Method and system for calculating torsion dynamic response of single pile in stratified soil

Abstract

The invention discloses a method and a system for calculating torsion dynamic response of a single pile in stratified soil in the technical field of pile foundation dynamic response analysis in geotechnical engineering. The method comprises the following steps: initializing control variables corresponding to each soil layer according to the layering condition of a layered soil body; iteratively executing the following operations until a preset convergence condition is met: according to the control variable corresponding to each soil layer, obtaining a torsion response characteristic of each soil layer through a soil body torsion response function; according to the torsion response characteristics, a control differential equation and a constraint equation set of each pile section are established, and a solution form of the control differential equation is obtained; calculating a displacement energy integral item, a shear strain energy integral item and a kinetic energy integral item of each soil layer according to a single-pile torsion dynamic response function in the solution form of the control differential equation, and updating a control variable corresponding to each soil layer; and after iteration is finished, a torsion response value at the pile top is calculated according to the converged single pile torsion dynamic response function, and a torsion impedance function of the single pile is obtained based on the torsion response value.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic response analysis of pile foundations in geotechnical engineering, and in particular to a method and system for calculating the torsional dynamic response of a single pile in layered soil. Background Art

[0002] With the development of large-scale infrastructure such as sea-crossing bridges, offshore wind turbines, and offshore floating platforms, the mechanical properties of single pile foundations under complex soil conditions have become a key issue in structural safety assessment. In practical engineering, single piles are often subjected to torsional loads generated by disturbances such as earthquakes, wind and waves, and equipment operation. Their dynamic response is influenced not only by the pile's own characteristics but also by the coupled control of factors such as pile-soil interaction and soil dynamic properties. To accurately assess the dynamic response of pile foundations under dynamic torsional loads, studying their torsional stiffness and soil-pile interaction characteristics is crucial.

[0003] Currently, the main research methods for the torsional dynamic response of single piles include analytical methods, boundary element methods, finite element methods, and impedance function methods. Many of these methods simplify the soil into a homogeneous single layer or elastic medium, or simply fit the shear response characteristics of the soil using simplified models in the frequency domain. While these methods can achieve a certain degree of computational accuracy under homogeneous or nearly homogeneous conditions, foundation soils often exhibit distinct vertical stratification under natural conditions, with significant differences in density, shear modulus, and damping properties between layers. These traditional methods struggle to accurately reflect the interlayer response transmission and the influence of soil parameters on the dynamic response of pile foundations.

[0004] Furthermore, existing research rarely considers the dynamic interaction between soil and piles from the perspective of energy coupling, lacking a modeling mechanism that can directly couple soil shear deformation, inertial effects, and pile responses. Therefore, a method for calculating the torsional dynamic response of piles, suitable for layered soils, with high physical accuracy and iterative control capabilities, is needed to meet the needs of engineering applications in complex foundation environments. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method and system for calculating the torsional dynamic response of a single pile in stratified soil. By establishing an energy coupling relationship between the soil and the pile, the dynamic response of a single pile under torsional load can be modeled and numerically solved in a complex foundation environment. The method is particularly suitable for engineering scenarios where the soil has obvious vertical stratification characteristics.

[0006] In order to solve the above technical problems, the present invention is implemented by adopting the following technical solutions:

[0007] In a first aspect, the present invention provides a method for calculating the torsional dynamic response of a single pile in layered soil, comprising:

[0008] According to the stratification of the stratified soil, the control variables corresponding to each soil layer are initialized;

[0009] Iteratively performs the following operations until the preset convergence conditions are met:

[0010] According to the control variables corresponding to the soil layers, the torsional response characteristics of the soil layers are obtained through the soil torsional response function;

[0011] According to the torsional response characteristics, a control differential equation and a constraint equation group of each pile segment are established;

[0012] Obtaining a solution form of the control differential equation according to the control differential equation and the constraint equation group, wherein the solution form of the control differential equation includes a characteristic root and a single pile torsional dynamic response function;

[0013] Calculating the displacement energy integral term, the shear strain energy integral term, and the kinetic energy integral term of each soil layer according to the single pile torsional dynamic response function;

[0014] updating the control variables corresponding to each soil layer according to the displacement energy integral term, the shear strain energy integral term, and the kinetic energy integral term of each soil layer;

[0015] After the iteration is completed, the torsional response value at the pile top is calculated according to the converged single pile torsional dynamic response function, and the torsional impedance function of the single pile is obtained based on the torsional response value.

[0016] Optionally, the soil torsional response function is as follows:

[0017]

[0018] in, Represents soil, Indicates the serial number, represents the radial coordinate, Indicates the The torsional response attenuation coefficient of the soil layer is represents the first-order modified Bessel function of the second kind, Indicates the Control variables of the soil layer, Indicates the radius of a single pile.

[0019] Optionally, the torsional response characteristics include a shear strain energy term, a displacement response term, and an additional mass term;

[0020] The shear strain energy term is calculated by the following formula:

[0021]

[0022] in, Indicates the The shear strain energy term of the soil layer is Indicates the Dynamic shear modulus of the soil layer, Indicates the The shear modulus of the soil layer, Indicates the The damping ratio of the soil layer, , represents a constant;

[0023] The displacement response term is calculated by the following formula:

[0024]

[0025] in, Indicates the Displacement response term of the soil layer;

[0026] The additional mass term is calculated by the following formula:

[0027]

[0028] in, Indicates the The additional mass term of the soil layer, Indicates the Density of the soil layer.

[0029] Optionally, the control differential equation is as follows:

[0030]

[0031] in, represents the vertical coordinate, represents the torsional dynamic response function of a single pile, represents the shear modulus of a single pile, represents the polar moment of inertia of a single pile, Indicates the The displacement response of the soil layer is Indicates the The shear strain energy term of the soil layer is Indicates the The additional mass term of the soil layer, represents the density of the pile, represents the torsional load frequency;

[0032] The constraint equations are as follows:

[0033]

[0034] in, Indicates that the single pile is Layer soil and The vertical coordinate of the boundary between the soil layers, Indicates that the single pile is The vertical coordinate of the soil layer is The torsional dynamic response value at Indicates that the single pile is The vertical coordinate of the soil layer is The torsional dynamic response value at Indicates the The displacement response of the soil layer is Indicates the vertical coordinate of the top position of the single pile, Indicates the vertical coordinate of the bottom position of the single pile, Indicates the length of a single pile, Indicates the bottom soil number, Indicates that the single pile is The torsional dynamic response value at the vertical coordinate of the bottom position of a single pile in the layer soil, represents the simple harmonic torsional excitation load, represents the amplitude of the simple harmonic torsional excitation load, , Indicates time.

[0035] Optionally, the solution of the control differential equation is in the form of:

[0036]

[0037] in, Indicates the Undetermined coefficients of the general solution of the soil layer, Indicates that the single pile is Characteristic roots of the soil layer, Represents a constant.

[0038] Optionally, the calculation formula for the integral term of the displacement energy of each soil layer is:

[0039]

[0040] in, Indicates the The integral term of the displacement energy of the soil layer is: represents the radius of a single pile, represents a constant;

[0041] The calculation formula for the integral term of the shear strain energy of each soil layer is:

[0042]

[0043] in, Indicates the The integral term of shear strain energy of the soil layer;

[0044] The calculation formula for the kinetic energy integral term of each soil layer is:

[0045]

[0046] in, Indicates the The integral term of kinetic energy of soil layer.

[0047] Optionally, based on the displacement energy integral term, shear strain energy integral term, and kinetic energy integral term of each soil layer, the control variables of each soil layer are updated using the following formula:

[0048]

[0049] in, Indicates the Control variables of the soil layer, Indicates the The integral term of the displacement energy of the soil layer is: Indicates the The integral term of shear strain energy of the soil layer is: Indicates the The integral term of the kinetic energy of the soil layer is: represents the torsional load frequency.

[0050] Optionally, the preset convergence condition is as follows:

[0051]

[0052] in, Indicates the convergence state, Indicates convergence, Indicates non-convergence, Indicates the current round, Indicates the current round Middle Control variables of the soil layer, Indicates the previous round Middle Control variables of the soil layer, Indicates the preset convergence accuracy.

[0053] Optionally, the calculation formula for the torsional response value at the pile top is:

[0054]

[0055] in, represents the torsional response value at the pile top, Indicates the Undetermined coefficients of the general solution of the soil layer, Indicates the Characteristic roots of the soil layer, represents a constant, represents the vertical coordinate at the top of the pile;

[0056] The torsional impedance function of the monopile is as follows:

[0057]

[0058] in, represents the torsional complex impedance of a single pile, Indicates the The shear modulus of the soil layer, represents the amplitude of the simple harmonic torsional excitation load, Indicates the radius of a single pile.

[0059] In a second aspect, the present invention provides a system for calculating the torsional dynamic response of a single pile in stratified soil, applicable to the method for calculating the torsional dynamic response of a single pile in stratified soil according to any one of the first aspects, comprising:

[0060] The initialization module is used to initialize the control variables corresponding to each soil layer according to the stratification of the stratified soil body;

[0061] The iterative update module is used to iteratively perform the following operations until the preset convergence conditions are met:

[0062] According to the control variables corresponding to the soil layers, the torsional response characteristics of the soil layers are obtained through the soil torsional response function;

[0063] According to the torsional response characteristics, a control differential equation and a constraint equation group of each pile segment are established;

[0064] Obtaining a solution form of the control differential equation according to the control differential equation and the constraint equation group, wherein the solution form of the control differential equation includes a characteristic root and a single pile torsional dynamic response function;

[0065] Calculating the displacement energy integral term, the shear strain energy integral term, and the kinetic energy integral term of each soil layer according to the single pile torsional dynamic response function;

[0066] updating the control variables corresponding to each soil layer according to the displacement energy integral term, the shear strain energy integral term, and the kinetic energy integral term of each soil layer;

[0067] The torsional impedance function acquisition module is used to: after the iteration is completed, calculate the torsional response value at the pile top according to the converged single pile torsional dynamic response function, and obtain the torsional impedance function of the single pile based on the torsional response value.

[0068] Compared with the existing technology, the beneficial effects achieved by the present invention are:

[0069] 1. By establishing an iterative mechanism for controlling variables in a soil-pile coupling system in layered soil, we achieve high-precision calculations of the torsional dynamic response of a single pile under complex foundation conditions. Compared with existing calculation methods based on simplified homogeneous soil or semi-analytical fitting, this method offers significant advantages in theoretical integrity, physical accuracy, and engineering adaptability.

[0070] 2. This method is applicable to soil layer systems with any number and parameter configuration, significantly improving the ability to express the heterogeneous characteristics of actual foundations;

[0071] 3. By introducing an iterative structure of control variables based on energy variation, this method fully considers the combined effects of soil shear deformation, added mass, and inertia on pile response, achieving physically self-consistent modeling of the dynamic response process. The pile segment response equation adopts an exponential analytical expression, which achieves high computational efficiency while maintaining theoretical rigor.

[0072] 4. This method is applicable to frequency domain response calculation and modal parameter extraction. It can be widely used in the dynamic analysis and structural design of various pile foundation systems such as offshore wind power pile foundations, floating platform anchor piles, and marine engineering platforms under wind, wave, or seismic loads. It has good application prospects and engineering promotion value. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 Flowchart of a method for calculating the torsional dynamic response of a single pile in layered soil according to an embodiment of the present invention;

[0074] Figure 2 A schematic diagram of a pile-soil model provided according to an embodiment of the present invention;

[0075] Figure 3 A schematic diagram of parameters of a single pile and various soil layers provided according to an embodiment of the present invention;

[0076] Figure 4 Graph showing the calculation results of the real part of the torsional complex impedance of a single pile according to an embodiment of the present invention;

[0077] Figure 5 Calculation results of the imaginary part of the torsional complex impedance of a single pile according to an embodiment of the present invention

[0078] In the figure, 1-single pile, 2-soil. DETAILED DESCRIPTION

[0079] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0080] It should be noted that the term "and / or" in this document simply describes an association between related objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. Furthermore, the character " / " in this document generally indicates that the related objects are in an "or" relationship.

[0081] Example 1:

[0082] The embodiment of the present invention discloses a method for calculating the torsional dynamic response of a single pile in layered soil, referring to Figure 1 Shown, including:

[0083] S1, initialize the control variables corresponding to each soil layer according to the stratification of the stratified soil;

[0084] S2, iteratively performs the following operations until the preset convergence conditions are met:

[0085] S2.1, obtaining the torsional response characteristics of each soil layer through the soil torsional response function according to the control variables corresponding to each soil layer;

[0086] S2.2, establishing the governing differential equations and constraint equations for each pile segment based on the torsional response characteristics;

[0087] S2.3, obtaining a solution form of the governing differential equation based on the governing differential equation and the set of constraint equations, wherein the solution form of the governing differential equation includes a characteristic root and a single pile torsional dynamic response function;

[0088] S2.4, calculating the displacement energy integral, shear strain energy integral, and kinetic energy integral of each soil layer based on the single pile torsional dynamic response function;

[0089] S2.5, updating the control variables corresponding to each soil layer according to the displacement energy integral term, the shear strain energy integral term, and the kinetic energy integral term of each soil layer;

[0090] S3, after the iteration is completed, the torsional response value at the pile top is calculated according to the converged single pile torsional dynamic response function, and the torsional impedance function of the single pile is obtained based on the torsional response value.

[0091] Specifically, in step S1, refer to Figure 2 The pile-soil model used in this embodiment is shown. The soil parameters include the thickness, density, shear modulus and damping ratio of each layer of soil. The single pile parameters include the pile length, pile diameter and pile body torsional stiffness parameters. The soil parameters and single pile parameters in this embodiment are set as reference. Figure 3 As shown; set the initial control variables of each soil layer. The control variables are used to control the attenuation law of the torsional response of the soil layer. Their values will directly affect the Bessel response function. The shape of the soil layer further affects the shear stress transmission capacity of the pile body; in this embodiment, the initial value of the control variable is set to a constant 1.0.

[0092] In step S2, the preset convergence conditions are as follows:

[0093]

[0094] in, Indicates the convergence state, Indicates convergence, Indicates non-convergence, Indicates the current round, Indicates the current round Middle Control variables of the soil layer, Indicates the previous round Middle Control variables of the soil layer, Indicates the preset convergence accuracy.

[0095] In step S2.1, the soil torsional response function is as follows:

[0096]

[0097] in, Represents soil, Indicates the serial number, represents the radial coordinate, Indicates the The torsional response attenuation coefficient of the soil layer is represents the first-order modified Bessel function of the second kind, Indicates the Control variables of the soil layer, Indicates the radius of a single pile.

[0098] The torsional response characteristics include shear strain energy, displacement response, and additional mass. The shear strain energy is calculated using the following formula:

[0099]

[0100] in, Indicates the The shear strain energy term of the soil layer is Indicates the Dynamic shear modulus of the soil layer, Indicates the The shear modulus of the soil layer, Indicates the The damping ratio of the soil layer, , Represents a constant.

[0101] The displacement response term is calculated by the following formula:

[0102]

[0103] in, Indicates the Displacement response of the soil layer.

[0104] The additional mass term is calculated by the following formula:

[0105]

[0106] in, Indicates the The additional mass term of the soil layer, Indicates the Density of the soil layer.

[0107] In step S2.2, the governing differential equation is constructed based on the total energy variation principle of the pile-soil system, and its expression is as follows:

[0108]

[0109] in, represents the vertical coordinate, represents the torsional dynamic response function of a single pile, represents the shear modulus of a single pile, represents the polar moment of inertia of a single pile, Indicates the The displacement response of the soil layer is Indicates the The shear strain energy term of the soil layer is Indicates the The additional mass term of the soil layer, represents the density of the pile, represents the torsional load frequency.

[0110] The expression of the constraint equations is as follows:

[0111]

[0112] in, Indicates that the single pile is Layer soil and The vertical coordinate of the boundary between the soil layers, Indicates that the single pile is The vertical coordinate of the soil layer is The torsional dynamic response value at Indicates that the single pile is The vertical coordinate of the soil layer is The torsional dynamic response value at Indicates the The displacement response of the soil layer is Indicates the vertical coordinate of the top position of the single pile, Indicates the vertical coordinate of the bottom position of the single pile, Indicates the length of a single pile, Indicates the bottom soil number, Indicates that the single pile is The torsional dynamic response value at the vertical coordinate of the bottom position of a single pile in the layer soil, represents the simple harmonic torsional excitation load, represents the amplitude of the simple harmonic torsional excitation load, , Indicates time.

[0113] The process of establishing the constraint equation group includes:

[0114] The continuity condition of the pile rotation response is established at the interface between adjacent soil layers to ensure the Layer soil and The torsional dynamic response function of the pile segment in the soil layer is at the connection point Satisfaction ;

[0115] Establish the continuity condition of shear stress response at the interface of adjacent soil layers to ensure the Layer soil and The shear stress function of the pile segment in the soil layer satisfies ;

[0116] At the top of the pile Position meets external torque boundary conditions ;

[0117] At the bottom of the pile The position satisfies the displacement boundary condition , that is, the torsional deformation at the bottom of the pile is zero;

[0118] Combining the above continuity conditions and boundary conditions, we can obtain a set of constraint equations.

[0119] In step S2.3, the solution of the control differential equation is:

[0120]

[0121] in, Indicates the Undetermined coefficients of the general solution of the soil layer, Indicates that the single pile is Characteristic roots of the soil layer, Represents a constant.

[0122] In step S2.4, the calculation formula for the integral term of the displacement energy of each soil layer is:

[0123]

[0124] in, Indicates the The integral term of the displacement energy of the soil layer is: represents the radius of a single pile, Represents a constant.

[0125] The calculation formula for the integral term of the shear strain energy of each soil layer is:

[0126]

[0127] in, Indicates the The integral term of shear strain energy of the soil layer.

[0128] The calculation formula for the kinetic energy integral term of each soil layer is:

[0129]

[0130] in, Indicates the The integral term of kinetic energy of soil layer.

[0131] In step S2.5, based on the displacement energy integral term, shear strain energy integral term, and kinetic energy integral term of each soil layer, the control variables of each soil layer are updated using the following formula:

[0132]

[0133] in, Indicates the Control variables of the soil layer, Indicates the The integral term of the displacement energy of the soil layer is: Indicates the The integral term of shear strain energy of the soil layer is: Indicates the The integral term of the kinetic energy of the soil layer is: represents the torsional load frequency.

[0134] In step S3, the calculation formula of the torsional response value at the pile top is:

[0135]

[0136] in, represents the torsional response value at the pile top, Indicates the Undetermined coefficients of soil layers, Indicates the Characteristic roots of the soil layer, represents a constant, represents the vertical coordinate at the top of the pile;

[0137] The torsional impedance function of the monopile is as follows:

[0138]

[0139] in, represents the torsional complex impedance of a single pile, Indicates the The shear modulus of the soil layer, represents the amplitude of the simple harmonic torsional excitation load, Indicates the radius of a single pile.

[0140] In this embodiment, the convergence of all control variables was achieved through three rounds of iteration. The calculation process was stable and the convergence speed was fast. In order to further analyze the influence of soil layer distribution on the torsional response of the pile, different first layer soil thicknesses were selected as variables and their ratio to the pile length was set to Take 0.2, 0.4, 0.6, 0.8 and 1.0 respectively and perform comparative calculations. The results are as follows Figure 4 As shown in the figure, where the shear modulus of the first layer of soil is set to , the shear modulus of the second soil layer is set to , and satisfies , that is, the stiffness of the first layer of soil is lower than that of the second layer of soil, forming a soft-hard layered structural feature.

[0141] from Figure 4 It can be seen that at the set dimensionless frequency ( represents the shear wave velocity of the soil), the real part of the torsional complex impedance of the pile (i.e. equivalent stiffness) decreases gradually with the increase of the thickness of the first soil layer, and the reduction rate shows a trend of first fast and then slow. When the first soil layer is thick (such as ), the stiffness changes tend to be stable, indicating that the overlying soil layer has a critical effect on the regulation of the system stiffness; Figure 5 The imaginary part of the torsional complex impedance is shown The variation trend of the equivalent damping with frequency shows that the imaginary part value increases significantly after exceeding a certain cutoff frequency, reflecting that the equivalent damping of the system increases with the increase of the excitation frequency. In addition, the cutoff frequency decreases with the increase of the thickness of the first layer of soil, indicating that the fluctuation control ability of the shallow soil has a significant impact on the high-frequency impedance behavior; in particular, when When the values are 0.6, 0.8 and 1.0, the calculation results show that the real and imaginary parts of the pile head torsional complex impedance are basically equal, indicating that within this parameter range, the system has exhibited a stable frequency response characteristic.

[0142] In summary, this method achieves accurate calculation of the torsional dynamic response of a single pile in a stratified foundation through an iterative calculation process of control variables based on the energy variation principle, taking into account the stratified characteristics of the soil and the pile-soil interaction. This provides an efficient and accurate solution for pile foundation design and foundation dynamic response analysis.

[0143] Example 2:

[0144] Based on the same inventive concept as the first embodiment, the present invention discloses a system for calculating the torsional dynamic response of a single pile in layered soil, which is applicable to any method for calculating the torsional dynamic response of a single pile in layered soil in the first embodiment, comprising:

[0145] The iterative update module is used to iteratively perform the following operations until the preset convergence conditions are met:

[0146] According to the control variables corresponding to the soil layers, the torsional response characteristics of the soil layers are obtained through the soil torsional response function;

[0147] According to the torsional response characteristics, a control differential equation and a constraint equation group of each pile segment are established;

[0148] Obtaining a solution form of the control differential equation according to the control differential equation and the constraint equation group, wherein the solution form of the control differential equation includes a characteristic root and a single pile torsional dynamic response function;

[0149] Calculating the displacement energy integral term, the shear strain energy integral term, and the kinetic energy integral term of each soil layer according to the single pile torsional dynamic response function;

[0150] updating the control variables corresponding to each soil layer according to the displacement energy integral term, the shear strain energy integral term, and the kinetic energy integral term of each soil layer;

[0151] The torsional impedance function acquisition module is used to: after the iteration is completed, calculate the torsional response value at the pile top according to the converged single pile torsional dynamic response function, and obtain the torsional impedance function of the single pile based on the torsional response value.

[0152] The specific functional implementation of each of the above modules can be found in the relevant content of the method in Example 1 and will not be elaborated on here.

[0153] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0154] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0155] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0156] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0157] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which are all protected by the present invention.

Claims

1. A method for calculating the torsional dynamic response of a single pile in layered soil, characterized in that: include: According to the stratification of the stratified soil, the control variables corresponding to each soil layer are initialized; Iteratively performs the following operations until the preset convergence conditions are met: According to the control variables corresponding to the soil layers, the torsional response characteristics of the soil layers are obtained through the soil torsional response function; According to the torsional response characteristics, a control differential equation and a constraint equation group of each pile segment are established; Obtaining a solution form of the control differential equation according to the control differential equation and the constraint equation group, wherein the solution form of the control differential equation includes a characteristic root and a single pile torsional dynamic response function; Calculating the displacement energy integral term, the shear strain energy integral term, and the kinetic energy integral term of each soil layer according to the single pile torsional dynamic response function; updating the control variables corresponding to each soil layer according to the displacement energy integral term, the shear strain energy integral term, and the kinetic energy integral term of each soil layer; After the iteration is completed, the torsional response value at the pile top is calculated according to the converged single pile torsional dynamic response function, and the torsional impedance function of the single pile is obtained based on the torsional response value.

2. The method for calculating the torsional dynamic response of a single pile in layered soil according to claim 1, characterized in that: The soil torsional response function is as follows: in, Represents soil, Indicates the serial number, represents the radial coordinate, Indicates the The torsional response attenuation coefficient of the soil layer is represents the first-order modified Bessel function of the second kind, Indicates the Control variables of the soil layer, Indicates the radius of a single pile.

3. The method for calculating the torsional dynamic response of a single pile in layered soil according to claim 2, characterized in that: The torsional response characteristics include shear strain energy term, displacement response term and additional mass term; The shear strain energy term is calculated by the following formula: in, Indicates the The shear strain energy term of the soil layer is Indicates the Dynamic shear modulus of the soil layer, Indicates the The shear modulus of the soil layer, Indicates the The damping ratio of the soil layer, , represents a constant; The displacement response term is calculated by the following formula: in, Indicates the Displacement response term of the soil layer; The additional mass term is calculated by the following formula: in, Indicates the The additional mass term of the soil layer, Indicates the Density of the soil layer.

4. The method for calculating the torsional dynamic response of a single pile in layered soil according to claim 1, wherein: The governing differential equation is as follows: in, represents the vertical coordinate, represents the torsional dynamic response function of a single pile, represents the shear modulus of a single pile, represents the polar moment of inertia of a single pile, Indicates the The displacement response of the soil layer is Indicates the The shear strain energy term of the soil layer is Indicates the The additional mass term of the soil layer, represents the density of the pile, represents the torsional load frequency; The constraint equations are as follows: in, Indicates that the single pile is Layer soil and The vertical coordinate of the boundary between the soil layers, Indicates that the single pile is The vertical coordinate of the soil layer is The torsional dynamic response value at Indicates that the single pile is The vertical coordinate of the soil layer is The torsional dynamic response value at Indicates the The displacement response of the soil layer is Indicates the vertical coordinate of the top position of the single pile, Indicates the vertical coordinate of the bottom position of the single pile, Indicates the length of a single pile, Indicates the bottom soil number, Indicates that the single pile is The torsional dynamic response value at the vertical coordinate of the bottom position of a single pile in the layer soil, represents the simple harmonic torsional excitation load, represents the amplitude of the simple harmonic torsional excitation load, , Indicates time.

5. The method for calculating the torsional dynamic response of a single pile in layered soil according to claim 4, characterized in that: The solution of the governing differential equation is: in, Indicates the Undetermined coefficients of the general solution of the soil layer, Indicates that the single pile is Characteristic roots of the soil layer, Represents a constant.

6. The method for calculating the torsional dynamic response of a single pile in layered soil according to claim 5, characterized in that: The calculation formula for the integral term of the displacement energy of each soil layer is: in, Indicates the The integral term of the displacement energy of the soil layer is: represents the radius of a single pile, represents a constant; The calculation formula for the integral term of the shear strain energy of each soil layer is: in, Indicates the The integral term of shear strain energy of the soil layer; The calculation formula for the kinetic energy integral term of each soil layer is: in, Indicates the The integral term of kinetic energy of soil layer.

7. The method for calculating the torsional dynamic response of a single pile in layered soil according to claim 1, wherein: According to the displacement energy integral term, shear strain energy integral term and kinetic energy integral term of each soil layer, the control variables of each soil layer are updated by the following formula: in, Indicates the Control variables of the soil layer, Indicates the The integral term of the displacement energy of the soil layer is: Indicates the The integral term of shear strain energy of the soil layer is: Indicates the The integral term of the kinetic energy of the soil layer is: represents the torsional load frequency.

8. The method for calculating the torsional dynamic response of a single pile in layered soil according to claim 1, wherein: The preset convergence conditions are as follows: in, Indicates the convergence state, Indicates convergence, Indicates non-convergence, Indicates the current round, Indicates the current round Middle Control variables of the soil layer, Indicates the previous round Middle Control variables of the soil layer, Indicates the preset convergence accuracy.

9. The method for calculating the torsional dynamic response of a single pile in layered soil according to claim 1, wherein: The calculation formula of the torsional response value at the pile top is: in, represents the torsional response value at the pile top, Indicates the Undetermined coefficients of the general solution of the soil layer, Indicates the Characteristic roots of the soil layer, represents a constant, represents the vertical coordinate at the top of the pile; The torsional impedance function of the monopile is as follows: in, represents the torsional complex impedance of a single pile, Indicates the The shear modulus of the soil layer, represents the amplitude of the simple harmonic torsional excitation load, Indicates the radius of a single pile.

10. A system for calculating the torsional dynamic response of a single pile in stratified soil, applicable to the method for calculating the torsional dynamic response of a single pile in stratified soil according to any one of claims 1 to 9, characterized in that: include: Initialization module, used to initialize the control variables corresponding to each soil layer according to the stratification of the stratified soil body; The iterative update module is used to iteratively perform the following operations until the preset convergence conditions are met: According to the control variables corresponding to the soil layers, the torsional response characteristics of the soil layers are obtained through the soil torsional response function; According to the torsional response characteristics, a control differential equation and a constraint equation group of each pile segment are established; Obtaining a solution form of the control differential equation according to the control differential equation and the constraint equation group, wherein the solution form of the control differential equation includes a characteristic root and a single pile torsional dynamic response function; Calculating the displacement energy integral term, the shear strain energy integral term, and the kinetic energy integral term of each soil layer according to the single pile torsional dynamic response function; updating the control variables corresponding to each soil layer according to the displacement energy integral term, the shear strain energy integral term, and the kinetic energy integral term of each soil layer; The torsional impedance function acquisition module is used to: after the iteration is completed, calculate the torsional response value at the pile top according to the converged single pile torsional dynamic response function, and obtain the torsional impedance function of the single pile based on the torsional response value.

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