Method for calculating long-term settlement of solidified soil composite pipe pile

Abstract

This invention relates to a method for calculating the settlement state of pipe piles embedded in solidified soil. The steps are as follows: establishing a theoretical model of the solidified soil composite pipe pile-soil system; dividing the soil around the pile into a series of annular layers, and considering the differences in properties between the solidified soil around the pile, the transition zone, and the surrounding undisturbed soil, establishing equilibrium formulas for the soil around the pile in any layer under vertical load, the soil core solidification, and the pipe pile under vertical load; solving the soil around the pile equilibrium formula using Laplace transform and the method of separation of variables, and obtaining the side friction resistance of the soil around the pile to the outer wall of the pipe pile by recursively applying the continuity condition between adjacent layers, solving the soil core solidification equilibrium formula, and obtaining the side friction resistance of the soil core solidification to the inner wall of the pipe pile; solving the pipe pile equilibrium formula, and obtaining the amplitude-frequency response of the pile top displacement based on the continuity condition of the pile-soil system, and obtaining the calculation formula for the pile top settlement under any vertical load at any time through inverse Fourier transform and convolution.

Description

Technical Field

[0001] The present invention relates to a method for calculating the long-term settlement of composite pipe piles in solidified soil, which is a method for calculating the settlement state of pipe piles buried in solidified soil. Background Technology

[0002] Solidified soil composite pipe piles are a novel type of pile foundation. This method involves drilling holes using a spiral drilling rig, injecting a green, low-carbon solidifying agent slurry, mixing it with the in-situ soil to form a fluidized solidified soil, and then placing precast pipe piles into the holes. The piles are driven in by their own weight, forming a pile-solidified soil composite load-bearing system. The pile core is completely filled with solidified soil, and the pile perimeter is also encased in solidified soil. A transition zone of a certain thickness is formed on the outer side of the solidified soil around the pile due to the penetration and diffusion of the solidifying agent slurry, and the surrounding area is undisturbed soil. The settlement of pile foundations is crucial to the safety of buildings and has received considerable attention from researchers, leading to the development of a series of settlement calculation methods.

[0003] Methods such as the elastic theory method, load transfer method, and shear displacement method exist. The elastic theory method treats both the pile and soil as ideal linear elastic bodies, using the theory of elastic half-space to calculate the additional stress caused by the pile load in the soil. Settlement is then obtained by integrating and summing over the depth of the compressible soil layer. The load transfer method discretizes the pile into several elements, simplifying the interaction between each element and the surrounding soil as a spring, and calculates pile settlement by assuming the distribution functions of the pile's side and end resistance. The shear displacement method treats the soil around the pile as an elastic medium composed of an infinitely thin concentric cylindrical shell, assuming that the deformation of the soil around the pile under the action of the pile is mainly shear deformation, thus calculating the deformation of the pile-soil system.

[0004] However, existing calculation methods cannot reflect the development law of pile foundation settlement over time and cannot be used for predictive analysis of long-term pile foundation settlement. Therefore, it is necessary to provide a new solution to meet practical needs. Summary of the Invention

[0005] In view of this, the present invention provides a method for calculating the long-term settlement of solidified soil composite pipe piles, which can obtain the pile top settlement of solidified soil composite pipe piles at any time and under any vertical load, thereby realizing the prediction of the long-term settlement development law of solidified soil composite pipe piles.

[0006] A method for calculating the long-term settlement of solidified soil composite pipe piles includes the following steps:

[0007] S1. Establish a theoretical model of the solidified soil composite pipe pile-soil system;

[0008] S2. Divide the soil around the pile into a series of annular layers, and consider the differences in properties between the solidified soil around the pile, the transition zone and the undisturbed soil on the periphery. The properties of the soil inside each layer are approximately considered to be homogeneous along the radial direction. Based on this, the soil is considered as a cohesive damping material. Establish the equilibrium formulas for the soil around the pile in any layer under vertical load and the equilibrium formulas for the solidified soil in the pile core. Establish the equilibrium formulas for the pipe pile under vertical load and list the boundary conditions of the pile-soil system.

[0009] S3. The equilibrium formula of the soil around the pile is solved by Laplace transform and separation of variables. Based on the continuity condition between adjacent layers, the side friction resistance of the soil around the pile to the outer wall of the pipe pile is obtained by recursively solving the equilibrium formula of the solidified soil in the pile core. The side friction resistance of the solidified soil in the pile core to the inner wall of the pipe pile is obtained by solving the equilibrium formula of the solidified soil in the pile core.

[0010] S4. Solve the equilibrium formula for the pipe pile, and obtain the amplitude-frequency response of the pile top displacement based on the continuity condition of the pile-soil system. On this basis, obtain the calculation formula for the pile top settlement under any vertical load at any time through inverse Fourier transform and convolution.

[0011] The boundary conditions for the pile-soil system are:

[0012] (1) The pipe pile is made of linear elastic material, and the soil around the pile and the core of the pile is made of viscoelastic material. Its damping form is viscous damping.

[0013] (2) The bottom of the pipe pile, the soil around the pile and the solidified soil inside the pile core are all viscoelastic supports. The soil around the pile includes the solidified soil around the pile, the transition zone and the original soil around the pile.

[0014] (3) The top of the soil around the pile and the solidified soil inside the pile core are free boundaries;

[0015] (4) The pipe pile, the soil around the pile and the solidified soil inside the pile core are in complete contact, and the displacement of the pile-soil system is coordinated and the stress is continuous;

[0016] (5) The layers of the solidified soil around the pile meet the conditions of displacement coordination and stress continuity.

[0017] Specifically, in S1, a theoretical analysis model of the solidified soil composite pipe pile-soil system under vertical load is established, where the length, inner radius, and outer radius of the precast pipe pile are H, H, and H, respectively. p r c and r w The vertical load q(t) acting on the pile top;

[0018] The precast pipe pile is surrounded by solidified soil within a predetermined range around the pile and the pile core. Due to the diffusion effect of the curing agent slurry during the mixing and drilling process, a transition zone will be formed around the solidified soil around the pile. The soil properties in the transition zone gradually change radially, and the outer part of the transition zone is undisturbed undisturbed soil.

[0019] To account for the influence of complex surrounding soil on the outer wall of the pipe pile, it is divided into m concentric layers radially. Layer 1 represents the solidified soil around the pile, layer m is the undisturbed soil, and layers 2, 3, i, ..., m-1 are transition zones. The soil properties within each layer are radially homogeneous, but the soil properties differ between layers. The ends of the pile-soil system are all viscoelastic supports, with the pile bottom support stiffness and damping coefficient being k... b and δ b The bottom support stiffness and damping coefficient of the i-th layer of soil around the pile are k i and δ i The bottom support stiffness and damping coefficient of the pile core soil are k, respectively. c and δ c .

[0020] Specifically, step S2 includes,

[0021] The solidified soil around the pile, the transition zone, and the surrounding undisturbed soil are divided radially into a series of annular layers. An equilibrium formula for any layer under vertical load is established.

[0022] (1);

[0023] In the formula: Let be the vertical displacement of the soil around the pile in the i-th ring. , and , respectively, are the Lame constant, shear modulus, and viscous damping coefficient of the soil surrounding the i-th pile layer.

[0024] Specifically, step S2 includes establishing a balance formula for the solidified soil in the pile core:

[0025] (2);

[0026] In the formula: This refers to the vertical displacement of the soil solidified in the pile core. , and These represent the Lame constant, shear modulus, and viscous damping coefficient of the soil in the pile core solidification process.

[0027] Specifically, step S2 includes the following: the equilibrium formula for the pipe pile under vertical load can be expressed as follows:

[0028] (3);

[0029] In the formula: E represents the vertical displacement of the pipe pile. p A p ρ p These are the elastic modulus, cross-sectional area, and density of the pipe pile, respectively. and These represent the side friction resistance of the pipe pile to the soil around the pile and the soil around the pile core, respectively.

[0030] Specifically, step S2 includes the following: the boundary conditions of the pile-soil system are:

[0031] The boundary conditions at the top and bottom of the soil around the pile are respectively

[0032] (4);

[0033] (5).

[0034] Specifically, step S2 includes setting the boundary conditions at the top and bottom of the pile core soil as follows:

[0035] (6);

[0036] (7);

[0037] Displacement and shear stress continuity between adjacent soil layers around the pile:

[0038] (8);

[0039] (9);

[0040] The displacement of the outermost layer of soil around the pile is zero at infinity.

[0041] (10);

[0042] Boundary conditions at the pile top and pile bottom:

[0043] (11);

[0044] (12);

[0045] In the formula: and These are the stiffness and damping coefficient of the soil at the pile bottom, respectively.

[0046] Furthermore, the displacement and stress between the pile and the surrounding soil are continuous:

[0047] (13);

[0048] (14);

[0049] Displacement and stress continuity between the pile core and the pile:

[0050] (15);

[0051] (16);

[0052] In the formula: and These are the shear stresses between the pile and the surrounding soil, and between the pile and the core soil, respectively.

[0053] Step S3 specifically includes:

[0054] Applying a Laplace transform to equation (1) yields...

[0055] (17);

[0056] In the formula: For u i The Laplace transform form.

[0057] make Formula (17) can be decomposed into the following two formulas:

[0058] (18);

[0059] (19);

[0060] In the formula:

[0061] The solutions to formulas (18) and (19) are expressed as follows:

[0062] (20);

[0063] (twenty one);

[0064] In the formula: A i B i C i and D i All are coefficients determined by boundary conditions; and These are the first and second type zero-order modified Bessel functions, respectively.

[0065] Based on formulas (20) and (21) and combined with boundary condition formulas (4) and (5), the displacement amplitude of the soil around any pile ring can be obtained as follows:

[0066] (twenty two);

[0067] In the formula: A in B in and C inAll are coefficients determined by the boundary conditions, n=1,2,…; and These are the first and second type zero-order modified Bessel functions, respectively; and They are determined by the following formulas respectively:

[0068] (twenty three);

[0069] In the formula: , is the dimensionless support complex stiffness. ω is the angular frequency.

[0070] (twenty four);

[0071] The shear stress between the soil surrounding adjacent pile layers can be expressed as

[0072] (25);

[0073] In the formula: and These are the first-order modified Bessel functions of the first and second classes, respectively.

[0074] From the boundary condition formulas (8) and (9), we can obtain

[0075] When i = m-1:

[0076] (26);

[0077] When i = 1, 2, ..., m-2:

[0078] (27);

[0079] Solve formula (2), and combine it with the core soil in the pile. Given a boundary condition where the displacement is a finite value, the displacement amplitude of the pile core soil can be obtained as follows:

[0080] (28);

[0081] In the formula: For u c The Laplace transform form; A cn These are coefficients to be determined; and They are obtained from the following formulas respectively:

[0082] (29);

[0083] In the formula: , which is the dimensionless complex stiffness of the support;

[0084] (30);

[0085] The shear stress between the core soil and the inner wall of the pipe pile can be expressed as:

[0086] (31);

[0087] Specifically, in S4:

[0088] Based on formulas (25), (31), and boundary condition formulas (14) and (16), and using the Laplace transform method, formula (3) can be written as

[0089] (32);

[0090] Solving formula (32) yields

[0091] (33);

[0092] In the formula: ; .

[0093] Because the properties of the soil around the pile and the soil in the pile core are the same, it is possible to make Therefore, formula (33) can be written as:

[0094] (34);

[0095] According to the boundary condition formulas (13) and (15), we can obtain

[0096] (35);

[0097] (36);

[0098] From formulas (35) and (36), we can obtain

[0099] (37);

[0100] In the formula: .

[0101] Substituting formula (37) into formula (36) yields...

[0102] (38);

[0103] In the formula:

[0104] Multiply both sides of formula (38) by Integrating over [0, Hp] and combining this with the orthogonality of the intrinsic function system, we can obtain...

[0105] (39);

[0106] In the formula: ; ; ;

[0107] Substituting formulas (37) and (39) into formula (34), the pile displacement can be expressed as:

[0108] (40);

[0109] From formula (40) and boundary condition formula (12), we can obtain that

[0110] (41);

[0111] The amplitude-frequency response of the pile top displacement can be expressed as follows:

[0112] (42)

[0113] Using the inverse Fourier transform, the pile top settlement under a unit vertical load can be obtained as follows:

[0114] (43);

[0115] When a vertical load q(t) is applied to the pile top, the pile top settlement can be expressed as:

[0116] (44);

[0117] In the formula: for The Fourier transform form;

[0118] Thus, a formula for calculating pile top settlement under any time and any vertical load is obtained, which can be used to predict the long-term settlement of solidified soil composite pipe piles.

[0119] An electronic device includes one or more processors for storing one or more programs, which, when executed by the one or more processors, cause the one or more processors to perform the aforementioned method for calculating the long-term settlement of solidified soil composite pipe piles.

[0120] A storage medium storing a computer program, wherein the computer program is configured to execute the aforementioned method for calculating the long-term settlement of solidified soil composite pipe piles when running. Attached Figure Description

[0121] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0122] Figure 2 This is a schematic cross-sectional view of the solidified soil composite pipe pile embedded in the solidified soil in an embodiment of the present invention. Detailed Implementation

[0123] The following is in conjunction with the appendix Figure 1-2 The present invention will be further illustrated by the embodiments.

[0124] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0125] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0126] The following are examples of the invention "A method for calculating the long-term settlement of solidified soil composite pipe piles", covering specific data, steps, variables, formula applications and calculation scenarios.

[0127] like Figure 1 As shown, a method for calculating the long-term settlement of solidified soil composite pipe piles includes the following steps:

[0128] (1) Establish a theoretical model of the solidified soil composite pipe pile-soil system;

[0129] (2) Divide the soil around the pile into a series of ring layers, and consider the differences in properties between the solidified soil around the pile, the transition zone and the original soil in the outer perimeter. The properties of the soil inside each ring layer are approximately considered to be homogeneous along the radial direction. On this basis, the soil is considered as a cohesive damping material. Establish the equilibrium equations for the soil around the pile and the solidified soil of the pile core in any ring under vertical load, and establish the equilibrium equations for the pipe pile under vertical load. List the boundary conditions of the pile-soil system.

[0130] (3) The equilibrium equation of the soil around the pile is solved by using the Laplace transform and the method of separation of variables. Based on the continuity condition between adjacent layers, the side friction resistance of the soil around the pile to the outer wall of the pipe pile is obtained by recursively solving the equilibrium equation of the solidified soil in the pile core. The side friction resistance of the solidified soil in the pile core to the inner wall of the pipe pile is obtained by solving the equilibrium equation of the solidified soil in the pile core.

[0131] (4) Solve the equilibrium equation of the pipe pile and obtain the amplitude-frequency response of the pile top displacement based on the continuity condition of the pile-soil system. On this basis, obtain the calculation formula of the pile top settlement under any time and any vertical load through inverse Fourier transform and convolution.

[0132] like Figure 2 As shown, a theoretical analysis model of the solidified soil composite pipe pile-soil system under vertical load is established. The length, inner radius, and outer radius of the precast pipe pile are H, ... p r c and r w A vertical load q(t) is applied at the pile top. Due to its unique construction process, a certain area around the pile and the pile core are encased in solidified soil. Due to the diffusion effect of the solidifying agent slurry during the mixing and drilling process, a transition zone is formed around the solidified soil. The soil properties in the transition zone gradually change radially, while the outer edge of the transition zone is undisturbed undisturbed soil. To consider the influence of the complex surrounding soil on the outer wall of the pipe pile, it is divided into m concentric layers radially. Concentric layer 1 represents the solidified soil around the pile, concentric layer m is the undisturbed soil, and concentric layers 2, 3, i, ..., m-1 are the transition zones. The soil properties within each concentric layer are radially homogeneous, but the soil properties differ between concentric layers. The ends of the pile-soil system are all viscoelastic supports, with the pile bottom support stiffness and damping coefficient being k, respectively. b and δ b The bottom support stiffness and damping coefficient of the i-th layer of soil around the pile are k i and δ i The bottom support stiffness and damping coefficient of the pile core soil are k, respectively. c and δ c .

[0133] The following assumptions are made during the calculation:

[0134] (1) The pipe pile is made of linear elastic material, and the soil around the pile and the core of the pile is made of viscoelastic material. Its damping form is viscous damping.

[0135] (2) The bottom of the pipe pile, the surrounding soil, and the core soil are all viscoelastic supports;

[0136] (3) The top of the soil around the pile and the soil in the pile core are free boundaries;

[0137] (4) The pipe pile is in complete contact with the surrounding soil and the core soil, and the displacement of the pile-soil system is coordinated and the stress is continuous.

[0138] (5) The soil layers around the pile meet the conditions of displacement coordination and stress continuity.

[0139] Step (2) is as follows:

[0140] The solidified soil around the pile, the transition zone, and the surrounding undisturbed soil are divided into a series of annular layers along the radial direction. The equilibrium equation for any layer under vertical load is established as follows:

[0141] (1)

[0142] In the formula: Let be the vertical displacement of the soil around the pile in the i-th ring. , and , respectively, are the Lame constant, shear modulus, and viscous damping coefficient of the soil surrounding the i-th pile layer.

[0143] Similarly, the equilibrium equations for the solidified soil core are established:

[0144] (2)

[0145] In the formula: This refers to the vertical displacement of the soil solidified in the pile core. , and These represent the Lame constant, shear modulus, and viscous damping coefficient of the soil in the pile core solidification process.

[0146] The equilibrium equation for a pipe pile under arbitrary vertical load can be expressed as follows:

[0147] (3)

[0148] In the formula: E represents the vertical displacement of the pipe pile. p A p ρ p These are the elastic modulus, cross-sectional area, and density of the pipe pile, respectively. and These represent the side friction resistance of the pipe pile to the soil around the pile and the soil around the pile core, respectively.

[0149] The boundary conditions for the pile-soil system described in step (2) are as follows:

[0150] The boundary conditions at the top and bottom of the soil around the pile are respectively

[0151] (4)

[0152] (5)

[0153] Similarly, the boundary conditions at the top and bottom of the pile core soil are respectively

[0154] (6)

[0155] (7)

[0156] Displacement and shear stress continuity between adjacent soil layers around the pile:

[0157] (8)

[0158] (9)

[0159] The displacement of the outermost layer of soil around the pile is zero at infinity.

[0160] (10)

[0161] Boundary conditions at the pile top and pile bottom:

[0162] (11)

[0163] (12)

[0164] In the formula: and These are the stiffness and damping coefficient of the soil at the pile bottom, respectively.

[0165] Displacement and stress continuity between the soil around the pile and the pile:

[0166] (13)

[0167] (14)

[0168] Displacement and stress continuity between the pile core and the pile:

[0169] (15)

[0170] (16)

[0171] In the formula: and These are the shear stresses between the pile and the surrounding soil, and between the pile and the core soil, respectively.

[0172] Step (3) is as follows:

[0173] Applying the Laplace transform to equation (1), we can obtain

[0174] (17)

[0175] In the formula: For u i The Laplace transform form.

[0176] make Equation (17) can be decomposed into the following two equations:

[0177] (18)

[0178] (19)

[0179] In the formula:

[0180] The solutions to equations (18) and (19) can be expressed as follows:

[0181] (20)

[0182] (twenty one)

[0183] In the formula: A i B i C i and D i All are coefficients determined by boundary conditions; and These are the first and second type zero-order modified Bessel functions, respectively.

[0184] Based on equations (20) and (21) and combined with boundary condition equations (4) and (5), the displacement amplitude of the soil around any pile ring is obtained as follows:

[0185] (twenty two)

[0186] In the formula: A in B in and C in All are coefficients determined by the boundary conditions, n=1,2,…; and These are the first and second type zero-order modified Bessel functions, respectively; and They are determined by the following equations respectively:

[0187] (twenty three)

[0188] In the formula: , is the dimensionless support complex stiffness. ω is the angular frequency.

[0189] (twenty four)

[0190] The shear stress between the soil surrounding adjacent pile layers can be expressed as:

[0191] (25)

[0192] In the formula: and These are the first-order modified Bessel functions of the first and second classes, respectively.

[0193] From the boundary condition equations (8) and (9), we can obtain

[0194] When i = m-1:

[0195] (26)

[0196] When i = 1, 2, ..., m-2:

[0197] (27)

[0198] Solve equation (2), and combine it with the soil in the pile core. Given the boundary condition that the displacement is a finite value, the displacement amplitude of the pile core soil can be obtained as follows:

[0199] (28)

[0200] In the formula: For u c The Laplace transform form; A cn These are coefficients to be determined; and They are obtained from the following equations respectively:

[0201] (29)

[0202] In the formula: , which is the dimensionless support complex stiffness.

[0203] (30)

[0204] The shear stress between the core soil and the inner wall of the pipe pile can be expressed as:

[0205] (31)

[0206] Step (4) is as follows:

[0207] Based on equations (25) and (31) and boundary condition equations (14) and (16), and using the Laplace transform method, equation (3) can be written as

[0208] (32)

[0209] Solving equation (32) yields

[0210] (33)

[0211] In the formula: ; .

[0212] Since the properties of the soil around the pile and the soil in the pile core are the same, it is possible to make Therefore, equation (33) can be written as:

[0213] (34)

[0214] According to the boundary condition equations (13) and (15), we can obtain

[0215] (35)

[0216] (36)

[0217] From equations (35) and (36), we can obtain

[0218] (37)

[0219] In the formula: .

[0220] Substituting equation (37) into equation (36) yields

[0221] (38)

[0222] In the formula:

[0223] Multiply both sides of equation (38) by Integrating over [0, Hp] and combining this with the orthogonality of the intrinsic function system, we can obtain...

[0224] (39)

[0225] In the formula: ; ; .

[0226] Substituting equations (37) and (39) into equation (34), the pile displacement can be expressed as:

[0227] (40)

[0228] From equation (40) and boundary condition equation (12), we can obtain

[0229] (41)

[0230] The amplitude-frequency response of the pile top displacement can be expressed as:

[0231] (42)

[0232] Using the inverse Fourier transform, the pile top settlement under a unit vertical load can be obtained as follows:

[0233] (43)

[0234] When a vertical load q(t) is applied to the top of the pile, the settlement at the top of the pile can be expressed as follows:

[0235] (44)

[0236] In the formula: for The Fourier transform form of .

[0237] Thus, a formula for calculating pile top settlement under any time and any vertical load is obtained, which can be used to predict the long-term settlement of solidified soil composite pipe piles.

Claims

1. A method for calculating the long-term settlement of solidified soil composite pipe piles, characterized in that, Includes the following steps: S1. Establish a theoretical model of the solidified soil composite pipe pile-soil system; S2. Divide the soil around the pile into a series of annular layers, and consider the differences in properties between the solidified soil around the pile, the transition zone and the undisturbed soil on the periphery. The soil properties inside each layer are radially homogeneous. Based on this, the soil is considered as a cohesive damping material. Establish the equilibrium formulas for the soil around the pile in any layer under vertical load and the equilibrium formulas for the solidified soil in the pile core. Establish the equilibrium formulas for the pipe pile under vertical load and list the boundary conditions of the pile-soil system. S3. The equilibrium formula of the soil around the pile is solved by Laplace transform and separation of variables. Based on the continuity condition between adjacent layers, the side friction resistance of the soil around the pile to the outer wall of the pipe pile is obtained by recursively solving the equilibrium formula of the solidified soil in the pile core. The side friction resistance of the solidified soil in the pile core to the inner wall of the pipe pile is obtained by solving the equilibrium formula of the solidified soil in the pile core. S4. Solve the equilibrium formula for the pipe pile, and obtain the amplitude-frequency response of the pile top displacement based on the continuity condition of the pile-soil system. On this basis, obtain the calculation formula for the pile top settlement under any vertical load at any time through inverse Fourier transform and convolution.

2. The method for calculating the long-term settlement of solidified soil composite pipe piles according to claim 1, characterized in that, The boundary conditions for the pile-soil system are: (1) The pipe pile is made of linear elastic material, and the soil around the pile and the core of the pile is made of viscoelastic material. Its damping form is viscous damping. (2) The bottom of the pipe pile, the soil around the pile and the solidified soil inside the pile core are all viscoelastic supports. The soil around the pile includes the solidified soil around the pile, the transition zone and the original soil around the pile. (3) The top of the soil around the pile and the solidified soil inside the pile core are free boundaries; (4) The pipe pile, the solidified soil around the pile and the solidified soil inside the pile core are in complete contact, and the displacement of the pile-soil system is coordinated and the stress is continuous. (5) The soil layers around the pile meet the conditions of displacement coordination and stress continuity.

3. The method for calculating the long-term settlement of solidified soil composite pipe piles according to claim 1, characterized in that, In S1, a theoretical analysis model of the solidified soil composite pipe pile-soil system under vertical load is established. The length, inner radius, and outer radius of the precast pipe pile are H, ... p r c and r w The vertical load q(t) acting on the pile top; The precast pipe pile is surrounded by solidified soil within a predetermined range around the pile and the pile core. Due to the diffusion effect of the curing agent slurry during the mixing and drilling process, a transition zone will be formed around the solidified soil around the pile. The soil properties in the transition zone gradually change radially, and the outer part of the transition zone is undisturbed undisturbed soil. To account for the influence of the complex surrounding soil on the outer wall of the pipe pile, it is divided into m concentric layers radially. Layer 1 represents the solidified soil around the pile, layer m is the undisturbed soil, and layers 2, 3, i, ..., m-1 are transition zones. The soil properties within each layer are radially homogeneous, but the soil properties differ between layers. The ends of the pile-soil system are all viscoelastic supports. The pile-soil system includes the pipe pile, the surrounding soil, and the solidified soil within the pile core. The pile bottom support stiffness and damping coefficient are k... b and δ b The bottom support stiffness and damping coefficient of the i-th layer of soil around the pile are k i and δ i The bottom support stiffness and damping coefficient of the pile core soil are k, respectively. c and δ c .

4. The method for calculating the long-term settlement of solidified soil composite pipe piles according to claim 1, characterized in that, Step S2 includes, The solidified soil around the pile, the transition zone, and the surrounding undisturbed soil are divided radially into a series of annular layers. An equilibrium formula for any layer under vertical load is established. (1)； In the formula: Let be the vertical displacement of the soil around the i-th pile ring; , and , respectively, are the Lame constant, shear modulus, and viscous damping coefficient of the soil surrounding the i-th pile layer.

5. The method for calculating the long-term settlement of solidified soil composite pipe piles according to claim 1, characterized in that, Step S2 includes establishing a balance formula for the solidified soil in the pile core: (2)； In the formula: This refers to the vertical displacement of the soil solidified in the pile core. , and These represent the Lame constant, shear modulus, and viscous damping coefficient of the soil in the pile core solidification process.

6. The method for calculating the long-term settlement of solidified soil composite pipe piles according to claim 1, characterized in that, Step S2 includes the following: the equilibrium formula for the pipe pile under vertical load can be expressed as follows: (3)； In the formula: E represents the vertical displacement of the pipe pile. p A p ρ p These are the elastic modulus, cross-sectional area, and density of the pipe pile, respectively. and These represent the side friction resistance of the pipe pile to the soil around the pile and the soil around the pile core, respectively.

7. The method for calculating the long-term settlement of solidified soil composite pipe piles according to claim 2, characterized in that, Step S2 includes the following: the boundary conditions of the pile-soil system are: The boundary conditions at the top and bottom of the soil around the pile are respectively (4)； (5)。 8. The method for calculating the long-term settlement of solidified soil composite pipe piles according to claim 2, characterized in that, Step S2 includes setting the boundary conditions for the top and bottom of the pile core soil as follows: (6)； (7)； Displacement and shear stress continuity between adjacent layers of soil around the pile: (8)； (9)； The displacement of the outermost layer of soil around the pile is zero at infinity. (10)； Boundary conditions at the pile top and pile bottom: (11)； (12)； In the formula: and These are the stiffness and damping coefficient of the soil at the pile bottom, respectively.

9. The method for calculating the long-term settlement of a solidified soil composite pipe pile according to claim 2, characterized in that, Displacement and stress continuity between the soil around the pile and the pile: (13)； (14)； Displacement and stress continuity between the pile core and the pile: (15)； (16)； In the formula: and These are the shear stresses between the pile and the surrounding soil, and between the pile and the core soil, respectively.

10. The method for calculating the long-term settlement of a solidified soil composite pipe pile according to claim 1, characterized in that, Step S3 specifically includes: Applying a Laplace transform to equation (1) yields... (17)； In the formula: For u i The Laplace transform form; make Formula (17) can be decomposed into the following two formulas: (18)； (19)； In the formula: ; The solutions to formulas (18) and (19) are expressed as follows: (20)； (21)； In the formula: A i B i C i and D i All are coefficients determined by boundary conditions; and These are the first and second type zero-order modified Bessel functions, respectively.

11. The method for calculating the long-term settlement of a solidified soil composite pipe pile according to claim 10, characterized in that, Based on formulas (20) and (21) and combined with boundary condition formulas (4) and (5), the displacement amplitude of the soil around any pile ring can be obtained as follows: (22)； In the formula: A in B in and C in All are coefficients determined by the boundary conditions, n=1,2,…; and These are the first and second type zero-order modified Bessel functions, respectively; and They are determined by the following formulas respectively: (23)； In the formula: , which is the dimensionless support complex stiffness. Angular frequency; (24)； The shear stress between the soil surrounding adjacent pile layers can be expressed as (25)； In the formula: and These are the first-order modified Bessel functions of the first and second classes, respectively.

12. The method for calculating the long-term settlement of solidified soil composite pipe piles according to claim 8, characterized in that, From the boundary condition formulas (8) and (9), we can obtain When i = m-1: (26)； When i = 1, 2, ..., m-2: (27)； Solve formula (2), and combine it with the core soil in the pile. Given a boundary condition where the displacement is a finite value, the displacement amplitude of the pile core soil can be obtained as follows: (28)； In the formula: For u c The Laplace transform form; A cn These are coefficients to be determined; and They are obtained from the following formulas respectively: (29)； In the formula: , which is the dimensionless complex stiffness of the support; (30)； The shear stress between the core soil and the inner wall of the pipe pile can be expressed as: (31)。 13. The method for calculating the long-term settlement of a solidified soil composite pipe pile according to claim 11, characterized in that, In S4: Based on formulas (25), (31), and boundary condition formulas (14) and (16), and using the Laplace transform method, formula (3) can be written as (32)； Solving formula (32) yields (33)； In the formula: ; ; Because the properties of the soil around the pile and the soil in the pile core are the same, it is possible to make Therefore, formula (33) can be written as: (34)； According to the boundary condition formulas (13) and (15), we can obtain (35)； (36)； From formulas (35) and (36), we can obtain (37)； In the formula: ; Substituting formula (37) into formula (36) yields... (38)； In the formula: ; Multiply both sides of formula (38) by Integrating over [0, Hp] and combining this with the orthogonality of the intrinsic function system, we can obtain... (39)； In the formula: ; ; ; Substituting formulas (37) and (39) into formula (34), the pile displacement can be expressed as: (40)； From formula (40) and boundary condition formula (12), we can obtain that (41)； The amplitude-frequency response of the pile top displacement can be expressed as follows: (42) Using the inverse Fourier transform, the pile top settlement under a unit vertical load can be obtained as follows: (43)； When a vertical load q(t) is applied to the pile top, the pile top settlement can be expressed as: (44)； In the formula: for The Fourier transform form; Thus, a formula for calculating pile top settlement under any time and any vertical load is obtained, which can be used to predict the long-term settlement of solidified soil composite pipe piles.

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