A method for correcting buckling critical load of super-long pile considering attenuation of soil stiffness around pile

Abstract

This invention discloses a method for correcting the buckling critical load of ultra-long piles considering the attenuation of the stiffness of the soil around the pile, relating to the field of pile foundation stability analysis technology in geotechnical engineering. The invention includes the following steps: Step S1, obtaining pile-soil foundation parameters in layers; Step S2, establishing a depth-deformation bivariate model for the stiffness attenuation of the soil around the pile; Step S3, constructing an attenuation-type bivariate foundation buckling control equation; Step S4, dimensionless processing and coupled attenuation iteration-eigenvalue solution; Step S5, calculating the corrected value of the buckling critical load; Step S6, buckling instability discrimination and safety evaluation; Step S7, parameter inversion optimization and establishment of a dedicated database. This invention achieves accurate and efficient calculation of the buckling critical load of ultra-long piles by establishing a depth-deformation bivariate stiffness attenuation model, constructing a buckling control equation with coupled attenuation characteristics, and proposing analytical correction coefficients.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering pile foundation stability analysis technology, and in particular relates to a method for correcting the critical buckling load of ultra-long piles that considers the attenuation of the stiffness of the soil around the pile. It can be widely applied to the buckling analysis and stability design of ultra-long piles in geotechnical engineering such as high-rise buildings, long-span bridges, offshore wind power foundations, and deep foundation pit support. It has significant economic and social benefits and strong industrial applicability. Background Technology

[0002] Ultra-long piles (pile length L≥50m or length-to-diameter ratio≥50) are widely used in geotechnical engineering fields such as high-rise buildings, long-span bridges, and offshore wind power foundations. Their vertical bearing capacity and buckling stability are core indicators in engineering design. Under vertical loads, ultra-long piles undergo slight lateral deformation, and the soil around the pile will experience stress redistribution due to this lateral deformation, resulting in varying degrees of decrease in soil stiffness. At the same time, the stiffness of the soil around the pile shows a clear variation pattern with increasing depth; the greater the depth, the stronger the soil's restraining effect, and the lower the sensitivity to stiffness decrease.

[0003] Traditional methods for calculating the critical buckling load of ultra-long piles are mainly based on Euler buckling theory or Winkler foundation beam theory, both of which assume constant soil stiffness around the pile, neglecting the coupled attenuation characteristics of soil stiffness with depth and lateral deformation. For example, the classic m-method uses a linearly varying subgrade coefficient but does not consider stiffness softening under load; existing improved methods only consider stiffness attenuation of a single variable (such as only considering depth attenuation or only considering deformation attenuation), which cannot truly reflect the mechanical properties of pile-soil interaction.

[0004] The aforementioned methods have drawbacks, leading to overestimation of the calculated critical buckling load and resulting in unsafe engineering designs that can easily cause buckling instability accidents in ultra-long piles. Furthermore, existing technologies lack directly applicable correction formulas for the critical buckling load in engineering projects, relying heavily on complex numerical simulations, which are computationally inefficient and difficult to reconcile with current engineering standards.

[0005] Therefore, developing a method for correcting the buckling critical load of ultra-long piles that considers the coupling attenuation of pile-surround soil stiffness, is accurate in calculation, and can be applied in engineering is of great engineering significance and theoretical value. Summary of the Invention

[0006] The purpose of this invention is to provide a method for correcting the buckling critical load of ultra-long piles that considers the stiffness attenuation of the soil around the pile. By establishing a depth-deformation bivariate stiffness attenuation model, constructing a buckling control equation with coupled attenuation characteristics, and proposing analytical correction coefficients, the invention achieves accurate and efficient calculation of the buckling critical load of ultra-long piles. This solves the problems of existing calculations of the buckling critical load of ultra-long piles neglecting the coupled attenuation of the stiffness of the soil around the pile, resulting in unsafe results, and lacking engineering-based correction formulas.

[0007] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution:

[0008] This invention provides a method for correcting the critical buckling load of ultra-long piles considering the attenuation of the stiffness of the soil around the pile, comprising the following steps:

[0009] Step S1: Layered acquisition of pile-soil foundation parameters: Using a combination of geological drilling, in-situ testing and indoor geotechnical testing, pile-soil foundation parameters are collected layer by layer to establish a discrete array of soil layer profiles.

[0010] Step S2: Establish a depth-deformation bivariate pile perimeter soil stiffness attenuation model: Define the depth attenuation factor. and load-deformation attenuation factor We constructed formulas for the attenuation of the pile perimeter soil bed coefficient and the attenuation of the shear stiffness in relation to the coupling depth and lateral deformation.

[0011] Step S3: Construct the buckling control equation of the attenuated two-parameter foundation: Introduce the stiffness attenuation model established in step S2 into the two-parameter foundation model to construct the buckling control equation of the ultra-long pile considering stiffness attenuation.

[0012] Step S4, Dimensionless processing and attenuation iteration-eigenvalue coupling solution: The buckling control equation is dimensionless, and the Galerkin method is used to discretize the dimensionless equation, so that the lateral deflection of the pile is expressed as a linear combination of buckling mode functions.

[0013] Step S5: Calculate the correction value for the critical buckling load: based on the converged lateral deflection distribution of the pile. Substituting into the stiffness attenuation formula, the actual soil stiffness at each depth is obtained. and Calculate the soil stiffness attenuation correction factor according to the correction factor calculation formula. Ultimately, the formula was corrected. We obtained the corrected value of the critical buckling load for ultra-long piles, taking into account the attenuation of the stiffness of the soil around the pile.

[0014] Step S6, Buckling Instability Judgment and Safety Assessment: Based on the correction value of the critical buckling load. Compared with the actual vertical load The ratio of the two values ​​is used to determine the buckling instability and safety of ultra-long piles.

[0015] Step S7, Parameter Inversion Optimization and Dedicated Database Establishment: Using the measured or numerical simulation results of pile buckling as the target, invert and optimize the depth attenuation index. and soil softening coefficient Establish a dedicated parameter library for the project.

[0016] As a preferred technical solution, the specific process for obtaining pile-soil foundation parameters in step S1 is as follows:

[0017] Step S11: Determine the stratification principle: based on the range of pile lengths of ultra-long piles (e.g., ...). Using the boundary as the boundary, the soil layers through which the piles penetrate are divided into calculation layers (rather than simple geological layers).

[0018] Step S12: Collect pile body parameters (directly or indirectly): Pile body elastic modulus Moment of inertia of cross section Pile length Pile diameter Aspect Ratio ;

[0019] Step S13: Soil stratification parameter acquisition: Initial subgrade coefficient Initial shear stiffness Critical lateral strain Ultimate lateral displacement Cohesion / Internal friction angle ;

[0020] Step S14, Load and Constraint Parameter Acquisition: Acquire vertical axial load. Pile top constraint conditions; Pile bottom constraint conditions;

[0021] Step S15, Parameter Validation and Outlier Handling: Perform consistency validation on the parameters, remove outliers, and organize all parameters into a two-dimensional array according to the calculation layer;

[0022] Step S16: Determine the initial value of the attenuation characteristic parameter: Determine the depth attenuation index. and soil softening coefficient .

[0023] As a preferred technical solution, in step S11, when the thickness of the same geological layer is greater than 10m, according to... Subdivide the calculation layers; the interfaces between different geological layers must be decomposed as calculation layers, and the pile top must also be considered. Pile bottom The area is forcibly subdivided (the soil stiffness attenuation has the most significant impact on buckling in this region), and each calculation layer is numbered; the numbering rules are as follows:

[0024] No. Layer depth range is (Pile top) (Pile bottom), record the center depth of each layer. .

[0025] As a preferred technical solution, in step S2, a depth attenuation factor is defined. and load-deformation attenuation factor The specific formula is as follows:

[0026] ; ;

[0027] In the formula, It is a natural constant. The depth decay index, To calculate the depth of the point, This refers to the total length of the extra-long piles. For depth Lateral deflection of the pile body, This represents the ultimate lateral displacement of the soil around the pile. This is the soil softening coefficient; The dimensionless depth is used to eliminate the influence of the absolute value of the pile length on the attenuation factor; This is a dimensionless lateral deformation used to eliminate the influence of the absolute value of displacement on the attenuation factor;

[0028] According to the defined depth attenuation factor and load-deformation attenuation factor Formulas for attenuation of the pile perimeter soil bed coefficient and shear stiffness in relation to coupling depth and lateral deformation are constructed as follows:

[0029] , ;

[0030] In the formula, This is the soil subgrade coefficient around the pile. This represents the initial soil subgrade coefficient around the piles. This represents the actual shear stiffness of the soil surrounding the pile. This represents the initial shear stiffness of the soil surrounding the pile.

[0031] As a preferred technical solution, in step S3, a shear stiffness term is introduced based on the foundation model, and simultaneously, the shear stiffness term is adjusted according to depth. With lateral deformation Substituting the coupled attenuated soil stiffness around the pile into the governing equation, an attenuated two-parameter buckling governing equation for ultra-long piles is established, as follows:

[0032] ;

[0033] In the formula, The elastic modulus of the pile material. Let the moment of inertia of the pile cross section be , This is the fourth derivative of lateral deflection with respect to depth. The vertical axial load applied to the top of the pile. This is the second derivative of the lateral deflection with respect to depth.

[0034] As a preferred technical solution, the specific process of dimensionless processing and decay iteration-eigenvalue coupling solution in step S4 is as follows:

[0035] Step S41: Define dimensionless variables for depth, lateral deflection, vertical load, subgrade coefficient and shear stiffness in the buckling control equation. According to the composite function differentiation rule, convert the derivative terms in the attenuated two-parameter ultra-long pile buckling control equation into dimensionless form to obtain the dimensionless buckling control equation.

[0036] According to the chain rule, the derivative terms in the original equation can be transformed into dimensionless form:

[0037] For example, the first derivative: Second derivative: Third derivative: ;

[0038] Substituting the above dimensionless variables After eliminating common terms, the equation becomes a dimensionless equation:

[0039] ;

[0040] After dimensionless transformation, the equation contains only dimensionless variables, eliminating the interference of physical dimensions such as pile length, pile diameter, and material modulus, making the algorithm universal and applicable to ultra-long piles of different sizes and materials.

[0041] Step S42: Using the Galerkin method, the dimensionless lateral deflection is expressed as a linear combination of buckling mode functions, substituted into the equation, and weighted integral to form a system of eigenvalue equations;

[0042] Dimensionless lateral deflection Represented as buckling mode function linear combination, In the formula, The mode order is... The mode shape coefficients to be determined are... To satisfy the standardized buckling mode functions of the pile top and pile bottom boundary conditions;

[0043] Substituting the deflection expansion into the dimensionless buckling control equation and multiplying by the mode shape function And in the interval Integrating, setting the residual to 0, and rearranging, we obtain the eigenvalue equation:

[0044] ;

[0045] Among them, the stiffness matrix quality matrix shear stiffness matrix ;

[0046] Step S43: Starting from the initial stiffness, obtain the lateral deflection of the pile by solving the eigenvalue equations. Update the attenuation stiffness of the soil around the pile according to the lateral deflection and iterate cyclically until the relative error between two adjacent buckling critical loads meets the preset convergence accuracy. Output the converged buckling critical load and the lateral deflection distribution of the pile.

[0047] As a preferred technical solution, the specific process of the iterative loop in step S43 is as follows:

[0048] Step S431: Initialize parameters: Take the initial stiffness without attenuation. Set convergence precision Number of iterations initial eigenvalues ;

[0049] Step S432, Solving the nth iteration: , Substituting the eigenvalue equations from step S42, the mode shape coefficients are obtained. Dimensionless initial buckling critical load and deflection distribution ;

[0050] Step S433, Update stiffness parameters: Convert to dimensional deflection Substituting into the stiffness attenuation formula, we obtain the updated result. and Then convert to dimensionless stiffness and ;

[0051] Step S434, Convergence Judgment: Calculate the relative error of the load between two adjacent iterations. ,like The iteration converges, and the output is a dimensional initial buckling critical load. Lateral deflection distribution of pile body ;like ,make Return to step S432 and continue iterating.

[0052] As a preferred technical solution, in step S5, the soil stiffness attenuation correction coefficient is calculated. The specific formula is:

[0053] ;

[0054] In the formula, For the first ultra-long pile First-order buckling mode function, is the second derivative of the mode shape function.

[0055] As a preferred technical solution, in step S6, the criteria for judging and evaluating the buckling instability of ultra-long piles are as follows: Calculate the safety factor. Safety factor Compared with the allowable safety factor specified in the standard In comparison, if If the buckling stability of the ultra-long pile meets the design requirements; If the excessively long pile is deemed to have a risk of buckling instability, the design needs to be optimized by increasing the pile diameter, adjusting the pile length, or reinforcing the soil around the pile.

[0056] As a preferred technical solution, in step S7, the critical load of the test pile buckling or the critical load of the high-precision numerical simulation is used as the target value. An objective function is constructed with the depth attenuation index ξ and the soil softening coefficient η as optimization variables and the goal of minimizing the sum of squared residuals between the calculated value and the target value. The optimal depth attenuation index and the optimal soil softening coefficient are obtained by iterative solution using the least squares method. The optimal parameters are associated with the soil layer type, pile length, pile diameter, and pile material parameters of the corresponding project and stored to establish a special parameter library for buckling calculation of ultra-long piles, which is used for rapid calculation and parameter reuse under similar geological and pile type conditions.

[0057] The present invention has the following beneficial effects:

[0058] (1) This invention constructs a depth-deformation dual-variable pile-surround soil stiffness attenuation model and introduces it into the Winkler-Pasternak dual-parameter foundation beam theory, establishing an attenuation-type buckling control equation that is more in line with the real pile-soil interaction mechanism. This breaks through the calculation deviation caused by the traditional method using constant stiffness or single-factor attenuation assumptions, and significantly improves the theoretical rationality and calculation accuracy of ultra-long pile buckling analysis.

[0059] (2) This invention proposes a complete algorithm for dimensionless, Galerkin discretization and decay iteration-eigenvalue coupling solution, which transforms the nonlinear variable coefficient buckling differential equation into an algebraic eigenvalue problem that can be directly solved in engineering. While ensuring convergence and reliability, it greatly reduces the solution complexity and can achieve high-precision calculation without relying on large numerical simulation software, thus significantly enhancing applicability and practicality.

[0060] (3) This invention provides a correction coefficient for the stiffness attenuation of soil around the pile and an analytical correction formula, which can directly correct the traditional buckling critical load and establish a safety factor discrimination and instability risk assessment system. It realizes a closed-loop design of the whole process from parameter input, load correction, stability discrimination to optimization suggestions, which is convenient for engineering designers to use directly and can effectively avoid buckling instability risk caused by unsafe calculation.

[0061] (4) This invention optimizes the depth attenuation index and soil softening coefficient by inverting the results of test pile measurements or numerical simulations, and establishes a project-specific parameter library to transform empirical values ​​into accurate parameters that are site-adapted, thereby further improving the calculation reliability under different geological conditions and pile types. Without increasing the cost of exploration and testing, it significantly improves the safety and economy of ultra-long pile foundation design, and has outstanding industrial applicability and promotion value.

[0062] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0063] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 This is a flowchart of a method for correcting the critical buckling load of ultra-long piles that takes into account the attenuation of the stiffness of the soil around the pile, according to the present invention. Detailed Implementation

[0065] 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, 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.

[0066] Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0067] To make the purpose, technical solution, and advantages of this application clearer, the following description is provided in conjunction with the appendix. Figure 1 The present application will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the application.

[0068] Please see Figure 1 As shown, the present invention is a method for correcting the critical buckling load of ultra-long piles considering the attenuation of the stiffness of the soil around the pile, including step S1, obtaining pile-soil foundation parameters in layers: using a combination of geological drilling, in-situ testing and indoor geotechnical testing, pile-soil foundation parameters are collected in layers to establish a discrete array of soil layer profiles.

[0069] Step S2: Establish a depth-deformation bivariate pile perimeter soil stiffness attenuation model: Define the depth attenuation factor. and load-deformation attenuation factor We constructed formulas for the attenuation of the pile perimeter soil bed coefficient and the attenuation of the shear stiffness in relation to the coupling depth and lateral deformation.

[0070] Step S3: Construct the buckling control equation of the attenuated two-parameter foundation: Introduce the stiffness attenuation model established in step S2 into the two-parameter foundation model to construct the buckling control equation of the ultra-long pile considering stiffness attenuation.

[0071] Step S4, Dimensionless processing and attenuation iteration-eigenvalue coupling solution: The buckling control equation is dimensionless, and the Galerkin method is used to discretize the dimensionless equation, so that the lateral deflection of the pile is expressed as a linear combination of buckling mode functions.

[0072] Step S5: Calculate the correction value for the critical buckling load: based on the converged lateral deflection distribution of the pile. Substituting into the stiffness attenuation formula, the actual soil stiffness at each depth is obtained. and Calculate the soil stiffness attenuation correction factor according to the correction factor calculation formula. Ultimately, the formula was corrected. We obtained the corrected value of the critical buckling load for ultra-long piles, taking into account the attenuation of the stiffness of the soil around the pile.

[0073] Step S6, Buckling Instability Judgment and Safety Assessment: Based on the correction value of the critical buckling load. Compared with the actual vertical load The ratio of the two values ​​is used to determine the buckling instability and safety of ultra-long piles.

[0074] Step S7, Parameter Inversion Optimization and Dedicated Database Establishment: Using the measured or numerical simulation results of pile buckling as the target, invert and optimize the depth attenuation index. and soil softening coefficient Establish a dedicated parameter library for the project.

[0075] In step S1, the specific process for obtaining pile-soil foundation parameters in layers is as follows:

[0076] Step S11: Determine the stratification principle: based on the range of pile lengths of ultra-long piles (e.g., ...). Using the boundary as the boundary, the soil layers through which the piles penetrate are divided into calculation layers (rather than simple geological layers).

[0077] When the thickness of the same geological layer is greater than 10m, according to Subdivide the calculation layers; the interfaces between different geological layers must be decomposed as calculation layers, and the pile top must also be considered. Pile bottom The area is forcibly subdivided (the soil stiffness attenuation has the most significant impact on buckling in this region), and each calculation layer is numbered; the numbering rules are as follows:

[0078] No. Layer depth range is (Pile top) (Pile bottom), record the center depth of each layer. .

[0079] Step S12: Collect pile body parameters (directly or indirectly): Pile body elastic modulus Moment of inertia of cross section Pile length Pile diameter Aspect Ratio ;

[0080] Specifically, the elastic modulus of the pile body It can be collected through concrete block compressive strength tests (GB / T50081), directly extracted from engineering design documents, and verified through ultrasonic testing; sectional moment of inertia Calculations are performed based on the pile cross-section shape, such as the formula for calculating a circular pile as follows: Square piles Pile length Based on construction drawings and borehole testing (measuring rope / ultrasonic), the pile diameter was determined. The length-to-diameter ratio was determined by using borehole drilling inspection (hole diameter gauge) and reinforcement cage fabrication drawings. By calculating the value Verify whether the definition of an ultra-long pile is met. ).

[0081] Step S13: Soil stratification parameter acquisition: Initial subgrade coefficient Initial shear stiffness Critical lateral strain Ultimate lateral displacement Cohesion / Internal friction angle ;

[0082] Specifically, the initial bed coefficient Plate load tests were conducted: three test points were arranged on each layer, and the average value was used to calculate the initial shear stiffness. Critical lateral strain was obtained through shear wave velocity experiments and triaxial shear experiments. Indoor geotechnical tests were conducted: uniaxial compression / direct shear tests of soil were performed, and the strain value corresponding to the inflection point of the stress-strain curve was recorded; ultimate lateral displacement was also measured. In-situ lateral load tests were conducted to determine the ultimate deformation value of the soil along the pile and the cohesion. / Internal friction angle The results were obtained through direct shear experiments and triaxial experiments, respectively.

[0083] Step S14, Load and Constraint Parameter Acquisition: Acquire vertical axial load. Pile top constraint conditions; Pile bottom constraint conditions;

[0084] Specifically, vertical axial load The data collection method involves using engineering design documents (superstructure load + pile self-weight) and deducting the correction value for the pile group effect. The pile top constraint conditions are determined according to the design drawings (hinged / fixed / free): if the pile top is rigidly connected to the pile cap, it is fixed; if it is hinged, it is hinged. The pile bottom constraint conditions are determined according to the characteristics of the bearing layer (embedded in bedrock, it is fixed; suspended in soft soil, it is free).

[0085] Step S15, Parameter Validation and Outlier Handling: Perform consistency validation on the parameters, remove outliers, and organize all parameters into a two-dimensional array according to the calculation layer;

[0086] Specifically, consistency checks include those performed at the same computational layer. , It must conform to empirical rules (such as sandy soil) > Cohesive soil The greater the depth Larger); outlier removal uses The criteria remove outliers from the experiment, and missing layer parameters are supplemented by interpolation from adjacent layers.

[0087] Step S16: Determine the initial value of the attenuation characteristic parameter: Determine the depth attenuation index. and soil softening coefficient Depth Decay Index and soil softening coefficient This is obtained through regional engineering experience values ​​or back analysis results of projects with similar opinions in the same region.

[0088] In step S2, the depth attenuation factor is defined. and load-deformation attenuation factor The specific formula is as follows:

[0089] ; ;

[0090] In the formula, It is a natural constant. The depth decay index, To calculate the depth of the point, This refers to the total length of the extra-long piles. For depth Lateral deflection of the pile body, This represents the ultimate lateral displacement of the soil around the pile. This is the soil softening coefficient; The dimensionless depth is used to eliminate the influence of the absolute value of the pile length on the attenuation factor; This is a dimensionless lateral deformation used to eliminate the influence of the absolute value of displacement on the attenuation factor;

[0091] Specifically, when (Pile top): This indicates that the soil constraint at the pile top is weakest, with no initial depth decay; when (Pile bottom): This indicates that the soil at the pile bottom has the strongest constraint, and the degree of depth attenuation is... To decide (e.g.) hour, (The pile bottom stiffness decreased by approximately 39.4%).

[0092] when (Without deformation) The soil stiffness does not decrease due to deformation;

[0093] when (Limit deformation), then ,like hour, The soil stiffness decreased by 85% (entering the strong softening stage).

[0094] In specific implementation, taking the ultra-long piles of a certain coastal bridge as an example ( , , , For example:

[0095] When depth (Midpoint of the pile): This indicates that the soil stiffness at this depth decreases by approximately 22.12% due to the depth effect; the lateral deflection of the pile at this depth... ; This indicates that the soil stiffness at this deformation decreases by approximately 51% due to the deformation effect; after coupled attenuation, the subgrade coefficient at this depth... That is, the total attenuation is about 61.84%, which intuitively reflects the superposition effect of bivariate attenuation.

[0096] According to the defined depth attenuation factor and load-deformation attenuation factor Formulas for attenuation of the pile perimeter soil bed coefficient and shear stiffness in relation to coupling depth and lateral deformation are constructed as follows:

[0097] , ;

[0098] In the formula, This is the soil subgrade coefficient around the pile. This represents the initial soil subgrade coefficient around the piles. This represents the actual shear stiffness of the soil surrounding the pile. This represents the initial shear stiffness of the soil surrounding the pile.

[0099] This step S2 uses the depth attenuation factor. and load-deformation attenuation factor Simultaneously, the initial bed coefficient and initial shear stiffness After correction, the actual soil stiffness that simultaneously reflects the depth effect and deformation softening is obtained. , This allows for precise correction of the critical buckling load of ultra-long piles.

[0100] In step S3, a shear stiffness term is introduced into the foundation model, and the shear stiffness term is adjusted based on depth. With lateral deformation Substituting the coupled attenuated soil stiffness around the pile into the governing equation, an attenuated two-parameter buckling governing equation for ultra-long piles is established, as follows:

[0101] ;

[0102] In the formula, The elastic modulus of the pile material. Let the moment of inertia of the pile cross section be , This is the fourth derivative of lateral deflection with respect to depth. The vertical axial load applied to the top of the pile. This is the second derivative of the lateral deflection with respect to depth.

[0103] Specifically, a two-parameter foundation model with a shear stiffness term is selected, which includes: normal elastic constraints (subgrade coefficient). ) and shear transfer constraints (shear stiffness) Substituting this into step S2 yields the actual soil stiffness, which simultaneously reflects the depth effect and deformation softening. , This makes the stiffness no longer a constant, but changes in real time with depth and deformation;

[0104] micro-segments of the pile body Establish the equilibrium conditions for vertical, horizontal, bending moment, and shear force: the bending moment is determined by... Provides axial force The additional bending moment is The normal reaction force of the soil is Soil shear constraint ;

[0105] Combining all terms of the equilibrium equations, we get: .

[0106] In practice, the specific parameters are as follows: pile length Pile diameter Elastic model of pile body Moment of inertia of cross section Vertical load at pile top The pile top is hinged, and the pile bottom is fixed.

[0107] The initial stiffness of the soil layers is stratified as follows: Within the range, , ;exist Within the range, , ;exist Within the range, , ;

[0108] When calculating attenuation stiffness, depth is used. For example, = Iterate to the deflection at that point ;get ;

[0109] therefore, ; ;

[0110] Substituting into the governing equation, at this position: ;

[0111] The equation is to be solved as follows: The pile body is discretized in 0.5m increments, and a variable coefficient equation of the above form is constructed for each node to form a complete set of equations. At the same time, combined with boundary conditions, a complete attenuation-type buckling control equation system is obtained, which is used for subsequent iterative solution of critical loads. By constructing buckling control equations that are more consistent with the actual pile-soil interaction, the calculation deviation caused by the traditional constant stiffness assumption is overcome, making the buckling analysis of ultra-long piles safer, more accurate, and more reliable in engineering.

[0112] In step S4, the specific process of dimensionless processing and decay iteration-eigenvalue coupling solution is as follows:

[0113] Step S41: Define dimensionless variables for depth, lateral deflection, vertical load, subgrade coefficient and shear stiffness in the buckling control equation. According to the composite function differentiation rule, convert the derivative terms in the attenuated two-parameter ultra-long pile buckling control equation into dimensionless form to obtain the dimensionless buckling control equation.

[0114] According to the chain rule, the derivative terms in the original equation can be transformed into dimensionless form:

[0115] For example, the first derivative: Second derivative: Third derivative: ;

[0116] Substituting the above dimensionless variables After eliminating common terms, the equation becomes a dimensionless equation:

[0117] ;

[0118] After dimensionless transformation, the equation contains only dimensionless variables, eliminating the interference of physical dimensions such as pile length, pile diameter, and material modulus, making the algorithm universal and applicable to ultra-long piles of different sizes and materials.

[0119] Step S42: Using the Galerkin method, the dimensionless lateral deflection is expressed as a linear combination of buckling mode functions, substituted into the equation, and weighted integral to form a system of eigenvalue equations;

[0120] Dimensionless lateral deflection Represented as buckling mode function linear combination, In the formula, The mode order is... The mode shape coefficients to be determined are... To satisfy the standardized buckling mode functions of the pile top and pile bottom boundary conditions, such as the first mode of a hinged-fixed pile: ;

[0121] Substituting the deflection expansion into the dimensionless buckling control equation and multiplying by the mode shape function And in the interval Integrating, setting the residual to 0, and rearranging, we obtain the eigenvalue equation:

[0122] ;

[0123] Among them, the stiffness matrix quality matrix shear stiffness matrix ;

[0124] Step S43: Starting from the initial stiffness, obtain the lateral deflection of the pile by solving the eigenvalue equations. Update the attenuation stiffness of the soil around the pile according to the lateral deflection and iterate cyclically until the relative error between two adjacent buckling critical loads meets the preset convergence accuracy. Output the converged buckling critical load and the lateral deflection distribution of the pile.

[0125] In step S43, the specific process of the iterative loop is as follows:

[0126] Step S431: Initialize parameters: Take the initial stiffness without attenuation. Set convergence precision Number of iterations initial eigenvalues ;

[0127] Step S432, Solving the nth iteration: , Substituting the eigenvalue equations from step S42, the mode shape coefficients are obtained. Dimensionless initial buckling critical load and deflection distribution ;

[0128] Step S433, Update stiffness parameters: Convert to dimensional deflection Substituting into the stiffness attenuation formula, we obtain the updated result. and Then convert to dimensionless stiffness and ;

[0129] Step S434, Convergence Judgment: Calculate the relative error of the load between two adjacent iterations. ,like The iteration converges, and the output is a dimensional initial buckling critical load. Lateral deflection distribution of pile body ;like ,make Return to step S432 and continue iterating.

[0130] In practical implementation, the basic parameters are: pile length Pile diameter , Initial bed coefficient ( )for Initial shear stiffness ( )for The convergence accuracy is The first-order mode shape function is The specific implementation process is as follows:

[0131] The parameters are dimensionless, specifically including: dimensionless depth of... The dimensionless bed coefficient is The dimensionless shear stiffness is Then the dimensionless equation is ;

[0132] Take the first mode shape ,but: , Substituting into Galerkin's integral, we get:

[0133] ,Depend on Simplifying, we get:

[0134] .

[0135] After iterative convergence, the dimensionless load is: The dimensionless initial critical load is Pile top deflection ( ): .

[0136] The initial buckling critical load is finally obtained through the attenuation iteration-eigenvalue coupling algorithm in this embodiment. Compared to the traditional constant stiffness method ( The results are closer to the actual measured values, verifying the effectiveness and accuracy of the algorithm.

[0137] The specific iterative solution process is as follows:

[0138] First iteration: Take , The initial lateral deflection is obtained by solving. (Maximum deflection at the pile top) Initial buckling critical load ;

[0139] Second iteration: Substituting into the attenuation formula, we obtain the updated result. and (such as the first floor) ), and solve again to obtain (Maximum deflection at the pile top) ), ;

[0140] Third iteration: Solving after updating stiffness yields the result. ;

[0141] Fourth iteration: Solving after updating stiffness yields the result. ;

[0142] Convergence criteria: Continue iterating;

[0143] 8th iteration: Solving for the result The 9th iteration yielded If the convergence condition is met, then determine The final lateral deflection distribution of the pile body (Maximum deflection at the pile top) ).

[0144] In step S5, the soil stiffness attenuation correction factor is calculated. The specific formula is:

[0145] ;

[0146] In the formula, For the first ultra-long pile First-order buckling mode function, is the second derivative of the mode shape function.

[0147] Specifically, correction factor The core is the ratio of the actual stiffness integral effect to the initial stiffness integral effect, while also coupling the influence of shear stiffness. This is the normal stiffness attenuation correction term. The shear stiffness attenuation correction term is obtained by numerical integration. In the formula, For depth step size, take the following in engineering The corrected buckling critical load is calculated as follows: In the formula, The initial critical buckling load is obtained at the convergence point of the iteration in step S4. The actual critical load considering soil stiffness attenuation.

[0148] Correction coefficient The attenuation effects of normal stiffness and shear stiffness are incorporated simultaneously, overcoming the shortcomings of traditional methods that only consider normal stiffness. The correction coefficient is calculated by weighted integral of mode function instead of simple arithmetic mean, which is more in line with the energy distribution law of pile buckling deformation. At the same time, the correction formula is in analytical form and can be directly applied in engineering, which is different from the "black box calculation" of traditional numerical simulation.

[0149] In practice, the depth step size is taken. Using a trapezoidal integral, the numerator (actual stiffness integral) of the normal stiffness attenuation correction term is: The denominator (initial stiffness integral) of the normal stiffness attenuation correction term is: Then the normal correction term .

[0150] The numerator (shear stiffness integral) of the shear stiffness attenuation correction term is: The denominator of the shear stiffness attenuation correction term (the integral of the pile's bending stiffness) is: The shearing correction term is .

[0151] Calculate the correction factor : ; Calculate the corrected critical load .

[0152] Trial assembly and critical load testing The relative error between the corrected value and the measured value in this invention is: However, calculations using traditional methods revealed that the initial stiffness was calculated to be... The error compared to the actual test was 184.67%.

[0153] The validation results show that the inclusion and The correction factor can accurately reflect the influence of soil stiffness attenuation, and the corrected critical load is in high agreement with the measured value.

[0154] In step S6, the criteria for judging and evaluating the buckling instability of ultra-long piles are as follows: Calculate the safety factor. In the formula, The actual vertical axial load on the pile top in the engineering design; the safety factor Compared with the allowable safety factor specified in the standard In comparison, if If the buckling stability of the ultra-long pile meets the design requirements; If the excessively long pile is deemed to have a risk of buckling instability, the design needs to be optimized by increasing the pile diameter, adjusting the pile length, or reinforcing the soil around the pile.

[0155] Specifically, the buckling critical load correction value based on the pile surrounding soil stiffness reduction obtained in step S5 is... The buckling safety factor of ultra-long piles is calculated, and the allowable safety factor specified in the current geotechnical engineering code is used to determine whether there is a risk of buckling instability of ultra-long piles. If there is a risk of instability, targeted engineering optimization measures are proposed to form a closed-loop process of "judgment-evaluation-optimization".

[0156] Determine the allowable safety factor for buckling based on the characteristics of ultra-long pile engineering. Curve allowable safety factor As shown in the table below:

[0157]

[0158] The instability criteria are shown in the table below:

[0159]

[0160] Based on the difference between the safety factor and the allowable value, the instability risk is classified and the evaluation conclusion is clarified, as shown in the table below:

[0161]

[0162] In practical implementation, the calculated buckling safety factor is: ;

[0163] Instability is determined as follows: This is classified as a high-risk buckling instability pile. The ultra-long pile presents a serious risk of buckling instability and requires severe optimization measures. Risk level: Level IV. Evaluation conclusion: The buckling stability of the piles is far from meeting the requirements of the coastal bridge project. If construction is carried out according to the original design, it is easy to cause engineering accidents such as pile buckling instability and excessive settlement of the bridge foundation.

[0164] The project will be optimized, and the specific optimization plan is as follows:

[0165] Option 1: Increase the pile diameter (from 2.0m to 2.5m); Optimized pile section moment of inertia: (Original ); Improved bending stiffness of pile body: Recalculate the corrected critical load: ; Optimized safety factor: (still (This requires further optimization); therefore, Option 1 is not perfect.

[0166] Option 2: Increase pile diameter + shorten pile length (pile diameter 2.5m, pile length reduced from 60m to 50m): Recalculate the corrected critical load: ; Optimized safety factor: ; Judgment result: There is no risk of instability, and the risk level has been reduced to level two. After adopting the optimized scheme of "2.5m pile diameter + 50m pile length", the buckling safety factor of the ultra-long pile meets the specification requirements, the risk of instability is eliminated, and it can be put into engineering application.

[0167] Step S6's core principle is to determine instability through a comparison of safety factors. It is the ratio of "actual load" to "corrected critical load", directly reflecting the pile's buckling resistance; the judgment criterion needs to be combined with the allowable safety factor determined by the current code. Different engineering scenarios Different values ​​are used to ensure that the judgment results conform to the actual engineering situation; after the instability judgment, clear risk classification and optimization measures are required to form a closed-loop process. This is the key innovation of this invention that distinguishes it from traditional methods; the implementation examples have verified the practicality of the judgment process. The optimized safety factor meets the specification requirements and effectively eliminates the risk of buckling instability.

[0168] In step S7, the critical load of the test pile buckling measured or the critical load of the high-precision numerical simulation is used as the target value. An objective function is constructed with the depth attenuation index ξ and the soil softening coefficient η as optimization variables and the goal of minimizing the sum of squared residuals between the calculated value and the target value. The optimal depth attenuation index and the optimal soil softening coefficient are obtained by iterative solution using the least squares method. The optimal parameters are associated with the soil layer type, pile length, pile diameter and pile material parameters of the corresponding project and stored to establish a special parameter library for buckling calculation of ultra-long piles, which can be used for rapid calculation and parameter reuse under similar geological and pile type conditions.

[0169] Specifically, using the measured critical load of pile buckling or the result of high-precision numerical simulation as the target value, the objective function is constructed using the least squares method, and the depth attenuation index ξ and the soil softening coefficient η are inverted and optimized. The optimized parameters are then stored in association with engineering geological conditions and pile type parameters to establish a project-specific parameter library, providing accurate parameter support for similar projects.

[0170] Representative measured results of pile buckling or high-precision data simulation results were selected as the inversion target values. The buckling test of the test piles was conducted through full-scale field test piles. The load-displacement curve at the pile top was collected, and the load value corresponding to the "displacement mutation point" was taken as the measured critical load. (Right now High-precision numerical simulations were performed using finite element software such as ABAQUS / PLAXIS to establish a refined model considering pile-soil contact and soil elastoplasticity, and to calculate the critical load for numerical simulation. (Right now ).

[0171] With depth decay index and soil softening coefficient To optimize the variables, with the objective of minimizing the sum of squared residuals between the corrected value and the target value, the objective function is constructed as follows: In the formula, The number of inversion samples, For the first root test pile corresponding The correction value for the critical buckling load.

[0172] The least squares method is used for inversion: The least squares method is a classic method for inverting engineering parameters. Its core is to obtain the optimal parameter solution by finding that the partial derivatives of the objective function are zero.

[0173] ;

[0174] ;

[0175] The above system of equations is solved using the Newton-Raphson iterative method, and the convergence condition is: ;in, , This represents the number of iterations. If the geological conditions and pile type parameters of a new project match the entries in the library by ≥80%, the optimized parameters can be directly called; if the matching degree is <80%, the parameters in the library are used as the initial values, and only a few iterations are needed to obtain the new parameters, which greatly improves the calculation efficiency.

[0176] This step transforms empirical parameters into precise measured / numerical simulation optimization parameters through least squares inversion, significantly improving the computational accuracy of the correction method. The inversion objective function uses the criterion of "minimizing the sum of squared residuals" while taking into account the statistical characteristics of multiple test pile samples, making the optimization results more reliable. The project-specific parameter library enables the associated storage and reuse of "parameter-geology-pile type," solving the problem of repeated inversion for different projects, which is an important practical innovation of this invention. The implementation examples verify the effectiveness of the inversion process, with the relative error between the calculated and measured values ​​of the optimized parameters being less than 0.5%, and the application of the parameter library can significantly improve computational efficiency.

[0177] It is worth noting that the various units included in the above system embodiments are only divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of each functional unit are only for easy differentiation and are not used to limit the scope of protection of the present invention.

[0178] Furthermore, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware, and the corresponding program can be stored in a computer-readable storage medium.

[0179] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for correcting the critical buckling load of ultra-long piles considering the attenuation of soil stiffness around the pile, characterized in that, Includes the following steps: Step S1: Layered acquisition of pile-soil foundation parameters: Using a combination of geological drilling, in-situ testing and indoor geotechnical testing, pile-soil foundation parameters are collected layer by layer to establish a discrete array of soil layer profiles. Step S2: Establish a depth-deformation bivariate pile perimeter soil stiffness attenuation model: Define the depth attenuation factor. and load-deformation attenuation factor We constructed formulas for the attenuation of the pile perimeter soil bed coefficient and the attenuation of the shear stiffness in relation to the coupling depth and lateral deformation. Step S3: Construct the buckling control equation of the attenuated two-parameter foundation: Introduce the stiffness attenuation model established in step S2 into the two-parameter foundation model to construct the buckling control equation of the ultra-long pile considering stiffness attenuation. Step S4, Dimensionless processing and attenuation iteration-eigenvalue coupling solution: The buckling control equation is dimensionless, and the Galerkin method is used to discretize the dimensionless equation, so that the lateral deflection of the pile is expressed as a linear combination of buckling mode functions. Step S5: Calculate the correction value for the critical buckling load: based on the converged lateral deflection distribution of the pile. Substituting into the stiffness attenuation formula, the actual soil stiffness at each depth is obtained. and Calculate the soil stiffness attenuation correction factor according to the correction factor calculation formula. Ultimately, the formula was corrected. We obtained the corrected value of the critical buckling load for ultra-long piles, taking into account the attenuation of the stiffness of the soil around the pile. Step S6, Buckling Instability Judgment and Safety Assessment: Based on the correction value of the critical buckling load. Compared with the actual vertical load The ratio of the two values ​​is used to determine the buckling instability and safety of ultra-long piles. Step S7, Parameter Inversion Optimization and Dedicated Database Establishment: Using the measured or numerical simulation results of pile buckling as the target, invert and optimize the depth attenuation index. and soil softening coefficient Establish a dedicated parameter library for the project.

2. The method for correcting the critical buckling load of ultra-long piles considering the attenuation of soil stiffness around the pile, as described in claim 1, is characterized in that... In step S1, the specific process for obtaining pile-soil foundation parameters in layers is as follows: Step S11: Determine the layering principle: Using the length range of the ultra-long pile as the boundary, divide the soil layers penetrated by the pile into calculation layers; Step S12: Collect pile parameters: pile elastic modulus Moment of inertia of cross section Pile length Pile diameter Aspect Ratio ; Step S13: Soil stratification parameter acquisition: Initial subgrade coefficient Initial shear stiffness Critical lateral strain Ultimate lateral displacement Cohesion / Internal friction angle ; Step S14, Load and Constraint Parameter Acquisition: Acquire vertical axial load. Pile top constraint conditions; Pile bottom constraint conditions; Step S15, Parameter Validation and Outlier Handling: Perform consistency validation on the parameters, remove outliers, and organize all parameters into a two-dimensional array according to the calculation layer; Step S16: Determine the initial value of the attenuation characteristic parameter: Determine the depth attenuation index. and soil softening coefficient .

3. The method for correcting the critical buckling load of ultra-long piles considering the attenuation of soil stiffness around the pile, as described in claim 1, is characterized in that... In step S11, when the thickness of the same geological layer is greater than 10m, according to... Subdivide the calculation layers; the interfaces between different geological layers must be decomposed as calculation layers, and the pile top must also be considered. Pile bottom The scope is forcibly subdivided, and each calculation layer is numbered; the specific numbering rules are as follows: the soil layers traversed by the ultra-long piles are divided according to geological stratification. The computational layer, the first Layer depth range is , Record the center depth of each layer For each calculation layer, soil stratification parameters are collected to form a discretized parameter matrix.

4. The method for correcting the critical buckling load of ultra-long piles considering the attenuation of soil stiffness around the pile, as described in claim 1, is characterized in that... In step S2, the depth attenuation factor is defined. and load-deformation attenuation factor The specific formula is as follows: ； ； In the formula, It is a natural constant. The depth decay index, To calculate the depth of the point, This refers to the total length of the extra-long piles. Let z be the lateral deflection of the pile at depth z. This represents the ultimate lateral displacement of the soil around the pile. This is the soil softening coefficient; According to the defined depth attenuation factor and load-deformation attenuation factor Formulas for attenuation of the pile perimeter soil bed coefficient and shear stiffness in relation to coupling depth and lateral deformation are constructed as follows: ， ； In the formula, This is the soil subgrade coefficient around the pile. This represents the initial soil subgrade coefficient around the piles. This represents the actual shear stiffness of the soil surrounding the pile. This represents the initial shear stiffness of the soil surrounding the pile.

5. The method for correcting the critical buckling load of ultra-long piles considering the attenuation of soil stiffness around the pile, as described in claim 1, is characterized in that... In step S3, a shear stiffness term is introduced into the foundation model, and the shear stiffness term is adjusted according to depth. With lateral deformation Substituting the coupled attenuated soil stiffness around the pile into the governing equation, an attenuated two-parameter buckling governing equation for ultra-long piles is established, as follows: ； In the formula, The elastic modulus of the pile material. Let the moment of inertia of the pile cross section be , This is the fourth derivative of lateral deflection with respect to depth. The vertical axial load applied to the top of the pile. This is the second derivative of the lateral deflection with respect to depth.

6. The method for correcting the critical buckling load of ultra-long piles considering the attenuation of soil stiffness around the pile, as described in claim 1, is characterized in that... In step S4, the specific process of dimensionless processing and decay iteration-eigenvalue coupled solution is as follows: Step S41: Define dimensionless variables for depth, lateral deflection, vertical load, subgrade coefficient and shear stiffness in the buckling control equation. According to the composite function differentiation rule, convert the derivative terms in the attenuated two-parameter ultra-long pile buckling control equation into dimensionless form to obtain the dimensionless buckling control equation. Step S42: Using the Galerkin method, the dimensionless lateral deflection is expressed as a linear combination of buckling mode functions, substituted into the equation, and weighted integral to form a system of eigenvalue equations; Step S43: Starting from the initial stiffness, obtain the lateral deflection of the pile by solving the eigenvalue equations. Update the attenuation stiffness of the soil around the pile according to the lateral deflection and iterate cyclically until the relative error between two adjacent buckling critical loads meets the preset convergence accuracy. Output the converged buckling critical load and the lateral deflection distribution of the pile.

7. The method for correcting the critical buckling load of ultra-long piles considering the attenuation of soil stiffness around the pile, as described in claim 1, is characterized in that... In step S43, the specific process of the iterative loop is as follows: Step S431: Initialize parameters: Take the initial stiffness without attenuation. Set convergence precision Number of iterations initial eigenvalues ; Step S432, Solving the nth iteration: , Substituting the eigenvalue equations from step S42, the mode shape coefficients are obtained. Dimensionless initial buckling critical load and deflection distribution ; Step S433, Update stiffness parameters: Convert to dimensional deflection Substituting into the stiffness attenuation formula, we obtain the updated result. and Then convert to dimensionless stiffness and ; Step S434, Convergence Judgment: Calculate the relative error of the load between two adjacent iterations. ,like The iteration converges, and the output is a dimensional initial buckling critical load. Lateral deflection distribution of pile body ;like ,make Return to step S432 and continue iterating.

8. The method for correcting the critical buckling load of ultra-long piles considering the attenuation of soil stiffness around the pile, as described in claim 1, is characterized in that... In step S5, the soil stiffness attenuation correction coefficient is calculated. The specific formula is: ； In the formula, For the first ultra-long pile First-order buckling mode function, is the second derivative of the mode shape function.

9. The method for correcting the critical buckling load of ultra-long piles considering the attenuation of soil stiffness around the pile, as described in claim 1, is characterized in that... In step S6, the criteria for judging and evaluating the buckling instability of ultra-long piles are as follows: Calculate the safety factor. Safety factor Compared with the allowable safety factor specified in the standard In comparison, if If the buckling stability of the ultra-long pile meets the design requirements; If the excessively long pile is deemed to have a risk of buckling instability, the design needs to be optimized by increasing the pile diameter, adjusting the pile length, or reinforcing the soil around the pile.

10. The method for correcting the critical buckling load of ultra-long piles considering the attenuation of soil stiffness around the pile, as described in claim 1, is characterized in that... In step S7, the critical load of the test pile buckling measured or the critical load of the high-precision numerical simulation is used as the target value. An objective function is constructed with the depth attenuation index ξ and the soil softening coefficient η as optimization variables and the goal of minimizing the sum of squared residuals between the calculated value and the target value. The optimal depth attenuation index and the optimal soil softening coefficient are obtained by iterative solution using the least squares method. The optimal parameters are associated with the soil layer type, pile length, pile diameter and pile material parameters of the corresponding project and stored to establish a special parameter library for buckling calculation of ultra-long piles, which is used for rapid calculation and parameter reuse under similar geological and pile type conditions.

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