Pile-soil nonlinear interaction rigidity-damping cooperative matching interface displacement model calculation method

Abstract

According to the method, a brand-new Naggar-Iwan interface model is established between a pile body and a deformed soil body, so that the synergistic effect between a soil disaster body and a pile disaster-bearing body is simulated. Based on a pile-soil co-working principle and an elastic theory, an elastic-plastic model is adopted to represent and establish a relationship between pile-soil interface frictional resistance and relative displacement, a pile is divided into a plurality of micro-segment units according to a transfer principle, a micro-element is taken for stress analysis, and soil displacement outside the pile-soil interface is calculated by combining boundary conditions and adopting a shear displacement method; according to the generalized Hooke's law strength theory, stress analysis is carried out on each mass point, a generalized structural force-displacement transfer function is constructed by utilizing the basic principle of dynamics, then a complex matrix operation principle in a complex variable function domain is utilized to carry out simplified calculation on a stiffness matrix [K] and a damping matrix [C], and horizontal and vertical displacements of a Naggar-Iwan interface model are obtained; and finally, according to the pile-soil displacement continuous boundary condition, the pile is completely attached to the soil body, and the displacement of the pile can be solved through superposition of the displacement of the soil body and the displacement of the interface Naggar-Iwan model.

Description

Technical Field

[0001] The invention belongs to the technical field of pile foundation design, and in particular relates to a calculation method for a stiffness-damping coordinated matching interface displacement model of pile-soil nonlinear interaction. Background Art

[0002] Due to the diversity of my country's terrain, some high-level highways or railways need to be built on poor soil. Diseased soil is fragile and vulnerable, and earthquakes can easily induce soil deformation and damage in projects. Therefore, the instability characteristics and control technology of soil deformation induced by earthquakes in high-intensity earthquake areas, which in turn affects the pile-soil system, have become key scientific issues that need to be urgently solved in geotechnical earthquake engineering. At present, there are still the following problems in design.

[0003] (1) Lack of comprehensive evaluation methods: There are many existing methods for evaluating pile-soil damage under earthquake conditions, but they focus on the sliding shear failure form of soil and the stress deformation of bridges, and lack a comprehensive evaluation method that integrates the two. This makes it difficult to fully understand the true situation of pile-soil interaction damage under earthquake in actual projects.

[0004] (2) Single mechanism model: The traditional soil damage mechanism model under earthquake action is relatively single and cannot fully consider the complex interactions in the geological disaster process, which leads to inaccurate estimation of building structure damage.

[0005] (3) Data model limitations: Data models are often limited by data quality and samples, and it is difficult to accurately reflect the overall situation of pile-soil damage under earthquake action. Traditional data models are prone to failure under high complexity and uncertainty.

[0006] (4) Engineering decision-making needs: There is an urgent need for prevention and safety assessment of disasters such as earthquakes in engineering. The shortcomings of traditional evaluation methods make engineering decisions face greater risks. Summary of the invention

[0007] The existing technology cannot fully evaluate the pile-soil damage under earthquake action, and a new method is needed to comprehensively consider the mechanism and data to improve the accuracy and comprehensiveness of the evaluation. Therefore, the present invention aims to solve the shortcomings of the existing technology and proposes a calculation model for the nonlinear interaction between piles and soil in an orthogonal system under bidirectional earthquake action to cope with complex and changeable engineering environments.

[0008] To this end, the present invention adopts the following technical solutions:

[0009] A method for calculating a pile-soil nonlinear interaction stiffness-damping coordinated matching interface displacement model is provided, characterized in that it comprises the following steps:

[0010] Step 1: Determine the interface model

[0011] 1.1 Collection of pile-soil parameter information

[0012] Collect the time history parameters of earthquake action, soil condition information and pile foundation structure design parameters;

[0013] The time history parameters of earthquake action include: earthquake duration, acceleration-time curve, and number of sampling points;

[0014] Soil condition information includes: soil layer thickness, weight of each soil layer, elastic modulus, shear modulus, shear wave velocity, Poisson's ratio;

[0015] The design parameters of pile foundation structure include: pile cross-sectional shape, pile diameter, spacing, length, elastic modulus and density of pile concrete;

[0016] 1.2 Construction of interface model

[0017] Based on the horizontal dynamic response of piles under transient dynamic loads and simple harmonic loads and the softening phenomenon under cyclic loads, the dynamic stress-strain relationship of soft clay is described in combination with the modified Masing formula, and the Naggar-Iwan model of the interface interaction between soil and pile is established;

[0018] 1.3 Basic assumptions of the interface model and establishment of coefficient equations

[0019] The Naggar model is established in the lateral direction between the pile and the soil, and at the same time, the Iwan model is established at the bottom of the pile and the soil; this model structure is used to describe the deformation of the soil and the pile when the pile and the soil interact under bidirectional earthquake conditions;

[0020] Assume that the earthquake wave acting on the pile foundation is U g e iωt , and use this to establish a cylindrical coordinate system (r, z), where the circular frequency is ω, the time is t, the pile radius is r0, the pile height is H, and the soil thickness is h;

[0021] To facilitate the analysis, the following assumptions are made:

[0022] ① The pile foundation is simulated by linear viscoelastic Euler, and the cross-sectional shape of the pile foundation is circular;

[0023] ② The soil is regarded as an isotropic, homogeneous viscoelastic medium; the damping used in the soil material is hysteresis damping that is independent of frequency;

[0024] ③ In the pile-soil system, the deformation of the two is small deformation vibration, the contact surface between the two is good, and no slip occurs;

[0025] ④ Divide the deformation of the pile foundation and the soil into two directions: transverse and longitudinal, ignoring the longitudinal displacement caused by transverse vibration and the transverse displacement during longitudinal vibration;

[0026] The established Naggar-Iwan model structure is simplified to a spring-damper system, in which the expressions of pile spring, soil spring, pile damping and soil damping coefficients are expressed as follows:

[0027] ① For the Iwan model adopted vertically:

[0028]

[0029] Where:

[0030] G b is the shear modulus; V sb is Poisson's ratio; ρ b is the density pile;

[0031] C sb is the shear wave velocity; A P is the cross-sectional area of ​​the pile;

[0032] ② For the horizontally adopted Naggar model:

[0033]

[0034] Where: (Charge intensity ratio coefficient)

[0035] G mi =G maxi (1-η i )(Shear modulus of soil around pile in the i-th soil layer corrected according to strain level)

[0036] C ph =C sh =α0M+α1K

[0037]

[0038] V i is the Poisson's ratio of the i-th soil layer; r0 is the radius in the near field = pile radius;

[0039] h i is the thickness of the i-th soil layer; r1 is the outer radius of the near field ≈ 3 times the outer diameter of the pile;

[0040] G maxi The maximum shear modulus of the i-th soil layer ≈ the initial shear modulus;

[0041] P iis the force on the nonlinear spring of the i-th soil layer = the horizontal force at the pile-soil interface;

[0042] P ui The ultimate load of the nonlinear spring of the i-th soil layer = the ultimate bearing capacity of the soil around the pile;

[0043] α0 and α1 are mass and stiffness proportional coefficients.

[0044] Step 2: Determination of pile-soil coupled dynamic equations and boundary conditions

[0045] 2.1 Coupled dynamic equations of soil around piles

[0046] The displacement response of the soil medium in the scattered field under earthquake action is expressed as u r (r,θ,z)e iωt and u θ (r,θ,z)e iωt , the coupled dynamic equations representing the radial and circumferential displacements of the soil are expressed as:

[0047]

[0048] Where:

[0049]

[0050] λ s * is the soil complex Lame constant;

[0051] V s is the soil Poisson’s ratio;

[0052] G s * is the complex shear modulus of soil;

[0053] β s is the soil hysteresis damping;

[0054] ρ s is the soil mass density;

[0055] 2.2 Dynamic control equation of pile

[0056] Based on the Euler-Bernoulli beam theory, when the interaction between pile and soil in the lateral and longitudinal directions is simplified to the Naggar-Iwan model structure, the impact of the earthquake condition is input at the end of the spring. Through numerical simulation analysis, it is found that the bidirectional seismic coupling effect is similar to the result of the single horizontal or vertical effect and the effect is more significant. It participates in the interaction of the elastic half space formed between pile and soil in the form of stress.

[0057] Horizontal displacement of the pile in the soil ω p e iωt The dynamic control equation represented by (z) is:

[0058]

[0059] Where:

[0060] E p I is the bending stiffness of the pile foundation; ρ p is the pile density; A is the cross-sectional area of ​​the pile;

[0061] w p is the horizontal displacement of the pile body; z is the axial coordinate of the pile body; t is the time;

[0062] P d is the nonlinear dynamic reaction force of the soil around the pile per unit pile length; p is the hysteresis damping of the bridge pile;

[0063] C is the stiffness coefficient and damping coefficient of the soil around the pile per unit length of the bridge pile;

[0064] 2.3 Establishing system boundary conditions

[0065] Establish the system boundary conditions based on the above assumptions and dynamic equations;

[0066] Boundary conditions at the top of the pile:

[0067]

[0068] Elastic half-space surface boundary conditions:

[0069]

[0070] Where: is the x-direction displacement of the soil scattering field in the rectangular coordinate system

[0071] Pile-soil boundary conditions:

[0072]

[0073] Boundary conditions at infinite soil displacement:

[0074]

[0075] Step 3: Calculation of pile-soil deformation displacement equation

[0076] 3.1 Calculation of soil displacement around piles

[0077] Based on the pile-soil joint working principle and elastic theory, a model expression of the relationship between the pile side friction and the relative displacement of the pile-soil interface is established. According to the pile-soil interface load transfer principle, the pile is divided into several micro-segment units, and a micro-element is taken for force analysis. Combined with the boundary conditions, the shear displacement method is used to calculate the soil displacement outside the pile-soil interface.

[0078] The soil around the pile is divided into two parts: the soil at the pile-soil interface and the soil outside the pile-soil interface. The soil at the pile-soil interface produces nonlinear slip with the pile, and the thickness of this part of the soil is ignored during calculation; the soil outside the pile-soil interface produces shear deformation.

[0079] A micro-segment of the pile body at a certain depth z within the range of the pile body is taken as the research object, and the soil layer around the pile is regarded as a rigid disk in an infinite plane. The pile is divided into several micro-segment units, and a micro-element is taken for force analysis. According to the characteristics of the problem, the whole is divided into two, that is, only the case of a semi-infinite plane is considered.

[0080] Since the elastic-plastic model is very simple and widely used in practical engineering applications, the elastic-plastic model can be used to characterize the relationship between the pile-soil interface friction and relative displacement:

[0081]

[0082] Where: τ max is the ultimate friction resistance of the soil on the pile side; k is the spring stiffness; S pu is the relative displacement value of the pile-soil interface corresponding to the pile side friction resistance reaching the limit;

[0083] The shear displacement method is used to calculate the soil displacement outside the pile-soil interface. According to the shear displacement principle, the shear strain of the soil unit at a depth of z and a distance of r from the central axis of the pile is: Then the shear stress is:

[0084] Where: G s is the soil shear modulus;

[0085] According to the equilibrium condition:

[0086] Where: r0 is the radius of the pile. When r=r0, then: τ(z,r)=τ p (z)

[0087] Combining the above formula, we can get:

[0088]

[0089] Therefore, according to the formula, the displacement of the soil outside the pile-soil interface can be obtained as:

[0090]

[0091] The pile is divided into several micro-segments, and a micro-element is taken for force analysis. For small-diameter piles, the effect of the pile's deadweight on the bearing capacity can be ignored. According to the force balance condition, we can get:

[0092]

[0093] Where: P(z) is the axial force of the pile; U p is the circumference of the pile;

[0094] Take the microelement elastic deformation equal to the displacement difference d between the top and bottom of the pile sp

[0095] According to Hooke's law:

[0096] Where: E is the elastic modulus of the pile; A is the cross-sectional area of ​​the pile;

[0097] Derivative the above formula and substitute the relevant formula into it, we can get:

[0098]

[0099] Where: d is the pile diameter;

[0100] make Integrating the above formula, we can get:

[0101] Combined with the selected pile microelement, the boundary conditions can be analyzed to obtain:

[0102]

[0103] Where: l is the pile length; P0 is the pile top load;

[0104] Substituting the boundary conditions into the above formula, we can get the correlation coefficient:

[0105]

[0106] Substituting the parameters C1 and C2 into the above formula, we can obtain the distribution expressions of pile axial force, relative displacement and lateral friction along the pile body in the elastic stage:

[0107]

[0108] Substituting the above formula, the displacement of the soil outside the pile-soil interface at depth z can be obtained as follows:

[0109]

[0110] 3.2 Interface model displacement calculation

[0111] For the Naggar-Iwan model, let Z0 be the displacement of the base input, Z1 be the absolute displacement of the lateral particle, and Z2 be the absolute displacement of the longitudinal particle; at the same time, let U1 be the displacement of the lateral particle relative to its equilibrium position, and U2 be the displacement of the longitudinal particle relative to its equilibrium position, then:

[0112] The force analysis of the center of mass of the particle is:

[0113]

[0114] List the equilibrium equations for the transverse and longitudinal directions separately:

[0115]

[0116] Substitute the above formulas into the formula,

[0117]

[0118] The above formula can be rewritten as:

[0119] The equation is solved in the complex domain, assuming that the displacement caused by the earthquake load is: Z0 = A0 [cos (ω n t)+isin(ω n t)]

[0120] Then: Z0″=-A0ω n 2 [cos(ω n t)+isin(ω n t)]

[0121] Among them, ω n is the instantaneous excitation frequency of the earthquake load, and substitute it into {P eff}middle,

[0122] have to:

[0123] Let the solution of the equation be:

[0124] Then we have:

[0125] Substituting the above formula into

[0126]

[0127] After sorting, we can get:

[0128] Step 4: Superposition solution of pile-soil displacement and deformation

[0129] According to the pile-soil displacement continuity boundary condition and the pile is completely attached to the soil, the pile displacement can be solved by superposition of soil displacement and interface Naggar-Iwan model displacement;

[0130] In the lateral direction of the pile, the displacement of the soil is:

[0131]

[0132] The interface model displacement is:

[0133]

[0134] Therefore, the lateral displacement of the pile is:

[0135]

[0136] In the longitudinal direction of the pile, since the longitudinal displacement generated by lateral vibration is ignored when analyzing the interface Naggar-Iwan model, the analysis of the longitudinal displacement of the soil can directly consider the longitudinal displacement of the interface Naggar-Iwan model:

[0137]

[0138] The beneficial effects of the present invention are:

[0139] 1. Considering the nonlinear Naggar-Iwan model of stiffness-damping as the interface model of interaction

[0140] According to the horizontal dynamic response of the pile under transient dynamic load and simple harmonic load and the softening phenomenon under cyclic load, the dynamic stress-strain relationship of soft clay is described in combination with the modified Masing formula, and the Naggar-Iwan model of the interface interaction between soil and pile is established. The Naggar model divides the soil around the pile into two parts, near field and far field, and is composed of nonlinear springs, dampers and sliding units. It takes into account the nonlinearity of the soil around the pile, the discontinuity of the deformation of the pile-soil interface, the energy dissipation caused by various damping, and the load ratio. The influence of factors on the dynamic response of the pile foundation is considered. Through this model, the equivalent linear stiffness of the dynamic response of a single pile, damping and the dynamic interaction coefficient of the pile group can be obtained; the Iwan series model is composed of a series of linear elastoplastic elements in series, each of which is composed of a linear spring with a stiffness of E and a yield stress of σ i The Coulomb friction plate is composed of. An important feature of this model is that it satisfies the plastic increment theory, and the strain is easily divided into elastic and plastic parts. For the established Naggar-Iwan model structure, it can be simplified to a spring-damper system, and the pile spring, soil spring, pile damping and soil damping coefficients are established according to the relevant parameters of the pile and soil.

[0141] 2. Displacement calculation method of pile-soil structure considering stiffness-damping coupling under bidirectional seismic waves

[0142] Based on the Euler-Bernoulli beam theory, when the interaction between piles and soil in the lateral and longitudinal directions is simplified to the Naggar-Iwan model structure, the impact of the seismic condition is input at the end of the spring. Through numerical simulation analysis, it is found that the bidirectional seismic coupling effect is similar to the result of single horizontal or vertical action and the impact is more significant, participating in the interaction of the elastic half-space formed between piles and soil in the form of stress.

[0143] The soil around the bridge pile is divided into two parts: the soil at the pile-soil interface and the soil outside the pile-soil interface. The soil at the pile-soil interface produces nonlinear slip with the pile body, and the thickness of this part of the soil is ignored during calculation; the soil outside the pile-soil interface produces shear deformation. Based on the principle of pile-soil joint working and elastic theory, an elastic-plastic model is used to characterize the relationship between the friction resistance and relative displacement of the pile-soil interface, and a model expression for the relationship between the pile side friction resistance and the relative displacement of the pile-soil interface is established. Then, according to the pile-soil interface load transfer principle, the pile is divided into several micro-segment units, and a micro-element is taken for force analysis. Then, combined with the boundary conditions, the shear displacement method is used to calculate the soil displacement outside the pile-soil interface. According to the strength theory of generalized Hooke's law, the force analysis of each particle is carried out. Using the basic principles of dynamics, the generalized structural force-displacement transfer function is constructed, and then the complex matrix operation principle in the complex variable function domain is used to simplify the calculation of the stiffness matrix [K] and the damping matrix [C]. Finally, according to the pile-soil displacement continuity boundary condition and the pile is completely attached to the soil, the pile displacement can be solved by superposition of soil displacement and interface Naggar-Iwan model displacement. BRIEF DESCRIPTION OF THE DRAWINGS

[0144] Figure 1 It is a process flow diagram of the present invention;

[0145] Figure 2 It is a schematic diagram of the pile-soil interface displacement model established by the present invention;

[0146] Figure 3 It is a three-dimensional graph of pile lateral displacement calculated by MATLAB of the present invention;

[0147] Figure 4 It is a two-dimensional diagram of the longitudinal displacement of the pile calculated by MATLAB of the present invention. DETAILED DESCRIPTION

[0148] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments:

[0149] Examples:

[0150] (1) Project Background

[0151] The bridge pile-soil deformation disaster under a certain earthquake is taken as a typical pile foundation engineering prototype. The bridge pile foundation is made of ordinary concrete with a circular cross-section shape and a density of ρ = 2100kg / m 3 Radius r0 = 250 mm, pile length L = 12 m, the soil layer at the bottom of the pile is sandy clay, the elastic modulus E = 35, and the Poisson's ratio V sb =0.36;γ i =18.1kN / m 2 ρ i =1.72g / cm 3 ;

[0152] Assume that the design parameters of the soil around the pile in the i-th soil layer are: The i-th soil layer is assumed to be clay soil with a soil layer thickness of h i =4m; calculate the midpoint weight of soil layer i γ i =18.1kN / m 2 ; Density ρ i =1.72g / cm 3 ; Poisson's ratio V i =0.35; elastic modulus E = 6; r0 is the inner radius of the near field = pile radius = 0.25m; r1 is the outer radius of the near field ≈ 3 times the outer diameter of the pile ≈ 0.75m; P i The force on the nonlinear spring of the i-th soil layer = the horizontal force P at the pile-soil interface i =75kN / m 2 ; The depth of the midpoint of the designed soil layer i from the ground surface is less than the calculated critical depth; The undrained shear strength Cu of the i-th soil layer i =15kP a ; J i =0.2~0.5, 0.35 is acceptable;

[0153] Step 1: Determine the interface model

[0154] From the relationship between shear modulus and elastic modulus: Substituting the data into the result:

[0155]

[0156] Shear wave speed:

[0157]

[0158] The Naggar model used in the transverse direction, the bridge pile spring, soil spring, bridge pile damping and soil damping coefficients are:

[0159] make

[0160] Substituting the proposed data, we can get:

[0161]

[0162] The shear modulus expression of the soil around the bridge pile in the i-th soil layer corrected according to the strain level is: G mi =G maxi (1-η i )

[0163] The expression of the charge intensity ratio coefficient is:

[0164] Where: P ui The ultimate load of the nonlinear spring of the i-th soil layer = the ultimate bearing capacity of the soil around the bridge pile

[0165] P ui =(3Cu i d+γ i z i d+J i Cu i z i )h i

[0166] Substituting the relevant data, we can get:

[0167] P ui =(3Cu i d+γ i z i d+J i Cu i z i )h i

[0168] =(3*15*0.25*2+20*2*0.25*2+0.35*15*2)*4

[0169] =212kN / m 2

[0170] Combining the above expressions, we can get:

[0171]

[0172] In the Naggar model established horizontally: M = m in =πr1 2 ρ i h i

[0173] Substitute the data into:

[0174] M=πr1 2 ρ i hi =π*0.75 2 *19*4

[0175] =134.30309(kg)

[0176] C ph =C sh =α0M+α1K

[0177] In the formula, α0 and α1 are mass and stiffness proportional coefficients. According to the actual situation, α0 = 0.25; α1 = 0.5

[0178] C ph =C sh =α0M+α1K

[0179] =0.5*134.30309+0.25*706.5752

[0180] =67.151545+176.6438=243.795(N*s / m)

[0181] Step 2: Determination of coupled dynamic equations and boundary conditions of pile-soil

[0182] ① Soil displacement around bridge piles

[0183] Substitute the data calculated in the previous step into:

[0184] K=706.5752; r0=0.25m; E=6; L=12m; d=0.5m;

[0185]

[0186] A=πr 2 =π*0.25 2 =0.19635(m 2 )

[0187]

[0188] ②Model displacement

[0189] According to the dimensions designed in the above steps, substitute them into the formula:

[0190] A=πr 2 =π*0.25 2 =0.19635(m 2 );

[0191] The Iwan model used vertically,

[0192]

[0193] M2=πr1 2 ρ i h i =π*0.75 2 *17.2*4=121.5796

[0194] m2=πr0 2 ρ i h i =π*0.25 2 *17.2*4=13.5088(kg)

[0195] The Naggar model adopted horizontally,

[0196]

[0197] M1=πr1 2 ρ i h i =π*0.75 2 *19*4

[0198] =134.30309(kg)

[0199] C ph =C sh =α0M+α1K

[0200] =0.5*134.30309+0.25*706.5752

[0201] =67.151545+176.6438=243.795(N*s / m)

[0202] m1=πr0 2 ρ i h i =π*0.25 2 *19*4=14.9226(kg)

[0203]

[0204]

[0205] ③ The displacement of the bridge pile can be solved by superposition of soil displacement and interface Naggar-Iwan model displacement to obtain the lateral displacement of the bridge pile:

[0206]

[0207] The longitudinal displacement of the bridge pile is:

[0208]

[0209] Determine the bridge pile top load:

[0210] The design value of the effect controlled by the variable load should be calculated as follows:

[0211]

[0212] Assuming the calculated width of the beam span is 8m, the standard value of the proposed load is: permanent load (including the beam's own weight) g k =A0*25=0.19635*25=4.90875(kN / m)

[0213] Variable load: g k =B*3=8*3=24(kN / m)

[0214] Permanent concentrated load at mid-span: P G =100kN

[0215] Standard values ​​of bending moments caused by permanent loads:

[0216] M g =1 / 8g k l 2 +1 / 4P G l=1 / 8*4.90875*8 2 +1 / 4*100*8=239.27(kN*m)

[0217] Standard values ​​of bending moments caused by variable loads:

[0218] M g =1 / 8q k l 2 =1 / 8*24*8 2 =192(kN*m)

[0219] The combinations of variable load effect controls are:

[0220] M1=1.2*239.27+1.4*1.0*192=555.924(kN*m)

[0221] The combinations for controlling permanent load effects are:

[0222] M2=1.35*239.27+1.4*1.0*0.7*192=511.1745(kN*m)

[0223] The standard combinations of load effects are:

[0224] M k =192+239.27=431.27(kN*m)

[0225] The frequency domain combination of load effects is:

[0226] M f =192+0.6*239.27=335.562(kN*m)

[0227] The quasi-permanent combination of load effects is:

[0228] M q =192+0.5*239.27=311.635(kN*m)

[0229] According to the above proposal, the range of P0 is (2493.08,3450.16) kN, ω n The range is (0, 15) Hz and is substituted into the following displacement formula to solve;

[0230]

[0231] From this formula, we can get that when ω n When the value is 5.7965, the displacement deviation is the largest, which is the most dangerous earthquake frequency for bridge piles.

[0232] In the longitudinal direction of the bridge pile, since the longitudinal displacement generated by the lateral vibration is ignored when analyzing the interface Naggar-Iwan model, the longitudinal displacement of the soil can be directly considered in the analysis of the interface Naggar-Iwan model:

[0233] ω n The range is (0, 15) Hz and is substituted into the following displacement formula to solve:

[0234]

Claims

1. A method for calculating the stiffness-damping coordinated matching interface displacement model of pile-soil nonlinear interaction, characterized in that it comprises the following steps: Step 1: Determine the interface model 1.1 Collection of pile-soil parameter information Collect the time history parameters of earthquake action, soil condition information and pile foundation structure design parameters; 1.2 Construction of interface model Based on the horizontal dynamic response of piles under transient dynamic loads and simple harmonic loads and the softening phenomenon under cyclic loads, the dynamic stress-strain relationship of soft clay is described in combination with the modified Masing formula, and the Naggar-Iwan model of the interface interaction between soil and pile is established; 1.3 Basic assumptions of the interface model and establishment of coefficient equations A Naggar model is established in the lateral direction between the pile and the soil, and an Iwan model is established at the bottom of the pile and the soil. This model structure is used to describe the deformation of the soil and the pile when the pile and the soil interact under bidirectional earthquake conditions. Step 2: Determination of pile-soil coupled dynamic equations and boundary conditions 2.1 Coupled dynamic equations of soil around piles The displacement response of the soil medium in the scattered field under the action of earthquake is expressed as u r (r,θ,z)e iωt and u θ (r,θ,z)e iωt , the coupled dynamic equations representing the radial and circumferential displacements of the soil are expressed as: Where: G s * =G s * (1+2iβ s ) λ s * is the soil complex Lame constant; V s is the soil Poisson’s ratio; G s * is the complex shear modulus of soil; β s is the soil hysteresis damping; ρ s is the soil mass density; 2.2 Dynamic control equation of pile Based on the Euler-Bernoulli beam theory, when the interaction between pile and soil in the lateral and longitudinal directions is simplified to the Naggar-Iwan model structure, the impact of the earthquake condition is input at the end of the spring. Through numerical simulation analysis, it is found that the bidirectional seismic coupling effect is similar to the result of the single horizontal or vertical effect and the effect is more significant. It participates in the interaction of the elastic half space formed between pile and soil in the form of stress. Horizontal displacement of the pile in the soil ω p e iωt The dynamic control equation represented by (z) is: Where: E p * =E p (1+2iβ p ) E p I is the bending stiffness of the pile foundation; ρ p is the pile density; A is the cross-sectional area of ​​the pile; ω p is the horizontal displacement of the pile body; z is the axial coordinate of the pile body; t is the time; P d is the nonlinear dynamic reaction force of the soil around the pile per unit pile length; β p is the pile hysteresis damping; C is the stiffness coefficient and damping coefficient of the soil around the pile within unit pile length; 2.3 Establishing system boundary conditions Establish the system boundary conditions based on the above assumptions and dynamic equations; Boundary conditions at the top of the pile: Elastic half-space surface boundary conditions: Where: is the x-direction displacement U of the soil scattering field in the rectangular coordinate system r s cosθ-U θ s sinθU x s Pile-soil boundary conditions: Boundary conditions at infinite soil displacement: Step 3: Calculation of pile-soil deformation displacement equation 3.1 Calculation of soil displacement around piles The elastic-plastic model is used to characterize the relationship between the pile-soil interface friction and relative displacement: Where: τ max is the ultimate friction resistance of the soil on the pile side; k is the spring stiffness; S pu is the relative displacement value of the pile-soil interface corresponding to the pile side friction resistance reaching the limit; Calculation of soil displacement outside the pile-soil interface using the shear displacement method ； According to the shear displacement principle, the shear strain of the soil unit at the depth z and the distance r from the central axis of the bridge pile is: Then the shear stress is: Where: G s is the soil shear modulus; According to the equilibrium condition: Where: r 0 is the radius of the pile, when r = r 0 When τ(z,r)=τ p (z) Combining the above formula, we can get: Therefore, according to the formula, the displacement of the soil outside the pile-soil interface can be obtained as: The pile is divided into several micro-segments, and a micro-element is taken for force analysis. For small-diameter piles, the effect of the pile's deadweight on the bearing capacity can be ignored. According to the force balance condition, we can get: Where: P(z) is the axial force of the pile; U p is the circumference of the pile; Take the microelement elastic deformation equal to the displacement difference d between the top and bottom of the pile sp According to Hooke's law: Where: E is the elastic modulus of the pile; A is the cross-sectional area of ​​the pile; Derivative the above formula and substitute the relevant formula into it, we can get: Where: d is the diameter of the pile; make Integrating the above formula, we can get: Combined with the selected pile microelement, the boundary conditions can be analyzed to obtain: Where: l is the length of the pile; P 0 is the top load of the pile; Substituting the boundary conditions into the above formula, we can get the correlation coefficient: Set parameter C 1 , C 2 Substituting into the above formula, we can get the distribution expressions of the axial force, relative displacement and lateral friction resistance of the pile along the pile body in the elastic stage: Substituting the above formula, the displacement of the soil outside the pile-soil interface at depth z can be obtained as follows: 3.2 Interface model displacement calculation For the Naggar-Iwan model, assume that Z 0 is the displacement of the base input, Z 1 is the absolute displacement of the particle in the lateral direction, Z 2 is the absolute displacement of the longitudinal particle; at the same time, let U 1 is the lateral displacement of the particle relative to its equilibrium position, U 2 is the displacement of the longitudinal particle relative to its equilibrium position: The force analysis of the center of mass of the particle is: List the equilibrium equations for the transverse and longitudinal directions separately: Substitute the above formulas into the formula, The above formula can be rewritten as: The equation is solved in the complex domain, assuming that the displacement caused by the earthquake load is: Z 0 =A 0 [cos(ω n t)+isin(ω n t)] Then: Z 0 ″ = -A 0 ω n 2 [cos(ω n t) + isin(ω n t)] in, ω n is the instantaneous excitation frequency of the earthquake load, and substitute it into {P eff }middle, have to: Let the solution of the equation be: Then we have: Substituting the above formula into After sorting, we can get: Step 4: Superposition solution of pile-soil displacement and deformation According to the pile-soil displacement continuity boundary condition and the pile is completely attached to the soil, the pile displacement can be solved by superposition of soil displacement and interface Naggar-Iwan model displacement; In the lateral direction of the pile, the displacement of the soil is: The interface model displacement is: Therefore, the lateral displacement of the pile is: In the longitudinal direction of the pile, since the longitudinal displacement generated by lateral vibration is ignored when analyzing the interface Naggar-Iwan model, the analysis of the longitudinal displacement of the soil can directly consider the longitudinal displacement of the interface Naggar-Iwan model:

2. The method for calculating the stiffness-damping coordinated matching interface displacement model of pile-soil nonlinear interaction according to claim 1 is characterized in that the time history parameters of the earthquake action in step 1.1 include: earthquake duration, acceleration over time curve, and number of sampling points; Soil condition information includes: soil layer thickness, weight of each soil layer, elastic modulus, shear modulus, shear wave velocity, Poisson's ratio; The design parameters of pile foundation structure include: pile cross-sectional shape, pile diameter, spacing, length, elastic modulus and density of pile concrete.

3. The method for calculating the stiffness-damping coordinated matching interface displacement model of pile-soil nonlinear interaction according to claim 1, It is characterized in that In step 1.3, the basic assumptions of the interface model and the steps for establishing the coefficient equation are as follows: Assume that the earthquake wave acting on the pile foundation is U g e iωt , and use this to establish a cylindrical coordinate system (r, z), where the circular frequency is ω, the time is t, and the pile radius is r 0 , the pile height is H, and the soil thickness is h; To facilitate the analysis, the following assumptions are made: ① The pile foundation is simulated by linear viscoelastic Euler, and the cross-sectional shape of the pile foundation is circular; ② The soil is regarded as an isotropic, homogeneous viscoelastic medium; the damping used in the soil material is hysteresis damping that is independent of frequency; ③ In the pile-soil system, the deformation of the two is small deformation vibration, the contact surface between the two is good, and no slip occurs; ④ Divide the deformation of the pile foundation and the soil into two directions: transverse and longitudinal, ignoring the longitudinal displacement caused by transverse vibration and the transverse displacement during longitudinal vibration; The established Naggar-Iwan model structure is simplified to a spring-damper system, in which the expressions of pile spring, soil spring, pile damping and soil damping coefficients are expressed as follows: ① For the Iwan model adopted vertically: Where: G b is the shear modulus; V sb is Poisson's ratio; ρ b is the density pile; C sb is the shear wave velocity; A P is the cross-sectional area of ​​the pile; ② For the horizontally adopted Naggar model: Where: (Charge intensity ratio coefficient) G mi =G maxi (1-η i )(Shear modulus of soil around pile in the i-th soil layer corrected according to strain level) C ph =C sh =a 0 M+a 1 K M=m ni =πr 1 2 r i h i V i is the Poisson's ratio of the i-th soil layer; r 0 The radius in the near field = the pile radius; h i is the thickness of the i-th soil layer; r 1 The outer radius of the near field is ≈ 3 times the outer diameter of the pile; G maxi The maximum shear modulus of the i-th soil layer ≈ the initial shear modulus; P i is the force on the nonlinear spring of the i-th soil layer = the horizontal force at the pile-soil interface; P ui The ultimate load of the nonlinear spring of the i-th soil layer = the ultimate bearing capacity of the soil around the pile; α 0 , α 1 is the mass and stiffness proportionality coefficient.

Images