A method for analyzing horizontal dynamic response of a single pile under earthquake S shear wave

Abstract

The embodiment of the present invention discloses a method for analyzing the horizontal dynamic response of a single pile under the action of an earthquake S shear wave, which includes: S1, based on the characteristic parameters of the foundation soil, creating a soil dynamic balance equation considering the influence of the foundation soil on the earthquake S shear wave; S2, combining the Euler beam and the Pasternak foundation model, creating a dynamic balance equation of the pile body unit; S3, determining the relationship between the pile body rotation angle, bending moment, shear force and the pile body horizontal displacement coefficient and creating a corresponding coefficient equation group; S4, determining the dynamic balance equation corresponding to the pile body displacement and internal force coefficient at the bottom of the pile; S5, determining the dynamic balance equation corresponding to the pile top displacement and the rotation angle coefficient, and then completing the analysis of the horizontal dynamic response process of the single pile under the action of the earthquake S shear wave. The present invention simplifies the soil around the pile into a Pasternak foundation, considers the pile foundation horizontal vibration force analysis of the earthquake S shear wave propagation in the layered soil under the action of the pile top axial force, and can provide theoretical guidance and reference for the seismic design of pile foundation engineering.

Description

Technical Field

[0001] The invention relates to the technical field of pile foundation vibration analysis, and in particular to a method for analyzing horizontal dynamic response of a single pile under the action of an earthquake S shear wave. Background Art

[0002] In recent years, pile foundations have been commonly damaged in major earthquakes. When an earthquake occurs, the pile foundation will vibrate due to the seismic waves in the foundation soil, and the vibration of the pile will also change the movement of the foundation soil around the pile. When studying the dynamic response of pile foundations under earthquakes, the interaction between pile and soil motion is a key factor.

[0003] Therefore, more and more scholars have conducted relevant research on the horizontal dynamic response of pile foundations under seismic waves. The study of the dynamic response of piles under lateral seismic loads is usually divided into numerical solutions and analytical solutions. Numerical solutions require a lot of computer resources and time, and cannot guarantee mathematical rigor. There are few methods in the analytical solution that can simply reveal the influence of soil shear deformation on the calculation results. However, most of these studies currently only simplify the soil around the pile into a Winkler foundation during the vibration analysis of the pile foundation, and do not fully consider the influencing factors of its shear deformation, especially the seismic wave action properties and their influence on the pile-soil interaction system. Summary of the invention

[0004] Based on this, in order to solve the shortcomings of the existing technology, a method for analyzing the horizontal dynamic response of a single pile under the action of seismic S shear wave is proposed.

[0005] A method for analyzing horizontal dynamic response of a single pile under the action of earthquake S shear waves, characterized by comprising:

[0006] S1. Based on the characteristic parameters of foundation soil, a soil dynamic equilibrium equation is created considering the influence of foundation soil on earthquake S shear wave, wherein the characteristic parameters of foundation soil include elastic shear modulus, viscous damping coefficient, mass density and horizontal displacement;

[0007] S2. Based on the soil dynamic equilibrium equation, combined with the Euler beam and Pasternak foundation model, a dynamic equilibrium equation of the pile unit is created;

[0008] S3, based on the dynamic equilibrium equation of the pile body unit, determine the relationship between the pile body rotation angle, bending moment, shear force and the pile body horizontal displacement coefficient and create a corresponding coefficient equation group;

[0009] S4, based on the coefficient equation group, determining the dynamic equilibrium equation corresponding to the pile bottom and pile body displacement and internal force coefficient;

[0010] S5. Determine the dynamic equilibrium equation corresponding to the pile top displacement and the rotation coefficient, and then complete the analysis of the horizontal dynamic response process of a single pile under the action of earthquake S shear wave.

[0011] Optionally, in one embodiment, the step of creating a soil dynamic equilibrium equation taking into account the influence of the foundation soil on the earthquake S shear wave based on the foundation soil characteristic parameters in S1 includes:

[0012] S11. Determine the characteristic parameters of each soil layer of the foundation soil, including the elastic shear modulus Viscous damping coefficient and mass density and horizontal displacement

[0013] S12. Based on the characteristic parameters, a free site soil dynamic balance equation is created. The corresponding free site soil dynamic balance equation is:

[0014]

[0015] In the formula, is the shear stress, t is the time, and z is the depth of the soil layer;

[0016] because It is expressed as:

[0017]

[0018] Viscous damping coefficient of viscoelastic materials ω is the excitation circular frequency,

[0019] Substituting formula (2) into formula (1), we get:

[0020]

[0021] S13, based on horizontal displacement The displacement steady-state solution in the frequency domain is to transform formula (3), and the horizontal displacement The displacement steady-state solution in the frequency domain is of the form: Substituting into formula (3), we get:

[0022]

[0023] S14. Create the displacement amplitude of the jth layer. Under the action of the upward and downward shear waves at depth z, the horizontal displacement The time-independent partial solution corresponds to the equation

[0024]

[0025] Among them, the complex shear modulus C1 , C 2 is the coefficient to be solved;

[0026] S15. Obtain the exponential form of equation (5), the corresponding equation is:

[0027]

[0028] In the formula, N-1≥j≥1, N represents the number of bedrock layers, E j 、F j is the amplitude coefficient, is the wave number;

[0029] S16, creating a conversion relationship equation between the top layer, i.e., the first soil layer, and any layer of amplitude coefficient, and the corresponding equation creation process is:

[0030] Due to the wave number Complex shear wave velocity Then formula (6) is

[0031]

[0032]

[0033] Substituting equations (7) and (8) into equation (1), we can obtain:

[0034]

[0035] Since the shear stress and displacement are continuous at the interface between the jth layer and the j+1th layer of soil, that is:

[0036]

[0037] h j It refers to the thickness of each soil layer;

[0038] Substituting equation (6) and equation (9) into equation (10), we get:

[0039]

[0040] The corresponding recursive formula is determined as:

[0041]

[0042] In the formula, Defined as wave number impedance, let the coefficient matrix (2×2) obtained in the above formula be T j , then the conversion equation between the top layer (the first layer of soil) and the amplitude coefficient of any layer is:

[0043]

[0044] Among them, the transfer function

[0045] In the formula, N-1≥j≥1, N represents the number of bedrock layers, E j 、F j is the amplitude coefficient,

[0046] S17. Create the soil dynamic equilibrium equation considering the influence of foundation soil on earthquake S shear wave. The corresponding equation creation process is:

[0047] According to the first layer free ground boundary condition: τ 1 (0) = 0, then E 1 =F 1 , and let n = N-1, we get:

[0048]

[0049] and

[0050]

[0051] Substituting the above formula into formula (6), we get:

[0052]

[0053] Optionally, in one embodiment, the dynamic equilibrium equation of the pile body unit in S2 is:

[0054]

[0055] In the formula, is the horizontal displacement of the j-th pile unit mass point, is the free field motion displacement; E p ,I p 、m p are the elastic modulus, section moment of inertia and mass per unit length of the pile respectively; and are the stiffness coefficient, damping coefficient and foundation shear stiffness of the foundation soil around the j-th pile layer; B 0 =0.9(1.5d+0.5) is the calculated width of the pile, ε is the reduction factor considering the separation between the pile and the soil, and is taken as 0.6~0.9.

[0056] Optionally, in one embodiment, the step of determining the relationship between the pile body rotation angle, bending moment, shear force and the pile body horizontal displacement coefficient and creating a corresponding coefficient equation group in S3 includes:

[0057] Various parameters and Determined by the following formula:

[0058]

[0059]

[0060]

[0061]

[0062] Where U 0 is the maximum displacement of ground motion; the shear wave number of soil around the pile Shear wave velocity of soil around pile and are the elastic modulus, density, damping coefficient and Poisson's ratio of the soil around the pile; dimensionless frequency is the thickness of the foundation soil shear layer, d refers to the pile diameter;

[0063] Since the horizontal displacement of the pile is expressed as:

[0064]

[0065] In the formula, is the horizontal displacement amplitude of the pile body particle,

[0066] Let W p =E p I p , Substituting equation (21) into equation (16) we can further obtain the following equations:

[0067]

[0068] In the formula, E p ,I p , B 0 are the elastic modulus of the pile, the moment of inertia of the pile section, and the calculated width of the pile, respectively. p is the defined coefficient, N 0 is the axial force on the pile top;

[0069] Obviously, the homogeneous general solution corresponding to formula (22) is:

[0070]

[0071] In the formula, coefficient The value is determined by the set boundary conditions;

[0072] The special solution of formula (23) is:

[0073]

[0074] Then the complete solution of formula (23) is expressed as:

[0075]

[0076] Based on the Euler beam theory, the relationship between the pile body rotation angle, bending moment, shear force and pile body horizontal displacement is:

[0077]

[0078]

[0079]

[0080] Combining equations (25) and (26), we get the following coefficient equations:

[0081]

[0082] In the formula,

[0083]

[0084] When j = 1, z = 0, substituting into equation (27), the transfer integral constant of the first section of the pile is:

[0085]

[0086] At the cross sections of the pile body at the jth and j-1th sections, the horizontal displacement, rotation angle, bending moment and shear force of the pile are continuous, that is:

[0087]

[0088] Combining equations (27), (28) and (29), we get the coefficient matrix equations as follows:

[0089]

[0090] Optionally, in one embodiment, the step of determining the dynamic equilibrium equation corresponding to the pile bottom and pile body displacement and the internal force coefficient based on the coefficient equation group in S4 includes:

[0091] Combining equations (30), (25) and (26), we can obtain the displacement and internal force transfer equations of the j-th pile bottom:

[0092]

[0093] Further, according to the boundary continuity condition of the pile segment, the displacement and internal force expression equations of the pile bottom and body are obtained by combining equations (30) and (31):

[0094]

[0095] Considering the boundary conditions at the bottom of the pile, further simplifying formula (32) yields:

[0096]

[0097] In the formula,

[0098]

[0099] Optionally, in one embodiment, the step of determining the dynamic equilibrium equation corresponding to the pile top displacement and the rotation coefficient in S5 comprises:

[0100] definition The dynamic equilibrium equation corresponding to the pile top displacement and rotation angle is further obtained from formula (33):

[0101]

[0102]

[0103] Implementing the embodiments of the present invention will have the following beneficial effects:

[0104] The present application proposes a method for analyzing the horizontal dynamic response of a pile foundation under the action of an earthquake S shear wave based on a Pasternak foundation. The patent of the present invention uses an analytical method to simplify the soil around the pile into a Pasternak foundation, and considers the horizontal vibration force analysis of the pile foundation under the action of the axial force at the pile top, which can better simulate the restraining effect of the soil around the pile on the pile body, and can be applied to the problem of the horizontal vibration dynamic response of the pile foundation under the action of an earthquake S shear wave, and can provide theoretical guidance and reference for the seismic design of pile foundation engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] 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 work.

[0106] in:

[0107] Figure 1 A flowchart of steps corresponding to the method described in an embodiment;

[0108] Figure 2 A vibration analysis principle diagram corresponding to the method described in one embodiment; DETAILED DESCRIPTION

[0109] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0110] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art of the technical field of the present invention. The terms used herein in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. It is understood that the terms "first", "second", etc. used in the present invention can be used to describe various elements in this article, but these elements are not limited by these terms. These terms are only used to distinguish the first element from another element. For example, without departing from the scope of the present application, the first element can be referred to as the second element, and similarly, the second element can be the first element. Both the first element and the second element are elements, but they are not the same element.

[0111] When the applicant studied the horizontal dynamic response of pile foundation under the action of seismic waves, it was found that the foundation soil has the property of amplifying (or reducing) the action of seismic waves. In view of this characteristic, how to reasonably and effectively process the input seismic waves of bedrock to consider its influence on the pile-soil interaction system; Based on the above-mentioned design concept, in this embodiment, a method for analyzing the horizontal dynamic response of a single pile under the action of seismic S shear waves is specially proposed, such as Figure 1-2 As shown, the method includes:

[0112] S1. Based on the characteristic parameters of foundation soil, a soil dynamic equilibrium equation is created considering the influence of foundation soil on earthquake S shear wave, wherein the characteristic parameters of foundation soil include elastic shear modulus, viscous damping coefficient, mass density and horizontal displacement;

[0113] S2. Based on the soil dynamic equilibrium equation, combined with the Euler beam and Pasternak foundation model, a dynamic equilibrium equation of the pile unit is created;

[0114] S3, based on the dynamic equilibrium equation of the pile body unit, determine the relationship between the pile body rotation angle, bending moment, shear force and the pile body horizontal displacement coefficient and create a corresponding coefficient equation group;

[0115] S4, based on the coefficient equation group, determining the dynamic equilibrium equation corresponding to the pile bottom and pile body displacement and internal force coefficient;

[0116] S5. Determine the dynamic equilibrium equation corresponding to the pile top displacement and the rotation coefficient, and then complete the analysis of the horizontal dynamic response process of a single pile under the action of earthquake S shear wave.

[0117] From the above content, it can be seen that the present application adds the influence of bedrock on seismic waves into the dynamic balance equation by constructing the dynamic balance equation of soil under the influence of earthquake S shear wave, and combines the Euler beam and Pasternak foundation model to establish the dynamic balance equation corresponding to the pile bottom displacement and internal force coefficient and the dynamic balance equation corresponding to the pile top displacement and rotation coefficient, thereby completing the pile-soil interaction analysis process in the horizontal dynamic response of a single pile under the action of earthquake S shear wave.

[0118] In some specific embodiments, in step S1,

[0119] Assume that the properties of each soil layer are expressed by the elastic shear modulus Viscous damping coefficient and mass density and horizontal displacement The soil dynamic equilibrium equation of free site can be expressed as:

[0120] Assume that the properties of each soil layer are expressed by the elastic shear modulus Viscous damping coefficient and mass density and horizontal displacement The soil dynamic equilibrium equation of free site can be expressed as:

[0121]

[0122] In the formula, is the shear stress, t is the time, and z is the depth of the soil layer;

[0123] because It is expressed as:

[0124]

[0125] Viscous damping coefficient of viscoelastic materials ω is the excitation circular frequency,

[0126] Substituting formula (2) into formula (1), we get:

[0127]

[0128] Based on horizontal displacement The displacement steady-state solution in the frequency domain is to transform formula (3), and the horizontal displacement The displacement steady-state solution in the frequency domain is of the form: Substituting into formula (3), we get:

[0129]

[0130] Substituting formula (2) into formula (1), we get:

[0131]

[0132] Create the displacement amplitude of the jth layer. Under the action of upgoing and downgoing shear waves at depth z, the horizontal displacement

[0133] The time-independent partial solution corresponds to the equation

[0134]

[0135] Among them, the complex shear modulus

[0136] Obtain the exponential form of equation (5), the corresponding equation is:

[0137]

[0138] The first and second terms on the right side of the above equation can be regarded as the upward and downward wave solutions in the j-th layer (N-1≥j≥1, N represents the bedrock layer), E j 、F j is the volatility coefficient; is the wave number;

[0139] Create the conversion relationship equation between the top layer, i.e. the first layer of soil, and the amplitude coefficient of any layer. The corresponding equation creation process is:

[0140] Due to the wave number Complex shear wave velocity Then formula (6) is

[0141]

[0142]

[0143] Substituting equations (7) and (8) into equation (1), we can obtain:

[0144]

[0145] Since the shear stress and displacement are continuous at the interface between the jth layer and the j+1th layer of soil, that is:

[0146]

[0147] Substituting equation (6) and equation (9) into equation (10), we get:

[0148]

[0149] The corresponding recursive formula is determined as:

[0150]

[0151] In the formula, Defined as wave number impedance, let the coefficient matrix (2×2) obtained in the above formula be T j , then the conversion equation between the top layer (the first layer of soil) and the amplitude coefficient of any layer is:

[0152]

[0153] Among them, the transfer function

[0154] From the above formula, it can be seen that for a given angular frequency, the transfer function It depends on the soil properties of the first to nth layers, and has nothing to do with the earthquake input. Therefore, the soil dynamic equilibrium equation under the influence of the foundation soil on the earthquake S shear wave is created, and the corresponding equation creation process is:

[0155] According to the first layer free ground boundary condition: τ 1 (0) = 0, then E 1 =F 1 , and let n = N-1, we get:

[0156]

[0157] and

[0158]

[0159] Substituting the above formula into formula (6), we get:

[0160]

[0161] In some specific embodiments, in step S2, the dynamic equilibrium equation of the pile unit is obtained by integrating the relevant theories of Euler beam and Pasternak foundation model as follows:

[0162]

[0163] In the formula, is the horizontal displacement of the unit mass point of the j-th section of active pile I, is the free field motion displacement; E p ,I p 、m p are the elastic modulus, section moment of inertia and mass per unit length of the pile respectively; and are the stiffness coefficient, damping coefficient and foundation shear stiffness of the foundation soil around the j-th pile layer; B 0 =0.9(1.5d+0.5) is the calculated width of the pile, ε is the reduction factor considering the separation between the pile and the soil, generally taken as 0.6~0.9.

[0164] In some specific embodiments, in step S3:

[0165] The steps of determining the relationship between the pile body rotation angle, bending moment, shear force and the pile body horizontal displacement coefficient and creating a corresponding coefficient equation group include:

[0166] Various parameters and Determined by the following formula:

[0167]

[0168]

[0169]

[0170]

[0171] Where U 0 is the maximum displacement of ground motion; the shear wave number of soil around the pile Shear wave velocity of soil around pile and are the elastic modulus, density, damping coefficient and Poisson's ratio of the soil around the pile; dimensionless frequency is the thickness of the foundation soil shear layer, and the value is taken according to the literature recommendations

[0172] Since the horizontal displacement of the pile is expressed as:

[0173]

[0174] In the formula, is the horizontal displacement amplitude of the pile body particle,

[0175] Let W p =E p I p , Substituting equation (21) into equation (16) we can further obtain the following equations:

[0176]

[0177] In the formula, Obviously, the homogeneous general solution corresponding to formula (22) is:

[0178]

[0179] In the formula, coefficient The value is determined by the set boundary conditions;

[0180] The special solution of formula (23) is:

[0181]

[0182] Then the complete solution of formula (23) is expressed as:

[0183]

[0184] Based on the Euler beam theory, the relationship between the pile body rotation angle, bending moment, shear force and pile body horizontal displacement is:

[0185]

[0186]

[0187]

[0188] Combining equations (25) and (26), we get the following coefficient equations:

[0189]

[0190] In the formula,

[0191]

[0192] When j = 1, z = 0, the relevant parameters of the first layer of soil are obtained and substituted into equation (27) to obtain the transfer integral constant of the first section of the pile:

[0193]

[0194] At the cross sections of the pile body at the jth and j-1th sections, the horizontal displacement, rotation angle, bending moment and shear force of the pile are continuous, that is:

[0195]

[0196] Combining equations (27), (28) and (29), we get the coefficient matrix equations as follows:

[0197]

[0198] Based on the coefficient equation group, the steps of determining the dynamic equilibrium equation corresponding to the pile bottom and pile body displacement and the internal force coefficient include:

[0199] Combining equations (30), (25) and (26), we can obtain the displacement and internal force transfer equations of the j-th pile bottom:

[0200]

[0201] Further, according to the boundary continuity condition of the pile segment, the displacement and internal force expression equations of the pile bottom and body are obtained by combining equations (30) and (31):

[0202]

[0203] Considering the boundary conditions at the bottom of the pile, further simplifying formula (32) yields:

[0204]

[0205] In the formula,

[0206]

[0207] The steps for determining the dynamic equilibrium equation corresponding to the pile top displacement and the rotation coefficient include: selecting the corresponding matrix It is a 4×4 matrix. Select the coefficients of the row and column in the matrix as needed. For example, in this example, the subscript 32 is selected, which means the coefficient of the 3rd row and 2nd column in the matrix is ​​selected.

[0208] definition The dynamic equilibrium equation corresponding to the pile top displacement and rotation angle is further obtained from formula (33):

[0209]

[0210]

[0211] Implementing the embodiments of the present invention will have the following beneficial effects:

[0212] In this application, the soil around the pile is equivalent to a layered Pasternak foundation, and the pile foundation is simplified to an Euler beam model, so that the horizontal dynamic response analysis method of the pile foundation under the action of earthquake S shear waves based on the Pasternak foundation model is applied to the field of pile foundation vibration research for the first time.

[0213] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A method for analyzing the horizontal dynamic response of a single pile under the action of earthquake S shear waves. It is characterized in that include: S1. Based on the characteristic parameters of foundation soil, a soil dynamic equilibrium equation is created considering the influence of foundation soil on earthquake S shear wave, wherein the characteristic parameters of foundation soil include elastic shear modulus, viscous damping coefficient, mass density and horizontal displacement; S2. Based on the soil dynamic equilibrium equation, combined with the Euler beam and Pasternak foundation model, a dynamic equilibrium equation of the pile unit is created; S3, based on the dynamic equilibrium equation of the pile body unit, determine the relationship between the pile body rotation angle, bending moment, shear force and the pile body horizontal displacement coefficient and create a corresponding coefficient equation group; S4, based on the coefficient equation group, determining the dynamic equilibrium equation corresponding to the pile bottom and pile body displacement and internal force coefficient; S5. Determine the dynamic equilibrium equation corresponding to the pile top displacement and the rotation coefficient, and then complete the analysis of the horizontal dynamic response process of the single pile under the action of the earthquake S shear wave; The step of creating a soil dynamic equilibrium equation considering the influence of the foundation soil on the earthquake S shear wave based on the foundation soil characteristic parameters in S1 includes: S11. Determine the characteristic parameters of each soil layer of the foundation soil required for creating the equation, including the elastic shear modulus viscous damping coefficient and mass density as well as horizontal displacement S12. Based on the characteristic parameters, a free site soil dynamic balance equation is created. The corresponding free site soil dynamic balance equation is: In the formula, is the shear stress, t is the time, and z is the depth of the soil layer; because It is expressed as: Viscous damping coefficient of viscoelastic materials ω is the excitation circular frequency, Substituting formula (2) into formula (1), we get: S13, based on horizontal displacement The displacement steady-state solution in the frequency domain is to transform formula (3), and the horizontal displacement The displacement steady-state solution in the frequency domain is of the form: Substituting into formula (3), we get: S14. Create the displacement amplitude of the jth layer. Under the action of the upward and downward shear waves at depth z, the horizontal displacement The time-independent partial solution corresponds to the equation Among them, the complex shear modulus C 1 , C 2 is the coefficient to be solved; S15. Obtain the exponential form of equation (5), the corresponding equation is: In the formula, N-1≥j≥1, N represents the number of bedrock layers, E j 、F j is the amplitude coefficient, is the wave number; S16, creating a conversion relationship equation between the top layer, i.e., the first soil layer, and any layer of amplitude coefficient, and the corresponding equation creation process is: Due to the wave number Complex shear wave velocity Then formula (6) is Substituting equations (7) and (8) into equation (1), we can obtain: Since the shear stress and displacement are continuous at the interface between the jth layer and the j+1th layer of soil, that is: Substituting equation (6) and equation (9) into equation (10), we get: The corresponding recursive formula is determined as: In the formula, Defined as wave number impedance, let the coefficient matrix (2×2) obtained in the above formula be T j , then the conversion equation between the top layer (the first layer of soil) and the amplitude coefficient of any layer is: Among them, the transfer function In the formula, N-1≥j≥1, N represents the number of bedrock layers, E j 、F j is the volatility coefficient; S17. Create the soil dynamic equilibrium equation considering the influence of foundation soil on earthquake S shear wave. The corresponding equation creation process is: According to the first layer free ground boundary condition: τ 1 (0) = 0, then E 1 =F 1 , and let n = N-1, we get: and Substituting the above formula into formula (6), we get: In step S2, the dynamic equilibrium equation of the pile unit is obtained by integrating the relevant theories of Euler beam and Pasternak foundation model as follows: In the formula, is the horizontal displacement of the unit mass point of the j-th section of active pile I, is the free field motion displacement; E p ,I p 、m p are the elastic modulus, section moment of inertia and mass per unit length of the pile respectively; and are the stiffness coefficient, damping coefficient and foundation shear stiffness of the foundation soil around the j-th pile layer; B 0 =0.9(1.5d+0.5) is the calculated width of the pile, ε is the reduction factor considering the separation between the pile and the soil, and is taken as 0.6~0.

9.

2. According to the method for analyzing the horizontal dynamic response of a single pile under the action of earthquake S shear waves as described in claim 1, It is characterized in that The step of determining the relationship between the pile body rotation angle, bending moment, shear force and the pile body horizontal displacement coefficient and creating a corresponding coefficient equation group in S3 includes: Various parameters and Determined by the following formula: Where U 0 is the maximum displacement of ground motion; the shear wave number of soil around the pile Shear wave velocity of soil around pile and are the elastic modulus, density, damping coefficient and Poisson's ratio of the soil around the pile; dimensionless frequency is the thickness of the foundation soil shear layer, d refers to the pile diameter; Since the horizontal displacement of the pile is expressed as: In the formula, is the horizontal displacement amplitude of the pile body particle, Let W p =E p I p , Substituting equation (21) into equation (16) we can further obtain the following equations: In the formula, E p ,I p , B 0 are the elastic modulus of the pile, the moment of inertia of the pile section, and the calculated width of the pile, respectively. p is the defined coefficient, N 0 is the axial force on the pile top; Obviously, the homogeneous general solution corresponding to formula (22) is: In the formula, coefficient The value is determined by the set boundary conditions; The special solution of formula (23) is: Then the complete solution of formula (23) is expressed as: Based on the Euler beam theory, the relationship between the pile body rotation angle, bending moment, shear force and pile body horizontal displacement is: Combining equations (25) and (26), we get the following coefficient equations: In the formula, When j = 1, z = 0, substituting into equation (27), the transfer integral constant of the first section of the pile is: At the cross sections of the pile body at the jth and j-1th sections, the horizontal displacement, rotation angle, bending moment and shear force of the pile are continuous, that is: Combining equations (27), (28) and (29), we get the coefficient matrix equations as follows:

3. The method for analyzing the horizontal dynamic response of a single pile under the action of earthquake S shear waves according to claim 2, It is characterized in that The step of determining the dynamic equilibrium equation corresponding to the pile bottom and pile body displacement and the internal force coefficient in S4 based on the coefficient equation group includes: Combining equations (30), (25) and (26), we can obtain the displacement and internal force transfer equations of the jth pile bottom: Further, according to the boundary continuity condition of the pile segment, the displacement and internal force expression equations of the pile bottom and body are obtained by combining equations (30) and (31): Considering the boundary conditions at the bottom of the pile, further simplifying formula (32) yields: In the formula, 4. The method for analyzing the horizontal dynamic response of a single pile under the action of earthquake S shear waves according to claim 3, It is characterized in that The step of determining the dynamic equilibrium equation corresponding to the pile top displacement and the rotation coefficient in S5 includes: definition The dynamic equilibrium equation corresponding to the pile top displacement and rotation angle is further obtained from formula (33):

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