General solution method for integral equation of horizontal bearing characteristic of pile body composite foundation

Abstract

The invention discloses an integral equation general solution method for horizontal bearing characteristics of a pile body composite foundation, which comprises the following steps of: S1, establishing a pile body composite foundation schematic diagram consisting of N (N = n1 * n2) foundation piles and a coordinate system {0, x, y, z} thereof, and dividing the pile body composite foundation schematic diagram into m subunits by taking a pile diameter d as a side length; determining the load resultant force V (y, 0) of the top of each subunit according to the horizontal load H0 of the upper structure borne by the foundation; s2, the pile-soil system is decomposed into semi-infinite space expansion soil and virtual pile units, and stress analysis schematic diagrams of the corresponding units are obtained; obtaining analytic expressions of pile body deflection # imgabs0 # and bending moment # imgabs1 # according to static equilibrium conditions and geometric conditions of the ith (i = 1,..., N) virtual pile unit; and S5, the lateral displacement # imgabs2 # of the extended soil unit at the corresponding position of the ith virtual pile is obtained based on the Mindlin solution, according to the lateral displacement coordination condition of the semi-infinite space extended soil and the virtual pile unit at the corresponding position, an integral control equation of the horizontal bearing characteristic of the pile body composite foundation is established, and then the pile body deflection and the internal force of the pile body composite foundation are obtained.

Description

Technical Field

[0001] The invention belongs to the technical fields of road engineering, bridge engineering and composite pile foundation engineering, and particularly relates to a general solution method of an integral equation of horizontal bearing characteristics of a pile composite foundation based on elastic theory. Background Art

[0002] Pile composite foundation technology is widely used in foundation reinforcement projects of road projects, bridge projects and large-scale infrastructure construction. Its main function is to bear the combined vertical and horizontal loads of the upper structure. When the pile composite foundation is used for foundation reinforcement of the anchor foundation, in addition to bearing the deadweight load of the anchor foundation, it also needs to bear the horizontal load transmitted by the upper main cable to ensure that the horizontal displacement and horizontal bearing capacity of the anchor foundation meet the design requirements. For horizontally loaded pile composite foundations, the horizontal load directly acting on the top of the pile is called active load, and the horizontal load acting on the top of the soil between the piles is called passive load. Existing theoretical analysis methods, including the Winkler foundation reaction method and the py curve method, are difficult to analyze the horizontal bearing characteristics of the pile composite foundation under the combined action of active and passive loads. In actual engineering, the design criteria of pile composite foundations have gradually changed from bearing capacity control to displacement control, that is, the pile-soil system is basically in an elastic state under actual load conditions. Based on this, the pile composite foundation of this patent is decomposed into virtual pile units and semi-infinite space extended soil units. The horizontal displacement of the virtual pile unit and the extended soil unit under horizontal loads is analyzed based on the elastic theory. Combined with the horizontal displacement coordination conditions of the two at corresponding positions, an integral control equation with the pile body bending moment and the horizontal displacement of the pile top and pile end as unknown quantities is established, and a general solution method for the integral equation of the horizontal bearing characteristics of the pile composite foundation is proposed.

[0003] On-site full-scale tests require a lot of manpower, material resources and construction time. References: Liu HL, Kong GQ, et al. Performances of Large-Diameter Cast-in-Place Concrete Pipe Piles and Pile Groups under Lateral Loads [J]. Journal of Performance of Constructed Facilities, 2013, 27 (2): 191-202. Indoor scaled tests can overcome the shortcomings of on-site full-scale tests. The test results can not only guide engineering design, but also compare and verify the theoretical and numerical analysis results. References: Li L., Liu X., et al. Experimental and numerical study on the static lateral performance of monopile and hybrid pile foundation [J]. Ocean Engineering, 2022, 255 and Georgiadis M., Anagnostopoulos C., et al. Centrifugal testing of laterally loaded piles in sand [J]. Can Geotech JV29, N2, April 1992, P208–216, 1992, 30(1), but its time and economic costs make this method unsuitable for preliminary analysis, design and parameter analysis of composite foundations with horizontally loaded piles.

[0004] In terms of theoretical analysis, the analysis of the bearing characteristics of horizontally loaded pile composite foundations based on the Winkler foundation reaction method and the py curve method is significantly dependent on the selection of parameters and is not suitable for the preliminary analysis and design of the bearing characteristics of horizontally loaded pile composite foundations. The elastic theory proposed by Poulos is widely used to analyze pile group foundations. This method overestimates the shear effect of the soil, especially for loose sand and soft soil. At the same time, its analysis results on the interaction between piles and soil are generally larger than the actual situation. Reference: HGPoulos, EHDavis. Pile foundation analysis and design [M]. Canada, 1980, and it is difficult to deal with the problems of non-equal length pile group foundations and composite foundations located on the inclined bedrock surface. A large number of studies based on the boundary element method are all aimed at high-cap pile group foundations. For low-cap pile group foundations and pile composite foundations, since the soil between piles bears part of the load, their bearing characteristics will be significantly different from those of high-cap pile group foundations. At present, there are few studies on the bearing characteristics of pile composite foundations under horizontal loads.

[0005] Numerical simulation has great advantages in dealing with complex pile group foundation types, complex boundary conditions and nonlinear analysis, but the selection of correct and reasonable constitutive relations and their parameter values ​​is the key to the reliability of simulation results. References: Heidari B., Akbari Garakani A., et al. Energy piles under lateral loading: Analytical and numerical investigations [J]. Renewable Energy, 2022, 182: 172-191 and Watford M., Templeman J., et al. Numerical analysis of the deep soil failure mechanism for perimeter pile groups [J]. Géotechnique Letters, 2022, 12 (1): 27-34. Summary of the invention

[0006] The present invention proposes a general solution method for the integral equation for the horizontal bearing characteristics of a pile composite foundation. The method is used for the preliminary analysis, design, and parameter analysis of the horizontal bearing characteristics of a pile composite foundation, overcoming the manpower, material resources, and construction period costs of on-site full-scale tests and indoor model tests; the method further decomposes the pile-soil system into virtual pile units and extended soil units on the basis of the elastic theory analysis method, and establishes a general solution method for the integral equation by combining the horizontal displacement coordination conditions of the two at corresponding positions, overcoming the deficiency of the large interaction coefficient of the pile-soil analysis in the traditional elastic theory; the method is based on analyzing the horizontal bearing characteristics of the pile composite foundation in the elastic stage, and the analysis parameters are only the elastic modulus E and the Poisson's ratio μ, which do not require a large number of experiments and are simple and easy to obtain; the method overcomes the deficiency that the Winkler foundation reaction method and the py curve method cannot directly analyze the bearing characteristics of the pile composite foundation under the joint action of active loads and passive loads, expands the analysis and application scope of the elastic theory in the pile composite foundation, and provides theoretical support for the rapid analysis of the horizontal bearing characteristics of the pile composite foundation in engineering.

[0007] To achieve the above object, the present invention provides the following technical solution: a general solution method of the integral equation of the horizontal bearing characteristics of a pile composite foundation, the method comprising the following steps:

[0008] Step 1: Establish a schematic diagram of a composite foundation consisting of N, i.e., N = n1 × n2, foundation piles and its coordinate system {0, x, y, z}, according to Figure 1 As shown;

[0009] The number of rows and columns of the pile composite foundation is defined according to the direction of load action, that is, when the horizontal distributed load V(y,0) is distributed in the positive direction along the y-axis, the number of rows of the pile composite foundation is calculated from right to left, with a total of n1 rows, and the number of piles in each row, that is, the number of columns is n2; the pile diameter d, the pile bending stiffness E p I p , pile spacing s, pile length l of the tth row t , the outer expansion width b of the cushion layer is respectively Figure 1 As shown; the soil between piles is regarded as a linear elastic body, E s , v represent the compression modulus and Poisson’s ratio respectively;

[0010] Assuming that the foundation bears the horizontal load H0 of the upper structure along the positive direction of the y-axis, due to the influence of the cushion layer, the top of the pile composite foundation is regarded as a free constraint condition, and the horizontal load H0 is mainly balanced by the friction resistance between the foundation and the cushion layer. The friction resistance is transmitted from the top of the cushion layer to the bottom of the cushion layer, and then acts on the top of the foundation pile and the soil between the piles; considering the influence of the foundation self-weight and the vertical eccentric load transmitted from the upper structure, the vertical stress and horizontal stress at the bottom of the foundation are unevenly distributed;

[0011] Step 2: Decompose the pile-soil system into semi-infinite space extended soil and virtual pile units, and obtain the force analysis diagram of the corresponding units. Figure 2 As shown;

[0012] Taking the i-th foundation pile as an example, the pile-soil system is decomposed into semi-infinite space extended soil and virtual pile units, that is, Figure 2 The parameters of the extended soil are the same as those of the original soil between piles. The virtual pile unit is regarded as a one-dimensional Bernoulli-Euler beam, and its elastic modulus E * =E p -E s ;

[0013] Figure 2 middle, represents the horizontal load acting directly on the top of the i-th virtual pile unit, The effect will cause the pile body to produce lateral deflection This then causes unbalanced soil resistance around the pile; and They represent the soil pressure, shear force and bending moment of the ith virtual pile at depth z. According to Newton's third law, the corresponding force analysis diagram of the extended soil is obtained, namely: Figure 2 ,in Figure 2 The signs shown are all positive;

[0014] Step 3: Analyze the i-th virtual pile unit in combination with Bernoulli-Euler beam theory;

[0015] According to the microunit, Figure 2 The static equilibrium conditions and geometric conditions can be obtained:

[0016]

[0017] in, and is an undetermined parameter; as shown in formula (1), Depend on The numerical integration is more accurate than the numerical differentiation, so we choose is the basic unknown quantity; practice shows that due to the influence of cumulative errors, the accuracy of two numerical integrations is much less than that of one numerical integration, so It is expressed as:

[0018]

[0019] Where:

[0020]

[0021] When the contribution of the extended soil to the bending moment of the pile is ignored, the bending moment and lateral displacement of the virtual pile are understood as the bending moment and lateral displacement of the real pile;

[0022] Step 4: Consider the extended soil as a semi-infinite elastic body and analyze the extended soil unit under the assumption of small deformation and linear elasticity;

[0023] The loads acting on the extended soil are: 1) the unbalanced earth pressure generated by the ith virtual pile unit at depth z 2) The resultant force at the top of the extended soil unit at the corresponding position of the i-th virtual pile is , and the horizontal load V(y,0) acting on the top of the remaining extended soil units; 3) the shear force generated at the end of the i-th virtual pile and bending moment When the virtual pile tip is assumed to have small deformation and small rotation, the Right now

[0024]

[0025] Therefore, the extended soil unit at the corresponding position of the i-th virtual pile is taken as the research object, and its lateral deflection Expressed as

[0026]

[0027] in, is the Green function, which indicates the lateral displacement caused by the uniformly distributed load with a resultant force of unit 1 acting on the Π(ξ) section of the jth (i.e., j=1,…,m) unit at the Π(z) section of the ith (i=1,…,N) unit. Obtained by integrating the basic solution of Mindlin;

[0028] For Green's function When z = ξ, there is a singular solution. Therefore, the last term in equation (7) is integrated by parts, and equation (7) is expressed as:

[0029]

[0030] Step 5: According to the lateral displacement coordination conditions of the semi-infinite space extended soil and the virtual pile unit at the corresponding position, the integral control equation of the horizontal bearing characteristics of the pile composite foundation is established;

[0031] According to the lateral displacement coordination condition between the semi-infinite space extended soil and the virtual pile unit at the corresponding position, we have

[0032]

[0033] Therefore, combining equations (4), (8) and (9), the pile-soil interaction problem of the horizontally loaded pile composite foundation is transformed into a problem of solving the second kind of Fredholm integral equation. The governing equation is expressed as:

[0034]

[0035] The basic unknown quantity of the control equation is the bending moment of the virtual pile. and lateral displacement of pile top Lateral displacement of pile tip Combined with MATLAB, the relevant unknown quantities are solved to fully determine the bearing characteristics and displacement mechanism of the pile composite foundation.

[0036] Preferably, in step one, when the pile composite foundation is divided into m sub-units with the pile diameter d as the side length, the load resultant at the top of each sub-unit is expressed as V(y,0), where V(y,0) indicates that the load resultant is only a function of the y coordinate, and its magnitude is related to factors such as vertical stress and pile-soil stiffness ratio.

[0037] Preferably, in step five, the rotation angle and shear force of each pile body are obtained by equation (4) and equation (2).

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. The present invention is used for preliminary analysis, design and parameter analysis of the horizontal bearing characteristics of pile composite foundation, overcoming the manpower, material resources and construction period costs existing in on-site full-scale tests and indoor model tests;

[0040] 2. Based on the elastic theory analysis method, this method further decomposes the pile-soil system into virtual pile units and extended soil units, and establishes the general solution method of the integral equation by combining the horizontal displacement coordination conditions of the two at corresponding positions, thus overcoming the deficiency of the large pile-soil interaction coefficient in the traditional elastic theory analysis;

[0041] 3. This method is based on analyzing the horizontal bearing characteristics of the pile composite foundation in the elastic stage. The analysis parameters are only the elastic modulus E and Poisson's ratio μ, which do not require a large number of tests and are simple and easy to obtain;

[0042] 4. This method overcomes the shortcomings of the Winkler foundation reaction method and the py curve method that cannot directly analyze the bearing characteristics of pile composite foundations under the combined action of active loads and passive loads, expands the analysis and application scope of elastic theory in pile composite foundations, and provides theoretical support for the rapid analysis of the horizontal bearing characteristics of pile composite foundations in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 The pile composite foundation and load distribution diagram of the present invention;

[0044] Figure 2 The pile-soil system decomposition diagram and symbol regulations of the present invention;

[0045] Figure 3 The displacement and bending moment distribution diagram of the three-pile composite foundation of the present invention;

[0046] Figure 4 is a flow chart of the present invention;

[0047] Figure 5 It is a schematic diagram of horizontal load analysis of the pile composite foundation of the present invention;

[0048] Figure 6 is the pile unit deflection distribution diagram of the present invention, load condition 1;

[0049] Figure 7 is the pile unit deflection distribution diagram of the present invention, load condition 2;

[0050] Figure 8 is the pile unit rotation angle distribution diagram of the present invention, load condition 1;

[0051] Fig. 9 is the pile unit rotation angle distribution diagram of the present invention, load condition 2;

[0052] Fig.10 is the bending moment distribution diagram of the pile unit of the present invention, load condition 1;

[0053] Fig.11 is the bending moment distribution diagram of the pile unit of the present invention, load condition 2;

[0054] Fig.12 It is a schematic diagram of the analysis model of the present invention;

[0055] Fig.13 It is the top displacement distribution diagram of the pile unit of the present invention, load condition 1;

[0056] Fig.14 The top displacement distribution diagram of the pile unit of the present invention, load condition 2;

[0057] Fig.15 It is the extreme value variation diagram of the bending moment of the pile unit of the present invention, load condition 1;

[0058] Fig.16 This is the extreme value variation diagram of the bending moment of the pile unit of the present invention, load condition 2. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] Embodiment 1:

[0061] Analysis on horizontal bearing characteristics of 11×1 unequal length pile composite foundation.

[0062] The 11×1 non-uniform length pile composite foundation is taken as the research object. It is assumed that the length of the piles along the width direction of the foundation, that is, the x-axis, is the same, that is, the length of the piles in the same row is the same. Suppose that along the length direction of the foundation, that is, the y-axis, there are n1 rows, and the length of the side piles is l n1 =l1=10m, l6=20m, the pile length is parabolic distribution, that is, Figure 5 , the parameters of the foundation pile and soil are as follows: pile diameter d = 1m, pile spacing s = 3d, E p =30GPa, E s =10MPa, v=0.25, considering the outer expansion size of the cushion layer b=d. Among them, the horizontal load on the top of each unit considers two conditions. When the vertical load is eccentric or forms a combined load with the upper curved rectangle, the vertical stress on the top of each unit is unevenly distributed, which leads to uneven distribution of the horizontal stress transmitted to the top of each unit. This subsection assumes that the horizontal stress transmitted to the top of each unit under this load condition changes linearly along the length of the foundation, that is, the y-axis, that is, the load value changes linearly in a triangular shape, which is recorded as load condition 1; when the vertical stress transmitted to the top of each unit is uniformly distributed, the horizontal stress on the top of each unit is also uniformly distributed, which is load condition 2. The maximum value of the horizontal load within the foundation range is recorded as V(0) and V(0)=100kN.

[0063] The deflection curves of the pile unit under the two load conditions are shown as follows: Figure 6 , Figure 7 By differentiating the pile unit disturbance curve, the corresponding rotation angle curve is obtained, as shown in Figure 8 , Fig. 9 shown.

[0064] The bending moment curves of piles under two load conditions are shown in Fig.10 , Fig.11 shown.

[0065] Embodiment 2:

[0066] Pile-soil stiffness ratio E p / E s Influence on the horizontal bearing characteristics of 11×1 unequal length pile composite foundation.

[0067] There are many types of vertical reinforcement bodies in actual engineering, including crushed stone piles, CFG piles, and plain concrete piles. The stiffness of different types of vertical reinforcement piles varies greatly. Therefore, this case discusses the pile-soil stiffness ratio E. p / E s The influence of non-equal length pile composite foundation bearing characteristics and displacement mechanism is proposed to l1 = 20m, l 11 =5m, the length of each row of piles changes linearly, such as Fig.12 As shown, the pile-soil stiffness ratio E p / E s =20~3000, other parameters are the same as before. Different pile-soil stiffness ratio E p / E s The horizontal displacements of the top of a typical pile unit under the load conditions are as follows: Fig.13 , Fig.14 Different load conditions and pile-soil stiffness ratio E p / E s The maximum bending moment value M of each pile body under the condition tm Respectively Fig.15 , Fig.16 shown.

[0068] In summary, since there is no field test data of the pile composite foundation under horizontal load, the present invention now compares and analyzes the 3×1 pile composite foundation under horizontal load with the FEM method. The arrangement and main parameters of the pile composite foundation are as follows: Figure 3 shown. Figure 3 a is the lateral displacement distribution diagram of pile 1, and b is the bending moment distribution diagram of pile 1. Two working conditions are considered for the elastic modulus of the foundation pile. When E p =200MPa and 30GPa, which correspond to the CFG piles and reinforced concrete piles in the project respectively. Considering that the gravel cushion is arranged on the top of the composite foundation, it is assumed that a horizontally distributed load with a load concentration of q acts on the top of the pile composite foundation. In the numerical model, the pile unit is simulated by a solid unit, and the distance from the four side boundaries to the edge of the pile composite foundation is set to 3l, and the model height is also set to 3l. The trial calculation shows that this boundary condition has no effect on the analysis results. Different E p / E s Under the working condition, the displacement and bending moment distribution diagram of pile 1 obtained by FEM and theoretical model analysis is shown in Figure 3 As shown in the figure, it can be seen that the theoretical solution and the FEM solution are basically consistent. This method is used to analyze the horizontal bearing characteristics of pile composite foundation.

[0069] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0070] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A general solution method for the integral equation of the horizontal bearing characteristics of pile composite foundation, characterized by: The method comprises the following steps: Step 1: Establish a schematic diagram of a pile composite foundation consisting of N, i.e., N = n1 × n2 foundation piles and its coordinate system {0, x, y, z}, as shown in Figure 1; The number of rows and columns of the pile composite foundation is defined according to the direction of load action, that is, when the horizontal distributed load V(y,0) is distributed in the positive direction along the y-axis, the number of rows of the pile composite foundation is calculated from right to left, with a total of n1 rows, and the number of piles in each row, that is, the number of columns is n2; the pile diameter d, the pile bending stiffness E p I p , pile spacing s, pile length l of the tth row t , the cushion layer expansion width b is as shown in Figure 1; the soil between piles is regarded as a linear elastic body, E s , v represent the compression modulus and Poisson’s ratio respectively; Assuming that the foundation bears the horizontal load H0 of the upper structure along the positive direction of the y-axis, due to the influence of the cushion layer, the top of the pile composite foundation is regarded as a free constraint condition, and the horizontal load H0 is mainly balanced by the friction between the foundation and the cushion layer. The friction is transmitted from the top of the cushion layer to the bottom of the cushion layer, and then acts on the top of the foundation pile and the soil between the piles; considering the influence of the foundation deadweight and the vertical eccentric load transmitted from the upper structure, the vertical stress and horizontal stress at the bottom of the foundation are unevenly distributed; Step 2: Decompose the pile-soil system into semi-infinite space extended soil and virtual pile units, and obtain the force analysis schematic diagram of the corresponding units, as shown in Figure 2; Taking the i-th foundation pile as an example, the pile-soil system is decomposed into semi-infinite space extended soil and virtual pile unit, as shown in Figure 2; the parameters of the extended soil are the same as the original soil between piles, and the virtual pile unit is regarded as a one-dimensional Bernoulli-Euler beam, and its elastic modulus E * =E p -E s ; In Figure 2, represents the horizontal load acting directly on the top of the i-th virtual pile unit, The effect will cause the pile body to produce lateral deflection This then causes unbalanced soil resistance around the pile; and They represent the soil pressure, shear force and bending moment of the ith virtual pile at depth z, respectively. According to Newton's third law, the corresponding force analysis diagram of the extended soil is obtained, namely, FIG2 , where all the symbols shown in FIG2 are positive; Step 3: Analyze the i-th virtual pile unit in combination with Bernoulli-Euler beam theory; According to the micro-unit, that is, the static equilibrium condition and geometric condition of Figure 2, we can get: in, and is an undetermined parameter; as shown in formula (1), Depend on The numerical integration is more accurate than the numerical differentiation, so we choose is the basic unknown quantity; practice shows that due to the influence of cumulative errors, the accuracy of two numerical integrations is much less than that of one numerical integration, so It is expressed as: Where: When the contribution of the extended soil to the bending moment of the pile is ignored, the bending moment and lateral displacement of the virtual pile are understood as the bending moment and lateral displacement of the real pile; Step 4: Consider the extended soil as a semi-infinite elastic body and analyze the extended soil element under the assumption of small deformation and linear elasticity; The loads acting on the extended soil are: 1) the unbalanced earth pressure generated by the ith virtual pile unit at depth z 2) The resultant force at the top of the extended soil unit at the corresponding position of the i-th virtual pile is , and the horizontal load V(y,0) acting on the top of the remaining extended soil units; 3) the shear force generated at the end of the i-th virtual pile and bending moment When the virtual pile tip is assumed to have small deformation and small rotation, the Right now Therefore, the extended soil unit at the corresponding position of the i-th virtual pile is taken as the research object, and its lateral deflection Expressed as in, is the Green function, which indicates the lateral displacement caused by the uniformly distributed load with a resultant force of unit 1 acting on the Π(ξ) section of the jth (i.e., j=1,…,m) unit at the Π(z) section of the ith (i=1,…,N) unit. Obtained by integrating the basic solution of Mindlin; For Green's function When z = ξ, there is a singular solution. Therefore, the last term in equation (7) is integrated by parts, and equation (7) is expressed as: Step 5: According to the lateral displacement coordination conditions of the semi-infinite space extended soil and the virtual pile unit at the corresponding position, the integral control equation of the horizontal bearing characteristics of the pile composite foundation is established; According to the lateral displacement coordination condition between the semi-infinite space extended soil and the virtual pile unit at the corresponding position, we have Therefore, combining equations (4), (8) and (9), the pile-soil interaction problem of the horizontally loaded pile composite foundation is transformed into a problem of solving the second kind of Fredholm integral equation. The governing equation is expressed as: The basic unknown quantity of the control equation is the bending moment of the virtual pile. and lateral displacement of pile top Lateral displacement of pile tip Combined with MATLAB, the relevant unknown quantities are solved to fully determine the bearing characteristics and displacement mechanism of the pile composite foundation.

2. The method for solving the integral equation of the horizontal bearing characteristics of the pile composite foundation according to claim 1 is characterized by: In step 1, when the pile composite foundation is divided into m sub-units with the pile diameter d as the side length, the load resultant at the top of each sub-unit is expressed as V(y,0), where V(y,0) means that the load resultant is only a function of the y coordinate, and its size is related to the factors of vertical stress and pile-soil stiffness ratio.

3. The method for solving the integral equation of the horizontal bearing characteristics of the pile composite foundation according to claim 1 is characterized by: In step 5, the rotation angle and shear force of each pile are obtained by equation (4) and equation (2).

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