Calculation method of horizontal bearing reliability of slope foundation piles based on active learning Kriging model

Abstract

The present invention provides a method for calculating the horizontal bearing reliability of slope foundation piles based on an active learning Kriging model, comprising the following steps: determining the specific type and distribution of random variables that affect the horizontal bearing reliability of slope foundation piles and generating a corresponding sample library; extracting input samples and calculating the horizontal bearing function of slope foundation piles using a theoretical analysis model for the horizontal bearing of transmission tower foundation piles in slope sections to form an initial sample pair; constructing a Kriging model based on the current sample input-output data; and solving the failure probability using the Kriging model for the current sample library. By combining the theoretical analysis model for the horizontal bearing reliability of transmission tower foundation piles in slope sections and the active learning Kriging model, the computational efficiency can be significantly improved for the problem of horizontal bearing reliability of slope foundation piles, and the horizontal bearing reliability of transmission tower foundation piles in slope sections can be evaluated under actual computational conditions. This provides a way to further analyze the impact mechanism of random factors and slope effects on reliability.

Description

Technical Field

[0001] The present invention relates to the technical field of transmission tower pile foundation reliability analysis, and in particular to a method for calculating the horizontal bearing reliability of slope foundation piles based on an active learning Kriging model. Background Art

[0002] During the construction of power transmission lines in mountainous areas, many transmission towers are located on steep terrain with complex geological conditions. Compared to foundation piles on flat ground, transmission tower foundation piles on slopes lack soil on one side, resulting in more complex internal forces and deformations under horizontal loads. Therefore, when constructing infrastructure in mountainous areas and other special terrain conditions, particular attention should be paid to the safety and stability of the horizontal bearing capacity of foundation piles on sloped sections.

[0003] Domestic and international scholars have conducted extensive research on the horizontal bearing characteristics of slope piles. These include analyzing the effects of slope distance and slope ratio on the horizontal bearing deformation of piles; studying the key factors influencing the horizontal bearing capacity of piles based on model tests; investigating the mechanism by which the spatial effect of slopes influences pile displacement and internal forces under horizontal loads; and analyzing the ultimate failure modes of horizontally loaded rigid piles on slope sections, based on which a mapping formula between bearing capacity and slope toe has been fitted. However, these studies primarily employ deterministic analysis methods, focusing on the mechanism by which slopes influence the bearing characteristics of piles. However, in reality, parameters such as piles and soils have strong stochastic characteristics, resulting in significant uncertainty in the horizontal bearing performance of piles.

[0004] Uncertainty is a major safety hazard affecting the horizontal bearing capacity of pile foundations. To mitigate the resulting safety issues, many researchers have employed reliability analysis methods to assess the horizontal bearing capacity of pile foundations. However, current research primarily relies on traditional reliability theories such as the verification point method, response surface methods, and Monte Carlo simulations. These methods struggle to ensure efficient and convergent solutions for the complex and high-dimensional limit state equations of pile foundations. Furthermore, these studies primarily focus on flat-ground pile foundations, with limited consideration given to the horizontal bearing reliability of pile foundations on sloped sections. Summary of the Invention

[0005] The present invention aims to at least solve the problem in the prior art that the research on the horizontal bearing characteristics of slope foundation piles is mostly based on deterministic analysis methods, focusing on the influence mechanism of slope on the stress characteristics of foundation piles. However, in fact, parameters such as piles and soil have strong random characteristics, and the horizontal bearing performance of foundation piles shows obvious uncertainty. The uncertainty factor is a major safety hazard affecting the horizontal bearing of foundation piles; although some technologies use reliability analysis methods to evaluate the horizontal bearing performance of foundation piles, related research is mainly based on traditional reliability theories such as verification point method, response surface, Monte Carlo, etc. for analysis. Faced with high-dimensional and complex foundation pile limit state equations, it is difficult to ensure solution efficiency and convergence; and its research objects are mostly flat foundation piles, and less consideration is given to the horizontal bearing reliability of foundation piles in slope sections, making it difficult to provide effective guidance for the reliability analysis of transmission tower pile foundations and the optimization of transmission tower pile foundation design parameters, which is one of the technical problems affecting the safety and stability of the transmission system.

[0006] To this end, the present invention provides a method for calculating the horizontal bearing reliability of slope foundation piles based on an active learning Kriging model.

[0007] The present invention provides a method for calculating the horizontal bearing reliability of slope foundation piles based on an active learning Kriging model, comprising the following steps:

[0008] S1. Determine the specific type and distribution of random variables that affect the horizontal bearing reliability of slope foundation piles and generate a corresponding sample library;

[0009] S2. Extract input samples and calculate the horizontal bearing function of the slope foundation piles using the theoretical analysis model of the horizontal bearing of the transmission tower foundation piles on the slope section to form an initial sample pair;

[0010] S3, constructing a Kriging model based on the current sample input-output data;

[0011] S4. For the current sample library, the Kriging model is used to solve the failure probability.

[0012] The method for calculating the horizontal bearing reliability of slope foundation piles based on the active learning Kriging model according to the above technical solution of the present invention may also have the following additional technical features:

[0013] In the above technical solution, a theoretical analysis model of the horizontal bearing capacity of the transmission tower foundation piles on the slope section is established based on the deformation differential equation of the slope pile foundation, including:

[0014] S21. Considering the slope effect, according to the pile stress analysis model, establish the deformation and deflection differential equation of the slope section pile;

[0015] S22. Solve the deformation and deflection differential equation of the slope pile established in S21 by using the central difference theory, combine the control differential equations of each node of the pile with the boundary condition equations, and establish the horizontal displacement matrix equation of the slope pile including the virtual node displacement;

[0016] S23. By solving the horizontal displacement matrix equation of the slope foundation pile established in S22, the horizontal displacement of the slope transmission tower foundation piles at each position under different horizontal loads and the rotation angle, bending moment and shear force of the slope section foundation piles are obtained.

[0017] In the above technical solution, the horizontal bearing function of the slope foundation pile is constructed according to different failure modes, and the failure modes include horizontal displacement exceeding limit mode and material yield mode;

[0018] When the failure mode is the horizontal displacement exceeding limit mode, the horizontal bearing function of the slope foundation pile is:

[0019] g d (s)=d(s)-D l

[0020] When the failure mode is the material yield mode, the horizontal bearing capacity function of the slope foundation pile is:

[0021] g M (s)=M(s)-M l

[0022] Among them, g d (s) is the horizontal displacement function of the pile foundation, g d (s)>0 means the pile is in a safe state, g d (s) < 0 indicates pile failure, g d (s) = 0 indicates that the foundation pile is in the limit state; s is a random variable that affects the horizontal bearing reliability of the slope foundation pile; d(s) is the horizontal displacement value of the foundation pile calculated based on the theoretical analysis model of the horizontal bearing of the transmission tower foundation pile on the slope section; D l is the horizontal displacement limit;

[0023] g M (s) is the yield function of the pile material; M(s) is the pile bending moment value calculated based on the theoretical analysis model of the horizontal bearing of the transmission tower pile on the slope; M l is the bending bearing capacity.

[0024] In the above technical solution, the Kriging model described in S3 evaluates the performance function by fitting the physical process instead of the theoretical analysis process;

[0025] The Kriging model is:

[0026]

[0027]

[0028] Among them, F and R are the regression function value matrix and correlation function value matrix corresponding to the input samples respectively; Y is the actual response matrix of the system; N is the number of input samples; r is the correlation function vector between the unknown input point and the input sample.

[0029] In the above technical solution, the reliability analysis method EGRA is also used in step S3 to optimize the Kriging model, and the samples corresponding to the maximum value of the expected feasibility function EF are solved as optimized samples to update the Kriging model.

[0030] In the above technical solution, solving the sample corresponding to the maximum value of the expected feasibility function EF as the optimization sample to update the Kriging model includes:

[0031] S31, calculating the EF function value corresponding to the current sample, and determining whether it meets the convergence criterion;

[0032] S32. When the convergence requirements are met, S4 can be executed; otherwise, the best updated sample pair must be determined through the EF function and numerical simulation, and the sample corresponding to the maximum value of the expected feasibility function EF is solved as the optimized sample to update the Kriging model until the EF function value corresponding to the current sample meets the convergence requirements.

[0033] In any of the above technical solutions, the Kriging model established by S3 is combined with the Monte Carlo simulation process MCS, and the failure probability of the slope foundation piles is calculated by statistically analyzing the Kriging model responses corresponding to different random variables that affect the horizontal bearing reliability of the slope foundation piles.

[0034] In the above technical solution, it is characterized in that the method for calculating the failure probability of slope foundation piles is:

[0035]

[0036] Among them, P f is the failure probability; is the simulated failure probability; n mc is the number of samples; I(g) is the fault indication function.

[0037] In any of the above technical solutions, the accuracy of the simulated failure probability is measured by calculating the coefficient of variation of the failure probability COV; the calculation method of the horizontal bearing reliability of the slope foundation pile also includes:

[0038] S5. Calculate the coefficient of variation of the failure probability COV. If COV is lower than the threshold value, the iteration ends and the current analysis result is the exact solution of the failure probability. Otherwise, the sample size needs to be adjusted and updated until the termination criteria are met.

[0039] In the above technical solution, the calculation method of the failure probability variation coefficient COV is:

[0040]

[0041] in, is the simulated failure probability; n mc is the sample size.

[0042] In summary, due to the adoption of the above technical features, the beneficial effects of the present invention are:

[0043] Based on the theoretical analysis model of the horizontal bearing capacity of transmission tower foundation piles on slope sections and combined with the active learning Kriging model, an efficient reliability analysis method for slope transmission tower foundation piles is proposed. This method can greatly improve the calculation efficiency while ensuring accuracy. On this basis, combined with actual projects, the horizontal bearing capacity reliability of slope transmission tower foundation piles and the influence mechanism of different factors on the reliability are evaluated and analyzed.

[0044] Additional aspects and advantages of the invention will become apparent from the description which follows, or may be learned by practice of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments with reference to the accompanying drawings, in which:

[0046] Figure 1 This is a flow chart of a method for calculating the horizontal bearing reliability of slope foundation piles based on an active learning Kriging model according to an embodiment of the present invention;

[0047] Figure 2 This is a diagram of a force analysis model for slope pile foundations in a method for calculating the horizontal bearing reliability of slope pile foundations based on an active learning Kriging model according to an embodiment of the present invention;

[0048] Figure 3 This is a comparative analysis diagram of the horizontal displacement calculation results of the theoretical analysis of the horizontal bearing of piles and the finite element simulation analysis in a slope pile horizontal bearing reliability calculation method based on the active learning Kriging model according to one embodiment of the present invention;

[0049] Figure 4 This is a comparative analysis diagram of the calculation results of pile body bending moment from theoretical analysis of pile horizontal bearing and finite element simulation analysis in a slope pile horizontal bearing reliability calculation method based on an active learning Kriging model in one embodiment of the present invention. DETAILED DESCRIPTION

[0050] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that, in the absence of conflict, the embodiments of the present application and the features therein can be combined with each other.

[0051] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0052] Refer to the following Figures 1 to 4 The following describes a method for calculating the horizontal bearing reliability of slope foundation piles based on an active learning Kriging model according to some embodiments of the present invention.

[0053] Some embodiments of the present application provide a method for calculating the horizontal bearing reliability of slope foundation piles based on an active learning Kriging model.

[0054] like Figures 1 to 4 As shown, the first embodiment of the present invention proposes a method for calculating the horizontal bearing reliability of slope foundation piles based on an active learning Kriging model, comprising the following steps:

[0055] S1. Determine the specific types and distribution of random variables that affect the horizontal bearing reliability of slope foundation piles and generate a corresponding sample library. Random variables that affect the horizontal bearing reliability of slope foundation piles include pile and soil random variables, such as pile length, pile diameter, elastic modulus, soil resistance proportional coefficient, horizontal load borne by the pile top, bending moment, etc.

[0056] S2. Extract input samples and calculate the horizontal bearing function of the slope foundation piles using the theoretical analysis model of the horizontal bearing of the transmission tower foundation piles on the slope section to form an initial sample pair;

[0057] Based on the deformation differential equation of the slope pile foundation, a theoretical analysis model for the horizontal bearing of the transmission tower foundation piles in the slope section is established, including:

[0058] S21. Considering the slope effect, according to the pile stress analysis model, establish the deformation and deflection differential equation of the slope section pile;

[0059] S22. Solve the deformation and deflection differential equation of the slope pile established in S21 by using the central difference theory, combine the control differential equations of each node of the pile with the boundary condition equations, and establish the horizontal displacement matrix equation of the slope pile including the virtual node displacement;

[0060] S23. By solving the horizontal displacement matrix equation of the slope foundation pile established in S22, the horizontal displacement of the slope transmission tower foundation piles at each position under different horizontal loads and the rotation angle, bending moment and shear force of the slope section foundation piles are obtained.

[0061] Constructing the horizontal bearing function of the slope foundation pile according to different failure modes, wherein the failure modes include a horizontal displacement exceeding limit mode and a material yielding mode;

[0062] When the failure mode is the horizontal displacement exceeding limit mode, the horizontal bearing function of the slope foundation pile is:

[0063] g d (s)=d(s)-D l

[0064] When the failure mode is the material yield mode, the horizontal bearing capacity function of the slope foundation pile is:

[0065] g M (s)=M(s)-M l

[0066] Among them, g d (s) is the horizontal displacement function of the pile foundation, g d (s)>0 means the pile is in a safe state, g d (s) < 0 indicates pile failure, g d (s) = 0 indicates that the foundation pile is in the limit state; s is a random variable that affects the horizontal bearing reliability of the slope foundation pile; d(s) is the horizontal displacement value of the foundation pile calculated based on the theoretical analysis model of the horizontal bearing of the transmission tower foundation pile on the slope section; D l is the horizontal displacement limit;

[0067] g M (s) is the yield function of the pile material; M(s) is the pile bending moment value calculated based on the theoretical analysis model of the horizontal bearing of the transmission tower pile on the slope; M l is the bending bearing capacity.

[0068] S3, constructing a Kriging model based on the current sample input-output data;

[0069] The Kriging model described in S3 evaluates the performance function by fitting the physical process instead of the theoretical analysis process;

[0070] The Kriging model is:

[0071]

[0072]

[0073] Among them, F and R are the regression function value matrix and correlation function value matrix corresponding to the input samples respectively; Y is the actual response matrix of the system; N is the number of input samples; r is the correlation function vector between the unknown input point and the input sample.

[0074] In some embodiments, step S3 further uses a reliability analysis method EGRA to optimize the Kriging model, and solves the sample corresponding to the maximum value of the expected feasibility function EF as the optimized sample to update the Kriging model.

[0075] Solving the sample corresponding to the maximum value of the expected feasibility function EF as the optimization sample to update the Kriging model includes:

[0076] S31, calculating the EF function value corresponding to the current sample, and determining whether it meets the convergence criterion;

[0077] S32. When the convergence requirements are met, S4 can be executed; otherwise, the best updated sample pair must be determined through the EF function and numerical simulation, and the sample corresponding to the maximum value of the expected feasibility function EF is solved as the optimized sample to update the Kriging model until the EF function value corresponding to the current sample meets the convergence requirements.

[0078] S4. For the current sample library, the Kriging model is used to solve the failure probability.

[0079] The Kriging model established by S3 is combined with the Monte Carlo simulation process MCS. The failure probability of slope foundation piles is calculated by statistically analyzing the Kriging model responses corresponding to different random variables affecting the horizontal bearing reliability of slope foundation piles.

[0080] The method for calculating the failure probability of slope foundation piles is:

[0081]

[0082] Among them, P f is the failure probability; is the simulated failure probability; n mc is the number of samples; I(g) is the fault indication function.

[0083] The expression of the fault indication function is:

[0084]

[0085] In some embodiments, the accuracy of the simulated failure probability is measured by calculating the failure probability variation coefficient COV; the slope foundation pile horizontal bearing reliability calculation method further includes:

[0086] S5. Calculate the coefficient of variation of the failure probability COV. If COV is lower than the threshold value, the iteration ends and the current analysis result is the exact solution of the failure probability. Otherwise, the sample size needs to be adjusted and updated until the termination criteria are met.

[0087] The calculation method of the coefficient of variation of failure probability COV is:

[0088]

[0089] in, is the simulated failure probability; n mc is the sample size.

[0090] The second embodiment of the present invention proposes a method for calculating the horizontal bearing reliability of slope foundation piles based on the active learning Kriging model, and on the basis of the first embodiment, as shown in FIG. Figures 1 to 4 As shown, the following steps are included:

[0091] Determine the specific types and distributions of pile and soil random variables and generate corresponding sample libraries.

[0092] Input samples are extracted through Latin hypercube design, and the horizontal bearing capacity function of slope foundation piles is calculated using the theoretical analysis model of horizontal bearing capacity of transmission tower foundation piles on slope sections to form initial sample pairs.

[0093] A Kriging model is constructed based on the current sample input-output data to replace the numerical simulation evaluation function.

[0094] The EF function value corresponding to the current sample is calculated to determine whether the convergence criterion is met. In this embodiment, convergence is determined when the EF function value is less than 0.001.

[0095] When the convergence requirements are met, the next step can be executed; otherwise, the best updated sample pair needs to be determined through EF function and numerical simulation, and the Kriging model is updated until the convergence requirements are met.

[0096] For the current sample library, the Kriging model is used to solve the failure probability.

[0097] Calculate the coefficient of variation of the failure probability COV. If COV < 5%, the iteration ends and the current analysis result is the exact solution to the failure probability. Otherwise, the sample size needs to be adjusted and updated until the termination criteria are met.

[0098] The third embodiment of the present invention proposes a method for calculating the horizontal bearing reliability of slope foundation piles based on the active learning Kriging model, and on the basis of any of the above embodiments, as Figures 1 to 4 As shown, a theoretical analysis model of the horizontal bearing capacity of the transmission tower foundation piles on the slope section is established based on the deformation differential equation of the slope pile foundation, including:

[0099] S21. Considering the slope effect, according to the pile stress analysis model, establish the deformation and deflection differential equation of the slope section pile;

[0100] like Figure 1As shown in the figure, under the action of pile top load, the transmission tower foundation pile in the slope section includes the slope-affected part l1 and the embedded part l2. Due to the slope in front of the foundation pile, there is an open surface, which leads to asymmetry of the soil on both sides of the foundation pile. This weakens the horizontal resistance of the soil in the slope-affected section to a certain extent, which is the "slope effect". Among them, the length of the slope-affected section is:

[0101] l1=λd tanθ

[0102] Among them, λ is the slope effect reduction coefficient, which is generally taken as 3-5; d is the pile diameter; θ is the slope gradient.

[0103] Considering the above slope effect, according to the force analysis model, the deformation and deflection differential equation of the slope section foundation pile can be obtained as follows:

[0104]

[0105] Where EI is the bending stiffness of the pile; x is the horizontal displacement of the pile; y is the distance from the deformation calculation point to the pile top; C(y) is the foundation resistance coefficient on the pile side; B is the calculated width of the pile. When the pile diameter d≤1m, B=0.9(1.5d+0.5); otherwise, B=0.9(d+1).

[0106] For the pile side foundation resistance coefficient, in order to consider the influence of the slope effect, the m method can be used for estimation:

[0107]

[0108] Among them, m is the foundation resistance proportional coefficient. Starting from 15°, for every 15° increase in slope, m decreases by an average of 45%.

[0109] S22. Solve the deformation and deflection differential equation of the slope pile established in S21 by using the central difference theory, combine the control differential equations of each node of the pile with the boundary condition equations, and establish the horizontal displacement matrix equation of the slope pile including the virtual node displacement;

[0110] First, the load-influence depth H of the pile foundation is divided into n equal parts, and two additional virtual nodes are set at each end, for a total of (n+5) nodes. After the node division is completed, the boundary conditions need to be determined. Pile foundation boundary conditions actually include four types: hinged, embedded, elastically embedded, and free. For transmission tower foundation piles, the main consideration is that the pile top is free and the pile end is embedded in the soil. The boundary condition difference formats are as follows:

[0111] Pile top

[0112] Pile end

[0113] Among them, x iis the horizontal displacement at different nodes of the pile (i=-1, -2, N+1, N+2 are the top and end virtual nodes, i=0, N are the top and end nodes respectively, and the rest can be deduced by analogy); L and M are the lateral load and bending moment respectively; s is the distance between nodes.

[0114] The governing differential equations at different nodes of the slope transmission tower foundation pile are:

[0115] Slope influence section

[0116] Embedded section

[0117] On this basis, the control differential equations of each node of the pile and the boundary condition equations are combined to obtain the matrix equation for solving the horizontal displacement of the slope pile including the virtual node displacement:

[0118]

[0119] Among them, a i,j are the coefficients of each node in the pile differential equation, i and j represent the calculation nodes from the pile top to the pile end and the node numbers in the recursive relationship. k,h is the coefficient of each node in the boundary condition, k = 1, 2, 3, 4, corresponding to different boundary equations, and h is the node number of the corresponding boundary.

[0120] S23. By solving the horizontal displacement matrix equation of the slope foundation pile established in S22, the horizontal displacement of the slope transmission tower foundation piles at each position under different horizontal loads and the rotation angle, bending moment and shear force of the slope section foundation piles are obtained.

[0121] Since the differential format of the slope section pile rotation angle, bending moment and shear force can be expressed as:

[0122]

[0123] Among them, γ i 、M i 、L i are the rotation angle, bending moment and shear force at different nodes of the pile foundation. Substituting the calculated horizontal displacement of the pile foundation into the above formula, the corresponding rotation angle, bending moment and shear force can be obtained.

[0124] Verify the accuracy of the theoretical analysis model for the horizontal bearing of transmission tower foundation piles on slope sections established above:

[0125] A finite element model of the slope foundation pile was established using ABAQUS for verification. The soil was simulated based on the Mohr-Coulomb theory, with constraints on the lateral displacements on the left and right sides and the bottom surface displacement in three directions. Symmetrical constraints were applied to the front of the soil to improve computational efficiency. Surface-to-surface contact was established between the pile foundation and the soil, with hard contact in the normal direction and friction contact in the tangential direction. The friction coefficient was calculated using the formula:

[0126]

[0127] Where μ is the friction coefficient; is the friction angle.

[0128] The horizontal displacement and bending moment of the foundation piles in the 30° slope section under the action of a horizontal force of 1000kN and a bending moment of 1500kN·m were calculated using the finite element model and the analytical model respectively. The results of the two methods are compared in Figure 3 and Figure 4 ; Figure 3 In the figure, most of the lines on the left are the results of the analytical model, and most of the lines on the right are the results of the finite element model; Figure 4 In the figure, most of the lines on the left are the results of the finite element model, and most of the lines on the right are the results of the analytical model.

[0129] from Figure 3 、 Figure 4 It can be seen that the theoretical analysis results of the horizontal bearing of the foundation piles have the same overall change trend as the finite element simulation results, and the calculated results are similar. Although there are some deviations in local areas, the maximum relative deviation does not exceed 5% (the horizontal displacement deviation of the pile top is 0.78%, and the maximum bending moment deviation of the pile body is 4.4%), which verifies the accuracy and effectiveness of the theoretical analysis model.

[0130] The fourth embodiment of the present invention proposes a method for calculating the horizontal bearing reliability of slope foundation piles based on the active learning Kriging model, and based on any of the above embodiments, as Figures 1 to 4 As shown, the failure of the laterally loaded piles mainly includes two modes: horizontal displacement exceeding the limit and material yielding. The horizontal bearing function of the slope piles is constructed for different failure modes, and the failure modes include horizontal displacement exceeding the limit mode and material yielding mode.

[0131] When the failure mode is the horizontal displacement exceeding limit mode, the horizontal bearing function of the slope foundation pile is:

[0132] g d (s)=d(s)-D l

[0133] When the failure mode is the material yield mode, the horizontal bearing capacity function of the slope foundation pile is:

[0134] g M (s)=M(s)-M l

[0135] Among them, g d (s) is the horizontal displacement function of the pile foundation, g d (s)>0 means the pile is in a safe state, g d (s) < 0 indicates pile failure, g d (s) = 0 indicates that the foundation pile is in the limit state; s is the random variable that affects the horizontal bearing reliability of the slope foundation pile, that is, the random vector of the pile, soil, etc. system; d(s) is the horizontal displacement value of the foundation pile calculated according to the theoretical analysis model of the horizontal bearing of the transmission tower foundation pile on the slope section; D l is the horizontal displacement limit;

[0136] g M (s) is the yield function of the pile material; M(s) is the pile bending moment value calculated based on the theoretical analysis model of the horizontal bearing of the transmission tower pile on the slope; M l is the bending bearing capacity.

[0137] The fifth embodiment of the present invention proposes a method for calculating the horizontal bearing reliability of slope foundation piles based on the active learning Kriging model, and based on any of the above embodiments, as Figures 1 to 4 As shown in the figure, the performance function of slope pile foundations includes a highly complex analysis process for the pile's horizontal bearing capacity. Using traditional reliability theory can lead to difficulties such as inaccurate solutions and excessive computational scale. Kriging technology, however, can replace complex theoretical analysis processes by fitting complex physical processes, making it possible to efficiently and accurately evaluate the performance function.

[0138] The Kriging model considers a complex system as a Gaussian static random process, which includes two parts: linear regression and random state:

[0139]

[0140] Among them, x, are the input and corresponding output analog values respectively; f(x) T is the regression function vector that fits the overall law; β is the regression coefficient vector; z(x) has a mean of 0 and a variance of The stationary Gaussian process is used to describe the detail deviation, and its covariance matrix is:

[0141]

[0142] Among them, x i 、x j are different types of input variables in x; R(x i ,x j) is x i 、x j The spatial correlation function of , usually the Gaussian function.

[0143] After the input sample is determined, the regression coefficient vector β and the process variance It can be calculated using the generalized least squares estimation method:

[0144]

[0145]

[0146] Among them, F and R are the regression function value matrix and correlation function value matrix corresponding to the input samples respectively; Y is the actual response matrix of the system; N is the number of input samples.

[0147] On this basis, the optimal linear unbiased estimate and mean square error of the system response at the unknown input point can be derived as follows:

[0148]

[0149]

[0150] Where r is the correlation function vector between the unknown input point and the input sample; u = F T R -1 rf.

[0151] It should be noted that the initial Kriging model is significantly affected by the sample distribution and number, and often fails to accurately simulate the system response. Therefore, the model must be continuously updated through active learning functions to improve fitting accuracy. This embodiment uses an efficient global reliability analysis method widely used in the field of reliability for optimization. This method updates the proxy model by solving for the sample corresponding to the maximum value of the expected feasibility function EF as the optimization sample.

[0152] The sixth embodiment of the present invention proposes a method for calculating the horizontal bearing reliability of slope foundation piles based on the active learning Kriging model, and based on any of the above embodiments, as Figures 1 to 4As shown in the figure, a real-world project is used as an example. A section of the Jinshang-Hubei ±800kV UHVDC transmission line passes through the mountainous area of Ganzi Prefecture, Sichuan Province. The slope ranges from 25° to 45°, sometimes exceeding 50°, and averages 40°. The transmission tower foundations in this area are pile-column foundations constructed with C25 concrete. The pile length H is 15m, the pile diameter d is 2.5m, the elastic modulus E is 28GPa, and the coefficient of variation of the pile parameters is 0.025. The soil resistance proportional coefficient m averages 60MN / m², with a coefficient of variation of 0.25. The pile top is subjected to a horizontal load L of 1000kN and a bending moment M of 1500kN·m, with a coefficient of variation of 0.25. The pile bending bearing capacity is 8295kN·m, and the pile top displacement limit is 10mm.

[0153] Based on the above calculation conditions and parameters, Figure 1 The slope pile reliability analysis process shown in the figure calculates the probability of pile failure under lateral load.

[0154] Assuming that the uncertainty parameters (s = [H, d, E, m, L, M]) of the transmission line in this section follow a normal distribution and are mutually independent, a sample library of random variables is first generated using normal distribution theory, with a sample size of 105 selected for the initial iteration. Next, 50 different input vectors are selected using Latin hypercube sampling and substituted into the horizontal load-bearing theoretical model to obtain the corresponding pile displacements and bending moments, thereby evaluating the performance function. The slope gradient is assumed to have an average value of 40°, and the slope effect reduction factor is set to 4. An initial Kriging model is constructed based on the sample pairs consisting of input vectors and performance function values. The model is optimized using the EF active learning function until the convergence criterion of the EF function is less than 0.001. The Kriging model then rapidly outputs the performance function values corresponding to the sample library. The MCS method is then used to calculate the approximate failure probability and coefficient of variation. This process is repeated until the coefficient of variation is less than 5%, ultimately completing the failure probability calculation. The results of the Kriging model and the Monte Carlo method are compared in the following table.

[0155] Table 1 Comparison of calculation results of different reliability analysis methods

[0156]

[0157] The failure probability calculated using the MCS method can generally be considered an accurate result. As can be seen from the table above, the failure mode of pile displacement exceeding the limit is more likely to occur than material yield, and the lateral deformation of the pile is more sensitive when horizontally loaded. In terms of reliability analysis method performance, the failure probabilities simulated by the Kriging model method and the MCS method are basically consistent, with a maximum relative error of only 2.1%. In addition, under the premise of ensuring that the coefficient of variation of the two methods is less than 0.05, the MCS needs to complete 2×10 6The numerical analysis process requires only 311 times, while the Kriging model method requires only 311 times at most, and the total running time of the algorithm program is greatly shortened; this shows that the pile reliability analysis method based on the Kriging model can significantly reduce the computational cost while ensuring accuracy, and achieve efficient solution of the limit state equation of complex pile foundations.

[0158] The combined application of a theoretical analysis model for the horizontal bearing capacity of transmission tower foundation piles on sloped sections and an active learning Kriging model significantly improves computational efficiency and assesses the reliability of horizontal bearing capacity of transmission tower foundation piles on sloped sections under practical computational conditions. This provides a path for further analyzing the impact of random factors and slope effects on reliability.

[0159] In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any suitable manner in any one or more embodiments or examples.

[0160] Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the horizontal bearing reliability of slope foundation piles based on active learning Kriging model, characterized in that: The following steps are involved: S1. Determine the specific type and distribution of random variables that affect the horizontal bearing reliability of slope foundation piles and generate a corresponding sample library; S2. Extract input samples and calculate the horizontal bearing function of the slope foundation piles using the theoretical analysis model of the horizontal bearing of the transmission tower foundation piles on the slope section to form an initial sample pair; S3, constructing a Kriging model based on the current sample input-output data; S4. For the current sample library, use the Kriging model to solve the failure probability; Constructing the horizontal bearing function of the slope foundation pile according to different failure modes, wherein the failure modes include a horizontal displacement exceeding limit mode and a material yielding mode; When the failure mode is the horizontal displacement exceeding limit mode, the horizontal bearing function of the slope foundation pile is: When the failure mode is the material yield mode, the horizontal bearing capacity function of the slope foundation pile is: in, is the horizontal displacement function of the pile foundation, Indicates that the foundation pile is in a safe state. Indicates that the foundation pile has failed. Indicates that the foundation pile is in the ultimate state; is the random variable that affects the horizontal bearing reliability of slope foundation piles; is the horizontal displacement value of the foundation pile calculated based on the theoretical analysis model of the horizontal bearing capacity of the transmission tower foundation pile on the slope section; is the horizontal displacement limit; is the yield function of the pile material; is the pile bending moment value calculated based on the theoretical analysis model of the horizontal bearing capacity of the transmission tower foundation piles on the slope section; is the bending bearing capacity; The Kriging model described in S3 evaluates the performance function by fitting the physical process instead of the theoretical analysis process; The Kriging model is: in, 、 are the regression function value matrix and the correlation function value matrix corresponding to the input samples respectively; is the actual response matrix of the system; is the number of input samples; is the correlation function vector between the unknown input point and the input sample.

2. The method for calculating the horizontal bearing reliability of slope foundation piles based on the active learning Kriging model according to claim 1 is characterized in that: Based on the deformation differential equation of the slope pile foundation, a theoretical analysis model for the horizontal bearing of the transmission tower foundation piles in the slope section is established, including: S21. Considering the slope effect, according to the pile stress analysis model, establish the deformation and deflection differential equation of the slope section pile; S22. Solve the deformation and deflection differential equation of the slope pile established in S21 by using the central difference theory, combine the control differential equations of each node of the pile with the boundary condition equations, and establish the horizontal displacement matrix equation of the slope pile including the virtual node displacement; S23. By solving the horizontal displacement matrix equation of the slope foundation pile established in S22, the horizontal displacement of the slope transmission tower foundation piles at each position under different horizontal loads and the rotation angle, bending moment and shear force of the slope section foundation piles are obtained.

3. The method for calculating the horizontal bearing reliability of slope foundation piles based on the active learning Kriging model according to claim 1 is characterized in that: In step S3, the reliability analysis method EGRA is also used to optimize the Kriging model, and the samples corresponding to the maximum value of the expected feasibility function EF are used as optimized samples to update the Kriging model.

4. The method for calculating the horizontal bearing reliability of slope foundation piles based on the active learning Kriging model according to claim 3 is characterized in that: Solving the sample corresponding to the maximum value of the expected feasibility function EF as the optimization sample to update the Kriging model includes: S31, calculating the EF function value corresponding to the current sample, and determining whether it meets the convergence criterion; S32. When the convergence requirements are met, S4 can be executed; otherwise, the best updated sample pair must be determined through the EF function and numerical simulation, and the sample corresponding to the maximum value of the expected feasibility function EF is solved as the optimized sample to update the Kriging model until the EF function value corresponding to the current sample meets the convergence requirements.

5. The method for calculating the horizontal bearing reliability of slope foundation piles based on the active learning Kriging model according to any one of claims 1 to 4, characterized in that: The Kriging model established by S3 is combined with the Monte Carlo simulation process MCS. The failure probability of slope foundation piles is calculated by statistically analyzing the Kriging model responses corresponding to different random variables affecting the horizontal bearing reliability of slope foundation piles.

6. The method for calculating the horizontal bearing reliability of slope foundation piles based on the active learning Kriging model according to claim 5 is characterized in that: The method for calculating the failure probability of slope foundation piles is: in, is the failure probability; is the simulated failure probability; is the sample size; is the fault indication function.

7. The method for calculating the horizontal bearing reliability of slope foundation piles based on the active learning Kriging model according to any one of claims 1 to 4, characterized in that: The accuracy of the simulated failure probability is measured by calculating the coefficient of variation of the failure probability COV. The calculation method of the horizontal bearing reliability of the slope foundation pile also includes: S5. Calculate the coefficient of variation of the failure probability COV. If COV is lower than the threshold value, the iteration ends and the current analysis result is the exact solution of the failure probability. Otherwise, the sample size needs to be adjusted and updated until the termination criteria are met.

8. The method for calculating the horizontal bearing reliability of slope foundation piles based on the active learning Kriging model according to claim 7 is characterized in that: The calculation method of the coefficient of variation of failure probability COV is: in, is the simulated failure probability; is the sample size.

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