A dynamic calculation method for a rigid-flexible combined reinforcement structure of a slope considering coordinated force

Abstract

The present invention discloses a dynamic calculation method for a rigid-flexible combined reinforcement structure of a slope considering coordinated force, which relates to the technical field of dynamic calculation methods for rigid-flexible combined reinforcement structures of slopes. The calculation method includes the following steps: S1: Establish a dynamic equilibrium differential equation considering the force coordination of the cable-frame structure and the rock and soil mass; S2: Give the boundary conditions of the dynamic equilibrium differential equation; S3: Give the initial conditions of the dynamic equilibrium differential equation; S4: Solve in combination with the boundary and 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 seismic action and the cable axial force function; S5: Calculate the acceleration, displacement, bending moment and axial force at different times according to the functions obtained in step S4. By considering coordinated force, the present invention can more accurately calculate the deformation and force of the rigid-flexible combined reinforcement structure of the slope under dynamic action, and provide technical support for the design of the rigid-flexible combined reinforcement structure of the slope under seismic load.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic calculation methods for rigid-flexible combined reinforcement structures of slopes, and particularly relates to a dynamic calculation method for rigid-flexible combined reinforcement structures of slopes considering coordinated force bearing. Background Technique

[0002] China is located between the Circum-Pacific seismic belt and the Himalayas-Mediterranean seismic belt. Affected by strong plate extrusion, the active fault zones are tectonically active and strong earthquakes are widely distributed. As one of the most destructive secondary disasters in earthquakes, seismic landslides have caused huge losses to the ecological environment, infrastructure and life safety. Many infrastructure facilities in China cross earthquake-prone areas with active fault structures. Under the action of earthquakes near active fault zones, high and steep slopes along the line are extremely prone to instability and failure, posing severe challenges to the construction and operation of infrastructure. In order to effectively improve the stability of these slopes, in recent years, traditional retaining structure types such as anti-slide piles, cable anti-slide piles and cable ground beams have been mainly formed, but they are difficult to meet the actual needs of seismic reinforcement for high and steep slopes in strong earthquake areas. To effectively solve the problem of seismic reinforcement for high and steep slopes in strong earthquake areas, a rigid-flexible combined reinforcement structure for slopes (a combined reinforcement structure composed of a rigid frame structure and a flexible cable) has emerged as the times require.

[0003] At present, the analysis and calculation of rigid-flexible combined reinforcement structures for slopes mainly adopt the static method, and the seismic design method mainly adopts the pseudo-static method based on the static method. This method is relatively reasonable for static analysis, but for dynamic analysis, this method is too simplified. This is because in the past traditional methods, the earthquake action was regarded as an inertial force applied to the structure, without involving the characteristics of earthquake motion. The seismic wave propagates from the earthquake source through the slope rock and soil mass to the structure, causing the vibration of the structure, and the inertial force generated by the structure vibration acts on the rock and soil mass in turn. Due to the differences in the mechanical properties of the slope rock and soil mass, the reinforcement structure and the cable material, the force-bearing capacities and the interactions of the three are also significantly different. Therefore, the coordinated force bearing among the cable-frame structure-rock and soil mass must be considered under earthquake action. Summary of the Invention

[0004] In view of the above problems, the present invention aims to provide a dynamic calculation method for rigid-flexible combined reinforcement structures of slopes considering coordinated force bearing.

[0005] The technical solution of the present invention is as follows:

[0006] A dynamic calculation method for rigid-flexible combined reinforcement structures of slopes considering coordinated force bearing includes the following steps:

[0007] S1: Based on D'Alembert's principle and the sign function, establish a dynamic equilibrium differential equation considering the coordinated force bearing among the cable-frame structure-rock and soil mass;

[0008] S2: Give the boundary conditions of the dynamic equilibrium differential equation according to force balance and deformation continuity;

[0009] S3: Give the initial conditions of the dynamic equilibrium differential equation according to the displacement and velocity at the initial moment;

[0010] S4: Solve the dynamic equilibrium differential equation by combining 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 seismic action and the axial force function of the anchor cable;

[0011] S5: Calculate the acceleration, displacement, bending moment and axial force at different moments according to the functions obtained in step S4.

[0012] Preferably, in step S1, the dynamic equilibrium differential equation includes:

[0013] (1) The dynamic equilibrium differential equation below the rear pile foundation rock:

[0014] (1)

[0015] In the formula: is the elastic modulus of the frame pile; is the moment of inertia of the front and rear piles; is the horizontal displacement below the rear pile foundation rock; is the micro-element length of the front and rear piles; is the mass per unit length of the front and rear piles; is the time; is the foundation coefficient of the bedrock; is the width of the rear pile; is the input horizontal ground motion; is the length below the rear pile foundation rock;

[0016] (2) The dynamic equilibrium differential equation below the front pile foundation rock:

[0017] (2)

[0018] In the formula: is the horizontal displacement below the front pile foundation rock; is the length below the front pile foundation rock;

[0019] (3) The dynamic equilibrium differential equation between the front pile foundation covering interface and the secondary beam:

[0020] (3)

[0021] (4)

[0022] In the formula: is the horizontal displacement between the front pile foundation covering interface and the secondary beam; is the foundation coefficient of the overburden soil; is the length between the front pile foundation covering interface and the secondary beam;

[0023] (4) The dynamic equilibrium differential equation between the rear pile foundation covering interface and the secondary beam:

[0024] (5)

[0025] In the formula: is the horizontal displacement between the rear pile foundation covering interface and the secondary beam;

[0026] (5) The dynamic equilibrium differential equation between the connection of the rear pile and the secondary beam and the top cross beam:

[0027] (6)

[0028] In the formula: is the horizontal position between the connection of the rear pile and the secondary beam and the top cross beam; is the length between the connection of the front pile and the secondary beam and the lower anchor cable; is the length between the lower anchor cable and the upper anchor cable of the front pile; is the length between the upper anchor cable of the front pile and the top of the overburden; is the length between the top of the overburden of the front pile and the connection of the front pile and the cross beam;

[0029] (6) The dynamic equilibrium differential equation between the connection of the front pile and the secondary beam and the lower anchor cable:

[0030] (7)

[0031] (8)

[0032] In the formula: is the horizontal displacement between the connection of the front pile and the secondary beam and the lower anchor cable;

[0033] (7) The dynamic equilibrium differential equation between the lower anchor cable and the upper anchor cable of the front pile:

[0034] (9)

[0035] (10)

[0036] In the formula: is the horizontal displacement between the lower anchor cable and the upper anchor cable of the front pile;

[0037] (8) The dynamic equilibrium differential equation between the upper anchor cable of the front pile and the top of the overburden:

[0038] (11)

[0039] (12)

[0040] Wherein: is the horizontal displacement between the anchor cable above the front pile and the top of the overburden layer;

[0041] (9) Dynamic equilibrium differential equation between the top of the front pile overburden layer and the connection between the front pile and the crossbeam:

[0042] (13)

[0043] Wherein: is the horizontal displacement between the top of the front pile overburden layer and the connection between the front pile and the crossbeam;

[0044] (10) Dynamic equilibrium differential equation of the crossbeam:

[0045] (14)

[0046] Wherein: is the moment of inertia of the crossbeam; is the vertical displacement of the crossbeam; is the infinitesimal length of the crossbeam and secondary beam; is the mass per unit length of the crossbeam; is the length of the crossbeam and secondary beam;

[0047] (11) Dynamic equilibrium differential equation of the secondary beam:

[0048] (15)

[0049] Wherein: 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.

[0050] Preferably, in step S2, the boundary conditions include:

[0051] (1) Boundary conditions at the bottom of the rear pile:

[0052] (16)

[0053] (17)

[0054] (2) Boundary conditions at the bottom of the front pile:

[0055] (18)

[0056] (19)

[0057] (3) Boundary conditions of the front pile body at the bedrock-overburden interface:

[0058] (20)

[0059] In the formula: is the order of differentiation;

[0060] (4) Boundary conditions of the rear pile body at the bedrock-overburden interface:

[0061] (21)

[0062] (5) Boundary conditions at the lower cable are:

[0063] (22)

[0064] (23)

[0065] In the formula: is the angle between the lower cable and the horizontal line; is the elastic modulus of the cable;

[0066] (6) Boundary conditions at the upper cable are:

[0067] (24)

[0068] (25)

[0069] In the formula: is the angle between the upper cable and the horizontal line;

[0070] (7) Boundary conditions of the front pile body at the top of the overburden layer:

[0071] (26)

[0072] (8) Boundary conditions at the top of the front pile:

[0073] (27)

[0074] (28)

[0075] (29)

[0076] (30)

[0077] (31)

[0078] (9) Boundary conditions at the top of the rear pile:

[0079] (32)

[0080] (33)

[0081] (34)

[0082] (10)Boundary conditions at the connection between the left end of the secondary beam and the front pile:

[0083] (35)

[0084] (36)

[0085] (37)

[0086] (38)

[0087] (39)

[0088] (40)

[0089] (11)Boundary conditions at the connection between the right end of the secondary beam and the rear pile:

[0090] (41)

[0091] (42)

[0092] (43)

[0093] (44)

[0094] (45)

[0095] (46).

[0096] Preferably, in step S3, the initial conditions include:

[0097] (47)

[0098] (48)

[0099] (49)

[0100] (50).

[0101] Preferably, in step S4, solving the dynamic equilibrium differential equation specifically includes the following sub-steps:

[0102] S41: Use the difference operation to combine the control difference equations at all nodes and the continuity conditions of each node into a system of linear equations represented by a matrix, and obtain the displacement vectors of each node by solving the matrix.

[0103] S42: Use interpolation and fitting methods to find the distribution function of the displacement of the rigid-flexible combined reinforcement structure of the slope.

[0104] S43: Use the displacement coordination relationship at the connection between the anchor cable and the frame structure to find the axial force function of the anchor cable.

[0105] S44: Take the second derivative of the distribution function of the displacement of the rigid-flexible combined reinforcement structure of the slope with respect to time to obtain the distribution function of the acceleration of each part of the frame structure; take the second derivative of the distribution function of the displacement of the rigid-flexible combined reinforcement structure of the slope with respect to its length direction to obtain the distribution function of the bending moment of each part of the frame structure.

[0106] The beneficial effects of the present invention are as follows:

[0107] By considering the coordinated force, the present invention can more accurately calculate the deformation and force of the rigid-flexible combined reinforcement structure of the slope under dynamic action, and provide technical support for the design of the rigid-flexible combined reinforcement structure of the slope under seismic load. Description of the Drawings

[0108] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0109] Figure 1 It is a schematic flow chart of the dynamic calculation method for the rigid-flexible combined reinforcement structure of the slope considering coordinated force according to the present invention;

[0110] Figure 2 It is a schematic diagram of the slope reinforced by the rigid-flexible combined reinforcement structure;

[0111] Figure 3 It is a schematic diagram of the calculation model of the rigid-flexible combined reinforcement structure of the slope;

[0112] Figure 4 It is a schematic diagram of the shaking table model test model and the layout of monitoring points of the rigid-flexible combined reinforcement structure of the slope in a specific embodiment;

[0113] Figure 5 It is a schematic diagram of the model size of the rigid-flexible combined reinforcement structure of the slope in a specific embodiment;

[0114] Figure 6 Layout diagram of structural bending moment measurement points in a specific embodiment

[0115] Figure 7 Input ground motion waveform diagram of the shaking table test in a specific embodiment

[0116] Figure 8 Schematic diagram of the comparison results between the theoretical and test values of the acceleration at the A-P3 measurement point in a specific embodiment

[0117] Figure 9 Schematic diagram of the comparison results between the theoretical and test values of the displacement at the D1 measurement point in a specific embodiment

[0118] Figure 10 Schematic diagram of the comparison results between the theoretical and test values of the anchor cable axial force at the F1 measurement point in a specific embodiment

[0119] Figure 11 Schematic diagram of the comparison results between the theoretical and test values of the bending moment at the M6 measurement point in a specific embodiment

[0120] Figure 12 Envelope diagram of the theoretical and test bending moments of the frame structure in a specific embodiment Detailed implementation manners

[0121] The present invention will be further described below in conjunction with the accompanying drawings and embodiments. It should be noted that, without conflict, the embodiments in the present application and the technical features in the embodiments can be combined with each other. It should be pointed out that unless otherwise specified, all technical and scientific terms used in the present application have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs. The terms "including" or "comprising" and the like used in the present invention disclosure mean that the elements or objects appearing before the term cover the elements or objects listed after the term and their equivalents, without excluding other elements or objects.

[0122] As Figure 1 shown, the present invention provides a dynamic calculation method for a rigid-flexible combined reinforcement structure of a slope considering coordinated force, including the following steps:

[0123] S1: Based on D'Alembert's principle and the sign function, establish a dynamic equilibrium differential equation considering the coordinated force of the anchor cable-frame structure-rock and soil mass.

[0124] In a specific embodiment, when establishing the dynamic equilibrium differential equation, the rigid-flexible combined reinforcement structure of the slope reinforces the slope as Figure 2 shown, and the calculation model of the rigid-flexible combined reinforcement structure of the slope is as Figure 3 shown. The dynamic equilibrium differential equation includes:

[0125] (1) Dynamic equilibrium differential equation below the post-pile foundation rock (EF section):

[0126] (1)

[0127] Where: is the elastic modulus of the frame pile; are the moments of inertia of the front and rear piles; is the horizontal displacement below the post-pile foundation rock; are the infinitesimal lengths of the front and rear piles; are the masses per unit length of the front and rear piles; is the time; is the foundation coefficient of the bedrock; is the width of the rear pile; is the input horizontal ground motion; is the length below the post-pile foundation rock;

[0128] (2) Dynamic equilibrium differential equation below the front-pile foundation rock (GH section):

[0129] (2)

[0130] Where: is the horizontal displacement below the front-pile foundation rock; is the length below the front-pile foundation rock;

[0131] (3) Dynamic equilibrium differential equation between the front-pile foundation interface and the secondary beam (HC section):

[0132] (3)

[0133] (4)

[0134] Where: is the horizontal displacement between the front-pile foundation interface and the secondary beam; is the foundation coefficient of the overburden soil; is the length between the front-pile foundation interface and the secondary beam;

[0135] (4) Dynamic equilibrium differential equation between the post-pile foundation interface and the secondary beam (EB section):

[0136] (5)

[0137] Where: is the horizontal displacement between the post-pile foundation interface and the secondary beam;

[0138] (5) Dynamic equilibrium differential equation between the connection point of the rear pile and the secondary beam (Point B) and the top cross beam (AB section):

[0139] (6)

[0140] In the formula: is the horizontal position between the connection of the rear pile and the secondary beam and the top cross beam; is the length between the connection of the front pile and the secondary beam and the lower anchor cable; is the length between the lower anchor cable and the upper anchor cable under the front pile; is the length between the upper anchor cable and the top of the overburden layer under the front pile; is the length between the top of the overburden layer of the front pile and the connection of the front pile and the cross beam;

[0141] (6) Dynamic equilibrium differential equation between the connection of the front pile and the secondary beam (point C) and the lower anchor cable (CM section):

[0142] (7)

[0143] (8)

[0144] In the formula: is the horizontal displacement between the connection of the front pile and the secondary beam and the lower anchor cable;

[0145] (7) Dynamic equilibrium differential equation between the lower anchor cable of the front pile (point M) and the upper anchor cable (point N) (MN section):

[0146] (9)

[0147] (10)

[0148] In the formula: is the horizontal displacement between the lower anchor cable and the upper anchor cable under the front pile;

[0149] (8) Dynamic equilibrium differential equation between the upper anchor cable of the front pile (point N) and the top of the overburden layer (point P) (NP section):

[0150] (11)

[0151] (12)

[0152] In the formula: is the horizontal displacement between the upper anchor cable of the front pile and the top of the overburden layer;

[0153] (9) Dynamic equilibrium differential equation between the top of the overburden layer of the front pile (point P) and the connection of the front pile and the cross beam (point D) (PD section):

[0154] (13)

[0155] In the formula: is the horizontal displacement between the top of the front pile covering layer and the connection between the front pile and the cross beam;

[0156] (10) Dynamic equilibrium differential equation of the cross beam (AD section):

[0157] (14)

[0158] In the formula: is the moment of inertia of the cross beam; is the vertical displacement of the cross beam; is the differential length of the cross beam and secondary beam; is the mass per unit length of the cross beam; is the length of the cross beam and secondary beam;

[0159] (11) Dynamic equilibrium differential equation of the secondary beam (BC section):

[0160] (15)

[0161] In the formula: 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.

[0162] S2: Give the boundary conditions of the dynamic equilibrium differential equation according to force balance and deformation continuity.

[0163] In a specific embodiment, the boundary conditions include:

[0164] (1) Boundary conditions at the bottom of the rear pile:

[0165] (16)

[0166] (17)

[0167] That is, the relative displacement and rotation angle at the bottom of the rear pile (point F) are both 0;

[0168] (2) Boundary conditions at the bottom of the front pile:

[0169] (18)

[0170] (19)

[0171] That is, the relative displacement and rotation angle at the bottom of the front pile (point G) are both 0;

[0172] (3) Boundary conditions at the interface between the front pile and the foundation covering layer:

[0173] (20)

[0174] Wherein: is the order of derivative;

[0175] That is, the front pile body satisfies the continuity conditions of displacement, rotation angle, shear force and bending moment at the base-overburden interface (point H);

[0176] (4) Boundary conditions of the rear pile body at the base-overburden interface:

[0177] (21)

[0178] That is, the rear pile body satisfies the continuity conditions of displacement, rotation angle, shear force and bending moment at the base-overburden interface (point E);

[0179] (5) Boundary conditions at the lower cable (point M) are:

[0180] (22)

[0181] (23)

[0182] Wherein: is the included angle between the lower cable and the horizontal line; is the elastic modulus of the cable;

[0183] (6) Boundary conditions at the upper cable (point N) are:

[0184] (24)

[0185] (25)

[0186] Wherein: is the included angle between the upper cable and the horizontal line;

[0187] (7) Boundary conditions of the front pile body at the top of the overburden layer (point P):

[0188] (26)

[0189] That is, the front pile body satisfies the continuity conditions of displacement, rotation angle, shear force and bending moment at the top of the overburden layer (point P);

[0190] (8) Boundary conditions at the top of the front pile (point D):

[0191] (27)

[0192] That is, the vertical displacement at point D is 0;

[0193] (28)

[0194] That is, the sum of the bending moments at point D is 0;

[0195] (29)

[0196] That is, the deformation curvature (rotation angle) at point D is equal;

[0197] (30)

[0198] That is, the horizontal displacements at point D and at the top of the rear pile (point A) are equal;

[0199] (31)

[0200] That is, the shear forces at point D of the CD rod and at point A of the rear pile BA rod are equal;

[0201] (9)Boundary conditions at the top of the rear pile (point A):

[0202] (32)

[0203] That is, the vertical displacement at point A is 0;

[0204] (33)

[0205] That is, the sum of the bending moments at point A is 0;

[0206] (34)

[0207] That is, the deformation curvatures (rotation angles) at point A are equal;

[0208] (10)Boundary conditions at the connection between the left end of the secondary beam and the front pile (point C):

[0209] (35)

[0210] That is, the vertical displacement at point C is 0;

[0211] (36)

[0212] That is, the sum of the bending moments at point C is 0;

[0213] (37)

[0214] That is, the horizontal displacements of the upper and lower parts of point C are equal;

[0215] (38)

[0216] That is, the deformation curvatures (rotation angles) of the upper and lower parts of point C are equal;

[0217] (39)

[0218] That is, the deformation curvatures (rotation angles) of the lower part and the right part of point C are equal;

[0219] (40)

[0220] That is, the horizontal displacement at point C is equal to the horizontal displacement at point B;

[0221] (11)Boundary conditions at the connection between the right end of the secondary beam and the rear pile (point B):

[0222] (41)

[0223] That is, the vertical displacement at point B is 0;

[0224] (42)

[0225] That is, the sum of the bending moments at point B is 0;

[0226] (43)

[0227] That is, the horizontal displacements of the upper and lower parts at point B are equal;

[0228] (44)

[0229] That is, the deformation curvatures (angles of rotation) of the upper and lower parts at point B are equal;

[0230] (45)

[0231] That is, the deformation curvatures (angles of rotation) of the lower part and the left part at point B are equal;

[0232] (46)

[0233] That is, the shear forces at point B of the CB rod and at point A of the rear pile DA rod are equal.

[0234] S3: Give the initial conditions of the dynamic equilibrium differential equation according to the displacement and velocity at the initial moment.

[0235] In a specific embodiment, the initial conditions include:

[0236] (47)

[0237] (48)

[0238] (49)

[0239] (50).

[0240] In the above embodiment, when i = 1, That is , representing the horizontal displacement below the post-pile foundation rock, and the same applies to others; when has i = 1, is , representing the vertical displacement of the crossbeam, and the same applies to others.

[0241] S4: Solve the dynamic equilibrium differential equation in combination with the boundary conditions and the initial conditions to obtain the distribution functions of the acceleration, displacement, and bending moment of each part of the rigid-flexible combined reinforcement structure of the slope under seismic action and the axial force function of the anchor cable.

[0242] In a specific embodiment, solving the dynamic equilibrium differential equation specifically includes the following sub-steps:

[0243] S41: Use the difference operation to combine the control difference equations at all nodes and the continuity conditions of each node into a linear equation set represented by a matrix, and obtain the displacement vector of each node through matrix solution;

[0244] S42: Use interpolation and fitting methods to obtain the distribution function of the displacement of the rigid-flexible combined reinforcement structure of the slope;

[0245] S43: Use the displacement coordination relationship at the connection between the anchor cable and the frame structure to obtain the axial force function of the anchor cable;

[0246] S44: Take the second derivative of the distribution function of the displacement of the rigid-flexible combined reinforcement structure of the slope with respect to time to obtain the distribution function of the acceleration of each part of the frame structure; take the second derivative of the distribution function of the displacement of the rigid-flexible combined reinforcement structure of the slope with respect to its length direction to obtain the distribution function of the bending moment of each part of the frame structure.

[0247] In the present invention, the dynamic equilibrium differential equation is a coupled non-linear fourth-order differential equation, and it is difficult to solve a strict analytical solution. In the above embodiment, the finite difference method is used to solve the seismic response of the anchor-pulled frame pile structure. By using the difference operation, solving the partial differential equation is transformed into solving an algebraic equation set, which is equivalent to degrading the high-order partial differential equation into a linear equation set that is conducive to matrix programming for solution, so that a high-order accurate numerical solution and high stability of the numerical results can be obtained.

[0248] According to the standard finite difference principle, the frame structure is divided into N equal parts along its length direction, and the finite difference formats of each differential term in the dynamic equilibrium differential equation are respectively:

[0249] (51)

[0250] (52)

[0251] (53)

[0252] (54)

[0253] In the formula: is the displacement of each equal division unit; , , , , are the displacements of unit nodes i+1, i-1, i, i+2, i-2 respectively; is the length of each equal division unit;

[0254] The rigid-flexible combined reinforcement structure of the slope is discretized according to a uniform and infinitesimal length. By using the difference operation, the finite difference format of the motion equation of each micro segment of the structure is given. The control difference equations at all nodes and the continuity conditions of each node are combined into a linear equation set represented by a matrix. By solving the matrix, the displacement vectors of each node are obtained. Then, the continuous function U of the displacement distribution of the rigid-flexible combined reinforcement structure of the slope can be obtained by interpolation and fitting. Then, the axial force function of the cable anchor is obtained by using the displacement coordination relationship at the connection between the cable anchor and the frame structure. The second derivative of the displacement distribution function with respect to time is taken to obtain the distribution function of the acceleration of each part of the frame structure. The second derivative of the displacement distribution function with respect to its length direction is taken to obtain the distribution function of the bending moment of each part of the frame structure.

[0255] S5: Calculate the acceleration, displacement, bending moment and axial force at different times according to the functions obtained in step S4.

[0256] In a specific embodiment, taking the rigid-flexible combined reinforcement structure of a slope in a certain place as an example, the dynamic calculation method of the rigid-flexible combined reinforcement structure of the slope considering coordinated force is used to calculate the theoretical value of its structure dynamics, and a shaking table model test is carried out to obtain the test value. The effectiveness of the present invention is proved by comparing the test value and the theoretical value.

[0257] In this embodiment, the layout of the shaking table model test model and monitoring points is as Figure 4 shown, and the values and units of the model parameters in the test are shown in Table 1:

[0258] Table 1 Values and units of model parameters in the test

[0259]

[0260] The size of the test model is 3.4m×1.5m×1.5m (length×width×height). The size of the rigid-flexible combined reinforcement structure model of the slope is as Figure 5 shown, and the layout of the structure bending moment measurement points is as Figure 6 shown.

[0261] The initial prestress of the anchor cable is set to 7.8 N. In the shaking table test, under the action of the sine wave with an amplitude of 0.05 g and a frequency of 4 Hz as shown in Figure 7 , the theoretical values and test values of the acceleration at the A-P3 measuring point of the structure, the displacement at the D1 measuring point, the axial force of the anchor cable at the F1 measuring point, and the bending moment at the M6 measuring point are as shown in Figures 8 - 11 . The comparison results of the bending moment envelope diagram of the structure are as shown in Figure 12 . It can be seen from Figures 8 - 12 that the theoretical values calculated by the present invention are relatively close to the test values of the shaking table model test. The dynamic calculation method of the rigid-flexible combined reinforcement structure of the slope considering coordinated stress can accurately calculate the deformation and stress of the rigid-flexible combined reinforcement structure of the slope under dynamic action.

[0262] In summary, the present invention can consider the stress coordination among the anchor cable-frame structure-rock and soil mass, and calculate the dynamics of the rigid-flexible combined reinforcement structure of the slope more accurately. Compared with the prior art, the present invention has made remarkable progress.

[0263] The above is only a preferred embodiment of the present invention, and does not impose any form of limitation on the present invention. Although the present invention has been disclosed above with a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments by using the above-disclosed technical content without departing from 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 still fall 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, a dynamic equilibrium differential equation considering the coordination of the forces between the anchor cable, the frame structure and the rock and soil mass is established; the dynamic equilibrium 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; 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 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）。 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 S3, the initial conditions include: （47） （48） （49） （50）。 4. The dynamic calculation method of the slope rigid-flexible combined reinforcement structure considering coordinated force according to any one of claims 1 to 3, 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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