A calculation method for the axial ultimate pull-out bearing capacity of positive spiral pile foundation

Abstract

The present invention discloses a method for calculating the axial ultimate pullout bearing capacity of a positive spiral pile foundation, comprising constructing a pile-soil interface contact normal compressive stress function and a contact tangential friction stress function; constructing an equivalent relationship between the pullout resistance on the positive spiral pile pullout surface and the shear resistance on the cylindrical shear failure surface of the foundation soil, obtaining the horizontal force and circumferential torque of the soil acting on the positive spiral pile pullout surface; obtaining the equivalent concentrated load of the horizontal force and its action point; obtaining the radial load acting on the positive spiral pile pullout surface of the foundation soil, obtaining the additional radial stress on the cylindrical shear failure surface of the foundation soil; obtaining the applicable conditions of the additional shear resistance calculation formula based on the additional radial stress limit summation calculation formula; constructing a calculation formula for the axial ultimate pullout bearing capacity of the positive spiral pile foundation, and obtaining the calculation formula for the axial ultimate pullout bearing capacity of the positive spiral pile foundation. The method solves the problem that existing methods cannot accurately obtain the axial ultimate pullout bearing capacity of the positive spiral pile foundation.

Description

Technical Field

[0001] The present 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, a reasonable and accurate assessment of the bearing capacity of pile foundations is of great significance. The bearing capacity of pile foundations is directly related to the stability and safety of the superstructure. Accurate assessment of pile foundation bearing capacity can prevent major accidents such as structural instability, tilting, or collapse. Proper assessment of pile foundation bearing capacity can optimize design, avoid unnecessary costs caused by conservative designs and safety hazards caused by risky designs, and effectively control project costs while ensuring safety. Proper assessment of pile foundation bearing capacity helps to promptly identify potential problems during construction, ensuring that construction quality meets design requirements, thereby improving the quality of the entire project. It also reduces the environmental impact of construction and avoids material waste. Accurate assessment of pile foundation bearing capacity can also extend the service life of buildings or structures, reducing the need for repairs and reinforcement work during operation due to foundation problems. Accurate assessment of pile foundation bearing capacity is particularly important in complex geological conditions. It can help select the appropriate pile type and construction method, ensuring the reliability and safety of the foundation. Evaluating pile foundation bearing capacity in accordance with building codes and regulations 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 projects, and has a significant impact on project safety, cost control, environmental protection, and regulatory compliance.

[0003] Helical piles (spiral blade piles, threaded nail piles, and bored and 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 pile types used in engineering practice. Special-shaped piles are used in engineering construction to increase the pile-soil contact area, improve the pile-soil interaction, and optimize load sharing between the pile and soil. This aims to enhance the bearing capacity and stability of the pile-soil system, while reducing deformation and settlement, thereby reducing project costs, improving project reliability, and extending the service life of the project. Unlike traditional pile foundations, which have geometric shapes such as cylinders, tori, or rectangular blocks, special-shaped piles have irregular structures, making the reasonable and accurate assessment of the bearing capacity of various special-shaped pile foundations a major challenge in engineering practice. The positive helical pile, a new special-shaped pile type that has emerged in the past decade, 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 yet 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 their excellent axial compressive and pull-out bearing capacity. They can provide higher axial compressive 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, resulting in 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 twisting structure of the positive spiral pile results in a soil squeezing effect within the buried depth range of the pile during installation and under load. The geometric nonlinearity, material nonlinearity, and contact nonlinearity caused by the large deformation of the foundation soil due to the pile-soil interaction far exceed the assumptions of axisymmetry, plane strain, and small deformation.

[0005] Therefore, under contradictory assumptions, classical theoretical methods such as the circular hole expansion theory, strain path method, bearing capacity theory, shear displacement method, and load transfer method are no longer directly applicable to analyzing pile-soil interaction problems involving positive spiral piles or providing analytical solutions to the penetration resistance and bearing capacity of positive spiral piles. Furthermore, in the classical cylindrical shear model, the calculation of the axial ultimate pullout bearing capacity of the pile foundation only considers the initial horizontal in-situ stress of the foundation soil. This model is suitable for pile types that do not produce a lateral compression effect on the surrounding soil during the pile extraction process, such as spiral blade piles and threaded steel piles. However, under axial pullout loads, positive spiral piles will compress the surrounding soil, resulting in additional radial stress in the foundation soil. Because the classical cylindrical shear model ignores this effect, it seriously underestimates the axial ultimate pullout bearing capacity of the positive spiral pile foundation. 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, so as 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 spur screw pile foundation comprises the following steps:

[0009] S1: Based on the pore 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. Based on the Coulomb friction law, the contact tangential friction stress function of the pile-soil interface is constructed from the 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, an equivalent relationship between the pullout resistance on the pullout surface of the positive spiral 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. This is to obtain the contact normal compressive stress at the edge of the pullout surface when the positive spiral pile foundation reaches the ultimate bearing capacity state under the action of axial pullout load;

[0012] S4: Based on 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 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, a 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 pore expansion theory of geotechnical media and the differential geometric structure characteristics of the positive spiral 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 of a certain cross section of the positive screw pile foundation; n d0 Indicates 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 a certain cross section of the pile-soil system; d represents the diameter of the spiral structure of the positive spiral pile;

[0022] S12: Based on Coulomb 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 small 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 pulling surface of the positive spiral pile; 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 pull-out 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 Integral to get

[0043]

[0044] S34: For a positive spiral pile with a torsion angle α of 45°, the pull-out resistance ΔQ can be calculated based on the corresponding relationship between the positive spiral surface torsion angle α and the distance-to-diameter ratio n.R0 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 numerically equal;

[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 spiral 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 equivalence 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 The 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 action of 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 ΔE0 of the horizontal force on a single drawing surface, and its 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 small 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

[0061] dM R0 =R·dH R0

[0062]

[0063] 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

[0064] 2ΔE0b=ΔM0

[0065]

[0066] 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:

[0067]

[0068] ΔR0=ΔE0cosω。

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

[0070] 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 in magnitude and opposite in direction to the radial load ΔR0;

[0071] S52: The radial load reaction force ΔR′0 on the two drawing surfaces is evenly distributed on the cylindrical shear failure surface, and the

[0072] 2ΔR′0=πdσ r1 ·dZ

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

[0074] S53: Based on the radial load ΔR0 and the equivalent concentrated load ΔE0, 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 spiral 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 step S6 specifically includes the following steps:

[0079] S61: Based on the pore expansion theory of geotechnical 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, the additional radial stress σ is obtained according to S2 to S4 combined with S51 to S53. r1 In the state, the secondary additional radial stress σ is generated on the cylindrical shear failure surface due to the compression of the foundation soil by the pulling surface of the positive spiral pile. r2 , whose expression is

[0081]

[0082] S62: Based on the constructed pile-soil interface contact stress function, the i-th additional radial stress σ can be obtained according to S2 to S4 and combined with S11 to S54 and S61. 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 summation formula of geometric series, and setting the common ratio parameter k, and according to the additional radial stress σ on the cylindrical shear failure surface 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 Get the additional shear resistance P 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 limit summation calculation 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 ultimate axial pull-out bearing capacity of the spur screw pile foundation; P s W represents the shear resistance of 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 density 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 P 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 pore expansion in geotechnical 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 force 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 ultimate 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 sum 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 sum 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 of 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 is a brief introduction to 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 any creative labor.

[0103] Figure 1 This is a flow chart of the method for calculating the axial ultimate pull-out bearing capacity of a spur spiral pile foundation according to 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 the theoretical model for calculating the ultimate pull-out bearing capacity of the spur screw pile foundation in this embodiment;

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

[0109] Figure 7 Schematic diagram of the vertical displacement ΔD generated by the positive spiral pile and the space ah squeezed out by the microelement ad on the pulling surface in the foundation soil when the positive spiral 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] Figure 9 Schematic diagram of the effect of contact stress on the drawing surface in this embodiment;

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

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

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

[0115] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall 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 pore 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. Based on the Coulomb friction law, the contact tangential friction stress function of the pile-soil interface is constructed from the 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 the positive spiral pile and their external normal directions: Figure 3 (a) is a schematic diagram of the surface classification of positive spiral piles; Figure 3 (b) is a schematic diagram of the normal direction of the out-of-plane drawing; 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 direction of the outer normal of the bottom surface

[13] Schematic diagram;

[0119] like Figure 4 Schematic diagram showing 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 parametric equations of the positive helical surface in the spatial rectangular coordinate system are as follows (1) and (2). The degree of twist 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 4b (spatial rectangular coordinate system) and formula (3). In actual engineering, the geometric characteristic of the positive spiral pile structure is that the thickness t is much smaller than the diameter d and length l, so it is reasonable to analyze it as a positive spiral surface with zero thickness to a certain extent. 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 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 based on the classic cylindrical shear model. The error caused by this simplified treatment is usually acceptable and ignored in engineering practice.

[0120]

[0121] Consider that there is only the initial horizontal stress σ on the cylindrical shear failure surface h Action situation: 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 originally in contact with it until it separates, while the pull-out surface continues to squeeze the foundation soil 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 force interaction 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 transferred to the tensile 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 spiral 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 spiral surface is.

[0126] dS=dR·dl h (5)

[0127] During the axial pulling loading process, the pulling surface of the positive spiral pile continuously squeezes the foundation soil in contact with it. On the pulling surface side of the positive spiral pile, points with different radial distances (from the pile axis) exert different degrees of squeezing 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 action of axial tensile load, the vertical displacement generated by the positive screw pile is set as ΔD; then Figure 6The space squeezed out by the pulling surface of the spiral microelement ad in the foundation soil is a hexahedron ah, and its volume ΔV is:

[0128] ΔV=sinθ·ΔD·dS (6) and 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. The larger the radial distance R, the larger the space squeezed out of the micro area (such as microelement ad) in the foundation soil. The pore expansion theory of geotechnical media believes that the pore expansion pressure inside the geotechnical 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 In the state, when the positive screw pile foundation reaches the ultimate bearing capacity state under the action of axial tensile load, in any cross section of the pile-soil system, the contact normal compressive stress at the edge of the tensile surface is set to n d0 Based on the theoretical framework of pore expansion in geotechnical 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 (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 Indicates the initial horizontal stress σ in the foundation soil hIn 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 is the diameter of the spiral structure of the positive spiral pile foundation; μ is 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 As shown. 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 Figure 9 As shown, Figure 9 (a) Schematic diagram of the effect of contact normal compressive stress; Figure 9 (b) Schematic diagram of the effect of contact tangential friction stress; Figure 9 (c) Schematic diagram of the vertical and horizontal components of contact stress.

[0137] Depend on Figure 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 spiral 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, an equivalent relationship between the pullout resistance on the pullout surface of the positive spiral 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. This is to obtain the contact normal compressive stress at the edge of the pullout surface when the positive spiral pile foundation reaches the ultimate bearing capacity state under the action of axial pullout load;

[0142] S31: Obtain the vertical force dQ concentrated on a preset small 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 small segment of the 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 pulling surface of the positive spiral pile; 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 pull-out 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 is d0 It 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 Integral to get

[0155]

[0156] S34: For a positive spiral pile with a torsion angle α of 45°, the pull-out resistance ΔQ can be calculated based on the corresponding relationship between the positive spiral surface torsion angle α and the distance-to-diameter ratio n. 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 The contact stress is transferred 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 h The expression is

[0161]

[0162] Where: l represents the length of the positive spiral pile; σ h represents the initial horizontal ground stress; The friction angle is the shear strength index of the foundation soil; c is 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 equivalence 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 The shear resistance P on the cylindrical shear failure surface h , solve and obtain the initial horizontal stress σ of the foundation soil hIn 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: Based on the contact normal compressive stress and the horizontal component of the contact stress at the edge of the pull-out surface, the horizontal force and circumferential torque acting on the pull-out surface of the positive spiral pile are obtained. Based on the moment equivalence principle, the equivalent concentrated load of the horizontal force and its action point are obtained from the circumferential torque acting on the pull-out surface of the positive spiral pile. Based on the equivalent concentrated load and its action point, the radial load acting on the pull-out surface of the positive spiral pile by the foundation soil is obtained.

[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 spiral 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 ΔE0 of the horizontal force on a single drawing surface, and its 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 small 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

[0178] dM R0 =R·dH R0 (29)

[0179]

[0180] 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

[0181] 2ΔE0b=ΔM0 (31)

[0182]

[0183] 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:

[0184]

[0185] ΔR0=ΔE0cosω (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, 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 in magnitude and opposite in direction to the radial load ΔR0;

[0189] S52: The radial load reaction force ΔR′0 on the two drawing surfaces is evenly distributed on the cylindrical shear failure surface, and the

[0190] 2ΔR′0=πdσ r1 ·dZ (35)

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

[0192] S53: Based on the radial load ΔR0 and the equivalent concentrated load ΔE0, 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 spiral 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 Figure 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 transferred 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 in the state r1 , which is also transmitted to the surface of the positive spiral pile in the form of additional contact stress, then based on the pore expansion theory of geotechnical 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 in the state 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 in the state r1 , which is transferred 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 Figure 9 To express, no further details are given here.

[0204] The additional radial stress σ r1 Under the condition, in any cross section of the pile-soil system, the contact normal compressive stress at the edge of the straight screw 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 based on the same principle. 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 transferred 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 equivalence relation is

[0207] ΔP r1 =ΔQ R1 (40)

[0208] And the additional shear resistance P r1 and additional pull-out resistance ΔQR1 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 the same as obtaining the additional radial stress σ r1 The derivation process is the same as that of , and 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 ;

[0211] In this embodiment, the “additional contact normal compressive stress n d1 "The calculation process involved in the following is omitted, because from the derivation process of formula (8) to formula (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 exhaustive examples. Therefore, the following statement is made: "By analogy, it can be known that the i-th additional radial stress σ ri The expression is as shown in formula (42).

[0212] S62: Based on the constructed pile-soil interface contact stress function, the i-th additional radial stress σ can be obtained according to S2 to S4 and combined with S51 to S54 and S61. 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 summation formula of geometric series, and setting the common ratio parameter k, and according to the additional radial stress σ on the cylindrical shear failure surface ri To obtain the total additional radial stress σr , 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 Get the additional shear resistance P 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 meets the applicable conditions is obtained, specifically

[0219] In this embodiment, the common ratio parameter k is actually the geometric progression σ ri In order to discuss the problem of the sum of the limit of geometric series, 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 value 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. In the field of geotechnical engineering, based on the theoretical foundation of soil mechanics and combined with engineering practice experience, the internal friction angle is one of the shear strength indicators of soil based on the Mohr-Coulomb strength criterion. Its value range is usually between 0 and 48 degrees. In actual engineering, the pile-soil interface friction angle δ is generally not greater than 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 will not be greater than 1; therefore, taking into full consideration the various working conditions that may exist at the pile-soil interface, it is believed that the value range of the pile-soil interface friction angle δ is between 0 and 45°.

[0223] The pile-soil interface friction angle δ and the internal friction angle of the foundation soil For variables, draw a bivariate three-dimensional surface plot of parameter k, such as Figure 11 As shown;

[0224] Depend on Figure 11 It can be seen that when When the interval of is [0, 48] and the interval of δ is [0, 45], the interval of k is [0, 1.24] (rounded to two decimal places). First, from a mathematical perspective, according to the characteristics of the geometric sequence and combined with Equation (36), Equation (42) and Equation (44), the value range of the parameter k is divided into three cases: 1 ≤ k ≤ 1.24, 0 < k < 1, and k = 0; then, an analysis and discussion are carried out in view of the actual geotechnical engineering background, the physical meaning reflected by different value cases of the parameter k is described, and the applicable conditions of the calculation method for the axial ultimate uplift bearing capacity of the positive spiral pile foundation proposed by the present invention are clarified:

[0225] (1) 1 ≤ k ≤ 1.24

[0226] When k = 1, each additional radial stress σ ri is the same; when 1 < k ≤ 1.24, the additional radial stress σ ri increases successively. 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 calculation method for the axial ultimate uplift bearing capacity of the positive spiral pile foundation proposed by the present invention 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 a state where the internal friction angle of the foundation soil is very large but the pile-soil interface friction angle δ is very small at the same time.

[0228] (2) 0 < k < 1

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

[0230]

[0231]

[0232] (3) k = 0

[0233] According to formula (46) and Figure 11 It can be seen that the internal friction angle of the foundation soil is When it is 0, the value of parameter k is 0. However, it should be noted that the additional radial stress σ r The value of is not 0. From formula (36), we can know that the primary additional radial stress σ r1 It can also be written in the form of formula (49), in which case σ r1 The value of is not 0; and from formula (42), for the condition i≥2, the i-th additional radial stress σ ri The value of must be 0. Therefore, the additional radial stress σ r1 It is the total additional radial stress σ generated on the cylindrical shear failure surface r , there is σ r =σ r1 ;

[0234]

[0235] The physical meaning of this situation is that under the axial pull-out loading condition, although the pull-out surface of the positive spiral pile continues to squeeze the soil in contact with it, and generates additional radial stress σ in the soil around the pile r , but because of the internal friction angle of the foundation soil is 0 (such as saturated soft clay), so the additional pull-out resistance P calculated by integrating Equation (54) is r Also equal to 0. Therefore, when the internal friction angle of the foundation soil is When it is 0, the shear resistance P on the cylindrical shear failure surface s The calculation formula is as shown in formula (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 spur 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: Figure 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] Based on the theoretical framework of the cylindrical shear model, S7 constructs a calculation formula for the axial ultimate pullout bearing capacity of the spur spiral pile foundation according to the additional shear resistance, and realizes the calculation of the axial ultimate pullout bearing capacity of the spur spiral pile foundation in combination with applicable conditions;

[0241] Specifically, the calculation formula for the axial ultimate pull-out bearing capacity of the spur screw pile foundation constructed in S7 is:

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

[0243]

[0244]

[0245]

[0246]

[0247] W p =ρgdtl (56)

[0248] Where: P represents the ultimate axial pull-out bearing capacity of the spur screw pile foundation; P s W represents the shear resistance of 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 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, and based on the idea of ​​the small pore expansion theory of rock and soil media and the soil squeezing effect of the pile body, the present invention 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 ; Among them, 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. Due to the large difference in density (heavyness) between steel and soil, the present invention considers and calculates the contribution of the pile body's deadweight and the soil body's 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 surrounded by the cylindrical shear failure surface. The weight of the soil embedded in the pile structure, W s It should be noted that the positive spiral pile usually has a pile shaft and 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 axial tensile loading, the tensile 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 stress σ h There should also be an additional radial stress σ r Therefore, the shear resistance P s The calculation of the load must take into account the effects of this additional radial stress. In fact, unlike soil-squeezing piles, which are defined by the soil-squeezing effect produced during installation and construction, positive spiral piles exert a squeezing effect on the foundation soil during installation and construction, as well as under axial loading. In theory, under axial loading, this soil-squeezing effect produced by the inner surface of the positive spiral pile on the foundation soil becomes more pronounced as the degree of pile torsion increases.

[0251] During the axial pull-out loading process, the intersection of 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 is 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 generated by the pulling surface of the positive spiral pile squeezing the soil around the pile.

[0256] Formula (57) is 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 in the state 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, that is, when the additional radial stress σ 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 spiral 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 spur 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 a pile foundation reaches its ultimate bearing capacity under axial pullout loads, if a cylindrical shear failure mode occurs within the foundation soil surrounding the pile, the ultimate pullout bearing capacity of the pile foundation can be calculated based on the cylindrical shear model. The classic cylindrical shear model assumes that under axial pullout loads, the pile itself does not fail, but rather shear failure occurs on a cylindrical surface within the foundation soil surrounding the pile.

[0266] For screw-nail pile foundations and spiral blade pile foundations with a pitch that meets certain requirements, cylindrical shear failure occurs in the foundation soil surrounding the pile when the pile reaches its ultimate bearing capacity under axial pullout load. Under the action of axial pullout load, the spiral structure (spiral blades or threads) of the screw pile shears the soil around the pile, inducing shear failure in the foundation soil. The shear failure gradually propagates along a cylindrical surface centered on the pile axis, with the diameter of the spiral structure as its diameter, and the distance between the bottom and top spiral structures as its height. As the pile moves vertically upward, the soil embedded in the spiral structure shifts relative to the surrounding soil, ultimately forming a complete cylindrical shear failure surface 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 piles and threaded nail piles, 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 top 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 diameter of the pile shaft, the bearing capacity of the top spiral structure P 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 here. 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 =K0σ v (66)

[0273] σ v =γ′Z (67)

[0274]

[0275] μ=tanδ (69)

[0276] Where: l1 and d1 are the length and diameter of the pile shaft within the burial depth range; l2 and d2 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 foundation soil based on the Mohr-Coulomb strength criterion; c and are the shear strength index of foundation soil, cohesion and internal friction angle; σ v and σ h are the vertical stress and horizontal stress in the foundation soil, respectively; K0 is 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; and Z is the depth within the foundation soil.

[0277] It should be noted that the gravity W of the soil within 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, the calculation formula for the axial ultimate pull-out bearing capacity P of the spiral blade pile foundation in clay soil is given as Equation (70);

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

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

[0280] B. Bearing characteristics of spur screw pile foundation under axial pullout load

[0281] A positive spiral pile is usually made of a strip of 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 to a twisting machine, and the steel plate is twisted by applying torque in the long axis direction using the twisting machine. The limitations of the twisting processing method lie in the maximum torsional capacity (maximum torque) that the torsional machine can provide and the mechanical properties of the steel itself. Of course, after the steel plate is twisted, some of its material properties will change (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 between 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 has shown that positive spiral piles with a torsion angle of 45° perform best in terms of axial bearing capacity. Therefore, the positive spiral piles discussed in this invention all refer to positive spiral piles with a torsion angle of 45°.

[0282] Studies have shown that when the positive spiral 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 for this is that as the pile moves vertically upward during the pull-out process, the positive spiral structure compresses the surrounding foundation soil, causing additional horizontal stress in the foundation soil within a certain range around the pile. This in turn increases the radial stress acting on the cylindrical shear failure surface. If only the initial horizontal in-situ stress is used to calculate the shear resistance on the cylindrical shear failure surface, the axial ultimate pull-out bearing capacity of the positive spiral pile foundation will be severely 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 a shear effect 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 screw nail pile has only a shear effect 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 a shear effect on the foundation soil, but also exerts a compressive effect 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 ultimate axial pullout bearing capacity of a spur helical pile foundation, the foundation soil does exhibit a cylindrical shear failure mode when the spur helical pile foundation reaches its ultimate bearing capacity under axial pullout loading. This phenomenon suggests that a calculation method for the ultimate axial pullout bearing capacity of a spur helical pile foundation can be derived based on the theoretical framework of the classical cylindrical shear model.

[0284] The present invention provides a method for calculating the axial ultimate pullout bearing capacity of a positive spiral pile foundation, which has rigorous mathematical logic, clear physical meaning, and is easy to apply in practical engineering projects. This method can reasonably and accurately determine the axial ultimate pullout bearing capacity of a positive spiral pile foundation and optimize the structural design of the positive spiral pile based on different foundation soil conditions to ensure that its pullout performance is maximized in engineering projects. This invention can provide a theoretical basis and technical reference for the design, construction, and testing of positive spiral piles, promoting their safer, more reliable, and more economical use in geotechnical and foundation engineering facility construction.

[0285] The documents involved in this embodiment are as follows:

[0286] [1] Zhang DJY, Chalaturnyk R, Robertson PK, 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 EngineersInternational Foundation Congress and Equipment Expo 2009-Contemporary Topicsin Deep Foundations.Orlando,Florida,United States,March 15-19,2009:472-479.

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

[0289] [4]Sakr M.Installation and performance characteristics of highcapacity helical piles in cohesionless soils[J].DFI Journal-TheJournal of theDeep 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 ofscrew 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 performance 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] Atsushi Hirata, Shigeo Furukaji, Jiang Shengcheng, Tsunero Goto. Research on directional resistance calculation method Kaguki [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., Translated. 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 above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above 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 spur screw pile foundation, characterized in that: The specific steps include: S1: Based on the pore 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. Based on the Coulomb friction law, the contact tangential friction stress function of the pile-soil interface is constructed from the 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, an equivalent relationship between the pullout resistance on the pullout surface of the positive spiral 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. This is to obtain the contact normal compressive stress at the edge of the pullout surface when the positive spiral pile foundation reaches the ultimate bearing capacity state under the action of axial pullout load; S4: Based on 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 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, a 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: Said S1 specifically comprises the following steps: S11: Based on the small pore expansion theory of geotechnical media and the differential geometric structure characteristics of the positive spiral 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 of a certain cross section of the positive screw pile foundation; n d0 Indicates 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 a certain cross section of the pile-soil system; d represents the diameter of the spiral structure of the positive spiral pile; S12: Based on Coulomb 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, 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 small 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 pulling surface of the positive spiral pile; 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 pull-out 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 Integral to get S34: For a positive spiral pile with a torsion angle α of 45°, the pull-out resistance ΔQ can be calculated based on the corresponding relationship between the positive spiral surface torsion angle α and the distance-to-diameter ratio n. 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 spiral 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 equivalence 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 The shear resistance P on the cylindrical shear failure surface h , solve and obtain the initial horizontal stress σ of 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 includes 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 small 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. The 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 in magnitude and opposite in direction to the radial load ΔR0; S52: The radial load reaction force ΔR′0 on the two drawing surfaces is evenly distributed on the cylindrical shear failure surface, and the 2ΔR′0=πdσ r1 ·dZ Where: σ 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 stress σ h In the state, due to the compression of the foundation soil by the pulling surface of the positive spiral 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. The 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 includes the following steps: S61: Based on the pore expansion theory of geotechnical 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 is obtained. r1 In the state, the secondary additional radial stress σ is generated on the cylindrical shear failure surface due to the compression of the foundation soil by the pulling surface of the positive spiral pile. r2 , whose expression is S62: Based on the constructed pile-soil interface contact stress function, the i-th additional radial stress σ can be obtained according to S2 to S4 and combined with S51 to S54 and S61. ri , whose expression is 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 Based on the summation formula of geometric series, and setting the common ratio parameter k, and according to the additional radial stress σ on the cylindrical shear failure surface 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 Get the additional shear resistance P r Applicable conditions of the calculation formula; The applicable condition is that the common ratio parameter k must satisfy 0≤k<1; Then the limit summation calculation formula of the total additional radial stress that meets the applicable conditions is obtained as follows:

8. The 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 spiral pile foundation constructed in S7 is P = P s +W P +W s Where: P represents the ultimate axial pull-out bearing capacity of the spur screw pile foundation; P s W represents the shear resistance of 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 density 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 P 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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