A method, system and storage medium for determining additional stress of pile foundation

Abstract

The present invention discloses a method, system and storage medium for determining additional stress of a pile foundation, and relates to the field of engineering design technology. The method for determining additional stress of a pile foundation includes: determining the vertical additional stress σz1 at any point outside the axis generated by the uniformly distributed load at the pile end of the pile foundation; determining the vertical additional stress σz2 generated at point M by the uniformly distributed resistance on the pile side of the pile foundation; determining the vertical additional stress σz3 generated at point M by the linearly increased resistance on the pile side of the pile foundation; and determining the additional stress σz=σz1+σz2+σz3 at each point of the pile foundation within the plane range within the depth range of the pile end. By adopting the method, system and storage medium for determining additional stress of a pile foundation, a calculation program can be compiled on a calculation software platform to quickly calculate the vertical additional stress at any point in an elastic body in a semi-infinite space under the action of pile foundation load.

Description

Technical Field

[0001] The present invention relates to the technical field of engineering design, and in particular to a method, system and storage medium for determining additional stress of a pile foundation. Background Art

[0002] The calculation of additional stress under pile foundations is fundamental to calculating foundation settlement. However, the current "Code for Design of Building Foundations" (GB 5007-2Q11) and "Technical Specification for Building Pile Foundations" (JGJ94-2Q08) have several deficiencies in calculating additional stress under pile foundation loads. First, the calculation of additional stress under pile side resistance assumes that the pile side resistance is distributed along the pile axis rather than on the outer surface of the pile side, which does not conform to actual working conditions and the variability increases with increasing pile diameter. Second, the additional stress coefficient at any point must be determined by looking up a table based on parameters such as the pile diameter ratio (the ratio of pile length to pile diameter) and the depth-to-length ratio (the ratio of calculated depth to pile length), which often leads to calculation errors, is complex, and is not suitable for programmatic calculations. Third, it is difficult to quickly understand the changing characteristics of additional stress at multiple planar points along a depth profile. Summary of the Invention

[0003] The present invention aims to solve at least one of the technical problems existing in the prior art. To this end, the present invention proposes a method for determining additional stress in a pile foundation, which can quickly calculate the vertical additional stress at any point in an elastic body in a semi-infinite space under the action of pile foundation load.

[0004] The present invention also provides a pile foundation additional stress determination system having the above pile foundation additional stress determination method.

[0005] The present invention also provides a computer-readable storage medium having the above-mentioned method for determining additional stress of a pile foundation.

[0006] A method for determining additional stress in a pile foundation according to an embodiment of the first aspect of the present invention includes:

[0007] Determine the vertical additional stress σz1 at any point outside the axis caused by the uniformly distributed load at the pile end of the pile foundation;

[0008] Determine the vertical additional stress σz2 generated at point M by the uniformly distributed resistance on the pile side of the pile foundation;

[0009] Determine the vertical additional stress σz3 generated at point M by the linear increase resistance of the pile side;

[0010] Determine the additional stress σz=σz1+σz2+σz3 at each point of the pile foundation within the plane range and within the depth range of the pile end.

[0011] The method for determining additional stress in a pile foundation according to an embodiment of the present invention has at least the following beneficial effects: Based on the Mindlin solution for additional stress under the action of concentrated forces in a semi-infinite body, and taking into account the pile diameter, the present invention derives Mindlin analytical expressions for the vertical additional stress at any point on or beyond the pile axis, as well as for the additional stress under the action of pile side resistance. Using these analytical expressions, a calculation program compiled on the Matlab software platform can rapidly calculate the vertical additional stress at any point in a semi-infinite elastic body under pile foundation load, generate data files, and plot single-point additional stress curves and additional stress plane contour maps, providing key basic data for calculating foundation settlement under pile foundation load.

[0012] According to some embodiments of the present invention, the method for determining σz1 includes:

[0013]

[0014] Where:

[0015] p is the pile tip load intensity (kPa), r is the pile foundation radius (m), h is the pile length (m), z is the calculated depth from the ground (m) (z>h), μ is the Poisson's ratio of the rock and soil layer at depth z, and θ is the central angle of the pile tip section (radians);

[0016] Completing five double integrals of (1) will give the additional stress σ under the pile foundation axis: z The analytical expression of is (2):

[0017]

[0018] Set the coordinate origin at the center o of the pile end and x as the horizontal distance from the pile center. Then the vertical additional stress under the concentrated force pρdρdθ on the micro area is still calculated using double integral. At this time, R1 and R2 are as follows:

[0019]

[0020]

[0021] Substitute R1 and R2 into formula (1), and express the five integrals of r in formula (1) as D1, D2, D3, D4, and D5, respectively, that is:

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] First, perform the integration operation on D1:

[0028]

[0029] Similarly, we can get:

[0030]

[0031]

[0032]

[0033]

[0034] Multiplying 2π by equations (3) to (7) respectively completes the integration of θ, and substituting it into equation (1), we can obtain the analytical formula for the vertical additional stress at any point outside the axis caused by the uniformly distributed load at the pile end, which is the following equation (8):

[0035]

[0036] According to some embodiments of the present invention, the method for determining σz2 includes:

[0037] Assume that the radius of the pile foundation is r, the depth of the pile into the soil is D, and the uniformly distributed resistance on the pile side is P; the depth of point M from the ground is z, and the horizontal distance from the center of the pile is x;

[0038] By integrating along the pile length, we can obtain the integral expression of the vertical additional stress generated by the uniformly distributed resistance on the pile side at point M, which is the following formula (9):

[0039]

[0040] Where:

[0041] Completing five double integrals for equation (9) yields the following calculation results:

[0042]

[0043] Where:

[0044]

[0045] According to some embodiments of the present invention, the method for determining σz3 includes:

[0046]

[0047] Where:

[0048] Integrating h in formula (11) yields the following formula (12):

[0049]

[0050] Wherein A, B, F, m, and n are the same as those in formula (10).

[0051] According to some embodiments of the present invention, based on equations (8), (10), and (12), a method for determining the additional stress σz between the pile foundations includes:

[0052] Determine the pile length h1 and pile length h2 of pile 1 and pile 2, the pile spacing S between piles 1 and 2, the pile top load P, the soil Poisson's ratio μ, the pile end resistance ratio α, and the pile side uniform resistance ratio β;

[0053] Calculate the additional stress σz1 at each point within the plane range [-Q, S+Q] of pile 1 within the depth range of 1 to 2Qm below the pile end;

[0054] Calculate the additional stress σz2 at each point within the plane range [-Q, S+Q] of pile 1 within the depth range of 1 to 2Qm below the pile end;

[0055] Calculate the additional stress σz3 at each point within the plane range [-Q, S+Q] of pile 1 within the depth range of 1 to 2Qm (spacing 1m) below the pile end;

[0056] Calculate the additional stress σz=σz1+σz2+σz3 at each point within the plane range [-Q, S+Q] of pile 1 within the depth range of 1 to 2Qm below the pile end;

[0057] Calculate the additional stress σz1 at each point within the plane range [-Q, S+Q] of pile 2 within the depth range of 1 to 2Qm below the pile end;

[0058] Calculate the additional stress σz2 at each point within the plane range [-Q, S+Q] of pile 2 within the depth range of 1 to 2Qm below the pile end;

[0059] Calculate the additional stress σz3 at each point within the plane range [-Q, S+Q] of pile 2 within the depth range of 1 to 2Qm below the pile tip;

[0060] Calculate the additional stress σz=σz1+σz2+σz3 at each point in the plane range [-Q, S+Q] of pile 2 within the depth range of 1 to 2Qm below the pile end.

[0061] According to some embodiments of the present invention, when calculating σz1, σz2 and z3, points with an interval of 1m are selected for calculation within the plane range [-Q, S+Q], and points with an interval of 1m are selected for calculation within a depth of 1 to 2Qm below the pile end.

[0062] According to some embodiments of the present invention, the method further includes plotting the obtained additional stress σz as a curve graph or a contour line graph of a profile of the additional stress σz.

[0063] According to an embodiment of the second aspect of the present invention, a system for determining additional stress in a pile foundation includes a memory and a processor, wherein a program for determining additional stress in a pile foundation is stored in the memory, and the processor runs the program for determining additional stress in a pile foundation, so that the system for determining additional stress in a pile foundation executes the method for determining additional stress in a pile foundation of the above embodiment.

[0064] The system for determining the additional stress of a pile foundation according to an embodiment of the present invention has at least the following beneficial effects: by adopting this determination system, a calculation program can be compiled on a calculation software platform to quickly calculate the vertical additional stress at any point in a semi-infinite space elastic body under the action of the pile foundation load.

[0065] According to some embodiments of the present invention, a graphics processing system is further provided for collecting the additional stress σz data processed by the processor and generating a curve graph and an additional stress σz profile contour graph.

[0066] According to a third aspect of an embodiment of the present invention, a computer-readable storage medium stores a program for determining additional stress of a pile foundation. When the program for determining additional stress of a pile foundation is executed by a processor, the method for determining additional stress of a pile foundation according to the above embodiment is implemented.

[0067] The computer-readable storage medium according to an embodiment of the present invention has at least the following beneficial effects: by adopting the computer-readable storage medium, a calculation program can be compiled on a calculation software platform to quickly calculate the vertical additional stress at any point in a semi-infinite space elastic body under the action of pile foundation load.

[0068] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0070] Figure 1 This is a flow chart of a method for determining additional stress in a pile foundation according to an embodiment of the present invention;

[0071] Figure 2This is a schematic diagram of additional stress calculation under the pile axis according to an embodiment of the present invention;

[0072] Figure 3 A schematic diagram of calculating the additional stress outside the pile axis according to an embodiment of the present invention;

[0073] Figure 4 This is a schematic diagram of calculating additional stress under the action of uniform resistance on the pile side taking into account the pile diameter according to an embodiment of the present invention;

[0074] Figure 5 This is a schematic diagram of calculating additional stress generated by linearly increasing pile side friction in accordance with an embodiment of the present invention;

[0075] Figure 6 This is a flow chart of a method for calculating the additional stress σz between pile foundations according to an embodiment of the present invention;

[0076] Figure 7 This is a graph of additional foundation stress σz (-10≤x≤-6) according to an embodiment of the present invention;

[0077] Figure 8 This is a curve diagram of additional foundation stress σz (-5≤x≤-1) according to an embodiment of the present invention;

[0078] Figure 9 This is a curve diagram of additional foundation stress σz (0≤x≤4) according to an embodiment of the present invention;

[0079] Figure 10 This is a curve diagram of additional foundation stress σz (5≤x≤9) according to an embodiment of the present invention;

[0080] Figure 11 This is a graph of additional foundation stress σz (x=10) according to an embodiment of the present invention;

[0081] Figure 12 This is a contour diagram of the additional stress σz section of the foundation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0082] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0083] In the description of the present invention, it should be understood that descriptions involving orientation, such as the orientation or positional relationship indicated by up, down, etc., are based on the orientation or positional relationship shown in the accompanying 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 orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0084] In the description of the present invention, "a plurality" refers to more than two. The use of "first" or "second" is solely for the purpose of distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of the indicated technical features, or implicitly indicating the order of the indicated technical features.

[0085] In the description of the present invention, unless otherwise clearly defined, terms such as setting, installing, and connecting should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0086] Reference Figure 1 As shown, the present invention discloses a method for determining additional stress of a pile foundation, comprising:

[0087] Determine the vertical additional stress σz1 at any point outside the axis caused by the uniformly distributed load at the pile end of the pile foundation;

[0088] Determine the vertical additional stress σz2 generated at point M by the uniformly distributed resistance on the pile side of the pile foundation;

[0089] Determine the vertical additional stress σz3 generated at point M by the linear increase resistance of the pile side;

[0090] Determine the additional stress σz=σz1+σz2+σz3 at each point of the pile foundation within the plane range and within the depth range of the pile end.

[0091] Based on the Mindlin solution for additional stress under concentrated forces in a semi-infinite body, this paper considers the pile diameter and derives Mindlin analytical expressions for the vertical additional stress at any point along the pile axis and beyond, as well as for the additional stress under pile side resistance. Using these analytical expressions, a calculation program developed on the Matlab software platform can rapidly calculate the vertical additional stress at any point in a semi-infinite elastic body under pile foundation load. This program generates data files, plots single-point additional stress curves, and plots additional stress contours on the plane, providing key data for calculating foundation settlement under pile foundation load.

[0092] In some embodiments of the present invention, reference Figure 2 As shown, the method for determining σz1 includes:

[0093]

[0094] Where:

[0095] p is the pile tip load intensity (kPa), r is the pile foundation radius (m), h is the pile length (m), z is the calculated depth from the ground (m) (z>h), μ is the Poisson's ratio of the rock and soil layer at depth z, and θ is the central angle of the pile tip section (radians);

[0096] Completing five double integrals of (1) will give the additional stress σ under the pile foundation axis: z The analytical expression of is (2):

[0097]

[0098] refer to Figure 3 As shown, the coordinate origin is set at the center o of the pile end, and x is the horizontal distance from the pile center. Then the vertical additional stress under the concentrated force pρdρdθ on the micro area is still obtained by double integral. At this time, R1 and R2 are as follows:

[0099]

[0100]

[0101] Substitute R1 and R2 into formula (1), and express the five integrals of r in formula (1) as D1, D2, D3, D4, and D5, respectively, that is:

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] First, perform the integration operation on D1:

[0108]

[0109] Similarly, we can get:

[0110]

[0111]

[0112]

[0113]

[0114] Multiplying 2π by equations (3) to (7) respectively completes the integration of θ, and substituting it into equation (1), we can obtain the analytical formula for the vertical additional stress at any point outside the axis caused by the uniformly distributed load at the pile end, which is the following equation (8):

[0115]

[0116] In some embodiments of the present invention, reference Figure 4 As shown, the method for determining σz2 includes:

[0117] Assume that the radius of the pile foundation is r, the depth of the pile into the soil is D, and the uniformly distributed resistance on the pile side is P; the depth of point M from the ground is z, and the horizontal distance from the center of the pile is x;

[0118] By integrating along the pile length, we can obtain the integral expression of the vertical additional stress generated by the uniformly distributed resistance on the pile side at point M, which is the following formula (9):

[0119]

[0120]

[0121] Where:

[0122] Completing five double integrals for (9) yields the following calculation results:

[0123]

[0124] Where:

[0125]

[0126] In some embodiments of the present invention, reference Figure 5 As shown, the method for determining σz3 includes:

[0127]

[0128] Where:

[0129] Integrating h in formula (11) yields the following formula (12):

[0130]

[0131] Wherein A, B, F, m, and n are the same as those in formula (10).

[0132] In some embodiments of the present invention, reference Figure 6As shown, based on equations (8), (10), and (12), the method for determining the additional stress σz between pile foundations includes:

[0133] Determine the pile length h1 and pile length h2 of pile 1 and pile 2, the pile spacing S between piles 1 and 2, the pile top load P, the soil Poisson's ratio μ, the pile end resistance ratio α, and the pile side uniform resistance ratio β;

[0134] Calculate the additional stress σz1 at each point within the plane range [-Q, S+Q] of pile 1 within the depth range of 1 to 2Qm below the pile end;

[0135] Calculate the additional stress σz2 at each point within the plane range [-Q, S+Q] of pile 1 within the depth range of 1 to 2Qm below the pile end;

[0136] Calculate the additional stress σz3 at each point within the plane range [-Q, S+Q] of pile 1 within the depth range of 1 to 2Qm (spacing 1m) below the pile end;

[0137] Calculate the additional stress σz=σz1+σz2+σz3 at each point within the plane range [-Q, S+Q] of pile 1 within the depth range of 1 to 2Qm below the pile end;

[0138] Calculate the additional stress σz1 at each point within the plane range [-Q, S+Q] of pile 2 within the depth range of 1 to 2Qm below the pile end;

[0139] Calculate the additional stress σz2 at each point within the plane range [-Q, S+Q] of pile 2 within the depth range of 1 to 2Qm below the pile end;

[0140] Calculate the additional stress σz3 at each point within the plane range [-Q, S+Q] of pile 2 within the depth range of 1 to 2Qm below the pile tip;

[0141] Calculate the additional stress σz=σz1+σz2+σz3 at each point in the plane range [-Q, S+Q] of pile 2 within the depth range of 1 to 2Qm below the pile end.

[0142] In some embodiments of the present invention, when calculating σz1, σz2, and z3, within the plane range [-Q, S+Q], points with a spacing of 1 m are selected for calculation. Within a depth of 1 to 2Q m below the pile end, points with a spacing of 1 m are selected for calculation. It should be noted that when only a single pile is in operation, S = 0, and the calculation is performed directly on pile 1.

[0143] In some embodiments of the present invention, the obtained additional stress σz is plotted as a curve graph or a contour line graph of a profile of the additional stress σz.

[0144] Specific calculation example:

[0145] Basic conditions of the calculation example: pile diameter is 2m, pile length is 20m, pile top load is 10000kN, pile tip resistance ratio α = 0.2, pile side uniform resistance ratio β = 0.2, soil layer Poisson's ratio μ = 0.35, calculate the additional stress under the action of a single pile.

[0146] ①Show the additional stress curve at each point

[0147] The vertical additional stress (σz) curve of the foundation at each point in the range [-10, S+10] is displayed in sequence at 1m intervals (single pile action, S=0), such as Figures 7 to 11 In the figure, the horizontal axis is the additional stress value (unit: kPa), the vertical axis is the depth value (unit: m), and the calculated depth of each point is 20m.

[0148] ②Display the contour map of additional foundation stress

[0149] After displaying the additional stress curve for each point, the program then displays the additional stress contour diagrams for these points, such as Figure 12 shown.

[0150] ②Save data file

[0151] The data files are stored in two formats: Word document and DAT. The latter is mainly convenient for generating contour maps in other mapping software (such as Surfer drawing software).

[0152] In summary, this paper, based on the Mindlin solution for additional stress under concentrated forces in a semi-infinite body and taking into account the pile diameter, derives Mindlin analytical expressions for the vertical additional stress at any point on or off the pile axis, as well as for the additional stress under pile side resistance. Using these analytical expressions, a calculation program developed on the Matlab software platform can rapidly calculate the vertical additional stress at any point in a semi-infinite elastic body under pile foundation loads. This program generates data files, plots single-point additional stress curves, and plots additional stress contours on the plane, providing key fundamental data for calculating foundation settlement under pile foundation loads.

[0153] In addition, to solve the above technical problems, the present invention also discloses a system for determining additional stress of a pile foundation, including a memory and a processor, wherein a program for determining additional stress of a pile foundation is stored in the memory, and the processor runs the program for determining additional stress of a pile foundation, so that the system for determining additional stress of a pile foundation executes the method for determining additional stress of a pile foundation of the above embodiment.

[0154] Since the pile foundation additional stress determination system adopts all the technical solutions of the pile foundation additional stress determination method of the above-mentioned embodiment, by adopting this determination system, a calculation program can be compiled on a calculation software platform to quickly calculate the vertical additional stress at any point in the semi-infinite space elastic body under the action of the pile foundation load.

[0155] In some embodiments of the present invention, a graphics processing system is further provided for collecting the additional stress σz data processed by the processor and generating a curve graph and an additional stress σz profile contour graph.

[0156] In addition, to solve the above technical problems, the present invention also discloses a computer-readable storage medium, on which a program for determining the additional stress of a pile foundation is stored. The program for determining the additional stress of a pile foundation is executed by a processor to implement the method for determining the additional stress of a pile foundation according to the above embodiment.

[0157] Since the computer-readable storage medium adopts all the technical solutions of the method for determining the additional stress of the pile foundation in the above embodiment, it at least has all the beneficial effects brought by the technical solutions of the above embodiment, which will not be repeated here.

[0158] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can 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 can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0159] 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 produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. 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.

[0160] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work 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 The function specified in one or more boxes.

[0161] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0162] In a typical configuration, a computing device includes one or more processors (CPUs), input / output interfaces, network interfaces, and memory.

[0163] The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0164] Computer-readable media include permanent and non-permanent, removable and non-removable media that can implement information storage using any method or technology. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission media that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transitory computer-readable media, such as modulated data signals and carrier waves. The preferred embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the specific details of the aforementioned embodiments. Within the scope of the technical concept of the present invention, various simple variations of the technical solution of the present invention can be made, and these simple variations fall within the scope of protection of the present invention.

[0165] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in the relevant technical field without departing from the scope of the present invention.

Claims

1. A method for determining additional stress in a pile foundation, characterized in that: include: Determine the vertical additional stress σz1 at any point outside the axis caused by the uniformly distributed load at the pile end of the pile foundation; Determine the vertical additional stress σz2 generated at point M by the uniformly distributed resistance on the pile side of the pile foundation; Determine the vertical additional stress σz3 generated at point M by the linear increase resistance of the pile side; Determine the additional stress σz=σz1+σz2+σz3 at each point of the pile foundation within the plane range and within the depth range of the pile end; The method for determining σz1 includes: （1） Where: , ; is the pile tip load intensity (kPa), r is the pile foundation radius (m), h is the pile length (m), z is the calculated depth from the ground (m) (z>h), μ is the Poisson's ratio of the rock and soil layer at depth z, and θ is the central angle of the pile tip section; The method for determining σz2 includes: Assume that the radius of the pile foundation is r, the depth of the pile into the soil is D, and the uniformly distributed resistance on the pile side is P; the depth of point M from the ground is z, and the horizontal distance from the center of the pile is x; By integrating along the pile length, we can obtain the integral expression of the vertical additional stress generated by the uniformly distributed resistance on the pile side at point M, which is the following formula (9): （9） Where: , ; The method for determining σz3 includes: （11） Where: , .

2. The method for determining additional stress of a pile foundation according to claim 1, wherein: Complete five double integrals for (1) to obtain the additional stress under the pile foundation axis: The analytical expression of is (2): （2） Set the coordinate origin at the center o of the pile end, is the horizontal distance from the pile center, then the vertical additional stress under the concentrated force pρdρdθ on the micro area is obtained by double integration. At this time, R1 and R2 are as follows: Will 、 Substitute into formula (1) and represent the five integrals of r in formula (1) with D1, D2, D3, D4, and D5, respectively, that is: ； ； ； ； ； First of all, Perform integration operations: = = + = - + + （3） Similarly, we can get: D2= - + + (4) （5） （6） （7） Multiply 2π by equations (3) to (7) to complete the integration of θ, and substitute it into equation (1) to obtain the analytical expression of the vertical additional stress at any point outside the axis caused by the uniformly distributed load at the pile end, which is the following equation (8): （8）。 3. The method for determining additional stress of a pile foundation according to claim 2, wherein: Completing five double integrals for (9) yields the following calculation results: (10) Where: 。 4. The method for determining additional stress of a pile foundation according to claim 3, wherein: The integration of formula (11) with respect to h yields the following formula (12): （12） In the formula 、 、 、 、 Same as formula (10) above.

5. The method for determining additional stress of a pile foundation according to claim 4, characterized in that: Based on equations (8), (10), and (12), the method for determining the additional stress σz between the pile foundations includes: Determine the pile length h1 and pile length h2 of pile 1 and pile 2, the pile spacing S between piles 1 and 2, the pile top load P, the soil Poisson's ratio μ, the pile end resistance ratio α, and the pile side uniform resistance ratio β; Calculate the additional stress σz1 at each point within the plane range [-Q, S+Q] of pile 1 within the depth range of 1 to 2Qm below the pile end; Calculate the additional stress σz2 at each point within the plane range [-Q, S+Q] of pile 1 within the depth range of 1 to 2Qm below the pile end; Calculate the additional stress σz3 at each point within the plane range [-Q, S+Q] of pile 1 within the depth range of 1 to 2Qm (spacing 1m) below the pile end; Calculate the additional stress σz=σz1+σz2+σz3 at each point within the plane range [-Q, S+Q] of pile 1 within the depth range of 1 to 2Qm below the pile end; Calculate the additional stress σz1 at each point within the plane range [-Q, S+Q] of pile 2 within the depth range of 1 to 2Qm below the pile end; Calculate the additional stress σz2 at each point within the plane range [-Q, S+Q] of pile 2 within the depth range of 1 to 2Qm below the pile end; Calculate the additional stress σz3 at each point within the plane range [-Q, S+Q] of pile 2 within the depth range of 1 to 2Qm below the pile tip; Calculate the additional stress σz=σz1+σz2+σz3 at each point in the plane range [-Q, S+Q] of pile 2 within the depth range of 1 to 2Qm below the pile end.

6. The method for determining additional stress of a pile foundation according to claim 5, characterized in that: When calculating the σz1, σz2 and z3, within the plane range [-Q, S+Q], points with an interval of 1m are selected for calculation, and within a depth of 1 to 2Qm below the pile end, points with an interval of 1m are selected for calculation.

7. The method for determining additional stress of a pile foundation according to claim 5, characterized in that: The method further includes plotting the obtained additional stress σz as a curve graph and an additional stress σz profile contour graph.

8. A system for determining additional stress in pile foundations, characterized in that: The system comprises a memory and a processor, wherein the memory stores a program for determining additional stress of a pile foundation, and the processor runs the program for determining additional stress of a pile foundation, so that the system for determining additional stress of a pile foundation executes the method for determining additional stress of a pile foundation according to any one of claims 1 to 7.

9. The system for determining additional stress of pile foundation according to claim 8, characterized in that: It also includes a graphics processing system for collecting the additional stress σz data processed by the processor and generating a curve graph and an additional stress σz profile contour graph.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a program for determining additional stress of a pile foundation. When the program for determining additional stress of a pile foundation is executed by a processor, the method for determining additional stress of a pile foundation according to any one of claims 1 to 7 is implemented.

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