A method for predicting the anti-tilting bearing capacity of a three-cylinder foundation suitable for sandy soil

Abstract

This invention relates to the field of computer-aided engineering and engineering structure simulation technology, and discloses a method for predicting the overturning bearing capacity of a three-tube foundation suitable for sandy soil. The method includes extracting geometric data of the tubes and soil properties data of the sandy soil, establishing foundation design parameters and site soil parameters, calculating the ultimate tensile bearing capacity and overturning bearing capacity of the single-tube foundation using the formulas for the ultimate tensile bearing capacity and the ultimate overturning bearing capacity of the single-tube foundation, calculating the tube spacing ratio and length-to-diameter ratio of the three-tube foundation, and querying and determining whether the stress failure mode of the three-tube foundation is the single-tube resistance development mode or the single-tube resistance fully utilized mode. Calculations are then performed according to the calculation formula for mode one or mode two, achieving rapid and accurate prediction of the overturning capacity of the three-tube foundation.

Description

Technical Field

[0001] This invention relates to the field of computer-aided engineering and engineering structure simulation technology, specifically to a method for predicting the overturning bearing capacity of a three-cylinder foundation suitable for sandy soil. Background Technology

[0002] Suction cylinder foundations, with their convenient transportation and installation, reusability, and excellent load-bearing capacity, have been applied in offshore wind turbine generators and various marine engineering structures. Among them, the three-cylinder foundation connects three suction cylinders of the same size into a whole through a superstructure or foundation, which improves the overall anti-tilting capacity of the foundation and combines structural stability with economy.

[0003] However, current methods for predicting the overturning capacity of three-cylinder foundations are mostly based on cohesive soil foundations. Their calculation theories are primarily grounded in limit equilibrium theories applicable to clay or finite element fitting results under specific working conditions. Since sand is a frictional material, its shear strength depends on effective stress, internal friction angle, and density, which are fundamentally different from the mechanical properties of cohesive soil. Directly applying calculation models based on clay to sand conditions leads to significant errors in the calculation results, failing to meet the accuracy requirements of engineering design. Furthermore, current design and analysis methods often fail to accurately reflect the nonlinear influence of key geometric parameters such as the aspect ratio and spacing ratio of the cylinders on the overturning performance when dealing with the stress mechanism of three-cylinder foundations. They also typically neglect the overturning moment generated by the rotation of individual cylinders within the multi-cylinder system, resulting in discrepancies between the calculated results and the actual bearing capacity. In the absence of suitable simplified calculation models, engineering design often relies on large-scale finite element numerical simulations or physical model tests, which increases the design cycle and cost, making it difficult to achieve rapid and reliable parametric evaluation. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for predicting the overturning bearing capacity of a three-cylinder foundation suitable for sandy soil. This method solves the problems that existing technologies are mostly designed for cohesive soils, making it difficult to adapt to the frictional mechanical properties of sandy soils. Furthermore, it does not fully consider the influence of the length-to-diameter ratio and the spacing between cylinders on the pull-out and overturning resistance of a single cylinder, resulting in insufficient calculation accuracy and low efficiency under different geometric dimensions and soil properties.

[0005] To achieve the above objectives, the present invention provides the following technical solution: Geometric data of the cylinder and soil properties of the sand were extracted from external data and summarized and defined as basic design parameters and site soil parameters, respectively, to provide physical model parameters for subsequent calculations.

[0006] A single-tube stress model is established to obtain the benchmark bearing capacity. Using the foundation design parameters and the site soil parameters, the ultimate tensile bearing capacity of the single-tube foundation is calculated according to the formula for the ultimate tensile bearing capacity of a single-tube foundation. The ultimate tensile bearing capacity of the single-tube foundation is based on the vertical friction mechanism generated when the sidewall of the tube is compressed in sandy soil. It is obtained by calculating the average lateral effective earth pressure and the outer surface area of ​​the sidewall, combined with the tangent of the friction angle between the tube wall and the soil.

[0007] Simultaneously, the ultimate bearing capacity of the monotube foundation is calculated based on the formula for calculating the ultimate bearing capacity of the monotube foundation. This step involves the superposition of the moment of contact pressure relative to the bottom center point, the frictional moment of the cylinder wall relative to the bottom center point, and the bending moment resistance generated by the end earth pressure. Specifically, obtaining the bending moment resistance generated by the end earth pressure involves determining the bearing capacity coefficient using the internal friction angle of the soil and calculating the resistance moment generated by the earth pressure at the bottom end face of the cylinder using a preset geometric integral coefficient.

[0008] Determine the stress failure mode of the three-tube system. Calculate the length-to-diameter ratio and tube spacing ratio using the aforementioned basic design parameters, and consult a stress failure mode lookup chart to determine the corresponding stress failure mode. Then, determine whether the stress failure mode is a single-tube resistance development mode or a single-tube resistance full utilization mode. The critical boundary curve in the stress failure mode lookup chart is determined based on finite element numerical simulation results under different geometric parameter conditions. Based on the position of the coordinate point determined by the length-to-diameter ratio and tube spacing ratio relative to the critical boundary curve in the stress failure mode lookup chart, determine the stress failure mode.

[0009] When the failure mode is determined to be the single-tube resistance development mode, the ultimate tensile and toppling bearing capacities of the single-tube foundation are used to calculate the ultimate toppling bearing capacity of the three-tube foundation according to the Stage 1 calculation formula, and this is used as the prediction result. In this calculation logic, the length-to-diameter ratio and the tube spacing ratio are introduced as nonlinear correction factors to calculate the toppling moment provided by the rotation of the tension tube, the toppling moment provided by the tensile force of the tension tube, and the toppling moment provided by the rotation of the compression tube, and the above sub-items are summed. The calculation of each sub-item uses correction terms or correction coefficients to calculate the nonlinear variation value of the bearing capacity under close spacing.

[0010] When the failure mode is determined to be the single-tube resistance fully utilized mode, the ultimate tensile bearing capacity and the ultimate toppling bearing capacity of the single-tube foundation are used to calculate the ultimate toppling bearing capacity of the three-tube foundation according to the calculation formula of mode two, and this is used as the prediction result. This calculation logic is based on the rigid body geometry relationship of the three-tube foundation rotating about the line connecting the two compression tubes, and determines the equivalent geometric lever arm; by multiplying the equivalent geometric lever arm by the ultimate tensile bearing capacity of the single-tube foundation as the toppling moment provided by the tensile force of the tension tube, and by using twice the ultimate toppling bearing capacity of the single-tube foundation as the toppling moment provided by the rotation of the compression tube, the two are linearly superimposed to obtain the ultimate toppling capacity of the system.

[0011] This invention provides a method for predicting the overturning bearing capacity of a three-cylinder foundation in sandy soil. It has the following beneficial effects: 1. The prediction method proposed in this invention constructs a Mode 1 calculation formula including nonlinear correction and a Mode 2 calculation formula based on superposition, which can describe the mechanical behavior of three-tube foundations under different tube spacings. By introducing the aspect ratio and tube spacing ratio as correction factors, the prediction accuracy of three-tube foundations with different aspect ratios and tube spacings is improved.

[0012] 2. The failure mode discrimination mechanism established in this invention based on the stress failure mode query diagram distinguishes between the single-tube resistance development mode and the single-tube resistance full utilization mode. This phased prediction strategy conforms to the physical change law of three-tube foundations from mutual interference of stress fields to independent rigid body rotation, and the physical meaning of each parameter is clear. Combined with the definition method of the stress failure mode query diagram, it facilitates engineers to match applicable calculation models according to the geometric layout of the actual project, and to conduct structural performance analysis and design optimization.

[0013] 3. The method of this invention improves the efficiency and practicality of overturning verification. Only conventional soil layer parameters and foundation geometric parameters need to be input, and the ultimate overturning bearing capacity can be calculated through analytical formulas. This reduces the reliance on large-scale finite element simulation or physical model test in traditional design. It is easy to embed into various general computing environments or foundation design software, and can provide data support for batch evaluation and parametric selection of offshore wind power foundations. Attached Figure Description

[0014] Figure 1 This is a flowchart of a method for predicting the overturning bearing capacity of a three-cylinder foundation applicable to sandy soil, according to the present invention. Figure 2 This is a schematic diagram illustrating the vertical frictional resistance distribution principle of the monotube foundation under vertical load according to the present invention. Figure 3 This is a schematic diagram illustrating the lateral earth pressure distribution principle of the monotube foundation under overturning moment according to the present invention. Figure 4This is a flowchart illustrating the calculation of the overall ultimate overturning bearing capacity of a three-tube foundation according to the present invention. Figure 5 This is a query diagram of the stress failure modes of the present invention; Figure 6 This is a comparison chart of the load-bearing capacity predictions of the present invention. Detailed Implementation

[0015] The technical solutions in 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, and 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.

[0016] Please see the appendix Figure 1 and attached Figure 5 This invention provides a method for predicting the overturning bearing capacity of a three-cylinder foundation suitable for sandy soil, comprising the following steps: Step S1: Obtain the foundation geometry and soil physical parameters. Extract the geometric data of the three-cylinder foundation to be predicted and the soil properties data of the sandy soil at the foundation site from external data (including three-cylinder foundation design drawings, design specifications, engineering geological survey reports, etc.).

[0017] The cylinder geometry data includes cylinder diameter, burial depth, cylinder sidewall thickness, and cylinder spacing; the sand soil properties data include effective unit weight of the soil, internal friction angle of the soil, and contact friction angle between the cylinder wall and the soil.

[0018] The extracted and determined data are defined as basic design parameters and site soil parameters, respectively.

[0019] Step S2: Calculate the ultimate bearing capacity of the monotube foundation. Using the foundation design parameters and site soil parameters, establish a monotube stress model. Based on the vertical skin friction mechanism generated when the sidewall of the monotube is under compression in sand, calculate the ultimate tensile bearing capacity of the monotube foundation according to the formula for the ultimate tensile bearing capacity of a monotube. The formula for the ultimate tensile bearing capacity of a monotube is as follows: ; In the formula: This refers to the ultimate tensile strength of a monotube foundation. Pi; The diameter of the cylinder; The height of the cylinder wall is equal to the burial depth. ; The effective unit weight of the soil; This is the lateral pressure coefficient; The friction angle between the cylinder wall and the soil; This is the operator for the tangent trigonometric function.

[0020] Using the foundation design parameters and site soil parameters, the bending moment resistance generated by the end earth pressure at the bottom face of the cylinder is calculated according to the end resistance formula. The end resistance formula is as follows: ; ; ; ; In the formula: This refers to the ultimate total bearing capacity; This refers to the thickness of the cylinder sidewall; The effective unit weight of the soil; The internal friction angle of the soil; is the base of the natural logarithm; and This is the soil bearing capacity coefficient; For burial depth; This refers to the bending moment resistance generated by the end earth pressure; The radius of the cylindrical foundation is given.

[0021] Based on the assumption of a broken-line distribution of contact pressure, integral calculations are performed on different regions of the cylinder wall to obtain the torque of the contact pressure relative to the bottom center point O and the frictional torque of the cylinder wall relative to the bottom center point O. Then, combined with the bending moment resistance generated by the end earth pressure, the ultimate bearing capacity of the monotube foundation is calculated according to the formula for calculating the ultimate bearing capacity of a monotube. The formula for calculating the ultimate bearing capacity of a monotube is as follows: ; In the formula: This represents the ultimate overturning bearing capacity of a monotube foundation. The torque of the contact pressure relative to the bottom center point O; The frictional torque is the force exerted by the cylinder wall relative to the bottom center point O. This refers to the bending moment resistance generated by the earth pressure at the end.

[0022] Step S3: Calculate the ultimate overturning bearing capacity of the three-tube foundation. Using the tube spacing and tube diameter in the foundation design parameters, and by consulting the stress failure mode lookup diagram, determine the corresponding stress failure mode, and then determine whether the stress failure mode is the single-tube resistance development mode (mode one) or the single-tube resistance fully utilized mode (mode two).

[0023] If the failure mode is determined to be Mode 1 by the failure mode lookup diagram (e.g., the coordinate point determined by the aspect ratio and the tube spacing ratio is located to the left of or on the critical boundary curve in the failure mode lookup diagram), then using the foundation design parameters, the ultimate tensile bearing capacity of the single-tube foundation, and the ultimate overturning bearing capacity of the single-tube foundation, calculate the overturning moment provided by the rotation of the tension tube, the overturning moment provided by the tensile force of the tension tube, and the overturning moment provided by the rotation of the compression tube, respectively. Then, sum the above items according to the calculation formula for Mode 1 to obtain the ultimate overturning bearing capacity of the three-tube foundation. The calculation formula for Mode 1 is as follows: ; In the formula: This represents the ultimate overturning resistance capacity of the three-tube foundation. The anti-tilting moment provided for the rotation of the tension tube; The anti-tilting moment provided for the pull-out resistance of the tension tube; The anti-tilting moment provided for the rotation of the pressure cylinder.

[0024] If the failure mode is determined to be Mode 2 based on the failure mode lookup diagram (e.g., the coordinate point determined by the aspect ratio and the cylinder spacing ratio is located to the right of the critical boundary curve in the failure mode lookup diagram), then the mutual interference between the cylinders can be ignored. The line connecting the geometric centers of the two compression cylinders is determined as the axis of rotation, and 1.5 times the cylinder spacing is determined as the equivalent geometric lever arm. Using the ultimate tensile bearing capacity, the ultimate overturning bearing capacity, and the equivalent geometric lever arm of the single-cylinder foundation, the ultimate overturning bearing capacity of the three-cylinder foundation is calculated according to the calculation formula of Mode 2 to obtain the ultimate overturning bearing capacity. The calculation formula of Mode 2 is as follows: ; In the formula: This represents the ultimate overturning resistance capacity of the three-tube foundation. The distance between cylinders; This refers to the ultimate tensile strength of a monotube foundation. This represents the ultimate overturning bearing capacity of a monotube foundation.

[0025] The detailed steps of the method for predicting the overturning bearing capacity of a three-cylinder foundation suitable for sandy soil, provided in this embodiment of the invention, are as follows: Step S1: Obtain basic geometric and soil physical parameters. This step is fundamental to the predictive model calculation. Its core lies in transforming engineering design drawings and geological survey data into boundary conditions and physical parameters that the mechanical calculation model can recognize. Accurate input of geometric and soil parameters is a prerequisite for ensuring the accuracy of subsequent calculations of lateral earth pressure, skin friction integration, and overturning moment. This step specifically includes the following steps: Step S101: Determine the foundation design parameters. Extract the geometric data of the three-cylinder foundation to be predicted from external data. External data includes, but is not limited to, three-cylinder foundation design drawings, design specifications, project overview documents, etc. The cylinder geometry data determines the contact area between the foundation and the soil and the lever arm length, specifically including: cylinder diameter. burial depth Cylinder sidewall thickness Cylinder spacing .

[0026] Among them, the cylinder diameter The outer diameter of the cylindrical section of the suction cylinder; burial depth The effective depth to which the suction cylinder wall penetrates below the mud surface corresponds to the cylinder wall height in the subsequent mechanical model. Cylinder sidewall thickness The average thickness of the cylinder wall affects the force-bearing area at the ends; cylinder spacing. It is the straight-line distance between the centers of the three suction cylinders arranged in an equilateral triangle.

[0027] Step S102: Determine site soil parameters. Extract sandy soil property data for the foundation site from external data. External data primarily comes from engineering geological survey reports or in-situ test data. The extracted sandy soil property data specifically includes: effective unit weight of soil. Angle of friction with soil And the contact friction angle between the cylinder wall and the soil.

[0028] According to the principles of soil mechanics, the effective unit weight of soil The vertical effective stress at different depths is determined, which in turn affects the horizontal earth pressure acting on the cylinder wall through the lateral pressure coefficient; the internal friction angle of the soil. The shear strength index of sandy soil is usually derived through correlation derivation from triaxial shear test or standard penetration test.

[0029] Furthermore, it is necessary to analyze and obtain the friction angle between the cylinder wall and the soil. This invention selects applicable standards or empirical formulas based on the interaction mechanism between the two, thereby quantitatively determining the friction angle between the cylinder wall and the soil. .

[0030] Friction angle between cylinder wall and soil It is an index characterizing the ultimate shear strength of the interface between a structure and soil when relative shear displacement occurs. This parameter is usually smaller than the internal friction angle of the soil. As a specific implementation method, for conventional offshore wind turbine steel suction cylinder foundations (steel-sand interface), values ​​can be selected according to relevant marine geotechnical engineering specifications such as API RP 2GEO; for example, taking... Or take based on empirical formulas .

[0031] Through the above steps, the effective unit weight of the soil is determined. , soil internal friction angle and the friction angle between the cylinder wall and the soil The summary is defined as site soil parameters.

[0032] See appendix Figure 2 and attached Figure 3 Step S2: Calculate the ultimate bearing capacity of the single-cylinder foundation. This step aims to calculate the bearing capacity indicators of a single suction cylinder under independent working conditions, including pull-out resistance and tilting moment limits, providing basic data for the subsequent analysis of the three-cylinder system. This step specifically includes the following steps: Step S201: Calculate the ultimate tensile bearing capacity of the monotube foundation. Ultimate tensile bearing capacity of the monotube foundation. It refers to the ultimate bearing capacity that a single suction cylinder foundation can provide under vertical loads, relying on the shear friction between the cylinder sidewall and the surrounding sand.

[0033] Figure 2 middle This represents the vertical downward load acting on the top of the cylinder. The calculated depth of the cylinder (its physical meaning corresponds to the cylinder wall height) or burial depth ), The trapezoidal areas with upward arrows on both sides of the cylinder, representing the center point of the cylinder's bottom, demonstrate that the effective lateral earth pressure acting on the outer wall of the cylinder increases linearly along the depth direction, thereby generating upward vertical frictional resistance. Figure 2 The bottom left corner is marked This indicates that the effective unit weight of the soil is used as the basis for measurement. and lateral pressure coefficient The relevant terms in the expression for the maximum effective lateral earth pressure obtained from the calculation.

[0034] In principle, the vertical bearing mechanism of a suction cylinder in a sandy soil foundation follows the law of friction. The sidewalls of the cylinder do not directly bear the normal support of the soil, but rather balance the external vertical load through the shear stress at the contact surface between the cylinder wall and the soil. As the depth increases, the self-weight stress of the soil increases, leading to an increase in the horizontal earth pressure acting on the cylinder wall, which in turn allows the deeper soil to provide greater frictional resistance.

[0035] Based on the Mohr-Coulomb failure criterion and the effective stress principle in soil mechanics, it is assumed that the cylinder wall is in a state of limit equilibrium, and the magnitude of the side wall friction depends on the effective lateral earth pressure and the interface friction coefficient. Since sand is a granular material, its effective unit weight is basically constant in the depth direction, so it can be assumed that the vertical effective stress increases linearly with depth.

[0036] To simplify calculations and facilitate engineering applications, this invention employs the equivalent uniformly distributed load method, i.e., taking a depth range (0 to...) The average lateral effective earth pressure This serves as the calculation benchmark. The average stress is multiplied by the outer surface area of ​​the cylinder sidewall. and interfacial friction coefficient The ultimate tensile strength of a single cylinder can then be obtained. The calculation is performed using the formula for the ultimate tensile strength of a single cylinder: ; In the formula: The ultimate tensile bearing capacity of a single-cylinder foundation is the ultimate frictional resistance provided by the sidewall of a single cylinder. Pi; The diameter of the cylinder; The height of the cylinder wall is equal to the burial depth. ; The effective unit weight of the soil reflects the effective weight of the soil skeleton under buoyancy. This is the lateral pressure coefficient, which reflects the change in the stress state of the surrounding soil during the installation of the suction cylinder; The friction angle between the cylinder wall and the soil is denoted as , which characterizes the roughness of the cylinder wall and the shear friction characteristics between soil particles. This is the operator for the tangent trigonometric function.

[0037] In this embodiment, for a sand foundation installed using conventional suction sinking, the lateral pressure coefficient is... The coefficient of earth pressure at rest can be approximated, with a specific value ranging from 0.35 to 0.5 (for example, it can be determined using the formula...). Estimate, of which (The internal friction angle of the soil), or determined based on the recommended value provided in the engineering geological survey report. The ultimate tensile bearing capacity of the monotube foundation obtained through the above calculations. This method is used to evaluate the pull-out stability of a single cylinder. It neglects the contribution of end resistance under pull-out conditions (a conservative approach), focusing primarily on sidewall friction as the dominant factor. The assumptions regarding lateral earth pressure distribution and the principle of frictional integral involved in the formula are standard techniques in geotechnical mechanics analysis and will not be elaborated upon here.

[0038] Step S202: Calculate the bearing capacity coefficient at the end of the single cylinder and the bending moment resistance generated by the end earth pressure. This step quantitatively calculates the squeezing effect on the soil at the bottom end (top of the cylinder wall) of the suction cylinder foundation during rotation.

[0039] When the cylinder rotates under the action of overturning moment, the axis of rotation is usually located at the geometric center of the cylinder or on the compression side. The bottom end face of the cylinder wall presses against the deep soil, forcing local shear failure in the bottom soil, thereby mobilizing the ultimate bearing capacity of the deep soil. This end resistance is distributed along the circumference of the cylinder wall, forming a reverse moment relative to the center of rotation that can resist the tilting of the foundation.

[0040] Based on Terzaghi's or Wesick's foundation bearing capacity theory, the annular bottom of the suction cylinder is considered as a deeply buried strip foundation. Its ultimate bearing capacity mainly consists of two parts: one part is the resistance formed by the self-weight and shear of the soil within the cylinder wall thickness (self-weight term), and the other part is the surcharge resistance formed by the weight of the soil above the cylinder bottom plane (surcharge term). The contribution weights of these two items depend on the internal friction angle of the soil. The internal friction angle of the soil in the site soil parameters is used... Calculate the soil bearing capacity coefficient and .

[0041] Soil bearing capacity coefficient The contribution coefficient of surcharge (i.e., vertical earth pressure at depth) to the ultimate bearing capacity is calculated using the following formula: ; Soil bearing capacity coefficient Characterizing the base width (in this embodiment, corresponding to the thickness of the cylinder sidewall) The contribution coefficient of soil self-weight to the ultimate bearing capacity is calculated using the following formula: ; In the formula: The internal friction angle of the soil is extracted from the site soil parameters. is the base of the natural logarithm, taken as a constant (approximately 2.718).

[0042] After obtaining the bearing capacity coefficient, the cylinder sidewall thickness is combined with the foundation design parameters. burial depth and the effective unit weight of soil in the site soil parameters The ultimate total bearing capacity is calculated based on the end resistance formula. In this calculation, the thickness of the cylinder sidewall is... Foundation width equivalent to the general bearing capacity formula This bearing capacity This represents the ultimate compressive stress that a unit area of ​​the cylinder wall can withstand.

[0043] Furthermore, considering the annular geometric features and stress distribution at the bottom of the cylinder, the ultimate total bearing capacity is integrated along the circumference of the bottom of the cylinder to calculate the bending moment resistance generated by the end earth pressure produced by the earth pressure at the bottom face of the cylinder. The calculation formula is as follows: ; ; In the formula: This refers to the ultimate total bearing capacity; The radius of the cylindrical foundation is determined by the cylindrical diameter in the foundation design parameters. The conversion yields, i.e. 1.58 is the geometric integral coefficient, a shape correction value obtained by integrating the stress distribution on the annular cross-section and calculating the moments (this value is approximately equal to...). ), used to convert the bearing capacity per unit area into the overall resistance moment.

[0044] The bending moment resistance generated by the end earth pressure obtained from the above calculations This will be an important component of the monotube's anti-tilting capacity and will participate in the subsequent calculation of the total bending moment. The derivation process of the bearing capacity coefficient in the formula and the theoretical background of the foundation failure mode are well-known technical principles in the field of geotechnical mechanics and will not be elaborated here.

[0045] Step S203: Calculate the ultimate anti-tilting bearing capacity of a single cylinder. This step is based on the kinematic assumption of rigid body rotation of the cylinder and the earth pressure distribution assumption under the limit equilibrium state. The anti-tilting moment that the sidewall of a single suction cylinder can provide under the rotational failure mode is quantitatively solved by integral calculation.

[0046] Figure 3 In the diagram, A, B, C, and D represent the four stress-bearing regions that divide the surface of the cylinder along the circumference. Represents the bottom center point. The depth of the rotation point representing the cylinder wall (corresponding rotation point depth coefficient) ), This represents the depth at which the passive earth pressure on the cylinder wall surface reaches its peak value in the loading direction; Figure 3 The broken line with a horizontal arrow indicates the distribution of Coulomb and Rankine active and passive earth pressures generated in the surrounding soil when the cylinder rotates. Figure 3 The Chinese logo , , , , , The expressions represent the values ​​at the corresponding depths based on the active earth pressure coefficient (...). ), passive earth pressure coefficient ( and effective unit weight of soil The calculated peak theoretical earth pressure at each inflection point.

[0047] Determine the soil pressure coefficient and depth distribution parameters. When the suction cylinder is subjected to an external overturning moment, the cylinder rotates around a center of rotation (rotation point) located at a certain depth below the mud surface. At this time, the front side of the cylinder wall (compression side) is subjected to passive soil resistance above the rotation point and active soil pressure below the rotation point; while the stress state of the rear side of the cylinder wall (tension side) is the opposite.

[0048] To characterize this active-passive state transition occurring along the depth direction, this invention employs a polygonal earth pressure distribution model. In this model, two key depth control parameters are introduced: the rotation point depth coefficient. and the depth coefficient of maximum passive earth pressure .

[0049] Rotation point depth coefficient Defined as the depth of the rotation point of the cylinder wall With the height of the cylinder wall (i.e., burial depth) The ratio of ) This coefficient reflects the vertical position of the axis of rotation.

[0050] Maximum passive earth pressure depth coefficient Defined as the depth at which the passive earth pressure on the surface of the cylinder wall reaches its maximum value in the loading direction. With the height of the cylinder wall The ratio ( ).

[0051] In this embodiment, parameters and The value is determined based on model tests or numerical simulations of suction cylinder foundations in typical sandy soil. As a preferred implementation parameter, the rotation point depth coefficient... The value is 0.84, which is the depth coefficient of maximum passive earth pressure. The value is 0.67.

[0052] At the same time, based on the soil internal friction angle in the site soil parameters and the friction angle between the cylinder wall and the soil Calculate the earth pressure coefficient under various stress states. and These are the Coulomb coefficients for active and passive earth pressure, respectively, taking into account wall friction; and These are the active and passive earth pressure coefficients, respectively, based on Rankine's theory (or without considering wall friction). Active earth pressure coefficients corrected for specific regions (smoothing correction coefficients for transitional zones). The formulas for these coefficients are determined based on classical soil mechanics theory (e.g., (and other modified forms), the specific derivation process will not be listed here.

[0053] Calculate the moment of contact pressure relative to the bottom center point O. Based on the direction of the overturning moment and the circumferential geometry of the cylinder, divide the cylinder wall into four integration regions A, B, C, and D (e.g., using the load direction as a reference, expand the soil-facing side and the soil-repelling side along the circumference). Calculate the moment generated by the contact earth pressure about the center of rotation in each region. Calculate the bending moment component generated by the contact earth pressure in each region using the following formula: ; ; ; ; Adding the four components together yields the total torque of the contact pressure relative to the bottom center point O. .

[0054] In the formula: Let A, B, C, and D be the bending moment components generated by the contact earth pressure in the four regions of the cylinder wall, respectively. The operator for cosine and trigonometric functions; Calculate the frictional torque of the cylinder wall relative to the bottom center point O. When the cylinder rotates, the relative slippage between the cylinder wall and the soil generates tangential friction, which forms a resisting torque about the center of rotation.

[0055] Calculate the frictional bending moment values ​​of each component using the following formulas: ; ; ; ; Adding the four components together, we get the total bending moment generated by the sidewall friction. .

[0056] In the formula: Let A, B, C, and D be the bending moment components generated by the sidewall friction in the four regions of the cylinder wall, respectively. The operator for sine and trigonometric functions; Coulomb earth pressure coefficient; is the Rankine earth pressure coefficient.

[0057] Summarize and calculate the ultimate overturning capacity of the single cylinder. Consider the moment of the contact pressure relative to the bottom center point O. Frictional torque of the cylinder wall relative to the bottom center point O and the bending moment resistance generated by the end earth pressure calculated in step S202. The ultimate overturning capacity of a single-tube foundation is calculated by linear superposition based on the formula for calculating the ultimate overturning capacity of a single-tube foundation: ; In the formula: The ultimate bearing capacity against overturning of a single suction cylinder foundation is a comprehensive indicator that reflects the maximum overturning resistance of a single suction cylinder in sand under the combined action of side wall earth pressure, side wall friction, and end resistance. The torque of the contact pressure relative to the bottom center point O; The frictional torque is the force exerted by the cylinder wall relative to the bottom center point O. This refers to the bending moment resistance generated by the earth pressure at the end.

[0058] This will be used as a basic calculation indicator and input into the calculation model of the ultimate overturning bearing capacity of the subsequent three-tube foundation.

[0059] See appendix Figure 4 and Figure 5 Step S3: Calculate the ultimate overturning capacity of the three-cylinder foundation. Based on the single-cylinder performance indicators obtained in the previous steps, this step selects an applicable mechanical model through logical judgment and calculates the ultimate overturning capacity of the entire three-cylinder system. This step specifically includes the following steps: Step S301: Determine the stress failure mode stage. A three-tube foundation consists of three single tubes rigidly connected by a superstructure. When subjected to overturning loads, its overall bearing capacity is controlled by the degree of interference between the soil stress fields of the individual tubes. This is achieved using the embedment depth in the foundation design parameters. cylinder diameter and cylinder spacing Calculate the length-to-diameter ratio And the ratio of cylinder spacing .

[0060] When determining the stress-induced failure mode, this invention introduces a stress-induced failure mode lookup chart. This lookup chart uses the cylinder spacing ratio as an indicator. The x-axis represents the aspect ratio. The vertical axis represents the critical boundary curves within it, which are the critical geometric limits that distinguish failure modes. These curves are constructed by fitting finite element numerical simulation results under a large number of different geometric parameter conditions.

[0061] The specific judgment logic is as follows: First, determine the length-to-diameter ratio obtained from the calculation in the stress failure mode query diagram. And the ratio of cylinder spacing The corresponding coordinate point; then, observe the positional relationship of this coordinate point relative to the critical boundary curve in the figure: If the coordinate point is located to the left of or on the critical boundary curve in the stress failure mode query diagram, the stress failure mode is determined to be the single-cylinder resistance development mode (mode one). In this case, the overall bearing capacity of the three cylinders is less than the linear superposition value of the bearing capacities of each individual cylinder, and the calculation formula of mode one must be used for calculation.

[0062] If the coordinate point is located to the right of the critical boundary curve, the failure mode is determined to be the single-tube resistance fully utilized mode (mode two). In this case, the three-tube foundation exhibits ideal rigid body rotational failure, and the calculation formula based on the geometric lever arm of mode two needs to be used for calculation.

[0063] Among them, the critical boundary curve in the stress failure mode query diagram is the critical geometric limit for distinguishing failure modes, which is constructed by fitting the results of finite element numerical simulation under a large number of different geometric parameter conditions.

[0064] Step S302: Calculation based on the calculation formula of Mode 1. When the mode determination result in step S301 is the single-tube resistance development mode (Mode 1), it indicates that the spacing between the tubes of the three-tube foundation is relatively small. Under this condition, the ultimate overturning bearing capacity of the three-tube foundation is not equal to the simple algebraic sum of the ultimate overturning bearing capacities of each single tube.

[0065] Therefore, this invention establishes a nonlinear correction method, introducing the aspect ratio. And the ratio of cylinder spacing As a dimensionless correction factor, the calculation formula of Mode 1 is constructed to calculate the ultimate overturning bearing capacity of the three-tube foundation.

[0066] Specifically, the toppling resistance capacity is calculated. In the single-tube resistance development model (Model 1), the overall toppling resistance capacity of the three-tube foundation is decomposed into three modified contribution components: the toppling moment provided by the rotation of the tension tube. The anti-tilting moment provided by the pull-out force of the tension tube and the anti-tilting moment provided by the rotation of the pressure cylinder .

[0067] Using the burial depth in the foundation design parameters cylinder diameter Cylinder spacing And the ultimate tensile bearing capacity of the monotube foundation obtained in the previous steps. Ultimate bearing capacity of monotube foundations Calculate the above three items separately.

[0068] Anti-tilting moment provided by the rotation of the tension tube The contribution of a single cylinder located on one side of the center of rotation (the tension side) to resist tilting moment during its own rotation is represented by the following formula: ; Anti-tilting moment provided by pull-out force of the tension tube The formula for calculating the moment contribution of the tension-bearing cylinder to the center of rotation by overcoming vertical side friction (pull-out force) is as follows: ; Anti-tilting moment provided by the rotation of the pressure cylinder The sum of the anti-tilting moment contributions provided by the two cylinders located on the other side of the rotation center (the pressure side) during their own rotation is calculated using the following formula: ; The numerical coefficients (including constant and exponential terms) in the above formulas are specific fitting parameters for sandy soil foundation conditions. These parameters were determined through multivariate nonlinear regression analysis based on a broad finite element limit analysis (FELA) database and model test results. They quantitatively describe the performance of different... and Under the combined configuration, the reduction or amplification factor of the bearing capacity of each component relative to the single-tube reference value.

[0069] Summarize and calculate the ultimate overturning bearing capacity of the three-tube foundation. Summate the three sub-items calculated in step S3021, and obtain the ultimate overturning bearing capacity of the three-tube foundation according to the calculation formula of Mode 1. : ; In the formula: The ultimate overturning bearing capacity of the three-tube foundation is the ultimate overturning bearing capacity that the three-tube foundation as a whole can withstand under the single-tube resistance development mode. These are the anti-tilting moment provided by the rotation of the tension cylinder, the anti-tilting moment provided by the pull-out force of the tension cylinder, and the anti-tilting moment provided by the rotation of the compression cylinder, respectively.

[0070] By employing the above-mentioned calculation formula including a nonlinear correction term in Mode 1, this invention can quantitatively calculate the bearing capacity change under the condition of small tube spacing ratio, correcting the calculation deviation of the traditional linear superposition method in the design of closely arranged three-tube foundations.

[0071] Step S303: Geometric calculation based on the calculation formula of Mode 2. When the mode determination result in step S301 is the single-tube resistance fully utilized mode (Mode 2), it indicates that the tube spacing of the three-tube foundation is relatively large. Under this condition, the overall failure mode of the three-tube foundation is manifested as the overall rigid body rotation about a specific geometric axis.

[0072] Establish a geometric and mechanical model. Based on the principle of minimum potential energy, the foundation tends to rotate about the axis that provides the maximum resisting torque. For a three-cylinder foundation arranged in an equilateral triangle, under a unidirectional horizontal load, its axis of rotation is the line connecting the geometric centers of the two compression cylinders.

[0073] Based on this rigid body rotation mechanism, the anti-tilting capacity of the three-cylinder foundation can be decomposed into the following two linearly superimposed parts: The anti-tilting moment provided by the pull-out force of the tension cylinder is the reverse moment provided by the sidewall friction force of the single cylinder (tension cylinder) located on the other side of the rotation axis due to the upward pull-out action. In this embodiment, based on the isotropic assumption of the frictional characteristics of sand, the transient contribution of the negative pressure suction inside the cylinder is ignored (safety bias design), and the ultimate pull-out force of the tension cylinder is approximately equal to the ultimate vertical bearing capacity of the single-cylinder foundation. (Considering only the side friction resistance). Its lever arm adopts an equivalent geometric lever arm that takes into account engineering experience correction (i.e., 1.5 times the cylinder spacing).

[0074] The anti-tilting moment provided by the rotation of the compression cylinders comes from the two compression cylinders located on the axis of rotation. As the overall frame tilts, the cylinder walls themselves also rotate relative to the soil. Since these two cylinders act as fulcrums of rotation, their end resistance and sidewall stress are at their ultimate limits. Therefore, each compression cylinder contributes to the ultimate anti-tilting bearing capacity of a complete monotube foundation. .

[0075] The ultimate overturning capacity of the three-tube foundation was calculated. This was done using the tube spacing parameters from the foundation design. And the ultimate tensile bearing capacity of the monotube foundation obtained in the previous steps. Ultimate bearing capacity of monotube foundations Based on the calculation formula of Mode 2, a geometric linear superposition calculation was performed to obtain the ultimate overturning bearing capacity of the three-tube foundation. : ; In the formula: The ultimate overturning bearing capacity of the three-tube foundation is the ultimate overturning bearing capacity that the three-tube foundation as a whole can withstand under the mode where the resistance of the single tube is fully utilized. The distance between cylinders; This is a geometric correction factor (or equivalent force arm factor) used to calculate the contribution of the pull-out force of the tension cylinder to the anti-tilting moment. The perpendicular length from the vertex of the tension cylinder to the opposite side (axis of rotation) is... (Approximately 0.866S); 2 represents the number coefficient of the pressure cylinder, indicating that the anti-tilting moment contribution mainly comes from the two pressure cylinders that serve as the fulcrum of rotation.

[0076] Through the above steps, under the condition of wide cylinder spacing, the calculation formula of Mode 2 is used to directly calculate the sum of the anti-tilting moment provided by the pull-out force of the tension cylinder amplified by the equivalent geometric lever arm and the anti-tilting moment provided by the rotation of the compression cylinder, thereby obtaining the ultimate anti-tilting bearing capacity of the three-cylinder foundation.

[0077] See appendix Figure 5 and Figure 6 To verify the technical solution of the present invention, this embodiment selects a typical offshore wind farm area as the application scenario. The sea area has a subtropical monsoon climate with complex sea conditions, and the seabed is mainly composed of medium-dense fine sand. The anti-tilting bearing capacity prediction method provided in this invention was applied to calculate and verify the proposed jacket-type three-cylinder foundation.

[0078] Step S1: Obtaining basic geometric and soil physical parameters: First, based on the method in step S1, extract the key parameters required for the calculation: Basic design parameters: cylinder diameter ; Burial depth (i.e., calculating depth) ); Cylinder sidewall thickness Cylinder spacing This embodiment sets four typical operating conditions, with operating condition one including... (Right now )and (Right now Working condition two includes (Right now )and (Right now The cylinder is made of steel and has a certain degree of surface roughness.

[0079] Site soil parameters: Effective unit weight of soil soil internal friction angle The value is taken from the geological survey report. The angle of friction between the cylinder wall and the soil Based on the friction angle between sand and steel, this embodiment takes... (Right now ).

[0080] Step S2, Calculation of the ultimate bearing capacity of a single-tube foundation: Based on the model in step S2, the independent performance indices of a single tube are first calculated: Take the lateral pressure coefficient Based on the formula for the ultimate tensile bearing capacity of a monotube foundation, calculate the ultimate tensile bearing capacity of the monotube foundation. The calculated value was verified by finite element numerical simulation, and the error was only 4%, which met the engineering requirements.

[0081] The soil bearing capacity coefficient was calculated. Thus, the ultimate total bearing capacity is derived. Bending moment resistance generated by end earth pressure Calculation of the torque of the contact pressure relative to the bottom center point O (taking area B as an example): Substitute the rotation point coefficient. and Calculated Combined with the torque of the contact pressure in other areas relative to the bottom center point O ( ) and the frictional torque of the cylinder wall relative to the bottom center point O ( The ultimate overturning bearing capacity of the monotube foundation is obtained by summing these values. The finite element verification results show that the error in this step is controlled within 2.6%.

[0082] Step S3: Calculation of the ultimate overturning bearing capacity of the three-tube foundation: Based on the logic of step S3, pattern determination and bearing capacity prediction are performed for different spacing ratios. In this embodiment, the foundation length-to-diameter ratio is calculated based on the foundation design parameters. .exist Figure 5 The stress-failure mode lookup diagram shown below, on the vertical axis... On the horizontal line, according to the cylinder spacing ratio corresponding to each working condition Determine the location of the coordinate point on the graph: To fully verify the predictive accuracy of this invention under different stress failure modes, this embodiment selects a representative point located to the left of the critical boundary curve (taking the cylinder spacing ratio). This is used as a verification condition for the single-cylinder resistance development mode (Mode 1), and a representative point located to the right of the critical boundary curve is selected (the cylinder spacing ratio is taken as the value of the single-cylinder resistance development mode). This serves as a verification condition for the single-tube resistance fully exerted mode (Mode 2).

[0083] Operating Condition 1: Narrow Cylinder Spacing (Mode 1 Verification) calculate The values ​​are 1.0 and 1.5 respectively, determined by the aspect ratio of 0.75 and the aforementioned cylinder spacing ratio. Figure 5 The coordinates identified during the search are all located to the left of the critical boundary curve, indicating that the failure mode is the single-tube resistance development mode (Mode 1). At this point, the calculation formula for Mode 1 (including...) is applied. and Calculation of the nonlinear correction term: when hour: Anti-tilting moment provided by the rotation of the tension tube The anti-tilting moment provided by the pull-out force of the tension tube The anti-tilting moment provided by the rotation of the pressure cylinder .

[0084] Summary of Results: Ultimate Overturning Capacity of Three-Cylinder Foundation .

[0085] when hour: Anti-tilting moment provided by the rotation of the tension tube The anti-tilting moment provided by the pull-out force of the tension tube The anti-tilting moment provided by the rotation of the pressure cylinder .

[0086] Summary of Results: Ultimate Overturning Capacity of Three-Cylinder Foundation .

[0087] Operating Condition 2: Wide Cylinder Spacing Operating Condition (Verification of Mode 2) calculate The values ​​are 2.0 and 2.5 respectively, determined by the aspect ratio of 0.75 and the aforementioned cylinder spacing ratio. Figure 5 The coordinates identified during the search are all located to the right of the critical boundary curve, indicating that the failure mode is the single-tube resistance fully utilized mode (Mode 2). At this point, the calculation is performed according to the Mode 2 calculation formula (rigid body linear superposition): when hour: ; when hour: ; Combining the calculation results of working condition 1 and working condition 2, and the appendix Figure 6 The verification curve shown indicates that: Calculation results show that as the cylinder spacing ratio increases, the contribution of the pull-out force to the tilting moment increases significantly (due to the increase in lever arm), and the change in bearing capacity caused by the change in force mode is accurately captured due to the use of the correct coordinate point position determination mechanism.

[0088] As attached Figure 6 As shown in the figure, the horizontal axis represents the cylinder spacing ratio ( The vertical axis represents the bearing capacity ( ), The solid line in the figure represents the continuous prediction curve calculated using the method of this invention (including the calculation formulas for Mode 1 and Mode 2). The continuous prediction curve is obtained by substituting continuous variables into the calculation. The triangular scatter points in the figure represent the data points obtained through finite element simulation verification. As can be seen from the figure, the method of the present invention has a high degree of agreement with the finite element results in the entire range, which verifies the accuracy of the segmented prediction model based on the stress failure mode query map.

Claims

1. A method for predicting the overturning bearing capacity of a three-cylinder foundation suitable for sandy soil, characterized in that, Includes the following steps: Extract the cylindrical geometry data and sandy soil properties data from external sources, and summarize and define them as basic design parameters and site soil parameters; Using the aforementioned basic design parameters and site soil parameters, the tensile ultimate bearing capacity of the monotube foundation is calculated according to the formula for the ultimate tensile bearing capacity of a monotube foundation, and the overturning ultimate bearing capacity of the monotube foundation is calculated by summarizing the formula for the ultimate overturning bearing capacity of a monotube foundation. The length-to-diameter ratio and the cylinder spacing ratio are calculated using the basic design parameters, and the corresponding stress failure mode is determined by querying the stress failure mode discrimination diagram. Then, it is determined whether the stress failure mode is a single cylinder resistance development mode or a single cylinder resistance full utilization mode. When the stress failure mode is determined to be the single-tube resistance development mode, the ultimate tensile bearing capacity of the single-tube foundation and the ultimate overturning bearing capacity of the single-tube foundation are used to calculate the ultimate overturning bearing capacity of the three-tube foundation according to the calculation formula of mode one as the prediction result. When the stress failure mode is determined to be the single-tube resistance fully utilized mode, the ultimate overturning bearing capacity of the three-tube foundation is calculated as the prediction result using the foundation design parameters, the ultimate tensile bearing capacity of the single-tube foundation, and the ultimate overturning bearing capacity of the single-tube foundation, according to the calculation formula of mode two.

2. The method for predicting the overturning bearing capacity of a three-cylinder foundation suitable for sandy soil according to claim 1, characterized in that, The steps of extracting the cylindrical geometry data and sandy soil property data from external data and summarizing and defining them as basic design parameters and site soil parameters specifically include: Extract the cylinder diameter, burial depth, and cylinder spacing of the three-cylinder foundation to be predicted from the external data, and summarize the above data to define the foundation design parameters; The effective unit weight of the soil, the internal friction angle of the soil, and the contact friction angle between the cylinder wall and the soil at the site of the foundation are extracted from the external data, and the effective unit weight of the soil, the internal friction angle of the soil, and the friction angle between the cylinder wall and the soil are summarized and defined as the soil parameters of the site.

3. The method for predicting the overturning bearing capacity of a three-cylinder foundation suitable for sandy soil according to claim 2, characterized in that, The steps for calculating the ultimate tensile bearing capacity of a single-tube foundation based on the formula for the ultimate tensile bearing capacity of a single-tube foundation specifically include: The average effective lateral earth pressure acting on the sidewall of the cylinder is calculated using the effective unit weight of the soil, the burial depth, and the lateral pressure coefficient. The outer surface area of ​​the sidewall of the cylinder is calculated using the cylinder diameter and the burial depth. The ultimate tensile bearing capacity of the single cylinder foundation is obtained by multiplying the outer surface area of ​​the sidewall of the cylinder, the average effective lateral earth pressure of the sidewall of the cylinder, and the tangent of the friction angle between the cylinder wall and the soil. The soil bearing capacity coefficient is calculated using the internal friction angle of the soil. Combined with the thickness of the sidewall of the cylinder, the burial depth, and the effective unit weight of the soil, the ultimate total bearing capacity is calculated according to the end resistance formula. Using the ultimate total bearing capacity and geometric integral coefficient, the bending moment resistance generated by the end earth pressure is calculated according to the end resistance formula. The geometric integral coefficients are set based on the shape correction values ​​obtained by integrating the stress distribution on the annular cross section. Using the aforementioned basic design parameters and the aforementioned site soil parameters, integral calculations are performed on different areas of the cylinder wall to obtain the torque of the contact pressure relative to the bottom center point and the friction torque of the cylinder wall friction force relative to the bottom center point. The contact pressure relative to the bottom center point, the frictional torque of the cylinder wall relative to the bottom center point, and the bending moment resistance generated by the end soil pressure are superimposed and summarized according to the single cylinder anti-tilting moment calculation formula to obtain the anti-tilting ultimate bearing capacity of the single cylinder foundation; The ratio of the rotation point depth of the cylinder wall to the burial depth is set as the rotation point depth coefficient, and the ratio of the depth at which the passive earth pressure on the cylinder wall surface reaches its peak value in the loading direction to the burial depth is set as the maximum passive earth pressure depth coefficient. The active earth pressure coefficient and the passive earth pressure coefficient are calculated using the internal friction angle of the soil and the friction angle between the cylinder wall and the soil. By using the rotation point depth coefficient, the maximum passive earth pressure depth coefficient, the active earth pressure coefficient, and the passive earth pressure coefficient, integral calculations are performed on different regions of the cylinder wall to obtain the torque of the contact pressure relative to the bottom center point and the friction torque of the cylinder wall relative to the bottom center point.

4. The method for predicting the overturning bearing capacity of a three-cylinder foundation suitable for sandy soil according to claim 2, characterized in that, The steps for determining the corresponding stress failure mode by querying the stress failure mode query diagram specifically include: The length-to-diameter ratio is calculated using the burial depth and the cylinder diameter, and the cylinder spacing ratio is calculated using the cylinder spacing and the cylinder diameter; In the stress failure mode query diagram, determine the coordinate points corresponding to the length-to-diameter ratio and the cylinder spacing ratio; If the coordinate point is located to the left of or on the critical boundary curve in the stress failure mode query diagram, the stress failure mode is determined to be the single-tube resistance development mode. If the coordinate point is located to the right of the critical boundary curve, the stress failure mode is determined to be the mode in which the single-cylinder resistance is fully utilized. The critical boundary curves in the stress failure mode query diagram are determined based on the finite element numerical simulation results under different geometric parameter conditions.

5. The method for predicting the overturning bearing capacity of a three-cylinder foundation suitable for sandy soil according to claim 2, characterized in that, The specific steps for calculating the ultimate overturning bearing capacity of the three-tube foundation according to the calculation formula of Mode 1 include: Using the ultimate overturning bearing capacity of the monotube foundation, combined with the correction terms for the length-to-diameter ratio and the tube spacing ratio, the overturning moment provided by the rotation of the tension tube is calculated; The product of the equivalent geometric lever arm and the ultimate tensile bearing capacity of the single-tube foundation is used as the anti-tilting moment provided by the tensile force of the tension tube, and the bending moment provided by the tensile force on the tension tube is calculated by combining the tube spacing ratio correction term. Using the ultimate anti-tilting bearing capacity of the monotube foundation, combined with the correction terms for the length-to-diameter ratio and the tube spacing ratio, the anti-tilting moment provided by the rotation of the compression tube is calculated; Based on the calculation formula of Mode 1, the anti-tilting moment provided by the rotation of the tension cylinder, the anti-tilting moment provided by the pull-out force of the tension cylinder, and the anti-tilting moment provided by the rotation of the compression cylinder are summed to obtain the ultimate anti-tilting bearing capacity of the three-cylinder foundation.

6. The method for predicting the overturning bearing capacity of a three-cylinder foundation suitable for sandy soil according to claim 2, characterized in that, The steps for calculating the ultimate overturning bearing capacity of the three-tube foundation according to the calculation formula of Mode 2 specifically include: The line connecting the geometric centers of the two pressure cylinders is defined as the axis of rotation, and 1.5 times the distance between the cylinders is defined as the equivalent geometric lever arm; Using the cylinder spacing, the pull-out ultimate bearing capacity of the single-cylinder foundation, the overturning ultimate bearing capacity of the single-cylinder foundation, and the equivalent geometric lever arm in the foundation design parameters, the ultimate overturning bearing capacity of the three-cylinder foundation is obtained by linear superposition calculation according to the calculation formula of Mode 2.

7. The method for predicting the overturning bearing capacity of a three-cylinder foundation suitable for sandy soil according to claim 6, characterized in that, The specific steps for performing linear superposition calculation based on the calculation formula of Mode 2 are as follows: The product of the equivalent geometric lever arm and the ultimate tensile strength of the single-tube foundation is used as the anti-tilting moment provided by the tensile strength of the tension tube. Twice the ultimate anti-tilting moment of the single-tube foundation is used as the anti-tilting moment provided by the rotation of the compression tube. The ultimate anti-tilting moment of the three-tube foundation is obtained by adding the anti-tilting moment provided by the tensile strength of the tension tube and the anti-tilting moment provided by the rotation of the compression tube.

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