Anchor cable chair type pile power calculation method considering soil-structure interaction

Abstract

The invention discloses an anchor cable and chair type pile power calculation method considering soil-structure interaction, which comprises the following steps: S1, establishing a power balance differential equation considering anchor cable-chair type pile-rock-soil body interaction, and considering the difference of interaction between a chair type pile and front and back soil bodies by means of a sign function; s2, continuously providing boundary conditions of a dynamic balance differential equation according to stress balance and deformation; s3, giving an initial condition of a dynamic balance differential equation according to the displacement and the speed at the initial moment; s4, solving the dynamic balance differential equation in combination with boundary and initial conditions to obtain a distribution function of acceleration, displacement and bending moment of each part of the anchor cable chair type pile and an axial force function of the anchor cable under the action of an earthquake; and S5, according to the function obtained in the step S4, deformation and stress of the chair type pile at different moments are obtained through calculation. According to the method, the deformation and stress of the anchor cable chair type pile under the dynamic effect can be accurately calculated, and a theoretical basis is provided for dynamic analysis and aseismic design of the anchor cable chair type pile.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic calculation methods for cable - anchored chair - type piles, and particularly to a dynamic calculation method for cable - anchored chair - type piles considering soil - structure interaction. 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, earthquake - induced 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 - steep slopes along the line are extremely prone to instability and failure, posing severe challenges to the construction and operation of infrastructure. In recent years, traditional retaining structure types such as anti - slide piles, cable - anchored anti - slide piles and cable - anchored ground beams have been mainly formed to effectively improve the stability of these slopes, but they are difficult to meet the actual needs of seismic reinforcement for high - steep slopes in strong earthquake areas. To effectively solve the problem of seismic reinforcement for high - steep slopes in strong earthquake areas, the cable - anchored chair - type pile structure has emerged.

[0003] At present, the analysis and calculation of cable - anchored chair - type piles 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 added to the structure, without involving the characteristics of earthquake motion. However, seismic waves propagate 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 mechanical properties and interaction between the slope rock and soil mass, the reinforcement structure and the cable material, their mechanical characteristics and interaction also show obvious differences. Therefore, the interaction between the cable - anchored chair - type pile and the rock and soil mass must be considered under earthquake action. Summary of the Invention

[0004] Aiming at the above problems, the present invention aims to provide a dynamic calculation method for cable - anchored chair - type piles considering soil - structure interaction.

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

[0006] A dynamic calculation method for cable - anchored chair - type piles considering soil - structure interaction, comprising the following steps:

[0007] S1: Based on D'Alembert's principle, establish a dynamic equilibrium differential equation considering the interaction between the cable - anchored chair - type pile and the rock and soil mass. When establishing the dynamic equilibrium differential equation, the difference in the interaction between the chair - type pile and the front and rear soil masses is considered by means of the sign function;

[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 cable - anchored chair - type pile under seismic action and the axial force function of the 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 rock of the back pile foundation:

[0014]

[0015] Where: E is the elastic modulus of the chair - type pile; I c1 is the moment of inertia of the back pile; u 1 is the horizontal displacement below the rock of the back pile foundation; y is the micro - element length of the front pile and the back pile; m 1 is the mass per unit length of the back pile; t is the time; k 1 is the foundation coefficient of the rock foundation; b is the cross - section width of the chair - type pile; u g is the input horizontal ground motion; h 1 is the length below the rock of the back pile foundation;

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

[0017]

[0018] Where: I c2 is the moment of inertia of the front pile; u 3 is the horizontal displacement below the rock of the front pile foundation; m 2 is the mass per unit length of the front pile; h 2 is the length below the rock of the front pile foundation;

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

[0020]

[0021] Where: u 4 is the horizontal displacement between the interface of the front pile foundation covering layer and the cross - beam; k 2 is the foundation coefficient of the overburden soil; h 3is the length between the front pile foundation covering interface and the crossbeam;

[0022] (4) Dynamic equilibrium differential equation between the rear pile foundation covering interface and the crossbeam:

[0023]

[0024] In the formula: u 2 is the horizontal displacement between the rear pile foundation covering interface and the crossbeam;

[0025] (5) Dynamic equilibrium differential equation between the connection of the front pile and the crossbeam and the lower anchor cable:

[0026]

[0027] In the formula: u 5 is the horizontal displacement between the connection of the front pile and the crossbeam and the lower anchor cable; h 4 is the length between the connection of the front pile and the crossbeam and the lower anchor cable;

[0028] (6) Dynamic equilibrium differential equation between the lower anchor cable of the front pile and the upper anchor cable:

[0029]

[0030] In the formula: u 6 is the horizontal displacement between the lower anchor cable of the front pile and the upper anchor cable; h 5 is the length between the lower anchor cable of the front pile and the upper anchor cable;

[0031] (7) Dynamic equilibrium differential equation between the upper anchor cable of the front pile and the top of the overburden layer:

[0032]

[0033] In the formula: u 7 is the horizontal displacement between the upper anchor cable of the front pile and the top of the overburden layer; h 6 is the length between the upper anchor cable of the front pile and the top of the overburden layer;

[0034] (8) Dynamic equilibrium differential equation of the crossbeam:

[0035]

[0036] In the formula: I c3 is the moment of inertia of the crossbeam; y 1 is the vertical displacement of the crossbeam; u is the microelement length of the crossbeam; m 3 is the mass per unit length of the crossbeam; l is the length of the crossbeam.

[0037] Preferably, in step S2, the boundary conditions include:

[0038] (1) Boundary conditions at the bottom of the rear pile:

[0039] u 1 | y＝0 = 0 (13)

[0040]

[0041] (2) Boundary conditions at the bottom of the front pile:

[0042] u 3 | y＝0 = 0 (15)

[0043]

[0044] (3) Boundary conditions at the interface between the front pile and the base - overlying layer:

[0045]

[0046] Where: n is the order of differentiation;

[0047] (4) Boundary conditions at the interface between the rear pile and the base - overlying layer:

[0048]

[0049] (5) Boundary conditions at the lower cable:

[0050]

[0051] Where: α is the angle between the lower cable and the horizontal line; k is the elastic modulus of the cable;

[0052] (6) Boundary conditions at the upper cable:

[0053]

[0054] Where: β is the angle between the upper cable and the horizontal line;

[0055] (7) Boundary conditions at the top of the front pile:

[0056]

[0057] (8) Boundary conditions at the connection between the left end of the cross - beam and the front pile:

[0058] y 1 | u＝0 = 0 (25)

[0059]

[0060]

[0061] (9) Boundary conditions at the connection between the right end of the crossbeam and the rear pile:

[0062] y 1 | u＝l = 0 (30)

[0063]

[0064] Preferably, in step S3, the initial conditions include:

[0065] u i | t＝0 = 0 (i = 1, 2, 3,..., 7) (35)

[0066]

[0067] y 1 | t＝0 = 0 (37)

[0068]

[0069] Preferably, in step S4, solving the dynamic equilibrium differential equation specifically includes the following sub-steps:

[0070] S41: Using 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 obtaining the displacement vectors of each node through matrix solution;

[0071] S42: Using interpolation and fitting methods to obtain the continuous function of the displacement distribution of the chair-shaped pile;

[0072] S43: Using the displacement coordination relationship at the connection between the cable anchor and the chair-shaped pile to obtain the axial force function of the cable anchor;

[0073] S44: Taking the second derivative of the displacement distribution function of the chair-shaped pile with respect to time to obtain the distribution function of the acceleration of each part of the chair-shaped pile; taking the second derivative of the displacement distribution function of the chair-shaped pile with respect to its length direction to obtain the distribution function of the bending moment of each part of the chair-shaped pile.

[0074] The beneficial effects of the present invention are:

[0075] By considering the soil-structure interaction, the present invention can more accurately calculate the deformation and stress of the cable anchor chair-shaped pile under dynamic action, providing technical support for the design of the cable anchor chair-shaped pile under seismic load. Description of the Drawings

[0076] 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 drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0077] Figure 1 It is a schematic flow chart of the dynamic calculation method of the cable - anchored chair - type pile considering soil - structure interaction of the present invention;

[0078] Figure 2 It is a schematic diagram of the slope reinforced by the cable - anchored chair - type pile;

[0079] Figure 3 It is a schematic diagram of the calculation model of the cable - anchored chair - type pile;

[0080] Figure 4 It is a schematic diagram of the shaking table model test model of the slope reinforced by the cable - anchored chair - type pile and the layout of monitoring points in a specific embodiment;

[0081] Figure 5 It is a schematic diagram of the model size of the cable - anchored chair - type pile in a specific embodiment;

[0082] Figure 6 It is a schematic diagram of the layout of the bending moment measuring points of the chair - type pile in a specific embodiment;

[0083] Figure 7 It is a schematic diagram of the input ground motion waveform of the shaking table test in a specific embodiment;

[0084] Figure 8 It is a schematic diagram of the comparison result of the theoretical value and the test value of the acceleration at the A1 measuring point in a specific embodiment;

[0085] Figure 9 It is a schematic diagram of the comparison result of the theoretical value and the test value of the displacement at the D1 measuring point in a specific embodiment;

[0086] Figure 10 It is a schematic diagram of the comparison result of the theoretical value and the test value of the cable axial force at the F1 measuring point in a specific embodiment;

[0087] Figure 11 It is a schematic diagram of the comparison result of the theoretical value and the test value of the cable bending moment at the M7 measuring point in a specific embodiment. Specific embodiments

[0088] 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 may 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 disclosure of the present invention 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.

[0089] As Figure 1 shown, the present invention provides a dynamic calculation method for cable - chair - type piles considering soil - structure interaction, including the following steps:

[0090] S1: Based on D'Alembert's principle, establish a dynamic equilibrium differential equation considering the interaction of cable - chair - type piles and rock - soil mass. When establishing the dynamic equilibrium differential equation, the difference in the interaction between the chair - type pile and the front and rear soil masses is considered by means of the sign function.

[0091] In a specific embodiment, when establishing the dynamic equilibrium differential equation, the slope reinforced by the cable - chair - type pile is as Figure 2 shown, and the calculation model of the cable - chair - type pile is as Figure 3 shown. The dynamic equilibrium differential equation includes:

[0092] (1) The dynamic equilibrium differential equation for the part of the rear pile below the bedrock (BC section):

[0093]

[0094] In the formula: E is the elastic modulus of the chair - type pile; I c1 is the moment of inertia of the rear pile; u 1 is the horizontal displacement of the rear pile below the bedrock; y is the micro - element length of the front pile and the rear pile; m 1 is the mass per unit length of the rear pile; t is the time; k 1 is the foundation coefficient of the bedrock; b is the cross - sectional width of the chair - type pile; u g is the input horizontal ground motion; h 1 is the length of the rear pile below the bedrock;

[0095] (2) The dynamic equilibrium differential equation for the part of the front pile below the bedrock (DE section):

[0096]

[0097] In the formula: I c2 is the moment of inertia of the front pile; u 3 is the horizontal displacement of the front pile below the bedrock; m 2 is the mass per unit length of the front pile; h 2is the length below the front pile foundation rock;

[0098] (3) Dynamic equilibrium differential equation between the front pile foundation covering interface and the crossbeam (EF section):

[0099]

[0100] In the formula: u 4 is the horizontal displacement between the front pile foundation covering interface and the crossbeam; k 2 is the foundation coefficient of the overburden soil; h 3 is the length between the front pile foundation covering interface and the crossbeam;

[0101] (4) Dynamic equilibrium differential equation between the rear pile foundation covering interface and the crossbeam (AB section):

[0102]

[0103] In the formula: u 2 is the horizontal displacement between the rear pile foundation covering interface and the crossbeam;

[0104] (5) Dynamic equilibrium differential equation between the connection point of the front pile and the crossbeam (point F) and the lower anchor cable (point M) (FM section):

[0105]

[0106] In the formula: u 5 is the horizontal displacement between the connection point of the front pile and the crossbeam and the lower anchor cable; h 4 is the length between the connection point of the front pile and the crossbeam and the lower anchor cable;

[0107] (6) Dynamic equilibrium differential equation between the lower anchor cable of the front pile (point M) and the upper anchor cable (point N) (MN section):

[0108]

[0109] In the formula: u 6 is the horizontal displacement between the lower anchor cable and the upper anchor cable of the front pile; h 5 is the length between the lower anchor cable and the upper anchor cable of the front pile;

[0110] (7) 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):

[0111]

[0112] In the formula: u 7 is the horizontal displacement between the upper anchor cable of the front pile and the top of the overburden layer; h 6 is the length between the upper anchor cable of the front pile and the top of the overburden layer;

[0113] (8) Dynamic equilibrium differential equation of the cross beam (AF section):

[0114]

[0115] Where: I c3 is the moment of inertia of the cross beam; y 1 is the vertical displacement of the cross beam; u is the infinitesimal length of the cross beam; m 3 is the mass per unit length of the cross beam; l is the length of the cross beam.

[0116] S2: Give the boundary conditions of the dynamic equilibrium differential equation according to force balance and deformation continuity.

[0117] In a specific embodiment, the boundary conditions include:

[0118] (1) Boundary conditions at the bottom of the rear pile (point C):

[0119] u 1 | y＝0 = 0 (13)

[0120]

[0121] That is, the relative displacement and rotation angle at the bottom of the rear pile (point C) are both 0;

[0122] (2) Boundary conditions at the bottom of the front pile (point D):

[0123] u 3 | y＝0 = 0 (15)

[0124]

[0125] That is, the relative displacement and rotation angle at the bottom of the front pile (point D) are both 0;

[0126] (3) Boundary conditions at the interface between the front pile and the base-overlying rock (point E):

[0127]

[0128] Where: n is the order of differentiation;

[0129] That is, at the interface between the front pile and the base-overlying rock (point E), the displacement, rotation angle, shear force, and bending moment are continuous; (4) Boundary conditions at the interface between the rear pile and the base-overlying rock (point B):

[0130]

[0131] That is, at the interface between the rear pile and the base-overlying rock (point B), the displacement, rotation angle, shear force, and bending moment are continuous; (5) Boundary conditions at the lower cable (point M) are:

[0132]

[0133] In the formula: α is the included angle between the lower anchor cable and the horizontal line; k is the elastic modulus of the anchor cable;

[0134] (6) The boundary conditions at the upper anchor cable (point N) are:

[0135]

[0136] In the formula: β is the included angle between the upper anchor cable and the horizontal line;

[0137] (7) The boundary conditions at the top of the front pile (point P):

[0138]

[0139] That is, both the rotation angle and the bending moment at point P are zero;

[0140] (8) The boundary conditions at the connection between the left end of the crossbeam and the front pile (point F):

[0141] y 1 | u＝0 = 0 (25)

[0142] That is, the vertical displacement at point F is zero;

[0143]

[0144] That is, the sum of the bending moments at point F is 0;

[0145]

[0146] That is, the horizontal displacements of the upper and lower parts of point F are equal;

[0147]

[0148] That is, the deformation curvatures (rotation angles) of the upper and lower parts of point F are equal;

[0149]

[0150] That is, the horizontal displacement at point F is equal to the horizontal displacement at point A;

[0151] (9) The boundary conditions at the connection between the right end of the crossbeam and the rear pile (point A):

[0152] y 1 | u＝l = 0 (30)

[0153] That is, the vertical displacement at point A is zero;

[0154]

[0155] That is, the sum of the bending moments at point A is 0;

[0156]

[0157] That is, the deformation curvatures (angles of rotation) at point A are equal;

[0158]

[0159] That is, the shear forces at point A and point F of the AF rod are equal;

[0160]

[0161] That is, the shear forces at point A and point B of the AB rod are equal;

[0162] S3: Give the initial conditions of the dynamic equilibrium differential equation according to the displacement at the initial moment and the velocity at the initial moment.

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

[0164] u i | t＝0 = 0 (i = 1, 2, 3,..., 7) (35)

[0165]

[0166] y 1 | t＝0 = 0 (37)

[0167]

[0168] In the above embodiment, when i = 1 for u i u i is u 1 , representing the horizontal displacement below the post-pile foundation rock, and the same applies to others.

[0169] S4: Combine the boundary conditions and the initial conditions to solve the dynamic equilibrium differential equation, and obtain the distribution functions of the accelerations, displacements, and bending moments of each part of the cable chair pile under seismic action and the axial force function of the cable.

[0170] In a specific embodiment, the solution of the dynamic equilibrium differential equation specifically includes the following sub-steps:

[0171] 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 system represented by a matrix, and obtain the displacement vector of each node through matrix solution;

[0172] S42: Use interpolation and fitting methods to find the continuous function of the distribution of the chair pile displacement;

[0173] S43: Obtain the axial force function of the cable anchor by using the displacement coordination relationship at the connection between the cable anchor and the chair-shaped pile;

[0174] S44: Take the second derivative of the distribution function of the displacement of the chair-shaped pile with respect to time to obtain the distribution function of the acceleration of each part of the chair-shaped pile; take the second derivative of the distribution function of the displacement of the chair-shaped pile with respect to its length direction to obtain the distribution function of the bending moment of each part of the chair-shaped pile.

[0175] 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 cable anchor chair-shaped pile. By using the difference operation, the solution of the partial differential equation is transformed into the solution of an algebraic equation system, which is equivalent to degrading the high-order partial differential equation into a linear equation system that is conducive to matrix programming for solution. In this way, a high-order accurate numerical solution and high stability of the numerical results can be obtained.

[0176] According to the standard finite difference principle, the chair-shaped pile 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:

[0177]

[0178]

[0179] Where: U(y) is the displacement of each equal part unit; U(i + 1), U(i - 1), U(i), U(i + 2), U(i - 2) are the displacements of unit nodes i + 1, i - 1, i, i + 2, i - 2 respectively; h is the length of each equal part unit;

[0180] Discretize the cable anchor chair-shaped pile with a uniform small length, use the difference operation, and give the finite difference format of the motion equation of each micro-segment of the structure. Combine all the control difference equations at the nodes and the continuous conditions of each node into a linear equation system represented by a matrix. By solving the matrix, the displacement vector of each node is obtained, and then the continuous function U of the displacement distribution of the cable anchor chair-shaped pile can be obtained by interpolation and fitting method. 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 chair-shaped pile. Take the second derivative of the displacement distribution function with respect to time to obtain the distribution function of the acceleration of each part of the chair-shaped pile. Take the second derivative of the displacement distribution function with respect to its length direction to obtain the distribution function of the bending moment of each part of the chair-shaped pile.

[0181] S5: Calculate the acceleration, displacement, bending moment and axial force at different times according to the functions obtained in step S4.

[0182] In a specific embodiment, taking the slope reinforcement with cable - anchored chair - type piles in a certain place as an example, the dynamic calculation method of cable - anchored chair - type piles considering soil - structure interaction described in the present invention is used to calculate the deformation and force of the chair - type piles and obtain the theoretical values, and a shaking table model test is carried out to obtain the test values. The effectiveness of the present invention is proved by comparing the test values and the theoretical values.

[0183] In this embodiment, the layout of the shaking table model test model and monitoring points is as Figure 4 shown. The values and units of the model parameters in the test are shown in Table 1:

[0184] Table 1 Values and units of model parameters in the test

[0185] Serial number Parameter Physical meaning Value Unit 1 E Elastic modulus of chair - type pile <![CDATA[8.125×10 8 > Pa 2 <![CDATA[I c1 > Moment of inertia of rear pile <![CDATA[1.76×10 -6 > <![CDATA[m 4 > 3 <![CDATA[I c2 > Moment of inertia of front pile <![CDATA[2.79×10 -6 > <![CDATA[m 4 > 4 <![CDATA[I c3 > Moment of inertia of cross - beam <![CDATA[1.76×10 -6 > <![CDATA[m 4 > 5 k Elastic modulus of anchor cable <![CDATA[4.875×10 9 > Pa 6 b Cross - sectional width of chair - type pile 0.05 m 7 <![CDATA[m 1 > Mass per unit length of rear pile 9 kg / m 8 <![CDATA[m 2 > Mass per unit length of front pile 10.5 kg / m 9 <![CDATA[m 3 > Mass per unit length of cross - beam 9 kg / m 10 α Angle between lower anchor cable and horizontal line 25 ° 11 β Angle between upper anchor cable and horizontal line 23 °

[0186] The size of the test model is 3.4m×1.5m×1.5m (length×width×height). The size of the cable - anchored chair - type pile model is as Figure 5 shown. The layout of the moment measuring points of the chair - type pile is as Figure 6 shown.

[0187] The initial prestress of the cable is set to 7.8 N. Under the action of a sine wave with an amplitude of 0.05g and a frequency of 4 Hz input in the shaking table test, the theoretical values and test values of the acceleration at the A1 measuring point, the displacement at the D1 measuring point, the cable axial force at the F1 measuring point, and the moment at the M7 measuring point of the chair - type pile are as Figure 7 shown. It can be seen from Figures 8 - 11 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 cable - anchored chair - type piles considering soil - structure interaction described in the present invention can accurately calculate the deformation and force of cable - anchored chair - type piles under dynamic action. Figures 8 - 11 In summary, the present invention can calculate the deformation and force of cable - anchored chair - type piles under dynamic action more accurately by considering soil - structure interaction. Compared with the prior art, the present invention has made remarkable progress.

[0188] As described above, it is only a preferred embodiment of the present invention, and there is no any form of limitation to the present invention. Although the present invention has been disclosed above with the 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 within the scope of the technical solution of the present invention. However, as long as it does not depart from the content of the technical solution of the present invention, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

[0189] ​

Claims

1. A dynamic calculation method for anchor chair piles considering soil-structure interaction, characterized in that: The following steps are involved: S1: Based on the D'Alembert principle, a dynamic equilibrium differential equation considering the interaction between the anchor cable, the chair pile and the rock and soil mass is established. When establishing the dynamic equilibrium differential equation, the difference in the interaction between the chair pile and the front and rear soil masses is considered by means of a symbolic function; 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 anchor chair pile under the 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 anchor chair pile considering soil-structure interaction 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: Where: E is the elastic modulus of the chair pile; I c1 is the moment of inertia of the rear pile; u1 is the horizontal displacement of the rear pile below the bedrock; y is the micro-element length of the front and rear piles; m1 is the unit length mass of the rear pile; t is time; k1 is the bedrock foundation coefficient; b is the cross-sectional width of the chair pile; u g is the input horizontal ground motion; h1 is the length of the rear pile below the bedrock; (2) Dynamic equilibrium differential equation below the front pile bedrock: Where: I c2 is the moment of inertia of the front pile; u3 is the horizontal displacement of the front pile below the bedrock; m2 is the mass per unit length of the front pile; h2 is the length of the front pile below the bedrock; (3) Dynamic equilibrium differential equation between the front pile foundation interface and the beam: Where: u4 is the horizontal displacement between the front pile foundation interface and the beam; k2 is the foundation coefficient of the covering layer soil; h3 is the length between the front pile foundation interface and the beam; (4) Dynamic equilibrium differential equation between the rear pile foundation interface and the beam: Where: u2 is the horizontal displacement between the rear pile foundation interface and the beam; (5) Dynamic equilibrium differential equation between the front pile and the crossbeam connection and the anchor cable below: Where: u5 is the horizontal displacement between the connection between the front pile and the crossbeam and the lower anchor cable; h4 is the length between the connection between the front pile and the crossbeam and the lower anchor cable; (6) Dynamic equilibrium differential equation between the anchor cable below the front pile and the anchor cable above it: Where: u6 is the horizontal displacement between the anchor cable below the front pile and the anchor cable above; h5 is the length between the anchor cable below the front pile and the anchor cable above; (7) Dynamic equilibrium differential equation between the anchor cable above the front pile and the top of the overburden: Where: u7 is the horizontal displacement between the anchor cable above the front pile and the top of the covering layer; h6 is the length between the anchor cable above the front pile and the top of the covering layer; (8) Dynamic equilibrium differential equation of the beam: Where: I c3 is the moment of inertia of the beam; y1 is the vertical displacement of the beam; u is the infinitesimal length of the beam; m3 is the mass per unit length of the beam; l is the length of the beam.

3. The anchor chair pile dynamic calculation method considering soil-structure interaction 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: u1| y＝0 ＝0 (13) (2) Boundary conditions at the bottom of the front pile: u3| y＝0 ＝0 (15) (3) Boundary conditions of the front pile at the base-cover interface: Where: n is the order of differentiation; (4) Boundary conditions of the rear pile at the base-cover interface: (5) The boundary conditions at the lower anchor cable are: Where: α is the angle between the lower anchor cable and the horizontal line; k is the elastic modulus of the anchor cable; (6) The boundary conditions at the upper anchor cable are: Where: β is the angle between the upper anchor cable and the horizontal line; (7) Boundary conditions at the top of the front pile: (8) Boundary conditions at the connection between the left end of the beam and the front pile: y1| u＝0 ＝0 (25) (9) Boundary conditions at the connection between the right end of the beam and the rear pile: y1| u＝l ＝0 (30) 4. The anchor chair pile dynamic calculation method considering soil-structure interaction according to claim 3 is characterized in that: In step S3, the initial conditions include: in i | t＝0 =0(i=1,2,3,...,7) (35) y1| t＝0 ＝0 (37) 5. The anchor chair pile dynamic calculation method considering soil-structure interaction 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: Using interpolation and fitting methods to find the distribution continuous function of chair pile displacement; S43: Calculate the axial force function of the anchor cable by using the displacement coordination relationship between the anchor cable and the chair pile connection; S44: taking a second derivative of the chair pile displacement distribution function with respect to time to obtain a distribution function of the acceleration of each part of the chair pile; taking a second derivative of the chair pile displacement distribution function with respect to its length direction to obtain a distribution function of the bending moment of each part of the chair pile.

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