Two-parameter foundation pile group horizontal dynamic response analysis method under action of earthquake S waves

Abstract

The invention discloses a two-parameter foundation pile group horizontal dynamic response analysis method under the action of earthquake S waves, and belongs to the field of pile foundation vibration analysis. The method comprises the following steps that S1, basic parameters are set, specifically, a foundation is simplified into a two-parameter Pasternak foundation, and a pile foundation is simplified into an Euler beam model; s3, establishing a pile-soil coupling horizontal vibration frequency domain analysis model; and S4, the relation between the pile displacement and the load is substituted into the pile-soil coupling horizontal vibration frequency domain analysis model, and the horizontal displacement value of each single pile is obtained through analysis. By the adoption of the two-parameter foundation group pile horizontal dynamic response analysis method under the earthquake S wave effect, the Pasternak foundation model is adopted, the shear effect of the soil body around the piles is considered, the constraint effect of the soil body around the piles on the pile bodies can be better simulated, an analytical solution method is adopted, and the method has the advantages that resources are saved, mathematical preciseness is guaranteed and the like; and theoretical guidance is provided for aseismic 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 double-parameter foundation pile group under the action of an earthquake S wave. Background Art

[0002] my country is a country prone to earthquakes. Frequent strong earthquakes in recent years have caused varying degrees of damage to various types of buildings and infrastructure. Among these disasters, S waves (shear waves), as an important component of seismic waves, have a particularly significant impact on the safety of pile-supported structures. S waves can induce strong horizontal vibrations, complicating the interaction between the foundation soil and the superstructure, thus posing a serious threat to the stability of buildings.

[0003] Existing research mainly focuses on the horizontal vibration characteristics of the pile-soil system under the action of S waves, and establishes frequency domain analytical models to analyze its dynamic response. However, these traditional models often fail to fully consider the following two key factors:

[0004] 1. Shear effect of soil around piles: When an earthquake occurs, the soil around the piles will experience complex shear deformation, which not only changes the mechanical properties of the soil, but also has a significant impact on the vibration characteristics of the piles. Ignoring this effect may lead to underestimation or overestimation of the dynamic response of the pile-soil system, thus affecting the accuracy of the structural design.

[0005] 2. Influence of axial static load on pile top: In actual engineering, the pile top usually bears axial static load from the superstructure. Under earthquake action, this prestress will have a significant impact on the pile body and its interaction with the surrounding soil. If this is ignored, the traditional model will not be able to accurately capture the overall dynamic behavior of the pile-supported structure, especially under extreme working conditions.

[0006] In summary, it can be seen that the existing models are difficult to fully reflect the overall dynamic characteristics of pile-supported structures under earthquake conditions, which directly affects the safety and reliability of the design. Summary of the invention

[0007] The purpose of the present invention is to provide a dual-parameter foundation pile group horizontal dynamic response analysis method under the action of earthquake S waves to solve the above technical problems.

[0008] To achieve the above object, the present invention provides a dual-parameter foundation pile group horizontal dynamic response analysis method under the action of earthquake S waves, comprising the following steps:

[0009] S1. Set basic parameters: simplify the foundation into a two-parameter Pasternak foundation, simplify the pile foundation into an Euler beam model, and set the soil parameters around the pile, pile parameters, the motion interaction load borne by each pile under the action of earthquake S waves, and boundary conditions;

[0010] S2. Analyze the relationship between pile displacement and load;

[0011] S3. Considering the soil shear effect and the influence of the axial static load on the pile top, a frequency domain analytical model of pile-soil coupling horizontal vibration is established;

[0012] S4. Substitute the relationship between the pile displacement and the load described in step S2 into the pile-soil coupled horizontal vibration frequency domain analytical model described in step S3, and obtain the horizontal displacement value of each single pile by analysis.

[0013] Preferably, the soil parameters surrounding the pile in step S1 include the elastic modulus E s , density ρ s , damping coefficient β s and Poisson's ratio s ;

[0014] Pile parameters include the number of piles n, elastic modulus E p 、Internal moment of inertia I p and mass per unit length m p ;

[0015] In step S1, it is assumed that a lateral earthquake is generated by the simple harmonic vibration of the bedrock. At this time, the earthquake load acts directly on the active pile and is transferred from the active pile to the passive pile through the soil. The boundary conditions are as follows:

[0016] u f (L,t)=u g e iωt (1);

[0017] u f (0,t)=0 (2);

[0018] In the formula, u f (L,t) represents the free field displacement at a distance L from the bedrock surface at time t; u g represents the displacement amplitude of bedrock; u f (0, t) represents the free field displacement of the bedrock surface at time t; e iwt represents the complex exponential function,

[0019] Preferably, the relationship between pile displacement and load in step S2 includes: (1) horizontal displacement of the earthquake source pile caused by the action of the earthquake S wave; (2) pile displacement caused by the influence of the active pile vibration on the passive pile when the two piles interact; (3) inertial load F caused by the interaction of motion borne by each pile under the action of the earthquake S wave i (4) the inertial load F of the pile body caused by the interaction of motion under the action of the earthquake S wave iThe additional displacement of the pile top is caused by the interaction between piles under the action of

[0020] Preferably, the frequency domain analytical model of pile-soil coupling horizontal vibration described in step S3 includes an active pile dynamic balance model and a passive pile dynamic balance model; wherein the active pile dynamic balance model is expressed as follows:

[0021]

[0022] In the formula, u p (z, t) represents the horizontal displacement of the active pile body mass point at position z at time t; and They represent the stiffness coefficient, damping coefficient and foundation shear stiffness of the soil around the pile respectively; u f (z,t) represents the free field displacement of the bedrock surface at position z at time t, and u f (z,t)=u f (z)e iωt ,u f (z) represents the depth function;

[0023] The expression of the passive pile dynamic balance model is as follows:

[0024]

[0025] In the formula, represents the horizontal displacement of the passive pile at position z at time t; u s (z,t) represents the site displacement caused by active pile vibration; N 0 Indicates the axial force.

[0026] Preferably, step S3 specifically includes the following steps:

[0027] S31, constructing an active pile dynamic balance model;

[0028] S311. Considering the horizontal stress balance of soil in the free field, the equilibrium equation of the free field is obtained as follows:

[0029]

[0030] Where q represents the wave number of the earthquake S wave, and q = ω / V s * , ω represents the angular frequency, represents the shear wave velocity of the earthquake S wave in the soil, V s is the propagation speed of earthquake S waves in soil,

[0031] S312, combining the boundary conditions described in formulas (1) and (2), solving formula (5) to obtain:

[0032]

[0033] In the formula, H represents the thickness of the soil layer;

[0034] S313. Combining the Euler beam model and the dual-parameter Pasternak foundation, the dynamic equilibrium model of the active pile body is obtained:

[0035]

[0036] in,

[0037] In the formula, a 0 represents dimensionless frequency, and a 0 =ωd / V s , d represents the foundation shear coefficient; λ s is the shear coefficient of the foundation soil, and λ s = 0, degenerating into Winkler foundation; U p (z) is the horizontal displacement amplitude of the pile body particle;

[0038] S32, constructing a passive pile dynamic balance model;

[0039] S321. Define the horizontal displacement of passive pile as:

[0040]

[0041] In the formula, represents the horizontal displacement amplitude of the passive pile at position z;

[0042] S322. Considering the dynamic interaction between the pile and the soil layer, the dynamic equilibrium model of the passive pile is obtained:

[0043]

[0044] Preferably, step S4 specifically includes the following steps:

[0045] S41. Analytical dynamic balance model of active piles

[0046] Set W P =E P I P , Then u p (z,t)=U p (z)e iωt Substituting into formula (3), we get:

[0047]

[0048] Among them, ξ2 , 4 and γ are dimensionless parameters, and

[0049] The solution corresponding to formula (8) is as follows:

[0050]

[0051] Among them, α, β and Γ are dimensionless parameters, and A 1 , A 2 , A 3 , A 4 All are undetermined coefficients;

[0052] At this time, based on the Euler beam theory, the relationship between the pile body rotation angle, bending moment, shear force and pile body horizontal displacement is obtained:

[0053]

[0054]

[0055]

[0056] In the formula, ψ p (z) represents the rotation angle of the pile body; M p (z) represents the bending moment of the pile; P p (z) represents the shear force of the pile body;

[0057] S42. Assuming that the geometric dimensions and material properties of the active pile and the passive pile are the same, derive the analytical solution of the horizontal dynamic response of the passive pile caused by the vibration of the active pile;

[0058] S421. Define the soil horizontal displacement attenuation function f(S,θ) as follows:

[0059]

[0060] Wherein, f(S,0) represents the value of function f(S,θ) when angle θ=0°; and r 0 represents the reference distance, S represents the position variable, Represents parameters related to material properties, V LI represents the velocity parameter related to material properties, Indicates when the angle The value of the function f(S,θ) when represents the shear wave velocity;

[0061] S422. Define the site displacement caused by active pile vibration as:

[0062]

[0063] In the formula, u s (z) represents the soil displacement varying with position z; represents the displacement of the active pile as a function of position z;

[0064] S423. Substituting formula (13) and formula (14) into formula (4), the following expression is obtained:

[0065]

[0066] In the formula, represents the displacement function under free field conditions;

[0067] S424. Ignore the general solution of the displacement of the active pile described in formula (14), and only consider the influence of the special solution of the displacement of the active pile on the free field displacement, and rewrite formula (14) as follows:

[0068] u s (z,t)=U s (z)e iωt =f(S,θ)e iωt (Γ-1)U f (z) (16);

[0069] S425. Substituting formula (16) into formula (15), we obtain:

[0070]

[0071] Where, t a is a dimensionless constant, and The solution corresponding to formula (17) is:

[0072]

[0073] In the formula, A 21 , A 22 , A 23 , A 24 are all unknown coefficients; K is a dimensionless constant, and

[0074]

[0075] Rewriting formula (10)-formula (12) yields:

[0076]

[0077]

[0078]

[0079] S43, based on pile-pile interaction factor The definition is obtained:

[0080]

[0081] In the formula, represents the horizontal displacement of the passive pile top caused by the active pile vibration; represents the horizontal displacement of the active pile top; U f (0) represents the free field displacement response; T represents the parameter related to the free field displacement response;

[0082] S44. Set the balance condition that the pile top cap must satisfy as follows:

[0083]

[0084] S45. Based on the linear superposition principle and the relationship between pile displacement and load, the pile displacement U of any pile in the pile group is obtained. (n×n) for:

[0085]

[0086] In the formula, represents the displacement solution of the seismic response of a single pile; Indicates the mutual influence of two piles; Inertia load F i The displacement of the pile body caused by the action; Inertia load F i Impact on piles;

[0087] in,

[0088]

[0089]

[0090] In the formula, represents the pile-pile interaction factor under seismic load; Inertia load F i pile-pile interaction factor under action;

[0091] S46, combined with formulas (24), (25), and (26), we obtain:

[0092]

[0093] S47. Solve formula (27) to obtain the horizontal displacement of the top of each pile in the pile group under the action of earthquake S waves.

[0094] Therefore, the present invention adopts the above-mentioned dual-parameter foundation pile group horizontal dynamic response analysis method under the action of earthquake S waves, which has the following beneficial effects:

[0095] 1. Improved accuracy: By simplifying the foundation into a two-parameter Pasternak foundation and combining it with the Euler beam model to simulate the behavior of the pile foundation, the actual soil-pile interaction can be more accurately reflected, thereby improving the accuracy of the calculation results;

[0096] 2. Consider multiple influencing factors: not only the characteristics of the pile itself (such as elastic modulus, section inertia moment, etc.) are considered, but also the influence of soil shear effect and axial static load on the pile top are comprehensively considered, making the analysis more comprehensive and better simulating the situation in the real environment;

[0097] 3. Establish a coupling model: By establishing a frequency domain analytical model of pile-soil coupling horizontal vibration, the transmission process of seismic waves from active piles to passive piles and the complex mechanical relationship between them are fully considered, providing a theoretical basis for studying the dynamic behavior of multi-pile systems;

[0098] 4. Refine the relationship between displacement and load: A detailed classification discussion is conducted on the relationship between pile displacement and load, including the horizontal displacement of the earthquake source pile, the displacement caused by the interaction between piles, the displacement of the pile body itself and the additional displacement, which helps to deeply understand the impact of different factors on the final results;

[0099] 5. The application of linear superposition principle combined with the relationship between pile displacement and load can effectively deal with the dynamic response problem of each pile in the pile group system under complex conditions, thereby improving the analysis efficiency and accuracy.

[0100] In summary, the analysis method described in the present invention can greatly improve the understanding and prediction capabilities of the dynamic response of pile group systems under the action of earthquake S waves, and has important guiding significance for seismic design.

[0101] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] Figure 1 It is a flow chart of a method for analyzing horizontal dynamic response of a double-parameter foundation pile group under the action of an earthquake S wave according to the present invention;

[0103] Figure 2 A pile-soil-pile interaction system diagram of a dual-parameter foundation pile group horizontal dynamic response analysis method under the action of an earthquake S wave according to the present invention;

[0104] Figure 3This is a simplified mechanical model diagram of pile-pile horizontal vibration of a dual-parameter foundation pile group horizontal dynamic response analysis method under the action of earthquake S waves described in the present invention. DETAILED DESCRIPTION

[0105] In order to make the purpose, technical scheme and advantages disclosed in the embodiments of the present invention clearer, the embodiments of the present invention are further described in detail in combination with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the embodiments of the present invention and are not used to limit the embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions.

[0106] It should be noted that the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or server that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units that are not explicitly listed or inherent to these processes, methods, products or devices.

[0107] The embodiments of the present invention are described in detail below in conjunction with the accompanying drawings.

[0108] In order to improve the disaster resistance of pile-supported structures in earthquakes, it is necessary to further study the influence mechanism of the shear effect of the soil around the pile and the axial static load on the pile top on the dynamic response of the structure, and develop more accurate and practical dynamic analysis methods to ensure that the structural design can better cope with the challenges brought by earthquakes.

[0109] Based on the above analysis, the present invention is designed as follows: Figure 1-Figure 3 As shown, a dual-parameter foundation pile group horizontal dynamic response analysis method under the action of earthquake S waves includes the following steps:

[0110] S1. Set basic parameters: simplify the foundation into a two-parameter Pasternak foundation, simplify the pile foundation into an Euler beam model, and set the soil parameters around the pile, pile parameters, the motion interaction load borne by each pile under the action of earthquake S waves, and boundary conditions;

[0111] The soil parameters around the pile in step S1 include the elastic modulus E s , density ρ s , damping coefficient β s and Poisson's ratio s ;

[0112] Pile parameters include the number of piles n, elastic modulus E p、Internal moment of inertia I p and mass per unit length m p ;

[0113] In step S1, it is assumed that a lateral earthquake is generated by the simple harmonic vibration of the bedrock. At this time, the earthquake load acts directly on the active pile and is transferred from the active pile to the passive pile through the soil. The boundary conditions are as follows:

[0114] u f (L,t)=u g e iωt (1);

[0115] u f (0,t)=0 (2);

[0116] In the formula, u f (L,t) represents the free field displacement at a distance L from the bedrock surface at time t; u g represents the displacement amplitude of bedrock; u f (0, t) represents the free field displacement of the bedrock surface at time t; e iwt represents the complex exponential function,

[0117] S2. Analyze the relationship between pile displacement and load;

[0118] The relationship between pile displacement and load in step S2 includes: (1) horizontal displacement of the source pile caused by the action of the earthquake S wave; (2) pile displacement caused by the influence of the active pile vibration on the passive pile when the two piles interact; (3) inertial load F caused by the interaction of motions borne by each pile under the action of the earthquake S wave i (4) the inertial load F of the pile body caused by the interaction of motion under the action of the earthquake S wave i The additional displacement of the pile top is caused by the interaction between piles under the action of

[0119] S3. Considering the soil shear effect and the influence of the axial static load on the pile top, a frequency domain analytical model of pile-soil coupling horizontal vibration is established;

[0120] The frequency domain analytical model of pile-soil coupling horizontal vibration described in step S3 includes an active pile dynamic balance model and a passive pile dynamic balance model; wherein the active pile dynamic balance model is expressed as follows:

[0121]

[0122] In the formula, u p (z, t) represents the horizontal displacement of the active pile body mass point at position z at time t; and They represent the stiffness coefficient, damping coefficient and foundation shear stiffness of the soil around the pile respectively; u f (z,t) represents the free field displacement of the bedrock surface at position z at time t, and u f (z,t)=u f (z)e iωt ,u f (z) represents the depth function;

[0123] The passive pile dynamic balance model expression is as follows:

[0124]

[0125] In the formula, represents the horizontal displacement of the passive pile at position z at time t; u s (z,t) represents the site displacement caused by active pile vibration; N 0 Indicates the axial force.

[0126] Step S3 specifically includes the following steps:

[0127] S31, constructing an active pile dynamic balance model;

[0128] S311. Considering the horizontal stress balance of soil in the free field, the equilibrium equation of the free field is obtained as follows:

[0129]

[0130] Where q represents the wave number of the earthquake S wave, and ω represents the angular frequency, represents the shear wave velocity of the earthquake S wave in the soil, V s is the propagation speed of earthquake S waves in soil,

[0131] S312, combining the boundary conditions described in formulas (1) and (2), solving formula (5) to obtain:

[0132]

[0133] In the formula, H represents the thickness of the soil layer;

[0134] S313. Combining the Euler beam model and the dual-parameter Pasternak foundation, the dynamic equilibrium model of the active pile body is obtained:

[0135]

[0136] in,

[0137] In the formula, a 0represents the dimensionless frequency, and a 0 = ωd / V s , where d represents the foundation shear coefficient; λ s is the shear coefficient of the foundation soil, and λ s = 0, degenerating into the Winkler foundation; U p (z) is the amplitude of the horizontal displacement of the pile body particle;

[0138] S32. Construct the dynamic equilibrium model of the passive pile;

[0139] S321. Define the horizontal displacement of the passive pile as:

[0140]

[0141] In the formula, represents the amplitude of the horizontal displacement of the passive pile at position z;

[0142] S322. Considering the dynamic interaction between the pile and the soil layer, obtain the dynamic equilibrium model of the pile body of the passive pile:

[0143]

[0144] S4. Substitute the relationship between the pile displacement and the load described in step S2 into the pile - soil coupling horizontal vibration frequency - domain analytical model described in step S3, and analytically obtain the horizontal displacement value of each single pile.

[0145] Step S4 specifically includes the following steps:

[0146] S41. Analyze the dynamic equilibrium model of the active pile

[0147] Set Then substitute u p (z,t) = U p (z)e iωt into formula (3), and obtain:

[0148]

[0149] where ξ 2 , ζ 4 and γ are all dimensionless parameters, and

[0150] Obtain the solution corresponding to formula (8) as follows:

[0151]

[0152] where α, β and Γ are all dimensionless parameters, and A 1 、A 2 、A3 , A 4 are all coefficients to be determined;

[0153] At this time, based on the Euler beam theory, the relationships between the pile body rotation angle, bending moment, shear force and the horizontal displacement of the pile body are obtained:

[0154]

[0155]

[0156]

[0157] In the formula, ψ p (z) represents the pile body rotation angle; M p (z) represents the pile body bending moment; P p (z) represents the pile body shear force;

[0158] S42. Assume that the geometric dimensions and material properties of the active pile and the passive pile are the same, and derive the analytical solution of the horizontal dynamic response of the passive pile caused by the vibration of the active pile;

[0159] S421. Define the expression of the soil horizontal displacement attenuation function f(S,θ) as follows:

[0160]

[0161] Among them, f(S,0) represents the value of the function f(S,θ) when the angle θ = 0°; and r 0 represents the reference distance, S represents the position variable, represents the parameter related to the material property, V LI represents the velocity parameter related to the material property, represents the value of the function f(S,θ) when the angle and represents the shear wave velocity;

[0162] S422. Define the displacement of the field caused by the vibration of the active pile as:

[0163]

[0164] In the formula, u s (z) represents the soil displacement varying with the position z; represents the displacement of the active pile varying with the position z;

[0165] S423. Substitute formula (13) and formula (14) into formula (4) to obtain the following expression:

[0166]

[0167] In the formula, represents the displacement function under free-field conditions;

[0168] S424. Ignoring the general solution of the displacement of the active pile described in formula (14) and only considering the influence of the particular solution of the displacement of the active pile on the free-field displacement, formula (14) is rewritten as:

[0169] u s (z, t) = U s (z)e iωt = f(S, θ)e iωt (Γ - 1)U f (z) (16);

[0170] S425. Substituting formula (16) into formula (15) gives:

[0171]

[0172] In the formula, t a is a dimensionless constant, and

[0173] The solution corresponding to formula (17) is obtained as:

[0174]

[0175] In the formula, A 21 、A 22 、A 23 、A 24 are all undetermined coefficients; K is a dimensionless constant, and

[0176] Rewriting formulas (10) - (12) gives:

[0177]

[0178]

[0179]

[0180] S43. According to the pile-pile interaction factor defined as:

[0181]

[0182] In the formula, represents the displacement of the top of the passive pile caused by the vibration of the active pile; represents the displacement of the top of the active pile; U f(0) represents the free field displacement response; T represents the parameter related to the free field displacement response;

[0183] S44. Set the balance condition that the pile top cap must satisfy as follows:

[0184]

[0185] S45. Based on the linear superposition principle and the relationship between pile displacement and load, the pile displacement U of any pile in the pile group is obtained. (n×n) for:

[0186]

[0187] In the formula, represents the displacement solution of the seismic response of a single pile; Indicates the mutual influence of two piles; Inertia load F i The displacement of the pile body caused by the action; Inertia load F i Impact on piles;

[0188] in,

[0189]

[0190]

[0191] In the formula, represents the pile-pile interaction factor under seismic load; Inertia load F i pile-pile interaction factor under action;

[0192] S46, combined with formulas (24), (25), and (26), we obtain:

[0193]

[0194] S47. Solve formula (27) to obtain the horizontal displacement of the top of each pile in the pile group under the action of earthquake S wave.

[0195] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A dual-parameter foundation pile group horizontal dynamic response analysis method under the action of earthquake S waves, characterized by: The following steps are involved: S1. Set basic parameters: simplify the foundation into a two-parameter Pasternak foundation, simplify the pile foundation into an Euler beam model, and set the soil parameters around the pile, pile parameters, the motion interaction load borne by each pile under the action of earthquake S waves, and boundary conditions; S2. Analyze the relationship between pile displacement and load; S3. Considering the soil shear effect and the influence of the axial static load on the pile top, a frequency domain analytical model of pile-soil coupling horizontal vibration is established; S4. Substitute the relationship between the pile displacement and the load described in step S2 into the pile-soil coupled horizontal vibration frequency domain analytical model described in step S3, and obtain the horizontal displacement value of each single pile by analysis.

2. The dual-parameter foundation pile group horizontal dynamic response analysis method under the action of earthquake S waves according to claim 1 is characterized by: The soil parameters around the pile in step S1 include the elastic modulus E s , density ρ s , damping coefficient β s and Poisson's ratio s ; Pile parameters include the number of piles n, elastic modulus E p 、Internal moment of inertia I p and mass per unit length m p ; In step S1, it is assumed that a lateral earthquake is generated by the simple harmonic vibration of the bedrock. At this time, the earthquake load acts directly on the active pile and is transferred from the active pile to the passive pile through the soil. The boundary conditions are as follows: the f (L,t)=u g and iωt (1); u f (0,t)=0 (2); In the formula, u f (L,t) represents the free field displacement at a distance L from the bedrock surface at time t; u g represents the displacement amplitude of bedrock; u f (0, t) represents the free field displacement of the bedrock surface at time t; e iwt represents the complex exponential function, 3. The dual-parameter foundation pile group horizontal dynamic response analysis method under the action of earthquake S waves according to claim 2 is characterized by: The relationship between pile displacement and load in step S2 includes: (1) horizontal displacement of the source pile caused by the action of the earthquake S wave; (2) pile displacement caused by the influence of the active pile vibration on the passive pile when the two piles interact; (3) inertial load F caused by the interaction of motions borne by each pile under the action of the earthquake S wave i (4) the inertial load F of the pile body caused by the interaction of motion under the action of the earthquake S wave i The additional displacement of the pile top is caused by the interaction between piles under the action of 4. The method for analyzing the horizontal dynamic response of a double-parameter pile group under the action of an earthquake S wave according to claim 3 is characterized in that: The frequency domain analytical model of pile-soil coupling horizontal vibration described in step S3 includes an active pile dynamic balance model and a passive pile dynamic balance model; wherein the active pile dynamic balance model is expressed as follows: In the formula, u p (z, t) represents the horizontal displacement of the active pile body mass point at position z at time t; and They represent the stiffness coefficient, damping coefficient and foundation shear stiffness of the soil around the pile respectively; u f (z,t) represents the free field displacement of the bedrock surface at position z at time t, and u f (z,t)=u f (z)e iωt ,u f (z) represents the depth function; The expression of the passive pile dynamic balance model is as follows: In the formula, represents the horizontal displacement of the passive pile at position z at time t; u s (z, t) represents the site displacement caused by active pile vibration; N0 represents the axial force.

5. The method for analyzing the horizontal dynamic response of a double-parameter pile group under the action of an earthquake S wave according to claim 4 is characterized in that: Step S3 specifically The following steps are involved: S31, constructing an active pile dynamic balance model; S311. Considering the horizontal stress balance of soil in the free field, the equilibrium equation of the free field is obtained as follows: Where q represents the wave number of the earthquake S wave, and ω represents the angular frequency, represents the shear wave velocity of the earthquake S wave in the soil, V s is the propagation speed of earthquake S waves in soil, S312, combining the boundary conditions described in formulas (1) and (2), solving formula (5) to obtain: In the formula, H represents the thickness of the soil layer; S313. Combining the Euler beam model and the dual-parameter Pasternak foundation, the dynamic equilibrium model of the active pile body is obtained: among them, in p (z,t)=U p (z)e iωt ; Where a0 represents the dimensionless frequency, and a0 = ωd / V s , d represents the foundation shear coefficient; λ s is the shear coefficient of the foundation soil, and λ s = 0, degenerating into Winkler foundation; U p (z) is the horizontal displacement amplitude of the pile body particle; S32, constructing a passive pile dynamic balance model; S321. Define the horizontal displacement of passive pile as: In the formula, represents the horizontal displacement amplitude of the passive pile at position z; S322. Considering the dynamic interaction between the pile and the soil layer, the dynamic equilibrium model of the passive pile is obtained:

6. The dual-parameter foundation pile group horizontal dynamic response analysis method under the action of earthquake S waves according to claim 5, characterized in that: Step S4 The specific steps include: S41. Analytical dynamic balance model of active piles Set W P =E P I P , Then u p (z,t)=U p (z)e i ωt Substituting into formula (3), we get: Among them, ξ 2 , 4 and γ are dimensionless parameters, and The solution corresponding to formula (8) is as follows: Among them, α, β and Γ are dimensionless parameters, and A1, 2, A3, and A4 are all undetermined coefficients; At this time, based on the Euler beam theory, the relationship between the pile body rotation angle, bending moment, shear force and pile body horizontal displacement is obtained: In the formula, ψ p (z) represents the rotation angle of the pile body; M p (z) represents the bending moment of the pile; P p (z) represents the shear force of the pile body; S42. Assuming that the geometric dimensions and material properties of the active pile and the passive pile are the same, derive the analytical solution of the horizontal dynamic response of the passive pile caused by the vibration of the active pile; S421. Define the soil horizontal displacement attenuation function f(S,θ) as follows: Wherein, f(S,0) represents the value of function f(S,θ) when angle θ=0°; and r0 represents the reference distance, S represents the position variable, Represents parameters related to material properties, V LI represents the velocity parameter related to material properties, Indicates when the angle The value of the function f(S,θ) when represents the shear wave velocity; S422. Define the site displacement caused by active pile vibration as: In the formula, u s (z) represents the soil displacement varying with position z; represents the displacement of the active pile as a function of position z; S423. Substituting formula (13) and formula (14) into formula (4), the following expression is obtained: In the formula, represents the displacement function under free field conditions; S424. Ignore the general solution of the displacement of the active pile described in formula (14), and only consider the influence of the special solution of the displacement of the active pile on the free field displacement, and rewrite formula (14) as follows: u s (z,t)=U s (z)e iωt =f(S,θ)e iωt (Γ-1)U f (z) (16); S425. Substituting formula (16) into formula (15), we obtain: Where, t a is a dimensionless constant, and The solution corresponding to formula (17) is: In the formula, A 21 , A 22 , A 23 , A 24 are all unknown coefficients; K is a dimensionless constant, and Rewriting formula (10)-formula (12) yields: S43, based on pile-pile interaction factor The definition is obtained: In the formula, represents the horizontal displacement of the passive pile top caused by the active pile vibration; represents the horizontal displacement of the active pile top; U f (0) represents the free field displacement response; T represents the parameter related to the free field displacement response; S44. Set the balance condition that the pile top cap must satisfy as follows: S45. Based on the linear superposition principle and the relationship between pile displacement and load, the pile displacement U of any pile in the pile group is obtained. (n×n) for: In the formula, represents the displacement solution of the seismic response of a single pile; Indicates the mutual influence of two piles; Inertia load F i The displacement of the pile body caused by the action; Inertia load F i Impact on piles; in, In the formula, represents the pile-pile interaction factor under seismic load; Inertia load F i pile-pile interaction factor under action; S46, combined with formulas (24), (25), and (26), we obtain: S47. Solve formula (27) to obtain the horizontal displacement of the top of each pile in the pile group under the action of earthquake S waves.

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