Method and device for analyzing torsional vibration of pipe pile in transverse isotropic unsaturated soil based on fractional derivative model and electronic equipment

Abstract

The invention provides a method and device for analyzing torsional vibration of a pipe pile in transverse isotropic unsaturated soil based on a fractional derivative model and electronic equipment. The method for analyzing the torsional vibration of the tubular pile in the transverse isotropic unsaturated soil based on the fractional derivative model comprises the following steps of: setting assumed conditions, introducing transverse isotropic and fractional derivative Kelvin viscoelastic models, constructing a three-dimensional constitutive relationship between pile peripheral soil and pile core soil, and constructing a torsional vibration model of the tubular pile in the transverse isotropic unsaturated soil. Obtaining a motion equation of the transverse isotropic unsaturated viscoelastic soil under the cylindrical coordinate system; deducing a seepage continuity equation of the transverse isotropic unsaturated soil; establishing a power control equation of the transverse isotropic unsaturated soil body; a tubular pile torsional vibration control equation based on an Euler-Bernoulli rod is established; deducing the torsion dynamic response of the pipe pile in the frequency domain; and the torsional vibration of the pipe pile is analyzed, and an analysis result is obtained. The purpose of improving the prediction precision of the dynamic response of the tubular pile under the complex soil body condition is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of engineering soil dynamics, and in particular relates to a torsional vibration analysis method, device and electronic equipment of a pipe pile in transversely isotropic unsaturated soil based on a fractional derivative model. Background Art

[0002] In geotechnical engineering, pile foundation is an important foundation form widely used in various buildings and structures. With the continuous improvement of foundation performance requirements in modern engineering, traditional pile foundation analysis methods can no longer meet the needs of accurate prediction under complex soil conditions. Pipe piles, as a common foundation treatment method, are widely used in the construction of buildings and infrastructure. Traditional mechanical analysis of pipe piles mainly focuses on vertical and horizontal bearing capacity, but with the improvement of engineering requirements, the torsional dynamic characteristics of pipe pile-soil interaction become particularly important under complex soil conditions, especially in transversely isotropic unsaturated soils.

[0003] Existing analysis methods are mostly based on classical mechanical models of integer derivatives, which have certain limitations when dealing with certain special soil properties and complex boundary conditions. In particular, the accuracy and applicability of traditional models are insufficient when describing the rheological properties and anisotropic characteristics of unsaturated soils. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention provides a torsional vibration analysis method, device and electronic equipment for pipe piles in transversely isotropic unsaturated soil based on a fractional derivative model, which at least partially solves the accuracy and applicability problems existing in the prior art.

[0005] In a first aspect, an embodiment of the present invention provides a method for analyzing torsional vibration of a pipe pile in transversely isotropic unsaturated soil based on a fractional derivative model, comprising:

[0006] S1: Set the assumptions. The assumptions are as follows: the soil is assumed to be a transversely isotropic, viscoelastic and homogeneous three-phase unsaturated porous medium, and each phase is compressible; the upper surface of the soil inside and outside the pipe pile is a free boundary, without normal or shear stress, and the soil surface is permeable to water and air; it is assumed that during the torsional vibration process, the pile-soil interface is continuous and gapless, and the system conforms to the small deformation assumption, and the vertical and radial displacements of the soil around the pile and the soil in the pile core are not considered;

[0007] S2: Based on the assumptions, the transversely isotropic and fractional derivative Kelvin viscoelastic models are introduced to construct the three-dimensional constitutive relationship of the soil around the pile and the soil in the pile core, and the motion equation of the transversely isotropic unsaturated viscoelastic soil in the cylindrical coordinate system is obtained;

[0008] S3: Considering the capillary pressure and inertial coupling effects between the liquid and gas phases, the seepage continuity equation for transversely isotropic unsaturated soil is derived;

[0009] S4: Combine step S2 and step S3 to establish the dynamic control equation of the transversely isotropic unsaturated soil based on the fractional derivative theory;

[0010] S5: Establish the control equation of the torsional vibration of the pipe pile based on the Euler-Bernoulli rod;

[0011] S6: The dynamic control equations of the transversely isotropic unsaturated soil around and in the pile core based on the fractional derivative theory are derived by the variable separation method. The boundary conditions and continuity conditions of the pile-soil interface are considered. Based on the pile torsional vibration control equation, the torsional dynamic response of the middle pipe pile in the frequency domain is derived.

[0012] S7: Using Fourier transform and convolution theorem, based on the torsional dynamic response of the pipe pile in the pilot frequency domain, the velocity and displacement time history curves of the pile top under the semi-sine excitation load in the time domain are derived, and the torsional vibration of the pipe pile is analyzed to obtain the analysis results.

[0013] Optionally, step S2 includes:

[0014] S21. Based on the elastic theory, the vibration equilibrium equation of the soil around and inside the pile is derived in axisymmetric coordinates;

[0015] S22. In order to accurately and reasonably describe the mechanical properties of the soil around and inside the pile, the fractional derivative Kelvin-Voigt viscoelasticity and transversely isotropic model are used to characterize the stress-strain relationship;

[0016] S23. For the torsional resonance problem of pipe piles embedded in viscoelastic soil, only the circumferential displacement of the soil around and inside the pipe pile is considered, while the vertical and radial displacements are ignored. Based on the vibration equilibrium equation and stress-strain relationship of the soil around and inside the pipe pile, the torsional vibration equation in the form of circumferential displacement of the fractional-order viscoelastic unsaturated transversely isotropic soil is established, thereby obtaining the motion equation of the transversely isotropic unsaturated viscoelastic soil in the cylindrical coordinate system.

[0017] Optionally, the vibration equilibrium equation of the soil around and inside the pile that is derived in step S21 includes:

[0018] The vibration equilibrium equations of the soil around and inside the pipe pile are derived based on the stress tensor and displacement components of the soil around and inside the pipe pile, the absolute mass density of the soil skeleton, liquid phase and gas phase, the soil porosity and the soil saturation.

[0019] Optionally, characterizing the stress-strain relationship in step S22 includes:

[0020] The stress-strain relationship is characterized based on the elastic constant tensor elements of transversely isotropic materials, the pore water pressure and pore gas pressure of the soil around and inside the piles, the solid skeleton bulk modulus of the soil around and inside the piles, the model parameters of the fractional derivative viscoelastic constitutive model, and the α-order Riemann-Liouville fractional derivative.

[0021] Optionally, the torsional vibration control equation of the pipe pile based on the Euler-Bernoulli rod is established in S5, including:

[0022] Treat the pile as an Euler-Bernoulli bar and take into account the damping coefficient of the pile material , the dynamic balance analysis of the pile differential unit is carried out, and the control equation of the torsional vibration of the pipe pile is obtained.

[0023] Optionally, the control equation of the torsional vibration of the pipe pile includes:

[0024] Torsion angle, shear modulus, polar moment of inertia and mass density of the pile.

[0025] Optionally, the boundary conditions and continuity conditions of the pile-soil interface considered in S6 include:

[0026] Boundary conditions of solid, liquid and gas phases on the surface outside and inside the pile;

[0027] Boundary conditions of the solid, liquid and gas phases outside and inside the pile at the bottom;

[0028] The displacement of the soil outside the pipe pile, the displacement of the soil inside the pipe pile, the continuity condition between the pipe pile and the soil around the pile, and the continuity condition between the pipe pile and the soil in the pile core.

[0029] In a second aspect, an embodiment of the present invention further provides a method and device for analyzing torsional vibration of a pipe pile in transversely isotropic unsaturated soil based on a fractional derivative model, comprising:

[0030] The condition setting module is used to set the assumptions. The assumptions are as follows: the soil is assumed to be a three-phase unsaturated porous medium that is transversely isotropic, viscoelastic, and homogeneous, and each phase is compressible; the upper surface of the soil inside and outside the pipe pile is a free boundary, without normal or shear stress, and the soil surface is permeable to water and air; it is assumed that during the torsional vibration process, the pile-soil interface is continuous and gapless, and the system conforms to the small deformation assumption, and the vertical and radial displacements of the soil around the pile and the soil in the pile core are not considered;

[0031] The construction module is used to introduce the transversely isotropic and fractional derivative Kelvin viscoelastic models based on the assumptions, construct the three-dimensional constitutive relationship of the soil around the pile and the soil in the pile core, and obtain the motion equation of the transversely isotropic unsaturated viscoelastic soil in the cylindrical coordinate system;

[0032] A derivation module for deriving the seepage continuity equation for transversely isotropic unsaturated soils taking into account the capillary pressure and inertial coupling effects between the liquid and gas phases;

[0033] Building module, used to combine the building module and the derivation module, and to establish the dynamic control equations of transversely isotropic unsaturated soil based on fractional derivative theory;

[0034] Torsional vibration module, used to establish the control equation of torsional vibration of pipe piles based on Euler-Bernoulli rod;

[0035] A response module is used to derive the dynamic control equations of the transversely isotropic unsaturated soil around the pile and the pile core based on the fractional derivative theory by using the variable separation method, consider the boundary conditions and continuity conditions of the pile-soil interface, and derive the torsional dynamic response of the middle pipe pile in the frequency domain based on the pipe pile torsional vibration control equation;

[0036] The analysis module is used to derive the velocity and displacement time history curves of the pile top under the semi-sine excitation load in the time domain based on the torsional dynamic response of the pipe pile in the pilot frequency domain by using Fourier transform and convolution theorem, analyze the torsional vibration of the pipe pile, and obtain the analysis result.

[0037] In a third aspect, an embodiment of the present invention further provides an electronic device, the electronic device comprising:

[0038] at least one processor; and,

[0039] a memory communicatively connected to the at least one processor; wherein,

[0040] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the torsional vibration analysis method of pipe piles in transversely isotropic unsaturated soil based on the fractional derivative model as described in any one of the first aspects.

[0041] The invention provides a method, device and electronic device for analyzing torsional vibration of pipe piles in transversely isotropic unsaturated soil based on a fractional derivative model. The method for analyzing torsional vibration of pipe piles in transversely isotropic unsaturated soil based on a fractional derivative model introduces fractional derivative theory to overcome the limitations of traditional analysis methods in dealing with rheological properties and memory effect of unsaturated soil, thereby achieving the purpose of improving the prediction accuracy of dynamic response of pipe piles under complex soil conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The above and other objects, features and advantages of the present invention will become more apparent through a more detailed description of exemplary embodiments of the present invention in conjunction with the accompanying drawings, wherein like reference numerals generally represent like components throughout the exemplary embodiments of the present invention.

[0043] Figure 1 It is a flow chart of a method for analyzing torsional vibration of a pipe pile in transversely isotropic unsaturated soil based on a fractional derivative model disclosed in an embodiment of the present invention;

[0044] Figure 2 A schematic diagram of a fractional-order viscoelastic model disclosed in an embodiment of the present invention;

[0045] Figure 3 This is a schematic diagram of a pipe pile-soil model disclosed in an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0047] It should be clear that the following embodiments of the present invention are described by specific specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in the field without making creative work belong to the scope of protection of the present invention.

[0048] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. It should be understood by those skilled in the art based on the invention that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this device and / or practice this method.

[0049] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention. The illustrations only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0050] Additionally, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects described may be practiced without these specific details.

[0051] As a mathematical tool that can describe the memory effect and non-local characteristics of materials, the fractional derivative model shows unique advantages in dealing with the mechanical behavior of complex media.

[0052] Transversely isotropic unsaturated soil is a soil with special mechanical properties, which exhibits different mechanical responses in different directions. This characteristic places higher demands on the dynamic analysis of pile foundations. The fractional derivative model can more accurately describe the complex dynamic behavior of this type of soil, providing theoretical support for the design and optimization of pile foundations in unsaturated soils.

[0053] like Figure 1 , Figure 2 and Figure 3 As shown, this embodiment discloses a method for analyzing torsional vibration of a pipe pile in transversely isotropic unsaturated soil based on a fractional derivative model, comprising the following steps:

[0054] S1: Consider the following assumptions: the soil is a transversely isotropic, viscoelastic, homogeneous three-phase unsaturated porous medium, and each phase is compressible; the upper surface of the soil inside and outside the pipe pile is a free boundary, without normal or shear stress, and the soil surface is permeable to water and air; it is assumed that during the torsional vibration process, the pile-soil interface is continuous and gapless, and the system conforms to the small deformation assumption; the vertical and radial displacements of the soil around the pile and the soil in the pile core are not considered;

[0055] S2: The transversely isotropic and fractional derivative Kelvin viscoelastic models are introduced to construct the three-dimensional constitutive relationship of the soil around the pile and the soil in the pile core, and the motion equation of the transversely isotropic unsaturated viscoelastic soil in the cylindrical coordinate system is obtained;

[0056] S3: Considering the capillary pressure and inertial coupling effects between the liquid and gas phases, the seepage continuity equation for transversely isotropic unsaturated soil is derived;

[0057] S4: Combine step S2 and step S3 to establish the dynamic control equation of the transversely isotropic unsaturated soil based on the fractional derivative theory;

[0058] S5: Establish the control equation of the torsional vibration of the pipe pile based on the Euler-Bernoulli rod;

[0059] S6: The dynamic governing equations of the transversely isotropic unsaturated soil around and in the pile core are derived based on the fractional derivative theory by the separation of variables method. The torsional dynamic response of the mid-tube pile in the frequency domain is derived by considering the boundary conditions and continuity conditions of the pile-soil interface.

[0060] S7: Using Fourier transform and convolution theorem, the velocity and displacement time history curves of the pile top under half-sine excitation load in the time domain are derived to analyze the torsional vibration of the pipe pile.

[0061] According to the assumption in step S1, step S2 is specifically as follows:

[0062] S21, β = 1 represents the unsaturated viscoelastic soil around the pile, while β = 2 represents the unsaturated viscoelastic soil inside the pile. The vibration equilibrium equations of the soil around and inside the pile are derived according to the elastic theory in axisymmetric coordinates as follows:

[0063] (1a),

[0064] (1b),

[0065] (1c),

[0066] in, denote the stress tensor and displacement components of the soil around and inside the pile, respectively. , , and Represent the absolute mass density of soil skeleton, liquid phase and gas phase respectively; n β represents the soil porosity, S rβ Indicates the degree of soil saturation.

[0067] S22. In order to accurately and reasonably describe the mechanical properties of the soil around and inside the pile, the fractional derivative Kelvin-Voigt viscoelasticity and transversely isotropic model are used to characterize the stress-strain relationship. Therefore, based on the fractional derivative model, the stress-displacement relationship of the transversely isotropic unsaturated soil is as follows:

[0068] (2a),

[0069] (2b),

[0070] (2c),

[0071] (2d),

[0072] (2e),

[0073] (2f),

[0074] Among them, C 11β , C 12β , C 13β , C 33β , C 44β and C 66β represents the elastic constant tensor element of the transversely isotropic material; p wβ and p aβ Indicates the pore water pressure and pore gas pressure of the soil around and inside the pile; K sβ Represents the bulk modulus of the solid skeleton of the soil around and inside the pile; , , and represent the model parameters of the fractional derivative viscoelastic constitutive model respectively; represents the α-order Riemann-Liouville fractional derivative, which is expressed as:

[0075] (3),

[0076] S23. For the torsional resonance problem of pipe piles embedded in viscoelastic soil, in order to simplify the calculation, only the circumferential displacement of the soil around and inside the pipe pile is considered, while the vertical and radial displacements are ignored. In this case, based on formulas (1) to (3), the torsional vibration equation of the circumferential displacement form of the fractional-order viscoelastic unsaturated transversely isotropic soil is established as follows:

[0077] (4),

[0078] In step 3, considering the capillary pressure and inertial coupling effects between the liquid phase and the gas phase, the seepage continuity equation of the transversely isotropic unsaturated soil is obtained as follows:

[0079] (5a),

[0080] (5b),

[0081] in, , , , , , , , , , .

[0082] Step S4, by combining equations (4) and (5), the dynamic control equation of the transversely isotropic unsaturated soil can be obtained as follows:

[0083] (6a),

[0084] (6b),

[0085] (6c),

[0086] in, , , represents the viscosity coefficient, , , , , , , .

[0087] Step S5, consider the pile as an Euler-Bernoulli bar and consider the damping coefficient of the pile material , the dynamic balance analysis of the pile differential unit is carried out, and the equation of the torsional vibration of the pipe pile is obtained as follows:

[0088] (7),

[0089] in, represents the torsion angle, , and are the shear modulus, polar moment of inertia and mass density of the pile, .

[0090] Preferably, the boundary conditions between the pile and the soil and the pile-soil continuity conditions are:

[0091] The boundary conditions of the solid, liquid and gas phases on the surface of the pile are:

[0092] (8),

[0093] (9),

[0094] The boundary conditions of the solid phase, liquid phase and gas phase at the bottom of the pile are:

[0095] (10),

[0096] (11),

[0097] The displacement of the soil outside the pile approaches zero at infinity:

[0098] (12),

[0099] The displacement of the soil inside the pile is a finite value:

[0100] (13),

[0101] The boundary conditions at the top and bottom of the pile are:

[0102] (14),

[0103] (15),

[0104] The continuity condition between the pipe pile and the soil around the pile is:

[0105] (16),

[0106] (17),

[0107] The continuity condition between the pipe pile and the pile core soil is:

[0108] (18),

[0109] (19),

[0110] Preferably, step 6 comprises the following specific steps:

[0111] S61: Solve the dynamic control equation of the soil around the pile. Specifically, substitute equations (6b) and (6c) into equation (6a) to obtain:

[0112] (20),

[0113] In the formula, .

[0114] Using the separation of variables method, , substituting it into formula (20) we can get:

[0115] (twenty one),

[0116] Formula (21) can be expressed again as:

[0117] (twenty two),

[0118] (twenty three),

[0119] In the formula, the constant and The following relationship needs to be satisfied:

[0120] (twenty four),

[0121] Solving equations (22) and (23), the general solution of the circumferential displacement of the soil around the pile is obtained as:

[0122] (25),

[0123] In the formula, and is an arbitrary constant whose value depends on the boundary conditions; and denote the modified Bessel functions of the first and second kind, respectively.

[0124] Substituting equation (25) into equations (8), (10) and (12), we can obtain:

[0125] (26),

[0126] (27),

[0127] Substituting equation (26) into equation (25), the circumferential displacement of the solid phase of the soil around the pile can be obtained as:

[0128] (28),

[0129] Substituting equation (28) into equation (17), we can obtain the friction force of the soil around the pile on the pipe pile:

[0130] (29),

[0131] S62: Solving the dynamic control equation of the pile core soil is consistent with the idea of ​​deriving the displacement of the soil around the pile. The circumferential displacement of the pile core soil is obtained as:

[0132] (30),

[0133] Substituting equation (30) into equations (9), (11) and (13), we can obtain:

[0134] (31),

[0135] (32),

[0136] Substituting equation (31) into equation (30), the circumferential displacement of the solid phase of the soil around the pile can be obtained as:

[0137] (33),

[0138] Substituting equation (33) into equation (19), we can obtain the friction force of the pile core soil on the pipe pile:

[0139] (34),

[0140] S63: Solve the dynamic control equations of the coupling system between the pipe pile and the soil around the pile and the pile core soil, specifically:

[0141] Substituting equation (29) and equation (34) into equation (7), we can obtain:

[0142] (35),

[0143] in, , .

[0144] Solving equation (35), we can get the torsion angle of the pile as:

[0145] (36),

[0146] in, , , .

[0147] Substituting equation (36) into equations (16) and (18), we can obtain:

[0148] (37),

[0149] (38),

[0150] Combining equation (37) and equation (38), we can get:

[0151] (39),

[0152] (40),

[0153] because , can be made , processing formula (37) yields:

[0154] (41),

[0155] in,

[0156] (42), (43),

[0157] Substituting formula (41) into formula (40), we can obtain:

[0158] (44),

[0159] Combining equation (36) with equation (14) and (15), we can obtain:

[0160] (45),

[0161] (46),

[0162] Substituting equations (41), (44), (45) and (46) into (36), the torsion angle of the pile is obtained as:

[0163] (47),

[0165] S64: The dimensionless torsional complex impedance of the pile top is:

[0166] (48),

[0167] In the formula, and It represents dynamic stiffness and dynamic damping, which respectively reflect the ability of the pile to resist deformation and the energy dissipation characteristics of the pile-soil system.

[0168] S65: The expression of the velocity admittance of the pile top is as follows:

[0169] (49),

[0170] In the formula, is the dimensionless parameter of velocity admittance, and its specific expression is:

[0171] (50),

[0172] S66: The torque applied to the top of the pile during the excitation process is usually simplified to a half-sine acceleration pulse and is expressed as:

[0173] (51),

[0174] By using the inverse Fourier transform and convolution theorem, the velocity response function of the pile top can be effectively derived, which can be used to detect the integrity of the pile body. The specific expression is:

[0175] (52),

[0176] The expression of dimensionless velocity response can be expressed as:

[0177]

[0178] In the formula, , , , .

[0179] According to formula (47), the torque expression of the pile body can be derived as:

[0180] (53).

[0181] The embodiment of the present invention is based on the fractional derivative model of the torsional vibration complex impedance calculation system of pipe piles in transversely isotropic unsaturated soil. The soil around the pipe piles and the soil in the pile core are both considered to be a porous viscoelastic soil mixed with solid, liquid and gas three phases, which is undoubtedly closer to the actual situation. The method disclosed in this embodiment can be completely degraded to the torsional vibration response of the pile foundation in saturated soil or single-phase elastic soil foundation. In addition, the pipe piles can also be degraded into solid piles. Therefore, the method disclosed in this embodiment has a wide range of applications, and the calculation results are more in line with actual projects. It can provide a theoretical basis for the scientificity and reliability of the design and construction of pipe piles in engineering fields such as bridges, docks, subways, and highways.

[0182] The embodiment of the present invention further discloses a method and device for analyzing torsional vibration of a pipe pile in transversely isotropic unsaturated soil based on a fractional derivative model, comprising:

[0183] The condition setting module is used to set the assumptions. The assumptions are as follows: the soil is assumed to be a three-phase unsaturated porous medium that is transversely isotropic, viscoelastic, and homogeneous, and each phase is compressible; the upper surface of the soil inside and outside the pipe pile is a free boundary, without normal or shear stress, and the soil surface is permeable to water and air; it is assumed that during the torsional vibration process, the pile-soil interface is continuous and gapless, and the system conforms to the small deformation assumption, and the vertical and radial displacements of the soil around the pile and the soil in the pile core are not considered;

[0184] The construction module is used to introduce the transversely isotropic and fractional derivative Kelvin viscoelastic models based on the assumptions, construct the three-dimensional constitutive relationship of the soil around the pile and the soil in the pile core, and obtain the motion equation of the transversely isotropic unsaturated viscoelastic soil in the cylindrical coordinate system;

[0185] A derivation module for deriving the seepage continuity equation for transversely isotropic unsaturated soils taking into account the capillary pressure and inertial coupling effects between the liquid and gas phases;

[0186] Building module, used to combine the building module and the derivation module, and to establish the dynamic control equations of transversely isotropic unsaturated soil based on fractional derivative theory;

[0187] Torsional vibration module, used to establish the control equation of torsional vibration of pipe piles based on Euler-Bernoulli rod;

[0188] A response module is used to derive the dynamic control equations of the transversely isotropic unsaturated soil around the pile and the pile core based on the fractional derivative theory by using the variable separation method, consider the boundary conditions and continuity conditions of the pile-soil interface, and derive the torsional dynamic response of the middle pipe pile in the frequency domain based on the pipe pile torsional vibration control equation;

[0189] The analysis module is used to derive the velocity and displacement time history curves of the pile top under the semi-sine excitation load in the time domain based on the torsional dynamic response of the pipe pile in the pilot frequency domain by using Fourier transform and convolution theorem, analyze the torsional vibration of the pipe pile, and obtain the analysis result.

[0190] In addition, an embodiment of the present invention further discloses an electronic device, the electronic device comprising:

[0191] at least one processor; and,

[0192] a memory communicatively connected to the at least one processor; wherein,

[0193] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute all or part of the steps of the torsional vibration analysis method of pipe piles in transversely isotropic unsaturated soil based on the fractional derivative model disclosed in this embodiment.

[0194] The basic principle of the present invention is described above in conjunction with specific embodiments. However, it should be pointed out that the advantages, strengths, effects, etc. mentioned in the present invention are only examples and not limitations, and it cannot be considered that these advantages, strengths, effects, etc. must be possessed by each embodiment of the present invention. In addition, the specific details disclosed above are only for the purpose of illustration and facilitation of understanding, rather than limitation, and the above details do not limit the present invention to being implemented by adopting the above specific details.

[0195] In the present invention, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is any such actual relationship or order between these entities or operations. The block diagrams of the devices, devices, equipment, and systems involved in the present invention are only illustrative examples and are not intended to require or imply that they must be connected, arranged, and configured in the manner shown in the block diagram. As will be appreciated by those skilled in the art, these devices, devices, equipment, and systems can be connected, arranged, and configured in any manner. Words such as "including", "comprising", "having", etc. are open words, referring to "including but not limited to", and can be used interchangeably with them. The words "or" and "and" used here refer to the words "and / or" and can be used interchangeably with them, unless the context clearly indicates otherwise. The words "such as" used here refer to the phrase "such as but not limited to", and can be used interchangeably with them.

[0196] Additionally, as used herein, "or" used in a list of items beginning with "at least one" indicates a separate list, so that, for example, a list of "at least one of A, B, or C" means A or B or C, or AB or AC or BC, or ABC (i.e., A and B and C). Furthermore, the word "exemplary" does not mean that the example described is preferred or better than other examples.

[0197] It should also be noted that in the system and method of the present invention, each component or each step can be decomposed and / or recombined. Such decomposition and / or recombination should be regarded as equivalent solutions of the present invention.

[0198] Various changes, substitutions, and modifications of the techniques described herein may be made without departing from the teachings defined by the appended claims. Furthermore, the scope of the claims of the present invention is not limited to the specific aspects of the processes, machines, manufactures, compositions of events, means, methods, and actions described above. Currently existing or later to be developed processes, machines, manufactures, compositions of events, means, methods, or actions that perform substantially the same functions or achieve substantially the same results as the corresponding aspects described herein may be utilized. Thus, the appended claims include such processes, machines, manufactures, compositions of events, means, methods, or actions within their scope.

[0199] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects without departing from the scope of the present invention. Therefore, the present invention is not intended to be limited to the aspects shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

[0200] The above description has been given for the purpose of illustration and description. In addition, this description is not intended to limit the embodiments of the present invention to the forms disclosed herein. Although a number of example aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, changes, additions and sub-combinations thereof.

Claims

1. A method for torsional vibration analysis of pipe piles in transversely isotropic unsaturated soil based on a fractional derivative model, characterized in that: include: S1: Set the assumptions. The assumptions are as follows: the soil is assumed to be a transversely isotropic, viscoelastic and homogeneous three-phase unsaturated porous medium, and each phase is compressible; the upper surface of the soil inside and outside the pipe pile is a free boundary, without normal or shear stress, and the soil surface is permeable to water and air; it is assumed that during the torsional vibration process, the pile-soil interface is continuous and gapless, and the system conforms to the small deformation assumption, and the vertical and radial displacements of the soil around the pile and the soil in the pile core are not considered; S2: Based on the assumptions, the transversely isotropic and fractional derivative Kelvin viscoelastic models are introduced to construct the three-dimensional constitutive relationship of the soil around the pile and the soil in the pile core, and the motion equation of the transversely isotropic unsaturated viscoelastic soil in the cylindrical coordinate system is obtained; S3: Considering the capillary pressure and inertial coupling effects between the liquid and gas phases, the seepage continuity equation for transversely isotropic unsaturated soil is derived; S4: Combine step S2 and step S3 to establish the dynamic control equation of the transversely isotropic unsaturated soil based on the fractional derivative theory; S5: Establish the control equation of the torsional vibration of the pipe pile based on the Euler-Bernoulli rod; S6: The dynamic control equations of the transversely isotropic unsaturated soil around and in the pile core based on the fractional derivative theory are derived by the variable separation method. The boundary conditions and continuity conditions of the pile-soil interface are considered. Based on the pile torsional vibration control equation, the torsional dynamic response of the middle pipe pile in the frequency domain is derived. S7: Using Fourier transform and convolution theorem, based on the torsional dynamic response of the pipe pile in the pilot frequency domain, the velocity and displacement time history curves of the pile top under the semi-sine excitation load in the time domain are derived, and the torsional vibration of the pipe pile is analyzed to obtain the analysis results.

2. The torsional vibration analysis method of pipe piles in transversely isotropic unsaturated soil based on fractional derivative model according to claim 1 is characterized in that: The step S2 comprises: S21. Based on the elastic theory, the vibration equilibrium equation of the soil around and inside the pile is derived in axisymmetric coordinates; S22. In order to accurately and reasonably describe the mechanical properties of the soil around and inside the pile, the fractional derivative Kelvin-Voigt viscoelasticity and transversely isotropic model are used to characterize the stress-strain relationship; S23. For the torsional resonance problem of pipe piles embedded in viscoelastic soil, only the circumferential displacement of the soil around and inside the pipe pile is considered, while the vertical and radial displacements are ignored. Based on the vibration equilibrium equation and stress-strain relationship of the soil around and inside the pipe pile, the torsional vibration equation in the form of circumferential displacement of the fractional-order viscoelastic unsaturated transversely isotropic soil is established, thereby obtaining the motion equation of the transversely isotropic unsaturated viscoelastic soil in the cylindrical coordinate system.

3. The torsional vibration analysis method of pipe piles in transversely isotropic unsaturated soil based on fractional derivative model according to claim 2 is characterized in that: The vibration equilibrium equation of the soil around and inside the pile derived in step S21 includes: The vibration equilibrium equations of the soil around and inside the pipe pile are derived based on the stress tensor and displacement components of the soil around and inside the pipe pile, the absolute mass density of the soil skeleton, liquid phase and gas phase, the soil porosity and the soil saturation.

4. The method for analyzing torsional vibration of pipe piles in transversely isotropic unsaturated soil based on fractional derivative model according to claim 2 is characterized in that: Characterizing the stress-strain relationship in step S22 includes: The stress-strain relationship is characterized based on the elastic constant tensor elements of transversely isotropic materials, the pore water pressure and pore gas pressure of the soil around and inside the piles, the solid skeleton bulk modulus of the soil around and inside the piles, the model parameters of the fractional derivative viscoelastic constitutive model, and the α-order Riemann-Liouville fractional derivative.

5. The method for analyzing torsional vibration of pipe piles in transversely isotropic unsaturated soil based on fractional derivative model according to claim 1 is characterized in that: In S5, the torsional vibration control equation of the pipe pile based on the Euler-Bernoulli rod is established, including: Treat the pile as an Euler-Bernoulli bar and take into account the damping coefficient of the pile material , the dynamic balance analysis of the pile differential unit is carried out, and the control equation of the torsional vibration of the pipe pile is obtained.

6. The method for analyzing torsional vibration of pipe piles in transversely isotropic unsaturated soil based on fractional derivative model according to claim 5 is characterized in that: The control equation of the torsional vibration of the pipe pile includes: Torsion angle, shear modulus, polar moment of inertia and mass density of the pile.

7. The method for analyzing torsional vibration of pipe piles in transversely isotropic unsaturated soil based on fractional derivative model according to claim 1 is characterized in that: The boundary conditions and continuity conditions of the pile-soil interface considered in S6 include: Boundary conditions of solid, liquid and gas phases on the surface outside and inside the pile; Boundary conditions of the solid, liquid and gas phases outside and inside the pile at the bottom; The displacement of the soil outside the pipe pile, the displacement of the soil inside the pipe pile, the continuity condition between the pipe pile and the soil around the pile, and the continuity condition between the pipe pile and the soil in the pile core.

8. A method and device for analyzing torsional vibration of pipe piles in transversely isotropic unsaturated soil based on a fractional derivative model, characterized in that: include: The condition setting module is used to set the assumptions. The assumptions are as follows: the soil is assumed to be a three-phase unsaturated porous medium that is transversely isotropic, viscoelastic, and homogeneous, and each phase is compressible; the upper surface of the soil inside and outside the pipe pile is a free boundary, without normal or shear stress, and the soil surface is permeable to water and air; it is assumed that during the torsional vibration process, the pile-soil interface is continuous and gapless, and the system conforms to the small deformation assumption, and the vertical and radial displacements of the soil around the pile and the soil in the pile core are not considered; The construction module is used to introduce the transversely isotropic and fractional derivative Kelvin viscoelastic models based on the assumptions, construct the three-dimensional constitutive relationship of the soil around the pile and the soil in the pile core, and obtain the motion equation of the transversely isotropic unsaturated viscoelastic soil in the cylindrical coordinate system; A derivation module for deriving the seepage continuity equation for transversely isotropic unsaturated soils taking into account the capillary pressure and inertial coupling effects between the liquid and gas phases; Building module, used to combine the building module and the derivation module, and to establish the dynamic control equations of transversely isotropic unsaturated soil based on fractional derivative theory; Torsional vibration module, used to establish the control equation of torsional vibration of pipe piles based on Euler-Bernoulli rod; A response module is used to derive the dynamic control equations of the transversely isotropic unsaturated soil around the pile and the pile core based on the fractional derivative theory by using the variable separation method, consider the boundary conditions and continuity conditions of the pile-soil interface, and derive the torsional dynamic response of the middle pipe pile in the frequency domain based on the pipe pile torsional vibration control equation; The analysis module is used to derive the velocity and displacement time history curves of the pile top under the semi-sine excitation load in the time domain based on the torsional dynamic response of the pipe pile in the pilot frequency domain by using Fourier transform and convolution theorem, analyze the torsional vibration of the pipe pile, and obtain the analysis result.

9. An electronic device, characterized in that: The electronic device comprises: at least one processor; and, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the torsional vibration analysis method of pipe piles in transversely isotropic unsaturated soil based on the fractional derivative model as described in any one of claims 1-7.

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