Method for determining settlement and internal force of stiffening core cement-soil composite pile under action of vertical dynamic load of pile top

Abstract

The invention relates to a method for determining settlement and internal force of a stiffening core cement soil composite pile under the action of a vertical dynamic load of a pile top, and belongs to the technical field of bridge engineering. According to a cement soil radial reinforcement range, decomposing the calculation model into a cement soil reinforcement area and a cement soil non-reinforcement area, and determining a soil modal function, a characteristic equation and a characteristic root related to depth in different areas; a pile infinitesimal body settlement control equation is established and solved, and a soil settlement expression is obtained; determining the soil resistance per unit length of the stiffening core and the pile periphery interface; obtaining a stiffness core settlement and axial strain expression based on the stiffness core infinitesimal body settlement control equation; solving unknown coefficients in the stiffness core settlement and axial strain expression; and under the condition of different cement soil reinforcement ranges, a depth change diagram of settlement and axial strain of the stiffening core cement soil composite pile and a pile top vertical rigidity frequency spectrum response diagram are drawn. According to the method, the stiffness, settlement and axial strain spectrum response rules of the pile top of the stiffening core cement soil composite pile under the action of the vertical dynamic load of the pile top can be better reflected.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering, and in particular relates to a method for determining the settlement and internal force of a reinforced core cement-soil composite pile under the vertical dynamic load on the pile top. Background Art

[0002] With the continuous development of economy and the continuous increase of transportation pressure, higher requirements are put forward for bridge construction, which not only needs to ensure the quality of engineering, but also shorten the construction period to meet the increasingly busy traffic needs. As a new type of pile foundation technology, the core cement soil composite pile inserts a rigid core pile (such as concrete precast pile or other rigid reinforcement) into the cement soil pile, giving full play to the pile side friction and pile end resistance. The core pile provides a higher axial bearing capacity, while the cement soil pile increases the contact area between the pile body and the surrounding soil body and improves the side friction resistance. The combination of the two significantly improves the bearing capacity of the composite pile, which can be several times higher than that of the simple cement soil pile. Compared with some traditional pile foundation construction methods, such as bored cast-in-place piles, its advantages are mainly reflected in: faster construction speed, which can shorten the construction period of the project; the noise and vibration generated during the construction process are relatively small, and the impact on the surrounding environment is small, especially suitable for areas with high environmental requirements such as urban areas; there is no large amount of mud discharge, which reduces the pollution to the environment. Although the core cement soil composite pile has been applied to a certain extent in engineering practice, the theoretical research on its bearing mechanism and deformation characteristics is not deep and complete enough. This has limited the further promotion and application of this technology to a certain extent, and also brought certain difficulties to engineering design and construction. Therefore, the proposed and established method for calculating the settlement and internal force of reinforced core cement-soil composite piles under the vertical dynamic load on the pile top has important engineering practical significance for evaluating the bearing capacity of bridge foundations and ensuring the safe and stable operation of bridges.

[0003] Through searching the existing technical literature, it is found that the current research methods for the settlement and internal force of reinforced core cement-soil composite piles under the vertical load on the pile top mainly adopt experimental research and theoretical analysis methods. In terms of experimental research, most of the existing research focuses on the static characteristics of reinforced core cement-soil composite piles, and the research on dynamic characteristics is still very limited; at the same time, limited by factors such as site specificity, test scale, geological conditions, climatic conditions and surrounding environmental interference, the field test results of reinforced core cement-soil composite piles may not fully represent the conditions of other sites, and the versatility and representativeness of the data are limited, making it difficult to fully reflect the performance and applicability of pile foundations under different conditions. In terms of theoretical research, Liu Hongbo et al. published an article entitled "Analysis of Longitudinal Dynamic Response of Rigid Composite Piles in Viscoelastic Unsaturated Soils" in Rock and Soil Mechanics in 2024. Based on the elastic dynamics theory, it is assumed that the outer pile and the core pile of the rigid composite pile are bonded together, and their small inharmonious deformations are ignored. It is found that reducing the outer radius of the concrete core pile and increasing the length of the composite pile are conducive to improving the longitudinal vibration resistance of the rigid composite pile; the radius of the concrete core pile is within the range of 40% to 60% of the total radius of the rigid composite pile, and the length of the rigid composite pile is within the range of 30 to 50 times its radius, which helps to exert the best vibration resistance while greatly saving costs. Therefore, considering the geological conditions and the settlement difference between the rigid core-cement soil-soil, the proposed settlement and internal force calculation method of the rigid core cement soil composite pile under the excitation of the vertical dynamic load at the pile top has very important theoretical research significance and application value. Summary of the invention

[0004] The purpose of the present invention is to provide a method for determining the settlement and internal force of a stiff-core cement-soil composite pile under the vertical dynamic load on the pile top, so that it can better reflect the relationship between the vertical dynamic load on the pile top and the pile top stiffness, thereby better controlling the vertical settlement of the composite pile and ensuring safe and stable operation under the vertical load on the upper part of the bridge.

[0005] To achieve the above object, the technical solution of the present invention is: a method for determining the settlement and internal force of a reinforced core cement-soil composite pile under a vertical dynamic load at the pile top, comprising:

[0006] S1. Determine the design parameters of the stiffener and cement soil, geological condition information, and the vertical dynamic load excitation parameters of the pile top;

[0007] S2. According to the radial reinforcement range of cement soil, the calculation model is decomposed into cement soil reinforcement area I and non-reinforced area II; among them, area I is further subdivided into sub-area 1 and sub-area 2; according to the stress and displacement continuity conditions at the soil interface and the Newton iteration method, the depth-related soil modal function, characteristic equation and characteristic root are determined by region; the depth-related soil modal function can reflect the natural boundary conditions of the soil layer and the vibration modes of each order of the soil body;

[0008] S3, establish the sedimentation w of the microelement of region j (j=1, 1) respectivelyj (r, z) control equation, and solve it to get the soil settlement expression w related to the radial r and depth z in area j. j (r, z); Compared with existing research papers, the calculation method proposed in this application is more universal for the situation where the length of the core pile is greater than the length of the cement soil in actual engineering. Therefore, the present invention establishes the soil modal function related to the depth by region, and uses the Fourier series accumulation technology to accumulate each order mode to obtain the soil settlement expression of region I and region II respectively;

[0009] S4. According to the elastic dynamic stress and displacement relationship, the partial derivative of soil settlement with respect to depth z and radius r is calculated to obtain the vertical stress σ inside the soil in region j. zj (r,z) and tangential stress τ rzj (r,z); the tangential stress τ rzj (r,z) is integrated along the circumference of the pile to obtain the soil resistance per unit length of the pile at the contact surface between the stiffening core and the cement soil, p(ω,z); compared with existing papers, on the one hand, existing studies assume that the stiffening core and the cement soil are strongly bonded together and ignore their uncoordinated deformation, that is, it is assumed that the deformation of the stiffening core is equivalent to the deformation of the cement soil. However, the present invention takes into account that under the action of the vertical load on the pile top, there is a displacement difference between the deformation of the stiffening core and the cement soil, and this displacement difference will affect the distribution law of the soil resistance per unit length of the pile and the dynamic stiffness of the pile top. Therefore, the present invention establishes a soil settlement expression by region, which can take into account the settlement difference between the stiffening core-cement soil-soil body;

[0010] S5. Establish the vertical stress balance equation of the core microelement, and obtain the core settlement w according to the relationship between stress and displacement. p (z) is the governing equation. Solving the governing equation, we can obtain the core settlement w expressed by the unknown coefficients. p (z) and the axial strain expression ε p (z);

[0011] S6. Solve the unknown coefficients according to the displacement and stress continuity conditions at the pile top, pile end, stiffening core and cement-soil interface;

[0012] S7. Draw the settlement of the reinforced cement-soil composite pile, the variation of the axial strain along the depth and the spectrum response diagram of the vertical stiffness at the pile top under different cement-soil reinforcement ranges.

[0013] In one embodiment of the present invention, in step S1,

[0014] The design parameters of the stiffener include: concrete elastic modulus, length, diameter, and density;

[0015] The design parameters of cement soil include: elastic modulus of cement soil, reinforcement depth, reinforcement radius, and density;

[0016] Geological condition information includes: soil layer density, thickness, dynamic elastic modulus, dynamic shear modulus, shear wave velocity, Poisson's ratio and soil damping ratio;

[0017] The excitation parameters of the vertical dynamic load on the pile top include: excitation amplitude and frequency.

[0018] In one embodiment of the present invention, in step S2, the soil modal function of region I is as follows:

[0019]

[0020] Among them, Z m (z) is the mth-order soil modal function in region 1; h Ιm is the mth order characteristic root of region Ι, and the characteristic equation is OK;h Ι is the characteristic root of region 1; H1 is the depth of cement soil reinforcement; H2 is the distance from the bottom of the cement soil reinforcement area to the bedrock; L is the thickness of the soil layer; η s1 is the ratio of longitudinal wave velocity to transverse wave velocity of cement soil; μ s1 is the dynamic shear modulus of cement soil; η s2 is the ratio of the longitudinal wave velocity to the transverse wave velocity of the soil; μ s2 is the dynamic shear modulus of soil;

[0021] The soil modal function of area П is as follows:

[0022]

[0023] in, is the m-th order soil modal function of the region; h Пm =(2m-1)π / 2L is the mth order characteristic root of region П.

[0024] In one embodiment of the present invention, in step S3, the soil settlement w j The expression of (r,z) is as follows:

[0025] w j (r,z)=G j (r)[C j sin(h j z)+D j cos(h j z)]

[0026] Wherein, j=1 represents the cement soil reinforced area, j=2 represents the unreinforced area; G j (r) = A j K0(q j r)+B j I0(q jr); K0(·) and I0(·) are the first and second kind of zeroth order modified Bessel functions, respectively; q j Need to meet η sj is the ratio of the longitudinal wave velocity to the transverse wave velocity, h j A is a series of characteristic roots to be found; j , B j , C j and D j are a series of unknown coefficients to be solved; k j is the wave number, is the complex shear wave velocity, satisfying the following relationship: c sj is the shear wave velocity, β s is the soil damping ratio; ω is the circular frequency of the vertical load excitation at the pile top.

[0027] In one embodiment of the present invention, in step S4, the vertical stress σ inside the soil zj (r,z) is as follows:

[0028]

[0029] Tangential stress τ rzj (r,z) is as follows:

[0030]

[0031] The soil resistance per unit length of the pile at the contact surface between the stiffener and the cement soil p(ω,z) satisfies the following formula

[0032]

[0033] Where, d is the pile diameter; is the function of the soil shear modulus in region 1 along the depth z, satisfying the following formula: and are the complex shear moduli of cement soil and unreinforced soil, respectively; H(·) is a step function; H1 is the reinforcement depth of cement soil; S(r0,z) is a 1-row, N-column matrix related to the depth, satisfying the following formula:

[0034] S(r0,z)=-{q 11 K1(q 11 r0)Z1(z)q 12 K1(q 12 r0)Z2(z)…q 1N K1(q 1N r0)Z N (z)}

[0035] is a 1-row, N-column matrix related to depth, satisfying the following formula:

[0036]

[0037] H2 is the distance from the bottom of the cement soil reinforcement area to the bedrock, H2 = L-H1; Φ is expressed as A2 is a matrix with 1 row and N columns, consisting of N unknown coefficients, expressed as A2 = {A 21 A 22 …A 2N}; matrix Γ, M, Λ, and The expression is as follows:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] in,

[0045] In one embodiment of the present invention, the settlement of the reinforced core cement-soil composite pile in step S5 is p (z) are as follows:

[0046] w p (z) = a p sin(λ p z)+b p cos(λ p z)+Y(z)(Γ p ) -1 Q p A2

[0047] Among them, a p and b p is the unknown coefficient to be determined; λ p =(ρ p ω 2 / E p ) 1 / 2 , ρ p E is the density of the core concrete; pis the elastic modulus of the reinforced concrete; ω is the excitation frequency; Y(z)={Y1(z),Y2(z),…,Y N (z)} T , Y m (z) = cos(h Пm z);Γ p is a matrix of N rows and N columns, expressed as

[0048]

[0049] Matrix Γ p The element in row l and column m Expressed as

[0050]

[0051] Q p is a matrix of N rows and N columns, expressed as

[0052]

[0053] Matrix Q p The element in row l and column m Expressed as

[0054]

[0055] Axial strain ε p (z), satisfying the following relationship:

[0056]

[0057] Axial stress σ p (z), satisfying the following relationship:

[0058] σ p (z) = E p ε p (z).

[0059] In one embodiment of the present invention, in step S6, the unknown coefficients are solved according to the displacement and stress continuity conditions at the pile top, pile end, stiffening core and cement soil interface, and the unknown coefficients include the general solution coefficient a of the pile to be solved. p 、b p And matrix A2 (N unknowns), a total of N+2 unknown coefficients, the boundary conditions are listed as follows:

[0060]

[0061] In one embodiment of the present invention, in step S7, the settlement of the reinforced cement-soil composite pile, the variation of the axial strain along the depth and the spectrum response diagram of the vertical stiffness of the pile top are plotted under different cement-soil reinforcement ranges.

[0062] The present invention also provides a system for determining the settlement and internal force of a reinforced core cement-soil composite pile under vertical dynamic loads on the pile top, comprising a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0063] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be executed by a processor are stored. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0064] Compared with the prior art, the present invention has the following beneficial effects: the present invention can better reflect the variation law of the top stiffness and internal force of the reinforced core cement-soil composite pile under the vertical dynamic load of the pile top with the excitation frequency, so as to more accurately evaluate the safety state of the bridge pile foundation under the vertical dynamic load. The method of the present invention is simple, practical, easy to promote, and has great application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is the force analysis diagram of the reinforced core cement-soil composite pile under the vertical dynamic load at the pile top.

[0066] Figure 2 Schematic diagram of soil settlement at different dimensionless radial distances r / d in the embodiment.

[0067] Figure 3 Schematic diagram of settlement of reinforced core cement-soil composite piles under different reinforcement ranges.

[0068] Figure 4 Schematic diagram of axial strain of reinforced core cement-soil composite piles under different reinforcement ranges in the embodiment.

[0069] Figure 5 Schematic diagram of the variation of the top stiffness of the reinforced core cement-soil composite pile with the excitation frequency under different reinforcement ranges in the embodiment.

[0070] Figure 6 Schematic diagram of the variation of the top stiffness of the reinforced core cement-soil composite pile with the excitation frequency at different reinforcement depths in the embodiment. DETAILED DESCRIPTION

[0071] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0072] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0073] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0074] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific position, be constructed and operated in a specific position, and therefore cannot be understood as limiting the present invention; the terms "first", "second", and "third" are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance; in addition, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be a connection between the two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0075] The present invention provides a method for determining the settlement and internal force of a reinforced core cement-soil composite pile under a vertical dynamic load on the pile top, comprising:

[0076] S1. Determine the design parameters of the stiffener and cement soil, geological condition information, and the vertical dynamic load excitation parameters of the pile top;

[0077] S2. According to the radial reinforcement range of cement soil, the calculation model is decomposed into cement soil reinforcement area I and non-reinforced area II; among them, area I is further subdivided into sub-area 1 and sub-area 2; according to the stress and displacement continuity conditions at the soil interface and the Newton iteration method, the depth-related soil modal function, characteristic equation and characteristic root are determined by region; the depth-related soil modal function can reflect the natural boundary conditions of the soil layer and the vibration modes of each order of the soil body;

[0078] S3, establish the sedimentation w of the microelement of region j (j=1, 1) respectively j (r, z) control equation, and solve it to get the soil settlement expression w related to the radial r and depth z in area j. j(r, z); Compared with existing research papers, the calculation method proposed in this application is more universal for the situation where the length of the core pile is greater than the length of the cement soil in actual engineering. Therefore, the present invention establishes the soil modal function related to the depth by region, and uses the Fourier series accumulation technology to accumulate each order mode to obtain the soil settlement expression of region I and region II respectively;

[0079] S4. According to the elastic dynamic stress and displacement relationship, the partial derivative of soil settlement with respect to depth z and radius r is calculated to obtain the vertical stress σ inside the soil in region j. zj (r,z) and tangential stress τ rzj (r,z); the tangential stress τ rzj (r,z) is integrated along the circumference of the pile to obtain the soil resistance per unit length of the pile at the contact surface between the stiffening core and the cement soil, p(ω,z); compared with existing papers, on the one hand, existing studies assume that the stiffening core and the cement soil are strongly bonded together and ignore their uncoordinated deformation, that is, it is assumed that the deformation of the stiffening core is equivalent to the deformation of the cement soil. However, the present invention takes into account that under the action of the vertical load on the pile top, there is a displacement difference between the deformation of the stiffening core and the cement soil, and this displacement difference will affect the distribution law of the soil resistance per unit length of the pile and the dynamic stiffness of the pile top. Therefore, the present invention establishes a soil settlement expression by region, which can take into account the settlement difference between the stiffening core-cement soil-soil body;

[0080] S5. Establish the vertical stress balance equation of the core microelement, and obtain the core settlement w according to the relationship between stress and displacement. p (z) is the governing equation. Solving the governing equation, we can obtain the core settlement w expressed by the unknown coefficients. p (z) and the axial strain expression ε p (z);

[0081] S6. Solve the unknown coefficients according to the displacement and stress continuity conditions at the pile top, pile end, stiffening core and cement-soil interface;

[0082] S7. Draw the settlement of the reinforced cement-soil composite pile, the variation of the axial strain along the depth and the spectrum response diagram of the vertical stiffness at the pile top under different cement-soil reinforcement ranges.

[0083] The following are specific implementation examples of the present invention.

[0084] Example 1

[0085] Step 1: Design parameters of the stiffener, cement soil, geological conditions information, and vertical dynamic load excitation parameters at the pile top. Figure 1 The stress analysis diagram of the reinforced core cement-soil composite pile under the vertical dynamic load on the pile top is shown in Table 1. The geological conditions of the pile foundation and bridge pier selected in this case are shown in Table 1.

[0086] Table 1 Core, cement soil and geological parameters

[0087]

[0088]

[0089] Step 2: Based on and The depth-dependent soil modal functions, characteristic equations and characteristic roots are determined regionally.

[0090] Step 3: Calculate the soil settlement expression w j (r,z). According to w j (r,z)=G j (r)[C j sin(h j z)+D j cos(h j z)] can determine the soil settlement at depth z and radial distance r in region j, Figure 2 The soil settlement at different dimensionless radial distances r / d is given;

[0091] Step 4: Based on and The vertical stress, tangential stress and soil resistance per unit length of the pile are calculated respectively.

[0092] Step 5: Solve the vertical stress equilibrium equation of the core microelement. According to w p (z) = a p sin(λ p z)+b p cos(λ p z)+Y(z)(Γ p ) -1 Q p A2 and Determine the core settlement w with unknown coefficients p (z) and axial strain ε p (z);

[0093] Step 6: According to the boundary conditions of pile top, pile end, and displacement continuity conditions at the interface between the stiffener and cement soil, Determine the unknown coefficients to be solved.

[0094] Step 7. Draw the settlement of the reinforced core cement-soil composite pile, the variation of the axial strain along the depth and the vertical stiffness spectrum response diagram of the pile top according to Formula 7 under different cement-soil reinforcement ranges and reinforcement depths. Figure 3 The settlement diagram of reinforced core cement-soil composite piles under different reinforcement ranges is given. Figure 4 The schematic diagram of axial strain of reinforced core cement-soil composite piles under different reinforcement ranges is given. Figure 5 A schematic diagram of the variation of the top stiffness of the reinforced cement-soil composite pile with the excitation frequency under different reinforcement ranges is given. Figure 6 A schematic diagram showing the variation of the top stiffness of reinforced core cement-soil composite piles with excitation frequency under different reinforcement depths is given.

[0095] The present invention also provides a system for determining the settlement and internal force of a reinforced core cement-soil composite pile under vertical dynamic loads on the pile top, comprising a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0096] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be executed by a processor are stored. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0097] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0098] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0099] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0100] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0101] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A method for determining the settlement and internal force of a reinforced core cement-soil composite pile under vertical dynamic load at the pile top, characterized in that: include: S1. Determine the design parameters of the stiffener and cement soil, geological condition information, and the vertical dynamic load excitation parameters of the pile top; S2. According to the radial reinforcement range of cement soil, the calculation model is decomposed into cement soil reinforcement area I and non-reinforced area II; among them, area I is further subdivided into sub-area 1 and sub-area 2; according to the stress and displacement continuity conditions at the soil interface and the Newton iteration method, the depth-related soil modal function, characteristic equation and characteristic root are determined by region; the depth-related soil modal function can reflect the natural boundary conditions of the soil layer and the vibration modes of each order of the soil body; S3, establish the sedimentation w of the microelement of region j (j=1, 1) respectively j (r, z) control equation, and solve it to get the soil settlement expression w related to the radial r and depth z in area j. j (r,z); S4. According to the elastic dynamic stress and displacement relationship, the partial derivative of soil settlement with respect to depth z and radius r is calculated to obtain the vertical stress σ inside the soil in region j. zj (r,z) and tangential stress τ rzj (r,z); the tangential stress τ rzj (r,z) is integrated along the circumference of the pile to obtain the soil resistance per unit length of the pile at the contact surface between the stiffener and the cement soil, p(ω,z); S5. Establish the vertical stress balance equation of the core microelement, and obtain the core settlement w according to the relationship between stress and displacement. p (z) is the governing equation. Solving the governing equation, we can obtain the core settlement w expressed by the unknown coefficients. p (z) and the axial strain expression ε p (z); S6. Solve the unknown coefficients according to the displacement and stress continuity conditions at the pile top, pile end, stiffening core and cement-soil interface; S7. Draw the settlement of the reinforced cement-soil composite pile, the variation of the axial strain along the depth and the spectrum response diagram of the vertical stiffness at the pile top under different cement-soil reinforcement ranges.

2. The method for determining the settlement and internal force of a reinforced core cement-soil composite pile under vertical dynamic load at the pile top according to claim 1, characterized in that: In step S1, The design parameters of the stiffener include: concrete elastic modulus, length, diameter, and density; The design parameters of cement soil include: elastic modulus of cement soil, reinforcement depth, reinforcement radius, and density; Geological condition information includes: soil layer density, thickness, dynamic elastic modulus, dynamic shear modulus, shear wave velocity, Poisson's ratio and soil damping ratio; The excitation parameters of the vertical dynamic load on the pile top include: excitation amplitude and frequency.

3. The method for determining the settlement and internal force of a reinforced core cement-soil composite pile under vertical dynamic load at the pile top according to claim 1, characterized in that: In step S2, the soil modal function of region I is as follows: Among them, Z m (z) is the mth-order soil modal function in region 1; h Ιm is the mth order characteristic root of region Ι, and the characteristic equation is OK;h Ι is the characteristic root of region 1; H1 is the depth of cement soil reinforcement; H2 is the distance from the bottom of the cement soil reinforcement area to the bedrock; L is the thickness of the soil layer; η s1 is the ratio of longitudinal wave velocity to transverse wave velocity of cement soil; μ s1 is the dynamic shear modulus of cement soil; η s2 is the ratio of the longitudinal wave velocity to the transverse wave velocity of the soil; μ s2 is the dynamic shear modulus of soil; The soil modal function of area П is as follows: in, is the m-th order soil modal function of the region; h Пm =(2m-1)π / 2L is the mth order characteristic root of region П.

4. The method for determining the settlement and internal force of a reinforced core cement-soil composite pile under vertical dynamic load at the pile top according to claim 1, characterized in that: In step S3, soil settlement w j The expression of (r,z) is as follows: w j (r,z)=G j (r)[C j sin(h j z)+D j cos(h j z)] Wherein, j=1 represents the cement soil reinforced area, j=2 represents the unreinforced area; G j (r) = A j K0(q j r)+B j I0(q j r); K0(·) and I0(·) are the first and second kind of zeroth order modified Bessel functions, respectively; q j Need to meet η sj is the ratio of the longitudinal wave velocity to the transverse wave velocity, h j A is a series of characteristic roots to be found; j , B j , C j and D j are a series of unknown coefficients to be solved; k j is the wave number, is the complex shear wave velocity, satisfying the following relationship: c sj is the shear wave velocity, β s is the soil damping ratio; ω is the circular frequency of the vertical load excitation at the pile top.

5. A method for determining the settlement and internal force of a reinforced core cement-soil composite pile under vertical dynamic load at the pile top according to claim 4, characterized in that: In step S4, the vertical stress inside the soil σ zj (r,z) is as follows: Tangential stress τ rzj (r,z) is as follows: The soil resistance per unit length of the pile at the contact surface between the stiffener and the cement soil p(ω,z) satisfies the following formula Where, d is the pile diameter; is the function of the soil shear modulus in region 1 along the depth z, satisfying the following formula: and are the complex shear moduli of cement soil and unreinforced soil, respectively; H(·) is a step function; H1 is the reinforcement depth of cement soil; S(r0,z) is a 1-row, N-column matrix related to the depth, satisfying the following formula: S(r0,z)=-{q 11 K1(q 11 r0)Z1(z)q 12 K1(q 12 r0)Z2(z)…q 1N K1(q 1N r0)Z N (With)} is a 1-row, N-column matrix related to depth, satisfying the following formula: H2 is the distance from the bottom of the cement soil reinforcement area to the bedrock, H2 = L-H1; Φ is expressed as A2 is a matrix with 1 row and N columns, consisting of N unknown coefficients, expressed as A2 = {A 21 A 22 …A 2N }; matrix Γ, M, Λ, and The expression is as follows: in, 6. A method for determining the settlement and internal force of a reinforced core cement-soil composite pile under vertical dynamic load at the pile top according to claim 5, characterized in that: In step S5, the settlement of the reinforced core cement-soil composite pile is w p (z) are as follows: w p (z)=a p sin(λ p z)+b p cos(λ p z)+Y(z)(Γ p ) -1 Q p A2 Among them, a p and b p is the unknown coefficient to be determined; λ p =(ρ p ω 2 / E p ) 1 / 2 , ρ p E is the density of the core concrete; p is the elastic modulus of the reinforced concrete; ω is the excitation frequency; Y(z)={Y1(z),Y2(z),…,Y N (z)} T , Y m (z) = cos(h Пm z);Γ p is a matrix of N rows and N columns, expressed as Matrix Γ p The element in row l and column m Expressed as Q p is a matrix of N rows and N columns, expressed as Matrix Q p The element in row l and column m Expressed as Axial strain ε p (z), satisfying the following relationship: Axial stress σ p (z), satisfying the following relationship: σ p (from)=E p ε p (With).

7. A method for determining the settlement and internal force of a reinforced core cement-soil composite pile under vertical dynamic load at the pile top according to claim 6, characterized in that: In step S6, the unknown coefficients are solved according to the displacement and stress continuity conditions at the pile top, pile end, stiffening core and cement soil interface. The unknown coefficients include the general solution coefficient a of the pile to be solved. p 、b p And matrix A2, a total of N+2 unknown coefficients, the boundary conditions are listed as follows:

8. The method for determining the settlement and internal force of a reinforced core cement-soil composite pile under vertical dynamic load at the pile top according to claim 1, characterized in that: In step S7, the settlement of the reinforced cement-soil composite pile, the variation of the axial strain along the depth and the spectrum response diagram of the vertical stiffness of the pile top are plotted under different cement-soil reinforcement ranges.

9. A system for determining the settlement and internal force of a reinforced core cement-soil composite pile under vertical dynamic load at the pile top, characterized in that: The method comprises a memory, a processor and computer program instructions stored in the memory and executable by the processor. When the processor executes the computer program instructions, the method steps as claimed in any one of claims 1 to 8 can be implemented.

10. A computer-readable storage medium storing computer program instructions that can be executed by a processor, wherein when the processor executes the computer program instructions, the method steps according to any one of claims 1 to 8 can be implemented.

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