Method for analyzing horizontal stress performance of pile foundation in layered transversely isotropic foundation

Abstract

This invention discloses a method for analyzing the horizontal stress performance of pile foundations in layered transversely isotropic foundations, belonging to the field of pile foundation design and analysis in geotechnical engineering. The method includes: establishing a theoretical model of the pile-soil system, treating the foundation as a multi-layered transversely isotropic material and the piles as Bernoulli-Euler beams; establishing the pile stress-displacement equation based on the finite difference method; establishing the soil stress-displacement equation based on the fundamental solution of the multi-layered transversely isotropic material; constructing the overall stress-displacement equation for a single pile; introducing pile-pile interaction coefficients to extend the single-pile model to pile group analysis; solving the equation system using the full principal component Gaussian elimination method and writing a FORTRAN program for automated calculation; verifying the correctness of the method through numerical examples and conducting parametric analysis. This invention is applicable to the horizontal stress analysis of single piles and pile groups in non-uniform, transversely isotropic foundations of any number of layers, providing a reliable numerical tool for pile foundation engineering design and safety assessment under complex geological conditions.

Description

Technical Field

[0001] This invention relates to the field of pile foundation design and analysis in geotechnical engineering, and specifically to a method for analyzing the horizontal stress performance of pile foundations in layered transversely isotropic foundations. Background Technology

[0002] This technology is mainly applied in civil engineering, building construction, marine engineering, and port engineering, especially in various engineering structures involving pile foundation design, such as offshore wind turbine foundations, high-rise building pile foundations, cross-sea bridge piers, port and wharf structures, offshore oil platforms, and power transmission tower foundations. These types of projects often face the combined effects of complex geological conditions and significant horizontal loads (such as wind loads, wave loads, and seismic forces). The stress and deformation characteristics of the pile foundation directly affect the safety and durability of the overall structure.

[0003] In non-uniform transversely isotropic foundations, the stress mechanism of pile foundations under horizontal loads is complex, and traditional analysis methods often fail to accurately reflect the non-uniformity of soil layers along the depth direction, material anisotropy, and spatial effects of pile-soil interaction. Specifically, existing technologies have the following limitations:

[0004] Most existing methods treat the foundation as a homogeneous or layered isotropic body, failing to fully consider the transverse isotropic characteristics commonly found in natural sedimentary soils, i.e., significant differences in horizontal and vertical mechanical properties, leading to deviations between analytical results and actual working conditions. Traditional analytical methods are mostly based on assumptions of a single soil layer or a finite number of layers, making them unsuitable for non-uniform foundations with arbitrary numbers of layers and continuously varying mechanical parameters along depth. While high-precision numerical methods (such as three-dimensional finite element methods) can simulate complex geological conditions well, their high computational cost and complex modeling make them inconvenient for rapid analysis and design optimization in practical engineering. Existing pile group analysis methods mostly rely on empirical reduction coefficients or simplification assumptions, failing to systematically consider the pile-soil-pile coupling effect in non-uniform transversely isotropic foundations, especially in the elastoplastic stage, where behaviors such as pile-soil interface decoupling and nonlinear soil softening are difficult to describe accurately. Therefore, there is an urgent need to develop a numerical analysis method for single piles and pile groups that can accurately describe the characteristics of non-uniform transverse isotropic foundations and has high computational efficiency, so as to improve the reliability and economy of pile foundation design under horizontal load conditions.

[0005] Currently, the following methods are mainly used domestically and internationally for the analysis of pile foundations under horizontal loads:

[0006] 1. Linear Elastic Foundation Reaction Method (Winkler Foundation Beam Method): This method simplifies the soil as a series of independent springs, reflecting the soil-pile interaction through the foundation reaction coefficient. Although the calculation is simple, it cannot consider the continuity of the soil and the stress diffusion effect, and is particularly difficult to apply to non-uniform, anisotropic foundations.

[0007] 2. Elastic theory method: Based on the fundamental solution of elastic half space such as the Mindlin solution, this method can partially reflect the continuity of soil, but it still assumes that the soil is a homogeneous isotropic material and cannot be directly extended to transversely isotropic foundations or multi-layered non-homogeneous strata.

[0008] 3. Py curve method: This method establishes a nonlinear relationship between the soil reaction force and pile displacement based on field or experimental data, and is widely used in engineering. However, Py curves are mostly based on experience with homogeneous or simple layered soils, lacking universality for non-uniform transversely isotropic foundations, and rely on empirical reduction in pile group analysis, resulting in insufficient theoretical basis.

[0009] 4. Numerical analysis methods: These include the finite element method, boundary element method, and finite layer method. While these methods can handle complex geological and load conditions, they often involve large computational loads and complex preprocessing, especially for large-scale pile group systems, where the efficiency of three-dimensional fine modeling and solution is relatively low. Furthermore, existing numerical methods still face technical bottlenecks in coupling transversely isotropic basic structures and achieving efficient solutions for non-uniform foundations with arbitrary numbers of layers.

[0010] In summary, existing methods have limitations in handling non-uniform transversely isotropic foundations, multi-pile interactions, and elastoplastic pile-soil interface behavior. Therefore, developing a numerical analysis method for pile-soil interactions based on fundamental solutions of multi-layer transversely isotropic materials, while balancing computational accuracy and efficiency, has significant theoretical and engineering application value. Summary of the Invention

[0011] To address the aforementioned problems, this invention provides a method for analyzing the horizontal stress performance of pile foundations in layered transversely isotropic foundations. This method enables a complete analysis process from single piles to pile groups, offering advantages such as high computational efficiency, high accuracy, and strong applicability. A method for analyzing the horizontal stress performance of pile foundations in layered transversely isotropic foundations.

[0012] The following is a detailed explanation of the method:

[0013] This invention employs a numerical method based on the fundamental solutions of multilayer transversely isotropic materials to perform elastoplastic numerical analysis of single piles and pile groups in non-uniform transversely isotropic foundations under horizontal loads. First, based on the Bernoulli-Euler beam theory and the finite difference method, the stress-displacement equation of the pile is established. Simultaneously, using the fundamental solutions of multilayer transversely isotropic materials, the stress-displacement equation of the soil is established. Then, using the displacement compatibility condition of the pile-soil interface in the elastic stage, the overall governing equation is derived, and the displacement and stress distribution of the pile under horizontal loads are obtained. To further analyze the pile group effect, the single-pile analysis model is extended to pile group analysis by introducing an inter-pile interaction coefficient. Numerical examples verify the advantages of this invention in terms of computational accuracy and efficiency, and parameter analysis explores the influence of various factors on the displacement and stress response of single piles and pile groups.

[0014] A method for analyzing the horizontal stress performance of pile foundations in layered transversely isotropic foundations includes the following steps:

[0015] S1: Establish a theoretical model of the pile-soil system. Based on the distribution of foundation soil layers, pile geometry, and material parameters of the target project, establish a mechanical model of a single pile or pile group in a non-uniform transversely isotropic foundation; wherein, the foundation is considered as a multi-layered transversely isotropic material, and the elastic parameters of each layer are determined by... The piles are described as Bernoulli-Euler beams.

[0016] S2: Deriving the Finite Difference Equation of Pile Stress and Displacement. Based on the Bernoulli-Euler beam theory, the differential equation of pile stress and displacement is established and transformed into a difference form using the finite difference method.

[0017] S3: Derive the stress-displacement equation of the soil at the pile-soil contact surface. Based on the fundamental solution of multilayer transversely isotropic materials, establish the stress-displacement equation of the soil at the pile-soil contact surface.

[0018] S4: Construct the overall stress-displacement equation for a single pile. Based on the displacement compatibility and stress compatibility conditions of the pile-soil contact surface, the finite difference equation of pile stress-displacement is coupled with the soil stress-displacement equation to establish the overall stress-displacement equation for a single pile; for pile groups, the pile-pile interaction coefficient is introduced to extend it into a pile group system equation.

[0019] S5: Numerical Solution and Program Implementation. The global equation system is solved using the full principal component Gaussian elimination method. A FORTRAN program is written to automate the entire calculation process from constructing the pile-soil stress-displacement equations to solving them. The program includes an input module, an equation construction module, an equation solving module, and a stress-displacement output module.

[0020] S6: Theoretical Verification and Numerical Analysis of the Linear Elastic Stage. The correctness of the proposed method is verified by comparing it with existing theoretical solutions; parametric numerical analysis is conducted to study the influence of factors such as pile length, pile diameter, pile-soil modulus ratio, and soil layer distribution on pile displacement and bending moment.

[0021] Preferably, step S1 specifically includes:

[0022] The following assumptions are made regarding the theoretical model of the pile-soil system: the foundation is assumed to be a semi-infinite body; each layer within the foundation is an elastic, homogeneous, and continuous transversely isotropic soil; the pile body undergoes only elastic deformation; the pile bottom is horizontal and smooth; and horizontal forces acting on the pile foundation will not cause vertical deformation. The suspended pile embedded in multiple layers of transversely isotropic soil has a diameter of... , length is The perimeter of the cross section is And the bending stiffness is A circular pile. It is divided into... There are 3 cylindrical units, with the middle unit having a length of 1. The lengths of the top and bottom units are The stress-displacement calculation point for the middle element is the midpoint of the pile side, and the stress-displacement calculation points for the top and bottom elements are the top and bottom points of the pile side, respectively. A coordinate system is established along the pile, with the origin at the pile edge point.

[0023] Transversely isotropic materials refer to materials with an elastic axis of symmetry. The materials are isotropic in a plane perpendicular to the axis of symmetry, but their properties differ along the direction of the axis of symmetry.

[0024] The stress-strain relationship of a transversely isotropic material can be expressed in matrix form as follows:

[0025]

[0026] in, , These are the elastic modulus, Poisson's ratio, and shear modulus in the isotropic plane, respectively. It is the elastic modulus along the axis of elastic symmetry; It is the Poisson's ratio of the strain in the isotropic plane caused by the action along the elastic axis of symmetry; It is the shear modulus in any plane including the elastic axis of symmetry.

[0027] The mechanical properties of non-homogeneous transversely isotropic materials are determined by independent elastic parameters. The description describes a non-uniform transversely isotropic material whose properties continuously vary along the spatial coordinates. It approximates this by discretizing the material layer into multiple transversely isotropic sublayers with constant mechanical properties. The fundamental solution for a multilayer transversely isotropic material consists of the displacement and stress fields of a three-dimensional layered elastic material in an infinite domain under concentrated load vectors. The fundamental solution for a multilayer transversely isotropic material assumes an arbitrary number of material layers. Through layer thickness Distinguish the spatial boundaries of each floor. Each floor is defined using... Five elastic parameters characterize its transversely isotropic mechanical properties. The layered material is bonded to a semi-infinite medium at both ends, and the displacement and vertical stress at the interface are continuous. Closed-loop solutions can be obtained for layered transversely isotropic materials with any number of layers, and the calculation accuracy is high.

[0028] Preferably, step S2 specifically includes:

[0029] Based on the Bernoulli-Euler beam theory, a differential equation for pile stress-displacement is established and transformed into a finite difference form using the finite difference method. Finally, the finite difference equation for single pile stress-displacement is derived by combining the pile end boundary conditions and the equilibrium conditions of pile force and bending moment.

[0030] The differential equation of stress-displacement in pile body and its difference form are expressed as follows:

[0031]

[0032]

[0033] The boundary conditions between the pile top and pile bottom are expressed in finite difference form as follows:

[0034]

[0035]

[0036] The equilibrium condition between pile force and bending moment is expressed as:

[0037]

[0038]

[0039] The finite difference equation for stress-displacement of a single pile is expressed as:

[0040]

[0041] In the above formula, and The pile body 3D displacement column vector and 3D stress column vector, This is the difference form of the pile stiffness matrix. The stress coefficient matrix, For external force column vectors, and All are coefficient row vectors.

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Preferably, step S3 specifically includes:

[0048] Based on the fundamental solution of multilayer transversely isotropic materials, a stress-displacement equation for soil at the pile-soil interface is established.

[0049] The soil stress-displacement equation is expressed as:

[0050]

[0051] in, The coefficient matrix obtained from the solution of the multi-layer transverse isotropic fundamental solution forms In the matrix This means Caused by uniform horizontal stress on the element Displacement at the corresponding point of the element.

[0052] The formula is expressed as:

[0053]

[0054] In the above formula There are three calculation formulas depending on the unit location:

[0055]

[0056]

[0057]

[0058] In the above In the calculation formula This refers to the multi-layered transverse isotropic fundamental solution, representing... Element (source point) along or When a unit force is applied in the direction of the force, it is effective for the following purposes. The displacement generated by the element (field point) is a two-point function. The internal and external integrations of the multi-layer transverse isotropic fundamental solution are used in the calculation. Numerical integration at Gaussian integration points.

[0059] Through calculation Thus, we obtained the formula for calculating the stress-displacement on the pile-soil contact surface.

[0060] Preferably, step S4 specifically includes:

[0061] By coupling the stress-displacement finite difference equation of a single pile with the stress-displacement calculation formula of the soil, and combining the pile-soil contact surface displacement and stress compatibility formula, the overall stress-displacement relationship of a single pile is obtained.

[0062] The formula for compatibility between pile-soil contact surface displacement and stress is expressed as follows:

[0063]

[0064]

[0065] The formula for the overall stress-displacement relationship of a single pile is expressed as:

[0066]

[0067] The overall stress-displacement relationship formula for a single pile can be used to solve for the overall displacement and stress of a single pile.

[0068] For pile groups, the pile-pile interaction coefficient is introduced, which expands the equations to form a pile group system equation.

[0069] Pile-pile interaction coefficient Represented as:

[0070]

[0071] Preferably, step S5 specifically includes:

[0072] The FORTRAN program includes the main program ATOP, the input subroutine INPUT, the subroutine MATR for establishing pile equations, the subroutine SOIL for establishing soil equations, the subroutine COUPLE for establishing global equations, the subroutine GAUSSSOL for solving Gaussian equations, the subroutine TRACT for stress calculation, and the subroutine DISPL for displacement calculation, etc.

[0073] The main program ATOP specifies the data storage directory, defines the upper limit of array storage space and storage area, specifies the input and output files, reads and analyzes key parameters, and calls subroutines for various purposes.

[0074] Subroutine INPUT: Reads information about piles and non-uniform transverse isotropic foundations from the input file, including the number of piles, the number and length of subdivisions, the diameter and length of piles, and the number and material information of foundation layers; outputs information about piles and foundations for verification.

[0075] Subroutine MATR: Establishes the horizontal displacement coefficient matrix of the pile body. and external force column vector Establish the stress-displacement equation for the pile body.

[0076] Subroutine SOIL: Utilizes the fundamental solution of a multilayer transversely isotropic material to calculate the displacement influence coefficient of the foundation soil and establish the horizontal displacement coefficient matrix of the foundation soil. Establish the stress-displacement equation for the foundation soil.

[0077] Subroutine COUPLE: Combines the finite difference equations of pile stress and displacement with the stress and displacement equations of the soil at the pile-soil interface to establish the overall equations for the interaction between the pile and the soil.

[0078] Subroutine GAUSSSOL: Solve equations using the Gaussian elimination method with full pivot.

[0079] Subroutine TRACT: Outputs the horizontal stress at each node of the pile body. .

[0080] Subroutine DISPL: Calculates the horizontal stress at each element node of the pile body. Substitute the stress-displacement formula of the soil at the pile-soil contact surface into the formula to calculate the horizontal displacement of each unit node of the pile body. .

[0081] Preferably, step S6 specifically includes:

[0082] Theoretical solutions verify the correctness of the proposed method; parametric case analysis is conducted to study the influence of factors such as pile length-to-diameter ratio, pile-soil modulus ratio, transversely isotropic soil properties, proportionality coefficient, and soil layer thickness on pile displacement and bending moment.

[0083] The method of the present invention has the following beneficial effects:

[0084] 1. Applicable to foundations of any number of layers, non-uniform, transversely isotropic, breaking through the limitations of the traditional homogeneous isotropic assumption;

[0085] 2. Combining analytical fundamental solutions with numerical methods, it achieves high computational efficiency and reliable accuracy;

[0086] 3. Provides a unified analysis framework for single piles and pile groups, supporting the optimized design of complex pile foundation systems;

[0087] 4. The program has a high degree of automation and is easy to integrate into the engineering design and verification process. Attached Figure Description

[0088] Figure 1 A single pile model of a two-layer transversely isotropic foundation under horizontal load;

[0089] Figure 2 This is a diagram showing the elastic field analysis of a single pile in a double-layer transversely isotropic foundation under horizontal load.

[0090] Figure 3 Displacement influence coefficient Change diagram;

[0091] Figure 4 This is a dimensionless displacement diagram of two piles along the depth under horizontal load. Detailed Implementation

[0092] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0093] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0094] The terms "comprising" or "including" as used in this invention mean that the element preceding the term encompasses the element listed after the term, and do not exclude the possibility of encompassing other elements. Terms such as "inner," "outer," "upper," and "lower" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. When the absolute position of the described object changes, the relative positional relationship may also change accordingly. In this invention, unless otherwise explicitly specified and limited, the term "attached" and similar terms should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral part; it can refer to a direct connection or an indirect connection through an intermediate medium; it can refer to the internal communication of two elements or the interaction relationship between two elements. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0095] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, tables, and embodiments.

[0096] Example 1

[0097] A method for analyzing the horizontal stress performance of pile foundations in layered transversely isotropic foundations includes the following steps:

[0098] S1: Establish a theoretical model of the pile-soil system. Based on the distribution of foundation soil layers, pile geometry, and material parameters of the target project, establish a mechanical model of a single pile or pile group in a non-uniform transversely isotropic foundation; wherein, the foundation is considered as a multi-layered transversely isotropic material, and the elastic parameters of each layer are determined by... The piles are described as Bernoulli-Euler beams.

[0099] Specifically, the elastic parameters of each uniform transversely isotropic layer can be expressed as:

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] in, , These are the elastic modulus, Poisson's ratio, and shear modulus in the isotropic plane, respectively. It is the elastic modulus along the axis of elastic symmetry; It is the Poisson's ratio of the strain in the isotropic plane caused by the action along the elastic axis of symmetry; It is the shear modulus in any plane including the elastic axis of symmetry.

[0106] S2: Deriving the Finite Difference Equation of Pile Stress and Displacement. Based on the Bernoulli-Euler beam theory, the differential equation of pile stress and displacement is established and transformed into a difference form using the finite difference method.

[0107] Based on the Bernoulli-Euler beam theory, a differential equation for pile stress-displacement is established and transformed into a finite difference form using the finite difference method. Finally, the finite difference equation for single pile stress-displacement is derived by combining the pile end boundary conditions and the equilibrium conditions of pile force and bending moment.

[0108] The finite difference equation for stress-displacement of a single pile is expressed as:

[0109]

[0110] In the above formula, and The pile body 3D displacement column vector and 3D stress column vector, This is the difference form of the pile stiffness matrix. The stress coefficient matrix, For external force column vectors, and All are coefficient row vectors.

[0111] S3: Derive the stress-displacement equation of the soil at the pile-soil contact surface. Based on the fundamental solution of multilayer transversely isotropic materials, establish the stress-displacement equation of the soil at the pile-soil contact surface.

[0112] Based on the fundamental solution of multilayer transversely isotropic materials, a stress-displacement equation for soil at the pile-soil interface is established.

[0113] The soil stress-displacement equation is expressed as:

[0114]

[0115] in, The coefficient matrix obtained from the solution of the multi-layer transverse isotropic fundamental solution forms In the matrix This means Caused by uniform horizontal stress on the element Displacement at the corresponding point of the element.

[0116] The formula is expressed as:

[0117]

[0118] S4: Construct the overall stress-displacement equation for a single pile. Based on the displacement compatibility and stress compatibility conditions of the pile-soil contact surface, the finite difference equation of pile stress-displacement is coupled with the soil stress-displacement equation to establish the overall stress-displacement equation for a single pile; for pile groups, the pile-pile interaction coefficient is introduced to extend it into a pile group system equation.

[0119] By coupling the stress-displacement finite difference equation of a single pile with the stress-displacement calculation formula of the soil, and combining the pile-soil contact surface displacement and stress compatibility formula, the overall stress-displacement relationship of a single pile is obtained.

[0120] The formula for compatibility between pile-soil contact surface displacement and stress is expressed as follows:

[0121]

[0122]

[0123] The formula for the overall stress-displacement relationship of a single pile is expressed as:

[0124]

[0125] The overall stress-displacement relationship formula for a single pile can be used to solve for the overall displacement and stress of a single pile.

[0126] For pile groups, the pile-pile interaction coefficient is introduced, which expands the equations to form a pile group system equation.

[0127] Pile-pile interaction coefficient Represented as:

[0128]

[0129] S5: Numerical Solution and Program Implementation. The global equation system is solved using the full principal component Gaussian elimination method. A FORTRAN program is written to automate the entire calculation process from constructing the pile-soil stress-displacement equations to solving them. The program includes an input module, an equation construction module, an equation solving module, and a stress-displacement output module.

[0130] The FORTRAN program includes the main program ATOP, the input subroutine INPUT, the subroutine MATR for establishing pile equations, the subroutine SOIL for establishing soil equations, the subroutine COUPLE for establishing global equations, the subroutine GAUSSSOL for solving Gaussian equations, the subroutine TRACT for stress calculation, and the subroutine DISPL for displacement calculation, etc.

[0131] S6: Theoretical Verification and Numerical Analysis of the Linear Elastic Stage. The correctness of the proposed method is verified by comparing it with existing theoretical solutions; parametric numerical analysis is conducted to study the influence of factors such as pile length, pile diameter, pile-soil modulus ratio, and soil layer distribution on pile displacement and bending moment.

[0132] Example 1:

[0133] To further illustrate the effectiveness of the method system for analyzing the horizontal stress performance of pile foundations in layered transversely isotropic foundations provided in this application, this embodiment demonstrates the entire process of numerical analysis of single piles and pile groups in non-uniform transversely isotropic foundations under horizontal loads, ultimately obtaining nodal displacement and bending moment diagrams along the depth of the pile-soil contact surface.

[0134] like Figure 1 As shown, this is a model diagram of a single pile in a two-layer transversely isotropic foundation under horizontal load. The transversely isotropic parameters of each layer are determined by... describe.

[0135] The implementation steps are as follows:

[0136] Initial setup and modeling:

[0137] Start the input module. The ratios of the parameters of the three transversely isotropic materials and the soil materials of the two examples are shown in Tables 1 and 2, respectively. Calculate the parameters of each transversely isotropic soil layer. Value. The length of the standard unit divided in a single pile is... Considering the ratio of the elastic modulus of the pile to that of the soil ( ), length-to-diameter ratio of single pile ( Four possible combinations. The top of the pile bears a horizontal load. effect.

[0138] The equation construction module is activated, dividing the pile body into 41 elements along the depth direction. The length of the pile top and bottom elements is half the length of the standard element. Based on the Bernoulli-Euler beam theory, the differential equation of pile stress and displacement is established and transformed into a difference form using the finite difference method. Based on the fundamental solution of multilayer transversely isotropic materials, the stress and displacement equation of the soil at the pile-soil interface is established. According to the displacement compatibility condition and stress compatibility condition of the pile-soil interface, the finite difference equation of pile stress and displacement is coupled with the stress and displacement equation of soil to establish the overall stress and displacement equation of a single pile.

[0139] Start the equation solving module and use the full principal component Gaussian elimination method to solve the global system of equations.

[0140] The stress-displacement output module is activated, outputting dimensionless displacement and bending moment along the normalized depth at the pile-soil contact surface, as follows: Figure 2 .

[0141] By introducing the pile-pile interaction coefficient, the pile group model can be analyzed. Using the same material properties as a single pile, but changing only the number of piles, the following results are obtained: Figure 3-4 The result.

[0142] Based on the above, this method successfully realized the linear elastic numerical analysis of piles from single piles to pile groups under horizontal loads, and fully demonstrated the systematicness and reliability of the method in dealing with the stress response of pile foundations in non-uniform transversely isotropic foundations.

[0143] Therefore, the numerical analysis method for single piles and pile groups in non-uniform transversely isotropic foundations under horizontal loads proposed in this invention addresses the problems of existing homogeneous isotropic methods based on Mindlin solutions being unable to handle layered and non-uniform transversely isotropic foundations, the high computational cost of the finite element method, and the inability of traditional analytical methods to consider complex pile-soil nonlinear interactions. It provides an efficient and high-precision numerical analysis framework based on multi-layer transversely isotropic fundamental solutions and beam theory. This method enables rapid calculation of pile displacement and stress fields, quantitative assessment of pile group interactions, and forms a complete automated analysis process of "modeling-solving-verification-output," providing a reliable numerical tool for pile foundation design and safety assessment under complex foundation conditions.

[0144] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that several improvements and modifications can be made to the present invention without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

[0145] Table 1. Parameter ratios of three transversely isotropic materials. Table 2. Soil materials in two calculation examples.

[0146]

Claims

1. A method for analyzing the horizontal stress performance of pile foundations in layered transversely isotropic foundations, characterized in that: Includes the following steps: S1: Establish a theoretical model of the pile-soil system; based on the distribution of foundation soil layers, pile geometry, and material parameters of the target project, establish a mechanical model of a single pile or pile group in a non-uniform transversely isotropic foundation; wherein the foundation is a multi-layer transversely isotropic material, and the elastic parameters of each layer are determined by... The piles are described as Bernoulli-Euler beams; S2: Derive the finite difference equation of pile stress and displacement; Based on the Bernoulli-Euler beam theory, establish the differential equation of pile stress and displacement, and transform it into a difference form using the finite difference method. S3: Derive the stress-displacement equation of the soil at the pile-soil contact surface; Based on the fundamental solution of multilayer transversely isotropic materials, establish the stress-displacement equation of the soil at the pile-soil contact surface. S4: Construct the overall stress-displacement equation for a single pile; based on the displacement compatibility and stress compatibility conditions of the pile-soil contact surface, couple the finite difference equation of pile stress-displacement with the soil stress-displacement equation to establish the overall stress-displacement equation for a single pile; for pile groups, introduce the pile-pile interaction coefficient to extend it into a pile group system equation. S5: Numerical solution and program implementation; The global equation system is solved using the full principal component Gaussian elimination method, and a FORTRAN program is written to automate the entire process from constructing the pile-soil stress-displacement equations to solving the equations; The program includes an input module, an equation construction module, an equation solving module, and a stress-displacement output module; S6: Theoretical verification and case analysis of linear elastic stage; conduct parametric case analysis based on the influence of pile length, pile diameter, pile-soil modulus ratio, and soil layer distribution on pile displacement and bending moment.

2. The method for analyzing the horizontal stress performance of pile foundations in layered transversely isotropic foundations according to claim 1, characterized in that: Step S1 specifically includes: In the theoretical model of the pile-soil system, the foundation is assumed to be a semi-infinite body, with each layer being an elastic, homogeneous, and continuous transversely isotropic soil. The pile body only undergoes elastic deformation, the pile bottom is horizontal and smooth, and horizontal forces acting on the pile foundation will not cause vertical deformation. The suspended pile embedded in multiple layers of transversely isotropic soil has a diameter of... , length is The perimeter of the cross section is And the bending stiffness is A circular pile; it is divided into There are 3 cylindrical units, with the middle unit having a length of 1. The lengths of the top and bottom units are The stress displacement calculation point of the middle unit is the middle point of the pile side, and the stress displacement calculation points of the top unit and the bottom unit are the top and bottom points of the pile side, respectively; a coordinate system is established along the pile, with the origin of the coordinate system being the edge point of the pile. Transversely isotropic materials refer to materials that have an elastic axis of symmetry within them. The materials are isotropic in a plane perpendicular to the axis of symmetry, but their properties differ along the direction of the axis of symmetry. The stress-strain relationship of a transversely isotropic material can be expressed in matrix form as follows: ； in, , These are the elastic modulus, Poisson's ratio, and shear modulus in the isotropic plane, respectively. It is the elastic modulus along the axis of elastic symmetry; It is the Poisson's ratio of the strain in the isotropic plane caused by the action along the elastic axis of symmetry; It is the shear modulus in any plane including the elastic axis of symmetry; The mechanical properties of non-homogeneous transversely isotropic materials are determined by independent elastic parameters. Description: The properties of a non-uniform transversely isotropic material vary continuously along the spatial coordinate direction. It is approximated by discretizing the material layer into multiple transversely isotropic sublayers with constant mechanical properties. The fundamental solution for a multilayer transversely isotropic material consists of the displacement and stress fields of a three-dimensional layered elastic material in an infinite domain under concentrated load vectors. The fundamental solution for a multilayer transversely isotropic material assumes an arbitrary number of material layers. Through layer thickness Distinguish the spatial scope of each floor; each floor is marked with... Five elastic parameters characterize its transversely isotropic mechanical properties; the layered material is bonded to a semi-infinite medium at both ends, and the displacement and vertical stress at the interface are continuous; a closed solution can be obtained for a layered transversely isotropic material with any number of layers, and the calculation accuracy is high.

3. The method for analyzing the horizontal stress performance of pile foundations in layered transversely isotropic foundations according to claim 1, characterized in that: Step S2 specifically includes: Based on the Bernoulli-Euler beam theory, a differential equation for pile stress-displacement is established and transformed into a finite difference form using the finite difference method. Finally, the finite difference equation for single pile stress-displacement is derived by combining the pile end boundary conditions and the equilibrium conditions of pile force and bending moment. The differential equation of stress-displacement in pile body and its difference form are expressed as follows: ； ； The boundary conditions between the pile top and pile bottom are expressed in finite difference form as follows: ； ； The equilibrium condition between pile force and bending moment is expressed as: ； ； The finite difference equation for stress-displacement of a single pile is expressed as: ； In the above formula, and The pile body 3D displacement column vector and 3D stress column vector, This is the difference form of the pile stiffness matrix. The stress coefficient matrix, For external force column vectors, and All are coefficient row vectors; ； ； ； ； 。 4. The method for analyzing the horizontal stress performance of pile foundations in layered transversely isotropic foundations according to claim 1, characterized in that: Step S3 specifically includes: Based on the fundamental solution of multilayer transverse isotropic materials, a stress-displacement equation for soil at the pile-soil interface is established. The soil stress-displacement equation is expressed as: ； in, The coefficient matrix obtained from the solution of the multi-layer transverse isotropic fundamental solution forms In the matrix This means Caused by uniform horizontal stress on the element Displacement at the corresponding point of the element; The formula is expressed as: ； In the above formula There are three calculation formulas depending on the unit location: ； ； ； In the above In the calculation formula This refers to the multi-layered transverse isotropic fundamental solution, representing... The unit is the source point along or When a unit force is applied in the direction of the force, it is effective for the following purposes. The displacement generated by a single element, i.e., a field point, is a two-point function; the multi-layer transverse isotropic fundamental solution is integrated internally and externally during calculation. Numerical integration at Gaussian integration points; through calculation The formula for calculating stress-displacement on the pile-soil contact surface is obtained.

5. The method for analyzing the horizontal stress performance of pile foundations in layered transversely isotropic foundations according to claim 1, characterized in that: Step S4 specifically includes: By coupling the stress-displacement finite difference equation of a single pile with the stress-displacement calculation formula of the soil, and combining the pile-soil contact surface displacement and stress compatibility formula, the overall stress-displacement relationship of a single pile is obtained. The formula for compatibility between pile-soil contact surface displacement and stress is expressed as follows: ； ； The formula for the overall stress-displacement relationship of a single pile is expressed as: ； The overall stress-displacement relationship formula for a single pile can be used to solve for the overall displacement and stress of a single pile. For pile groups, the pile-pile interaction coefficient is introduced, which expands the equations to a pile group system equation. Pile-pile interaction coefficient Represented as: 。 6. The method for analyzing the horizontal stress performance of pile foundations in layered transversely isotropic foundations according to claim 1, characterized in that: Step S5 specifically includes: The FORTRAN program includes the main program ATOP, the input subroutine INPUT, the subroutine MATR for establishing pile equations, the subroutine SOIL for establishing soil equations, the subroutine COUPLE for establishing global equations, the subroutine GAUSSSOL for solving Gaussian equations, the stress calculation subroutine TRACT, and the displacement calculation subroutine DISPL. The main program ATOP: specifies the data storage directory, defines the upper limit and storage area of ​​the array storage space; specifies the input and output files; reads and analyzes key parameters; and calls subroutines for various purposes. Subroutine INPUT: Reads information about piles and non-uniform transverse isotropic foundations from the input file, including the number of piles, the number and length of subdivisions, the diameter and length of piles, and the number and material information of foundation layers; outputs pile and foundation information. Subroutine MATR: Establishes the horizontal displacement coefficient matrix of the pile body. and external force column vector Establish the stress-displacement equation for the pile body; Subroutine SOIL: Utilizes the fundamental solution of a multilayer transversely isotropic material to calculate the displacement influence coefficient of the foundation soil and establish the horizontal displacement coefficient matrix of the foundation soil. Establish the stress-displacement equation for the foundation soil; Subroutine COUPLE: Combines the finite difference equations of pile stress and displacement with the stress and displacement equations of the soil at the pile-soil interface to establish the overall equations for the interaction between the pile and the soil. Subroutine GAUSSSOL: Solve equations using the Gaussian elimination method with full pivot; Subroutine TRACT: Outputs the horizontal stress at each node of the pile body. ; Subroutine DISPL: Calculates the horizontal stress at each element node of the pile body. Substitute the stress-displacement formula of the soil at the pile-soil contact surface into the formula to calculate the horizontal displacement of each unit node of the pile body. .

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