Method for calculating stress and displacement of foundation pile in soil body under action of axial load of pile top

Abstract

The invention belongs to the technical field of electric digital data processing and foundation engineering, and discloses a method for calculating stress and displacement of a foundation pile in a soil body under the action of a pile top axial load, which comprises the following steps of: taking the pile top as an origin of coordinates, and taking the downward direction of the longitudinal axis of a pile body as a z axis; according to the basic mechanical equilibrium condition of an infinitesimal body formed by the micro-section length randomly selected in the axial direction of the pile body, the boundary condition of the force at the top end of the pile and the deformation coordination relation between the bottom end of the pile and the foundation, characteristic variables reflecting the pile body stress and displacement distribution mode are solved; and according to the basic mechanical equilibrium condition of the infinitesimal body, the boundary condition of the force at the top end of the pile and the characteristic variables, the pile body axial displacement, the pile body axial force and the pile side surface friction resistance at different depths in the axial direction of the pile body are solved. The rapid and effective method and scientific basis are provided for design calculation and analysis of the foundation pile in the soil body under the action of the axial load of the pile top, and the method has important technical method significance and engineering application value.

Description

Technical Field

[0001] The invention relates to the technical field of electric digital data processing and foundation engineering, and in particular to a method for calculating the force and displacement of a foundation pile in soil under the action of an axial load on the pile top. Background Art

[0002] Pile foundation is a common foundation type in housing construction, railways, highways and other projects. It has the advantages of large bearing capacity and small settlement deformation, and is widely used in practice. In the pile group foundation in the actual stratum, the force and displacement of the base pile are an important reflection of the force and displacement of the pile group foundation, which is of great significance to the reasonable design of the pile group foundation.

[0003] Under the axial load on the pile top, the main forces and displacement behaviors of the pile, such as the pile axial force, pile side friction resistance, and pile axial displacement, all show a relatively complex nonlinear variation pattern along the depth. At present, the classical theory of the forces and displacements of the foundation pile in the soil under the axial load on the pile top only presents the general differential equation of the relationship between the axial force and the side friction resistance, and fails to obtain the analytical results of the pile axial force, pile side friction resistance, and pile axial displacement under the condition that only the pile top axial force is known. On the other hand, for the analysis of the forces and displacements of the foundation pile in the soil under the axial load on the pile top, numerical simulation methods such as finite element and finite difference are often used in the past. However, for the numerical simulation method, it is necessary to establish a numerical model first, and the rationality of the numerical model depends on factors such as model parameters, mesh accuracy, material constitutive model, and boundary conditions. Not only is the modeling process complicated and cumbersome, and there is interference from human subjective operation, but it is also difficult to have "inheritance" (different people need to start from modeling operations). The research on complex problems can still be used as a reference, but it is not conducive to the rapid analysis and operation of actual engineering and technical personnel.

[0004] It can be seen that there is currently no simplified theoretical calculation method for analyzing the variation of pile force and displacement along the depth in soil under the axial load on the pile top, which makes the relevant practical projects lack sufficient and reasonable basis, or the calculation and analysis operation process is cumbersome, mostly based on experience, and has blindness in design. Therefore, for the calculation of pile force and displacement in soil under the axial load on the pile top, a calculation method with reasonable concept, simple operation and practical operation 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 foundation piles in soil under the action of axial load on the pile top, which is simple and reasonable in concept and easy to operate in practice.

[0006] In order to achieve the above object, the present invention provides a method for calculating the force and displacement of foundation piles in soil under the action of axial load on the pile top, and the technical scheme is as follows:

[0007] The method for calculating the force and displacement of a foundation pile in soil under the axial load at the pile top includes the following steps:

[0008] Taking the top of the pile as the origin of coordinates, and the z-axis downward along the longitudinal axis of the pile, the basic mechanical equilibrium conditions of the microelement formed by any micro-segment length along the axial direction of the pile, as well as the boundary conditions of the force at the top of the pile and the deformation coordination relationship between the bottom of the pile and the foundation, the characteristic variables reflecting the force and displacement distribution pattern of the pile are solved;

[0009] Based on the basic mechanical equilibrium conditions of the microelement, the boundary conditions of the force at the top of the pile and the characteristic variables, the axial displacement of the pile at different depths along the axial direction of the pile, the axial force of the pile and the friction resistance on the pile side surface are solved.

[0010] As a further improvement of the above-mentioned method for calculating the force and displacement of the foundation pile in the soil under the axial load at the pile top: the calculation expression of the characteristic variable n is: Where n is the characteristic variable reflecting the force and displacement distribution pattern of the pile body, which is a positive dimensionless number; π is the circumference of a circle; r p is the radius of the pile; E p is the elastic modulus of the pile; l is the pile length; R0 is the equivalent calculated radius of the pile bottom; k0 is the vertical elastic resistance coefficient of the foundation at the bottom of the pile.

[0011] As a further improvement of the above-mentioned method for calculating the forces and displacements of foundation piles in soil under the action of axial load at the pile top:

[0012] The expression of the basic mechanical equilibrium condition of the microelement is:

[0013] The boundary condition of the force at the top of the pile is expressed as:

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

[0015] Where z is the depth from the top of the pile; P(z) is the axial force of the pile at the cross section at the depth z from the top of the pile; P′ is the first-order derivative of P(z) with respect to z; τ(z) is the friction resistance of the pile side surface at the depth z from the top of the pile; P t is the axial load at the top of the pile; ω(z) is the axial displacement of the pile at a depth z from the top of the pile; ω b is the ground settlement at the bottom of the pile.

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

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

[0018] As a further improvement of the above-mentioned method for calculating the forces and displacements of foundation piles in soil under the action of axial load at the pile top:

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

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

[0021] The calculation expression of the pile side surface friction 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] Where e is the natural index.

[0025] The advantages of the method for calculating the force and displacement of foundation piles in soil under the axial load on the pile top of the present invention are: first, the calculation method of the present invention fully considers the coordination of pile-soil deformation and the static balance of the pile body, and reflects the characteristics of the pile body, the soil body on the side of the pile and the foundation at the bottom of the pile. Secondly, the method for calculating the force and displacement of foundation piles in soil under the axial load on the pile top proposed by the present invention has a clear concept, a simple algorithm, and is convenient for quick operation. It has been verified that the calculation method of the present invention can be used to simply estimate and determine the force and displacement of foundation piles in soil under the axial load on the pile top without time-consuming, labor-intensive, and costly experiments or numerical simulation calculations, which is convenient for quick engineering design analysis.

[0026] It can be seen that the present invention is based on the coordination of pile-soil deformation and the static balance conditions of the pile body, and 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, 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 present invention is further described below in conjunction with the accompanying drawings and specific embodiments. 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 learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0030] Figure 2 The figure 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 The figure 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 pile side surface friction along the depth in an embodiment of the present invention. DETAILED DESCRIPTION

[0033] The present invention is described clearly and completely below in conjunction with the accompanying drawings. A person skilled 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 should be particularly noted that:

[0034] The technical solutions and technical features provided in each part of the present invention, including the following description, may be combined with each other if there is no conflict.

[0035] In addition, the embodiments of the present invention involved in the following description are generally only a part of the embodiments of the present invention, rather than all the embodiments. Therefore, based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0036] About the terms and units in the present invention: The terms "include", "have" and any variations thereof in the description and claims of the present invention and related parts are intended to cover non-exclusive inclusions.

[0037] The specific implementation of the method for calculating the force and displacement of foundation piles in soil under the axial load on the pile top of the present invention comprises the following steps:

[0038] Firstly, taking the top of the pile as the coordinate origin and the z-axis downward along the longitudinal axis of the pile, the basic mechanical equilibrium conditions of the microelement formed by any micro-segment length along the axial direction of the pile, as well as the boundary conditions of the force at the top of the pile and the deformation coordination relationship between the bottom of the pile and the foundation are used to solve the characteristic variables reflecting the force and displacement distribution pattern of the pile.

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

[0040]

[0041] The boundary condition of the force at the top of the pile is expressed as:

[0042]

[0043] The deformation coordination relationship between the pile bottom and the foundation is expressed as:

[0044] ω b =ω(l) Equation 3;

[0045] By combining equations 1 to 3, we can deduce the calculation expression of the characteristic variable n that reflects the force and displacement distribution mode of the pile body:

[0046]

[0047] Where z is the depth from the top of the pile; P(z) is the axial force of the pile at the cross section at the depth z from the top of the pile; P′ is the first-order derivative of P(z) with respect to z; τ(z) is the friction resistance of the pile side surface at the depth z from the top of the pile; P t is the axial load at the top of the pile; ω(z) is the axial displacement of the pile at a depth z from the top of the pile; ω b is the foundation settlement at the bottom of the pile; n is the characteristic variable reflecting the force and displacement distribution pattern of the pile body, which is a positive dimensionless number; π is the circumference of a circle; r p is the radius of the pile; E p is the elastic modulus of the pile; l is the pile length; R0 is the equivalent calculated radius of the pile bottom; k0 is the vertical elastic resistance coefficient of the foundation at the bottom of the pile.

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

[0049] In the formula, min means the minimum value; for end-bearing piles or column piles, R0 = r p ; S is the pile spacing; It 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 around the pile The calculation expression is:

[0051] Where M is the number of layers of soil on the pile side; i is the number of soil on the pile side starting from 1 from top to bottom, and h is i is the thickness of the soil mass beside the pile at the i-th layer; is the internal friction angle of the soil on the side of the i-th pile.

[0052] Among them, based on the basic mechanical equilibrium conditions of the microelement, the boundary conditions of the force at the top of the pile, and the characteristic variables, the calculation expressions of the pile axial displacement, pile axial force and pile side surface friction at different depths along the axial direction of the pile are solved 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] Where e is the natural index.

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

[0058] Figure 1 Schematic diagram of a pile in soil with the pile top bearing axial compressive load. Figure 1 As shown in Figure 1, the soil on the pile side is two layers of clay with different properties, and the pile end is pebble soil. The calculation parameters are shown in Table 1.

[0059] Table 1

[0060]

[0061] The calculation can be obtained:

[0062]

[0063] Substituting the relevant parameters into equation 4, we can obtain: Calculation yields n=3.222.

[0064] Further calculation of the intermediate calculation parameters yields:

[0065] Substituting the relevant parameters into equation 5, we can obtain:

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

[0067] Thus, the variation trends of the axial displacement of the reaction pile body, the axial force of the pile body and the friction resistance on the pile side surface with the 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 friction resistance on the pile side surface with the depth, the relationship curves of the axial displacement of the reaction pile body ω, the axial force of the pile body P and the friction resistance on the pile side surface τ and the depth z from the pile top can be further drawn.

[0068] The comparison diagram of the distribution curves of pile axial displacement ω, pile axial force P, and pile side surface friction resistance τ along the depth obtained by the ABAQUS numerical simulation method and the results of the present invention is shown in Figure 2 to Figure 4 It can be seen that the distribution patterns of pile axial displacement, pile axial force and pile side surface friction along the depth of the method of the present invention and the numerical simulation method are relatively consistent, and the maximum 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 actual engineering and reasonable.

[0069] The above is a description of the relevant contents of the present invention. A person skilled in the art will be able to implement the present invention based on these descriptions. Based on the above contents of the present invention, all other embodiments obtained by a person skilled in the art without making any creative work shall fall within the scope of protection of the present invention.

Claims

1. A method for calculating the force and displacement of foundation piles in soil under the action of axial load on the pile top, characterized by: The following steps are involved: Taking the top of the pile as the origin of coordinates, and the z-axis downward along the longitudinal axis of the pile, the basic mechanical equilibrium conditions of the microelement formed by any micro-segment length along the axial direction of the pile, as well as the boundary conditions of the force at the top of the pile and the deformation coordination relationship between the bottom of the pile and the foundation, the characteristic variables reflecting the force and displacement distribution pattern of the pile are solved; Based on the basic mechanical equilibrium conditions of the microelement, the boundary conditions of the force at the top of the pile and the characteristic variables, the axial displacement of the pile at different depths along the axial direction of the pile, the axial force of the pile and the friction resistance on the pile side surface are solved.

2. The method for calculating the force and displacement of a foundation pile in soil under the axial load at the pile top as claimed in claim 1, characterized in that: The calculation expression of the characteristic variable n is: Where n is the characteristic variable reflecting the force and displacement distribution pattern of the pile body, which is a positive dimensionless number; π is the circumference of a circle; r p is the radius of the pile; E p is the elastic modulus of the pile; l is the pile length; R0 is the equivalent calculated radius of the pile bottom; k0 is the vertical elastic resistance coefficient of the foundation at the bottom of the pile.

3. The method for calculating the force and displacement of foundation piles in soil under the axial load at the pile top as claimed in claim 2, characterized in that: The expression of the basic mechanical equilibrium condition of the microelement is: The boundary condition expression of the force at the top of the pile is: The deformation coordination relationship between the pile bottom and the foundation is expressed as: b =ω(l); Where z is the depth from the top of the pile; P(z) is the axial force of the pile at the cross section at the depth z from the top of the pile; P′ is the first-order derivative of P(z) with respect to z; τ(z) is the friction resistance of the pile side surface at the depth z from the top of the pile; P t is the axial load at the top of the pile; ω(z) is the axial displacement of the pile at a depth z from the top of the pile; ω b is the foundation settlement at the bottom of the pile.

4. The method for calculating the force and displacement of a foundation pile in soil under the axial load at the pile top as claimed in claim 2, characterized in that: The calculation expression of the equivalent calculation radius R0 of the pile bottom is: In the formula, min means the minimum value; for end-bearing piles or column piles, R0 = r p ; S is the pile spacing; It is the weighted average value of the internal friction angle of the soil on the pile side.

5. The method for calculating the force and displacement of foundation piles in soil under the axial load at the pile top as claimed in claim 4, characterized in that: Weighted average value of the internal friction angle of the soil around the pile The calculation expression is: Where M is the number of layers of soil on the pile side; i is the number of soil on the pile side starting from 1 from top to bottom; h i is the thickness of the soil mass beside the pile at the i-th layer; is the internal friction angle of the soil on the side of the i-th pile.

6. The method for calculating the force and displacement of a foundation pile in soil under the axial load at the pile top as claimed in claim 3, characterized in that: The calculation expression of the pile axial displacement is: ω(z) = Ae (-Bz) cos(Bz); The calculation expression of pile axial force is: The calculation expression of the pile side surface friction 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: Where e is the natural index.

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