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

Abstract

The invention discloses a tunnel portal upward slope anchor rod design method and device based on a generalized logarithmic spiral failure model, and the method comprises the steps: introducing a friction weight coefficient to represent the contribution weight of an internal friction angle in the strength of a rock-soil body, constructing the generalized logarithmic spiral failure model, and uniformly representing the spatial form characteristics of various rock-soil body fracture surfaces; based on the generalized logarithmic spiral damage model, a limit equilibrium analysis method is adopted, the center point of the generalized logarithmic spiral sliding surface is used as the center of moment, and tunnel upward slope safety coefficient mechanical expression is established; solving the most unfavorable sliding surface and the safety coefficient by adopting a gridding search analysis optimization method; the end wall anchor rods are included in a limit equilibrium system, the safety coefficient increment is calculated and converted into total additional resisting moment, the total additional resisting moment is distributed to all the upward slope anchor rods and the end wall anchor rods, the design bearing capacity of the single anchor rod is determined, and anchor rod parameter design is completed; according to the method, various rock-soil body fracture surface spatial form descriptions are unified, slope sliding and end wall treatment are considered as a whole, anchor rods are designed, and the integrity and reliability of reinforcing design are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel engineering, and more particularly to a tunnel portal upslope anchor rod design method and device based on a generalized logarithmic spiral failure model. BACKGROUND

[0002] The stability of the tunnel portal upslope is a key factor determining the safety of tunnel construction and long-term service performance. Currently, as transportation infrastructure continues to extend to 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 portal slope significantly disrupts the original stress balance of the rock mass. During the operation phase, the mechanical properties of the rock and soil continue to deteriorate under the action of long-term weathering and rainwater infiltration. In addition, the frequent occurrence of extreme weather, earthquakes and other sudden natural disasters can easily lead to sudden upslope sliding.

[0003] Currently, the stability analysis of the tunnel portal upslope mainly uses the limit analysis method and the limit equilibrium method. The limit equilibrium method is the most widely used in engineering practice because of its relatively simple calculation. This method simplifies the failure surface as a single circular arc or logarithmic spiral curve and calculates the safety factor of the slope body based on the static equilibrium condition. In addition, in the field of upslope anchor rod design, there is currently a lack of overall consideration, and conventional upslope anchor rods have limited effect on improving the stability of the end wall.

[0004] However, the existing slope safety factor calculation model and upslope anchor rod design method have many shortcomings, which are manifested in the following aspects: (1) The existing tunnel upslope stability analysis usually simplifies the failure surface as a single logarithmic spiral or circular arc curve, which simplifies the calculation process but has significant physical limitations: the former is mainly suitable for sandy soil dominated by internal friction angle, and the latter is more suitable for cohesive soil dominated by cohesion. However, most rock and soil bodies exhibit complex characteristics of both cohesion and internal friction angle, and their strength characteristics and failure mechanisms are jointly governed by both, making it difficult for traditional methods to accurately simulate the true failure trajectory of rock and soil bodies. (2) In the existing tunnel upslope anchor rod design, the upslope anchor rod and the end wall treatment are often treated independently, lacking a collaborative working mechanism, and it is difficult to fully utilize the comprehensive anti-sliding effect of both in slope treatment. Drilling anchor rods on the end wall can simultaneously reinforce the slope and enhance the stability of the end wall itself to some extent, but there is currently a lack of a design system that considers the upslope anchor rod and the end wall anchor rod as anti-sliding components and integrates them into the overall stability analysis of the slope body.

[0005] Therefore, the problem that needs to be solved by those skilled in the art is to overcome the limitations of traditional methods in terms of single failure surface shape and narrow application range, and to consider the slope sliding and end wall treatment in the design of tunnel upslope anchor rods. SUMMARY

[0006] In view of the above problems, the tunnel portal upside slope anchor rod design method and device based on the generalized logarithmic spiral failure model are proposed to overcome the above problems or at least partially solve the above problems.

[0007] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: The tunnel portal upside slope anchor rod design method based on the generalized logarithmic spiral failure model comprises: S1. The friction weight coefficient is calculated based on the cohesion and internal friction angle of the rock-soil mass, which is used to represent the contribution weight of the internal friction angle in the strength composition of the rock-soil mass, to construct the generalized logarithmic spiral failure model and uniformly represent the spatial morphological characteristics of the failure surface of various rock-soil masses; S2. Based on the generalized logarithmic spiral failure model, the limit equilibrium analysis method is adopted to establish the mechanical expression of the safety factor of the tunnel upside slope and the geometric parameter expression of the sliding surface with the center point of the generalized logarithmic spiral sliding surface as the centroid; S3. Based on the generalized logarithmic spiral failure model, the mechanical expression of the safety factor of the tunnel upside slope and the geometric parameter expression of the sliding surface, the analytical optimization method of gridding search is adopted to solve the most unfavorable sliding surface and the safety factor; S4. The end wall anchor rod is included in the overall limit equilibrium system as a system anti-sliding component, the required increment of the safety factor is calculated and converted into the required total additional resistance moment, the total additional resistance moment is distributed to each upside slope anchor rod and end wall anchor rod, the design bearing capacity of a single anchor rod is determined, and finally the design of the anchor rod parameters is completed.

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

[0009]

[0010] wherein, is the rotation radius of the generalized logarithmic spiral sliding body, is the rotation polar angle of the generalized logarithmic spiral sliding body, is the friction weight coefficient, is the initial rotation radius of the generalized logarithmic spiral sliding body, is the initial rotation polar angle of the generalized logarithmic spiral sliding body, is the cohesion of the rock-soil mass, is the internal friction angle of the rock-soil mass, is the specific weight of the rock-soil mass, is the vertical height of the generalized logarithmic spiral sliding surface.

[0011] Preferably, the specific content of the unified representation of the spatial morphological characteristics of the failure surface of various rock-soil masses is: When the internal friction angle of the rock-soil mass is = 0, corresponding to pure cohesive soil, friction weight coefficient μ = 0, the generalized logarithmic spiral curve degenerates into a circular arc; when the cohesion c = 0, corresponding to pure sandy soil, μ = 1, the generalized logarithmic spiral curve is a standard logarithmic spiral curve; when 0 < μ < 1, the generalized logarithmic spiral curve is a transition form between the circular arc and the standard logarithmic spiral curve.

[0012] Preferably, the specific content of step S2 includes: S21. For the tunnel slope excavation surface of any geometric shape, the coordinate system xOy is established with the intersection point O of the vertical line of the sliding surface starting point A and the horizontal line of the sliding surface ending point B as the origin, the sliding surface starting point A corresponding to the tensile crack position of the rear edge of the landslide, the slope foot being the sliding surface ending point B, corresponding to the shear outlet position of the front edge of the landslide, and ∠ABO being the slope α; S22. In the limit equilibrium analysis method, the sliding surface AB is in the form of a generalized logarithmic spiral, the sliding body rotates rigidly around the center point C of the generalized logarithmic spiral sliding surface, and according to the geometric characteristics of the calculation model, the mechanical expression for expressing the safety factor of the tunnel slope and the related geometric parameter expression of the sliding surface are obtained, including the initial rotation radius of the logarithmic spiral sliding body, the terminal rotation radius of the generalized logarithmic spiral sliding body, the distance between AB points, the rotation angle difference of the generalized logarithmic spiral sliding body, the initial rotation polar angle of the generalized logarithmic spiral sliding body, and the terminal rotation polar angle of the generalized logarithmic spiral sliding body.

[0013] Preferably, the mechanical expression for expressing the safety factor of the tunnel slope is specifically:

[0014]

[0015]

[0016]

[0017] wherein, is the safety factor of the tunnel slope, is the sliding torque of the generalized logarithmic spiral sliding body, is the anti-sliding torque, is the vertical height function of the sliding body, is the coordinate of the center point C of the generalized logarithmic spiral sliding surface of the sliding body rotating rigidly, and B is the calculation width of the tunnel slope.

[0018] Preferably, the specific content of step S3 is: S31. Substitute the sliding surface geometric parameter expression into the generalized logarithmic spiral failure model, and after simplification, obtain the sliding surface equation containing only the coordinates of the center point C of the generalized logarithmic spiral sliding surface unknowns; S32. Select a certain area in the coordinate system, and uniformly distribute points in a grid shape to 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 then a set of possible rotating center position points is obtained; S34. Calculate the safety factor of each rotating center corresponding to the tunnel upward slope using the mechanical expression of the safety factor, and take the minimum safety factor as the most unfavorable situation of slope instability to obtain the most unfavorable sliding surface and the corresponding minimum safety factor. Based on the coordinates of the rotating center corresponding to the minimum safety factor, the maximum values of the sliding moment, the anti-sliding moment and the vertical height of the generalized logarithmic spiral sliding body are obtained.

[0019] Preferably, the specific content of step S4 is: S41. Anchor rods are set in the calculation width direction of the upward slope to obtain the anchor rod arrangement range height of the upward slope, the anchor rod setting height of the end wall area, the slope of the upward slope, the horizontal inclination angle of the anchor rod, the slope of the tunnel end wall, the anchor rod force arm of the upward slope area, the anchor rod force arm of the end wall area, and the length of the anchor rod outside the slope body in the end wall area are derived from the geometric characteristics of the model; S42. Calculate the required increment of the safety factor and convert it into the required total additional anti-moment. The total additional anti-moment is distributed to each anchor rod to determine the design bearing capacity of a single anchor rod; S43. According to the theory of elasticity and the shear transfer theory, when the shear failure occurs at the interface between the anchoring area surrounding rock and the grouting body, the effective anchoring length of the anchor rod is calculated, and the parameters of the end wall anchor rod and the upward sliding anchor rod are obtained based on the maximum vertical height of the sliding body, the horizontal inclination angle of the anchor rod, and the length of the anchor rod outside the slope body in the end wall area.

[0020] Preferably, in step S41, the anchor rod force arm of the upward slope area , the anchor rod force arm of the end wall area , and the length of the anchor rod outside the slope body in the end wall area are respectively:

[0021]

[0022]

[0023]

[0024] wherein, is the coordinates of the center point C of the generalized logarithmic spiral sliding surface, h3 is the anchor rod arrangement range height of the upward slope, h2 is the setting height of the lowermost row of anchor rods of the upward slope, h1 is the setting height of the anchor rod in the end wall area, and h4 is the height of the anchor rod when it is exposed to the slope body in the end wall area, is the vertical height of the generalized logarithmic spiral sliding surface, is the slope of the upward slope, k:1 is the tunnel end wall slope; In step S42,

[0025]

[0026]

[0027]

[0028] wherein, is the safety factor increment, is the target safety factor, is the calculated safety factor, is the total additional moment, is the total designed bearing capacity of the anchor rod in the slope area, is the total designed bearing capacity of the anchor rod in the end wall area, is the designed bearing capacity of a single anchor rod, is the designed row number of the anchor rod in the slope area, is the designed row number of the anchor rod in the end wall area; In step S43, the effective anchoring length of the anchor rod is:

[0029] wherein, is the effective anchoring length of the anchor rod, is the standard value of the bonding strength, is the diameter of the anchor rod hole; The parameters of the end wall anchor rod and the sliding anchor rod in the slope are:

[0030] wherein, is the designed length of the anchor rod, is the maximum vertical height of the sliding body, is the horizontal inclination angle of the anchor rod, is the length of the anchor rod outside the slope in the end wall area.

[0031] Preferably, a computer readable storage medium has a computer program stored thereon, the program being executed by a processor to implement the tunnel portal slope anchor rod design method based on the generalized logarithmic spiral failure model.

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

[0033] Compared with the prior art, the tunnel portal upward slope anchor rod design method and device based on the generalized logarithmic spiral failure model have the following beneficial effects: The generalized logarithmic spiral failure model is constructed by innovatively introducing a friction weight coefficient to dynamically control the geometric shape of the failure surface, overcoming the limitations of traditional methods in terms of single failure surface shape and narrow application range, significantly improving the ability to describe the failure mechanism of different rock-soil bodies, unifying the mathematical description rules of the spatial shape of the failure surface of various rock-soil bodies, and accurately reproducing the continuous failure process and failure surface shape characteristics of various rock-soil materials from pure cohesive soil to pure sand. Based on the most unfavorable sliding surface dynamic search and safety factor limit equilibrium algorithm, an integrated calculation method for tunnel upward slope anchor rod reinforcement is proposed for multiple working conditions such as construction period, operation period and sudden slip rescue, breaking through the limitation of traditional slope reinforcement, and innovatively including the end wall anchor rod as a component of the anti-sliding force into the limit equilibrium system, thereby systematically improving the integrity and reliability of the reinforcement design. BRIEF DESCRIPTION OF DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are only embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor based on the provided drawings.

[0035] Figure 1 A schematic diagram of the tunnel portal upward slope anchor rod design method based on the generalized logarithmic spiral failure model provided in the embodiments of the present application; Figure 2 A schematic diagram of the upward slope safety factor calculation provided in the embodiments of the present application; Figure 3 A schematic diagram of the verification results of the tunnel upward slope safety factor provided in the embodiments of the present application; Figure 4 A schematic diagram of the tunnel upward slope anchor rod and end wall anchor rod parameter calculation provided in the embodiments of the present application; Figure 5 A schematic diagram of the actual engineering case calculation parameters provided in the embodiments of the present application; Figure 6 A schematic diagram of the anchor rod parameter scheme provided in the embodiments of the present application. DETAILED DESCRIPTION

[0036] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0037] The embodiments of the present application disclose a tunnel portal upside slope anchor rod design method based on a generalized logarithmic spiral failure model, like Figure 1 , comprising: S1. A friction weight coefficient is calculated based on the cohesion and internal friction angle of the rock-soil mass, used to represent the contribution weight of the internal friction angle in the strength composition of the rock-soil mass, a generalized logarithmic spiral failure model is constructed, and the spatial shape characteristics of the failure surface of various rock-soil masses are uniformly represented; S2. Based on the generalized logarithmic spiral failure model, a limit equilibrium analysis method is used, with the center point of the generalized logarithmic spiral sliding surface as the centroid, to establish a mechanical expression of the safety factor of the tunnel upside slope and a sliding surface geometric parameter expression; S3. Based on the generalized logarithmic spiral failure model, the mechanical expression of the safety factor of the tunnel upside slope and the sliding surface geometric parameter expression, an analytical optimization method of grid search is used to solve the most unfavorable sliding surface and the safety factor; S4. The end wall anchor rod is included in the overall limit equilibrium system as a system anti-slide component, the required increment of the safety factor is calculated and converted into the required total additional resistance moment, the total additional resistance moment is distributed to each upside slope anchor rod and end wall anchor rod, the design bearing capacity of a single anchor rod is determined, and finally the design of the anchor rod parameters is completed.

[0038] In order to further implement the above technical solutions, in step S1, the generalized logarithmic spiral failure model is specifically:

[0039]

[0040] wherein, is the generalized logarithmic spiral sliding body rotation radius, is the generalized logarithmic spiral sliding body rotation polar angle, is the friction weight coefficient, is the generalized logarithmic spiral sliding body initial rotation radius, is the generalized logarithmic spiral sliding body initial rotation polar angle, is the cohesion of the rock-soil mass, is the internal friction angle of the rock-soil mass, is the specific gravity of the rock-soil mass, is the vertical height of the generalized logarithmic spiral sliding surface.

[0041] In order to further implement the above technical solutions, the friction weight coefficient μ is introduced Characterize the internal friction angle of rock-soil mass In the overall strength, and based on the Mohr-Coulomb strength criterion to establish its function expression with cohesion And internal friction angle ; By means of friction weight coefficient μ The fracture surface morphology and cohesion And internal friction angle , unified characterization of the spatial morphology characteristics of various rock-soil mass fracture surface, the specific content is: When the internal friction angle of rock-soil mass =0, corresponding to the pure cohesive soil, friction weight coefficient μ=0, the generalized logarithmic spiral curve degenerates into a circular arc; When the cohesion c=0, corresponding to the pure sandy soil, μ=1, the generalized logarithmic spiral curve shows the standard logarithmic spiral curve; When 0<μ<1, the generalized logarithmic spiral curve shows a transition form between the circular arc and the standard logarithmic spiral curve.

[0042] In order to further implement the above technical solutions, such as Figure 2 , the specific content of step S2 includes: S21. For the tunnel slope excavation surface of any geometric shape, the coordinate system xOy is established with the intersection O of the vertical line of the sliding surface starting point A and the horizontal line of the sliding surface ending point B as the origin, the sliding surface starting point A corresponds to the tensile crack position of the landslide back edge, the coordinates are , , , the slope foot is the sliding surface ending point B, , , corresponding to the shear outlet position of the landslide front edge, the coordinates are , ∠ABO is the slope α; S22. In the limit equilibrium analysis method, the sliding surface AB is in the form of generalized logarithmic spiral, the sliding mass rotates rigidly around the generalized logarithmic spiral sliding surface center point C, according to the geometric characteristics of the calculation model, the mechanical expression of the slope safety factor and the related geometric parameter expression of the sliding surface are obtained, the geometric parameters include the initial rotation radius of the logarithmic spiral sliding mass, the termination rotation radius of the generalized logarithmic spiral sliding mass, the distance between AB points, the rotation angle difference of the generalized logarithmic spiral sliding mass, the initial rotation polar angle of the generalized logarithmic spiral sliding mass and the termination rotation polar angle of the generalized logarithmic spiral sliding mass.

[0043] In order to further implement the above technical solutions, the mechanical expression of the tunnel slope safety factor is specifically:

[0044] Based on the geometric relationship and function equation between the generalized logarithmic spiral slip surface and the slope surface, the vertical height function of the sliding body is established , and then the gravity micro-element and the arc length micro-element are derived ;

[0045]

[0046]

[0047] The moment micro-element is obtained by multiplying the force arm by the gravity micro-element , and the sliding moment of the generalized logarithmic spiral sliding body can be obtained by integrating the moment micro-element along the rotation angle :

[0048] The anti-sliding moment differential on the generalized unit soil strip along the logarithmic spiral slip surface can be represented by the normal force differential and the shear force differential on the slip surface:

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

[0050] The generalized logarithmic spiral failure model and are brought into , and the anti-sliding moment on the logarithmic spiral slip surface can be obtained by integrating along the polar coordinates :

[0051] wherein is the safety factor of the inverted slope, is the sliding moment of the generalized logarithmic spiral sliding body, is the anti-sliding moment, is the vertical height function of the sliding body, is the coordinate of the center point C of the generalized logarithmic spiral slip surface where the sliding body rotates rigidly, and B is the calculation width of the inverted slope.

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

[0053]

[0054] According to the geometric characteristics of the calculation model, the following equations are derived , 、 、 , the calculation formula is:

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] wherein, is the initial rotation radius of the generalized logarithmic spiral sliding body, is the terminal rotation radius of the generalized logarithmic spiral sliding body, is the distance of AB point, is the rotation angle difference of the generalized logarithmic spiral sliding body, is the initial rotation polar angle of the generalized logarithmic spiral sliding body, is the terminal rotation polar angle of the generalized logarithmic spiral sliding body.

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

[0062] In order to further implement the above technical scheme, the specific content of step S3 is: S31. Substitute the sliding surface geometric parameter expression into the generalized logarithmic spiral failure model, and after simplification, obtain the sliding surface equation containing only the coordinates of the center point of the generalized logarithmic spiral sliding surface unknowns; Specifically: substitute the terminal rotation polar angle of the generalized logarithmic spiral sliding body into the expression of the generalized logarithmic spiral failure model to obtain the calculation formula of the terminal rotation radius of the generalized logarithmic spiral sliding body:

[0063] Substitute the initial rotation radius of the logarithmic spiral sliding body, the terminal rotation radius of the generalized logarithmic spiral sliding body, the distance of AB point, the rotation angle difference of the generalized logarithmic spiral sliding body, the initial rotation polar angle of the generalized logarithmic spiral sliding body and the terminal rotation polar angle of the generalized logarithmic spiral sliding body obtained in S22 into the above equation, and after simplification, obtain the sliding surface equation containing only the coordinates of the rotation center C 、 unknowns; S32. Select a certain area in the coordinate system and uniformly distribute points in a grid shape to obtain the coordinates of each point; S33. Substituting 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 then a set of possible rotating center position points is obtained; in practical application, the larger the selected area, the more approximate solutions are obtained; the denser the points are distributed, the higher the solving accuracy is; S34. The safety factor of the tunnel's upward slope is calculated using the mechanical expression of the safety factor of the tunnel's upward slope, and the minimum safety factor is used as the most unfavorable situation of slope instability to obtain the most unfavorable sliding surface and the corresponding minimum safety factor, and based on the coordinates of the rotating center corresponding to the minimum safety factor, the maximum values of the sliding moment, the anti-sliding moment and the vertical height of the generalized logarithmic spiral sliding body are obtained.

[0064] In the present embodiment, in order to verify the rationality of the safety factor calculation method of the tunnel side-upward slope, a number of slope examples are selected for comparative analysis, as shown in Figure 3 The comparative results show that the minimum safety factor calculated by the method of the present application is highly consistent with the results of other methods, with an average error of less than 3%, verifying that the method has good calculation accuracy and engineering applicability.

[0065] In order to further implement the above technical solutions, as Figure 4 , the specific content of step S4 is: S41. Anchors are set in the width direction of the upward slope to obtain the height of the anchor arrangement range of the upward slope, the setting height of the anchor in the end wall area, the slope of the upward slope, the horizontal inclination angle of the anchor, the slope of the tunnel end wall, and the length of the anchor arm in the upward slope area, the anchor arm in the end wall area and the anchor slope body outside the end wall area are derived from the geometric characteristics of the model; S42. Calculate the required increment of the safety factor and convert it into the required total additional resistance moment, and distribute the total additional resistance moment to each anchor to determine the design bearing capacity of a single anchor; S43. According to the relevant provisions of the Technical Code for Rock Anchors and Shotcrete Support Engineering (GB 50086-2015), combined with the theory of elasticity and the shear transfer theory, when the shear failure occurs at the interface between the anchoring area surrounding rock and the grouting body, the effective anchoring length of the anchor is calculated, and combined with the maximum vertical height of the sliding body, the horizontal inclination angle of the anchor, and the length of the anchor slope body outside the end wall area, the parameters of the end wall anchor and the sliding anchor of the upward slope are obtained.

[0066] In order to further implement the above technical solutions, in step S41, the anchor arm in the upward slope area , the anchor arm in the end wall area , and the length of the anchor slope body outside the end wall area are respectively:

[0067]

[0068]

[0069]

[0070] wherein, h3 is the height of the anchor rod arrangement range of the upper slope, h2 is the height of the lowest row of anchor rod setting of the upper slope, h1 is the height of the anchor rod setting of the end wall area, h4 is the height of the anchor rod exposed from the slope body in the end wall area, is the vertical height of the generalized logarithmic spiral sliding surface, is the slope of the upper slope, is the horizontal inclination angle of the anchor rod setting, k:1 is the slope of the tunnel end wall; In step S42,

[0071]

[0072]

[0073]

[0074] wherein, is the safety factor increment, is the target safety factor, is the calculated safety factor, is the total additional resistance moment, is the design bearing capacity of the anchor rod in the upper slope area, is the design bearing capacity of the anchor rod in the end wall area, is the design bearing capacity of a single anchor rod, is the design row number of the anchor rod in the upper slope area, is the design row number of the anchor rod in the end wall area; In step S43, the effective anchoring length of the anchor rod is:

[0075] wherein, is the effective anchoring length of the anchor rod, is the standard value of the bond strength, which is taken from the Technical Code for Rock Anchor and Shotcrete Support Engineering, is the diameter of the anchor rod drilling; The parameters of the end wall anchor rod and the upper slope sliding anchor rod are:

[0076] wherein, is the design length of the anchor rod, is the maximum vertical height of the sliding body, is the horizontal inclination angle of the anchor rod setting, The length of the outer end wall area anchor rod slope body.

[0077] To further implement the above technical solutions, a computer readable storage medium has a computer program stored thereon, wherein the program is executed by a processor to implement a tunnel portal upslope anchor rod design method based on a generalized logarithmic spiral failure model.

[0078] To further implement the above technical solutions, a computer device includes a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement a tunnel portal upslope anchor rod design method based on a generalized logarithmic spiral failure model.

[0079] In another embodiment, a diameter of 32mm full threaded steel anchor rod is used for tunnel upslope reinforcement, and the required calculation parameters are as shown in the table. Figure 5 The computer device is used for calculation to obtain 、 , , 、 、 The formula in step S4 is substituted, and the anchor rod design row number of the upslope area is 3 or 4, and the anchor rod design row number of the end wall area is 1 or 0, and the specific scheme is selected according to the actual situation of the project. Figure 6 As shown in the table, the specific scheme is selected according to the actual situation of the project.

[0080] The embodiments in the specification are described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same and similar parts of each embodiment can be referred to each other. For the device disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the related parts can be referred to the method part.

[0081] The above description of the disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.​​

Claims

1. A tunnel portal anchor design method based on a generalized logarithmic spiral failure model, characterized in that, Comprise: S1. Based on the cohesion and internal friction angle of rock and soil, the corresponding friction weight coefficient is calculated to represent the contribution weight of internal friction angle in the strength of rock and soil, and a generalized logarithmic spiral failure model is constructed to represent the spatial shape characteristics of the failure surface of various rock and soil bodies; S2. Based on the generalized logarithmic spiral failure model, the limit equilibrium analysis method is used to establish the mechanical expression of the safety factor of the tunnel slope and the geometric parameter expression of the sliding surface with the center point of the generalized logarithmic spiral sliding surface as the centroid; S3. Based on the generalized logarithmic spiral failure model, the mechanical expression of the safety factor of the tunnel slope and the geometric parameter expression of the sliding surface, the analytical optimization method of grid search is used to solve the most unfavorable sliding surface and safety factor; S4. The end wall anchor rod is included in the overall limit equilibrium system as a system anti-slide component, the required increment of the safety factor is calculated and converted into the required total additional resistance moment, the total additional resistance moment is distributed to each slope anchor rod and end wall anchor rod, the design bearing capacity of a single anchor rod is determined, and finally the design of the anchor rod parameters is completed.

2. The method for tunnel portal anchor design based on generalized logarithmic spiral failure model according to claim 1, characterized in that, In step S1, the generalized logarithmic spiral failure model is specifically: wherein, is a generalized logarithmic helical slip body rotation radius, is a generalized logarithmic helical slip body rotation polar angle, is a friction weight coefficient, is a generalized logarithmic helical slip body initial rotation radius, is a generalized logarithmic helical slip body initial rotation polar angle, is a rock-soil body cohesion, is a rock-soil body internal friction angle, is a rock-soil body specific weight, is a generalized logarithmic helical slip surface vertical height.

3. The method of designing a tunnel portal anchor according to claim 1, wherein The specific content of the unified representation of the spatial shape characteristics of the failure surface of various rock and soil bodies is: When the internal friction angle of the rock-soil mass =0, corresponding to pure cohesive soil, the friction weight coefficient μ=0, and the generalized logarithmic spiral curve degenerates into a circular arc; when the cohesion c=0, corresponding to pure sandy soil, μ=1, and the generalized logarithmic spiral curve becomes a standard logarithmic spiral curve; when 0<μ<1, the generalized logarithmic spiral curve exhibits a transitional form between a circular arc and a standard logarithmic spiral curve.

4. The method for tunnel portal anchor design based on generalized logarithmic spiral failure model according to claim 1, characterized in that, The specific content of step S2 includes: S21. For the tunnel slope excavation surface of any geometric shape, a coordinate system xOy is established with the intersection point O of the vertical line of the sliding surface starting point A and the horizontal line of the sliding surface ending point B as the origin, the sliding surface starting point A corresponds to the tensile crack position of the landslide back edge, the slope toe is the sliding surface ending point B, corresponding to the shear outlet position of the landslide front edge, and ∠ABO is the slope α; S22. In the limit equilibrium analysis method, the sliding surface AB is in the form of a generalized logarithmic spiral, the sliding mass rotates rigidly around the center point C of the generalized logarithmic spiral sliding surface, and according to the geometric characteristics of the calculation model, the mechanical expression of the safety factor of the slope and the related geometric parameter expression of the sliding surface are obtained, the geometric parameters include the initial rotation radius of the logarithmic spiral sliding mass, the termination rotation radius of the generalized logarithmic spiral sliding mass, the AB point distance, the rotation angle difference of the generalized logarithmic spiral sliding mass, the initial rotation polar angle of the generalized logarithmic spiral sliding mass, and the termination rotation polar angle of the generalized logarithmic spiral sliding mass.

5. The method for tunnel portal anchor design based on generalized logarithmic spiral failure model according to claim 4, characterized in that, The mechanical expression of the safety factor of the tunnel slope is specifically: wherein, is the safety factor of the slope, is the generalized logarithmic spiral sliding torque of the sliding body, is the anti-sliding torque, is the vertical height function of the sliding body, is the coordinate of the center point C of the generalized logarithmic spiral sliding surface of the sliding body in rigid rotation, and B is the calculation width of the slope.

6. The method for tunnel portal anchor design based on generalized logarithmic spiral failure model according to claim 1, characterized in that, The specific content of step S3 is: S31. Substitute the sliding surface geometry parameter expression into the generalized logarithmic spiral failure model, and simplify to obtain the sliding surface equation containing only the generalized logarithmic spiral sliding surface center point coordinates unknowns S32. Select a certain area in the coordinate system and evenly distribute points in a grid shape to 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 then a set of possible rotation center position points are obtained; S34. The mechanical expression of the safety factor of the tunnel slope is used to calculate the safety factor corresponding to each rotation center, and the minimum safety factor is taken as the most unfavorable situation of slope instability, the most unfavorable sliding crack surface and the corresponding minimum safety factor are obtained, and based on the rotation center coordinates corresponding to the minimum safety factor, the maximum values of the sliding moment, the anti-sliding moment and the vertical height of the generalized logarithmic spiral sliding mass are obtained.

7. The method for tunnel portal anchor design based on generalized logarithmic spiral failure model according to claim 1, characterized in that, The specific content of step S4 is: S41. Anchor rods are set in the width direction of the high slope to obtain the height of the anchor rod arrangement range of the high slope, the setting height of the anchor rod in the end wall area, the slope of the high slope, the horizontal inclination of the anchor rod setting, the slope of the tunnel end wall, the force arm of the anchor rod in the high slope area, the force arm of the anchor rod in the end wall area, and the length of the anchor rod outside the slope body in the end wall area are derived from the geometric characteristics of the model; S42. The required increment of the safety factor is calculated, and is converted into the required total additional resistance moment. The total additional resistance moment is distributed to each anchor rod, and the design bearing capacity of a single anchor rod is determined; S43. According to the elastic mechanics theory and the shear transfer theory, when the interface between the surrounding rock and the grouting body in the anchoring area is sheared and damaged, the effective anchoring length of the anchor rod is calculated, and the parameters of the anchor rod in the end wall and the sliding anchor rod in the high slope are obtained in combination with the maximum vertical height of the sliding body, the horizontal inclination of the anchor rod setting, and the length of the anchor rod outside the slope body in the end wall area.

8. The method for tunnel portal anchor design based on generalized logarithmic spiral failure model according to claim 7, characterized in that, The force arm of the anchor rod in the upper slope area in step S41 The force arm of the anchor rod in the end wall area The outer length of the slope in the end wall area 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, wherein, is the safety factor increment, is the target safety factor, is the calculated safety factor, is the total additional moment, is the design bearing force resultant of the anchor rods in the upper slope area, is the design bearing force resultant of the anchor rods in the end wall area, is the design bearing force of a single anchor rod, is the design row number of the anchor rods in the upper slope area, is the design row number of the anchor rods in the end wall area. In step S43, the effective anchoring length of the anchor rod is: wherein is the effective anchoring length of the anchor rod, is the standard value of the bond strength, is the anchor rod borehole diameter; The parameters of the anchor rod in the end wall and the sliding anchor rod in the high slope are: wherein, is the design length of the anchor rod, is the maximum vertical height of the slide, is the horizontal inclination angle of the anchor rod, is the outer length of the anchor rod in the slope of the end wall area.

9. A computer readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the tunnel portal high slope anchor rod design method based on the generalized logarithmic spiral failure model according to any one of claims 1-8.

10. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to implement the tunnel portal high slope anchor rod design method based on the generalized logarithmic spiral failure model according to any one of claims 1-8.

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