and slope anchor design methods have many shortcomings, specifically in the following aspects: (1) Existing tunnel slope stability analysis usually simplifies the failure surface into a single logarithmic spiral or circular arc. Although this simplifies the calculation process, it has significant physical limitations: the former is mainly applicable to sandy soil dominated by internal friction angle, while the latter is more applicable to cohesive soil dominated by cohesion. However, most rock and soil masses exhibit composite characteristics of the combined action of cohesion and internal friction angle. Their strength characteristics and failure mechanisms are jointly dominated by the two, making it difficult for traditional methods to accurately simulate the real fracture trajectory of rock and soil masses. (2) In the existing tunnel slope anchor design, the slope anchor and the end wall treatment are often treated independently, lacking a collaborative working mechanism, making it difficult to give full play to their comprehensive anti-sliding effect in slope treatment; installing anchors on the end wall can, to a certain extent, simultaneously reinforce the slope and enhance the stability of the end wall itself, but there is currently a lack of a design system that integrates the slope anchor and the end wall anchor as anti-sliding components and incorporates them into the overall stability analysis of the slope.

[0005] Therefore, the problem that those skilled in the art urgently need to solve is: to overcome the limitations of traditional methods in terms of the single morphology of the fracture surface and the narrow scope of application, and to take into account both slope sliding and end wall treatment in the design of tunnel slope anchor bolts. Summary of the Invention

[0006] In view of the above problems, the present invention proposes a design method and device for tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model to overcome or at least partially solve the above problems.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for designing tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model includes: S1. Based on the cohesion and internal friction angle of the soil and rock mass, the corresponding friction weight coefficient is calculated and used to characterize the contribution weight of the internal friction angle in the strength composition of the soil and rock mass. A generalized logarithmic spiral failure model is constructed to uniformly characterize the spatial morphological features of the fracture surface of various soil and rock masses. S2. Based on the generalized logarithmic spiral failure model, the limit equilibrium analysis method is adopted, and the mechanical expression of the tunnel slope safety factor and the expression of the sliding surface geometric parameters are established with the center point of the generalized logarithmic spiral slip surface as the moment center. S3. Based on the generalized logarithmic spiral failure model, the mechanical expression of the tunnel slope safety factor, and the expression of the sliding surface geometric parameters, the most unfavorable sliding surface and safety factor are solved by the analytical optimization method of grid search. S4. Incorporate the end wall anchor as an anti-slip component into the overall limit equilibrium system, calculate the required increment of the safety factor and convert it into the required total additional resistance moment, distribute the total additional resistance moment to each slope anchor and end wall anchor, determine the design bearing capacity of a single anchor, and finally complete the design of the anchor parameters.

[0008] Preferably, in step S1, the generalized logarithmic spiral failure model is specifically as follows:

[0009]

[0010] in, The radius of rotation of the generalized logarithmic spiral sliding body. The polar angle of rotation for a generalized logarithmic spiral sliding body. This is the friction weighting coefficient. Let the initial radius of rotation of the generalized logarithmic spiral sliding body be . The initial polar angle of rotation for the generalized logarithmic spiral sliding body. For soil and rock mass cohesion, The internal friction angle of the rock and soil. The weight of the rock and soil is [not specified]. The vertical height of the generalized logarithmic spiral surface.

[0011] The preferred specific content for uniformly characterizing the spatial morphological features of fracture surfaces in various types of rock and soil masses includes: When the friction angle within the rock and soil When cohesion c = 0, corresponding to pure cohesive soil, the friction weight coefficient μ = 0, and the generalized logarithmic spiral curve degenerates into a circular arc; when cohesion c = 0, corresponding to pure sandy soil, μ = 1, and the generalized logarithmic spiral curve exhibits the standard logarithmic spiral curve; when 0 < μ < 1, the generalized logarithmic spiral curve exhibits a transitional form between the circular arc and the standard logarithmic spiral curve.

[0012] Preferably, step S2 includes the following: S21. For tunnel uphill excavation face with any geometric slope, establish a coordinate system xOy with the intersection point O of the vertical line of the starting point A and the horizontal line of the ending point B as the origin. The starting point A corresponds to the position of the tension crack at the rear edge of the landslide, the toe of the slope is the ending point B, which corresponds to the position of the shear exit at the front edge of the landslide, and ∠ABO is the slope α. S22. In the limit equilibrium analysis method, the slip surface AB is in the form of a generalized logarithmic spiral. The sliding body undergoes rigid rotation around the center point C of the generalized logarithmic spiral slip surface. Based on the geometric characteristics of the calculation model, the mechanical expression representing the safety factor of the slope and the relevant geometric parameter expressions of the slip surface are obtained. The geometric parameters include the initial rotation radius of the logarithmic spiral slip body, the final rotation radius of the generalized logarithmic spiral slip body, the distance between points AB, the rotation angle difference of the generalized logarithmic spiral slip body, the initial rotation polar angle of the generalized logarithmic spiral slip body, and the final rotation polar angle of the generalized logarithmic spiral slip body.

[0013] Preferably, the mechanical expression for the tunnel slope safety factor is as follows:

[0014]

[0015]

[0016]

[0017] in, For the slope safety factor, For the generalized logarithmic spiral sliding body sliding torque, To resist slip torque, Let the vertical height of the sliding body be a function of the vertical height of the sliding body. Let C be the coordinates of the center point C of the generalized logarithmic spiral sliding surface where the sliding body undergoes rigid rotation, and B be the calculated width of the uphill slope.

[0018] Preferably, the specific content of step S3 is as follows: S31. Substituting the geometric parameter expression of the sliding surface into the generalized logarithmic spiral failure model, the simplified result is obtained containing only the coordinates of the center point of the sliding surface of the generalized logarithmic spiral. Equations for a sliding surface with one unknown; S32. Select a region in the coordinate system, distribute points evenly in a grid pattern, and obtain the coordinates of each point; S33. Substitute the coordinates of each point into the simplified sliding surface equation. If the convergence accuracy requirement is met, it is considered as an analytical solution of the sliding surface equation, and thus a set of several possible rotation center positions is obtained. S34. Calculate the slope safety factor corresponding to each rotation center using the mechanical expression of the tunnel slope safety factor, and take the minimum safety factor as the most unfavorable case of slope instability to obtain the most unfavorable slip surface and the corresponding minimum safety factor. Based on the rotation center coordinates corresponding to the minimum safety factor, obtain the maximum values ​​of the sliding moment, anti-slip moment and vertical height of the generalized logarithmic spiral slip body.

[0019] Preferably, the specific content of step S4 is as follows: S41. Install anchor bolts in the direction of the calculated width of the upslope, obtain the height of the upslope anchor bolt arrangement range, the height of the end wall anchor bolts, the slope of the upslope, the horizontal inclination angle of the anchor bolts, and the slope of the tunnel end wall. Derive the anchor bolt lever arm, the end wall anchor lever arm, and the external length of the end wall anchor bolt from the geometric features of the model. S42. Calculate the required increment of the safety factor and convert it into the required total additional resistance moment. Distribute the total additional resistance moment to each anchor bolt and determine the design bearing capacity of a single anchor bolt. S43. Combining the theories of elasticity and shear force transmission, under the shear failure of the surrounding rock-grout interface in the anchorage zone, calculate the effective anchorage section length of the anchor rod, and combine the maximum vertical height of the sliding body, the horizontal inclination angle of the anchor rod, and the external length of the anchor rod in the end wall area to obtain the parameters of the end wall anchor rod and the slope sliding anchor rod.

[0020] Preferably, in step S41, the anchor bolt lever arm in the uphill area... Anchor arm in end wall area Length of anchor bolt outside the slope in the end wall area They are respectively:

[0021]

[0022]

[0023]

[0024] in, Let h3 be the coordinates of the center point C of the generalized logarithmic spiral slip surface, h2 be the height of the slope anchor arrangement range, h1 be the height of the bottom row of slope anchors, and h4 be the height of the end wall anchors exposed above the slope. The vertical height of the generalized logarithmic spiral surface. The slope is an upward slope. The horizontal inclination angle set for the anchor bolt, k:1 is the slope of the tunnel end wall; In step S42,

[0025]

[0026]

[0027]

[0028] in, For the safety factor increment, For the target safety factor, To calculate the safety factor, For the total additional resisting moment, The resultant force of the design bearing capacity of the anchor bolts in the slope area is as follows. The resultant force of the design bearing capacity of the anchor bolts in the end wall area, The design bearing capacity of a single anchor bolt. Design the number of rows of anchor bolts for the slope area. Design the number of rows of anchor bolts in the end wall area; In step S43, the effective anchorage length of the anchor bolt is:

[0029] in, This refers to the effective anchorage length of the anchor bolt. This is the standard value for bond strength. The diameter of the anchor bolt borehole; The parameters for end wall anchors and slope sliding anchors are as follows:

[0030] in, Design the length of the anchor bolt. This represents the maximum vertical height of the sliding body. The horizontal inclination angle set for the anchor bolt. This refers to the external length of the anchor bolt outside the slope in the end wall area.

[0031] Preferably, a computer-readable storage medium stores a computer program that, when executed by a processor, implements the aforementioned method for designing tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model.

[0032] Preferably, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the program to implement the aforementioned method for designing tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model.

[0033] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method and device for designing tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model, which has the following beneficial effects: By innovatively introducing a friction weight coefficient to construct a generalized logarithmic spiral failure model, the geometric morphology of the fracture surface is dynamically controlled, overcoming the limitations of traditional methods in terms of single fracture surface morphology and narrow applicability. This significantly improves the ability to characterize the failure mechanism of different soil and rock masses, unifies the mathematical description rules of the spatial morphology of fracture surfaces of various soil and rock masses, and can accurately reproduce the continuous failure process and fracture surface morphology characteristics of various soil and rock materials from pure cohesive soil to pure sand, as well as those in between. Based on the dynamic search of the most unfavorable slip surface and the limit balance algorithm of the safety factor, an integrated calculation method for tunnel slope anchor reinforcement is proposed, applicable to multiple working conditions such as construction, operation and emergency response to sudden slippage. It breaks through the limitations of traditional methods that only target slope reinforcement, and innovatively incorporates end wall anchors as a component of anti-slip force into the limit balance system. This systematically improves the overall integrity and reliability of the reinforcement design. It is not only suitable for conventional slope reinforcement during construction, but also effectively addresses complex risks such as end wall eccentric cracking and foundation instability caused by slope slippage. It provides reliable quantitative basis and technical support for the rapid assessment and scientific treatment of disasters at tunnel portals. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0035] Figure 1 This is a schematic diagram of a tunnel portal slope anchor bolt design method based on a generalized logarithmic spiral failure model provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the slope safety factor calculation provided in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the verification results of the tunnel slope safety factor provided in this embodiment of the invention. Figure 4 This is a schematic diagram illustrating the calculation of parameters for tunnel slope anchor bolts and end wall anchor bolts provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of the calculation parameters for an actual engineering case provided in the embodiments of the present invention; Figure 6 This is a schematic diagram of the anchor bolt parameter scheme provided in the embodiments of the present invention. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] This invention discloses a method for designing tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model, such as... Figure 1 ,include: S1. Based on the cohesion and internal friction angle of the soil and rock mass, the corresponding friction weight coefficient is calculated and used to characterize the contribution weight of the internal friction angle in the strength composition of the soil and rock mass. A generalized logarithmic spiral failure model is constructed to uniformly characterize the spatial morphological features of the fracture surface of various soil and rock masses. S2. Based on the generalized logarithmic spiral failure model, the limit equilibrium analysis method is adopted, and the mechanical expression of the tunnel slope safety factor and the expression of the sliding surface geometric parameters are established with the center point of the generalized logarithmic spiral slip surface as the moment center. S3. Based on the generalized logarithmic spiral failure model, the mechanical expression of the tunnel slope safety factor, and the expression of the sliding surface geometric parameters, the most unfavorable sliding surface and safety factor are solved by the analytical optimization method of grid search. S4. Incorporate the end wall anchor as an anti-slip component into the overall limit equilibrium system, calculate the required increment of the safety factor and convert it into the required total additional resistance moment, distribute the total additional resistance moment to each slope anchor and end wall anchor, determine the design bearing capacity of a single anchor, and finally complete the design of the anchor parameters.

[0038] To further implement the above technical solution, in step S1, the generalized logarithmic spiral failure model is specifically as follows:

[0039]

[0040] in, The radius of rotation of the generalized logarithmic spiral sliding body. The polar angle of rotation for a generalized logarithmic spiral sliding body. This is the friction weighting coefficient. Let the initial radius of rotation of the generalized logarithmic spiral sliding body be . The initial polar angle of rotation for the generalized logarithmic spiral sliding body. For soil and rock mass cohesion, The internal friction angle of the rock and soil. The weight of the rock and soil is [not specified]. The vertical height of the generalized logarithmic spiral surface.

[0041] To further implement the above technical solution, a friction weighting coefficient is used. Characterizing the internal friction angle of rock and soil The weight of the overall strength is determined, and its relationship with cohesion is established based on the Mohr-Coulomb strength criterion. and internal friction angle The functional expression; by using the friction weight coefficient Combining fracture surface morphology with cohesion and internal friction angle It provides a unified characterization of the spatial morphological features of fracture surfaces in various types of rock and soil bodies. The specific content includes: When the friction angle within the rock and soil When cohesion c = 0, corresponding to pure cohesive soil, the friction weight coefficient μ = 0, and the generalized logarithmic spiral curve degenerates into a circular arc; when cohesion c = 0, corresponding to pure sandy soil, μ = 1, and the generalized logarithmic spiral curve exhibits the standard logarithmic spiral curve; when 0 < μ < 1, the generalized logarithmic spiral curve exhibits a transitional form between the circular arc and the standard logarithmic spiral curve.

[0042] To further implement the above technical solutions, such as Figure 2 The specific content of step S2 includes: S21. For a tunnel upslope excavation face with an arbitrary geometric shape, establish a coordinate system xOy with the origin at the intersection O of the vertical line from the starting point A of the slip surface and the horizontal line from the ending point B of the slip surface. The starting point A of the slip surface corresponds to the location of the tension crack at the rear edge of the landslide, with coordinates as follows: , , The toe of the slope is the endpoint B of the slip surface. , The coordinates of the shear exit point at the leading edge of the landslide are: ∠ABO represents the slope α; S22. In the limit equilibrium analysis method, the slip surface AB is in the form of a generalized logarithmic spiral. The sliding body undergoes rigid rotation around the center point C of the generalized logarithmic spiral slip surface. Based on the geometric characteristics of the calculation model, the mechanical expression representing the safety factor of the slope and the relevant geometric parameter expressions of the slip surface are obtained. The geometric parameters include the initial rotation radius of the logarithmic spiral slip body, the final rotation radius of the generalized logarithmic spiral slip body, the distance between points AB, the rotation angle difference of the generalized logarithmic spiral slip body, the initial rotation polar angle of the generalized logarithmic spiral slip body, and the final rotation polar angle of the generalized logarithmic spiral slip body.

[0043] To further implement the above technical solution, the mechanical expression for the tunnel slope safety factor is as follows:

[0044] Based on the generalized logarithmic spiral sliding surface and the geometric relationship and functional equation of the slope, a function of the vertical height of the sliding body is established. Furthermore, the gravitational infinitesimal element and the arc length infinitesimal element are derived. ;

[0045]

[0046]

[0047] From gravity infinitesimal element Multiplying by the lever arm yields the torque element. Integrating the torque element along the rotation angle yields the generalized logarithmic spiral sliding torque:

[0048] Incremental component of antisliding moment on the slip surface along the logarithmic spiral on a generalized unit soil strip It can be determined by the infinitesimal component of the normal force on the slip surface. With shear force differential To indicate:

[0049] According to the Mohr-Coulomb strength criterion, we can obtain:

[0050] The generalized logarithmic spiral failure model and Substitute The antislip moment on the logarithmic spiral slip surface can be obtained by integrating along polar coordinates. :

[0051] in, For the slope safety factor, For the generalized logarithmic spiral sliding body sliding torque, To resist slip torque, Let the vertical height of the sliding body be a function of the vertical height of the sliding body. Let C be the coordinates of the center point C of the generalized logarithmic spiral sliding surface where the sliding body undergoes rigid rotation, and B be the calculated width of the uphill slope.

[0052] In this embodiment, the polar coordinate expression of the generalized logarithmic spiral curve is transformed into a rectangular coordinate system expression:

[0053]

[0054] Based on the geometric features of the computational model, we can further deduce... , , , The calculation formula is:

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] in, Let the initial radius of rotation of the generalized logarithmic spiral sliding body be . The final rotation radius of the generalized logarithmic spiral sliding body. The distance between points A and B is... For the difference in rotation angles of the generalized logarithmic spiral sliding body, The initial polar angle of rotation for the generalized logarithmic spiral sliding body. The polar angle at the termination of the rotation of the generalized logarithmic spiral sliding body.

[0061] Given the slope angle and slope height, the equation of the straight line of the slope can be derived: .

[0062] To further implement the above technical solution, the specific content of step S3 is as follows: S31. Substituting the geometric parameter expression of the sliding surface into the generalized logarithmic spiral failure model, the simplified result is obtained containing only the coordinates of the center point of the sliding surface of the generalized logarithmic spiral. Equations for a sliding surface with one unknown; Specifically: Substituting the polar angle of the final rotation of the generalized logarithmic spiral sliding body into the expression of the generalized logarithmic spiral failure model, we obtain the formula for calculating the final rotation radius of the generalized logarithmic spiral sliding body:

[0063] Substituting the initial rotation radius, final rotation radius, distance AB, rotation angle difference, initial polar angle, and final polar angle of the generalized logarithmic spiral body obtained in S22 into the above equations, after simplification, we can obtain the equation containing only the coordinates of the rotation center C. , Equations for a sliding surface with one unknown; S32. Select a region in the coordinate system, distribute points evenly in a grid pattern, and obtain the coordinates of each point; S33. Substitute the coordinates of each point into the simplified sliding surface equation. If the convergence accuracy requirement is met, it is considered an analytical solution of the sliding surface equation, and thus a set of several possible rotation center positions is obtained. In practical applications, the larger the area of ​​the selected region, the more approximate solutions are obtained; the denser the distribution of points, the higher the solution accuracy. S34. Calculate the slope safety factor corresponding to each rotation center using the mechanical expression of the tunnel slope safety factor, and take the minimum safety factor as the most unfavorable case of slope instability to obtain the most unfavorable slip surface and the corresponding minimum safety factor. Based on the rotation center coordinates corresponding to the minimum safety factor, obtain the maximum values ​​of the sliding moment, anti-slip moment and vertical height of the generalized logarithmic spiral slip body.

[0064] In this embodiment, to verify the rationality of the method for calculating the safety factor of the tunnel side slope, several slope examples are selected for comparative analysis, such as... Figure 3 As shown in the comparison results, the minimum safety factor calculated by the method of this invention is highly consistent with the results of other methods, with an average error of less than 3%, which verifies that the method has good calculation accuracy and engineering applicability.

[0065] To further implement the above technical solutions, such as Figure 4 The specific content of step S4 is as follows: S41. Install anchor bolts in the direction of the calculated width of the upslope, obtain the height of the upslope anchor bolt arrangement range, the height of the end wall anchor bolts, the slope of the upslope, the horizontal inclination angle of the anchor bolts, and the slope of the tunnel end wall. Derive the anchor bolt lever arm, the end wall anchor lever arm, and the external length of the end wall anchor bolt from the geometric features of the model. S42. Calculate the required increment of the safety factor and convert it into the required total additional resistance moment. Distribute the total additional resistance moment to each anchor bolt and determine the design bearing capacity of a single anchor bolt. S43. According to the relevant provisions of the "Technical Specification for Rock and Soil Anchors and Shotcrete Support Engineering" (GB 50086-2015), and combined with the theory of elasticity and shear force transmission, when the surrounding rock-grout interface of the anchorage zone is under shear failure, calculate the effective anchorage section length of the anchor, and combine the maximum vertical height of the sliding body, the horizontal inclination angle of the anchor, and the external length of the anchor in the end wall area to obtain the parameters of the end wall anchor and the slope sliding anchor.

[0066] To further implement the above technical solution, in step S41, the anchor arm in the slope area... Anchor arm in end wall area Length of anchor bolt outside the slope in the end wall area They are respectively:

[0067]

[0068]

[0069]

[0070] in, Let h3 be the coordinates of the center point C of the generalized logarithmic spiral slip surface, h2 be the height of the slope anchor arrangement range, h1 be the height of the bottom row of slope anchors, and h4 be the height of the end wall anchors exposed above the slope. The vertical height of the generalized logarithmic spiral surface. The slope is an upward slope. The horizontal inclination angle set for the anchor bolt, k:1 is the slope of the tunnel end wall; In step S42,

[0071]

[0072]

[0073]

[0074] in, For the safety factor increment, For the target safety factor, To calculate the safety factor, For the total additional resisting moment, The resultant force of the design bearing capacity of the anchor bolts in the slope area is as follows. The resultant force of the design bearing capacity of the anchor bolts in the end wall area, The design bearing capacity of a single anchor bolt. Design the number of rows of anchor bolts for the slope area. Design the number of rows of anchor bolts in the end wall area; In step S43, the effective anchorage length of the anchor bolt is:

[0075] in, This refers to the effective anchorage length of the anchor bolt. The standard value for bond strength is taken from the "Technical Specification for Rock and Soil Anchors and Shotcrete Support Engineering". The diameter of the anchor bolt borehole; The parameters for end wall anchors and slope sliding anchors are as follows:

[0076] in, Design the length of the anchor bolt. This represents the maximum vertical height of the sliding body. The horizontal inclination angle set for the anchor bolt. This refers to the external length of the anchor bolt outside the slope in the end wall area.

[0077] To further implement the above technical solution, a computer-readable storage medium storing a computer program is provided, characterized in that the program, when executed by a processor, implements a design method for tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model.

[0078] To further implement the above technical solution, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, when the processor executes the program, it implements a design method for tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model.

[0079] In another embodiment, taking a real-world engineering case as an example, it is proposed to use 32mm diameter fully threaded steel bar anchors for tunnel slope reinforcement. The required calculation parameters are as follows: Figure 5 As shown, calculations using computer equipment yield the following results. , , , , , After substituting the values ​​into the formulas in step S4, and taking the design number of anchor bolt rows in the slope area, The number of anchor bolt rows in the end wall area is 3 or 4. If the value is 1 or 0, the calculation results are as follows: Figure 6 The comparison options shown are Option 1 and Option 2. The specific option to be selected can be determined based on a comprehensive comparison of the actual situation of the project.

[0080] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0081] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A design method for tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model, characterized in that, include: S1. Based on the cohesion and internal friction angle of the soil and rock mass, the corresponding friction weight coefficient is calculated and used to characterize the contribution weight of the internal friction angle in the strength composition of the soil and rock mass. A generalized logarithmic spiral failure model is constructed to uniformly characterize the spatial morphological features of the fracture surface of various soil and rock masses. S2. Based on the generalized logarithmic spiral failure model, the limit equilibrium analysis method is adopted, and the mechanical expression of the tunnel slope safety factor and the expression of the sliding surface geometric parameters are established with the center point of the generalized logarithmic spiral slip surface as the moment center. S3. Based on the generalized logarithmic spiral failure model, the mechanical expression of the tunnel slope safety factor, and the expression of the sliding surface geometric parameters, the most unfavorable sliding surface and safety factor are solved by the analytical optimization method of grid search. S4. Incorporate the end wall anchor as an anti-slip component into the overall limit equilibrium system, calculate the required increment of the safety factor and convert it into the required total additional resistance moment, distribute the total additional resistance moment to each slope anchor and end wall anchor, determine the design bearing capacity of a single anchor, and finally complete the design of the anchor parameters. In step S1, the generalized logarithmic spiral failure model is specifically as follows: in, The radius of rotation of the generalized logarithmic spiral sliding body. The polar angle of rotation for a generalized logarithmic spiral sliding body. This is the friction weighting coefficient. Let the initial radius of rotation of the generalized logarithmic spiral sliding body be . The initial polar angle of rotation for the generalized logarithmic spiral sliding body. For the cohesion of the soil and rock mass, The internal friction angle of the rock and soil. The weight of the rock and soil is [not specified]. The vertical height of the generalized logarithmic spiral surface.

2. The method for designing tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model as described in claim 1, characterized in that, The specific content that uniformly characterizes the spatial morphological features of fracture surfaces in various types of rock and soil masses is as follows: When the friction angle within the rock and soil When cohesion c = 0, corresponding to pure cohesive soil, the friction weight coefficient μ = 0, and the generalized logarithmic spiral curve degenerates into a circular arc; when cohesion c = 0, corresponding to pure sandy soil, μ = 1, and the generalized logarithmic spiral curve exhibits the standard logarithmic spiral curve; when 0 < μ < 1, the generalized logarithmic spiral curve exhibits a transitional form between the circular arc and the standard logarithmic spiral curve.

3. The method for designing tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model as described in claim 1, characterized in that, The specific content of step S2 includes: S21. For tunnel uphill excavation face with any geometric slope, establish a coordinate system xOy with the intersection point O of the vertical line of the starting point A and the horizontal line of the ending point B as the origin. The starting point A corresponds to the position of the tension crack at the rear edge of the landslide, the toe of the slope is the ending point B, which corresponds to the position of the shear exit at the front edge of the landslide, and ∠ABO is the slope α. S22. In the limit equilibrium analysis method, the slip surface AB is in the form of a generalized logarithmic spiral. The sliding body undergoes rigid rotation around the center point C of the generalized logarithmic spiral slip surface. Based on the geometric characteristics of the calculation model, the mechanical expression representing the safety factor of the slope and the relevant geometric parameter expressions of the slip surface are obtained. The geometric parameters include the initial rotation radius of the logarithmic spiral slip body, the final rotation radius of the generalized logarithmic spiral slip body, the distance between points AB, the rotation angle difference of the generalized logarithmic spiral slip body, the initial rotation polar angle of the generalized logarithmic spiral slip body, and the final rotation polar angle of the generalized logarithmic spiral slip body.

4. The method for designing tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model as described in claim 3, characterized in that, The mechanical expression for the safety factor of the tunnel slope is as follows: in, For the slope safety factor, For the generalized logarithmic spiral sliding body sliding torque, To resist slip torque, Let the vertical height of the sliding body be a function of the vertical height of the sliding body. Let C be the coordinates of the center point C of the generalized logarithmic spiral sliding surface where the sliding body undergoes rigid rotation, and B be the calculated width of the uphill slope.

5. The method for designing tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model as described in claim 1, characterized in that, The specific content of step S3 is as follows: S31. Substituting the geometric parameter expression of the sliding surface into the generalized logarithmic spiral failure model, the simplified result is obtained containing only the coordinates of the center point of the sliding surface of the generalized logarithmic spiral. Equations of a sliding surface with one unknown; S32. Select a region in the coordinate system, distribute points evenly in a grid pattern, and obtain the coordinates of each point; S33. Substitute the coordinates of each point into the simplified sliding surface equation. If the convergence accuracy requirement is met, it is considered as an analytical solution of the sliding surface equation, and thus a set of several possible rotation center positions is obtained. S34. Calculate the slope safety factor corresponding to each rotation center using the mechanical expression of the tunnel slope safety factor, and take the minimum safety factor as the most unfavorable case of slope instability to obtain the most unfavorable slip surface and the corresponding minimum safety factor. Based on the rotation center coordinates corresponding to the minimum safety factor, obtain the maximum values ​​of the sliding moment, anti-slip moment and vertical height of the generalized logarithmic spiral slip body.

6. The method for designing tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model as described in claim 1, characterized in that, The specific content of step S4 is as follows: S41. Install anchor bolts in the direction of the calculated width of the upslope, obtain the height of the upslope anchor bolt arrangement range, the height of the end wall anchor bolts, the slope of the upslope, the horizontal inclination angle of the anchor bolts, and the slope of the tunnel end wall. Derive the anchor bolt lever arm, the end wall anchor lever arm, and the external length of the end wall anchor bolt from the geometric features of the model. S42. Calculate the required increment of the safety factor and convert it into the required total additional resistance moment. Distribute the total additional resistance moment to each anchor bolt and determine the design bearing capacity of a single anchor bolt. S43. Combining the theories of elasticity and shear force transmission, under the shear failure of the surrounding rock-grout interface in the anchorage zone, calculate the effective anchorage section length of the anchor rod, and combine the maximum vertical height of the sliding body, the horizontal inclination angle of the anchor rod, and the external length of the anchor rod in the end wall area to obtain the parameters of the end wall anchor rod and the slope sliding anchor rod.

7. The method for designing tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model as described in claim 6, characterized in that, In step S41, the anchor arm in the slope area Anchor arm in end wall area Length of anchor bolt outside the slope in the end wall area They are respectively: in, Let h3 be the coordinates of the center point C of the generalized logarithmic spiral slip surface, h2 be the height of the slope anchor arrangement range, h1 be the height of the bottom row of slope anchors, and h4 be the height of the end wall anchors exposed above the slope. The vertical height of the generalized logarithmic spiral surface. The slope is an upward slope. The horizontal inclination angle set for the anchor bolt, k:1 is the slope of the tunnel end wall; In step S42, in, For the safety factor increment, For the target safety factor, To calculate the safety factor, For the total additional resisting moment, For the generalized logarithmic spiral sliding body sliding torque, To resist slip torque, The resultant force of the design bearing capacity of the anchor bolts in the slope area is as follows. The resultant force of the design bearing capacity of the anchor bolts in the end wall area, The design bearing capacity of a single anchor bolt. Design the number of rows of anchor bolts in the uphill area. Design the number of rows of anchor bolts in the end wall area; In step S43, the effective anchorage length of the anchor bolt is: in, This refers to the effective anchorage length of the anchor bolt. This is the standard value for bond strength. The diameter of the anchor bolt borehole; The parameters for end wall anchors and slope sliding anchors are as follows: in, Design the length of the anchor bolt. This represents the maximum vertical height of the sliding body. The horizontal inclination angle set for the anchor bolt. This refers to the external length of the anchor bolt outside the slope in the end wall area.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements a method for designing tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model as described in any one of claims 1 to 7.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements a method for designing tunnel portal slope anchor bolts based on a generalized logarithmic spiral failure model as described in any one of claims 1 to 7.

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