Method for calculating axial ultimate uplift bearing capacity of positive screw pile foundation

Abstract

The invention discloses a positive screw pile foundation axial ultimate uplift bearing capacity calculation method. The method comprises the steps that a pile-soil interface contact normal pressure stress function and a contact tangential friction stress function are constructed; constructing an equivalent relationship between the uplift resistance on the right-hand screw pile drawing surface and the shear resistance on the cylindrical shear failure surface of the foundation soil body, and obtaining the horizontal force and the circumferential torque of the soil body acting on the right-hand screw pile drawing surface; obtaining an equivalent concentrated load of a horizontal force and an action point location thereof; the radial load of the foundation soil body acting on the right-hand screw pile drawing face is obtained, and the additional radial stress on the cylindrical shear failure face in the foundation soil body is obtained; obtaining application conditions of an additional shear resistance calculation formula according to an additional radial stress limit summation calculation formula; and a positive screw pile foundation axial ultimate uplift bearing capacity calculation formula is constructed, and the positive screw pile foundation axial ultimate uplift bearing capacity calculation formula is obtained. The problem that the axial ultimate uplift bearing capacity of the positive screw pile foundation cannot be accurately obtained through an existing method is solved.

Description

Technical Field

[0001] The invention relates to the technical field of geotechnical and foundation engineering, and in particular to a method for calculating the axial ultimate pull-out bearing capacity of a positive spiral pile foundation. Background Art

[0002] In geotechnical and foundation engineering, it is of great significance to reasonably and accurately evaluate the bearing capacity of pile foundation. The bearing capacity of pile foundation is directly related to the stability and safety of superstructure. Accurate evaluation of pile foundation bearing capacity can prevent major accidents such as structural instability, tilt or collapse. Reasonable evaluation of pile foundation bearing capacity can optimize the design, avoid unnecessary cost increase caused by conservative design and safety hazards caused by risky design, so as to effectively control the project cost under the premise of ensuring safety. Reasonable evaluation of pile foundation bearing capacity can help to timely discover potential problems in construction, ensure that the construction quality meets the design requirements, and thus improve the quality of the entire project; at the same time, it can also reduce the impact of construction on the environment and avoid material waste. Accurate evaluation of pile foundation bearing capacity can also extend the service life of buildings or structures and reduce maintenance and reinforcement work during use due to foundation problems. Under complex geological conditions, it is particularly important to accurately evaluate the bearing capacity of pile foundation, which can help select appropriate pile types and construction methods to ensure the reliability and safety of the foundation. Evaluating the bearing capacity of pile foundation in accordance with building regulations and specifications can avoid legal disputes and liability issues and ensure project compliance. In general, pile foundation bearing capacity assessment is a key link in the design and construction of geotechnical and foundation engineering, and has a significant impact on engineering safety, cost control, environmental protection, and compliance.

[0003] Spiral piles (spiral blade piles, threaded nail piles and bored threaded cast-in-place piles), wedge piles, expanded base piles, expanded diameter piles, bamboo piles, H-shaped piles, X-shaped piles and Y-shaped piles are all common special-shaped piles in engineering practice. Special-shaped piles are used in engineering construction to increase the pile-soil contact area, improve the pile-soil interaction relationship and optimize the pile-soil load sharing, so as to improve the bearing capacity of the pile-soil system, strengthen the stability of the pile-soil system and reduce the deformation and settlement of the pile-soil system, thereby achieving the purpose of reducing the project cost, improving the project reliability and extending the service life of the project. Different from the traditional pile foundation with a cylindrical, torus or rectangular geometric shape, the pile structure of the special-shaped pile has an irregular geometric shape, making it a major problem in engineering practice to reasonably and accurately evaluate the bearing capacity of various special-shaped pile foundations. The positive spiral pile is a new special-shaped pile that has emerged in the past decade. It originated in Japan and South Korea and has been widely used in infrastructure projects in the fields of construction, transportation, natural energy and agriculture. Around 2018, some pile foundation manufacturers in my country began to introduce this type of pile from Japan and South Korea. However, at present, the positive spiral pile has not been promoted and used in domestic infrastructure projects, so related practical examples are relatively rare.

[0004] The most significant advantage of positive spiral piles in engineering practice is that they have excellent axial compression and pull-out bearing performance, and can provide higher axial compression and pull-out bearing capacity than static pressure construction loads, and have good prospects for engineering application. However, the pile structure of the positive spiral pile is similar to the positive spiral surface in differential geometry, which leads to a highly nonlinear contact mode between the positive spiral pile and the foundation soil. The interaction problem of the pile-soil system has non-plane strain and non-axisymmetric properties. The unique three-dimensional twisted structure of the positive spiral pile makes the soil squeeze effect exist in the buried depth range of the pile body during the installation process and under the load state. The geometric nonlinearity, material nonlinearity and contact nonlinearity caused by the large deformation of the foundation soil caused by the pile-soil interaction have far exceeded the assumed premise conditions such as axisymmetry, plane strain and small deformation.

[0005] Therefore, under the assumption of contradictory premises, classical theoretical methods such as circular hole expansion theory, strain path method, bearing capacity theory, shear displacement method and load transfer method are no longer directly applicable to the analysis of pile-soil interaction problems involving positive spiral piles or to the analytical solution of the penetration resistance and bearing capacity of positive spiral piles. In addition, in the classical cylindrical shear model, the calculation of the axial ultimate pullout bearing capacity of the pile foundation only considers the initial horizontal ground stress of the foundation soil. This model is applicable to pile types that do not produce lateral compression effect on the soil around the pile during the pile extraction process, such as spiral blade piles and threaded steel piles. However, under the action of axial pullout load, the positive spiral pile will squeeze the soil around the pile, resulting in additional radial stress in the foundation soil. The classical cylindrical shear model seriously underestimates the axial ultimate pullout bearing capacity of the positive spiral pile foundation because it ignores this effect. Summary of the invention

[0006] The present invention provides a method for calculating the axial ultimate pull-out bearing capacity of a positive spiral pile foundation to overcome the above technical problems.

[0007] In order to achieve the above object, the technical solution of the present invention is:

[0008] A method for calculating the axial ultimate pull-out bearing capacity of a positive spiral pile foundation specifically comprises the following steps:

[0009] S1: Based on the small hole expansion theory of geotechnical media and the differential geometric structure characteristics of the positive screw pile, the pile-soil interface contact normal compressive stress function under the initial horizontal ground stress state is constructed; based on the Coulomb friction law, the contact tangential friction stress function is constructed according to the pile-soil interface contact normal compressive stress function;

[0010] S2: Obtain the vertical component and horizontal component of the contact stress between the positive screw pile and the foundation soil on the contact surface according to the pile-soil interface contact stress function;

[0011] S3: Based on the load transfer mechanism of the pile-soil system, the equivalent relationship between the pull-out resistance on the pull-out surface of the positive screw pile and the shear resistance on the cylindrical shear failure surface of the foundation soil is constructed according to the vertical component of the contact stress, so as to obtain the contact normal compressive stress at the edge of the pull-out surface when the positive screw pile foundation reaches the ultimate bearing capacity state under the action of axial pull-out load;

[0012] S4: According to the contact normal compressive stress and the horizontal component of the contact stress at the edge of the pulling surface, the horizontal force and the circumferential torque of the foundation soil acting on the pulling surface of the positive screw pile are obtained;

[0013] Based on the moment equivalence principle, the equivalent concentrated load of the horizontal force and its action point are obtained according to the circumferential torque acting on the pulling surface of the positive spiral pile; the radial load of the foundation soil acting on the pulling surface of the positive spiral pile is obtained according to the equivalent concentrated load and its action point;

[0014] S5: Based on Newton's third law, the radial load reaction force of the positive screw pile pulling surface on the foundation soil is obtained according to the radial load; the additional radial stress on the cylindrical shear failure surface in the foundation soil is obtained according to the radial load reaction force;

[0015] Based on the Mohr-Coulomb strength criterion and the additional radial stress on the cylindrical shear failure surface, the additional shear resistance generated by the foundation soil on the cylindrical shear failure surface is obtained.

[0016] S6: Based on the limit sum calculation principle of geometric series and the limit sum calculation formula of additional radial stress, the applicable conditions of the additional shear resistance calculation formula are obtained;

[0017] S7: Based on the theoretical framework of the cylindrical shear model, the calculation formula for the axial ultimate pullout bearing capacity of the spur spiral pile foundation is constructed according to the additional shear resistance, and the calculation of the axial ultimate pullout bearing capacity of the spur spiral pile foundation is realized in combination with applicable conditions.

[0018] Furthermore, the S1 specifically includes the following steps:

[0019] S11: Based on the small hole expansion theory of geotechnical media and the differential geometric structure characteristics of the positive screw pile, the normal compressive stress function of the pile-soil interface under the initial horizontal ground stress state is constructed as follows:

[0020]

[0021] Where: n R0 It represents the contact normal compressive stress at a radial distance R on the pulling surface in a certain cross section of the positive screw pile foundation; n d0 represents the initial horizontal stress σ in the foundation soil h In the state, when the positive screw pile foundation reaches the ultimate bearing capacity state under the action of axial tensile load, the contact normal compressive stress to be solved at the edge of the tensile surface in a certain cross section of the pile-soil system; d represents the spiral structure diameter of the positive screw pile;

[0022] S12: Based on Coulomb's friction law, the contact tangential friction stress function is constructed according to the contact normal compressive stress function of the pile-soil interface:

[0023] f R0 =μn R0

[0024] Where: μ represents the friction coefficient between the surface of the positive screw pile and the foundation soil; f R0 It represents the contact tangential friction stress between the positive screw pile and the foundation soil on the contact surface.

[0025] Furthermore, the vertical component of the contact stress and the horizontal component of the contact stress on the contact surface between the positive screw pile and the foundation soil obtained in S2 are expressed as follows:

[0026] q R0 =n R0 sinθ+f R0 cosθ

[0027] h R0 =n R0 cosθ-f R0 sinθ

[0028] Where: q R0 represents the vertical component of contact stress; h R0 represents the horizontal component of contact stress; θ represents the torsion angle between the positive screw pile and the foundation soil at a certain point on the contact surface.

[0029] Furthermore, the S3 specifically includes the following steps:

[0030] S31: Obtain the vertical force dQ concentrated on a preset micro area with a radial distance R on the pulling surface of the positive spiral pile R0 , then for any preset micro-segment pile-soil system with a longitudinal height of dZ, the pull-out resistance ΔQ acting on the pull-out surface of the positive spiral pile is R0 for

[0031] dQ R0 =q R0 ·dS

[0032]

[0033] dS=dR·dl h

[0034]

[0035] Where: dS represents the area of ​​any microelement on the pulling surface of the positive spiral pile; dR represents the radial width of the microelement on the pulling surface of the positive spiral pile; dl h represents the length of the spiral line on the side of the microelement of the positive spiral pile pulling surface; p represents the pitch of the positive spiral pile and the positive spiral surface;

[0036] S32: Based on the vertical component of the contact stress, according to step S31 and combined with the pile-soil interface contact stress function, the pullout resistance ΔQ R0 Rewrite as

[0037]

[0038] S33: Obtain the corresponding relationship between the torsion angle α of the positive helical surface and the pitch-to-diameter ratio n:

[0039]

[0040] According to the corresponding relationship between the helical torsion angle α and the distance-to-diameter ratio n, the pull-out resistance ΔQ R0 The integral calculation formula is further rewritten as

[0041]

[0042] And further rewrite the pull-out resistance ΔQ R0 Integrate to get

[0043]

[0044] S34: For a positive helical pile with a torsion angle α of 45°, according to the corresponding relationship between the torsion angle α of the positive helical surface and the distance-to-diameter ratio n, the pull-out resistance ΔQ can be calculated asR0 Simplified to

[0045]

[0046] S35: Based on the load transfer mechanism of the pile-soil system, the shear resistance P on the cylindrical shear failure surface under the initial horizontal ground stress state h The pull-out resistance Q on the pull-out surface of the positive screw pile R0 are equal in value;

[0047] Then, in any preset pile-soil system with a longitudinal height of dZ, the equivalent relationship between the pull-out resistance acting on the pull-out surface of the positive spiral pile and the shear resistance on the cylindrical shear failure surface is obtained as follows:

[0048] ΔP h =ΔQ R0

[0049] Among them, the shear resistance P on the cylindrical shear failure surface is h The expression is

[0050]

[0051] Where: l represents the length of the positive screw pile; σ h represents the initial horizontal ground stress; The internal friction angle represents the shear strength index of the foundation soil; c represents the cohesion index of the shear strength index of the foundation soil;

[0052] S36: Based on the equivalent relationship between the shear resistance on the cylindrical shear failure surface and the pull-out resistance on the positive spiral pile pull-out surface, according to the pull-out resistance ΔQ R0 Shear resistance P on the cylindrical shear failure surface h , solve and obtain the contact normal compressive stress at the edge of the pulling surface in any cross section of the pile-soil system when the positive screw pile foundation reaches the ultimate bearing capacity state under the axial pulling load under the initial horizontal ground stress σh of the foundation soil:

[0053]

[0054] Furthermore, the S4 specifically includes the following steps:

[0055] S41: Obtain the horizontal force dH concentrated on a preset small area on the pulling surface of the positive screw pile R0 , then for any preset micro-segment pile-soil system with a longitudinal height of dZ, the horizontal force ΔH acting on the pulling surface of the positive spiral pile is R0 for

[0056] dH R0 =h R0·dS

[0057]

[0058] S42: According to the horizontal force ΔH R0 Obtain the equivalent concentrated load ΔE of the horizontal force on a single drawing surface 0 , whose expression is

[0059]

[0060] S43: Define the pile axis of the positive spiral pile foundation as the rotation axis, and obtain the circumferential torque dM concentrated on a certain preset micro area on the positive spiral pile pulling surface R0 , then for any preset micro-segment pile-soil system with a longitudinal height of dZ, the circumferential torque ΔM acting on the pulling surface of the positive spiral pile is 0 for

[0061] dM R0 =R·dH R0

[0062]

[0063] S44: Based on the moment equivalence principle, according to the equivalent concentrated load ΔE 0 and circumferential torque ΔM 0 , obtain the equivalent concentrated load ΔE 0 The radial distance b from the action point to the pile axis is

[0064] 2ΔE 0 b=ΔM 0

[0065]

[0066] S45: Obtain the equivalent concentrated load ΔE based on the radial distance b 0 and its radial load ΔR 0 The angle ω of the load is used to obtain the equivalent concentrated load ΔE 0 Radial load ΔR 0 , whose expression is

[0067]

[0068] ΔR 0 =ΔE 0 cosω.

[0069] Furthermore, the S5 specifically includes the following steps:

[0070] S51: Based on Newton's third law, obtain the radial load reaction force ΔR′ of the positive screw pile on the foundation soil 0; That is, the radial load reaction force ΔR′ 0 and radial load ΔR 0 equal in magnitude and opposite in direction;

[0071] S52: The radial load reaction force ΔR′ on the two drawing surfaces 0 Evenly dispersed on the cylindrical shear failure surface, we can get

[0072] 2ΔR′ 0 =πdσ r1 ·dZ

[0073] Where: r1 Indicates radial load reaction force ΔR′ 0 The primary additional radial stress generated on the cylindrical shear failure surface;

[0074] S53: According to radial load ΔR 0 and equivalent concentrated load ΔE 0 , combined with step S52, the initial horizontal stress σ h In the state, due to the compression of the foundation soil by the pulling surface of the positive screw pile, the additional radial stress generated on the cylindrical shear failure surface is σ r1 , that is, the additional radial stress generated on the cylindrical shear failure surface in the foundation soil, and its expression is

[0075]

[0076] S54: Based on the Mohr-Coulomb strength criterion, obtain the additional radial stress σ r1 The additional shear resistance P generated by the foundation soil on the cylindrical shear failure surface is r1 , whose expression is

[0077]

[0078] Furthermore, the S6 specifically includes the following steps:

[0079] S61: Based on the small pore expansion theory of rock and soil media, according to the additional shear resistance P r1 It can be obtained that the additional radial stress σ r1 In the state, the additional contact normal compressive stress n is applied to any cross section of the pile-soil system. R1 and additional contact tangential friction stress f R1 ;

[0080] Based on the constructed pile-soil interface contact stress function, according to S2 to S4 combined with S51 to S53, the additional radial stress σ r1 In the state, due to the compression of the foundation soil by the pulling surface of the positive screw pile, the secondary additional radial stress σ is generated on the cylindrical shear failure surface.r2 , whose expression is

[0081]

[0082] S62: According to the constructed pile-soil interface contact stress function, according to S2 to S4 and combined with S11 to S54 and S61, the i-th additional radial stress σ can be obtained ri , whose expression is

[0083]

[0084] S63: Accumulate the additional radial stresses at each time to obtain the additional radial stress σ on the cylindrical shear failure surface r , whose expression is

[0085]

[0086] Based on the geometric series summation formula, the common ratio parameter k is set, and the additional radial stress σ on the cylindrical shear failure surface is calculated. ri To obtain the total additional radial stress σ r , whose expression is

[0087]

[0088]

[0089] S64: Based on the limit summation calculation principle of geometric series, according to the total additional radial stress σ r The additional shear resistance P is obtained r Applicable conditions of the calculation formula;

[0090] The applicable condition is that the common ratio parameter k must satisfy 0≤k<1;

[0091] Then the limiting summation formula of the total additional radial stress that meets the applicable conditions is obtained as follows:

[0092]

[0093] Furthermore, the calculation formula for the axial ultimate pull-out bearing capacity of the positive spiral pile foundation constructed in S7 is:

[0094] P=P s +W P +W s

[0095]

[0096]

[0097]

[0098]

[0099] W p =ρgdtl

[0100] Where: P represents the axial ultimate pull-out bearing capacity of the positive screw pile foundation; P s W represents the shear resistance of the foundation soil on the cylindrical shear failure surface; P W represents the self-weight of the positive screw pile; s represents the gravity of the soil embedded in the pile structure, i.e., the cylindrical shear failure surface; ρ represents the density of the steel of the pile itself; g represents the acceleration of gravity; Z represents the depth in the foundation soil; γ represents the natural gravity of the foundation soil; t represents the thickness of the pile; P r Indicates the additional radial stress σ r The additional shear resistance on the cylindrical shear failure surface under the action of h It represents the shear resistance generated on the shear failure surface of the cylinder under the initial horizontal ground stress state.

[0101] Beneficial effects: The present invention provides a method for calculating the axial ultimate pull-out bearing capacity of a positive spiral pile foundation. Based on the theory of small hole expansion in rock and soil media and the differential geometric structure characteristics of the positive spiral pile, the pile-soil interface contact stress function is established from the soil squeezing effect of the pile body. By analyzing the load transfer mechanism of the pile-soil system, the equivalent relationship between the shear resistance on the cylindrical shear failure surface and the vertical component on the pull-out surface of the positive spiral pile is constructed, and the specific distribution forms of the normal compressive stress and the contact tangential friction stress at the pile-soil interface are clarified. According to Newton's third law and the principle of moment equivalence, under the limit state of axial pull-out bearing capacity, how the horizontal force of the positive spiral pile acting on the foundation soil is dispersed to the soil around the pile is analyzed. The additional radial stress on the cylindrical shear failure surface is determined by combining the calculation principle of the limit summation of decreasing geometric series; based on the Mohr-Coulomb strength criterion, the additional shear resistance generated by the foundation soil on the cylindrical shear failure surface is obtained according to the additional radial stress on the cylindrical shear failure surface; according to the limit summation calculation formula of the additional radial stress, the applicable conditions of the calculation formula of the additional shear resistance are clarified; based on the classical cylindrical shear model theory, the calculation formula for the axial ultimate pullout bearing capacity of the positive spiral pile foundation is constructed according to the additional shear resistance, and combined with the applicable conditions to realize the calculation of the axial ultimate pullout bearing capacity of the positive spiral pile foundation, which greatly improves the calculation accuracy of the axial ultimate pullout bearing capacity of the positive spiral pile foundation. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0103] Figure 1 It is a flow chart of the method for calculating the axial ultimate pull-out bearing capacity of the spur screw pile foundation of the present invention;

[0104] Figure 2 Schematic diagram of the classic cylindrical shear model of the mainstream screw pile foundation in this embodiment;

[0105] Figure 3 Schematic diagram of various surfaces and external normal directions of the positive spiral pile in this embodiment;

[0106] Figure 4 Schematic diagram of the geometric relationship between the positive spiral pile and its torsion angle α and the distance-to-diameter ratio n in this embodiment;

[0107] Figure 5 Schematic diagram of a theoretical model for calculating the ultimate pull-out bearing capacity of a positive screw pile foundation in this embodiment;

[0108] Figure 6 Schematic diagram of the microelement ad of the positive helicoid in this embodiment;

[0109] Figure 7 Schematic diagram of the vertical displacement ΔD generated by the positive screw pile and the space ah squeezed out by the microelement ad on the pulling surface side in the foundation soil when the positive screw pile foundation reaches the ultimate bearing capacity state under the axial pulling load in this embodiment;

[0110] Figure 8 Schematic diagram of the contact stress effect at a certain point on the drawing surface in this embodiment;

[0111] Fig. 9 Schematic diagram of the effect of contact stress on the drawing surface in this embodiment;

[0112] Fig.10 is the additional radial stress σ on the cylindrical shear failure surface in this embodiment r1 Schematic diagram of the resulting mechanics;

[0113] Fig.11 is the dual variable (δ and ) 3D surface plot;

[0114] Fig.12 is the shear resistance P in this embodiment sSchematic diagram of the applicable conditions of the calculation formula. DETAILED DESCRIPTION

[0115] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are 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.

[0116] This embodiment provides a method for calculating the axial ultimate pull-out bearing capacity of a positive spiral pile foundation. Figure 1 As shown, the specific steps include:

[0117] S1: Based on the small hole expansion theory of geotechnical media and the differential geometric structure characteristics of the positive screw pile, the pile-soil interface contact normal compressive stress function under the initial horizontal ground stress state is constructed; based on the Coulomb friction law, the contact tangential friction stress function is constructed according to the pile-soil interface contact normal compressive stress function;

[0118] Specifically, the positive spiral pile is an extremely distorted spatial geometry. Wang et al. (2024)

[13] According to the geometric characteristics of the pile structure, the pile surface is divided into different types, and the external normals of each type of surface have different directions, such as Figure 3 As shown: the outer normals of a bottom surface (Bot.) and two outer surfaces (Out.1 and Out.2) are parallel and perpendicular to the axial direction respectively; the inner surface is divided into two compression surfaces (Com.1 and Com.2) and two pulling surfaces (Pul.1 and Pul.2). In this embodiment, the outer normal is neither perpendicular to the axial direction (except at the pile axis) nor parallel to the axial direction, and the outer normals of any points within one pitch of the axial length are different; and at a certain point inside the pile body, the outer normals of the compression surfaces and pulling surfaces on both sides are completely opposite. Figure 3 Represents various surfaces of positive screw piles and their external normal directions: Figure 3 (a) is a schematic diagram of the surface classification of positive screw piles; Figure 3 (b) is a schematic diagram of the normal direction of the out-of-plane normal line; Figure 3 (c) is a schematic diagram of the normal direction outside the compression plane; Figure 3 (d) is a schematic diagram of the outer normal direction of the outer surface; Figure 3 (e) is the outer normal direction of the bottom surface

[13] Schematic diagram;

[0119] like Figure 4 The schematic diagram shows the geometric relationship between the positive spiral pile and the torsion angle α and the distance-to-diameter ratio n. Figure 4 (a) The structure of the positive spiral pile is similar to the positive spiral surface in differential geometry. Figure 4 (b) is the geometric relationship between the torsion angle α and the distance-to-diameter ratio n, and the parameter equations of the positive helical surface in the spatial rectangular coordinate system are as follows (1) and (2). The degree of twisting of the positive helical surface can be reflected by the torsion angle α or the distance-to-diameter ratio n. The relationship between these two parameters is as follows: Figure 4 b (spatial rectangular coordinate system) and formula (3). In actual engineering, the geometric feature of the positive spiral pile structure is that the thickness t is much smaller than the diameter d and the length l, so it is reasonable to analyze it as a positive spiral surface with zero thickness. Therefore, during the pile extraction process, the friction resistance between the outer surface of the positive spiral pile and the soil around the pile is approximated as the shear resistance generated by the foundation soil in this area. The principle of calculating the shear resistance of the soil around the pile based on the classical cylindrical shear model is the same as that of mainstream spiral pile foundations such as spiral blade piles, threaded nail piles and bored threaded cast-in-place piles. The error caused by this simplified processing is usually acceptable and ignored in engineering practice.

[0120]

[0121] Consider that there is only initial horizontal stress σ on the cylindrical shear failure surface h Action: When under the action of axial pull-out load, the positive spiral pile produces vertical upward axial displacement, and the compression surface gradually moves away from the foundation soil that was originally in contact with it until it separates, while the pull-out surface continues to squeeze the foundation soil that is in contact with it; that is, under the axial pull-out loading state, the positive spiral pile and the foundation soil come into contact on the pull-out surface, and the interaction of forces between the two occurs on the pull-out surface. When the positive spiral pile foundation reaches the ultimate bearing capacity state, the shear resistance P generated on the cylindrical shear failure surface on the pile-soil contact surface h It is transmitted to the pulling surface of the pile in the form of contact stress.

[0122] Take a microelement ad with radial width dR and axial height dZ on the positive helical surface, such as Figure 6 As shown;

[0123] Depend on Figure 3 b, the length of the spiral line of segment ab dl h for

[0124]

[0125] Then the area dS of the infinitesimal element ad of the regular helicoid is.

[0126] dS=dR·dl h (5)

[0127] During the axial pull-out loading process, the pull-out surface of the positive spiral pile continuously squeezes the foundation soil in contact with it. On one side of the pull-out surface of the positive spiral pile, points with different radial distances (from the pile axis) exert different degrees of squeeze on the soil around the pile along the external normal direction. Figure 7 , when the positive screw pile foundation reaches the ultimate bearing capacity under the axial pull-out load, the vertical displacement of the positive screw pile is set to ΔD; then Figure 6 The space squeezed out by the pulling surface of the microelement ad in the foundation soil is a hexahedron ah, and its volume ΔV formula is:

[0128] ΔV=sinθ·ΔD·dS (6) Based on Figure 4 b. According to formula (3), formula (4) and formula (5) are combined to rewrite formula (6) as

[0129]

[0130] Since the volume ΔV of the hexahedron ah is proportional to the radial distance R of the point where the microelement ad of the pulling surface is located, during the axial pulling loading process, the pulling surface continues to squeeze the soil around the pile, and the larger the radial distance R of the micro-area (such as microelement ad), the larger the space squeezed out in the foundation soil. The small pore expansion theory of rock and soil media believes that the pore expansion pressure inside the rock and soil media is proportional to the pore expansion space.

[14] , then the smaller area with a larger radial distance R on the pulling surface is subjected to the contact normal compressive stress n from the reverse action of the foundation soil. R0 The larger the stress, the greater the stress. h When the positive screw pile foundation reaches the ultimate bearing capacity under the axial pull-out load, in any cross section of the pile-soil system, the contact normal compressive stress at the edge of the pull-out surface is set to n d0 Based on the theoretical framework of pore expansion in rock and soil media, the contact normal compressive stress n at the radial distance R on the drawing surface in the same cross section is R0 for

[0131]

[0132] When the positive spiral pile foundation reaches the ultimate bearing capacity state under the action of axial pull-out load, it is considered that there is relative sliding between the positive spiral pile and the foundation soil on the contact surface, and the direction vector of the relative sliding at any point on the pull-out surface is perpendicular to the radial direction and the outer normal direction of the point at the same time (that is, the angle with the Z axis is equal to the surface torsion angle θ at the point). Based on Coulomb's friction law, the contact normal compressive stress n at the same point is R0 Contact tangential friction stress f R0 The relationship between

[0133] f R0 =μn R0 (9)

[0134] Among them, n R0 It represents the contact normal compressive stress at the radial distance R on the pulling surface of the positive screw pile foundation in the same cross section; n d0 represents the initial horizontal stress σ in the foundation soil h In the state, when the positive spiral pile foundation reaches the ultimate bearing capacity state under the action of axial tensile load, the contact normal compressive stress to be solved at the edge of the tensile surface in any cross section of the pile-soil system; d represents the spiral structure diameter of the positive spiral pile foundation; μ represents the friction coefficient between the surface of the positive spiral pile foundation and the foundation soil; f R0 It represents the contact tangential friction stress between the positive screw pile and the foundation soil on the contact surface;

[0135] S2: Obtain the vertical component and horizontal component of the contact stress between the positive screw pile and the foundation soil on the contact surface according to the pile-soil interface contact stress function;

[0136] Specifically, for any point on the pulling surface of the positive screw pile, the contact normal compressive stress n R0 Contact tangential friction stress f R0 The effects of Figure 8 Taking two cross sections with an axial spacing of p / 2 on a positive spiral pile as an example, the contact normal compressive stress n is abstracted. R0 Contact tangential friction stress f R0 Effects on the drawing surface, such as Fig. 9 As shown, Fig. 9 (a) is a schematic diagram of the effect of contact normal compressive stress; Fig. 9 (b) is a schematic diagram of the effect of contact tangential friction stress; Fig. 9 (c) Schematic diagram of the vertical and horizontal components of contact stress.

[0137] Depend on Fig. 9 It can be known that the components of contact stress in the vertical and horizontal directions, that is, the vertical component of contact stress and the horizontal component of contact stress between the positive screw pile and the foundation soil on the contact surface are obtained according to the pile-soil interface contact stress function, and its expression is:

[0138] q R0 =n R0 sinθ+f R0 cosθ (10)

[0139] h R0 =n R0 cosθ-f R0 sinθ (11)

[0140] Where: q R0 represents the vertical component of contact stress; h R0 represents the horizontal component of contact stress; θ represents the torsion angle between the positive screw pile and the foundation soil at a certain point on the contact surface;

[0141] S3: Based on the load transfer mechanism of the pile-soil system, the equivalent relationship between the pull-out resistance on the pull-out surface of the positive screw pile and the shear resistance on the cylindrical shear failure surface of the foundation soil is constructed according to the vertical component of the contact stress, so as to obtain the contact normal compressive stress at the edge of the pull-out surface when the positive screw pile foundation reaches the ultimate bearing capacity state under the action of axial pull-out load;

[0142] S31: Obtain the vertical force dQ concentrated on a preset micro area with a radial distance R on the pulling surface of the positive spiral pile R0 It should be noted that the positive spiral pile has two pull-out surfaces. For any preset micro-segment pile-soil system with a longitudinal height of dZ, the pull-out resistance ΔQ acting on the pull-out surface of the positive spiral pile is R0 for

[0143] dQ R0 =q R0 ·dS (12)

[0144]

[0145] dS=dR·dl h (14)

[0146]

[0147] Where: dS represents the area of ​​any microelement on the pulling surface of the positive spiral pile; dR represents the radial width of the microelement on the pulling surface of the positive spiral pile; dl h represents the length of the spiral line on the side of the microelement of the positive spiral pile pulling surface; p represents the pitch of the positive spiral pile and the positive spiral surface;

[0148] S32: Based on the vertical component of the contact stress, according to step S31 and combined with the pile-soil interface contact stress function, the pullout resistance ΔQ R0 Rewrite as

[0149]

[0150] S33: Obtain the corresponding relationship between the torsion angle α of the positive helical surface and the pitch-to-diameter ratio n:

[0151]

[0152] It should be noted that the preset contact normal compressive stress n at the edge of the drawing surface d0It is only a function of the buried depth Z of the positive spiral pile. According to the corresponding relationship between the torsion angle α of the positive spiral surface and the distance-to-diameter ratio n, the pull-out resistance ΔQ R0 The integral calculation formula is further rewritten as

[0153]

[0154] And further rewrite the pull-out resistance ΔQ R0 Integrate to get

[0155]

[0156] S34: For a positive helical pile with a torsion angle α of 45°, according to the corresponding relationship between the torsion angle α of the positive helical surface and the distance-to-diameter ratio n, the pull-out resistance ΔQ can be calculated as R0 Simplified to

[0157]

[0158]

[0159] S35: Based on the load transfer mechanism of the pile-soil system, the shear resistance P on the cylindrical shear failure surface under the initial horizontal ground stress state h The pull-out resistance Q on the pull-out surface of the positive screw pile R0 are equal in value; that is, due to the shear resistance P on the cylindrical shear failure surface h In the form of contact stress, it is transmitted to the pile-soil contact surface, which is actually caused by the shear resistance P h The pull-out resistance Q acting on the pull-out surface of the positive spiral pile R0 , and the two are equal in value;

[0160] The shear resistance P on the cylindrical shear failure surface is h The expression is

[0161]

[0162] Where: l represents the length of the positive screw pile; σ h represents the initial horizontal ground stress; The friction angle represents the shear strength index of the foundation soil; c represents the cohesion index of the shear strength index of the foundation soil;

[0163] Then, in any preset pile-soil system with a longitudinal height of dZ, the equivalent relationship between the pull-out resistance acting on the pull-out surface of the positive spiral pile and the shear resistance on the cylindrical shear failure surface is obtained as follows:

[0164] ΔP h =ΔQ R0 (twenty three)

[0165] S36: Based on the equivalent relationship between the shear resistance on the cylindrical shear failure surface and the pull-out resistance on the positive spiral pile pull-out surface, according to the pull-out resistance ΔQ R0 Shear resistance P on the cylindrical shear failure surface h , solve and obtain the initial horizontal ground stress σ in the foundation soil h In the state, when the positive screw pile foundation reaches the ultimate bearing capacity state under the action of axial tensile load, the contact normal compressive stress at the edge of the tensile surface in any cross section of the pile-soil system is

[0166]

[0167] S4: According to the contact normal compressive stress and the horizontal component of the contact stress at the edge of the pulling surface, the horizontal force and circumferential torque of the foundation soil acting on the pulling surface of the positive spiral pile are obtained; and based on the moment equivalence principle, the equivalent concentrated load of the horizontal force and its action point are obtained according to the circumferential torque acting on the pulling surface of the positive spiral pile; the radial load of the foundation soil acting on the pulling surface of the positive spiral pile is obtained according to the equivalent concentrated load and its action point;

[0168] The specific steps include:

[0169] S41: Obtain the horizontal force dH concentrated on a preset small area on the pulling surface of the positive screw pile R0 , then for any preset micro-segment pile-soil system with a longitudinal height of dZ, the horizontal force ΔH acting on the pulling surface of the positive spiral pile is R0 for

[0170] dH R0 =h R0 ·dS (25)

[0171]

[0172] Define the function f(R) as

[0173]

[0174] It can be known that the horizontal force ΔH acting on the pulling surface of the positive screw pile is R0 The physical meaning is expressed as follows: In any small segment of pile-soil system with a longitudinal height of dZ, the horizontal force H R0 It is distributed on the drawing surface along the radial direction in the geometric form of function f(R);

[0175] S42: According to the horizontal force ΔH R0 Obtain the equivalent concentrated load ΔE of the horizontal force on a single drawing surface 0 , whose expression is

[0176]

[0177] S43: Define the pile axis of the positive spiral pile foundation as the rotation axis, and obtain the circumferential torque dM concentrated on a certain preset micro area on the positive spiral pile pulling surface R0 , then for any preset micro-segment pile-soil system with a longitudinal height of dZ, the circumferential torque ΔM acting on the pulling surface of the positive spiral pile is 0 for

[0178] dM R0 =R·dH R0 (29)

[0179]

[0180] S44: Based on the moment equivalence principle, according to the equivalent concentrated load ΔE 0 and circumferential torque ΔM 0 , obtain the equivalent concentrated load ΔE 0 The radial distance b from the action point to the pile axis is

[0181] 2ΔE 0 b=ΔM 0 (31)

[0182]

[0183] S45: Obtain the equivalent concentrated load ΔE based on the radial distance b 0 and its radial load ΔR 0 The angle ω of the load is used to obtain the equivalent concentrated load ΔE 0 Radial load ΔR 0 , whose expression is

[0184]

[0185] ΔR 0 =ΔE 0 cosω (34)

[0186] S5: Based on Newton's third law, the radial load reaction force of the positive screw pile pulling surface on the foundation soil is obtained according to the radial load; the additional radial stress on the cylindrical shear failure surface in the foundation soil is obtained according to the radial load reaction force; based on the Mohr-Coulomb strength criterion, the additional shear resistance generated by the foundation soil on the cylindrical shear failure surface is obtained according to the additional radial stress on the cylindrical shear failure surface;

[0187] The specific steps include:

[0188] S51: Based on Newton's third law, obtain the radial load reaction force ΔR′ of the positive screw pile on the foundation soil 0 ; That is, the radial load reaction force ΔR′0 and radial load ΔR 0 equal in magnitude and opposite in direction;

[0189] S52: The radial load reaction force ΔR′ on the two drawing surfaces 0 Evenly dispersed on the cylindrical shear failure surface, we can get

[0190] 2ΔR′ 0 =πdσ r1 ·dZ (35)

[0191] Where: r1 Indicates radial load reaction force ΔR′ 0 The primary additional radial stress generated on the cylindrical shear failure surface;

[0192] S53: According to radial load ΔR 0 and equivalent concentrated load ΔE 0 , combined with step S52, the initial horizontal stress σ h In the state, due to the compression of the foundation soil by the pulling surface of the positive screw pile, the additional radial stress generated on the cylindrical shear failure surface is σ r1 , that is, the additional radial stress generated on the cylindrical shear failure surface in the foundation soil, and its expression is

[0193]

[0194] And the additional radial stress σ generated on the cylindrical shear failure surface r1 The derivation process of its mechanical principles is as follows Fig.10 As shown;

[0195] S54: Based on the Mohr-Coulomb strength criterion, obtain the additional radial stress σ r1 The additional shear resistance P generated by the foundation soil on the cylindrical shear failure surface is r1 , whose expression is

[0196]

[0197] S6: Based on the limit sum calculation principle of geometric series and the limit sum calculation formula of additional radial stress, the applicable conditions of the additional shear resistance calculation formula are obtained;

[0198] The specific steps include:

[0199] S61: Due to the initial horizontal stress σ h In the state, shear resistance P is generated on the cylindrical shear failure surface. h , and it is transmitted to the surface of the positive screw pile in the form of contact stress;

[0200] Based on this, the additional radial stress σ r1 The additional shear resistance P is generated on the cylindrical shear failure surface r1 , which is also transmitted to the surface of the positive screw pile in the form of additional contact stress, then based on the small hole expansion theory of rock and soil media, it can be obtained that the additional radial stress σ r1 In the state, the additional contact normal compressive stress n is applied to any cross section of the pile-soil system. R1 and additional contact tangential friction stress f R1 ;

[0201] Based on the constructed pile-soil interface contact stress function, the secondary additional radial stress σ generated on the cylindrical shear failure surface due to the extrusion of the foundation soil by the positive spiral pile pulling surface is obtained according to S2 to S4 combined with S51 to S53. r2 , whose expression is

[0202]

[0203] In this embodiment, the initial horizontal stress σ h Shear resistance P is generated on the cylindrical shear failure surface h , which is transmitted to the surface of the positive spiral pile in the form of contact stress. r1 The additional shear resistance P is generated on the cylindrical shear failure surface r1 , which is transmitted to the surface of the positive screw pile in the form of additional contact stress, then the additional contact normal compressive stress n R1 and additional contact tangential friction stress f R1 The effect on the drawing surface can also be Figure 8 and Fig. 9 To express, no further elaboration is given here.

[0204] The additional radial stress σ r1 In any cross section of the pile-soil system, the contact normal compressive stress at the edge of the positive spiral pile pulling surface is set to n d1 ; The components of the additional contact stress in the vertical and horizontal directions are q R1 and h R1 , the two act on the pull-out surface, providing additional pull-out resistance Q of the positive screw pile. R1 And additional horizontal force H R1 . And obtain the additional radial stress σ r1 The derivation process is the same as that of . For any small segment of pile-soil system with a longitudinal height of dZ, the additional pull-out resistance ΔQ acting on the pull-out surface of the positive spiral pile is R1 for

[0205]

[0206] Similarly, because the additional shear resistance P on the cylindrical shear failure surface r1 It is transmitted to the pile-soil contact surface in the form of contact stress, so it is actually composed of additional shear resistance P r1 Contributes to the additional pull-out resistance Q acting on the pull-out surface of the positive screw pile R1 , the two are equal in value. Therefore, for any small segment of pile-soil system with a longitudinal height of dZ, the additional shear resistance ΔP r1 and additional pull-out resistance ΔQ R1 The equivalent relationship is

[0207] ΔP r1 =ΔQ R1 (40)

[0208] The additional shear resistance P r1 and additional pull-out resistance ΔQ R1 Substituting into the above formula, the solution is that the additional radial stress σ r1 The additional contact normal compressive stress n at the edge of the drawing surface under the state d1 for

[0209]

[0210] Similarly, the additional horizontal force H R1 The reaction force H′ R1 Acting on the foundation soil around the pile, a secondary additional radial stress σ is generated on the cylindrical shear failure surface r2 This part of the derivation process is similar to the process of obtaining the additional radial stress σ r1 The derivation process is the same as that of r1 In the state, the secondary additional radial stress σ acting on the cylindrical shear failure surface r2 ;

[0211] In this embodiment, the additional contact normal compressive stress n d1 "In the following, all the processes involved in the calculation are omitted, because from the derivation process from equation (8) to equation (41), the additional radial stress σ can be obtained r1 In the state, the secondary additional radial stress σ acting on the cylindrical shear failure surface r2 ; By the same logic, we can also get σ r3 , σ r4 , σ r5 , σ r6 ......σ rn , n is infinite, and it is impossible to give an exhaustive example. Therefore, the following statement is made: "By analogy, it can be known that the i-th additional radial stress σ ri The expression of is as shown in formula (42).

[0212] S62: According to the constructed pile-soil interface contact stress function, according to S2 to S4 and combined with S51 to S54 and S61, the i-th additional radial stress σ can be obtained ri , whose expression is

[0213]

[0214] S63: Accumulate the additional radial stresses at each time to obtain the additional radial stress σ on the cylindrical shear failure surface r , whose expression is

[0215]

[0216] Based on the geometric series summation formula, the common ratio parameter k is set, and the additional radial stress σ on the cylindrical shear failure surface is calculated. ri To obtain the total additional radial stress σ r , whose expression is

[0217]

[0218] S64: Based on the limit summation calculation principle of geometric series, according to the total additional radial stress σ r The additional shear resistance P is obtained r Applicable conditions of the calculation formula; the applicable conditions are that the common ratio parameter k must satisfy 0≤k<1; and then the limit summation calculation formula of the total additional radial stress that satisfies the applicable conditions is obtained, specifically

[0219] In this embodiment, the common ratio parameter k is actually the geometric sequence σ ri In order to discuss the problem of the sum of geometric series limits, the additional radial stress σ r It will not approach infinity and lose its physical meaning. The value of parameter k must be in the interval [0,1). Based on this, the limit sum principle of infinite decreasing geometric series can be used to calculate a certain k value. And this value is not infinite, but finite, and is based on the final additional radial stress σ r , analyze the additional pull-out bearing capacity of the positive screw pile foundation, and discuss the range of the parameter k.

[0220] From μ = tanδ, as well as Will Further rewritten as

[0221]

[0222] It can be seen that the parameter k is the friction angle δ between the pile-soil interface and the internal friction angle of the foundation soil. function. In the field of geotechnical engineering, based on the theoretical basis of soil mechanics and combined with engineering practice experience, one of the shear strength indexes of soil mass based on the Mohr-Coulomb strength criterion, the internal friction angle Its value range is usually between 0 and 48°. In actual engineering, the pile-soil interface friction angle δ generally does not exceed the internal friction angle of the foundation soil In addition, from the perspective of material mechanics, theoretically, the friction coefficient μ between steel and soil does not exceed 1; therefore, fully considering various possible working conditions at the pile-soil interface, it is considered that the value range of the pile-soil interface friction angle δ is between 0 and 45°.

[0223] Taking the pile-soil interface friction angle δ and the internal friction angle of the foundation soil as variables, draw a bivariate three-dimensional surface diagram of the parameter k, as Fig.11 shown;

[0224] From Fig.11 it can be seen that when the interval of is [0, 48] and the interval of δ is [0, 45], the interval of k is [0, 1.24] (retaining two decimal places). First, starting from the mathematical perspective, according to the characteristics of the geometric sequence and combined with Equation (36), Equation (42) and Equation (44), the value of the parameter k is divided into three cases: 1 ≤ k ≤ 1.24, 0 < k < 1, and k = 0; then analyze and discuss according to the actual geotechnical engineering background, describe the physical meaning reflected by different values of the parameter k, and clarify the applicable conditions of the proposed calculation method for the axial ultimate uplift bearing capacity of the positive spiral pile foundation:

[0225] (1) 1 ≤ k ≤ 1.24

[0226] When k = 1, the additional radial stresses σ ri are the same; when 1 < k ≤ 1.24, the additional radial stresses σ ri increase in sequence. Then when 1 ≤ k ≤ 1.24, the additional radial stress σ r on the cylindrical shear failure surface is infinite, and the additional shear resistance P r of the foundation soil calculated by integrating Equation (62) is also infinite, and the obtained uplift resistance P of the positive spiral pile is also infinite, which is obviously not in line with the actual situation physically.

[0227] Therefore, the proposed calculation method for the axial ultimate uplift bearing capacity of the positive spiral pile foundation is not applicable to the case of 1 ≤ k ≤ 1.24. In fact, the combination of the pile-soil interface friction angle δ and the internal friction angle of the foundation soil that satisfies the condition of 1 ≤ k ≤ 1.24 generally does not exist in geotechnical and foundation engineering; in other words, in engineering practice, it is usually difficult to generate an internal friction angle of the foundation soil A state where it is very large but at the same time the pile-soil interface friction angle δ is very small.

[0228] (2) 0 < k < 1

[0229] When 0 < k < 1, each additional radial stress σ ri Forms a decreasing geometric sequence. According to the limit formula for the sum of a decreasing geometric sequence, the additional radial stress σ r As shown in Equation (47), from Equation (52), the total shear resistance P generated by the foundation soil on the cylindrical shear failure surface can be obtained s As shown in Equation (48);

[0230]

[0231]

[0232] (3) k = 0

[0233] According to Equation (46) and Fig.11 It can be known that only when the internal friction angle of the foundation soil Is 0, the value of the parameter k is 0. However, it should be noted at this time that the additional radial stress σ r The value is not 0. From Equation (36), it can be known that the primary additional radial stress σ r1 Can also be written in the form of Equation (49), and at this time the value of σ r1 Is not 0; and from Equation (42), it can be known that for the condition of i ≥ 2, the i-th additional radial stress σ ri The value must be 0. Therefore, the primary additional radial stress σ r1 Is the total additional radial stress σ generated on the cylindrical shear failure surface r , and there is σ r = σ r1 ;

[0234]

[0235] The physical meaning reflected by this situation is that under the axial pulling load condition of the positive spiral pile, although its pulling surface continuously compresses the soil in contact with it and generates an additional radial stress σ r In the soil around the pile, but because the internal friction angle of the foundation soil Is 0 (such as saturated soft clay), the additional uplift resistance P calculated by integrating Equation (54) r Is also 0. Therefore, when the internal friction angle of the foundation soil Is 0, the calculation formula for the shear resistance P on the cylindrical shear failure surface s Is as shown in Equation (50);

[0236] P s = πdlc (50)

[0237] Therefore, based on the Mohr-Coulomb strength criterion, for the internal friction angle When the foundation soil condition is 0, the calculation method proposed in the present invention degenerates into the classical cylindrical shear model, which directly verifies the rationality and accuracy of the analytical solution of the axial ultimate pull-out bearing capacity of the positive spiral pile foundation given in the present invention.

[0238] In summary, the present invention proposes a method for calculating the axial ultimate pull-out bearing capacity of a positive spiral pile foundation, wherein the shear resistance P on the cylindrical shear failure surface in the foundation soil is s The calculation formula given is applicable under the following conditions: Fig.12 That is, the internal friction angle of the foundation soil The combination of the pile-soil interface friction angle δ must satisfy the value range of the parameter k calculated by formula (46) within the interval [0,1);

[0239] Based on the Mohr-Coulomb strength criterion, the additional shear resistance P generated by the foundation soil on the cylindrical shear failure surface is obtained according to the additional radial stress on the cylindrical shear failure surface. r ;

[0240] S7 is based on the theoretical framework of cylindrical shear model, and constructs the calculation formula of the axial ultimate pull-out bearing capacity of the positive spiral pile foundation according to the additional shear resistance, and realizes the calculation of the axial ultimate pull-out bearing capacity of the positive spiral pile foundation in combination with applicable conditions;

[0241] Specifically, the axial ultimate pull-out bearing capacity of the positive screw pile foundation constructed in S7 is calculated as follows:

[0242] P=P s +W P +W s (51)

[0243]

[0244]

[0245]

[0246]

[0247] W p =ρgdtl (56)

[0248] Where: P represents the axial ultimate pull-out bearing capacity of the positive screw pile foundation; P s W represents the shear resistance of the foundation soil on the cylindrical shear failure surface; P W represents the self-weight of the positive screw pile; srepresents the gravity of the soil embedded in the pile structure, i.e., the cylindrical shear failure surface; ρ represents the density of the steel of the pile itself; g represents the acceleration of gravity; Z represents the depth in the foundation soil; γ represents the natural gravity of the foundation soil; t represents the time parameter; P r Represents the additional shear resistance on the cylindrical shear failure surface; P h Represents the shear resistance generated on the cylindrical shear failure surface.

[0249] Although the classical cylindrical shear model underestimates the ultimate pull-out bearing capacity of the spiral pile foundation, when the spiral pile foundation reaches the ultimate bearing capacity under the action of the pull-out load, a cylindrical shear failure surface is indeed generated around the spiral pile in the foundation soil. Therefore, based on the theoretical framework of the classical cylindrical shear model and starting from the shear strength of the soil, the present invention starts from the soil squeezing effect based on the idea of ​​the small pore expansion theory of rock and soil media, and provides a method for determining the ultimate pull-out bearing capacity of the spiral pile foundation and a calculation formula. The theoretical model for calculating the ultimate pull-out bearing capacity of the spiral pile foundation is as follows: Figure 5 ; The cylindrical shear failure surface is coaxial, of the same diameter and at the same height as the pile structure of the spiral pile in the foundation soil. Since the density (heavyness) between steel and soil is quite different, the present invention considers and calculates the contribution of the pile body deadweight and soil gravity to the pull-out resistance separately. Therefore, the ultimate pull-out bearing capacity of the spiral pile foundation consists of three parts: the shear resistance P of the foundation soil on the cylindrical shear failure surface; s , the self-weight of the screw pile W p , and the weight of the soil embedded in the pile structure (surrounded by the cylindrical shear failure surface) W s It is worth noting that the volume of the pile must be excluded when calculating the volume of the soil enclosed by the cylindrical shear failure surface. The gravity of the soil embedded in the pile structure is W s It should be noted that the positive spiral pile usually has a pile shaft and a flange structure above the surface. The present invention only considers the deadweight W of the positive spiral pile within the burial depth range. p .

[0250] Under the axial pull-out loading state, the pull-out surface of the positive spiral pile exerts a compressive effect on the soil in contact with it, thereby generating additional stress in the soil around the pile, which increases the shear strength of the soil based on the Mohr-Coulomb strength criterion. This is different from the classical cylindrical shear model, in that the cylindrical shear failure surface around the positive spiral pile will not only have the initial horizontal ground stress σ h There should also be an additional radial stress σ r Therefore, the shear resistance P sThe calculation of must take into account the effect of this additional radial stress. In fact, unlike the soil squeezing pile defined by the soil squeezing effect during the installation and construction process, the positive spiral pile has a squeezing effect on the foundation soil during the installation and construction process and under axial loading; theoretically, under axial loading, this soil squeezing effect produced by the inner surface of the positive spiral pile on the foundation soil will become more obvious as the degree of pile torsion increases.

[0251] During the axial pull-out loading process, the interface between the pull-out surface and the outer surface of the positive spiral pile shears the foundation soil. Based on the Mohr-Coulomb strength criterion, when the positive spiral pile foundation reaches the ultimate bearing capacity state, the shear resistance P generated on the cylindrical shear failure surface s According to formula (57);

[0252]

[0253]

[0254] σ n =σ h +σ r (59)

[0255] Where: τ s is the shear strength of the foundation soil based on the Mohr-Coulomb strength criterion. It should be noted that it is different from formula (65); σ n is the total radial stress (compressive stress) acting on the cylindrical shear failure surface; σ r It is the additional radial stress on the cylindrical shear failure surface caused by the pulling surface of the positive spiral pile squeezing the soil around the pile.

[0256] Formula (57) can be further written into the form of formula (60);

[0257]

[0258] Where: The first term is the initial horizontal stress σ h The pull-out resistance P generated on the cylindrical shear failure surface h The second term is the additional radial stress σ generated on the cylindrical shear failure surface due to the compression of the soil around the pile by the pulling surface of the positive spiral pile r , which increases the shear resistance calculated based on the Mohr-Coulomb strength criterion. r In the state, an additional pull-out resistance P is generated on the cylindrical shear failure surface. r .

[0259] Therefore, we have the integral formula (61) and formula (62), where the key to the integral calculation of formula (62) is to determine the additional radial stress σ on the cylindrical shear failure surface: r ;

[0260]

[0261]

[0262] Then based on the final additional radial stress σ r , and the calculation formula for the axial ultimate pull-out bearing capacity of the positive screw pile foundation is obtained.

[0263] This embodiment also includes the following prior art knowledge, namely the classic cylindrical shear model of the mainstream screw pile foundation under axial pull-out load and the bearing characteristics of the positive screw pile foundation under axial pull-out load:

[0264] A. Classical cylindrical shear model of mainstream screw pile foundation under axial pullout load:

[0265] Generally, when the pile foundation reaches the ultimate bearing capacity under the action of axial pull-out load, if a cylindrical shear failure mode occurs in the foundation soil around the pile, then the ultimate pull-out bearing capacity of the pile foundation can be calculated based on the cylindrical shear model. The classic cylindrical shear model assumes that under the action of axial pull-out load, the pile itself will not be destroyed, but shear failure will occur on a cylindrical surface around the pile in the foundation soil.

[0266] For the screw nail pile foundation and the spiral blade pile foundation whose pitch meets certain conditions, when the bearing capacity reaches the limit state under the action of axial pull-out load, the foundation soil around the pile will experience cylindrical shear failure. Under the action of axial pull-out load, the spiral structure (spiral blade or thread) of the spiral pile shears the soil around the pile, causing shear failure of the foundation soil; the shear failure gradually expands along the cylindrical surface with the pile axis as the central axis, the spiral structure diameter as the diameter, and the distance between the bottom and top spiral structures as the height; as the pile moves vertically upward, the soil embedded in the spiral structure and the surrounding soil are relatively displaced, and finally a complete cylindrical shear failure surface is formed in the foundation soil.

[0267] Based on the classic cylindrical shear model, the theoretical calculation models for the axial ultimate pullout bearing capacity of two mainstream spiral pile foundations, spiral blade pile and threaded nail pile, are as follows: Figure 2 As shown, Figure 2 (a) Non-continuous spiral blade pile; Figure 2 (b) continuous spiral blade pile; Figure 2 (c) is a screw pile.

[0268] As shown in formula (63), the axial ultimate pull-out bearing capacity P of the mainstream screw pile foundation is mainly composed of three parts: [1-6] , respectively: the shear resistance P generated by the foundation soil on the cylindrical shear failure surface s, the friction resistance P provided by the friction between the pile shaft structure above the top spiral structure and the foundation soil f , and the bearing capacity P contributed by the topmost spiral structure (the spiral structure with one pitch from top to bottom) t It should be noted here that when the diameter of the spiral structure of the screw nail pile is close to the pile shaft diameter in value, the bearing capacity P of the top spiral structure can be ignored. t For the top spiral structure bearing capacity P t There is no unified understanding of the calculation of the spiral blade pile, so we will not introduce it in detail. t For related discussion, please refer to Lutenegger [7] , Nasr [8] With Mohajerani [9] Research work of scholars such as .

[0269] P=P s +P f +P t (63)

[0270]

[0271]

[0272] σ h =K 0 σ v (66)

[0273] σ v =γ′Z (67)

[0274]

[0275] μ=tanδ (69)

[0276] Where: l 1 and d 1 are the length and diameter of the pile shaft within the burial depth range; l 2 and d 2 are the distance between the bottom and top spiral structures and the diameter of the spiral structure respectively; τ s is the shear strength of the foundation soil based on the Mohr-Coulomb strength criterion; c and are the shear strength index of foundation soil, cohesion and internal friction angle; v and σ h are the vertical stress and horizontal stress in the foundation soil respectively; K 0is the static earth pressure coefficient; γ′ is the effective weight of the foundation soil; μ is the friction coefficient between the pile foundation surface and the foundation soil; δ is the friction angle between the pile foundation surface and the foundation soil; Z is the depth inside the foundation soil.

[0277] It should be noted that the gravity W of the soil in the cylindrical shear failure plane is not considered in equation (1). s The weight of the screw pile itself W p Therefore, Lutenegger [7] Based on the cylindrical shear model, for the spiral blade pile foundation in clay soil, the calculation formula for its axial ultimate pullout bearing capacity P is given as formula (70);

[0278] P=P s +P f +P t +W s +W p (70)

[0279] In fact, due to the limitation of the construction load (construction torque) that the construction machinery can provide, the size of spiral blade piles and threaded nail piles is usually not too large. Therefore, in actual engineering, the weight of the pile body W is usually ignored. p The soil gravity W in the cylindrical shear failure plane s The pull-out bearing capacity exerted.

[0280] B. Bearing characteristics of positive screw pile foundation under axial pull-out load

[0281] The positive spiral pile is usually made of a strip steel plate with a slender rectangular cross-section through a twisting process. The two ends of the steel plate in the long axis direction are fixed on the twisting machine respectively, and the steel plate is twisted by applying torque in the long axis direction of the steel plate using the twisting machine. The limitations of the twisting processing method are the maximum torsion capacity (maximum torque) that the torsion machine can provide and the mechanical properties of the steel itself. Of course, some properties of the steel plate will change after twisting (such as stiffness and strength), and excessive twisting may even cause the steel plate to break. Therefore, when using the twisting processing method to manufacture positive spiral piles, in order to prevent excessive plastic deformation of the steel, the angle (twist angle) formed by the edge of the positive spiral pile and the axial direction is usually not made to exceed 45°. On the other hand, at present, positive spiral piles with a torsion angle of 45° are widely used in engineering practice. In addition, Wang et al. (2022)

[10] Research work shows that the positive spiral pile with a torsion angle of 45° performs best in terms of axial bearing capacity. Therefore, the positive spiral piles discussed in the present invention all refer to positive spiral piles with a torsion angle of 45°.

[0282] Previous studies have shown that when the positive screw pile foundation reaches the ultimate bearing capacity under the action of axial pull-out load, a cylindrical shear failure mode will occur in the foundation soil. [11,12] However, the axial ultimate pull-out bearing capacity of the spur helical pile foundation calculated based on the classical cylindrical shear model is much smaller than the measured value in the model test.

[12] The reason is that as the pile moves vertically upward during the pulling process, the positive spiral structure exerts a compressive effect on the surrounding foundation soil, causing additional stress in the horizontal direction in the foundation soil within a certain range around the pile, thereby increasing the radial stress acting on the cylindrical shear failure surface. If only the initial horizontal ground stress is used to calculate the shear resistance on the cylindrical shear failure surface, the axial ultimate pullout bearing capacity of the positive spiral pile foundation will be seriously underestimated.

[0283] This embodiment is based on the classical cylindrical shear model of the mainstream spiral pile foundation under axial pull-out load and the bearing characteristics of the positive spiral pile foundation under axial pull-out load. In the classical cylindrical shear model, the pile structure only produces shearing action on the soil around the pile, and the cylindrical shear failure surface formed in the foundation soil is only affected by the initial horizontal ground stress. The shear strength of the foundation soil based on the Mohr-Coulomb strength criterion is given by formula (3), which can be used to integrally calculate the shear resistance on the cylindrical shear failure surface. Under axial pull-out loading conditions, the spiral structure of the spiral blade pile and the threaded nail pile is limited to shearing on the soil around the pile, so the classical cylindrical shear model can be directly applied to calculate its axial ultimate pull-out bearing capacity. However, for the positive spiral pile foundation under axial pull-out loading conditions, the positive spiral structure not only produces shearing action on the foundation soil, but also exerts extrusion action on the soil around the pile, resulting in the radial stress on the cylindrical shear failure surface being higher than the initial horizontal ground stress. Therefore, the classical cylindrical shear model cannot reasonably and accurately calculate the axial ultimate pull-out bearing capacity of the positive spiral pile foundation. Although the classical cylindrical shear model is not suitable for calculating the axial ultimate pullout bearing capacity of the positive spiral pile foundation, the foundation soil does show a cylindrical shear failure mode when the positive spiral pile foundation under axial pull-out loading reaches the ultimate bearing capacity state. This phenomenon suggests that the calculation method for the axial ultimate pullout bearing capacity of the positive spiral pile foundation can be further derived based on the theoretical framework of the classical cylindrical shear model.

[0284] The present invention provides a method for calculating the axial ultimate pull-out bearing capacity of a positive spiral pile foundation, which has rigorous mathematical logic, clear physical meaning, and is easy to apply in actual engineering. The method can reasonably and accurately determine the axial ultimate pull-out bearing capacity of the positive spiral pile foundation, and can optimize the structural design of the positive spiral pile according to different foundation soil conditions to ensure that the pull-out performance is maximized in engineering. The present invention can provide a theoretical basis and technical reference for the design, construction, and detection of positive spiral piles, and promote them to serve the construction of geotechnical and foundation engineering facilities more safely, reliably, and economically.

[0285] The literature involved in this embodiment is as follows:

[0286] [1] Zhang D J Y, Chalaturnyk R, Robertson P K, et al. Screw anchor test program (part II): field test results and design implication [C]. Proceedings of the 51st Canadian geotechnical conference, Edmonton. 1998, 1: 455 - 461.

[0287] [2] Tappenden K, Sego D, Robertson P. Load Transfer Behavior of Full - Scale Instrumented Screw Anchors [C]. / / American Society of Civil Engineers International Foundation Congress and Equipment Expo 2009 - Contemporary Topics in Deep Foundations. Orlando, Florida, United States, March 15 - 19, 2009: 472 - 479.

[0288] [3] Sakr M. Performance of helical piles in oil sand [J]. Canadian Geotechnical Journal, 2009, 46(9): 1046 - 1061.

[0289] [4] Sakr M. Installation and performance characteristics of high - capacity helical piles in cohesionless soils [J]. DFI Journal - The Journal of the Deep Foundations Institute, 2011, 5(1): 39 - 57.

[0290] [5]Livneh B,El Naggar M H.Axial testing andnumerical modeling ofsquare shaft helicalpiles under compressive and tensile loading[J].CanadianGeotechnical Journal,2008,45(8):1142-1155.

[0291] [6]Hawkins K,Thorsten R.Load Test Results-Large Diameter Helical PipePiles[C]. / / American Society of Civil Engineers International FoundationCongress and Equipment Expo 2009-Contemporary Topics in DeepFoundations.Orlando,Florida,United States,March 15-19,2009:488-495

[0292] [7]Lutenegger A J.Cylindrical shear or plate bearing?Uplift behaviorof multi-helix screw anchors in clay[J].Contemporary Issues in DeepFoundations,2009,185:456-463.

[0293] [8]Nasr M H.Large capacity screw piles[C]. / / Proceedings of theInternational Conference:Future Vision and Challenges forUrban Development.Cairo,Egypt,20-22 December,2004:1-15.

[0294] [9]Mohajerani A, Bosnjak D, Bromwich D.Analysis and design methods of screw piles:A review[J].Soils&Foundations,2016,56(1):115-128.

[0295]

[10] Wang K, Cui C, Ren J, et al.Model testing study on engineering performances of circular helicoid piles during the whole process of installation and bearing in sandy soil[J].Soils and Foundations,2022,62(3):101150.

[0296]

[11] Sato T, Otani J, Mukunoki T.Effect of shaft rotation of drivenspiral pile under pull-out loadings[C] / / Proceedings of the 19th International Conference on Soil Mechanics and Geotechnical Engineering.Seoul,Korea,2017:2853-2856.

[0297]

[12] Atsuo Hirata, Shigeo Furukaji, Seung-seung Kang, Tsuneo Goto. Study on the calculation method of axial resistance of spiral bars based on the interaction behavior with the ground[J]. Resources and Materials, 2005, 121(8):370-377.

[0298]

[13] Wang K, Cui C, ZhangP, et al.Numerical investigation of the installation process and bearing capacity of circular helicoid piles inundrained clay[J].Soils and Foundations,2024,64(1):101411.

[0299]

[14] Yu Haisui, Zhou Guoqing et al., Theory of small pore expansion in rock and soil media[M]. Beijing: Science Press, 2013.

[0300] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the axial ultimate pull-out bearing capacity of a positive screw pile foundation, characterized in that: The specific steps include: S1: Based on the small hole expansion theory of geotechnical media and the differential geometric structure characteristics of the positive screw pile, the pile-soil interface contact normal compressive stress function under the initial horizontal ground stress state is constructed; based on the Coulomb friction law, the contact tangential friction stress function is constructed according to the pile-soil interface contact normal compressive stress function; S2: Obtain the vertical component and horizontal component of the contact stress between the positive screw pile and the foundation soil on the contact surface according to the pile-soil interface contact stress function; S3: Based on the load transfer mechanism of the pile-soil system, the equivalent relationship between the pull-out resistance on the pull-out surface of the positive screw pile and the shear resistance on the cylindrical shear failure surface of the foundation soil is constructed according to the vertical component of the contact stress, so as to obtain the contact normal compressive stress at the edge of the pull-out surface when the positive screw pile foundation reaches the ultimate bearing capacity state under the action of axial pull-out load; S4: According to the contact normal compressive stress and the horizontal component of the contact stress at the edge of the pulling surface, the horizontal force and the circumferential torque of the foundation soil acting on the pulling surface of the positive screw pile are obtained; Based on the moment equivalence principle, the equivalent concentrated load of the horizontal force and its action point are obtained according to the circumferential torque acting on the pulling surface of the positive spiral pile; the radial load of the foundation soil acting on the pulling surface of the positive spiral pile is obtained according to the equivalent concentrated load and its action point; S5: Based on Newton's third law, the radial load reaction force of the positive screw pile pulling surface on the foundation soil is obtained according to the radial load; the additional radial stress on the cylindrical shear failure surface in the foundation soil is obtained according to the radial load reaction force; Based on the Mohr-Coulomb strength criterion and the additional radial stress on the cylindrical shear failure surface, the additional shear resistance generated by the foundation soil on the cylindrical shear failure surface is obtained. S6: Based on the limit sum calculation principle of geometric series, the applicable conditions of the additional shear resistance calculation formula are obtained according to the additional radial stress, and then the limit sum calculation formula of the total additional radial stress that meets the applicable conditions is obtained; S7: Based on the theoretical framework of the cylindrical shear model, the calculation formula for the axial ultimate pullout bearing capacity of the spur spiral pile foundation is constructed according to the limit sum calculation formula of the total additional radial stress, so as to realize the calculation of the axial ultimate pullout bearing capacity of the spur spiral pile foundation.

2. The method for calculating the axial ultimate pull-out bearing capacity of a spur screw pile foundation according to claim 1, characterized in that: The S1 specifically includes the following steps: S11: Based on the small hole expansion theory of geotechnical media and the differential geometric structure characteristics of the positive screw pile, the normal compressive stress function of the pile-soil interface under the initial horizontal ground stress state is constructed as follows: Where: n R0 It represents the contact normal compressive stress at a radial distance R on the pulling surface in a certain cross section of the positive screw pile foundation; n d0 represents the initial horizontal stress σ in the foundation soil h In the state, when the positive screw pile foundation reaches the ultimate bearing capacity state under the action of axial tensile load, the contact normal compressive stress to be solved at the edge of the tensile surface in a certain cross section of the pile-soil system; d represents the spiral structure diameter of the positive screw pile; S12: Based on Coulomb's friction law, the contact tangential friction stress function is constructed according to the contact normal compressive stress function of the pile-soil interface as f R0 =μn R0 Where: μ represents the friction coefficient between the surface of the positive screw pile and the foundation soil; f R0 It represents the contact tangential friction stress between the positive screw pile and the foundation soil on the contact surface.

3. The method for calculating the axial ultimate pull-out bearing capacity of a spur screw pile foundation according to claim 2 is characterized in that: The vertical component and horizontal component of the contact stress between the positive screw pile and the foundation soil on the contact surface obtained in S2 are expressed as q R0 =n R0 sinθ+f R0 cosθ h R0 =n R0 cosθ-f R0 sinθ Where: q R0 represents the vertical component of contact stress; h R0 represents the horizontal component of contact stress; θ represents the torsion angle between the positive screw pile and the foundation soil at a certain point on the contact surface.

4. The method for calculating the axial ultimate pull-out bearing capacity of a spur screw pile foundation according to claim 3 is characterized in that: The S3 specifically includes the following steps: S31: Obtain the vertical force dQ concentrated on a preset micro area with a radial distance R on the pulling surface of the positive spiral pile R0 , then for any preset micro-segment pile-soil system with a longitudinal height of dZ, the pull-out resistance ΔQ acting on the pull-out surface of the positive spiral pile is R0 dQ R0 =q R0 ·dS dS=dR·dl h Where: dS represents the area of ​​any microelement on the pulling surface of the positive spiral pile; dR represents the radial width of the microelement on the pulling surface of the positive spiral pile; dl h represents the length of the spiral line on the side of the microelement of the positive spiral pile pulling surface; p represents the pitch of the positive spiral pile and the positive spiral surface; S32: Based on the vertical component of the contact stress, according to step S31 and combined with the pile-soil interface contact stress function, the pullout resistance ΔQ R0 Rewrite as S33: Obtain the corresponding relationship between the torsion angle α of the positive helical surface and the pitch-to-diameter ratio n: According to the corresponding relationship between the helical torsion angle α and the distance-to-diameter ratio n, the pull-out resistance ΔQ R0 The integral calculation formula is further rewritten as And further rewrite the pull-out resistance ΔQ R0 Integrate to get S34: For a positive helical pile with a torsion angle α of 45°, according to the corresponding relationship between the torsion angle α of the positive helical surface and the distance-to-diameter ratio n, the pull-out resistance ΔQ can be calculated as R0 Simplified to S35: Based on the load transfer mechanism of the pile-soil system, the shear resistance P on the cylindrical shear failure surface under the initial horizontal ground stress state h The pull-out resistance Q on the pull-out surface of the positive screw pile R0 are equal in value; Then, in any preset pile-soil system with a longitudinal height of dZ, the equivalent relationship between the pull-out resistance acting on the pull-out surface of the positive spiral pile and the shear resistance on the cylindrical shear failure surface is obtained as ΔP h =ΔQ R0 Among them, the shear resistance P on the cylindrical shear failure surface is h The expression is Where: l represents the length of the positive screw pile; σ h represents the initial horizontal ground stress; The internal friction angle represents the shear strength index of the foundation soil; c represents the cohesion index of the shear strength index of the foundation soil; S36: Based on the equivalent relationship between the shear resistance on the cylindrical shear failure surface and the pull-out resistance on the positive spiral pile pull-out surface, according to the pull-out resistance ΔQ R0 Shear resistance P on the cylindrical shear failure surface h , solve and obtain the initial horizontal ground stress σ in the foundation soil h In the state, when the positive screw pile foundation reaches the ultimate bearing capacity state under the action of axial tensile load, the contact normal compressive stress at the edge of the tensile surface in any cross section of the pile-soil system is 5. The method for calculating the axial ultimate pull-out bearing capacity of a spur screw pile foundation according to claim 4 is characterized in that: The S4 specifically comprises the following steps: S41: Obtain the horizontal force dH concentrated on a preset small area on the pulling surface of the positive screw pile R0 , then for any preset micro-segment pile-soil system with a longitudinal height of dZ, the horizontal force ΔH acting on the pulling surface of the positive spiral pile is R0 dH R0 =h R0 ·dS S42: According to the horizontal force ΔH R0 Obtain the equivalent concentrated load ΔE0 of the horizontal force on a single drawing surface, and its expression is: S43: Define the pile axis of the positive spiral pile foundation as the rotation axis, and obtain the circumferential torque dM concentrated on a certain preset micro area on the positive spiral pile pulling surface R0 , then for any preset micro-segment pile-soil system with a longitudinal height of dZ, the circumferential torque ΔM0 acting on the pulling surface of the positive spiral pile is dM R0 =R·dH R0 S44: Based on the moment equivalence principle, according to the equivalent concentrated load ΔE0 and the circumferential torque ΔM0, the radial distance b from the action point of the equivalent concentrated load ΔE0 to the pile axis is obtained as S45: Obtain the angle ω between the equivalent concentrated load ΔE0 and its radial load ΔR0 according to the radial distance b to obtain the radial load ΔR0 of the equivalent concentrated load ΔE0, which is expressed as follows:

6. A method for calculating the axial ultimate pull-out bearing capacity of a spur screw pile foundation according to claim 5, characterized in that: The S5 specifically includes the following steps: S51: Based on Newton's third law, the radial load reaction force ΔR′0 of the positive screw pile acting on the foundation soil is obtained; that is, the radial load reaction force ΔR′0 is equal to the radial load ΔR0 in magnitude and opposite in direction; S52: The radial load reaction force ΔR′0 on the two drawing surfaces is evenly distributed on the cylindrical shear failure surface, and it can be obtained 2ΔR′0=πdσ r1 ·dZ Where: r1 It represents the primary additional radial stress generated by the radial load reaction force ΔR′0 on the cylindrical shear failure surface; S53: Based on the radial load ΔR0 and the equivalent concentrated load ΔE0, combined with step S52, the initial horizontal ground stress σ h In the state, due to the compression of the foundation soil by the pulling surface of the positive screw pile, the additional radial stress generated on the cylindrical shear failure surface is σ r1 , that is, the additional radial stress generated on the cylindrical shear failure surface in the foundation soil, and its expression is S54: Based on the Mohr-Coulomb strength criterion, obtain the additional radial stress σ r1 The additional shear resistance P generated by the foundation soil on the cylindrical shear failure surface is r1 , whose expression is 7. A method for calculating the axial ultimate pull-out bearing capacity of a spur screw pile foundation according to claim 6, characterized in that: The S6 specifically comprises the following steps: S61: Based on the small pore expansion theory of rock and soil media, according to the additional shear resistance P r1 It can be obtained that the additional radial stress σ r1 In the state, the additional contact normal compressive stress n is applied to any cross section of the pile-soil system. R1 and additional contact tangential friction stress f R1 ; Based on the pile-soil interface contact normal compressive stress function and contact tangential friction stress function, according to S2 to S4 combined with S51 to S53, the additional radial stress σ r1 In the state, due to the compression of the foundation soil by the pulling surface of the positive screw pile, the secondary additional radial stress σ is generated on the cylindrical shear failure surface. r2 , whose expression is S62: According to the constructed pile-soil interface contact stress function, according to S2 to S4 and combined with S51 to S54 and S61, the i-th additional radial stress σ can be obtained ri , whose expression is S63: Accumulate each additional radial stress to obtain the additional radial stress σ on the cylindrical shear failure surface r , whose expression is Based on the geometric series summation formula, the common ratio parameter k is set, and the additional radial stress σ on the cylindrical shear failure surface is calculated. ri To obtain the total additional radial stress σ r , whose expression is S64: Based on the limit summation calculation principle of geometric series, according to the total additional radial stress σ r The additional shear resistance P is obtained r Applicable conditions of the calculation formula; The applicable condition is that the common ratio parameter k must satisfy 0≤k<1; Then the limiting summation formula of the total additional radial stress that meets the applicable conditions is obtained as follows:

8. A method for calculating the axial ultimate pull-out bearing capacity of a spur screw pile foundation according to claim 7, characterized in that: The calculation formula for the axial ultimate pull-out bearing capacity of the positive screw pile foundation constructed in S7 is P = P s +W P +W s Where: P represents the axial ultimate pull-out bearing capacity of the positive screw pile foundation; P s W represents the shear resistance of the foundation soil on the cylindrical shear failure surface; P Represents the self-weight of the positive screw pile; W s represents the gravity of the soil embedded in the pile structure, i.e., the cylindrical shear failure surface; ρ represents the density of the steel of the pile itself; g represents the acceleration of gravity; Z represents the depth in the foundation soil; γ represents the natural gravity of the foundation soil; t represents the thickness of the pile; P r Indicates the additional radial stress σ r The additional shear resistance on the cylindrical shear failure surface under the action of h It represents the shear resistance generated on the shear failure surface of the cylinder under the initial horizontal ground stress state.

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