Pile-soil-structure dynamic interaction analysis method

Abstract

The invention provides a pile-soil-structure dynamic interaction analysis method, which belongs to the technical field of civil engineering, and obtains system data through three-scale physical model experiments: the first scale pays attention to microscopic soil behaviors, the second scale and the third scale are determined based on a multiphase fluid-solid coupling equation, and the third scale is determined based on a multiphase fluid-solid coupling equation; and respectively paying attention to the mesoscopic interface action and the macroscopic overall response. A pile-soil interface control equation and a pile structure coupling equation are established based on experimental data to form a basic equation set, a domain decomposition method is adopted to divide a calculation area into a fine grid near field and a rough grid far field, and a minimum spanning tree algorithm is applied to optimize grid division. Pile body stress distribution and a soil body deformation field are obtained through numerical solution, a pile foundation transverse displacement function is obtained through analysis solution, finally the pile body stress distribution and the soil body deformation field are combined to form a complete pile-soil-structure dynamic interaction model, and the technical problem that the pile-soil-structure dynamic interaction cross-scale effect is difficult to accurately simulate is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of civil engineering, and in particular relates to a pile-soil-structure dynamic interaction analysis method. Background Art

[0002] Pile foundations are crucial components connecting superstructures to soil. Studying their interaction mechanisms under dynamic loads (such as earthquakes and mechanical vibrations) is crucial for engineering safety. Traditional methods for analyzing pile-soil-structure dynamic interaction primarily rely on single-scale physical model tests or numerical simulation techniques, such as centrifuge model tests, shaking table experiments, and finite element analysis, to predict the response characteristics of pile foundations under dynamic loads.

[0003] However, existing technologies are generally subject to scale effects, i.e., the observed pile-soil interaction behavior at different scales varies significantly. Microscale experiments struggle to reflect macroscopic engineering properties, while large-scale engineering experiments cannot accurately capture microscopic mechanisms, making it difficult to directly apply research results to actual projects. Furthermore, traditional methods often consider the behavior of piles, soils, and structures in isolation, ignoring the complex coupling mechanisms of multiphase media at interfaces, particularly the nonlinear response characteristics under dynamic loads.

[0004] Currently, the engineering community lacks effective methods to systematically address the cross-scale effects of pile-soil-structure dynamic interactions. This makes it difficult to accurately establish the relationship between microscopic mechanisms and macroscopic responses, making it difficult to reliably predict the entire process from material parameters to structural responses. This hinders the safety assessment and optimal design of pile foundation projects in complex dynamic environments. In other words, existing technologies present a technical challenge in accurately simulating the cross-scale effects of pile-soil-structure dynamic interactions. Summary of the Invention

[0005] In view of this, the present invention provides a pile-soil-structure dynamic interaction analysis method, which can solve the technical problem in the prior art that the cross-scale effect of pile-soil-structure dynamic interaction is difficult to accurately simulate.

[0006] The present invention is implemented as follows: The present invention provides a pile-soil-structure dynamic interaction analysis method, which includes: conducting a first-scale physical model experiment to obtain first data; based on the first data, using the pile-soil interface multiphase fluid-solid coupling mechanism equation to calculate two scale inflection points, and determining the model sizes required for second-scale and third-scale experiments; performing second-scale and third-scale experiments to obtain second data and third data; establishing a basic equation group based on the first data, the second data and the third data; using the domain decomposition method to divide the calculation area into a near-field fine grid area and a far-field coarse grid area; applying the minimum spanning tree algorithm to optimize the grid division; numerically and analytically solving the basic equation group to obtain the pile body stress distribution, the soil deformation field and the pile foundation lateral displacement function; and merging the numerical solution and the analytical solution into a pile-soil-structure dynamic interaction model.

[0007] Among them, the first-scale physical model experiment is a micro-scale soil-single pile interaction test under laboratory conditions. The model size is defined as 1 / 100 to 1 / 50 of the actual pile foundation size, and the micro-dynamic response data is obtained through a vibration table and micro sensors.

[0008] Among them, the experimental feasibility scale range refers to the size range in which effective physical model tests can be carried out under laboratory and engineering site conditions, from the micron-level soil particle contact scale to the meter-level pile foundation scale, to ensure that the experimental data can accurately reflect the pile-soil structure interaction mechanism.

[0009] Among them, the multiphase fluid-solid coupling mechanism equation at the pile-soil interface is a set of partial differential equations that describes the deformation and stress transfer relationship between the fluid-solid two-phase medium between the pile and the soil under dynamic loads, taking into account the changes in soil pore water pressure and fluid seepage effects.

[0010] Among them, the scale inflection point refers to the critical size point where the dynamic response characteristics of pile-soil interaction change significantly with the change of physical model size, which is determined by dimensionless parameter analysis.

[0011] Among them, the model size of the second-scale experiment is the second size, which is calculated through the multiphase fluid-solid coupling mechanism equation of the pile-soil interface, focusing on the group behavior and interaction mechanism between the pile and the surrounding soil.

[0012] Among them, the model size of the third-scale experiment is the third size, which is calculated through the multiphase fluid-solid coupling mechanism equation of the pile-soil interface, and focuses on measuring the dynamic response characteristics of the overall structure and foundation system.

[0013] Among them, the basic equation group includes the pile-soil interface control equation and the pile-structure coupling equation; the pile-soil interface control equation is used to describe the mechanical behavior of the contact surface between the soil around the pile and the pile body. The input includes the soil density parameter in the first data, the pile foundation geometric parameters in the second data, and the load time history function in the third data. The output is the pile-soil interface stress distribution and displacement field.

[0014] Among them, the pile structure coupling equation is used to describe the relationship between the pile body response and the superstructure vibration transmission. The input includes the pile body material stiffness matrix in the second data, the structural mass distribution and the pile-soil interface stress distribution in the third data, and the output is the pile foundation lateral displacement function and the structural dynamic response.

[0015] Among them, the lateral displacement function of the pile foundation is a mathematical function that characterizes the displacement distribution law of the pile foundation along the depth under the action of horizontal load. It is related to soil parameters and load frequency and is a key indicator for evaluating the stability of the pile foundation; the pile body stress distribution is the distribution of axial stress, shear stress and bending moment along the pile length generated by the pile under vertical and lateral loads, which is obtained through numerical solution; the soil deformation field is the displacement, strain and stress distribution state generated by the soil under dynamic load, reflecting the stress transfer path during the interaction between the soil and the pile foundation.

[0016] The present invention organically connects the physical behaviors at different scales through three-scale experiments, and applies the multiphase fluid-solid coupling mechanism equation of the pile-soil interface to determine the key scale inflection point, thereby realizing a system analysis from micro to macro. This method breaks through the limitations of traditional single-scale analysis and effectively solves the scale effect problem of the pile-soil interface interaction. By establishing a unified set of basic equations and combining the domain decomposition method with the minimum spanning tree algorithm to optimize the calculation grid, an efficient and accurate combination of numerical solution and analytical solution is achieved, capturing the essential characteristics of the dynamic response of the pile-soil-structure system at different scales. The present invention successfully establishes a cross-scale analysis framework for the dynamic interaction between piles, soils and structures, enabling engineers to accurately predict the mechanical behavior of pile foundations under complex dynamic loads, realizing the organic unity of microscopic mechanism and macroscopic response, and solving the technical problem in the prior art that the cross-scale effect of the pile-soil-structure dynamic interaction is difficult to accurately simulate. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a flow chart of the method of the present invention.

[0018] Figure 2 Schematic diagram of the overall device for the first-scale experiment in Example 2.

[0019] Figure 3 This is a schematic diagram of the transparent organic glass soil box structure in Example 2.

[0020] Figure 4 Schematic diagram of the model pile and sensor arrangement in Example 2.

[0021] Figure 5 Schematic diagram of the microsensor system in Example 2. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0023] like Figure 1 FIG. 1 is a flow chart of a pile-soil-structure dynamic interaction analysis method provided by the present invention, and the method comprises the following steps: S01. Conduct a first-scale physical model experiment, using a scaled-down model directly defined under laboratory conditions to measure soil microscopic parameters and dynamic responses, and obtain first-scale experimental data, which are recorded as first data; S02. Based on the first data, calculate two scale inflection points within the experimental feasibility scale using the multiphase fluid-solid coupling mechanism equation at the pile-soil interface, and determine the model sizes required for the second and third scale experiments, which are recorded as the second size and the third size, respectively. S03, executing the second scale to construct the pile foundation physical model, executing the second scale experiment, obtaining the second scale experimental data, and recording it as the second data; executing the third scale to construct the pile foundation physical model, executing the third scale experiment, obtaining the third scale experimental data, and recording it as the third data; S04. Establishing and fitting a pile-soil structure dynamic interaction equation group based on the first data, the second data, and the third data, and recording it as a basic equation group; S05, dividing the calculation area of ​​the basic equation group into a near-field fine grid area and a far-field coarse grid area using a domain decomposition method, and defining a variable transfer rule at the regional boundary; S06. Applying a minimum spanning tree algorithm to optimize the grid division between the near-field fine grid area and the far-field coarse grid area to ensure optimal connectivity between the areas and reasonable allocation of computing resources; S07, numerically solving the basic equations to obtain a numerical solution, including pile stress distribution and soil deformation field; S08, analytically solving the basic equations to obtain an analytical solution, including a pile foundation lateral displacement function; S09. Combining the numerical solution and the analytical solution into a pile-soil structure dynamic interaction model, wherein the pile foundation lateral displacement function is used as a basic parameter, and the pile body stress distribution and the soil deformation field are used as boundary conditions.

[0024] The basic equation group includes the pile-soil interface control equation and the pile-structure coupling equation; The pile-soil interface control equation is used to describe the mechanical behavior of the contact surface between the soil around the pile and the pile body. The input includes the soil density parameter in the first data, the pile foundation geometric parameters in the second data, and the load time history function in the third data. The output is the stress distribution and displacement field of the pile-soil interface. The pile structure coupling equation is used to describe the relationship between the pile body response and the superstructure vibration transmission. The input includes the pile body material stiffness matrix in the second data, the structural mass distribution in the third data and the pile-soil interface stress distribution. The output is the pile foundation lateral displacement function and the structural dynamic response.

[0025] Among them, the first-scale physical model experiment specifically conducts a micro-scale soil-single pile interaction test under laboratory conditions. The model size is directly defined as 1 / 100 to 1 / 50 of the actual pile foundation size, and micro-dynamic response data is obtained through a vibration table and micro sensors.

[0026] Among them, the experimental feasibility scale range specifically refers to the size range in which effective physical model tests can be carried out under laboratory and engineering site conditions, from the micron-level soil particle contact scale to the meter-level pile foundation scale, to ensure that the experimental data can accurately reflect the pile-soil structure interaction mechanism.

[0027] Among them, the multiphase fluid-solid coupling mechanism equation at the pile-soil interface is specifically a set of partial differential equations that describes the deformation and stress transfer relationship between the fluid-solid two-phase medium between the pile and the soil under dynamic loads, taking into account the changes in soil pore water pressure and fluid seepage effects.

[0028] The scale inflection point specifically refers to the critical size point where the dynamic response characteristics of pile-soil interaction change significantly as the size of the physical model changes, and is determined through dimensionless parameter analysis.

[0029] Among them, the second-scale experiment specifically uses a medium-sized model to conduct dynamic testing of pile-soil interaction. The model size is the second size, and it is calculated through the multiphase fluid-solid coupling mechanism equation of the pile-soil interface, focusing on the group behavior and interaction mechanism between the pile and the surrounding soil.

[0030] Among them, the third-scale experiment specifically adopts a large-scale physical model test, the model size is the third size, and is calculated through the multiphase fluid-solid coupling mechanism equation of the pile-soil interface, focusing on measuring the dynamic response characteristics of the overall structure and foundation system.

[0031] Among them, the domain decomposition method specifically divides the complex calculation area into several sub-areas, uses a solution method of different precision in each sub-area, and realizes the parallel computing technology of solving the overall problem through the transfer of regional boundary variables.

[0032] Among them, the minimum spanning tree algorithm is specifically a graph theory algorithm used to find the minimum weight path connecting all grid nodes, ensuring the optimal connectivity of grid partitioning and minimizing computing resource consumption.

[0033] Among them, the lateral displacement function of the pile foundation is a mathematical function that characterizes the displacement distribution law of the pile foundation along the depth under the action of horizontal load. It is related to soil parameters and load frequency and is a key indicator for evaluating the stability of the pile foundation.

[0034] The pile stress distribution specifically refers to the distribution of axial stress, shear stress and bending moment generated by the pile body under vertical and transverse loads along the pile length, which is obtained through the numerical solution.

[0035] Among them, the soil deformation field is specifically the displacement, strain and stress distribution state generated by the soil under the action of dynamic load, reflecting the stress transfer path during the interaction between the soil and the pile foundation.

[0036] Among them, the structural dynamic response refers specifically to the acceleration, velocity and displacement response time and spectrum characteristics of the superstructure under earthquake or dynamic loads, which is an important indicator for evaluating the seismic performance of the structure.

[0037] The specific implementation of the above steps is described in detail below.

[0038] The specific implementation of step S01 involves selecting a model with a scale of 1 / 100 to 1 / 50 of the actual engineering pile foundation size and constructing a microscale physical model of the interaction between soil and a single pile under laboratory conditions. This physical model consists of a model soil, a model pile, and a supporting sensor system. First, a soil sample meeting the similarity ratio requirements is prepared, and its basic parameters, such as density, moisture content, and particle size distribution, are measured. A microsensor array, including pore water pressure sensors, earth pressure sensors, and accelerometers, is then embedded in the soil sample. The sensor spacing is set at 0.2 to 0.5 times the pile diameter, forming a three-dimensional sensor network. The model pile is then inserted into the soil, and strain gauges are placed along the pile shaft, with the strain gauges spaced no more than 1 times the pile diameter along the longitudinal direction. Finally, the entire model is mounted on a vibration table, and dynamic excitations of varying frequencies (5 to 100 Hz) and amplitudes (0.05 to 0.3 g) are applied. Data from each sensor is recorded, and soil microscopic parameters and dynamic response data are acquired to form the first data set. The purpose of this step is to obtain the soil micromechanical parameters and preliminary dynamic response characteristics under controlled laboratory conditions, providing basic data support for subsequent multi-scale analysis.

[0039] The specific implementation of step S02 is to construct a multiphase fluid-solid coupling mechanism equation at the pile-soil interface based on the first data. This equation takes into account soil skeleton deformation, pore water pressure changes, and fluid seepage effects, and mainly includes soil deformation control equations, fluid seepage equations, and interface contact equations. First, a soil constitutive model was established based on parameters such as soil density, porosity, and permeability from the first data set. The soil stress-strain relationship and pore water pressure variations were then analyzed to establish the fluid-structure coupling equations. The pile-soil interface contact parameters, including the friction angle, normal stiffness, and tangential stiffness, were then introduced to construct a complete set of multiphase fluid-structure coupling equations. This system of equations was then subjected to dimensional analysis, introducing the dimensionless parameter λ, which is the ratio of the pile diameter to the soil characteristic length. When λ approaches 0.1 and 1.0, respectively, the pile-soil interaction mechanism undergoes significant changes; these two values ​​represent the scale inflection points. Finally, based on these two scale inflection points, the dimensions of the second-scale experimental model were determined to be 1 / 20 to 1 / 10 of the actual pile foundation size (second scale), and the dimensions of the third-scale experimental model were determined to be 1 / 5 to 1 / 2 of the actual pile foundation size (third scale). The goal of this step was to identify key scale inflection points through theoretical analysis based on microscopic experimental data, allowing for the scientific design of subsequent physical model experiments at different scales.

[0040] The specific implementation of step S03 involves designing and executing second- and third-scale physical model experiments, respectively, based on the second and third dimensions determined in step S02. For the second-scale experiment, a medium-sized pile foundation physical model is first constructed, typically with a diameter of 30 to 100 mm. A sensor system, including pile body strain sensors, earth pressure sensors, displacement sensors, and accelerometers, is then installed within the model. Horizontal and vertical dynamic loads are then applied using a hydraulic loading system or a vibration table, with the load frequency range set to 2 to 40 Hz. Finally, the sensor data is recorded to obtain the pile foundation's geometric and material parameters, as well as the mesoscale dynamic response, forming a second dataset. For the third-scale experiment, a large-scale pile foundation physical model is first constructed, typically with a diameter of 100 to 500 mm, along with a simplified superstructure. A comprehensive sensing and monitoring system is then deployed, including monitoring points for pile foundation displacement, structural acceleration, and pile-soil interface stress. Seismic waves or dynamic loads resembling actual working conditions are then applied, with a loading frequency range of 0.5 to 10 Hz. Finally, the overall response data of the model is collected to obtain the structural mass distribution, load time history function, and large-scale dynamic characteristics, forming the third data set. This step aims to obtain the dynamic response characteristics of the pile-soil structure system at different scales, providing the experimental data foundation for establishing a complete pile-soil structure dynamic interaction model.

[0041] The specific implementation of step S04 is to establish and fit a set of equations for the dynamic interaction between the pile and the soil structure based on the first, second, and third data. First, the scale effect of the key parameters in the three data sets is analyzed to establish a scale conversion function. Then, a pile-soil interface control equation is constructed. This equation uses the soil density parameter in the first data, the pile foundation geometric parameters in the second data, and the load time history function in the third data as inputs to describe the mechanical behavior of the contact surface between the soil around the pile and the pile body. Next, a pile-structure coupling equation is constructed. This equation uses the pile body material stiffness matrix in the second data, the structural mass distribution, and the pile-soil interface stress distribution in the third data as inputs to describe the relationship between the pile body response and the vibration transmission of the superstructure. The parameters in the equations are then fitted using the least squares method, with the fitting error controlled within 5%. Finally, the pile-soil interface control equation and the pile-structure coupling equation are combined into a complete set of basic equations. The purpose of this step is to integrate multi-scale experimental data and establish a mathematical model that can accurately describe the mechanism of the dynamic interaction between the pile and the soil structure.

[0042] The specific implementation of step S05 is to use the domain decomposition method to divide the calculation area of ​​the basic equations. First, the geometric scope of the calculation area is determined, usually taking 3 times the pile length as the depth calculation boundary and 20 times the pile diameter as the horizontal calculation boundary. Then, the calculation area is divided into a near-field fine grid area and a far-field coarse grid area. The near-field area is usually 5 to 10 times the pile diameter, and the far-field area is the remaining calculation area. Then, a fine grid is used in the near-field area, with the grid size no larger than 1 / 10 of the pile diameter to accurately simulate the complex stress state of the pile-soil interface. In the far-field area, a coarse grid is used, with the grid size gradually increasing to 1 to 3 times the pile diameter to reduce the amount of calculation. Then, the regional boundary variable transfer rules are defined, including displacement continuity conditions, force balance conditions, and energy conservation conditions. Finally, a transition area is set at the junction of the two areas, with a width of 1 to 2 times the pile diameter, and a gradient grid is used to ensure a smooth transition in calculation accuracy. The purpose of this step is to reasonably divide the calculation area, balance the relationship between calculation accuracy and calculation efficiency, and lay the foundation for subsequent numerical solutions.

[0043] The specific implementation method of step S06 is to apply the minimum spanning tree algorithm to optimize the mesh division between the near-field fine mesh area and the far-field coarse mesh area. First, all mesh nodes in the calculation area are regarded as vertices in the graph, and the computational cost between adjacent nodes is regarded as the weight of the edge; then, a minimum spanning tree is constructed based on the Kruskal algorithm or the Prim algorithm. The algorithm starts from the edge with the smallest weight and gradually adds edges that do not form loops until all vertices are connected; then, the mesh division is optimized according to the minimum spanning tree structure to ensure optimal mesh connection and reasonable allocation of computing resources; then, the mesh quality is evaluated, including indicators such as mesh distortion and aspect ratio. The distortion is controlled to be above 0.6 and the aspect ratio is controlled to be within 1:5; finally, the adaptive mesh optimization technology is applied to further refine the mesh in areas with large stress gradients, and the mesh size can be reduced to 1 / 2 or 1 / 3 of the original. The purpose of this step is to obtain a high-quality computational mesh and improve the accuracy and efficiency of the numerical solution.

[0044] The specific implementation of step S07 is to numerically solve the basic equations to obtain the pile stress distribution and soil deformation field. First, select an appropriate numerical method, such as the finite element method, finite difference method or boundary element method; then set the solution parameters, including the time step, iteration accuracy and damping coefficient. The time step is usually set to 1 / 20 to 1 / 10 of the main excitation frequency period, and the iteration accuracy is set to ~ Next, the relevant parameters from the first to third data sets are imported, including material parameters, boundary conditions, and load conditions. Numerical calculations are then performed, using an implicit integration scheme to ensure computational stability and to control the energy balance error at each time step to no more than 3%. Finally, the calculation results are extracted to obtain the axial force, shear force, and bending moment distributions at different depths of the pile, as well as the displacement, strain, and stress fields of the soil. The goal of this step is to obtain the detailed mechanical response of the pile-soil system under dynamic loads through high-precision numerical simulation.

[0045] The specific implementation method of step S08 is to analytically solve the basic equations to obtain the pile foundation lateral displacement function. First, the basic equations are simplified, and the soil is assumed to be a Winkler foundation or a modified Py curve model. Then, the separation of variables method is introduced to express the pile foundation lateral displacement as a function product of depth and time. Then, an ordinary differential equation for the pile foundation lateral displacement is established, treating the pile as an elastic beam and the soil as a series of spring supports. The ordinary differential equation is then solved using the eigenvalue analysis method to obtain an analytical expression for the pile foundation lateral displacement function. Finally, the key parameters in the numerical solution are substituted into the analytical solution, and the parameters of the analytical model are optimized to keep the difference between the two within 10%. The purpose of this step is to obtain an analytical function that describes the pile foundation lateral displacement and provide a convenient and practical calculation tool for engineering applications.

[0046] The specific implementation of step S09 is to combine the numerical solution and the analytical solution into a pile-soil structure dynamic interaction model. First, the pile foundation lateral displacement function is used as the basic parameter. This function contains key variables such as soil stiffness, pile bending stiffness, and load frequency. Then, the pile stress distribution is used as the boundary condition, including the pile top bending moment, pile top shear force, and the location of the maximum bending moment of the pile body. Then, the soil deformation field is also used as the boundary condition, including the maximum displacement area of ​​the soil, the stress transfer path, and the soil damping characteristics. Then, a dynamic interaction model is established. The model can predict the pile foundation displacement, stress distribution, and superstructure response based on the input seismic waves or other dynamic loads. Finally, by comparing and verifying with the original experimental data, the error between the model prediction results and the experimental data should be controlled within 15%. The purpose of this step is to integrate the advantages of numerical solutions and analytical solutions to establish an accurate and practical pile-soil structure dynamic interaction model, providing a theoretical tool for engineering design and analysis.

[0047] Specifically, the principle behind this invention is that its technical principle is based on the multi-scale analysis and physical mechanism characterization of the dynamic interaction of the pile-soil-structure system. First, through scientifically designed three-scale physical model experiments, the dynamic response data of the pile-soil-structure system at different scales are systematically obtained, breaking through the limitations of single-scale experiments. The first-scale experiment focuses on microscopic soil behavior, the second-scale focuses on the mesoscopic pile-soil interface interaction, and the third-scale focuses on the overall macroscopic structural response. These three-scale experiments complement each other and comprehensively characterize the multi-scale dynamic characteristics of the complex system.

[0048] The core of this invention is to establish a theoretical bridge between scales through the multiphase fluid-solid coupling mechanism equation at the pile-soil interface, identify scale inflection points, and ensure the scientific nature of the experimental design and the consistency of the data. This equation takes into account the changes in soil pore water pressure and seepage effects, and accurately describes the complex coupling mechanism of the fluid-solid two-phase medium between piles and soil under dynamic loads. The basic equation set established based on experimental data includes the pile-soil interface control equation and the pile-structure coupling equation, which comprehensively characterizes the dynamic response characteristics of the pile-soil-structure system.

[0049] In terms of solution, this invention utilizes the domain decomposition method and the minimum spanning tree algorithm to optimize computational meshing, balancing computational accuracy and efficiency. The combined application of numerical and analytical solutions enables the model to accurately describe complex local stress distributions while providing an analytical expression of the global displacement function, providing a flexible and convenient analytical tool for engineering applications. This multi-scale, data-driven theoretical model construction approach achieves an organic unification of microscopic mechanisms and macroscopic responses, addressing the cross-scale effects in pile-soil-structure dynamic interaction analysis.

[0050] A specific embodiment 1 of the present invention is provided below. The specific implementation of each step in this embodiment 1 is described in detail as follows.

[0051] The specific implementation of step S01 is to select a model with a scale of 1 / 100 to 1 / 50 of the actual engineering pile foundation size, and construct a physical model of the interaction between micro-scale soil and single pile under laboratory conditions. The physical model consists of model soil, model pile and supporting sensor system. First, prepare a soil sample that meets the similarity ratio requirements and measure its density. , moisture content , particle grading and other basic parameters; then a micro sensor array is buried in the soil sample, including pore water pressure sensor, soil pressure sensor and acceleration sensor, and the sensor spacing is set to the pile diameter 0.2 to 0.5 times of the original diameter to form a three-dimensional sensor network; then the model pile is inserted into the soil and strain gauges are arranged in the pile body. The strain gauges are spaced no more than 1 times the pile diameter along the longitudinal direction of the pile body; finally, the entire model is installed on a vibration table, dynamic excitation of different frequencies (5 to 100 Hz) and amplitudes (0.05 to 0.3 g) is applied, and the data of each sensor is recorded. The first data obtained can be expressed in matrix form ,in is the soil density, is the moisture content, For cohesion, is the internal friction angle, is the soil deformation modulus, is the pore water pressure, is the soil stress, is the soil strain, The purpose of this step is to obtain the soil micromechanical parameters and preliminary dynamic response characteristics under controlled laboratory conditions, providing basic data support for subsequent multi-scale analysis.

[0052] The specific implementation method of step S02 is to construct a multiphase fluid-solid coupling mechanism equation at the pile-soil interface based on the first data. This equation takes into account the deformation of the soil skeleton, the change in pore water pressure and the fluid seepage effect, and mainly includes the soil deformation control equation, the fluid seepage equation and the interface contact equation. First, a soil constitutive model is established based on the parameters such as soil density, porosity, and permeability coefficient in the first data; then, the soil stress-strain relationship and the law of pore water pressure change are analyzed to establish a fluid-solid coupling equation. For saturated soil, the basic fluid-solid coupling equation can be expressed as: ; ; in, is the effective stress tensor of soil, is the acceleration due to gravity, is the displacement, is the permeability tensor, is the pore water pressure, is the water storage coefficient, is the Biot coefficient, is the volume strain. Then the pile-soil interface contact parameters are introduced, including the interface friction angle , normal stiffness and tangential stiffness , construct the interface contact equation: ; ; ;

[0053] in, is the interface shear stress, is the interfacial cohesion, is the interface normal stress, is the interface friction angle, is the normal displacement difference, is the tangential displacement difference, is the maximum shear stress. Then, dimensional analysis is performed and dimensionless parameters are introduced. , ,in is the pile diameter, is the characteristic length of the soil. When the values ​​approach 0.1 and 1.0, respectively, the pile-soil interaction mechanism undergoes significant changes. These two values ​​are the scale inflection points. Finally, based on these two scale inflection points, the size of the second-scale experimental model is determined to be 1 / 20 to 1 / 10 of the actual pile foundation size (second scale), and the size of the third-scale experimental model is determined to be 1 / 5 to 1 / 2 of the actual pile foundation size (third scale). The purpose of this step is to determine the key scale inflection points through theoretical analysis based on microscopic experimental data, and to scientifically design subsequent physical model experiments at different scales.

[0054] The specific implementation method of step S03 is to design and execute the second-scale and third-scale physical model experiments respectively based on the second and third dimensions determined in step S02. For the second-scale experiment, first construct a medium-sized pile foundation physical model, where the diameter of the model pile is usually 30 to 100 mm; then set up a sensor system in the model, including pile body strain sensors, soil pressure sensors, displacement sensors, and acceleration sensors; then use a hydraulic loading system or a vibration table to apply horizontal and vertical dynamic loads, with the load frequency range set to 2 to 40 Hz; finally, record the sensor data to obtain the pile foundation geometric parameters, material parameters, and mesoscale dynamic response, forming a second data set. .in is the elastic modulus of the pile material, is the pile section moment of inertia, is the pile diameter, For the pile length, is the pile material density, is the Poisson's ratio of the pile material, is the bending moment distribution of the pile body, is the shear force distribution of the pile body, For the third-scale experiment, a large-scale pile foundation physical model is first constructed. The diameter of the model pile is usually 100 to 500 mm, and a simplified superstructure is constructed. Then, a full-scale sensing monitoring system is arranged, including monitoring points for pile foundation displacement, structural acceleration, and pile-soil interface stress. Then, seismic waves or dynamic loads similar to actual working conditions are applied, with a loading frequency range of 0.5 to 10 Hz. Finally, the overall response data of the model is collected to obtain the structural mass distribution, load time history function, and large-scale dynamic characteristics to form the third data set. .in is the structural mass distribution function, is the damping distribution function, is the stiffness distribution function, is the load time history function, is the acceleration response time history, The purpose of this step is to obtain the dynamic response characteristics of the pile-soil structure system at different scales and provide experimental data basis for establishing a complete pile-soil structure dynamic interaction model.

[0055] The specific implementation of step S04 is to establish and fit the pile-soil structure dynamic interaction equations based on the first data, the second data and the third data. First, analyze the scale effect of the key parameters in the three data sets and establish the scale conversion function ,in is the scale effect coefficient, is a dimensionless parameter; then the pile-soil interface control equation is constructed. This equation takes the soil density parameter in the first data, the pile foundation geometric parameters in the second data, and the load time history function in the third data as input to describe the mechanical behavior of the contact surface between the soil around the pile and the pile body: ; ; ; in, is the soil displacement vector, is the soil density, is the soil stress tensor, is the interfacial force, is the soil stiffness matrix, is the soil strain tensor. Next, the pile-structure coupling equation is constructed. This equation uses the pile material stiffness matrix in the second data, the structural mass distribution in the third data, and the pile-soil interface stress distribution as input to describe the relationship between the pile response and the superstructure vibration transmission: ; ; in is the lateral displacement of the pile, is the depth coordinate, is the elastic modulus of the pile material, is the pile section moment of inertia, is the pile material density, is the cross-sectional area of ​​the pile, is the reaction force of soil on the pile, is the structural mass distribution function, is the damping distribution function, is the stiffness distribution function, is the structural displacement, is the external load, is the pile foundation reaction. The least squares method was then used to fit the parameters in the equation, keeping the fitting error within 5%. Finally, the governing equations for the pile-soil interface and the pile-structure coupling equations were combined to form a complete set of basic equations. The purpose of this step was to integrate multi-scale experimental data and establish a mathematical model that accurately describes the dynamic interaction mechanism between the pile and the soil.

[0056] The specific implementation of step S05 is to use the domain decomposition method to divide the calculation area of ​​the basic equations. First, determine the geometric range of the calculation area, usually taking the pile length 3 times of the depth is used as the calculation boundary, and the pile diameter 20 times of the horizontal direction is used as the calculation boundary; then the calculation area is divided into the near-field fine grid area and far-field coarse mesh region The near-field area is usually 5 to 10 times the pile diameter, and the far-field area is the remaining calculation area; then the near-field area is divided into fine grids, and the grid size is The size of the mesh is not larger than 1 / 10 of the pile diameter to accurately simulate the complex stress state of the pile-soil interface. In the far field, a coarse mesh is used, and the mesh size is Gradually increase to 1 to 3 times the pile diameter to reduce the amount of calculation; then define the area boundary The variable transfer rules on , including displacement continuity conditions, force balance conditions and energy conservation conditions: ; ; ; in, and are the displacements in the near field and far field, respectively, and are the stress tensors in the near field and far field, respectively, is the interface normal vector, and are the velocities in the near and far fields, respectively. Finally, a transition region is set at the junction of the two regions, with a width of 1 to 2 times the pile diameter. A gradient mesh is used to ensure a smooth transition in computational accuracy. This step aims to rationally divide the computational region, balancing accuracy and efficiency, and laying the foundation for subsequent numerical solutions.

[0057] The specific implementation of step S06 is to use the minimum spanning tree algorithm to optimize the grid division between the near-field fine grid area and the far-field coarse grid area. First, all the grid nodes in the calculation area are regarded as graphs. The vertex set in , the computational cost between adjacent nodes is considered as an edge set Weight ; Then construct the minimum spanning tree based on Kruskal algorithm , the implementation process of Kruskal algorithm is: sort all edges by weight from small to large, and the minimum spanning tree is initially Empty, examine each edge in order from small to large weight If you add an edge Will not be in the future If a loop is formed in join in In, until Include Then, the grid division is optimized according to the minimum spanning tree structure to ensure optimal grid connection and reasonable allocation of computing resources. The optimization objective function of the minimum spanning tree can be expressed as: ; in, For the edge The weight of and For the edge The mesh size corresponding to the two connected nodes, and is the weight coefficient, usually , The mesh quality was then evaluated, including the degree of mesh distortion. , aspect ratio The distortion is controlled above 0.6 and the aspect ratio is controlled within 1:5. Finally, adaptive mesh optimization technology is applied to further refine the mesh in areas with large stress gradients, reducing the mesh size to 1 / 2 or 1 / 3 of the original size. The purpose of this step is to obtain a high-quality computational mesh and improve the accuracy and efficiency of the numerical solution.

[0058] The specific implementation of step S07 is to numerically solve the basic equations to obtain the pile stress distribution and soil deformation field. First, select an appropriate numerical method, such as the finite element method; then set the solution parameters, including the time step , iteration accuracy and damping coefficient , the time step is usually taken as the main excitation frequency 1 / 20 to 1 / 10 of the cycle, that is , the iteration accuracy is set to ~ ; Then import the relevant parameters of the first data to the third data, including material parameters, boundary conditions and load conditions; then perform numerical calculations using Newmark- The implicit integration scheme ensures computational stability: ; ; in, 、 and Respectively The displacement, velocity and acceleration of the step, and is the integral parameter, usually taken as , Finally, the calculation results are extracted to obtain the axial forces of the pile at different depth sections. , shear force and bending moment distribution, and the displacement field of the soil , strain field and stress field The purpose of this step is to obtain the detailed mechanical response of the pile-soil system under dynamic loads through high-precision numerical simulation.

[0059] The specific implementation of step S08 is to analytically solve the foundation equations to obtain the pile foundation lateral displacement function. First, simplify the foundation equations and assume the soil to be a Winkler foundation or an improved Py curve model; then introduce the separation of variables method and express the pile foundation lateral displacement as depth and time Function product of ; Then, the ordinary differential equation for the lateral displacement of the pile foundation is established, treating the pile as an elastic beam and the soil as a series of spring supports: ; in, is the elastic modulus of the pile material, is the pile section moment of inertia, is the spatial part of the displacement function, is the soil horizontal reaction coefficient. The general solution of this equation is: ; in, , 、 、 and The coefficients are unknown and can be solved based on the boundary conditions. The ordinary differential equation is then solved using eigenvalue analysis to obtain an analytical expression for the pile foundation's lateral displacement function. Finally, the key parameters from the numerical solution are substituted into the analytical solution, and the parameters of the analytical model are optimized to keep the difference within 10%. This step aims to obtain an analytical function describing the pile foundation's lateral displacement, providing a convenient and practical calculation tool for engineering applications.

[0060] The specific implementation of step S09 is to combine the numerical solution and the analytical solution into a pile-soil structure dynamic interaction model. First, the pile foundation lateral displacement function is the basic parameter, which includes the soil stiffness , Pile bending stiffness and load frequency Other key variables: ; in, For the The order mode function, For the Then the stress distribution of the pile body is used as the boundary condition, including the bending moment at the pile top. , pile top shear force and the maximum bending moment position of the pile body ; Then the soil deformation field is also used as the boundary condition, including the maximum displacement area of ​​the soil, the stress transfer path and the soil damping characteristics; then the dynamic interaction model is established, which can be based on the input seismic wave or other dynamic loads , predict pile foundation displacement, stress distribution and superstructure response: ; in, For the order damping ratio, For the order natural frequency, For the Order generalized load, For the Finally, by comparing with the original experimental data, the verification indicators include the relative error of displacement. , stress relative error and frequency relative error , the error between the model prediction results and the experimental data should be controlled within 15%: ; ; ; in, and are the calculated displacement and experimental displacement, respectively. and are the calculated stress and the experimental stress, and The purpose of this step is to integrate the advantages of numerical solutions and analytical solutions, establish an accurate and practical pile-soil structure dynamic interaction model, and provide a theoretical tool for engineering design and analysis.

[0061] Optionally, the detailed solution process of step S07 is to numerically solve the basic equations using the finite element method to obtain the stress distribution of the pile body and the deformation field of the soil. First, a finite element model of the pile-soil-structure system is established, and the calculation area is divided into a finite number of units to form a discretized model. Beam units are used for piles, and the unit node degrees of freedom include displacement and rotation; solid units are used for soil, usually eight-node hexahedron units. The dynamic equilibrium equation for the entire system can be expressed as: ; in, is the mass matrix, is the damping matrix, is the stiffness matrix, is the node displacement vector, is the node load vector. The mass matrix The calculation uses a lumped mass matrix. For pile elements, the local mass matrix Expressed as: ; in, is the pile material density, is the cross-sectional area of ​​the pile, For the soil element, its mass matrix uses a consistent mass matrix, which is represented by the shape function The calculation shows that: ; in, is the soil density, is the shape function matrix, is the unit volume. Stiffness matrix It is assembled from the stiffness matrices of each unit. For pile units, its local stiffness matrix is Expressed as: ; in, is the elastic modulus of the pile material, is the moment of inertia of the pile section. For the soil element, its stiffness matrix is ​​composed of the strain-displacement matrix and elastic matrix The calculation shows that: ; in, Contains derivatives of shape functions, Contains the elastic parameters of the soil. Damping matrix Using the Rayleigh damping model: ; in, and is the Rayleigh damping coefficient, which can be obtained by the two modal damping ratios and and the corresponding circular frequency and Solution: ; Solving this equation yields: ; ; Usually the first and second modes are taken for calculation, that is, , Next, apply Newmark- The implicit integration method integrates the dynamic equilibrium equation in the time domain. The basic idea of ​​this method is to expand the Taylor series and assume that the displacement, velocity, and acceleration satisfy the following relationship: ; ; in, 、 and Respectively The displacement, velocity and acceleration vectors of the step, is the time step, and is the integral parameter, usually taken as , To ensure unconditional stability. Transforming the above formula, we can get: ; ; Substituting the first equation into the second, we obtain: ; Will and Substituting into the dynamic balance equation, we get: ; After finishing, we can get: ; make , As the right side of the equation, the above formula can be simplified as: ; Solving this equation, we can get Displacement of time Then, according to the previous relationship, we can calculate The speed of time and acceleration .

[0062] For the initial conditions, it is usually assumed that , , and solve according to the initial equilibrium equation : ; ; After completing the time domain integration, the stress and strain can be calculated from the displacement results. For pile elements, the pile bending moment and shear force The calculation is as follows: ; ; Pile axial force By axial displacement The calculation shows that: ; For soil elements, the strain is calculated from the displacement derivative: ; in, is the strain-displacement matrix. The stress is calculated from the strain using the constitutive relation: ; in, is the elastic matrix. For linear elastic isotropic materials, Young's modulus and Poisson's ratio Sure: ; After the calculation is completed, the results are extracted to form the pile stress distribution 、 and and soil deformation field , strain field and stress field The purpose of this step is to obtain the detailed mechanical response of the pile-soil system under dynamic loads through high-precision numerical simulation.

[0063] Optionally, the detailed solution process of step S08 is to analytically solve the basic equations to obtain the lateral displacement function of the pile foundation. First, simplify the model and assume that the soil is a Winkler foundation, that is, the soil is replaced by a series of independent springs, and the spring stiffness is the horizontal foundation reaction coefficient. The lateral bending of a pile under horizontal load can be described by the following fourth-order differential equation: ; in, is the elastic modulus of the pile material, is the pile section moment of inertia, For depth The lateral displacement at is the horizontal foundation reaction coefficient, is the pile diameter. To simplify the calculation, the characteristic parameter is introduced : ; Then the original equation can be simplified to: ; The general solution of this fourth-order ordinary differential equation can be expressed as: ; in, 、 、 and It is an undetermined coefficient and needs to be determined by boundary conditions. For free piles with fixed ends, the boundary conditions are: Pile top ( ): ; ; Pile bottom ( ): ; ; in, is the bending moment at the pile top, is the shear force at the pile top, is the pile length. Substitute the general solution into the boundary conditions and solve for the unknown coefficients. First, calculate the derivatives of the general solution: ; ; ; Will Substitute the second-order derivative expression and combine it with the pile top bending moment boundary condition: ; ; Will Substitute the third-order derivative expression and combine it with the shear boundary condition at the pile top: ; ; Will Substitute into the displacement expression and combine with the pile bottom displacement boundary condition: ; Will Substitute the first-order derivative expression and combine it with the boundary condition of the pile bottom rotation angle: ; This gives us four equations, containing four unknowns 、 、 and , these coefficients can be obtained by solving the linear equations. To facilitate the solution, the following notation is introduced: ; ; ; ; Then the two equations of the pile bottom boundary condition can be rewritten as: ; ; After finishing, we can get: ; ; Combining the previous two equations: ; ; After finishing, we can get: ; ; Will and Substitute the expression of into the pile bottom boundary condition equation, and we get and Two equations: ; ; Simplifying, we get: ; ; Further sorting, we get and The expression can then be inverted to and Substituting these four coefficients into the general solution expression, we can get the lateral displacement function of the pile The analytical expression of .

[0064] In order to consider the dynamic effect, the separation of variables method is used to express the lateral displacement of the pile as the depth and time Function product of : ; in, This is the spatial function solved above, is a time function that satisfies the ordinary differential equation: ; in, is the damping ratio, is the natural frequency of the system, is the external load, is the equivalent mass. The solution of this equation can be obtained by Duhamel integration: ; in, is the damped natural frequency of the damping system. For a given load function , the above equation can be solved by numerical integration method, and finally the complete analytical solution of the pile foundation lateral displacement is obtained: ; This analytical solution can easily calculate the change of the lateral displacement of piles at different depths over time, providing a theoretical basis for engineering design. At the same time, by differentiating the displacement function, the distribution of the bending moment and shear force of the pile body can be obtained: ; ; Through the above steps, the analytical solution process of the pile-soil-structure dynamic interaction is completed, and the analytical function describing the lateral displacement of the pile foundation is obtained, providing a convenient and practical calculation tool for engineering applications.

[0065] In order to better understand and implement the present invention, Example 2 of a specific application scenario of the present invention is provided below: In the design of a certain long-span bridge, it is necessary to evaluate the dynamic response characteristics of the high pile foundation of the pier under earthquake action. The pier pile foundation uses 8 bored cast-in-place piles with a diameter of 2m, a pile length of 45m, and a 3m thick abutment connection on the top of the pile. The pier height is 35m. The soil layer of the site is a 15m thick soft clay layer in the upper part, a 20m thick medium-dense sand layer in the middle part, and a strongly weathered rock layer in the lower part. In order to ensure the seismic safety of the bridge, the researchers decided to use the pile-soil-structure dynamic interaction analysis method to conduct a comprehensive evaluation of the project.

[0066] First, carry out the first-scale physical model experiment, such as Figure 2 As shown in the figure, the first scale experiment used a precision scale model device. The researchers selected a micro-scale model with a scale of 1:80, with a pile diameter of only 25mm and a pile length of 562.5mm. The experimental system mainly consists of three parts: a micro soil box, a model pile, and a full range of sensor monitoring systems. Figure 3 As shown, the soil box measures 600mm×600mm×600mm and is made of transparent organic glass, making it easy to observe internal deformation. The experimental soil is laid in layers according to the actual engineering site, including clay (thickness 187.5mm) in the upper part, sand (thickness 250mm) in the middle part, and simulated weathered rock layer (thickness 125mm) in the lower part. The sensing system is the core of the experiment, including 15 micro pore water pressure sensors (diameter only 3mm), 18 soil pressure sensors and 24 acceleration sensors, forming a three-dimensional monitoring network. Figure 4 As shown in Figure 1, strain gauges were placed every 25 mm on the model pile body, with a total of 20 measuring points. The entire model was installed on a high-precision electrodynamic vibration table. Harmonic excitations of different frequencies (5 Hz to 60 Hz) and amplitudes (0.05 g to 0.25 g) were applied through a computer control system. At the same time, a high-speed data acquisition system was used to record the data of each sensor. Figure 5 As shown in Table 1, the dynamic response characteristics of the pile-soil system at the micro scale are obtained. The experimental material parameters are shown in Table 1: Table 1. Material parameters of the first scale experiment

[0067] The researchers deployed 15 pore-water pressure sensors, 18 soil pressure sensors, and 24 accelerometers in the soil to form a three-dimensional sensing network. Strain gauges were placed every 25 mm along the model pile, for a total of 20 measurement points. The entire model was mounted on an electrodynamic vibration table and subjected to harmonic excitation at frequencies of 5 Hz, 10 Hz, 15 Hz, 25 Hz, 40 Hz, and 60 Hz, with peak accelerations of 0.05 g, 0.1 g, 0.15 g, 0.2 g, and 0.25 g. Data from each sensor was recorded to obtain the first data set. Some typical test results are shown in Table 2: Table 2 Typical test results of the first scale

[0068] Based on the first data, the researchers constructed the multiphase fluid-solid coupling mechanism equation of the pile-soil interface and introduced dimensionless parameters through dimensional analysis. ,in is the pile diameter, is the characteristic length of the soil. Through theoretical analysis, the two scale inflection points are determined to be and Based on this calculation, the size of the second-scale experimental model is 1:15 of the actual project (pile diameter 133mm), and the size of the third-scale experimental model is 1:4 of the actual project (pile diameter 500mm).

[0069] The second scale experiment used a medium-sized physical model with a scale of 1:15, a pile diameter of 133mm, and a pile length of 3m. The experimental device mainly includes a large soil box (4m×4m×4m), a model pile group (8 piles, arranged in the same way as the actual project), and a hydraulic servo loading system. The model piles are made of special cement mortar with a micro-doped silica fume, and the elastic modulus is MPa to simulate actual pile material performance. During the experiment, the researchers installed 36 strain gauges in the pile body, evenly distributed at different depths and orientations. A hydraulic servo loading system was used to apply horizontal and vertical dynamic loads at a frequency range of 2 to 35 Hz. A multi-channel data acquisition system was used to record the pile foundation's geometric parameters, material parameters, and mesoscale dynamic response characteristics, forming a second data set. The main parameters are shown in Table 3: Table 3 Main parameters and results of the second scale experiment

[0070] The third-scale experiment constructed a large-scale physical model approaching engineering scale, with a 1:4 scale, 500mm pile diameter, and 11.25m pile length. The experiment was conducted on a 15m x 15m earthquake-simulating shaking table with a maximum load capacity of 200 tons. The experimental apparatus consisted of a large model pile group (8 piles) and a simplified superstructure model. The researchers deployed a comprehensive sensing and monitoring system, including 48 pile foundation displacement measurement points, 36 structural acceleration measurement points, and 72 pile-soil interface stress monitoring points. Three typical seismic waves (El Centro, Taft, and Kobe) were applied during the experiment, with a maximum acceleration of 0.15g and a loading frequency range of 0.5–8Hz. The focus was on measuring the dynamic response characteristics of the entire pile-soil-structure system under seismic action. The overall model response data were collected, along with the structural mass distribution, load time history function, and large-scale dynamic characteristics. This data set formed the third dataset, providing large-scale experimental data support for the subsequent development of a complete dynamic interaction model. Selected test results are shown in Table 4. Table 4 Typical responses under different third-scale seismic waves

[0071] Based on experimental data at three scales, the researchers established a set of equations for the dynamic interaction between piles and soil structures. The pile-soil interface control equations used the modified Biot theory, taking into account the saturation and nonlinear characteristics of the soil; the pile-structure coupling equations used the Timoshenko beam model that takes into account shear deformation. The scale effect coefficients obtained by fitting are: Satisfy the relationship , the fitting error is 3.8%.

[0072] The domain decomposition method is used to divide the calculation area of ​​the basic equations. The range of the near-field fine grid area is 7 times the pile diameter (3.5m), and the grid size is 0.15m; the grid size of the far-field coarse grid area gradually increases from 0.3m to 5m. The minimum spanning tree algorithm is used to optimize the grid division, and the weight coefficient in the algorithm is , , the optimized mesh distortion The aspect ratio is 0.78 Control within 1:3.5.

[0073] The numerical solution uses the finite element method, and the time step , iteration accuracy , damping coefficient . Using Newmark- Implicit integration scheme, integration parameters , The calculation results show the distribution of axial force, shear force and bending moment at different depth sections of the pile body, as well as the displacement field, strain field and stress field distribution of the soil. The main calculation results are shown in Table 5: Table 5 Main results of numerical calculations

[0074] The basic equations are solved analytically, the soil is simplified into an improved Py curve model, and the separation of variables method is introduced to obtain the analytical expression of the pile foundation lateral displacement function: ; in, ,coefficient , , , , and are the time functions related to the load. The difference between the analytical solution and the numerical solution is controlled within 8.5%.

[0075] Finally, the numerical solution and analytical solution are combined into a pile-soil structure dynamic interaction model. This model uses the pile foundation lateral displacement function as the basic parameter and the pile body stress distribution and soil deformation field as the boundary conditions. It can predict the displacement, stress distribution and superstructure response of the pile foundation under different seismic excitations. The model prediction results are compared with the original experimental data to verify the relative error of displacement. The relative error of stress is 10.8%. The relative frequency error is 12.5%. The error is 7.3%, all controlled within 15%, meeting the accuracy requirements.

[0076] Traditional pile-soil-structure dynamic interaction analysis primarily uses the lumped parameter method or the continuum method. The lumped parameter method oversimplifies soil properties and cannot accurately simulate the complex pile-soil interface mechanism. While the continuum method takes into account soil continuity, it is computationally complex and struggles to reflect the nonlinear characteristics and deformation history effects of the soil. Furthermore, traditional methods are typically based on single-scale experimental data and cannot fully capture the response characteristics of the pile-soil system at different scales. The pile-soil-structure dynamic interaction analysis method employed in this embodiment systematically acquires full-scale data, from microscopic soil parameters to macroscopic structural responses, through physical model experiments at three different scales, overcoming the limitations of single-scale experiments. The introduced scale effect coefficient establishes a conversion relationship between different scales, enabling the effective integration of multi-scale data. A hybrid mesh model optimized using the domain decomposition method and the minimum spanning tree algorithm balances computational accuracy and efficiency, achieving an approximately 15% improvement in computational efficiency compared to the traditional uniform mesh model. By rationally combining numerical and analytical solutions, the model's accuracy is ensured while improving practicality, enabling engineers to rapidly assess the dynamic response of pile foundations under earthquakes. Verification results show that the prediction accuracy of this method is significantly better than that of traditional methods, providing reliable technical support for the seismic design of pile foundations of important engineering structures such as bridges.

[0077] It should be noted that the variables involved in the present invention are explained in detail as shown in Tables 6 and 7 below.

[0078] Table 6 Variable Explanation Table (Part I)

[0079] Table 7 Variable Explanation Table (Part II)

[0080] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of changes or replacements within the technical scope disclosed by the present invention, which should be covered by the scope of protection of the present invention.

Claims

1. A pile-soil-structure dynamic interaction analysis method, characterized in that: include: Conducting first-scale physical model experiments to obtain first data; Based on the first data, the multiphase fluid-solid coupling mechanism equation of the pile-soil interface is used to calculate the two-scale inflection points to determine the model size required for the second-scale and third-scale experiments; the second-scale and third-scale experiments are performed to obtain the second and third data; a basic set of equations is established based on the first, second, and third data; the domain decomposition method is used to divide the calculation area into a near-field fine grid area and a far-field coarse grid area; the minimum spanning tree algorithm is applied to optimize the grid division; the basic set of equations is numerically and analytically solved to obtain the pile body stress distribution, soil deformation field, and pile foundation lateral displacement function; the numerical and analytical solutions are combined into a pile-soil structure dynamic interaction model.

2. The pile-soil-structure dynamic interaction analysis method according to claim 1, characterized in that: The first-scale physical model experiment is a micro-scale soil-single pile interaction test under laboratory conditions. The model size is defined as 1 / 100 to 1 / 50 of the actual pile foundation size, and the micro-dynamic response data is obtained through a vibration table and micro sensors.

3. The pile-soil-structure dynamic interaction analysis method according to claim 2, characterized in that: The experimental feasibility scale range refers to the size range in which effective physical model testing can be carried out under laboratory and engineering site conditions.

4. The pile-soil-structure dynamic interaction analysis method according to claim 3, characterized in that: The multiphase fluid-solid coupling mechanism equation at the pile-soil interface is a set of partial differential equations that describes the deformation and stress transfer relationship between the fluid-solid two-phase medium between the pile and the soil under dynamic loads, taking into account the changes in soil pore water pressure and fluid seepage effects.

5. The pile-soil-structure dynamic interaction analysis method according to claim 4, characterized in that: The scale inflection point refers to the critical size point where the dynamic response characteristics of pile-soil interaction change significantly as the size of the physical model changes, and is determined through dimensionless parameter analysis.

6. The pile-soil-structure dynamic interaction analysis method according to claim 5, characterized in that: The model size of the second-scale experiment is the second size, which is calculated through the multiphase fluid-solid coupling mechanism equation of the pile-soil interface, focusing on the group behavior and interaction mechanism between the pile and the surrounding soil.

7. The pile-soil-structure dynamic interaction analysis method according to claim 6, characterized in that: The model size of the third-scale experiment is the third size, which is calculated through the multiphase fluid-solid coupling mechanism equation of the pile-soil interface, and focuses on measuring the dynamic response characteristics of the overall structure and foundation system.

8. The pile-soil-structure dynamic interaction analysis method according to claim 7, characterized in that: The basic equation group includes the pile-soil interface control equation and the pile-structure coupling equation; the pile-soil interface control equation is used to describe the mechanical behavior of the contact surface between the soil around the pile and the pile body. The input includes the soil density parameter in the first data, the pile foundation geometric parameters in the second data, and the load time history function in the third data. The output is the pile-soil interface stress distribution and displacement field.

9. The pile-soil-structure dynamic interaction analysis method according to claim 8, characterized in that: The pile-structure coupling equation is used to describe the relationship between the pile body response and the vibration transmission of the superstructure. The input includes the pile body material stiffness matrix in the second data, the structural mass distribution and the pile-soil interface stress distribution in the third data, and the output is the pile foundation lateral displacement function and the structural dynamic response.

10. The pile-soil-structure dynamic interaction analysis method according to claim 9, characterized in that: The lateral displacement function of a pile foundation is a mathematical function that characterizes the displacement distribution along its depth under horizontal loads. It is related to soil parameters and load frequency and is a key indicator for evaluating pile foundation stability. The pile stress distribution is the distribution of axial stress, shear stress, and bending moment along the length of the pile under vertical and lateral loads, obtained through numerical solutions. The soil deformation field is the displacement, strain and stress distribution state of the soil under the action of dynamic load, which reflects the stress transfer path during the interaction between the soil and the pile foundation.

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