Method for calculating axial ultimate pulling resistance and pulling torque of positive screw pile foundation

Abstract

The invention discloses a method for calculating axial ultimate pulling resistance and pulling resistance torque of a positive screw pile foundation, which comprises the following steps of: constructing a corresponding control equation and a boundary condition to solve and obtain a stress component of a plastic zone; the incidence relation between the outer radius of the plastic zone and the current small hole radius and small hole pressure is obtained; the behavior that the pulling surface of the positive screw pile extrudes soil around the pile under the action of axial pulling load is equivalent to the problem of round hole expansion, and the vertical and horizontal soil squeezing effects are regarded as the expansion process of a spherical hole and the expansion process of a cylindrical hole respectively; on the basis of a cylindrical hole expansion model with a non-zero initial radius, the reaming pressure is determined to correct a classic cylindrical shear model, so that the radial stress effect generated on a cylindrical shear failure surface due to the soil squeezing effect of a drawing surface is considered, and the uplift bearing capacity of the positive screw pile is accurately calculated; and the self-strengthening function of the positive screw pile is also explained theoretically.

Description

Technical Field

[0001] This invention relates to the field of calculation technology for the pull-out bearing capacity of pile foundations in geotechnical engineering, and in particular to a method for calculating the axial ultimate pull-out force and pull-out torque of a positive spiral pile foundation. Background Technology

[0002] In geotechnical and foundation engineering, assessing the bearing capacity of pile foundations is a critical technical issue in foundation design and construction, directly impacting the structural performance and long-term stability. The rationality of the bearing capacity assessment not only affects pile type selection, structural parameter determination, and construction process formulation, but also plays a vital role in preventing excessive deformation or structural instability caused by improper bearing capacity estimation. Through scientific bearing capacity analysis, design schemes can be optimized while meeting safety requirements, avoiding safety hazards or increased project costs due to design deviations. In engineering sites with complex geological conditions, accurate bearing capacity evaluation is particularly important for improving the reliability and applicability of foundation engineering, and is also a crucial guarantee that engineering design and construction meet relevant specifications.

[0003] In existing technologies, research on positive helical piles mainly focuses on model tests. [3, 4] (For example, considering the impact of installation method, pile structure, and soil conditions on installation resistance and axial bearing capacity) [5-12] Influence), in-situ test

[13] or finite element simulation [14-16] A few studies involved horizontal bearing capacity analysis. [3, 4] However, no method has yet been developed to accurately calculate the axial ultimate tensile strength of a positive spiral pile. Engineering practice shows that the ultimate tensile strength of a positive spiral pile is much higher than the theoretical calculation value based on the classical cylindrical shear model; this phenomenon is known as "self-reinforcing function." [2, 17] This phenomenon is precisely why a reasonable and accurate method for calculating the pull-out bearing capacity of spiral piles has not yet been developed. In engineering projects, in-situ load tests are required to determine the pull-out bearing capacity of spiral piles, which not only consumes a large amount of resources but also severely restricts the global promotion and application of spiral piles. Furthermore, the classic cylindrical shear model assumes that shear action only occurs on the soil during pile pull-out. [1, 10] Ignoring the additional radial stress generated by the pull-out surface of the helical pile compressing the surrounding soil, and calculating the shear strength of the cylindrical shear failure surface based solely on the initial horizontal ground stress, results in calculated values ​​that are far lower than measured values. [2, 10, 11] This cannot reflect the "self-reinforcing function." In addition, although the existing small pore expansion theory of soil and rock media has been applied to the bearing capacity calculation of structures such as plate anchors and helical blade piles, a mathematical and physical model has not yet been established based on the pile-soil interaction mechanism of positive helical piles to form a systematic calculation scheme for their pull-out bearing capacity. Therefore, the technical problem of accurately calculating the pull-out bearing capacity of positive helical piles still cannot be solved. Summary of the Invention

[0004] This invention provides a method for calculating the axial ultimate pull-out force and pull-out torque of a positive helical pile foundation, in order to overcome the above-mentioned technical problems.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows: A method for calculating the axial ultimate pull-out force and pull-out torque of a positive helical pile foundation, comprising the following steps: S1: The pull-out surface of the spiral pile is considered as the elastic zone, and the surrounding soil as the plastic zone. Based on the small-hole expansion theory, the behavior of the spiral pile pull-out surface squeezing the surrounding soil under axial tensile load is equivalent to a circular hole expansion problem. The strength yield criterion is used to construct the corresponding governing equations and boundary conditions. S2: Solve and obtain the stress components in the plastic region according to the governing equations and boundary conditions; and the stress components in the plastic region include radial stress and tangential stress; By utilizing the continuity of stress components at the elastic-plastic interface, the integral constant is obtained based on the radial stress and tangential stress. S3: Based on boundary conditions, obtain the correlation between the outer radius of the plastic zone and the current orifice radius and orifice pressure according to radial stress and integral constant; S4: The compressive force of the helical pile on the surrounding soil during pull-out is decomposed into vertical and horizontal components. Equivalent characterization is performed using a spherical hole expansion model and a cylindrical hole expansion model to obtain the vertical spherical hole and the horizontal cylindrical hole. It is also set that the vertical spherical hole and the horizontal cylindrical hole expand synchronously during axial pull-out loading. Based on the small hole expansion theory, it is confirmed that when the vertical spherical hole expands to the point where the radius of the plastic zone meets the set conditions, the helical pile reaches the ultimate limit state of axial pull-out bearing capacity. Based on the pile diameter and the radius of the plastic zone of the helical pile, the internal pressure of the small hole at the final expansion state is obtained according to the correlation in S3. The internal pressure of the small hole at the final expansion state is taken as the radial stress acting on the shear failure surface of the cylinder when the positive helical pile reaches the ultimate bearing capacity state under axial pull-out load. S5: Based on the cylindrical shear model, the shear strength of the soil is obtained from the radial stress obtained in S4, and the shear resistance on the cylindrical shear failure surface is obtained from the shear strength of the soil. S6: Obtain the angle between the direction of the shear resistance and the pile axis of the positive spiral pile, and decompose the shear resistance into vertical and horizontal components based on the angle. Calculate the ultimate pull-out force and ultimate torque of the positive spiral pile based on the vertical and horizontal components respectively, thereby realizing the calculation of the ultimate pull-out bearing capacity of the positive spiral pile.

[0006] Furthermore, the formula for constructing the governing equations described in S1 is as follows:

[0007] In the formula: Indicate design parameters; This represents the tangential stress in the stress components of the plastic zone; This represents the radial stress in the stress components of the plastic zone; This indicates the radius of the hole as it expands. The expression for the boundary condition is:

[0008]

[0009]

[0010] In the formula: This indicates that the hole radius is determined by the initial value. a 0 continuously increases to the current value a The corresponding pressure value; Indicates the initial pressure value; p Indicates the current pressure at the orifice; Indicates the amount of intermediate parameters; Indicates the internal friction angle of the soil; Indicates the cohesion of the soil; This indicates that the orifice expansion process satisfies Threshold of the strength yield criterion.

[0011] Furthermore, step S2 specifically includes the following steps: S21: Solve the governing equations and boundary conditions to obtain the stress components in the plastic region; and the stress components in the plastic region include radial stress. With tangential stress Its expression is:

[0012]

[0013] S22: Utilizing the continuity of stress components at the elastic-plastic interface, the integration constant is obtained based on radial and tangential stresses. Its expression is: .

[0014] Furthermore, the outer radius of the plastic zone is obtained in S3. c With the current aperture radius a With orifice pressure p The relationship between them is expressed as follows: .

[0015] Furthermore, step S4 specifically includes the following steps: S41: The squeezing effect of the positive helical pile pull-out surface on the soil around the pile is decomposed into vertical and horizontal components, and the vertical spherical hole and the horizontal cylindrical hole are obtained by equivalent characterization using the spherical hole expansion model and the cylindrical hole expansion model. At the same time, it is set that the vertical spherical hole and the horizontal cylindrical hole expand synchronously during the axial pull-out loading process. S42: Based on the small hole expansion theory, it is confirmed that when the vertical spherical hole expands to the point where the radius of the plastic zone meets the set conditions, the positive helical pile reaches the ultimate state of axial pull-out bearing capacity. And the expression for the set condition is:

[0016] In the formula: Indicates the proportionality coefficient; This indicates the outer boundary dimensions of the vertical spherical hole expansion model; S43: Based on the radius of the plastic zone that meets the set conditions. And take half the diameter of the positive spiral pile as the current small hole radius. a Substituting the value into the correlation obtained in S3, we obtain the internal pressure of the orifice at the final expansion state. ; S44: The internal pressure of the small hole at the final expansion state is taken as the radial stress acting on the cylindrical shear failure surface when the positive helical pile reaches the ultimate bearing capacity state under axial tensile load. for: .

[0017] Furthermore, S5 specifically includes the following steps: S51: Based on the cylindrical shear model, the shear strength of the soil is obtained from the radial stress obtained in S4:

[0018] In the formula: Indicates the shear strength of the soil; S52: The shear resistance on the cylindrical shear failure surface is obtained based on the soil shear strength as follows:

[0019] In the formula: Indicates shear resistance; These represent the burial depths of the bottom and top spiral structures, respectively. z Indicates the depth of the foundation soil.

[0020] Furthermore, step S6 specifically includes the following steps: S61: Obtain the angle between the direction of the force corresponding to the shear resistance and the axis of the helical pile. Its expression is:

[0021] In the formula: θ Indicates the pile's torsion angle; δ Indicates the friction angle at the pile-soil interface; S62: Based on the included angle, the shear resistance is decomposed into a vertical component and a horizontal component. The ultimate pull-out force and ultimate torque of the positive spiral pile are calculated based on the vertical component and the horizontal component respectively, thereby realizing the calculation of the ultimate pull-out bearing capacity of the positive spiral pile. The formulas for obtaining the ultimate pull-out force and ultimate torque of the spiral pile are as follows:

[0022]

[0023] In the formula: This represents the ultimate pull-out force of a helical pile; This indicates the ultimate torque of the helical pile.

[0024] Beneficial Effects: This invention provides a method for calculating the axial ultimate pull-out force and pull-out torque of a spiral pile foundation. By equating the behavior of the spiral pile's pull-out surface squeezing the surrounding soil under axial tensile load to a circular hole expansion problem, the vertical and horizontal soil squeezing effects are respectively considered as the expansion processes of a spherical hole and a cylindrical hole. Furthermore, based on the small-hole expansion theory of soil and rock media, the method follows... The ideal elastoplastic solution of the strength yield criterion determines the hole expansion pressure. Then, based on the cylindrical hole expansion model with a non-zero initial radius, the hole expansion pressure is determined to correct the classical cylindrical shear model. This takes into account the radial stress generated on the cylindrical shear failure surface due to the soil squeezing effect of the pull-out surface. This allows for the accurate calculation of the pull-out bearing capacity of the positive spiral pile, while also theoretically explaining the self-reinforcing function of the positive spiral pile. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart illustrating the calculation method for the axial ultimate pull-out force and pull-out torque of the positive helical pile foundation according to the present invention. Figure 2This is a schematic diagram showing the type classification of each surface of the positive helical pile in this embodiment; Figure 3 This is a schematic diagram of the outer normal direction of the inner surface of the positive helical pile in this embodiment; Figure 4 This is a schematic diagram illustrating the effect of contact stress under axial pull-out load on the pull-out surface of the positive helical pile in this embodiment; Figure 5 This is a schematic diagram of the classic cylindrical shearing model in this embodiment; Figure 6 This is a schematic diagram of the circular hole expansion model in geotechnical mechanics in this embodiment; Figure 7 This is a schematic diagram of the cylindrical shear model and the modified cylindrical shear model in this embodiment; Figure 8 This is a schematic diagram showing the synchronous expansion of the vertical spherical hole and the horizontal cylindrical hole in this embodiment; Figure 9 This is a schematic diagram of the shear failure surface of the cylindrical body in the foundation soil in this embodiment; Figure 10 This is a decomposed schematic diagram of the shear resistance on the cylindrical shear failure surface in this embodiment. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] This embodiment provides a method for calculating the axial ultimate pull-out force and pull-out torque of a positive helical pile foundation. In geotechnical and foundation engineering, the assessment of the bearing capacity of pile foundations is a key technical issue in foundation design and construction, and its results directly affect the structural performance and long-term stability. The rationality of the bearing capacity assessment is not only related to pile type selection, structural parameter determination, and construction technology formulation, but also plays a crucial role in preventing excessive deformation or structural instability caused by improper bearing capacity estimation. By conducting scientific bearing capacity analysis, design schemes can be optimized while meeting safety requirements, avoiding safety hazards or increased engineering costs due to design deviations. In engineering sites with complex geological conditions, accurate bearing capacity evaluation is particularly important for improving the reliability and applicability of foundation engineering, and is also an important guarantee that engineering design and construction meet relevant specifications.

[0029] Irregularly shaped piles are primarily used in engineering construction to increase the contact area between the pile and the soil, improve the interaction between them, enhance the bearing capacity of the pile foundation, strengthen its deformation stability, and extend its service life, thereby reducing project costs and improving project safety and reliability. Typical irregularly shaped pile foundations with inherent helical structures, such as drilled spiral cast-in-place piles, precast helical piles, and screw micro piles, have been widely used in engineering practice worldwide. Unlike traditional pile foundations with cylindrical, toroidal, or cuboid geometric shapes, the irregular geometric shapes of irregularly shaped piles make the reasonable and accurate assessment of their bearing capacity a major challenge in engineering practice. Circular helicoid piles are a relatively new type of irregularly shaped pile, developed in the last decade, and are made by twisting steel plates or casting steel. In engineering practice, the axial bearing capacity of the helical pile is exceptionally outstanding, with compressive bearing capacity exceeding twice the maximum static pressure construction load, and ultimate tensile bearing capacity far exceeding the theoretical value of the cylindrical shear model. Furthermore, this pile type boasts advantages such as relatively low cost, convenient construction, and strong adaptability to adverse geological conditions, combining economic efficiency with environmental friendliness. Currently, this pile type is widely used in construction, transportation, natural energy, and agriculture in China, Japan, and South Korea, demonstrating promising engineering application prospects.

[0030] A positive spiral pile is an extremely distorted spatial geometry. (Wang et al. (2024)) [1] Based on the geometric characteristics of the helical pile and its bearing mechanism under axial load, the pile surface is divided into four types, including a bottom surface, two outer surfaces, and two inner surfaces composed of two compression surfaces and two pull-out surfaces. Figure 2 As shown, except at the pile axis, the outer normal of the inner surface is neither perpendicular to nor parallel to the axial direction, and the outer normal at any point within one pitch of the axis is different for each point. Figure 3 As shown ((a) the direction of the outer normal of the pulled-out surface; (b) the direction of the outer normal of the compressed surface). Based on the differential geometry of the positive helical surface, it is easy to see that under any axial displacement state, the greater the radial distance at a point on the inner surface, the greater the degree of compression on the soil surrounding the pile. To demonstrate the effect of contact stress on the pulled-out surface, two assumptions are made here: First, the magnitude of the contact normal compressive stress at a certain point on the pile-soil interface is directly proportional to the degree of compression; second, the direction of relative sliding at a point on the pulled-out surface is simultaneously perpendicular to both the radial direction and the outer normal direction at that point (i.e., perpendicular to the outer normal direction). Z The included angle of the axis is equal to the angle of twist at that point. θ Under axial tensile loading conditions, the spacing of the positive helical piles is... pTaking two cross sections of / 2 as an example, the effect of contact stress on the drawing surface is abstracted, such as... Figure 4 The diagram shows (a) the effect of contact normal compressive stress on the pull-out surface; (b) the effect of contact tangential frictional stress on the pull-out surface; and (c) the combined effect of contact normal compressive stress and contact tangential frictional stress on the contact surface). Theoretically, given the specific distribution (form and value) of the contact stress at the pile-soil interface, the contact normal compressive stress and contact tangential frictional stress can be decomposed axially, then superimposed to synthesize the vertical component of the contact stress, and finally, area integration can be performed on the two pull-out surfaces to calculate the axial pull-out force of the helical pile. Similarly, the horizontal component of the contact stress can be used to calculate the pull-out torque of the pile. However, for this three-dimensional pile-soil interaction problem with high geometric and contact nonlinearity, determining the appropriate theory or method to reasonably and accurately determine the distribution of contact stress on the pull-out surface by the foundation soil is a challenge. Furthermore, due to the complex stress-strain constitutive behavior of the soil itself, the relationship between the contact normal compressive stress and the degree of compression at the pile-soil interface is difficult to quantify. Furthermore, when a helical pile foundation reaches its ultimate bearing capacity under axial tensile load, the foundation soil undergoes a cylindrical shear failure mode. [2] Meanwhile, considering the soil squeezing effect at the pull-out surface, which causes additional stress in the soil around the pile, [1] This inspired the use of the small-hole expansion theory to analyze the distribution of soil and rock media. Therefore, the method described in this embodiment is based on these two theoretical models to develop a method for calculating the pull-out bearing capacity of positive spiral piles. Under the framework of the small-hole expansion theory, the expansion pressure is determined based on the cylindrical hole expansion model with a non-zero initial radius, and the classical cylindrical shear model is modified. This takes into account the additional radial stress generated on the cylindrical shear failure surface due to the soil squeezing effect of the pull-out surface, so as to accurately calculate the pull-out bearing capacity of positive spiral piles and theoretically explain the self-reinforcing function of positive spiral piles.

[0031] like Figure 1 As shown, the method described in this embodiment specifically includes the following steps: S1: The pull-out surface of the spiral pile is considered as the elastic zone, and the surrounding soil as the plastic zone. Based on the small-hole expansion theory, the behavior of the spiral pile pull-out surface squeezing the surrounding soil under axial tensile load is equivalent to a circular hole expansion problem. The strength yield criterion is used to construct the corresponding governing equations and boundary conditions. Specifically, the small-hole expansion theory is a classic mechanical model used to simulate the gradual expansion of an initial hole under uniform internal pressure in an infinitely large homogeneous medium. The core value of this theory lies in its ability to clearly reveal the development law of the medium surrounding the hole from an elastic state to a plastic state, and to provide accurate solutions for the range of the plastic zone and stress redistribution. Its basic picture can be summarized as follows: as the pressure inside the hole gradually increases (e.g., caused by the compression of soil by the helical pile blades), the soil adjacent to the hole wall yields first, forming a plastic zone. Within this zone, the soil undergoes irreversible shear failure, and the stress state is controlled by the yield criterion of the soil. Outside the plastic zone, the soil remains in the elastic zone, and the stress changes conform to the laws of elasticity. The small-hole expansion theory has been widely used to calculate the ultimate bearing capacity of pile foundations and ground anchors. Since some physical quantities are repeatedly involved in the small-hole expansion theory analysis, for simplification, the following parameters are defined as constants in any given analysis, and are represented by parameters... k Distinguishing between cylindrical holes ( k =1) or spherical hole ( k =2) Problem, the parameters include:

[0032] In the formula: Indicates shear modulus; Indicates the elastic modulus; Indicates Poisson's ratio; This represents the equivalent elastic modulus, i.e., the constraint modulus. This indicates that the orifice expansion process satisfies The threshold of the strength yield criterion; Indicates the internal friction angle φ The number of parameters; Indicates the cohesion of the soil; like Figure 6 As shown, the initial pressure in the isotropic soil is assumed to be... p 0, During the orifice expansion process, the internal pressure changes from the initial value. p 0 continuously increases to the current value p The hole radius is determined by the initial value. a 0 continuously increases to the current value a Within the soil surrounding the hole, the stress at any point must satisfy the equilibrium equation, i.e., the governing equation: The formula for constructing the governing equations is as follows:

[0033] In the formula: Indicate design parameters; This represents the tangential stress in the stress components of the plastic zone; This represents the radial stress in the stress components of the plastic zone; The radius of the hole, representing the expansion of a circular hole, is the radius of any point in the soil surrounding the hole. The expression for the boundary condition is:

[0034]

[0035] In the formula: This indicates that the hole radius is determined by the initial value. a 0 continuously increases to the current value a The corresponding pressure value; Indicates the initial pressure value; p Indicates the current pressure at the orifice; Indicates the amount of intermediate parameters; Indicates the internal friction angle of the soil; S2: Solve the governing equations and boundary conditions to obtain the stress components in the plastic region; and the stress components in the plastic region include radial stress. With tangential stress Its expression is:

[0036]

[0037] In this embodiment, when the stress satisfies the yield condition, that is... Initial yielding first occurs on the inner wall of the orifice; after initial yielding, as the orifice pressure continues to increase, an outer radius of [missing information] will form near the inner wall of the orifice. c In the plastic region, the stress components must satisfy the equilibrium equation and the yield condition to obtain the radial stress. With tangential stress ; S22: Utilizing the continuity of stress components at the elastic-plastic interface, the integration constant is obtained based on radial and tangential stresses. Its expression is:

[0038] S3: Based on boundary conditions, the relationship between the outer radius of the plastic zone, the current orifice radius, and the orifice pressure is obtained according to radial stress and integral constant; specifically, the boundary conditions at the inner wall of the orifice are used. Combined radial stress Formulas and Integral Constants The outer radius of the plastic zone can be obtained. c With the current aperture radius a and orifice pressure pThe relationship between them is as follows:

[0039] S4: The compressive force of the helical pile on the surrounding soil during pull-out is decomposed into vertical and horizontal components. Equivalent characterization is performed using a spherical hole expansion model and a cylindrical hole expansion model to obtain the vertical spherical hole and the horizontal cylindrical hole. It is also set that the vertical spherical hole and the horizontal cylindrical hole expand synchronously during axial pull-out loading. Based on the small hole expansion theory, it is confirmed that when the vertical spherical hole expands to the point where the radius of the plastic zone meets the set conditions, the helical pile reaches the ultimate limit state of axial pull-out bearing capacity. Based on the pile diameter and the radius of the plastic zone of the helical pile, the internal pressure of the small hole at the final expansion state is obtained according to the correlation in S3. The internal pressure of the small hole at the final expansion state is taken as the radial stress acting on the shear failure surface of the cylinder when the positive helical pile reaches the ultimate bearing capacity state under axial pull-out load. The specific steps include: S41: The squeezing effect of the positive helical pile pull-out surface on the soil around the pile is decomposed into vertical and horizontal components, and the vertical spherical hole and the horizontal cylindrical hole are obtained by equivalent characterization using the spherical hole expansion model and the cylindrical hole expansion model. At the same time, it is set that the vertical spherical hole and the horizontal cylindrical hole expand synchronously during the axial pull-out loading process. Specifically, this embodiment equates the behavior of the helical pile under axial tensile load, where the pile surface squeezes the surrounding soil, to a circular hole expansion problem. The vertical and horizontal soil squeezing effects are respectively considered as the expansion processes of a spherical hole and a cylindrical hole. Based on the small-hole expansion theory of soil and rock media, and following the principle of... The ideal elastoplastic solution of the strength yield criterion is used to determine the reaming pressure. [18-20] Using this ultimate borehole expansion pressure as the radial stress (redistributed horizontal ground stress) on the cylindrical shear failure surface, the classical cylindrical shear model is modified within the framework of the small borehole expansion theory to calculate the pull-out bearing capacity of the positive helical pile considering the additional stress effect, and to reveal the mechanical essence of the self-reinforcing function phenomenon. S42: Based on the small hole expansion theory, it is confirmed that when the vertical spherical hole expands to the point where the radius of the plastic zone meets the set conditions, the positive helical pile reaches the ultimate state of axial pull-out bearing capacity. And the expression for the set condition is:

[0040] In the formula: Indicates the proportionality coefficient; This indicates the outer boundary dimensions of the vertical spherical hole expansion model; S43: Based on the radius of the plastic zone that meets the set conditions. And take half the diameter of the positive spiral pile as the current small hole radius. aSubstituting the value into the correlation obtained in S3, we obtain the internal pressure of the orifice at the final expansion state. ; S44: The internal pressure of the small hole at the final expansion state is taken as the radial stress acting on the cylindrical shear failure surface when the positive helical pile reaches the ultimate bearing capacity state under axial tensile load. for: .

[0041] In this embodiment, according to (2005) [2] and (2018)

[10] Model tests revealed that when a helical pile foundation reaches its ultimate bearing capacity under axial tensile load, the helical structure surrounding the pile within the foundation soil undergoes cylindrical shear failure. However, the axial ultimate tensile bearing capacity of the helical pile foundation calculated based on the classical cylindrical shear model is significantly lower than the measured value in the model tests. [2, 10 ,11] Based on the differential geometric characteristics of the positive helical pile structure, and combined with... (2018)

[10] Model experiments and (2024) [1] The numerical simulation results reveal that the root cause of this underestimation is that during pile extraction, the positive spiral structure not only directly applies shear force to the foundation soil, but its pull-out surface also exerts a squeezing effect on the soil surrounding the pile. This causes additional stress in the foundation soil within a certain range around the pile in the horizontal direction, thereby increasing the radial stress acting on the shear failure surface of the cylinder. If the initial horizontal ground stress is still used... Through formula To calculate the shear resistance on the shear failure surface of the cylinder. This would severely underestimate the axial ultimate tensile bearing capacity of the helical pile foundation, among which... The shear strength of the foundation soil based on the Mohr-Coulomb strength criterion; d The diameter of the helical structure; and φ These are the shear strength indices of the foundation soil, namely cohesion and internal friction angle. This refers to the horizontal stress in the foundation soil. K 0 represents the coefficient of earth pressure at rest; γ The effective unit weight of the foundation soil; z The depth of the foundation soil is given; therefore, the key issue is how to determine the radial stress on the shear failure surface of the cylinder. The core technical approach of the small-hole expansion theory is to equate the interaction between the structure and the soil (mainly the compressive behavior of the structure on the soil) to a small-hole expansion process within the soil. Then, the ultimate expansion pressure at the final state of this process is used to calculate the reaction force generated by the soil on the structure. For example, using the ultimate pressure solutions for spherical and cylindrical holes, the resistance at the pile tip and the pile body can be predicted respectively. Under axial pull-out loads, the interaction between the helical pile and the foundation soil is decoupled into the shearing action on the foundation soil at the interface between the pull-out surface and the outer surface, and the compressive action of the pull-out surface on the soil around the pile. Furthermore, the vertical and horizontal compressive actions of the pull-out surface on the soil around the pile are equated to the expansion processes of spherical and cylindrical holes, respectively. Next, the radial stress on the cylindrical shear failure surface is determined based on the cylindrical hole expansion model. ,like Figure 7 As shown.

[0042] Assuming an initial cylindrical hole with a diameter equal to the pile diameter exists in the foundation soil, and considering that the compressive force of the helical pile pull-out surface on the surrounding soil is decomposed into vertical and horizontal components, and equivalently represented using expansion models for both spherical and cylindrical holes, then to satisfy the deformation compatibility conditions of the foundation soil, during axial pull-out loading, it is assumed that the vertical spherical hole and the horizontal cylindrical hole expand synchronously. Figure 8 As shown ((a) pile-soil system; (b) synchronous expansion model of horizontal and vertical circular holes; (c) horizontal circular hole expansion model; (d) vertical circular hole expansion model). Based on the small hole expansion theory, when the vertical spherical hole expands to its plastic zone radius... c Satisfaction: At this point, the helical pile reaches its ultimate limit state of axial tensile bearing capacity; at this point, the horizontal cylindrical hole expands to its plastic zone radius. c The state is equal to that of a spherical hole, where m This represents the proportionality coefficient, and its value is less than or equal to 1. (2000)

[18] It is believed that due to the incompressibility of undrained clay, m The reasonable value is 1, meaning the plastic boundary is a free surface; while for soil with an internal friction angle, m The optimal value is approximately 0.5. It is worth noting that... (2018)

[21] Based on the inverse analysis method, and using experimental observations of sand at different densities from existing literature, we present... m The empirical formula for determining the value is:

[0043] Furthermore, in the utilization formula: Calculate the radius of the plastic zone of a positive spiral pile. c At that time, parameters HThe value selection rule is as follows: For the straight generatrix on the first predefined section of the positive helical structure of the positive helical pile, H The actual burial depth of the straight busbar should be taken; while for the remaining part of the positive spiral pile, H The pitch of the uniformly spiral structure is then taken as... In summary, when a helical pile reaches its ultimate bearing capacity under axial tensile load, the radial stress acting on the shear failure surface of the cylinder is... This refers to the internal pressure of a cylindrical hole at the final expansion state. ; S5: Based on the cylindrical shear model, the shear strength of the soil is obtained from the radial stress obtained in S4, and the shear resistance on the cylindrical shear failure surface is obtained from the shear strength of the soil. The specific steps include: S51: Based on the cylindrical shear model, the shear strength of the soil is obtained from the radial stress obtained in S4:

[0044] In the formula: Indicates the shear strength of the soil; S52: The shear resistance on the cylindrical shear failure surface is obtained based on the soil shear strength as follows:

[0045] In the formula: Indicates shear resistance; These represent the burial depths of the bottom and top spiral structures, respectively. z Indicates the depth of the foundation soil.

[0046] The cylindrical shearing model in this embodiment is as follows: Figure 5 As shown, for mainstream helical pile foundations such as small threaded piles and helical blade piles with certain pitch requirements, the foundation soil will exhibit a cylindrical shear failure mode when reaching the ultimate bearing capacity under axial tensile load. Therefore, the classical cylindrical shear method is often used to calculate the ultimate uplift bearing capacity of these two mainstream helical pile foundations. The classical cylindrical shear model assumes that under axial tensile load, the pile itself will not fail; instead, the pile structure shears the surrounding soil, causing shear failure of the foundation soil around the pile on a cylindrical surface. The foundation soil generates shear resistance along the axial direction on the cylindrical surface. This shear resistance contributes to the uplift bearing capacity of the pile foundation. Then it depends on the shear strength of the foundation soil The calculation is derived from the integral on the shear failure surface of the cylinder. Since the pile does not exert a lateral squeezing effect on the surrounding soil during axial tensile loading, it is based on... The strength yield criterion determines the shear strength of foundation soil. At that time, the radial stress acting on the shear failure surface of the cylinder is considered to be... That is, the initial horizontal ground stress. The expression for the cylindrical shearing model is:

[0047] In the formula: These represent the burial depths of the bottom and top spiral structures, respectively. S6: Obtain the angle between the direction of the force corresponding to the shear resistance and the pile axis of the positive spiral pile, and decompose the shear resistance into vertical and horizontal components according to the angle. Calculate the ultimate pull-out force and ultimate torque of the positive spiral pile according to the vertical and horizontal components respectively, thereby realizing the calculation of the ultimate pull-out bearing capacity of the positive spiral pile. The specific steps include: S61: In this embodiment, the classic cylindrical shear model assumes shear resistance on the failure surface. The direction is parallel to the pile axis; however, for a positive helical pile foundation, the shear resistance on the cylindrical shear failure surface... The direction is not parallel to the pile axis; its actual direction depends on the pile's torsion angle. θ Friction angle between pile and soil interface δ .like Figure 9 As shown ((a) pile-soil system; (b) direction of shear resistance on the cylindrical shear failure surface (3D); (c) direction of shear resistance on the cylindrical shear failure surface (2D)), this phenomenon originates from the pile-soil interaction mechanism at the edge of the pull-out surface: contact normal pressure Contact tangential friction force F f The combined force is F Its direction should be opposite to the shear resistance. Maintain consistency. Based on this mechanical relationship, shear resistance... Angle between the pile axis and the pile axis ω (Acute angle) can be quantitatively characterized, and its expression is:

[0048] In the formula: θ Indicates the pile's torsion angle; δ Indicates the friction angle at the pile-soil interface; S62: Based on the included angle, the shear resistance is decomposed into a vertical component and a horizontal component. The ultimate pull-out force and ultimate torque of the positive spiral pile are calculated based on the vertical component and the horizontal component respectively, thereby realizing the calculation of the ultimate pull-out bearing capacity of the positive spiral pile. In this embodiment, for the positive helical pile foundation under axial tensile load, the classical cylindrical shear model has been modified within the framework of the small hole expansion theory. Based on the modified cylindrical shear model, the ultimate pull-out force and torque of the positive helical pile can be obtained, such as... Figure 10 As shown, the formulas for obtaining the ultimate pull-out force and ultimate torque of the positive spiral pile are:

[0049]

[0050] In the formula: This represents the ultimate pull-out force of a helical pile; This indicates the ultimate torque of the helical pile.

[0051] Beneficial Effects: In the classical cylindrical shear model, the calculation of the axial ultimate pull-out bearing capacity of pile foundations only considers the initial horizontal ground stress of the foundation soil. This model is suitable for pile types that do not produce lateral squeezing effects on the soil around the pile during the pile extraction process, such as helical blade piles and threaded steel piles. However, under axial pull-out loads, helical piles will squeeze the soil around the pile, resulting in additional radial stress in the foundation soil. The classical cylindrical shear model seriously underestimates the axial ultimate pull-out bearing capacity of helical pile foundations because it ignores this effect. The method described in this embodiment equates the behavior of the helical pile pulling surface squeezing the soil around the pile under axial pull-out loads to the problem of circular hole expansion. The vertical and horizontal soil squeezing effects are regarded as the expansion processes of spherical holes and cylindrical holes, respectively. At the same time, based on the small hole expansion theory of soil and rock media, it follows the principle of yielding to ... The ideal elastoplastic solution of the strength yield criterion determines the expansion pressure. Then, based on a cylindrical hole expansion model with a non-zero initial radius, the expansion pressure is determined to correct the classical cylindrical shear model. This accounts for the radial stress generated on the cylindrical shear failure surface due to the soil squeezing effect at the pull-out surface. This allows for accurate calculation of the pull-out bearing capacity of the helical pile while also theoretically explaining its self-reinforcing function. In summary, the method described in this embodiment can reasonably and accurately determine the axial ultimate pull-out bearing capacity of the helical pile foundation. It also provides theoretical basis and technical reference for the design, construction, and testing of helical piles, promoting their safer, more reliable, and economically sound application in geotechnical and foundation engineering construction. Furthermore, it contributes to the widespread application of this technology in domestic infrastructure construction.

[0052] The references involved in this embodiment are as follows: [1]Wang, K., Cui, C., Zhang, P., Yasufuku, N., Xu, G., Wang, M.,2024. Numerical investigation of the installation process and bearingcapacity of circular helicoid piles in undrained clay. Soils and Foundations64 (1), 101411. [2]Hirata, A., Kokaji, S., Seung, K.S., Goto, T., 2005. Study on theestimation of the axial resistance of spiral bar based on interaction withground. Shigen-to-Sozai 121 (8), 370–377, in Japanese. [3]Jugdernamjil, A., Yasufuku, N., Tsamba, T., 2021. Ultimate lateralcapacity of rigid spiral pile under monotonic loading in dense sandy soil.Proceedings of the Thirty-first (2021) International Ocean and PolarEngineering Conference. Rhodes, Greece, Jun. 20-25, 1361–1368. [4]Kurokawa, T., Yasufuku, N., Ide, Y., Nagata, M., 2024. Horizontalresistance characteristics and simple evaluation method of coupled foundationfor vehicle protection fence utilizing pull-out resistance of cast ironspiral piles. Advances in Environmental Vibration and TransportationGeodynamics II, Lecture Notes in Civil Engineering 588, 185–207. [5]Sato, T., Hayashi, S., Harada, T., Otani, J., 2012.Characterization of vertical bearing capacity of spiral pile and observationof internal model ground using X-ray CT scanner. International JointSymposium on Urban Geotechnics for Sustainable Development, JS-Seoul 2012,Seoul, South Korea.. [6]Sato, T., Hayashi, S., Otani, J., 2013. Observation of internalmodel ground around the spiral pile on vertical loading condition using X-rayCT scanner. The 1st International Conference on Tomography of Materials andStructures. Ghent, Belgium, Jul. 1-5, 297–300. [7]Sato, T., Harada, T., Iwasa, N., Hayashi, S., Otani, J., 2015.Effect of shaft rotation of spiral piles under its installation on verticalbearing capacity. Japanese Geotechnical Journal 10 (2), 253–265, in Japanese. [8]Sato, T., Otani, J., Chevalier, B., Eskisar, T., 2016. Effect ofshaft rotation of driven spiral piles on vertical bearing capacity. JapaneseGeotechnical Society Special Publication 2 (36), 1304–1309. [9]Sato, T., Otani, J., Mukunoki, T., 2017. Effect of shaft rotationof driven spiral pile under pull-out loadings. Proceedings of the 19thInternational Conference on Soil Mechanics and Geotechnical Engineering.Seoul, South Korea, Sep. 17-21, 2853–2856.

[10] Gotoh, T., 2018. Study on the application of helical-bars forground reinforcement. PhD Thesis, Kumamoto University. (in Japanese).

[11] Wang, K., Cui, C., Ren, J., Yasufuku, N., Xu, G., 2022. Modeltesting study on engineering performances of circular helicoid piles duringthe whole process of installation and bearing in sandy soil. Soils andFoundations 62 (3), 101150.

[12] Kinashi, Y., Nishioka, H., 2023. Model tests on the effect ofconstruction accuracy on the pull-out resistance of spiral piles. JapaneseJournal of JSCE 79 (15), 22–15043, in Japanese.

[13] Fuke, Y., Okazaki T., Matsui, R., 2022. In-situ tests to evaluatethe structural performance of a large, imported steel-framed greenhouse. AIJJ. Technol. Des. 28 (70), 1236–1241, in Japanese.

[14] Yamauchi, R., Isobe, K., 2016. Bearing capacity characteristicsof a small diameter spiral pile subjected to combined load in soft clayground. No. 56 Technical Report of Japanese Geotechnical Society HokkaidoBranch, Jan., 63–70. (in Japanese).

[15] Yamauchi, R., Isobe, K., 2017. Bearing capacity characteristicsof a small diameter spiral pile in soft ground subjected to combined load.Proceedings of the 19th International Conference on Soil Mechanics andGeotechnical Engineering, Seoul, South Korea, Sep. 17-21, 2889–2892.

[16] Isobe, K., Yamauchi, R., 2017. Numerical simulation on bearingcapacity of a small diameter spiral pile in soft ground subjected to combinedload. The 15th International Conference of International Association forComputer Methods and Advances in Geomechanics, Wuhan, China, Oct. 10, 19–23.

[17] Kang, S. S., Hirata, A., Obara. Y., 2005. A method for estimatingof axial resistance of spiral bar developed as a new earth support system.Journal of the Korean Society of Civil Engineers 25 (6C), 387–394, in Korean.

[18] Yu, H. S., 2000. Cavity expansion methods in geomechanics.Springer Science&Business Media.

[19] Yu, HS, 1990. Cavity expansion theory and its application to the analysis of pressuremeters. PhD Thesis, Oxford University.

[20] Yu, HS, Houlsby, GT, 1991. Finite cavity expansion indilatant soils: loading analysis. Géotechnique 41 (2), 173–183. Zhuang, PZ, Yu, HS, 2018. Uplift resistance of horizontal stripanchors in sand: a cavity expansion approach. Géotechnique Letters 8 (4), 284–289. Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions 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 force and pull-out torque of a positive helical pile foundation, characterized in that, The specific steps include: S1: The pull-out surface of the spiral pile is considered as the elastic zone, and the surrounding soil as the plastic zone. Based on the small-hole expansion theory, the behavior of the spiral pile pull-out surface squeezing the surrounding soil under axial tensile load is equivalent to a circular hole expansion problem. The strength yield criterion is used to construct the corresponding governing equations and boundary conditions. S2: Solve and obtain the stress components in the plastic region according to the governing equations and boundary conditions; and the stress components in the plastic region include radial stress and tangential stress; By utilizing the continuity of stress components at the elastic-plastic interface, the integral constant is obtained based on the radial stress and tangential stress. S3: Based on boundary conditions, obtain the correlation between the outer radius of the plastic zone and the current orifice radius and orifice pressure according to radial stress and integral constant; S4: The squeezing effect of the positive helical pile pull-out surface on the soil around the pile is decomposed into vertical and horizontal components, and the vertical spherical hole and the horizontal cylindrical hole are obtained by equivalent characterization using the spherical hole expansion model and the cylindrical hole expansion model. At the same time, it is set that the vertical spherical hole and the horizontal cylindrical hole expand synchronously during the axial pull-out loading process. Based on the small hole expansion theory, it is confirmed that when the vertical spherical hole expands to the point where the radius of the plastic zone meets the set conditions, the positive helical pile reaches the ultimate limit state of axial pull-out bearing capacity. Based on the pile diameter and the radius of the plastic zone of the positive helical pile, the internal pressure of the small hole at the final expansion state is obtained according to the correlation of S3. The internal pressure of the small hole at the final expansion state is taken as the radial stress acting on the shear failure surface of the cylinder when the positive helical pile reaches the ultimate bearing capacity state under axial pull-out load. S5: Based on the cylindrical shear model, the shear strength of the soil is obtained from the radial stress obtained in S4, and the shear resistance on the cylindrical shear failure surface is obtained from the shear strength of the soil. S6: Obtain the angle between the direction of the force corresponding to the shear resistance and the pile axis of the positive helical pile, and decompose the shear resistance into a vertical component and a horizontal component according to the angle, and calculate the ultimate pull-out force and ultimate torque of the positive helical pile according to the vertical component and the horizontal component respectively.

2. The method for calculating the axial ultimate pull-out force and pull-out torque of a positive spiral pile foundation according to claim 1, characterized in that, The formula for constructing the governing equations in S1 is: In the formula: Indicate design parameters; This represents the tangential stress in the stress components of the plastic zone; This represents the radial stress in the stress components of the plastic zone; This indicates the radius of the hole as it expands. The expression for the boundary condition is: In the formula: This indicates that the hole radius is determined by the initial value. a 0 continuously increases to the current value a The corresponding pressure value; Indicates the initial pressure value; p Indicates the current pressure at the orifice; Indicates the amount of intermediate parameters; Indicates the internal friction angle of the soil; Indicates the cohesion of the soil; This indicates that the orifice expansion process satisfies Threshold of the strength yield criterion.

3. The method for calculating the axial ultimate pull-out force and pull-out torque of a positive spiral pile foundation according to claim 2, characterized in that, S2 specifically includes the following steps: S21: Solve the governing equations and boundary conditions to obtain the stress components in the plastic region; and the stress components in the plastic region include radial stress. With tangential stress Its expression is: S22: Utilizing the continuity of stress components at the elastic-plastic interface, the integration constant is obtained based on radial and tangential stresses. Its expression is: 。 4. The method for calculating the axial ultimate pull-out force and pull-out torque of a positive spiral pile foundation according to claim 3, characterized in that, Obtain the outer radius of the plastic zone in S3. c With the current aperture radius a With orifice pressure p The relationship between them is expressed as follows: 。 5. The method for calculating the axial ultimate pull-out force and pull-out torque of a positive spiral pile foundation according to claim 4, characterized in that, S4 specifically includes the following steps: S41: The squeezing effect of the positive helical pile pull-out surface on the soil around the pile is decomposed into vertical and horizontal components, and the vertical spherical hole and the horizontal cylindrical hole are obtained by equivalent characterization using the spherical hole expansion model and the cylindrical hole expansion model. At the same time, it is set that the vertical spherical hole and the horizontal cylindrical hole expand synchronously during the axial pull-out loading process. S42: Based on the small hole expansion theory, it is confirmed that when the vertical spherical hole expands to the point where the radius of the plastic zone meets the set conditions, the positive helical pile reaches the ultimate state of axial pull-out bearing capacity. And the expression for the set condition is: In the formula: Indicates the proportionality coefficient; This indicates the outer boundary dimensions of the vertical spherical hole expansion model; S43: Based on the radius of the plastic zone that meets the set conditions. And take half the diameter of the positive spiral pile as the current small hole radius. a Substituting the value into the correlation obtained in S3, we obtain the internal pressure of the orifice at the final expansion state. ; S44: The internal pressure of the small hole at the final expansion state is taken as the radial stress acting on the cylindrical shear failure surface when the positive helical pile reaches the ultimate bearing capacity state under axial tensile load. for: 。 6. The method for calculating the axial ultimate pull-out force and pull-out torque of a positive spiral pile foundation according to claim 5, characterized in that, S5 specifically includes the following steps: S51: Based on the cylindrical shear model, the shear strength of the soil is obtained from the radial stress obtained in S4: In the formula: Indicates the shear strength of the soil; S52: The shear resistance on the cylindrical shear failure surface is obtained based on the soil shear strength as follows: In the formula: Indicates shear resistance; These represent the burial depths of the bottom and top spiral structures, respectively. z Indicates the depth of the foundation soil.

7. The method for calculating the axial ultimate pull-out force and pull-out torque of a positive spiral pile foundation according to claim 6, characterized in that, S6 specifically includes the following steps: S61: Obtain the angle between the direction of the force corresponding to the shear resistance and the axis of the helical pile. Its expression is: In the formula: θ Indicates the pile's torsion angle; δ Indicates the friction angle at the pile-soil interface; S62: Decompose the shear resistance into vertical and horizontal components according to the included angle, and calculate the ultimate pull-out force and ultimate torque of the positive helical pile according to the vertical and horizontal components respectively. The formulas for obtaining the ultimate pull-out force and ultimate torque of the spiral pile are as follows: In the formula: This represents the ultimate pull-out force of a helical pile; This indicates the ultimate torque of the helical pile.

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