Pile foundation seismic response analysis method and system considering transverse inertial effect, storage medium and application of pile foundation seismic response analysis method and system

Abstract

The invention provides a pile foundation seismic response analysis method and system considering a transverse inertial effect, a storage medium and application of the pile foundation seismic response analysis method and system. Aiming at the problem that a pile-soil coupling vibration model in the prior art neglects the fractional order viscoelasticity characteristic of unsaturated soil and the transverse inertia effect of an uncoupled pile body, the invention provides a large-diameter end-bearing pile seismic response analysis model based on a fractional order viscoelasticity constitutive structure. A fractional derivative is introduced to describe the stress relaxation characteristic of an unsaturated soil skeleton, a Rayleigh-Love beam theory is combined to characterize the transverse deformation effect of a pile body, and a pile-soil coupling vibration control equation under the action of earthquake P waves is constructed. Laplacian transformation, potential function decomposition and operator decomposition methods are adopted to realize equation dimensionality reduction solution, a pile-soil interface continuous condition and a boundary constraint condition are synthesized, a theoretical analytical solution of vibration response in a frequency domain is obtained, and a theoretical basis is provided for aseismic design of a pile foundation in an unsaturated land area.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of geotechnical engineering anti-seismic technology, and in particular to a pile foundation seismic response analysis method and system considering lateral inertia effect, a storage medium and application thereof. BACKGROUND

[0002] In the field of pile foundation seismic response analysis, the traditional method is mostly based on the saturated soil assumption, adopts the integer order viscoelastic model and the Euler-Bernoulli beam theory, and thus ignores the solid-liquid-gas three-phase coupling effect in the unsaturated soil and the fractional order stress relaxation characteristics, and cannot accurately represent the hysteresis damping and memory effect of the soil body; secondly, the existing model fails to couple the axial vibration of the pile body and the lateral inertia effect, resulting in a deviation in the prediction of the dynamic response of the pile body under high-frequency seismic excitation; thirdly, the conventional analysis method cannot obtain the theoretical solution containing parameters such as lateral inertia, Poisson's ratio, saturation, and modulus ratio, resulting in that the parameter sensitivity analysis relies on numerical simulation and is low in efficiency. Although the research in recent years has improved the calculation accuracy through finite element-boundary element coupling, the calculation complexity is high. Therefore, it is an urgent need to develop a continuous medium analytical model that integrates the fractional order viscoelastic characteristics of unsaturated soil, transverse isotropy, and three-dimensional wave effect of the pile body, so as to realize efficient and accurate prediction of the frequency response characteristics of the pile foundation. SUMMARY

[0003] The present application aims to provide an improved friction pile torsional vibration analytical method to solve the problems in the background art.

[0004] To achieve the above-mentioned purpose, the present application provides the following technical solution: a pile foundation seismic response analysis method considering lateral inertia effect, characterized by comprising the following steps:

[0005] comprising the following steps:

[0006] S1: assuming that the soil body is a homogeneous, viscoelastic, isotropic unsaturated porous medium, the solid phase, liquid phase and gas phase are all compressible; the ground is permeable and gas-permeable, and the normal stress is zero; the stress and displacement are zero at a horizontal distance; the single pile is located at the bottom of the rigid bedrock, and the pile is assumed to be a Rayleigh-Love rod; the pile-soil system is subjected to the propagation of vertical seismic P waves, and is simulated by applying a time-harmonic displacement to the bedrock; the stress and displacement of the pile and the soil around the pile are continuous in the vibration, and the deformation of the pile-soil is small;

[0007] S2: based on the continuum mechanics framework and the Mualem theory, the regional average technique is used to quantify the permeation characteristics between the pore fluid and the solid phase skeleton, and combined with the van Genuchten classical unsaturated soil water characteristic curve, the unsaturated soil wave control equation is established based on the Biot type wave theory, and the Lame constant and the bulk compression modulus of the soil skeleton are represented as a fractional derivative Kelvin viscoelastic model;

[0008] S3: solving the dynamic response of the unsaturated soil under inertial interaction by introducing potential function, operator decomposition and other means;

[0009] S4: solving the free field wave response of the unsaturated soil under kinematic interaction by introducing potential function, operator decomposition and other means;

[0010] S5: establishing a vertical vibration equation based on Rayleigh-Love rod;

[0011] S6: solving the seismic response of the pile foundation under seismic P wave by using the continuity condition of the pile-soil contact surface.

[0012] Preferably, according to step S2, the wave equation of the unsaturated soil is:

[0013] (1a)

[0014] (1b)

[0015] (1c)

[0016] In the formula, is the solid phase displacement vector of the soil, and respectively represent the relative displacement of the pore water and the pore gas relative to the soil skeleton; , λ and μ are the Lame constants of the soil skeleton, is the effective stress coefficient, which is affected by the saturation, soil properties, dry-wet cycle history and loading-suction path. K s and K b are the compression modulus of the soil particles and the overall volume compression modulus of the soil skeleton, respectively. The subscripts s, w and a correspond to the solid phase particles, pore water and pore gas, respectively. , , is the intrinsic permeability coefficient of the soil, , , , , , , , S r represents the current water content state of the unsaturated soil, n is the volume porosity of the pore medium, α, m and d are the key constitutive parameters of the van Genuchten water retention model representing the water characteristic curve of the soil, , , , , , , , , , , , , , , .

[0017] Preferably, in step 2, the constitutive parameters characterizing the soil skeleton viscoelastic behavior by fractional derivative operator, and the vector equation is converted to the cylindrical coordinate system, and the control equation of fractional viscoelastic unsaturated soil can be derived by tensor operation as follows:

[0018] (2a)

[0019] (2b)

[0020] (2c)

[0021] (2d)

[0022] (2e)

[0023] (2f)

[0024] In the formula, , , , . , , , , , , , , , .

[0025] Preferably, step 3 is specifically as follows:

[0026] S31, by decoupling analysis of multiphase coupling dynamic behavior, the three-phase wave field is decomposed into the superposition form of scalar potential (Φ) and vector potential (Ψ), so as to build a systematic description framework of longitudinal wave and transverse wave modal characteristics. The relative motion among phases is expressed as follows:

[0027] (3)

[0028] S32, the non-saturated soil control equation (2) is decoupled by using the kinetic potential function formula (3), and in order to improve the universality of the model and simplify the numerical solution process, the system is dimensionless, and the coupling equation is obtained in the form of matrix:

[0029] (4)

[0030] (5)

[0031] In the formula, , , , , , , , , , , , , , , ,( ) represents the dimensionless form.

[0032] S33, in order to make the differential equation group have non-zero solution, the determinant of the coefficient matrix must satisfy the zero value condition. Let and , based on the operator decomposition theory, variable separation method, the scalar potential function and the vector potential function of each phase displacement field of unsaturated soil, the mathematical representation form is as follows:

[0033] (6)

[0034] In the formula, and respectively represent zero-order first and second modified Bessel functions, and are constants determined by the boundary conditions. Constants C 11 , C 12 , C 21 , C 22 , C 31 , C 32 , C 41 and C 42 , need to satisfy the following constraint relationship:

[0035] (7)

[0036] In the formula, , and are the roots of the following equation:

[0037] (8)

[0038] S34, According to the assumption in step S1, the radial displacement expression of pore water and pore gas is specifically as follows through mathematical physical derivation:

[0039] (9)

[0040] (10)

[0041] In the formula, , .

[0042] S35, According to the assumption in step S1, based on the analysis of the dynamic coupling effect of the pile-soil contact surface, the interface shear stress expression is:

[0043] (11)

[0044] In the formula, , , ,

[0045] , .

[0046] S36, Based on the three-dimensional wave coupling analysis of the pile-soil, the vertical vibration displacement response of the contact interface can be analytically characterized as follows:

[0047] (12)

[0048] In the formula, .

[0049] S37, The lateral displacement response form of the solid skeleton can be characterized as:

[0050] (13)

[0051] In the formula, .

[0052] Preferably, the step 4 is specifically:

[0053] S41, In the free field seismic response analysis, for the P wave propagation characteristics, it is usually assumed that the soil body is horizontally homogeneous, and the seismic wave mainly propagates vertically. Based on the wave theory of porous elastic medium, the displacement field of each point of the soil layer can be modeled by a one-dimensional wave equation, and thus the vertical wave control equation of the unsaturated soil body is as follows:

[0054] (14)

[0055] wherein, respectively represent the displacement response field distribution of the solid skeleton, pore water and pore gas in the free field of unsaturated soil. ,

[0056] ,

[0057] ,

[0058] .

[0059] S42, using the operator decomposition theory, the free field displacement expressions of the solid skeleton, pore water and pore gas are:

[0060] (15)

[0061] wherein, , u g represents the P-wave displacement amplitude.

[0062] S43, based on the linear superposition theory, the comprehensive displacement response of the pile-soil coupling vibration system is expressed as:

[0063] (16)

[0064] (17)

[0065] (18)

[0066] Preferably, the step 5 comprises the following specific steps:

[0067] S51, based on the Rayleigh-Love rod wave theory, and the Laplace integral transformation and dimensionless processing are performed on the pile foundation equation, and the dimensionless control equation in the frequency domain is derived as follows:

[0068] (19)

[0069] wherein, , .

[0070] S52, substituting formula (11) into formula (19), the vertical vibration displacement solution of the pile can be expressed as:

[0071] (20)

[0072] wherein, M and N are arbitrary constants, and .

[0073] S53, since , the transverse vibration displacement of the pile is:

[0074] (21)

[0075] Preferably, the step 6 comprises the following specific steps:

[0076] S61, according to the pile-soil continuity condition in step S1, substituting formula (12), (13), (15) and (16) into formula (20) and (21) to obtain:

[0077] (22)

[0078] (23)

[0079] S62, let Based on the characteristics of the hyperbolic cosine function and its mathematical association with the cosine function, the following expression can be derived:

[0080] (24)

[0081] S63, substituting the expressions of φ 1n , φ 2n and φ 3n into formula (22) and (23) to obtain:

[0082] (25)

[0083] (26)

[0084] In the formula, the expressions of η 1n , η 2n , η 3n and η 4n are:

[0085]

[0086]

[0087]

[0088]

[0089] S64, based on the orthogonal function characteristics, multiplying on both sides of formula (25), and performing orthogonal integral operation within the domain , the following eigen equation can be derived:

[0090] (27)

[0091] In the formula, .

[0092] S65, based on the orthogonal function characteristics, the same multiplication of formula (26) on both sides And perform orthogonal integral operation in the definition domain The following eigen equation can be derived:

[0093] (28)

[0094] S66, formula (27) and formula (28) are solved at the same time:

[0095] (29)

[0096] (30)

[0097] In the formula,

[0098] (31)

[0099] (32)

[0100] (33)

[0101] S67, the dynamic boundary constraint condition of the coupling interface of the pile top and the pile bottom under the excitation of the seismic P wave is:

[0102] (34)

[0103] (35)

[0104] S68, formula (20) is substituted into formula (34) and (35) to obtain:

[0105] (36)

[0106] S69, through the two core evaluation indexes of the kinematic amplification coefficient (A v ) of the pile top and the kinematic response coefficient (I v ) of the pile-soil coupling, the seismic dynamic response characteristics of the pile-soil system are systematically characterized, and the specific definitions are as follows:

[0107] (37)

[0108] (38).

[0109] The application also provides a pile foundation seismic response analysis system considering the transverse inertia effect, characterized by comprising:

[0110] A model construction module is configured to establish a geometric model and a material model of the friction pile and the virtual non-saturated soil pile;

[0111] An equation solving module is configured to derive and solve a torsional vibration control equation of the soil, the solid pile and the FUSP;

[0112] A response calculation module is configured to calculate the dynamic response of the pile top in the frequency domain and the time domain;

[0113] An output module is configured to output the complex stiffness, the velocity admittance, the torsional angle time history and the velocity time history curve of the pile top.

[0114] The application further provides a computer readable storage medium, which has a computer program stored thereon, and the computer program is executed by a processor to implement the analysis method.

[0115] The application further provides an application of the pile foundation seismic response analysis method considering the lateral inertia effect in predicting the dynamic response of the pile foundation in an unsaturated soil area under the action of an earthquake P wave and guiding the optimization of the pile foundation structure and the evaluation of the seismic performance

[0116] The application further provides an application of the pile foundation seismic response analysis method considering the lateral inertia effect in the seismic design of the pile foundation in a complex geological environment such as a coastal beach, an underground water level fluctuation area and an unsaturated loess area.

[0117] Compared with the prior art, the application has the following beneficial effects:

[0118] 1. The application solves the problems of the lack of the lateral inertia effect and the distortion of the soil body constitutive simplification in the traditional pile foundation seismic analysis by establishing a non-saturated soil fractional order viscoelastic pile soil coupling dynamic response model; the fractional derivative model is introduced to represent the non-saturated soil seepage-stress relaxation coupling effect, and the prediction accuracy of the soil body damping characteristics is effectively improved; the Rayleigh-Love beam theory is used to couple the three-dimensional wave characteristics of the pile body, and the axial-lateral inertia effect synergy mechanism of the pile foundation under the action of the seismic load is completely described; the non-saturated soil-pile full coupling frequency domain analytical solution is constructed, and the continuous mapping of the parameters such as the lateral inertia, the Poisson's ratio, the saturation and the modulus ratio on the impedance characteristics of the pile foundation is realized. Thus, the application provides theoretical support for the seismic design of the pile foundation in a complex geological environment such as a coastal beach and an underground water level fluctuation area, and the viscoelastic soil body constitutive adaptability and the complete dynamic response are provided. BRIEF DESCRIPTION OF DRAWINGS

[0119] Figure 1 It is a model schematic diagram of the application. DETAILED DESCRIPTION

[0120] Clearly, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the protection scope of the present application.

[0121] Please refer to Figure 1 In the embodiments of the present application, in order to solve the problems that the pile-soil coupling vibration model in the prior art ignores the fractional order viscoelasticity characteristics of unsaturated soil, does not couple the lateral inertia effect of the pile body, and lacks theoretical solution, the present application provides an end-bearing pile seismic response analysis and calculation method, which establishes a fractional order viscoelastic unsaturated soil-pile coupling wave model, combines operator decoupling and frequency domain analytical method, solves the problems that the traditional integer order constitutive model cannot characterize the stress relaxation memory effect of soil body and the high-frequency response distortion caused by the lack of lateral inertia term, and provides theoretical support for seismic design of pile foundation in unsaturated soil area.

[0122] The present application provides an improved friction pile torsional vibration analytical method, comprising the following steps:

[0123] S1: considering the following assumptions, the soil is a homogeneous, viscoelastic, isotropic unsaturated porous medium, the solid phase, liquid phase and gas phase are all compressible; the ground is permeable and gas-permeable, and the normal stress is zero; the stress and displacement are zero at a horizontal distance; the bottom of the single pile is located on the rigid bedrock, and the pile is assumed to be a Rayleigh-Love rod; the pile-soil system is subjected to the propagation of vertical seismic P wave, and is simulated by applying a time-harmonic displacement to the bedrock; the stress and displacement of the pile and the soil around the pile are continuous in vibration, and the deformation of the pile and the soil is small;

[0124] S2: based on the continuum mechanics framework and the Mualem theory, the permeability between the pore fluid and the solid phase skeleton is quantified by using the regional average technique, and combined with the van Genuchten classical unsaturated soil water characteristic curve, the unsaturated soil wave control equation is established based on the Biot type wave theory, and the Lame constant and the bulk compression modulus of the soil skeleton are characterized as a fractional derivative Kelvin viscoelastic model;

[0125] S3: the dynamic response of the unsaturated soil under inertial interaction is solved by introducing potential function and operator decomposition;

[0126] S4: the free field wave response of the unsaturated soil under motion interaction is solved by introducing potential function and operator decomposition;

[0127] S5: a vertical vibration equation based on Rayleigh-Love rod is established;

[0128] S6: The seismic response of the pile foundation subjected to P-wave is solved by using the continuity condition of the pile-soil contact surface.

[0129] According to step S2, the wave equation of the unsaturated soil body is:

[0130] (1a)

[0131] (1b)

[0132] (1c)

[0133] In the formula, is the solid phase displacement vector of the soil body, and respectively represent the relative displacement of the pore water and the pore gas relative to the soil skeleton; and μ are the Lame constants of the soil skeleton, is the effective stress coefficient, which is affected by the saturation, the soil properties, the history of dry-wet cycle and the loading-suction path. s and K b are the self-compression modulus of the soil particles and the overall volume compression modulus of the soil skeleton, respectively. The subscripts s, w and a correspond to the solid phase particles, the pore water and the pore gas, respectively. is the inherent permeability coefficient of the soil body, , S r represents the current water state of the unsaturated soil, n is the volume porosity of the pore medium, α, m and d are the key constitutive parameters of the van Genuchten water retention model for representing the water characteristic curve of the soil body, .

[0134] ​​​​​​​​​​​​​​​​​​​​​​In step 2, the constitutive parameters of the soil skeleton viscoelastic behavior are characterized by fractional differential operators, and the vector equation is converted to the cylindrical coordinate system, and the control equation of fractional viscoelastic unsaturated soil is derived by tensor operation:

[0135] (2a)

[0136] (2b)

[0137] (2c)

[0138] (2d)

[0139] (2e)

[0140] (2f)

[0141] In the formula, , , , . , , , , , , , , , .

[0142] Step 3 is specifically:

[0143] S31, by decoupling analysis of multiphase coupling dynamics, the three-phase wave field is decomposed into the superposition form of scalar potential (Φ) and vector potential (Ψ), so as to build a systematic description framework of longitudinal wave and transverse wave modal characteristics. The relative motion between each phase is expressed as follows:

[0144] (3)

[0145] S32, the dynamic potential function formula (3) is used to decouple the unsaturated soil body control equation (2), and in order to improve the universality of the model and simplify the numerical solution process, the system is dimensionless, and the coupled equation represented by matrix is obtained:

[0146] (4)

[0147] (5)

[0148] In the formula, , , , , , , , , , , , , , , ,( ) represents a dimensionless form.

[0149] S33, in order to make the differential equations exist non-zero solution, the coefficient matrix determinant must meet the zero value condition. Let and , based on the operator decomposition theory, variable separation method, the scalar potential function and vector potential function of each phase displacement field of unsaturated soil, its mathematical representation form is as follows:

[0150] (6)

[0151] In the formula, and respectively represent zero order first type and second type modified Bessel function, and are constants determined by boundary conditions. Constant C 11 , C 12 , C 21 , C 22 , C 31 , C 32 , C 41 and C 42 , need to meet the following constraint relationship:

[0152] (7)

[0153] In the formula, , and are the roots of the following equation:

[0154] (8)

[0155] S34, according to the assumption in step S1, through mathematical physics derivation, the radial displacement expression of pore water and pore gas is as follows:

[0156] (9)

[0157] (10)

[0158] In the formula, , .

[0159] S35, based on the dynamic coupling effect analysis of the pile-soil contact surface, the interface shear stress expression is:

[0160] (11)

[0161] wherein, , , ,

[0162] , .

[0163] S36, based on the three-dimensional wave theory coupling analysis of the pile-soil, the vertical vibration displacement response of the contact interface can be characterized as follows:

[0164] (12)

[0165] wherein, .

[0166] S37, the lateral displacement response of the solid skeleton can be characterized as:

[0167] (13)

[0168] wherein, .

[0169] The step 4 is specifically:

[0170] S41, in the free field seismic response analysis, for the P wave propagation characteristics, it is usually assumed that the soil body is homogeneous in horizontal direction, and the seismic wave is mainly propagated in vertical direction. Based on the wave theory of porous elastic medium, the displacement field of each point of the soil layer can be modeled by one-dimensional wave equation, and thus the vertical wave control equation of the unsaturated soil body can be obtained as follows:

[0171] (14)

[0172] wherein, respectively represent the displacement response field distribution of the solid skeleton, pore water and pore gas of the unsaturated soil in the free field. ,

[0173] ,

[0174] ,

[0175] .

[0176] S42, using operator decomposition theory, the free field displacement expression of solid skeleton, pore water and pore gas is:

[0177] (15)

[0178] In the formula, , u g P-wave displacement amplitude.

[0179] S43, based on linear superposition theory, the comprehensive displacement response of pile-soil coupling vibration system is expressed as: (16)

[0180] (17)

[0181] (18)

[0182] The step 5 includes the following specific steps:

[0183] S51, based on Rayleigh-Love rod wave theory, and Laplace integral transformation and dimensionless processing are carried out on pile foundation equation, and the dimensionless control equation in frequency domain is derived as follows:

[0184] (19)

[0185] In the formula, , .

[0186] S52, substituting formula (11) into formula (19) can obtain the vertical vibration displacement solution of pile, which can be expressed as:

[0187] (20)

[0188] In the formula, M and N are arbitrary constants, and .

[0189] S53, because The transverse vibration displacement of the pile is:

[0190] (21)

[0191] The step 6 includes the following specific steps:

[0192] S61, according to the pile-soil continuity condition in step S1, substituting formula (12), (13), (15) and (16) into formula (20) and (21) obtains:

[0193] (22)

[0194] (twenty three)

[0195] S62, Order Based on the properties of the hyperbolic cosine function and its mathematical relationship with the cosine function, the following expression can be derived:

[0196] (twenty four)

[0197] S63, φ 1n φ 2n and φ 3n Substituting the expressions into equations (22) and (23), we get:

[0198] (25)

[0199] (26)

[0200] In the formula, η 1n η 2n η 3n and η 4n The expression is:

[0201]

[0202]

[0203]

[0204]

[0205] S64. Based on the properties of orthogonal functions, multiply both sides of equation (25) by the same factor. and in the domain Performing orthogonal integration within the inner quadratic integral yields the following eigenvalue equations:

[0206] (27)

[0207] In the formula, .

[0208] S65. Based on the properties of orthogonal functions, multiply both sides of equation (26) by the same factor. and in the domain Performing orthogonal integration within the inner quadratic integral yields the following eigenvalue equations:

[0209] (28)

[0210] S66. Solving equations (27) and (28) simultaneously yields:

[0211] (29)

[0212] (30)

[0213] wherein,

[0214] (31)

[0215] (32)

[0216] (33)

[0217] S67, the dynamic boundary constraint condition of the pile top and pile bottom coupling interface under the excitation of the seismic P wave is:

[0218] (34)

[0219] (35)

[0220] S68, by substituting formula (20) into formula (34) and (35), the following formula can be obtained:

[0221] (36)

[0222] S69, by the two core evaluation indexes of the pile top kinematic amplification coefficient (A v ) and the pile-soil coupling kinematic response coefficient (I v ), the seismic dynamic response characteristics of the pile-soil system are systematically characterized, and the specific definitions are as follows:

[0223] (37)

[0224] (38)

[0225] The system for realizing the above-mentioned analysis method is characterized in that it comprises:

[0226] An input module is configured to receive pile-soil parameters, seismic wave parameters and boundary conditions.

[0227] A modeling module is configured to construct a fractional order viscoelastic model of unsaturated soil and a Rayleigh-Love pile body model.

[0228] A solving module is configured to solve the pile-soil coupling vibration response based on a potential function and an operator decomposition method.

[0229] An output module is configured to output the pile top amplification coefficient, the pile-soil coupling response coefficient and the displacement and stress distribution results.

[0230] A display module is configured to visually display the seismic response analysis results.

[0231] The module operation method refers to the analysis method content described above, and will not be described again.

[0232] The steps of a method or algorithm described in connection with the embodiments disclosed herein can be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module can reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.

[0233] The embodiments of the present disclosure also provide a computer readable storage medium, which stores a computer program. The program is executed by a processor to implement the filter rod storage scheduling method of any of the preceding embodiments.

[0234] In one or more exemplary embodiments, the functions described can be implemented in hardware, software, firmware, or any combination thereof. If implemented in software as a computer program product, the functions can be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage media can be any available media that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Also, any connection is properly termed a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of medium. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk and blu-ray disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media.

[0235] The present application also provides a pile foundation seismic response analysis method considering lateral inertia effect for predicting the dynamic response of pile foundation in unsaturated soil area under the action of P wave, guiding the application in the optimization of pile foundation structure and the evaluation of seismic performance

[0236] The application also provides application of the pile foundation earthquake response analysis method considering the lateral inertia effect in pile foundation seismic design in a complex geological environment such as a coastal beach, a groundwater level fluctuation area, an unsaturated loess area and the like.

[0237] It can be seen from the technical scheme that the application solves problems such as lack of lateral inertia effect and distortion of soil body constitutive simplification in traditional pile foundation seismic analysis by establishing a non-saturated soil fractional order viscoelastic pile-soil coupling dynamic response model: the fractional derivative model is introduced to represent the non-saturated soil seepage-stress relaxation coupling effect, so as to effectively improve the prediction accuracy of soil body damping characteristics; the Rayleigh-Love beam theory is used to couple the three-dimensional wave characteristics of the pile body, so as to completely depict the synergistic mechanism of axial-lateral inertia effect of the pile foundation under the seismic load; the non-saturated soil-pile full coupling frequency domain analytical solution is constructed, so as to realize continuous mapping of parameters such as lateral inertia, Poisson's ratio, saturation and modulus ratio on the impedance characteristics of the pile foundation. Thus, the application provides theoretical support for pile foundation seismic design in a complex geological environment such as a coastal beach, a groundwater level fluctuation area and the like, and has both viscoelastic soil body constitutive adaptability and complete dynamic response.

[0238] It will be obvious to a person skilled in the art that the application is not limited to the details of the foregoing exemplary embodiments, but that the application can be implemented in other concrete forms without departing from the spirit or essential characteristics of the application. Therefore, the embodiments should be considered as exemplary and not limiting in any way, the scope of the application being defined by the claims appended hereto rather than by the foregoing description, and it is intended to encompass all variations falling within the meaning and range of equivalents of the elements of the claims. Any reference signs in the claims should not be considered as limiting the claims in any way.

[0239] Furthermore, it should be understood that, although the present specification is described in terms of embodiments, not every implementation can contain all of the features that are described in a particular embodiment, this manner of describing the specification is merely for the sake of convenience and brevity, and one of ordinary skill in the art will readily understand that the application should be considered as an entirety, and the technical solutions in each embodiment can be properly combined to form other embodiments that can be understood by one of ordinary skill in the art.

Claims

1. A method for analyzing the seismic response of a pile foundation considering lateral inertia effects, characterized by, The method comprises the following steps: S1: assuming that the soil body is homogeneous, viscoelastic, isotropic, unsaturated and porous medium, the solid phase, liquid phase and gas phase are compressible; the ground is permeable and gas permeable, the normal stress is zero; the stress and displacement are zero at the horizontal infinity; the bottom of the single pile is located on the rigid bedrock, and the pile is assumed to be a Rayleigh-Love rod; the pile-soil system is subjected to the propagation of vertical seismic P wave, and the time-harmonic displacement is simulated by being applied to the bedrock; the stress and displacement of the pile and the soil around the pile are continuous in vibration; the deformation of the pile and the soil is small deformation; S2: based on the continuum mechanics framework and the Mualem theory, the permeability between the pore fluid and the solid skeleton is quantified by using the regional average technique, and the classical unsaturated soil water characteristic curve of van Genuchten is combined to establish the wave motion control equation of the unsaturated soil based on the Biot type wave motion theory; the Lame constant and the bulk compression modulus of the soil skeleton are characterized as a fractional derivative Kelvin viscoelastic model; S3: the dynamic response of the unsaturated soil body under inertial interaction is solved by introducing potential functions and operator decomposition; S4: the free field wave motion response of the unsaturated soil under kinematic interaction is solved by introducing potential functions and operator decomposition; S5: a vertical vibration equation based on the Rayleigh-Love rod is established; S6: the seismic response of the pile foundation subjected to the seismic P wave is solved by using the continuity condition of the pile-soil contact surface.

2. The method for analyzing the pile seismic response considering the lateral inertia effect according to claim 1, wherein, According to step S2, the wave motion equation of the unsaturated soil body is: (1a) (1b) (1c) wherein, is the solid phase displacement vector of the soil, and respectively represent the relative displacement of the pore water and the pore gas with respect to the soil skeleton; , λ and μ are the Lame constants of the soil skeleton, is the effective stress coefficient, which is influenced by the degree of saturation, soil properties, drying-wetting history and loading-suction path; K s and K b are the compression modulus of the soil particles and the bulk compression modulus of the soil skeleton, respectively; the subscripts s, w and a correspond to the solid phase particles, the pore water and the pore gas, respectively; , , is the intrinsic permeability coefficient of the soil, , , , , , , , S r represents the current water state of the unsaturated soil, n is the volumetric porosity of the porous medium, α, m and d are the key constitutive parameters of the van Genuchten water retention model representing the water characteristic curve of the soil, , , , , , , , , , , , , , , .

3. The method for analyzing the pile seismic response considering the lateral inertia effect according to claim 1, wherein, In step 2, the constitutive parameters of the soil skeleton viscoelastic behavior are characterized by fractional derivative operators, and the vector equation is converted to a cylindrical coordinate system, and the control equation of the fractional order viscoelastic unsaturated soil is derived by tensor operation: (2a) (2b) (2c) (2d) (2e) (2f) wherein , , , ; , , , , , , , , , .

4. The method for analyzing the pile seismic response considering the lateral inertia effect according to claim 1, wherein, The step 3 is specifically: S31, by decoupling analysis of the multiphase coupled dynamic behavior, the three-phase wave motion field is decomposed into the superposition form of scalar potential (Φ) and vector potential (Ψ), so as to construct a systematic description framework of longitudinal wave and transverse wave modal characteristics; wherein the relative motion between phases is expressed in the following form: (3) S32, the dynamic potential function (3) is used to decouple the unsaturated soil control equation (2), and the system is dimensionless to improve the universality of the model and simplify the numerical solution process, and the coupled equation is obtained in the form of matrix as: (4) (5) wherein , , , , , , , , , , , , , , , ( ) denotes a dimensionless form;​ S33、For the existence of non-zero solution of the differential equations, the determinant of the coefficient matrix must satisfy the zero value condition; let and Based on the operator decomposition theory and variable separation method, the mathematical representation forms of the scalar potential function and the vector potential function of each phase displacement field of unsaturated soil are as follows: (6) wherein and denote the zeroth order first and second kind modified Bessel functions, respectively, and are constants determined by the boundary conditions; the constants C 11 , C 12 , C 21 , C 22 , C 31 , C 32 , C 41 , and C 42 satisfy the following constraint relations: (7) wherein , and are the roots of the equation: (8) S34, according to the assumption in step S1, the radial displacement expressions of pore water and pore gas are specifically as follows: (9) (10) In the formulae, , ; S35, according to the assumption in step S1, based on the analysis of the dynamic coupling effect of the pile-soil contact surface, the interface shear stress expression is: (11) In the formulae, , , , ， ； S36, based on the three-dimensional wave motion theory coupling analysis of the pile-soil, the vertical vibration displacement response of the contact interface can be analytically characterized in the following form: (12) In the formulae, ; S37, the transverse displacement response form of the solid skeleton can be characterized as: (13) In the formulae, .

5. The method for analyzing the pile seismic response considering the lateral inertia effect according to claim 1, wherein, The step 4 is specifically: S41, in the analysis of the seismic response of the free field, the soil body is usually assumed to be homogeneous in the horizontal direction, and the seismic wave is mainly propagated vertically; based on the wave motion theory of porous elastic medium, the displacement field of each point in the soil layer can be modeled by a one-dimensional wave motion equation, and thus the vertical wave motion control equation of the unsaturated soil body is as follows: (14) In the formula, The displacement response field distribution of the solid skeleton, pore water and pore gas in the free field of unsaturated soil is respectively characterized; , ， ， ； S42, using the operator decomposition theory, the free field displacement expressions of the solid skeleton, pore water and pore gas are: (15) In the formula, , u g represents the P-wave displacement amplitude; S43, based on the linear superposition theory, the comprehensive displacement response expression of the pile-soil coupling vibration system is: (16) (17) (18)。 6. The method for analyzing the pile seismic response considering the lateral inertia effect according to claim 1, wherein, The step 5 includes the following specific steps: S51, based on the Rayleigh-Love rod wave theory, and Laplace integral transformation and dimensionless processing are performed on the pile foundation equation, and the dimensionless control equation in the frequency domain is derived as follows: (19) In the formulae, , ; S52, substituting formula (11) into formula (19) can obtain the vertical vibration displacement solution of the pile, which can be expressed as: (20) where M and N are arbitrary constants, and ; S53、Since The transverse vibration displacement of the pile is (21)。 7. The method for analyzing the pile seismic response considering the lateral inertia effect according to claim 1, wherein, The step 6 includes the following specific steps: S61, according to the pile-soil continuity condition in step S1, substituting formula (12), (13), (15) and (16) into formula (20) and (21) can obtain: (22) (23) S62, let Based on the hyperbolic cosine function characteristics and its mathematical relevance with the cosine function, the following expression can be derived: (24) S63, φ 1n , φ 2n and φ 3n Substituting the expressions of φ 1n , φ 2n and φ 3n into equations (22) and (23) gives (25) (26) wherein η 1n , η 2n , η 3n and η 4n are expressed by the following formulae: S64、based on the orthogonal function characteristics, multiply the same on both sides of formula (25) And perform an orthogonal integral operation within the domain The following eigen equation can be derived: (27) In the formulae, ; S65、Based on the orthogonal function characteristics, the same multiplication on both sides of formula (26) is performed , and the orthogonal integral operation is performed within the definition domain , and the following eigen equation can be derived: (28) S66, solving formula (27) and formula (28) at the same time can obtain: (29) (30) In the formula, (31) (32) (33) S67, the dynamic boundary constraint conditions of the coupling interface between the pile top and the pile bottom under the excitation of the P wave of the earthquake are: (34) (35) S68, substituting formula (20) into formula (34) and (35) can obtain: (36) S69, the pile top kinematic amplification coefficient (A v ) and the pile-soil coupling kinematic response coefficient (I v ) two core evaluation indexes, the system represents the pile-soil system seismic dynamic response characteristics, which are defined as follows: (37) (38)。 8. A system for carrying out the analytical method according to any one of claims 1 to 7, characterized in that, Including: The input module is used for receiving the pile-soil parameters, the seismic wave parameters and the boundary conditions; The modeling module is used for constructing the fractional order viscoelastic model of the unsaturated soil and the Rayleigh-Love pile body model; The solving module is used for solving the pile-soil coupling vibration response based on the potential function and the operator decomposition method; The output module is used for outputting the pile top amplification coefficient, the pile-soil coupling response coefficient and the displacement and stress distribution results; The display module is used for visually displaying the seismic response analysis results.

9. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to realize the analysis method of any one of claims 1 to 7.

10. Use of the method according to any one of claims 1 to 7 in the seismic design of geotechnical engineering, characterized in that, It is suitable for the seismic design of pile foundation in complex geological environments such as coastal beach, groundwater fluctuation area and unsaturated loess area.

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