Slope rigid-flexible combined reinforcing structure dynamic calculation method considering coordinated stress

Abstract

The invention discloses a dynamic calculation method for a side slope rigid-flexible combined reinforcing structure considering coordinated stress, and relates to the technical field of dynamic calculation methods for side slope rigid-flexible combined reinforcing structures. The calculation method comprises the following steps that S1, a dynamic balance differential equation considering anchor cable-frame structure-rock-soil body stress coordination is established; s2, giving boundary conditions of a dynamic balance differential equation; s3, initial conditions of a dynamic balance differential equation are given; s4, solving by combining boundary and initial conditions to obtain a distribution function of acceleration, displacement and bending moment of each part of the side slope rigid-flexible combined reinforcing structure and an anchor cable axial force function under the action of an earthquake; and S5, calculating according to the function obtained in the step S4 to obtain acceleration, displacement, bending moment and axial force at different moments. According to the method, the deformation and stress of the side slope rigid-flexible combined reinforcing structure under the dynamic effect can be more accurately calculated by considering the coordinated stress, and technical support is provided for design of the side slope rigid-flexible combined reinforcing structure under the earthquake load effect.

Description

Technical Field

[0001] The invention relates to the technical field of dynamic calculation methods for a slope rigid-flexible combined reinforcement structure, and in particular to a dynamic calculation method for a slope rigid-flexible combined reinforcement structure taking coordinated forces into consideration. Background Art

[0002] my country is located between the Pacific Rim Seismic Belt and the Himalayan-Mediterranean Seismic Belt. It is subject to strong plate compression, active fault zones, and widespread strong earthquakes. Earthquake landslides, as one of the most destructive secondary disasters in earthquakes, have caused huge losses to the ecological environment, infrastructure, and life safety. Many infrastructures in my country pass through earthquake-prone areas with active fault tectonic activities. Under the action of earthquakes near active fault zones, the high and steep slopes along the lines are very likely to become unstable and damaged, which brings severe challenges to the construction and operation of infrastructure. In order to effectively improve the stability of these slopes, traditional retaining structures such as anti-slide piles, anchor anti-slide piles, and anchor ground beams have been formed in recent years, but they are difficult to meet the actual needs of seismic reinforcement of high and steep slopes in strong earthquake areas. In order to effectively solve the problem of seismic reinforcement of high and steep slopes in strong earthquake areas, the slope rigid-flexible combined reinforcement structure (a combined reinforcement structure composed of a rigid frame structure and a flexible anchor cable) came into being.

[0003] At present, the static method is mainly used for the analysis and calculation of the rigid-flexible combined reinforcement structure of the slope, and the quasi-static method based on the static method is mainly used for its seismic design method. This method is relatively reasonable for static analysis, but it is too simplified for dynamic analysis. This is because the traditional method regards the earthquake action as an inertial force attached to the structure, without involving the characteristics of earthquake motion. The seismic wave propagates from the source through the slope rock and soil to the structure, causing the vibration of the structure, and the inertial force generated by the structural vibration in turn acts on the rock and soil. Due to the differences in the characteristics of the slope rock and soil, the reinforcement structure and the anchor material, the force capacity and interaction of the three are also significantly different. Therefore, under the action of earthquake, the coordinated force between the anchor cable, frame structure and rock and soil must be considered. Summary of the invention

[0004] In view of the above problems, the present invention aims to provide a dynamic calculation method for a slope rigid-flexible combined reinforcement structure taking into account coordinated forces.

[0005] The technical solution of the present invention is as follows: A dynamic calculation method for a slope rigid-flexible combined reinforcement structure considering coordinated forces includes the following steps: S1: Based on the D'Alembert principle and symbolic function, the dynamic equilibrium differential equation considering the coordination of the forces between anchor cable, frame structure and rock mass is established; S2: Continuously giving the boundary conditions of the dynamic equilibrium differential equation according to the force balance and deformation; S3: giving the initial conditions of the dynamic equilibrium differential equation according to the displacement at the initial moment and the velocity at the initial moment; S4: solving the dynamic equilibrium differential equation in combination with the boundary conditions and the initial conditions to obtain the distribution functions of acceleration, displacement and bending moment of each part of the rigid-flexible combined reinforcement structure of the slope under earthquake action and the axial force function of the anchor cable; S5: Calculate the acceleration, displacement, bending moment and axial force at different times according to the function obtained in step S4.

[0006] Preferably, in step S1, the dynamic balance differential equation includes: (1) Dynamic equilibrium differential equation below the pile foundation rock: (1) Where: is the elastic modulus of the frame pile; is the moment of inertia of the front and rear piles; is the horizontal displacement of the rear pile below the bedrock; is the microelement length of the front pile and the rear pile; is the mass per unit length of the front pile and the rear pile; For time; is the bedrock foundation coefficient; is the rear pile width; is the input horizontal ground motion; is the length of the rear pile below the bedrock; (2) Dynamic equilibrium differential equation below the front pile bedrock: (2) Where: is the horizontal displacement of the front pile below the bedrock; It is the length of the front pile below the bedrock; (3) Dynamic equilibrium differential equation between the front pile foundation interface and the secondary beam: (3) (4) Where: is the horizontal displacement between the front pile foundation cover interface and the secondary beam; is the foundation coefficient of the overburden soil; It is the length from the front pile foundation interface to the secondary beam; (4) Dynamic equilibrium differential equation between the rear pile foundation interface and the secondary beam: (5) Where: is the horizontal displacement between the rear pile foundation interface and the secondary beam; (5) Dynamic equilibrium differential equation between the connection between the rear pile and the secondary beam and the top cross beam: (6) Where: It is the horizontal position between the connection between the rear pile and the secondary beam and the top cross beam; It is the length between the connection between the front pile and the secondary beam and the anchor cable below; It is the length between the anchor cable below the front pile and the anchor cable above it; It is the length from the anchor cable above the front pile to the top of the overburden; It is the length from the top of the front pile cover to the connection between the front pile and the beam; (6) Dynamic equilibrium differential equation between the connection between the front pile and the secondary beam and the anchor cable below: (7) (8) Where: It is the horizontal displacement between the connection between the front pile and the secondary beam and the anchor cable below; (7) Dynamic equilibrium differential equation between the anchor cable below the front pile and the anchor cable above it: (9) (10) Where: It is the horizontal displacement between the anchor cable below the front pile and the anchor cable above it; (8) Dynamic equilibrium differential equation between the anchor cable above the front pile and the top of the overburden: (11) (12) Where: is the horizontal displacement between the anchor cable above the front pile and the top of the overburden; (9) Dynamic equilibrium differential equation between the top of the front pile covering layer and the connection between the front pile and the crossbeam: (13) Where: is the horizontal displacement between the top of the front pile cover and the connection between the front pile and the beam; (10) Dynamic equilibrium differential equation of the beam: (14) Where: is the moment of inertia of the beam; is the vertical displacement of the beam; is the microelement length of the crossbeam and secondary beam; is the mass per unit length of the beam; is the length of the cross beam and secondary beam; (11) Dynamic equilibrium differential equation of the secondary beam: (15) Where: is the moment of inertia of the secondary beam; is the vertical displacement of the secondary beam; is the mass per unit length of the secondary beam.

[0007] Preferably, in step S2, the boundary conditions include: (1) Boundary conditions at the bottom of the rear pile: (16) (17) (2) Boundary conditions at the bottom of the front pile: (18) (19) (3) Boundary conditions of the front pile at the base-cover interface: (20) Where: To find the derivative order; (4) Boundary conditions of the rear pile at the base-cover interface: (twenty one) (5) The boundary condition at the lower anchor cable is: (twenty two) (twenty three) Where: is the angle between the lower anchor cable and the horizontal line; is the elastic modulus of the anchor cable; (6) The boundary conditions at the upper anchor cable are: (twenty four) (25) Where: is the angle between the upper anchor cable and the horizontal line; (7) Boundary conditions of the front pile body at the top of the overburden: (26) (8) Boundary conditions at the top of the front pile: (27) (28) (29) (30) (31) (9) Boundary conditions at the rear pile top: (32) (33) (34) (10) Boundary conditions at the connection between the left end of the secondary beam and the front pile: (35) (36) (37) (38) (39) (40) (11) Boundary conditions at the connection between the right end of the secondary beam and the rear pile: (41) (42) (43) (44) (45) (46).

[0008] Preferably, in step S3, the initial conditions include: (47) (48) (49) (50).

[0009] Preferably, in step S4, solving the dynamic equilibrium differential equation specifically includes the following sub-steps: S41: using differential operations to combine the control differential equations at all nodes and the continuity conditions of each node into a linear equation system represented by a matrix, and obtaining the displacement vector of each node by solving the matrix; S42: Use interpolation and fitting methods to obtain the distribution function of the displacement of the slope rigid-flexible combined reinforcement structure; S43: Calculate the axial force function of the anchor cable by using the displacement coordination relationship between the anchor cable and the frame structure; S44: taking a second derivative of the displacement distribution function of the rigid-flexible combined reinforcement structure of the slope with respect to time to obtain a distribution function of the acceleration of each part of the frame structure; taking a second derivative of the displacement distribution function of the rigid-flexible combined reinforcement structure of the slope with respect to its length direction to obtain a distribution function of the bending moment of each part of the frame structure.

[0010] The beneficial effects of the present invention are: The present invention can more accurately calculate the deformation and stress of the slope rigid-flexible combined reinforcement structure under dynamic action by considering coordinated stress, and provide technical support for the design of the slope rigid-flexible combined reinforcement structure under seismic load. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0012] Figure 1 A schematic flow chart of a dynamic calculation method for a slope rigid-flexible combined reinforcement structure considering coordinated forces according to the present invention; Figure 2 The schematic diagram of the slope reinforcement with the rigid-flexible combined reinforcement structure is shown; Figure 3 This is a schematic diagram of the calculation model of the rigid-flexible combined reinforcement structure of the slope; Figure 4 A schematic diagram of a model for a shaking table model test of a rigid-flexible combined reinforcement structure of a slope and a layout diagram of monitoring points in a specific embodiment; Figure 5 It is a model size diagram of the rigid-flexible combined reinforcement structure of a slope in a specific embodiment; Figure 6 It is a diagram showing the arrangement of structural bending moment measurement points in a specific embodiment; Figure 7 A seismic waveform diagram for inputting a shaking table test in a specific embodiment; Figure 8 It is a schematic diagram of the comparison between the theoretical value and the experimental value of the acceleration at the A-P3 measuring point in a specific embodiment; Fig. 9 It is a schematic diagram of the comparison between the theoretical displacement value and the experimental value of the D1 measuring point in a specific embodiment; Fig.10 It is a schematic diagram of the comparison between the theoretical value and the test value of the anchor cable axial force at the F1 measuring point in a specific embodiment; Fig.11 It is a schematic diagram of the comparison between the theoretical value and the experimental value of the bending moment at the M6 ​​measuring point in a specific embodiment; Fig.12 It is an envelope diagram of theoretical bending moment and experimental bending moment of a frame structure in a specific embodiment. DETAILED DESCRIPTION

[0013] The present invention is further described below in conjunction with the accompanying drawings and embodiments. It should be noted that, in the absence of conflict, the embodiments in this application and the technical features in the embodiments can be combined with each other. It should be noted that, unless otherwise specified, all technical and scientific terms used in this application have the same meanings as those generally understood by those of ordinary skill in the art to which this application belongs. The words "including" or "comprising" and the like used in the disclosure of the present invention mean that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

[0014] like Figure 1 As shown, the present invention provides a dynamic calculation method for a slope rigid-flexible combined reinforcement structure considering coordinated forces, comprising the following steps: S1: Based on the D'Alembert principle and symbolic function, a dynamic equilibrium differential equation considering the coordination of the forces among anchor cable, frame structure and rock mass is established.

[0015] In a specific embodiment, when establishing the dynamic equilibrium differential equation, the slope is reinforced by the rigid-flexible combined reinforcement structure as follows: Figure 2 As shown in the figure, the calculation model of the slope rigid-flexible combined reinforcement structure is as follows: Figure 3 The dynamic equilibrium differential equation includes: (1) Dynamic equilibrium differential equation below the rear pile foundation rock (EF section): (1) Where: is the elastic modulus of the frame pile; is the moment of inertia of the front and rear piles; is the horizontal displacement of the rear pile below the bedrock; is the microelement length of the front pile and the rear pile; is the mass per unit length of the front pile and the rear pile; For time; is the bedrock foundation coefficient; is the rear pile width; is the input horizontal ground motion; is the length of the rear pile below the bedrock; (2) Dynamic equilibrium differential equation below the front pile bedrock (GH section): (2) Where: is the horizontal displacement of the front pile below the bedrock; It is the length of the front pile below the bedrock; (3) Dynamic equilibrium differential equation between the front pile foundation interface and the secondary beam (HC section): (3) (4) Where: is the horizontal displacement between the front pile foundation cover interface and the secondary beam; is the foundation coefficient of the overburden soil; It is the length from the front pile foundation interface to the secondary beam; (4) Dynamic equilibrium differential equation between the rear pile foundation interface and the secondary beam (EB segment): (5) Where: is the horizontal displacement between the rear pile foundation interface and the secondary beam; (5) Dynamic equilibrium differential equation from the connection point between the rear pile and the secondary beam (point B) to the top cross beam (segment AB): (6) Where: It is the horizontal position between the connection between the rear pile and the secondary beam and the top cross beam; It is the length between the connection between the front pile and the secondary beam and the anchor cable below; It is the length between the anchor cable below the front pile and the anchor cable above it; It is the length from the anchor cable above the front pile to the top of the overburden; It is the length from the top of the front pile cover to the connection between the front pile and the beam; (6) Dynamic equilibrium differential equation from the connection point between the front pile and the secondary beam (point C) to the lower anchor cable (CM section): (7) (8) Where: It is the horizontal displacement between the connection between the front pile and the secondary beam and the anchor cable below; (7) Dynamic equilibrium differential equation between the anchor cable below the front pile (point M) and the anchor cable above the pile (point N) (MN segment): (9) (10) Where: It is the horizontal displacement between the anchor cable below the front pile and the anchor cable above it; (8) Dynamic equilibrium differential equation between the anchor cable above the front pile (point N) and the top of the overburden (point P) (NP segment): (11) (12) Where: is the horizontal displacement between the anchor cable above the front pile and the top of the overburden; (9) Dynamic equilibrium differential equation between the top of the front pile covering layer (point P) and the connection between the front pile and the crossbeam (point D) (PD segment): (13) Where: is the horizontal displacement between the top of the front pile cover and the connection between the front pile and the beam; (10) Dynamic equilibrium differential equation of the beam (AD segment): (14) Where: is the moment of inertia of the beam; is the vertical displacement of the beam; is the microelement length of the crossbeam and secondary beam; is the mass per unit length of the beam; is the length of the cross beam and secondary beam; (11) Dynamic equilibrium differential equation of the secondary beam (BC segment): (15) Where: is the moment of inertia of the secondary beam; is the vertical displacement of the secondary beam; is the mass per unit length of the secondary beam.

[0016] S2: The boundary conditions of the dynamic equilibrium differential equation are continuously given according to the force balance and deformation.

[0017] In a specific embodiment, the boundary conditions include: (1) Boundary conditions at the bottom of the rear pile: (16) (17) That is, the relative displacement and rotation angle of the rear pile bottom (point F) are both 0; (2) Boundary conditions at the bottom of the front pile: (18) (19) That is, the relative displacement and rotation angle of the front pile bottom (point G) are both 0; (3) Boundary conditions of the front pile at the base-cover interface: (20) Where: To find the derivative order; That is, the front pile body meets the continuity conditions of displacement, rotation angle, shear force and bending moment at the base-cover interface (point H); (4) Boundary conditions of the rear pile at the base-cover interface: (twenty one) That is, the pile body of the rear pile meets the continuity conditions of displacement, rotation, shear force and bending moment at the base-cover interface (point E); (5) The boundary condition at the lower anchor cable (point M) is: (twenty two) (twenty three) Where: is the angle between the lower anchor cable and the horizontal line; is the elastic modulus of the anchor cable; (6) The boundary condition at the upper anchor cable (point N) is: (twenty four) (25) Where: is the angle between the upper anchor cable and the horizontal line; (7) Boundary conditions of the front pile at the top of the overburden (point P): (26) That is, the front pile body meets the continuity conditions of displacement, rotation, shear force and bending moment at the top of the covering layer (point P); (8) Boundary conditions at the front pile top (point D): (27) That is, the vertical displacement at point D is 0; (28) That is, the sum of the bending moments at point D is 0; (29) That is, the deformation curvature (angle) at point D is equal; (30) That is, the horizontal displacement at point D is equal to that at the top of the rear pile (point A); (31) That is, the shear force at point D of the CD rod is equal to that at point A of the rear pile BA rod; (9) Boundary conditions at the rear pile top (point A): (32) That is, the vertical displacement at point A is 0; (33) That is, the sum of the bending moments at point A is 0; (34) That is, the deformation curvature (angle) at point A is equal; (10) Boundary conditions at the connection between the left end of the secondary beam and the front pile (point C): (35) That is, the vertical displacement at point C is 0; (36) That is, the sum of the bending moments at point C is 0; (37) That is, the horizontal displacements of the upper and lower parts of point C are equal; (38) That is, the deformation curvature (angle) of the upper and lower parts of point C is equal; (39) That is, the deformation curvature (angle) of the lower part and the right part of point C are equal; (40) That is, the horizontal displacement of point C is equal to the horizontal displacement of point B; (11) Boundary conditions at the connection between the right end of the secondary beam and the rear pile (point B): (41) That is, the vertical displacement at point B is 0; (42) That is, the sum of the bending moments at point B is 0; (43) That is, the horizontal displacements of the upper and lower parts of point B are equal; (44) That is, the deformation curvature (angle) of the upper and lower parts of point B is equal; (45) That is, the deformation curvature (angle) of the lower part and the left part of point B is equal; (46) That is, the shear force at point B of the CB rod and at point A of the rear pile DA rod are equal.

[0018] S3: The initial conditions of the dynamic equilibrium differential equation are given according to the displacement at the initial moment and the velocity at the initial moment.

[0019] In a specific embodiment, the initial conditions include: (47) (48) (49) (50).

[0020] In the above embodiment, when When i=1, That is , represents the horizontal displacement below the bedrock of the rear pile, and the same is true for the others; when When i=1, That is , represents the vertical displacement of the beam, and the same goes for the others.

[0021] S4: Solving the dynamic equilibrium differential equation in combination with the boundary conditions and the initial conditions to obtain the distribution functions of acceleration, displacement and bending moment of each part of the rigid-flexible combined reinforcement structure of the slope under earthquake action and the axial force function of the anchor cable.

[0022] In a specific embodiment, solving the dynamic equilibrium differential equation specifically includes the following sub-steps: S41: using differential operations to combine the control differential equations at all nodes and the continuity conditions of each node into a linear equation system represented by a matrix, and obtaining the displacement vector of each node by solving the matrix; S42: Use interpolation and fitting methods to obtain the distribution function of the displacement of the slope rigid-flexible combined reinforcement structure; S43: Calculate the axial force function of the anchor cable by using the displacement coordination relationship between the anchor cable and the frame structure; S44: taking a second derivative of the displacement distribution function of the rigid-flexible combined reinforcement structure of the slope with respect to time to obtain a distribution function of the acceleration of each part of the frame structure; taking a second derivative of the displacement distribution function of the rigid-flexible combined reinforcement structure of the slope with respect to its length direction to obtain a distribution function of the bending moment of each part of the frame structure.

[0023] In the present invention, the dynamic equilibrium differential equation is a coupled nonlinear fourth-order differential equation, and it is difficult to solve a strict analytical solution. In the above embodiment, the seismic response of the anchor-pull frame pile structure is solved by using the finite difference method. By using differential operations, the partial differential equation is converted into a system of algebraic equations, which is equivalent to degenerating the high-order partial differential equation into a system of linear equations that is conducive to matrix programming for solution, so that a high-order precision numerical solution and high stability of the numerical results can be obtained.

[0024] According to the standard finite difference principle, the frame structure is divided into N equal units along its length direction. The finite difference formats of the differential terms in the dynamic equilibrium differential equation are: (51) (52) (53) (54) Where: is the displacement of each equally divided unit; , , , , are the displacements of unit nodes i+1, i-1, i, i+2, and i-2 respectively; is the length of each equal unit; The slope rigid-flexible combined reinforcement structure is discretized into uniform micro-lengths, and the finite difference format of the motion equation of each differential segment of the structure is given by differential operation. The control differential equations at all nodes and the continuity conditions of each node are combined into a linear equation system represented by a matrix. Through matrix solution, the displacement vector of each node is obtained, and then the distribution continuous function U of the displacement of the slope rigid-flexible combined reinforcement structure can be obtained by interpolation and fitting method. Then, the axial force function of the anchor cable is obtained by using the displacement coordination relationship at the connection between the anchor cable and the frame structure. The distribution function of the displacement is quadratically differentiated with respect to time to obtain the distribution function of the acceleration of each part of the frame structure. The distribution function of the displacement is quadratically differentiated in the length direction to obtain the distribution function of the bending moment of each part of the frame structure.

[0025] S5: Calculate the acceleration, displacement, bending moment and axial force at different times according to the function obtained in step S4.

[0026] In a specific embodiment, taking a slope rigid-flexible combined reinforcement structure at a certain location as an example, the dynamic calculation method for a slope rigid-flexible combined reinforcement structure considering coordinated forces described in the present invention is used to calculate its structural dynamics to obtain a theoretical value, and a vibration table model test is carried out to obtain a test value. The effectiveness of the present invention is demonstrated by comparing the test value with the theoretical value.

[0027] In this embodiment, the shaking table model test model and monitoring points are arranged as follows: Figure 4 The values ​​and units of the model parameters in the experiment are shown in Table 1: Table 1 Model parameter values ​​and units in the experiment

[0028] The test model size is 3.4m×1.5m×1.5m (length×width×height), and the slope rigid-flexible combined reinforcement structure model size is as follows: Figure 5 As shown in Figure 2, the structural bending moment measurement points are arranged as follows: Figure 6 shown.

[0029] The initial prestress of the anchor cable is set to 7.8N. In the shaking table test, the following is input: Figure 7 The results of the theoretical and experimental values ​​of the acceleration at the A-P3 measuring point, the displacement at the D1 measuring point, the anchor cable axial force at the F1 measuring point, and the bending moment at the M6 ​​measuring point under the action of a sine wave with an amplitude of 0.05g and a frequency of 4Hz are shown in the figure. Figure 8-Figure 11 As shown in Figure 2, the comparison results of the structural bending moment envelope diagram are as follows: Fig.12 As shown. Figure 8-Figure 12 It can be seen that the theoretical value calculated by the present invention is relatively close to the experimental value result of the shaking table model test. The dynamic calculation method of the slope rigid-flexible combined reinforcement structure considering coordinated force described in the present invention can accurately calculate the deformation and force of the slope rigid-flexible combined reinforcement structure under dynamic action.

[0030] In summary, the present invention can consider the force coordination among the anchor cable, the frame structure and the rock and soil mass, and more accurately calculate the dynamics of the rigid-flexible combined reinforcement structure of the slope. Compared with the prior art, the present invention has significant progress.

[0031] The above description is only a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A dynamic calculation method for slope rigid-flexible combined reinforcement structure considering coordinated forces, characterized in that: The following steps are involved: S1: Based on the D'Alembert principle and symbolic function, the dynamic equilibrium differential equation considering the coordination of the forces between anchor cable, frame structure and rock mass is established; S2: Continuously giving the boundary conditions of the dynamic equilibrium differential equation according to the force balance and deformation; S3: giving the initial conditions of the dynamic equilibrium differential equation according to the displacement at the initial moment and the velocity at the initial moment; S4: solving the dynamic equilibrium differential equation in combination with the boundary conditions and the initial conditions to obtain the distribution functions of acceleration, displacement and bending moment of each part of the rigid-flexible combined reinforcement structure of the slope under earthquake action and the axial force function of the anchor cable; S5: Calculate the acceleration, displacement, bending moment and axial force at different times according to the function obtained in step S4.

2. The dynamic calculation method of the slope rigid-flexible combined reinforcement structure considering coordinated force according to claim 1 is characterized in that: In step S1, the dynamic balance differential equation includes: (1) Dynamic equilibrium differential equation below the pile foundation rock: （1） Where: is the elastic modulus of the frame pile; is the moment of inertia of the front and rear piles; is the horizontal displacement of the rear pile below the bedrock; is the microelement length of the front pile and the rear pile; is the mass per unit length of the front pile and the rear pile; For time; is the bedrock foundation coefficient; is the rear pile width; is the input horizontal ground motion; is the length of the rear pile below the bedrock; (2) Dynamic equilibrium differential equation below the front pile bedrock: （2） Where: is the horizontal displacement of the front pile below the bedrock; It is the length of the front pile below the bedrock; (3) Dynamic equilibrium differential equation between the front pile foundation interface and the secondary beam: （3） （4） Where: is the horizontal displacement between the front pile foundation cover interface and the secondary beam; is the foundation coefficient of the overburden soil; It is the length from the front pile foundation interface to the secondary beam; (4) Dynamic equilibrium differential equation between the rear pile foundation interface and the secondary beam: （5） Where: is the horizontal displacement between the rear pile foundation interface and the secondary beam; (5) Dynamic equilibrium differential equation between the connection between the rear pile and the secondary beam and the top cross beam: （6） Where: It is the horizontal position between the connection between the rear pile and the secondary beam and the top cross beam; It is the length between the connection between the front pile and the secondary beam and the anchor cable below; It is the length between the anchor cable below the front pile and the anchor cable above it; It is the length from the anchor cable above the front pile to the top of the overburden; It is the length from the top of the front pile cover to the connection between the front pile and the beam; (6) Dynamic equilibrium differential equation between the connection between the front pile and the secondary beam and the anchor cable below: （7） （8） Where: It is the horizontal displacement between the connection between the front pile and the secondary beam and the anchor cable below; (7) The differential equation of dynamic balance between the anchor cable below the front pile and the anchor cable above it is: （9） （10） Where: It is the horizontal displacement between the anchor cable below the front pile and the anchor cable above it; (8) Dynamic equilibrium differential equation between the anchor cable above the front pile and the top of the overburden: （11） （12） Where: is the horizontal displacement between the anchor cable above the front pile and the top of the overburden; (9) The dynamic equilibrium differential equation between the top of the front pile covering layer and the connection between the front pile and the crossbeam is: （13） Where: is the horizontal displacement between the top of the front pile cover and the connection between the front pile and the beam; (10) Dynamic equilibrium differential equation of the beam: （14） Where: is the moment of inertia of the beam; is the vertical displacement of the beam; is the microelement length of the crossbeam and secondary beam; is the mass per unit length of the beam; is the length of the cross beam and secondary beam; (11) Dynamic equilibrium differential equation of the secondary beam: （15） Where: is the moment of inertia of the secondary beam; is the vertical displacement of the secondary beam; is the mass per unit length of the secondary beam.

3. The dynamic calculation method of the slope rigid-flexible combined reinforcement structure considering coordinated force according to claim 2 is characterized in that: In step S2, the boundary conditions include: (1) Boundary conditions at the bottom of the rear pile: （16） （17） (2) Boundary conditions at the bottom of the front pile: （18） （19） (3) Boundary conditions of the front pile at the base-cover interface: （20） Where: To find the derivative order; (4) Boundary conditions of the rear pile at the base-cover interface: （21） (5) The boundary condition at the lower anchor cable is: （22） （23） Where: is the angle between the lower anchor cable and the horizontal line; is the elastic modulus of the anchor cable; (6) The boundary conditions at the upper anchor cable are: （24） （25） Where: is the angle between the upper anchor cable and the horizontal line; (7) Boundary conditions of the front pile body at the top of the overburden: （26） (8) Boundary conditions at the top of the front pile: （27） （28） （29） （30） （31） (9) Boundary conditions at the rear pile top: （32） （33） （34） (10) Boundary conditions at the connection between the left end of the secondary beam and the front pile: （35） （36） （37） （38） （39） （40） (11) Boundary conditions at the connection between the right end of the secondary beam and the rear pile: （41） （42） （43） （44） （45） （46）。 4. The dynamic calculation method of the slope rigid-flexible combined reinforcement structure considering coordinated force according to claim 3 is characterized in that: In step S3, the initial conditions include: （47） （48） （49） （50）。 5. The dynamic calculation method of the slope rigid-flexible combined reinforcement structure considering coordinated force according to any one of claims 1 to 4, characterized in that: In step S4, solving the dynamic equilibrium differential equation specifically includes the following sub-steps: S41: using differential operations to combine the control differential equations at all nodes and the continuity conditions of each node into a linear equation system represented by a matrix, and obtaining the displacement vector of each node by solving the matrix; S42: Use interpolation and fitting methods to obtain the distribution function of the displacement of the slope rigid-flexible combined reinforcement structure; S43: Calculate the axial force function of the anchor cable by using the displacement coordination relationship between the anchor cable and the frame structure; S44: taking a second derivative of the displacement distribution function of the rigid-flexible combined reinforcement structure of the slope with respect to time to obtain a distribution function of the acceleration of each part of the frame structure; taking a second derivative of the displacement distribution function of the rigid-flexible combined reinforcement structure of the slope with respect to its length direction to obtain a distribution function of the bending moment of each part of the frame structure.

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