Calculation method for horizontal rigidity of foundation around pile

Abstract

The invention provides a simplified calculation method for seismic resistance of a storage tank considering pile-soil action, and belongs to the field of civil engineering and seismic engineering. Firstly, a pile-soil simplified model is established for pile-soil simplification; secondly, according to material attributes of a pile body and a soil body in engineering, soil body parameters in the pile-soil simplified model are calculated, and the parameters comprise rigidity and damping; and finally, taking the calculated soil parameters as material attribute parameters of a soil finite element part in the finite element model, establishing a storage tank-pile-soil finite element model by adopting finite element analysis, and performing numerical simulation to obtain a numerical simulation result, namely storage tank seismic response. According to the method, soil parameters can be accurately calculated, more accurate modeling data are provided, the overall analysis reliability is improved, and the storage tank aseismic design safety is improved; the pile-soil simplified model is suitable for a design scheme for rapidly evaluating and optimizing the storage tank foundation in engineering design; each calculation formula has good adaptability, and the method is suitable for storage tank foundation design and anti-seismic analysis under different engineering conditions.

Description

Technical Field

[0001] The invention belongs to the field of civil engineering and earthquake engineering, belongs to the seismic design of storage tanks, and particularly relates to a simplified calculation method for seismic resistance of storage tanks considering pile-soil effects. Background Art

[0002] A storage tank is a container for storing liquids or gases and is widely used in multiple industries, such as the storage of oil and natural gas. As a key energy storage facility, the structural safety of the tank is crucial, especially its stability under earthquakes. Storage tanks are usually built on pile foundations with large engineering scales. Once the pile foundation is damaged, it may cause the tank structure to become unstable or collapse, liquid leakage, endanger the safety of surrounding personnel, and cause serious economic losses. The mechanical behavior of the pile and soil in the pile foundation under earthquakes has a direct impact on the safety of the overall structure of the tank. Therefore, efficient and accurate evaluation of the dynamic response of the tank-pile-soil system under earthquakes is the key to the seismic design of storage tanks.

[0003] At present, in the seismic calculation of storage tanks, only the above-ground structure is usually focused, while the underground pile-soil effect is ignored or not fully considered. In the 1994 Northridge earthquake in Los Angeles, the design of some storage tanks did not fully consider the seismic effects such as the pile-soil effect. The ground movement caused by the earthquake caused uneven settlement of the tanks and their foundations. In the Bushehr earthquake in Iran in 2003, many oil storage tanks were severely damaged. Subsequent analysis showed that it was the design of many storage tanks that did not fully consider the behavior of the foundation and support system in the earthquake, which led to the failure of the tank body and foundation. Japan is an earthquake-prone area. The oil tanks in the oil depot were fully considered in the design of the pile-soil effect and seismic loads and the pile foundation was reinforced. In the 2011 Great East Japan Earthquake, these tanks were less damaged and no major leakage accidents occurred. It can be seen that the pile-soil effect is one of the key factors affecting the dynamic response of the tank structure under the action of earthquake. If the influence of the mechanical behavior of the pile and soil on the tank is not fully considered, it may lead to a large error between the seismic calculation results and the actual situation, which will affect the seismic design and safety assessment of the tank. In addition, since the pile foundation of a storage tank is usually large in scale, including the length and number of the piles, the numerical simulation of the seismic response analysis of the tank-pile-soil system often requires a lot of computing time and resources, limiting the widespread application of finite element models in engineering practice.

[0004] In summary, there is an urgent need for a simplified calculation method for the seismic resistance of storage tanks that takes into account the interaction between piles and soil. While ensuring the simulation accuracy of the dynamic response of the tank-pile-soil system, the calculation efficiency can be improved to enhance the applicability of the project, which is of great significance to improving the seismic design and safety assessment of storage tanks. Summary of the invention

[0005] The technical problem to be solved by the present invention is that, in view of the fact that the above-mentioned prior art does not fully consider the influence of soil in the seismic calculation of storage tanks and the low efficiency of numerical simulation calculation, a simplified calculation method for seismic resistance of storage tanks considering the effect of piles and soil is proposed, and in particular, a calculation formula for the horizontal stiffness coefficient of the foundation around piles is proposed for the calculation of soil parameters in the simplified pile-soil model.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A simplified calculation method for the seismic resistance of a storage tank considering the pile-soil effect is disclosed. The calculation method first simplifies the pile-soil and establishes a simplified pile-soil model; secondly, the soil parameters in the simplified pile-soil model are calculated according to the material properties of the pile and soil in the project, and the parameters include stiffness and damping; finally, the calculated soil parameters are used as the material property parameters of the soil finite element components in the finite element model, and the finite element analysis software ABAQUS is used to establish a storage tank-pile-soil finite element model, and the finite element model is numerically simulated to obtain the numerical simulation results, i.e., the seismic response of the storage tank. The method includes the following steps:

[0008] Step (1), after simplifying the pile-soil, a simplified pile-soil model is established.

[0009] The pile-soil is simplified according to the simplification principle and a simplified pile-soil model is established, where the pile-soil specifically refers to the pile body and the soil body.

[0010] The simplified principle is: the pile body is represented by a cylinder; the soil body is simplified and simulated by a spring-damper, and the mechanical behavior between the pile body and the soil body is intuitively reflected by the spring-damper, wherein the spring represents the stiffness of the soil body, that is, the resistance to deformation between the pile body and the soil body, and the damper represents the energy dissipation capacity between the pile body and the soil body during the deformation process.

[0011] Step (2), according to the material properties of the pile and soil in the project, calculate the spring-damper parameters of the simplified pile-soil model obtained in step (1), that is, the soil parameters, including the horizontal stiffness K of the foundation around the pile h , Horizontal damping of foundation around piles C h , vertical stiffness of foundation around pile K v , vertical damping of foundation around piles C v , vertical stiffness of pile tip foundation K b , vertical damping of pile tip foundation C b .

[0012] Step 2.1), when the soil is a single layer, the calculation formula is as follows:

[0013] S=βsH (1)

[0014] Wherein, S includes the horizontal stiffness of the foundation around the pile K h, Horizontal damping of foundation around piles C h , vertical stiffness of foundation around pile K v , vertical damping of foundation around piles C v ; β represents the pile group coefficient, according to the formula Calculate, where N p represents the number of piles; s represents the soil parameter coefficient corresponding to S, including the horizontal stiffness coefficient k of the foundation around the pile h , horizontal damping coefficient of foundation around pile c h , Vertical stiffness coefficient of foundation around pile k v , vertical damping coefficient of foundation around pile c v ; H represents the thickness of the soil.

[0015] Step 2.2), when the soil is divided into multiple layers, the division of the pile body is consistent with the soil body, and the junction between the top of the pile body and each layer of soil is taken as a node. The calculation formula of S at the i-th node is as follows:

[0016]

[0017] Where N represents the number of nodes of a single pile; s i represents the soil parameter coefficient corresponding to S calculated according to the material properties of the i-th layer of soil and pile; H i represents the thickness of the i-th soil layer.

[0018] Step 2.3), when the soil is one layer or divided into multiple layers, the vertical stiffness K of the pile tip foundation b The calculation formula is as follows:

[0019]

[0020] Wherein, B represents the diameter of the pile; G s represents the shear modulus of the soil; v s It represents the Poisson's ratio of soil.

[0021] Step 2.4), when the soil is one layer or divided into multiple layers, the vertical damping of the pile tip foundation C b The calculation formula is as follows:

[0022]

[0023] Among them, ρ s Represents the mass density of soil; V s Represents the shear wave velocity of the soil; A p represents the cross-sectional area of ​​the pile; ζ represents the damping ratio of the soil. When calculating the horizontal damping coefficient of the foundation around the pile, When calculating the vertical damping coefficient of the foundation around the pile and the vertical damping of the foundation at the pile tip, in represents the dimensionless mass ratio of pile to soil; ω s Represents the circular frequency of the soil.

[0024] Step 2.5), the horizontal stiffness coefficient k of the foundation around the pile h The calculation formula is as follows:

[0025]

[0026] Among them, E s represents the elastic modulus of the soil; B represents the diameter of the pile; E p Represents the elastic modulus of the pile; I p represents the cross-sectional inertia moment of the pile; v s represents the Poisson's ratio of the soil; G s represents the shear modulus of the soil; L represents the length of the pile.

[0027] Compared with the traditional formula, the formula (5) of the present invention fully considers the influence of the soil around the pile body, that is, in addition to considering the stiffness coefficient provided by the soil in front and behind the pile body due to deformation under the horizontal load, the stiffness coefficient provided by the soil in the other two directions due to friction with the pile body is also considered. The derivation process of formula (5) is as follows:

[0028] The calculation derivation of the stiffness coefficient provided by the deformation of the soil in front of and behind the pile body under the horizontal load is based on the elastic half-space foundation beam theory and the Winkler foundation beam theory. According to the above theory, it is easy to obtain the maximum moment formula of the beam on the elastic half-space foundation and the beam on the Winkler foundation under the vertical concentrated load. Then, according to the condition that the maximum moment formula is equal, fitting can be performed to approximately obtain the Winkler foundation stiffness coefficient k under the condition that the beam is subjected to the vertical concentrated load. h1 :

[0029]

[0030] Among them, E s represents the elastic modulus of the soil, b represents the width of the beam; E b represents the elastic modulus of the beam; I b represents the section moment of inertia of the beam; ν s It represents the Poisson's ratio of soil.

[0031] The beam on the Winkler foundation is simplified into a pile. At this time, under the action of horizontal concentrated load, there is a stiffness coefficient provided by soil deformation in front and behind the pile. Therefore, the stiffness coefficient of formula (6) is multiplied by 2, and then the relevant symbols are modified according to the characteristics of the beam and the pile. That is, the diameter B of the pile is used to replace the width b of the beam, and the elastic modulus E of the pile is used to replace the width b of the beam. p Instead of the elastic modulus E of the beamb , using the pile's cross-sectional inertia moment I p Instead of the section moment of inertia of the beam I b , the stiffness coefficient k′ provided by the soil in front of and behind the pile due to deformation under the horizontal load can be obtained h1 :

[0032]

[0033] The calculation of the stiffness coefficient provided by the soil in the other two directions due to friction with the pile is based on the deformation theory of the friction pile under vertical load and the assumption of pile rigidity. According to the equilibrium equation of the soil microelement around the pile, it is easy to obtain the displacement ω of the pile under vertical load. s :

[0034]

[0035] Where τ represents the shear stress at the contact point between the pile and the soil; G s represents the shear modulus of soil; r m Represents the influence radius, according to the formula r m =2.5L(1-υ s ) is calculated, where L is the length of the pile.

[0036] Formula (8) and vertical concentrated load Substituting into Hooke's law, the stiffness coefficient k provided by the soil in four directions of the pile due to friction with the pile under the vertical concentrated load is obtained: h2 :

[0037]

[0038] Divide the stiffness coefficient of formula (9) by 2, and then determine the relevant signs according to the load direction and pile characteristics, and the stiffness coefficient k′ provided by the soil in the other two directions due to friction with the pile under the horizontal concentrated load can be obtained. h2 :

[0039]

[0040] Comprehensively consider the stiffness coefficient provided by the soil in front and behind the pile due to deformation under the horizontal load and the stiffness coefficient provided by the soil in the other two directions due to friction with the pile, that is, k h =k' h1 +k' h2 , and the calculation formula for the horizontal stiffness coefficient of the foundation around the pile is obtained as shown in formula (5).

[0041] Step 2.6), the horizontal damping coefficient of the foundation around the pile c h The calculation formula is as follows:

[0042]

[0043] Where B is the diameter of the pile; ρ s Represents the mass density of soil; V s Represents the shear wave velocity of the soil; V La represents the Lysmer pseudo wave velocity of the soil; ζ represents the damping ratio of the soil. When calculating the horizontal damping coefficient of the foundation around the pile, When calculating the vertical damping coefficient of the foundation around the pile and the vertical damping of the foundation at the pile tip, in represents the dimensionless mass ratio of pile to soil; ω s Represents the circular frequency of the soil.

[0044] Step 2.7), the vertical stiffness coefficient k of the foundation around the pile v The calculation formula is as follows:

[0045]

[0046] Among them, G s represents the shear modulus of the soil; L represents the length of the pile; v s It represents the Poisson's ratio of soil.

[0047] Step 2.8), the vertical damping coefficient c of the foundation around the pile v The calculation formula is as follows:

[0048]

[0049] Step (3), using the soil parameters calculated in step (2) as the material property parameters of the soil finite element components, using the finite element analysis software ABAQUS to establish a tank-pile-soil finite element model, and performing numerical simulation to obtain the numerical simulation results, i.e., the seismic response of the tank.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] (1) The calculation formula for the horizontal stiffness coefficient of the foundation around piles proposed in the present invention can more accurately calculate the soil parameters by considering the stiffness coefficient provided by the soil due to friction with the pile body, reduce the error caused by the calculation formula used in the traditional method, and provide more accurate modeling data for the finite element model, thereby improving the reliability of the overall analysis.

[0052] (2) The calculation formula for the horizontal stiffness coefficient of the foundation around the pile proposed in the present invention fully considers the actual influence of the soil around the pile body, can more accurately reflect the actual dynamic behavior of the tank-pile-soil system under earthquake action, and improves the safety of the seismic design of the tank.

[0053] (3) The simplified pile-soil model established by the present invention can effectively simplify the complex pile-soil interaction. Despite the simplified processing, it can still maintain sufficient accuracy and is suitable for rapid evaluation and optimization of the design scheme of the tank foundation in engineering design.

[0054] (4) The calculation formula for the horizontal stiffness coefficient of the foundation around piles proposed in the present invention has good adaptability and can be adjusted and expanded according to the geological environment. It is suitable for the foundation design and seismic analysis of storage tanks under different engineering conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a flow chart of a simplified calculation method for earthquake resistance of a storage tank considering pile-soil action according to the present invention;

[0056] Figure 2 A simplified pile-soil model established in the storage tank-pile-soil system of the present invention;

[0057] Figure 3 This is a finite element model diagram established by ABAQUS in the present invention;

[0058] Figure 4 This is a comparison chart of the numerical simulation results of the present invention.

[0059] In the figure: 1 storage tank; 2 foundation; 3 pile body; 4 node; 5 spring-damper; 6 vibration table. DETAILED DESCRIPTION

[0060] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0061] Figure 1 The process of simplified calculation method for seismic resistance of storage tanks considering pile-soil interaction is intuitively demonstrated. The specific implementation measures are as follows:

[0062] Step (1), after simplifying the pile-soil, a simplified pile-soil model is established.

[0063] The pile-soil is simplified according to the following principles: the pile body is represented by a cylinder; the soil body is simplified by a spring-damper. The simplified model of this embodiment is connected according to the following principles: the storage tank 1 is connected to the pile body 3 by a cap 2; the soil body is divided into five layers as a whole, and the division of the pile body 3 is consistent with the soil body. The junction between the top of the pile body 3 and each layer is a node 4. The number of nodes 4 of a single pile body is N=5. The soil body is simplified to a spring-damper 5, and the node 4 is the connection point between the pile body 3 and the spring-damper 5. According to the simplification principle and the connection principle, a simplified pile-soil model is established, such as Figure 2 shown.

[0064] Step (2) is to calculate the parameters of the spring-damper, i.e., the soil parameters, of the simplified pile-soil model of step (1) according to the material properties of the pile and soil in the project as shown in Table 1 and Table 2, formulas (2) to (5) and formulas (11) to (13). For the simplified pile-soil model of this embodiment, the parameters of the spring-damper include the horizontal stiffness of the foundation around the pile at the i-th node of each pile (K h ) i , the horizontal damping of the foundation around the pile at the i-th node (C h ) i , the vertical stiffness of the foundation around the pile at the ith node (K v ) i , the vertical damping of the foundation around the pile at the i-th node (C v ) i , vertical stiffness of pile tip foundation K b , vertical damping of pile tip foundation C b ,like Figure 2 shown.

[0065] Table 1 Pile material properties

[0066] Diameter(m) Length(m) <![CDATA[Density (kg / m 3 )]]> <![CDATA[Modulus of elasticity (N / m 2 )]]> Quantity (root) 0.023 0.77 2550 <![CDATA[1.9×10 9 ]]> 4

[0067] Table 2 Soil material properties

[0068]

[0069] Step (3): The soil parameters calculated in step (2) are used as the material property parameters of the soil finite element components, and a tank-pile-soil finite element model is established using the finite element analysis software ABAQUS, and numerical simulation is performed to obtain the numerical simulation results, i.e., the acceleration response of the tank wall.

[0070] In step 3.1), the finite element components of the storage tank, pile, soil and shaking table are established. The storage tank is simulated by shell elements, the pile is simulated by beam elements, the soil is simulated by spring-damper elements, and the shaking table is simulated by solid elements.

[0071] Step 3.2), assign material properties to the finite element components of the storage tank, pile, soil and vibration table. The storage tank material of this embodiment is organic glass, the pile material properties are shown in Table 1, the material property parameters of the soil finite element component are the soil parameters calculated in step (2), and the material of the vibration table is steel plate.

[0072] Step 3.3), the finite element components of the storage tank, pile, soil and shaking table with material properties are assembled into a storage tank-pile-soil finite element model by binding connection, such as Figure 3As shown in Table 2, Table 3 and Table 4, numerical simulation results are obtained, namely the acceleration response of the tank wall. The results are compared with the actual test data under the same working conditions and the results obtained by the traditional method, that is, using the finite element simulation software ADINA to establish a finite element model for numerical simulation, as shown in Table 2, Table 3 and Table 4. Figure 4 shown.

[0073] In the traditional method, when the finite element simulation software ADINA is used to establish the tank-pile-soil finite element model, except for the different calculation formulas for the horizontal stiffness coefficient of the foundation around the pile in the material property parameters of the soil finite element components used, the unit types, material properties of the tank and pile body and the vibration table, and the connection method are all consistent with the present invention. h The calculation formula is as follows:

[0074]

[0075] Among them, E s represents the elastic modulus of the soil; B represents the diameter of the pile; E p Represents the elastic modulus of the pile; I p represents the cross-sectional inertia moment of the pile; ν s It represents the Poisson's ratio of soil.

[0076] Table 3 Acceleration response of the tank wall under test and different methods (unit: m / s 2 )

[0077] Tank wall height / (m) Real test data Traditional methods Simplified calculation method (the present invention) 0 2.106 3.059 2.259 0.1 2.475 3.168 2.525 0.4 2.964 3.393 3.036

[0078] Table 4 Errors of tank wall acceleration response under different methods

[0079] Tank wall height / (m) Traditional methods Simplified calculation method (the present invention) 0 45.26％ 7.27％ 0.1 27.99％ 2.01％ 0.4 14.49％ 2.44％

[0080] Combining Table 3, Table 4 and Figure 4 It can be seen that, compared with the traditional method, the acceleration response of the tank wall obtained by the finite element model established by the simplified calculation method for seismic resistance of a storage tank considering the pile-soil effect proposed by the present invention is more consistent with the actual test data and has a smaller error, that is, the soil parameters are calculated more accurately, and the actual situation of the tank-pile-soil system under earthquake action is better reflected. The simplified calculation method for seismic resistance of a storage tank considering the pile-soil effect proposed by the present invention uses a spring-damper to simplify the soil, and in particular, for the calculation of soil parameters in the simplified pile-soil model, a calculation formula for the horizontal stiffness coefficient of the foundation around the pile is proposed, which can more accurately simulate the dynamic response of the storage tank under earthquake action while saving computing resources.

[0081] Finally, it should be noted that the above examples are only used to illustrate the embodiments of the present invention and are not used to limit the scope of the present invention. After reading the present invention, those skilled in the art may make some modifications and improvements without departing from the concept of the present invention. These modifications and improvements and various equivalent modifications to the present invention belong to the protection scope of the present invention and fall within the scope defined by the claims attached to this application.

Claims

1. A method for calculating the horizontal stiffness of the foundation around a pile, characterized in that: The calculation method first simplifies the pile-soil and establishes a simplified pile-soil model; secondly, according to the material properties of the pile and soil in the project, the soil parameters in the simplified pile-soil model are calculated, and the parameters include stiffness and damping; finally, the calculated soil parameters are used as the material property parameters of the soil finite element components in the finite element model, and the finite element analysis software ABAQUS is used to establish a storage tank-pile-soil finite element model, and the finite element model is numerically simulated to obtain the numerical simulation results, namely the seismic response of the storage tank.

2. The method for calculating the horizontal stiffness of the foundation around piles according to claim 1, characterized in that: The following steps are involved: Step (1), simplifying the pile-soil according to the simplification principle to establish a simplified pile-soil model, wherein the pile-soil specifically refers to the pile body and the soil body; Step (2), according to the material properties of the pile and soil in the project, calculate the spring-damper parameters of the simplified pile-soil model obtained in step (1), that is, the soil parameters, including the horizontal stiffness K of the foundation around the pile h , Horizontal damping of foundation around piles C h , vertical stiffness of foundation around pile K v , vertical damping of foundation around piles C v , vertical stiffness of pile tip foundation K b , vertical damping of pile tip foundation C b ; Step 2.1), when the soil is a single layer, the calculation formula is as follows: S=βsH (1) Wherein, S includes the horizontal stiffness of the foundation around the pile K h , Horizontal damping of foundation around piles C h , vertical stiffness of foundation around pile K v , vertical damping of foundation around piles C v ; β represents the pile group coefficient, according to the formula Calculate, where N p represents the number of piles; s represents the soil parameter coefficient corresponding to S, including the horizontal stiffness coefficient k of the foundation around the pile h , horizontal damping coefficient of foundation around pile c h , Vertical stiffness coefficient of foundation around pile k v , vertical damping coefficient of foundation around pile c v ; H represents the thickness of the soil; Step 2.2), when the soil is divided into multiple layers, the division of the pile body is consistent with the soil body, and the junction between the top of the pile body and each layer of soil is taken as a node. The calculation formula of S at the i-th node is as follows: Where N represents the number of nodes of a single pile; s i represents the soil parameter coefficient corresponding to S calculated according to the material properties of the i-th layer of soil and pile; H i represents the thickness of the i-th soil layer; Step 2.3), when the soil is one layer or divided into multiple layers, the vertical stiffness of the pile tip foundation K b The calculation formula is as follows: Wherein, B represents the diameter of the pile; G s represents the shear modulus of the soil; v s represents the Poisson's ratio of the soil; Step 2.4), when the soil is one layer or divided into multiple layers, the vertical damping of the pile tip foundation C b The calculation formula is as follows: Among them, ρ s Represents the mass density of soil; V s Represents the shear wave velocity of the soil; A p represents the cross-sectional area of ​​the pile; ζ represents the damping ratio of the soil. When calculating the horizontal damping coefficient of the foundation around the pile, When calculating the vertical damping coefficient of the foundation around the pile and the vertical damping of the foundation at the pile tip, in represents the dimensionless mass ratio of pile to soil; ω s It represents the circular frequency of soil; Step 2.5), horizontal stiffness coefficient k of the foundation around the pile h The calculation formula is as follows: Among them, E s represents the elastic modulus of the soil; B represents the diameter of the pile; E p Represents the elastic modulus of the pile; I p represents the cross-sectional inertia moment of the pile; v s represents the Poisson's ratio of the soil; G s represents the shear modulus of the soil; L represents the length of the pile; Step 2.6), the horizontal damping coefficient of the foundation around the pile c h The calculation formula is as follows: Where B is the diameter of the pile; ρ s Represents the mass density of soil; V s Represents the shear wave velocity of the soil; V La represents the Lysmer pseudo wave velocity of the soil; ζ represents the damping ratio of the soil. When calculating the horizontal damping coefficient of the foundation around the pile, When calculating the vertical damping coefficient of the foundation around the pile and the vertical damping of the foundation at the pile tip, in represents the dimensionless mass ratio of pile to soil; ω s It represents the circular frequency of soil; Step 2.7), the vertical stiffness coefficient k of the foundation around the pile v The calculation formula is as follows: Among them, G s represents the shear modulus of the soil; L represents the length of the pile; v s represents the Poisson's ratio of the soil; Step 2.8), the vertical damping coefficient of the foundation around the pile c v The calculation formula is as follows: Step (3), using the soil parameters calculated in step (2) as the material property parameters of the soil finite element components, using the finite element analysis software ABAQUS to establish a tank-pile-soil finite element model, and performing numerical simulation to obtain the numerical simulation results, i.e., the seismic response of the tank.

3. The method for calculating the horizontal stiffness of the foundation around piles according to claim 1, characterized in that: The simplification principle of step (1) is as follows: the pile body is represented by a cylinder; the soil body is simplified and simulated by a spring-damper, and the mechanical behavior between the pile body and the soil body is intuitively reflected by the spring-damper, wherein the spring represents the stiffness of the soil body, that is, the resistance to deformation between the pile body and the soil body, and the damper represents the energy dissipation capacity between the pile body and the soil body during the deformation process.

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