Calculation method for the force and displacement of a foundation pile in soil under the action of axial load at the pile top

Abstract

The present invention belongs to the technical fields of electrical digital data processing and foundation engineering, and discloses a calculation method for the force and displacement of a foundation pile in soil under the action of axial load at the pile top, which includes the following steps: taking the pile top as the coordinate origin, with the z-axis downward along the longitudinal axis of the pile body, solving for the characteristic variables reflecting the force and displacement distribution patterns of the pile body from the basic mechanical equilibrium conditions of the microelement formed by the microsection length arbitrarily taken along the axial direction of the pile body, as well as the force boundary conditions at the pile top and the deformation coordination relationship between the pile bottom and the foundation; and solving for the axial displacement of the pile body, the axial force of the pile body, and the frictional resistance on the pile side surface at different depths along the axial direction of the pile body from the basic mechanical equilibrium conditions of the microelement, the force boundary conditions at the pile top, and in combination with the characteristic variables. The present invention provides a fast and effective method and a scientific basis for the design calculation and analysis of foundation piles in soil under the action of axial load at the pile top, and has important technical method significance and engineering application value.

Description

Technical Field

[0001] The present invention relates to the technical fields of electronic digital data processing and foundation engineering, and more particularly, to a method for calculating the force and displacement of a foundation pile in soil under the action of an axial load at the pile top. Background Art

[0002] Pile foundations are a common type of foundation in projects such as building construction, railways, and highways. They have advantages such as large bearing capacity and small settlement deformation, and are widely used in practice. In a group pile foundation in an actual stratum, the force and displacement of a foundation pile are important reflections of the force and displacement of the group pile foundation, and are of great significance for the rational design of the group pile foundation.

[0003] Under the action of an axial load at the pile top, the main force and displacement behaviors of the pile body, such as the axial force of the pile body, the side friction of the pile, and the axial displacement of the pile body, all show a relatively complex non-linear variation pattern along the depth. At present, regarding the force and displacement of a foundation pile in soil under the action of an axial load at the pile top, the classical theory only presents a general differential equation for the relationship between the axial force and the side friction, and no analytical results for the axial force of the pile body, the side friction of the pile, the axial displacement of the pile body, etc. can be obtained under the condition that only the axial force at the pile top is known. On the other hand, for the analysis of the force and displacement of a foundation pile in soil under the action of an axial load at the pile top, numerical simulation methods such as finite element and finite difference are often used. However, for numerical simulation methods, a numerical model needs to be established first, and the rationality of the numerical model depends on factors such as model parameters, mesh accuracy, material constitutive models, and boundary conditions. Not only is the modeling process complex and cumbersome, and there is interference from subjective human operations, but it is also difficult to have "inheritance" (different people need to start from the modeling operation). It can be used as a reference means for studying complex problems, but it is not conducive to the rapid analysis and operation of actual engineering technicians.

[0004] It can be seen that there is currently no simplified theoretical calculation method for analyzing the variation of the force and displacement of a foundation pile in soil under the action of an axial load at the pile top along the depth, resulting in a lack of sufficient and reasonable basis in relevant actual projects, or a cumbersome calculation and analysis operation process, mainly relying on experience, with blindness in design. Therefore, for the calculation of the force and displacement of a foundation pile in soil under the action of an axial load at the pile top, a calculation method with a reasonable concept, simplicity, and practical operability is urgently needed. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for calculating the force and displacement of a foundation pile in soil under the action of an axial load at the pile top, which is conceptually simple and reasonable and practically easy to operate.

[0006] To achieve the above object, the present invention provides a method for calculating the force and displacement of a foundation pile in soil under the action of an axial load at the pile top, and the technical solution is as follows:

[0007] Calculation method for the force and displacement of a foundation pile in soil under the action of an axial load at the pile top, comprising the following steps:

[0008] Taking the pile top as the coordinate origin, with the z-axis pointing downwards along the longitudinal axis of the pile, solving for the characteristic variables reflecting the force and displacement distribution patterns of the pile body from the basic mechanical equilibrium conditions of the infinitesimal element formed by the infinitesimal segment length taken arbitrarily along the axial direction of the pile body, as well as the force boundary conditions at the pile top and the deformation coordination relationship between the pile bottom and the foundation.

[0009] From the basic mechanical equilibrium conditions of the infinitesimal element and the force boundary conditions at the pile top, combined with the characteristic variables, solving for the axial displacement of the pile body, the axial force of the pile body, and the frictional resistance on the pile side surface at different depths along the axial direction of the pile body.

[0010] As a further improvement to the above calculation method for the force and displacement of a foundation pile in soil under the action of an axial load at the pile top: The calculation expression for the characteristic variable n is: In the formula, n is the characteristic variable reflecting the force and displacement distribution patterns of the pile body, a positive dimensionless number; π is the circumference ratio; r p is the radius of the pile body; E p is the elastic modulus of the pile body; l is the pile length; R0 is the equivalent calculation radius at the pile bottom; k0 is the vertical elastic resistance coefficient of the pile bottom foundation.

[0011] As a further improvement to the above calculation method for the force and displacement of a foundation pile in soil under the action of an axial load at the pile top:

[0012] The expression for the basic mechanical equilibrium conditions of the infinitesimal element is:

[0013] The expression for the force boundary conditions at the pile top is:

[0014] The expression for the deformation coordination relationship between the pile bottom and the foundation is: ω b = ω(l);

[0015] In the formula, z is the depth from the pile top; P(z) is the axial force of the pile body at the cross-section at the depth z from the pile top; P′ is the first derivative of P(z) with respect to z; τ(z) is the frictional resistance on the pile side surface at the depth z from the pile top; P t is the axial load at the pile top; ω(z) is the axial displacement of the pile body at the depth z from the pile top; ω b is the foundation settlement at the pile bottom.

[0016] As a further improvement to the above calculation method for the force and displacement of a foundation pile in soil under the action of an axial load at the pile top: The calculation expression for the equivalent calculation radius R0 at the pile bottom is: In the formula, min means taking the minimum value; for end-bearing piles or column piles, then take R0 = r p; S is the pile spacing; is the weighted average value of the internal friction angle of the soil on the pile side.

[0017] As a further improvement to the method for calculating the force and displacement of the foundation pile in the soil under the axial load on the pile top described above: the weighted average value of the internal friction angle of the soil on the pile side The calculation expression is: In the formula, M is the number of layers of the soil on the pile side; i is the sequential number starting from 1 from top to bottom of the soil on the pile side, and h i is the thickness of the soil on the pile side of the i-th layer; is the internal friction angle of the soil on the pile side of the i-th layer.

[0018] As a further improvement to the method for calculating the force and displacement of the foundation pile in the soil under the axial load on the pile top described above:

[0019] The calculation expression for the axial displacement of the pile body is: ω(z) = Ae (-Bz) cos(Bz);

[0020] The calculation expression for the axial force of the pile body is:

[0021] The calculation expression for the frictional resistance on the surface of the pile side is: τ(z) = r p E p AB 2 e (-Bz) sin(Bz);

[0022] A is an intermediate calculation parameter, and its calculation expression is:

[0023] B is an intermediate calculation parameter, and its calculation expression is:

[0024] In the formula, e is the natural exponent.

[0025] The advantages of the method for calculating the force and displacement of the foundation pile in the soil under the axial load on the pile top of the present invention are as follows: First, the calculation method of the present invention fully considers the pile-soil deformation coordination and the static equilibrium of the pile body, and reflects the characteristics of the pile body, the soil on the pile side, and the foundation at the pile bottom. Second, the method for calculating the force and displacement of the foundation pile in the soil under the axial load on the pile top proposed by the present invention has clear concepts and simple algorithms, which are convenient for quick operation. It has been verified that by using the calculation method of the present invention, it is possible to simply estimate and determine the force and displacement of the foundation pile in the soil under the axial load on the pile top without time-consuming, laborious, and costly tests or numerical simulation calculations, which is convenient for quick engineering design analysis.

[0026] It can be seen that based on the deformation coordination between the pile and the soil and the static equilibrium condition of the pile body, the present invention presents the force and displacement of the foundation pile in the soil under the axial load at the pile top in a simple calculation expression. The relevant parameters in the expression are easy to determine, and the actual operation is simple. It provides a fast and effective method and scientific basis for the design calculation and analysis of the foundation pile in the soil under the axial load at the pile top, and has important technical method significance and engineering application value.

[0027] The following further describes the present invention in conjunction with the accompanying drawings and specific embodiments. The additional aspects and advantages of the present invention will be partially given in the following description, partially become apparent from the following description, or be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The accompanying drawings constituting a part of the present invention are used to assist in understanding the present invention. The content provided in the accompanying drawings and the related descriptions in the present invention can be used to explain the present invention, but do not constitute an improper limitation to the present invention. In the accompanying drawings:

[0029] Figure 1 It is a schematic diagram of the foundation pile in the soil where the pile top bears the axial pressure load in the embodiment of the present invention.

[0030] Figure 2 It is a comparison diagram of the results of the method of the present invention and the numerical simulation method for the distribution curve of the axial displacement of the pile body along the depth in the embodiment of the present invention.

[0031] Figure 3 It is a comparison diagram of the results of the method of the present invention and the numerical simulation method for the distribution curve of the axial force of the pile body along the depth in the embodiment of the present invention.

[0032] Figure 4 It is a comparison diagram of the results of the method of the present invention and the numerical simulation method for the distribution curve of the skin friction along the depth on the side surface of the pile in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0033] The following clearly and completely describes the present invention in conjunction with the accompanying drawings. Those of ordinary skill in the art will be able to implement the present invention based on these descriptions. Before describing the present invention in conjunction with the accompanying drawings, it is particularly noted that:

[0034] The technical solutions and technical features provided in each part including the following description in the present invention can be combined with each other without conflict.

[0035] In addition, the embodiments of the present invention involved in the following description are usually only a part of the embodiments of the present invention, rather than all the embodiments. Therefore, all other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments of the present invention shall fall within the protection scope of the present invention.

[0036] Regarding the terms and units in the present invention. The terms "comprising", "having" and any variations thereof in the description, claims and relevant parts of the present invention are intended to cover non-exclusive inclusion.

[0037] The specific implementation manner of the calculation method for the force and displacement of the foundation pile in the soil under the axial load at the pile top of the present invention includes the following steps:

[0038] First, taking the pile top as the coordinate origin, with the z-axis downward along the longitudinal axis of the pile, based on the basic mechanical equilibrium conditions of the microelement formed by the micro-segment length taken arbitrarily along the axial direction of the pile, as well as the force boundary conditions at the pile top and the deformation coordination relationship between the pile bottom and the foundation, the characteristic variables reflecting the force and displacement distribution patterns of the pile body are solved.

[0039] Among them, the expression of the basic mechanical equilibrium conditions of the microelement is:

[0040]

[0041] The expression of the force boundary conditions at the pile top is:

[0042]

[0043] The expression of the deformation coordination relationship between the pile bottom and the foundation is:

[0044] ω b = ω(l) Equation 3;

[0045] By combining Equation 1 - Equation 3, the calculation expression of the characteristic variable n reflecting the force and displacement distribution patterns of the pile body is derived as:

[0046]

[0047] In the formula, z is the depth from the pile top; P(z) is the axial force of the pile body at the cross-section at the depth z from the pile top; P' is the first derivative of P(z) with respect to z; τ(z) is the skin friction of the pile side at the depth z from the pile top; P t is the axial load at the pile top; ω(z) is the axial displacement of the pile body at the depth z from the pile top; ω b is the foundation settlement at the pile bottom; n is the characteristic variable reflecting the force and displacement distribution patterns of the pile body, which is a positive dimensionless number; π is the pi; r p is the radius of the pile body; E p is the elastic modulus of the pile body; l is the pile length; R0 is the equivalent calculation radius at the pile bottom; k0 is the vertical elastic resistance coefficient of the pile bottom foundation.

[0048] The calculation expression of the equivalent calculation radius R0 at the pile bottom is:

[0049] In the formula, min represents taking the minimum value; for end-bearing piles or column piles, take R0 = r p ; S is the pile spacing; is the weighted average value of the internal friction angle of the soil on the pile side.

[0050] Weighted average value of the internal friction angle of the soil on the pile side The calculation expression is:

[0051] In the formula, M is the number of layers of the soil on the pile side; i is the sequential number starting from 1 from top to bottom of the soil on the pile side, h i is the thickness of the i-th layer of the soil on the pile side; is the internal friction angle of the i-th layer of the soil on the pile side.

[0052] Among them, from the basic mechanical equilibrium conditions of the microelement and the force boundary conditions at the pile top, combined with the characteristic variables, the calculation expressions for the axial displacement of the pile body, the axial force of the pile body, and the frictional resistance on the pile side surface at different depths along the axial direction of the pile body are obtained as follows:

[0053]

[0054] A is an intermediate calculation parameter, and its calculation expression is:

[0055] B is an intermediate calculation parameter, and its calculation expression is:

[0056] In the formula, e is the natural exponential.

[0057] The beneficial effects of the present invention are illustrated below through specific application examples.

[0058] Figure 1 It is a schematic diagram of a foundation pile in the soil where the pile top bears an axial pressure load. As Figure 1 shown, the soil on the pile side of the foundation pile is two layers of cohesive soil with different properties, and the pile end is pebble soil. Its calculation parameters are shown in Table 1.

[0059] Table 1

[0060]

[0061] It can be calculated that:

[0062]

[0063] Substitute the relevant parameters into Equation 4 to obtain: It is calculated that n = 3.222.

[0064] Further calculate the intermediate calculation parameters to obtain:

[0065] Substituting the relevant parameters into Equation 5 gives:

[0066] Wherein, the unit of the depth z from the pile top is m, the unit of the axial displacement ω(z) of the pile body at the depth z from the pile top is mm, the unit of the axial force P(z) of the pile body at the cross-section at the depth z from the pile top is kN, and the unit of the skin friction τ(z) of the pile side surface at the depth z from the pile top is kPa.

[0067] Thus, the variation trends of the axial displacement of the pile body, the axial force of the pile body, and the skin friction of the pile side surface with depth are obtained. In order to more clearly reflect the variation trends of the axial displacement of the pile body, the axial force of the pile body, and the skin friction of the pile side surface with depth, the relationship curves of the axial displacement ω of the pile body, the axial force P of the pile body, and the skin friction τ of the pile side surface with the depth z from the pile top can be further plotted.

[0068] The comparison diagrams of the distribution curves of the axial displacement ω of the pile body, the axial force P of the pile body, and the skin friction τ of the pile side surface along the depth obtained by the ABAQUS numerical simulation method and the results of the present invention are shown in Figures 2 to 4 . It can be seen that the distribution patterns of the axial displacement of the pile body, the axial force of the pile body, and the skin friction of the pile side surface of the method of the present invention and the numerical simulation method are respectively relatively consistent. The maximum values of the absolute values of the relative deviations between the two are 10.9%, 8.7%, and 9.2% respectively, all within 15%, which are acceptable in practical engineering and are reasonable.

[0069] The above describes the relevant content of the present invention. Those of ordinary skill in the art will be able to implement the present invention based on these descriptions. Based on the above content of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

Claims

1. A calculation method for the force and displacement of a foundation pile in soil under the action of axial load at the pile top, characterized in that: Including the following steps: Taking the top of the pile as the coordinate origin, with the downward direction along the longitudinal axis of the pile as the z-axis, based on the basic mechanical equilibrium conditions of the infinitesimal element formed by an infinitesimal section length arbitrarily taken along the axial direction of the pile, as well as the force boundary conditions at the top of the pile and the deformation coordination relationship between the bottom of the pile and the foundation, solving for the characteristic variables reflecting the force and displacement distribution patterns of the pile body; Based on the basic mechanical equilibrium conditions of the infinitesimal element and the force boundary conditions at the top of the pile, combined with the characteristic variables, solving for the axial displacement of the pile body, the axial force of the pile body, and the frictional resistance on the side surface of the pile at different depths along the axial direction of the pile; Wherein, The calculation expression of the characteristic variable n is as follows: The expression of the basic mechanical equilibrium condition of the infinitesimal element is as follows: The expression of the boundary condition of the force at the pile top is as follows: The expression for the deformation coordination relationship between the pile tip and the foundation is: ω b = ω(l); The calculation expression of the axial displacement of the pile body is: ω(z) = Ae (-Bz) cos(Bz); The calculation expression of the axial force of the pile body is as follows: The calculation expression for the skin friction on the pile side is: τ(z) = r p E p AB 2 e (-Bz) sin(Bz); A is an intermediate calculation parameter, and its calculation expression is: B is an intermediate calculation parameter, and its calculation expression is: In the formula, n is a characteristic variable reflecting the stress and displacement distribution patterns of the pile body, which is a positive dimensionless number; π is the pi; r p is the radius of the pile body; E p is the elastic modulus of the pile body; l is the pile length; R0 is the equivalent calculation radius at the pile bottom; k0 is the vertical elastic resistance coefficient of the pile bottom foundation; z is the depth from the pile top; P(z) is the axial force of the pile body at the cross-section at the depth z from the pile top; P′ is the first derivative of P(z) with respect to z; τ(z) is the skin friction on the pile side surface at the depth z from the pile top; P t is the axial load at the pile top; ω(z) is the axial displacement of the pile body at the depth z from the pile top; ω b is the foundation settlement at the pile bottom; e is the natural exponent.

2. The calculation method for the force and displacement of a basic pile in soil under the action of an axial load at the pile top according to claim 1, characterized in that: The calculation expression for the equivalent calculation radius R0 at the bottom of the pile is as follows: In the formula, "min" represents taking the minimum value; for end-bearing piles or column piles, take R0 = r p ; S is the pile spacing; is the weighted average of the internal friction angles of the soil on the pile side.

3. The calculation method for the force and displacement of a basic pile in soil under the action of an axial load at the pile top according to claim 2, characterized in that: The weighted average of the internal friction angle of the soil on the pile side The calculation expression is as follows: Where M is the number of layers of the soil on the pile side; i is the sequential number starting from 1 for the soil on the pile side from top to bottom; h i is the thickness of the soil on the pile side of the i-th layer; is the internal friction angle of the soil on the pile side of the i-th layer.

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