Finite element based analysis method and system for uplift performance of screw anchors

Abstract

The present application relates to the technical field of data processing, in particular to a screw anchor anti-pulling performance analysis method and system based on finite elements, comprising: obtaining a measured torque curve through a physical screwing-in test; initializing hardening soil model parameters and performing finite element simulation of the screwing-in process to obtain a simulated torque curve and an internal energy increment of an element; calculating a first difference between the simulated and measured torque curve trend components; evaluating soil quality differences at different depths using the frequency spectrum distribution of the measured torque curve fluctuation component to correct the internal energy increment of the element to obtain a comprehensive internal energy increment; determining model parameter errors based on a second difference between the measured total screwing-in work and the comprehensive internal energy increment and the first difference and correcting the parameters; and performing finite element analysis of the screw anchor anti-pulling process using the corrected parameters. The present application realizes calibration of soil model parameters and significantly improves the reliability of screw anchor anti-pulling performance analysis.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and specifically to a method and system for analyzing the pull-out performance of helical anchors based on the finite element method. Background Technology

[0002] As a crucial component for anchoring transmission line tower foundations, the pull-out performance analysis of helical anchors primarily relies on finite element numerical simulation. Conventional methods only simulate the pull-out process of the helical anchor, applying upward displacement or load to the soil model and evaluating pull-out performance by calculating the ultimate pull-out force. However, the actual installation process of helical anchors includes a screw-in stage (i.e., the helical anchor is drilled into the soil in a rotating manner). This stage causes compression and disturbance to the surrounding soil, altering its initial stress state and density, thus significantly affecting the load-bearing performance in the subsequent pull-out stage. Therefore, some improved methods have begun to simultaneously simulate the screw-in and pull-out processes, forming a cascaded simulation. That is, the process of the helical anchor screwing into the soil is simulated first, and then the pull-out process is simulated based on this, calculating the pull-out bearing capacity.

[0003] While cascaded simulations are theoretically closer to physical reality than single pull-out simulations, they face the challenge that the soil constitutive models used in finite element simulations (such as hardened soil models) contain multiple parameters (e.g., reference secant modulus, tangent modulus, cohesion, internal friction angle, etc.). These parameters directly determine the mechanical response of the soil during the screwing-in process. If the parameters of the hardened soil model are set improperly, the simulation results in the screwing-in stage will deviate from reality, and this error will be transmitted to the pull-out stage through the cascade relationship, leading to unreliable pull-out performance analysis results. Summary of the Invention

[0004] To address the problem of improper parameter settings in hardened soil model analysis, this invention provides a finite element method and system for analyzing the pull-out performance of helical anchors.

[0005] The finite element method for analyzing the pull-out performance of helical anchors and the system of the present invention adopt the following technical solution: One embodiment of the present invention provides a method for analyzing the pull-out performance of a helical anchor based on the finite element method, the method comprising the following steps: The curve of the screwing torque as the rotation angle when the helical anchor is screwed into the soil was measured by physical screwing test and recorded as the measured torque curve. The parameters of the hardened soil model are initialized, and a finite element simulation is performed on the process of the spiral anchor being screwed into the hardened soil model to obtain simulation results. The simulation results include the internal energy increment of each element in the hardened soil model and the simulated torque curve. The difference in the trend component between the simulated torque curve and the measured torque curve is denoted as the first difference. The spectral distribution of the fluctuation component of the measured torque curve is used to evaluate the soil quality differences of the hardened soil model at different depths. The soil quality differences at different depths are used to correct the internal energy increment of each element, and the sum of the corrected internal energy increments of all elements is denoted as the comprehensive internal energy increment. The error of the hardened soil model parameters is determined based on the difference between the total screwing work determined by the measured torque curve and the comprehensive internal energy increment, as well as the first difference. The hardened soil model parameters are then corrected based on the error. Finite element analysis was performed on the pull-out process of the helical anchor using the modified hardened soil model parameters.

[0006] Preferably, the specific steps for obtaining the trend component and the fluctuation component of the measured torque curve are as follows: Several sampling points are sampled from the measured torque curve; the sampling curve formed by all sampling points is called the initial curve; the initial curve is subjected to Fourier transform to obtain the first spectrum; the first spectrum is low-pass filtered using a preset cutoff frequency; the low-pass filtered first spectrum is subjected to inverse Fourier transform to obtain the trend component of the measured torque curve. The difference between the initial curve and the trend component is denoted as the fluctuation component of the measured torque curve.

[0007] Preferably, the difference in the trend component between the simulated torque curve and the measured torque curve is denoted as the first difference, and the specific steps include the following: The trend component of the measured torque curve is divided into several first segments, and the trend component of the simulated torque curve is divided into several second segments. The first and second segments with the same number are considered as each pair of segments, and the cosine similarity of each pair of segments is recorded as the similarity of each pair of segments. The mean of the similarities of all pairs of segments is recorded as the comprehensive similarity of the trend components between the simulated torque curve and the measured torque curve. The first difference is negatively correlated with the comprehensive similarity.

[0008] Preferably, the specific steps for evaluating the soil quality differences of the hardened soil model at different depths using the spectral distribution of the fluctuation component of the measured torque curve are as follows: The fluctuation component is divided into several third segments; the second spectrum of each third segment is obtained; the ingress depth corresponding to the mean of the abscissa of each third segment is obtained; for all third segments, the ingress depth and their second spectra are calculated, and the spectral difference between the two second spectra corresponding to any pair of ingress depths is calculated; the spectral difference corresponding to each pair of ingress depths is taken as the soil quality difference of the hardened soil model at any two soil layer depths.

[0009] Preferably, the specific steps for correcting the internal energy increment of each unit by utilizing soil quality differences at different depths are as follows: All the spiral depths constitute a depth sequence; a sampling depth is sampled every k elements from the depth sequence, where k represents the soil layer depth scale; the hardened soil model is divided into layers by using the mean of adjacent sampling depths as the soil layer dividing line, thus obtaining the soil layer represented by each sampling depth; For any two soil layers represented by any adjacent sampling depths, the difference in the internal energy increment of all units within the two soil layers is denoted as the energy difference between adjacent sampling depths. The difference between the energy difference corresponding to all adjacent sampling depths and the spectral difference corresponding to all adjacent sampling depths is used to obtain the soil layer characteristic error at the soil layer depth scale k. For several values ​​of soil depth scale k, the mean of the soil property error obtained under all values ​​is denoted as the soil property multi-scale error; optimize the internal energy increment of each element in the hardened soil model, and when the soil property multi-scale error reaches the minimum value, the corrected internal energy increment of each element is obtained.

[0010] Preferably, the specific steps for determining the hardened soil model parameters based on the difference between the total work done and the incremental internal energy determined by the measured torque curve, and the error in determining the hardened soil model parameters based on the first difference, include the following: The ratio of the difference between the total work of rotation and the increase in comprehensive internal energy to the total work of rotation is denoted as the second difference. The sum of the squares of the second difference and the squares of the first difference is denoted as the error of the hardened soil model parameters. The parameters of the hardened soil model are optimized using an optimization algorithm. The optimized hardened soil model parameters, which are obtained when the error of the hardened soil model parameters is minimized, are denoted as the corrected hardened soil model parameters.

[0011] Preferably, the specific steps of performing finite element analysis on the pull-out process of the helical anchor using the modified hardened soil model parameters are as follows: Finite element simulations of the screw anchor insertion and pull-out processes were performed using the modified hardened soil model parameters to obtain the load-displacement curves of the pull-out process. The maximum value of the load-displacement curve was recorded as the ultimate pull-out bearing capacity, and the ultimate pull-out bearing capacity and the load-displacement curves were used as the results of the screw anchor pull-out performance analysis.

[0012] Preferably, the specific steps for calculating the spectral difference between the two second spectra corresponding to any pair of insertion depths are as follows: Each second spectrum is divided into several sub-intervals, and the mean of the amplitudes of all frequency components in each sub-interval is recorded as the mean amplitude of each sub-interval. The absolute value of the difference between the two mean amplitudes of the same sub-intervals in the two second spectra is recorded as the local difference of each sub-interval. The mean of the local differences of all sub-intervals is recorded as the spectrum difference.

[0013] Preferably, the specific steps for obtaining the soil layer characteristic error at the soil layer depth scale k are as follows: In the hardened soil model, the summation of the internal energy increments of all elements within each soil layer is denoted as the first energy index at each sampling depth; the absolute value of the difference between the first energy indices of adjacent sampling depths is denoted as the energy difference between adjacent sampling depths; the energy differences corresponding to all adjacent sampling depths constitute an energy difference sequence; for the spectral differences between adjacent sampling depths, the spectral differences corresponding to all adjacent sampling depths constitute a spectral difference sequence. The energy difference sequence is normalized, and the spectral difference sequence is also normalized; the difference between the normalized energy difference sequence and the normalized spectral difference sequence is denoted as the soil characteristic error at the soil depth scale k.

[0014] Another embodiment of the present invention provides a finite element method-based helical anchor pull-out performance analysis system. This system includes a physical testing module; the physical testing module uses a hydraulic power head to drive the helical anchor into the soil layer; the physical testing module also includes a torque sensor and a rotary encoder for acquiring measured torque curves; the system also includes a finite element simulation module, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor runs the computer program, it first reads the measured torque curves obtained by the physical testing module, and then implements all the steps of the aforementioned finite element method-based helical anchor pull-out performance analysis method.

[0015] The beneficial effects of the technical solution of the present invention are: This invention calibrates the parameters of a hardened soil model by combining measured torque curves from physical screw-in tests with finite element simulations, effectively avoiding unreliable pull-out performance results caused by improper parameter settings. Overall, this invention uses the global trend information and local fluctuation spectrum information of the measured torque curves to correct the macroscopic trend and microscopic energy distribution of the simulation model, respectively, and optimizes parameters based on the principle of energy conservation. This allows the corrected hardened soil model to more realistically simulate the effect of actual soil on the helical anchor, significantly improving the accuracy and reliability of subsequent finite element analysis of the pull-out process.

[0016] Specifically, this invention effectively constrains the global optimization direction of model parameters by calculating the first difference between the trend components of the simulated torque curve and the measured torque curve. Simultaneously, it assesses soil differences at different depths using the spectral distribution of the fluctuation components of the measured torque curve and corrects the internal energy increment of each finite element element accordingly. This introduces local soil inhomogeneity information into the simulation model, enhancing its ability to represent actual soil layer changes. Furthermore, based on the difference between the measured total spindle work and the simulated comprehensive internal energy increment (the second difference), a parameter error function is constructed together with the first difference. This jointly optimizes the model parameters from both macroscopic trend and energy conservation dimensions, ensuring that the corrected hardened soil model parameters are as close as possible to the real soil. Ultimately, this lays the foundation for obtaining accurate ultimate pull-out bearing capacity and load-displacement curves of the helical anchor. Attached Figure Description

[0017] Figure 1 A flowchart illustrating the steps of a finite element-based helical anchor pull-out performance analysis method provided in an embodiment of the present invention; Figure 2 The load-displacement curve is provided for one embodiment of the present invention. Detailed Implementation

[0018] The following description, in conjunction with the accompanying drawings, details the specific scheme of the finite element-based helical anchor pull-out performance analysis method and system provided by this invention.

[0019] Please see Figure 1 The diagram illustrates a flowchart of a finite element-based method for analyzing the pull-out performance of a spiral anchor, according to an embodiment of the present invention. The method includes the following steps: Step S101: Through a physical screw-in test, test the screw-in torque curve as a function of rotation angle when the helical anchor is screwed into the soil, and record it as the measured torque curve.

[0020] A location is sampled in the target construction area (such as the construction area of ​​transmission line tower foundations). The helical anchor is screwed into the soil, and the torque applied during the screwing process and the rotation angle of the helical anchor are collected in real time. The curve of the screwing torque changing with the rotation angle is obtained and recorded as the measured torque curve.

[0021] The same helical anchor will produce torque-rotation curves of different shapes under different soil conditions. For example, differences in soil properties such as compaction, internal friction angle, and cohesion are directly reflected in the trend, amplitude, and fluctuation pattern of the torque curve. Therefore, the measured torque curve is essentially a fingerprint record of the mechanical properties of the soil and can be used to characterize the physical action of a specific soil on the helical anchor.

[0022] The torque-angle curve is obtained by a strain gauge torque sensor and an incremental rotary encoder. In this embodiment, the sampling frequency of the torque-angle curve is set to 100Hz.

[0023] Step S102: Initialize the parameters of the hardened soil model, perform finite element simulation on the process of the spiral anchor being screwed into the hardened soil model and obtain the simulation results. The simulation results include the internal energy increment of each element in the hardened soil model and the simulated torque curve. The difference between the trend component of the simulated torque curve and the measured torque curve is denoted as the first difference.

[0024] In a finite element simulation platform, numerical models of the helical anchor and the soil are established. The soil adopts a hardened soil constitutive model, referred to as the hardened soil model. A set of hardened soil model parameters (such as reference secant modulus, tangent modulus, cohesion, internal friction angle, etc.) are initialized, and finite element analysis is performed on the process of the helical anchor being screwed into the hardened soil model to obtain simulation results. The simulation results include two parts: one part is the simulated torque curve, that is, the curve of torque output by the model changing with the rotation angle; the other part is the internal energy increment of each finite element element in the hardened soil model, that is, the energy absorbed by each soil element during the screwing process.

[0025] This embodiment compares the simulated torque curve with the measured torque curve, extracts the trend components (i.e., the overall trend and smoothing shape of the curves), and calculates the difference between the trend components, denoted as the first difference. The first difference describes the degree of difference between the hardened soil model and the real soil at the macroscopic level. The larger the first difference, the more significant the deviation between the simulated torque curve and the measured torque curve in terms of overall curve shape, and the less accurately the global parameters of the hardened soil model can describe the effect of the real soil on the helical anchor; the smaller the first difference, the closer the hardened soil model is to the real soil in terms of global trend.

[0026] The purpose of using trend components to calculate the first difference is that the parameters of the hardened soil model are global parameters, and the trend component of the measured torque curve mainly affects the overall trend shape of the simulated curve. For the fluctuation components other than the trend component of the measured torque curve, these fluctuation components reflect local changes in soil at different depths. These local changes cannot be accurately matched by adjusting the global parameters alone, because the global parameters do not have the ability to distinguish by depth. Similarly, since the global parameters of the hardened soil model cannot accurately define the soil properties at different depths, the fluctuation components of the simulated torque curve are not very meaningful. Therefore, only the first difference in the trend components between the two is considered.

[0027] If the fluctuation component is also included in the first difference calculation, even if the parameters of the hardened soil model are very close to the real soil in terms of global trend, the difference of the fluctuation component will still make the overall difference very large, which will lead to the parameter optimization being misled. It will try to use global parameters to fit local details, which will lead to the parameters getting stuck in local optimum.

[0028] It should be noted that this embodiment uses Abaqus for finite element analysis, which supports the implementation of hardened soil models through the UMAT / VUMAT subroutines. Other embodiments can also use the built-in Modified Mohr-Coulomb / Cap model for approximation. Abaqus provides element-level energy output variables (ELEN, ALLIE, ALLSE, etc.), which can directly extract the internal energy increment of each element. The internal energy increment mentioned in this embodiment specifically refers to the sum of the elastic strain energy and plastic dissipation energy of each element. In addition, Abaqus also supports history output, which can define the output variable of torque as a function of rotation angle.

[0029] In this embodiment, the spiral anchor used for finite element analysis and the spiral anchor used for the physical screw-in test in step S101 have the same geometric parameters; the specific parameters are shown in Table 1 below: In this embodiment, the hardened soil model used in the finite element analysis is a cylinder with a diameter of 2000mm and a height of 3000mm (1000mm margin added to the anchor length). Both the hardened soil model and the helical anchor model use C3D8R (8-node hexahedral reduced integral element) elements. The mesh size for the hardened soil model is 10mm; the mesh size for the blades of the helical anchor model is 5mm, and the mesh size for the anchor rod is 10mm. Furthermore, during the finite element simulation, it is necessary to ensure that the rotation angle (or number of turns) of the helical anchor model is consistent with the rotation angle (or number of turns) of the helical anchor in the physical insertion test. The purpose is to ensure that the insertion process of the helical anchor model in the simulation is identical to that in the physical insertion test, thus making the difference between the simulation and physical experiments only in the soil.

[0030] Since finite element simulation and the use of Abaqus software are both conventional techniques, this embodiment will not describe them in further detail.

[0031] The parameters and their initial values ​​for the hardened soil model in this embodiment are shown in Table 2 below: Step S103: Use the spectral distribution of the fluctuation component of the measured torque curve to evaluate the soil quality difference of the hardened soil model at different depths, and use the soil quality difference at different depths to correct the internal energy increment of each unit.

[0032] The measured torque curves described above not only represent the overall trend but also contain rich local details. Specifically, when the helical anchor traverses different soil layers at different depths, the torque curves exhibit local fluctuations. The magnitude and frequency of these fluctuations reflect the differences in soil composition at different depths. For example, when the helical anchor moves from a relatively loose soil layer to a denser soil layer, the torque suddenly increases, forming a local peak on the curve.

[0033] This embodiment extracts the fluctuation component of the measured torque curve (i.e., the fluctuation part remaining after removing the trend component from the curve) and performs spectral analysis on the fluctuation component to obtain its distribution at different frequency components. Since the fluctuation of the torque curve is mainly caused by the helical anchor passing through soil layers of different depths, the spectral distribution of the fluctuation component can be directly mapped to the soil quality differences at different depths. The higher the frequency and the larger the amplitude, the more drastic the soil quality changes at the corresponding depth.

[0034] Using the soil quality differences determined by the aforementioned spectral distribution, the internal energy increment of each element in the hardened soil model is corrected. Specifically, since the parameters of the hardened soil model can only be macroscopically controlled, the local simulation details of the hardened soil model cannot be affected by the parameters. Therefore, the local simulation details of the hardened soil model (specifically, the internal energy increment of each element in this embodiment) may significantly deviate from the local physical details in real soil. For elements corresponding to a certain depth range in the simulation, the magnitude of their internal energy increment is adjusted according to the soil quality differences at that depth, making the corrected internal energy increment distribution closer to the energy absorption characteristics of real soil. This correction process injects the local soil quality information contained in the measured torque curve into the finite element simulation results, enabling the hardened soil model to not only match the real soil in a global trend but also approximate the real soil in local details.

[0035] Step S104: The sum of the corrected internal energy increments of all units is recorded as the comprehensive internal energy increment; the error of the hardened soil model parameters is determined based on the difference between the total work of rotation determined by the measured torque curve and the comprehensive internal energy increment, as well as the first difference; and the hardened soil model parameters are corrected based on the error.

[0036] The summation of the internal energy increments of all elements after correction yields the comprehensive internal energy increment. Based on physical principles, the total work done by the external environment on the spiral anchor during its insertion process (total insertion work) should be entirely converted into the internal energy increment of the soil (ignoring secondary dissipations such as frictional heat). Therefore, the difference between the total insertion work and the comprehensive internal energy increment constitutes an energy-level verification indicator: the smaller this difference, the closer the finite element simulation is to the actual insertion process in terms of energy conservation.

[0037] Based on the first difference (global trend difference) and the energy difference (difference between total work done and the increase in comprehensive internal energy), the error of the hardened soil model parameters is determined comprehensively. This error reflects deviations in two dimensions: deviation from the shape of the torque curve (first difference) and deviation from energy conservation (energy difference). Based on this error, the hardened soil model parameters are corrected to obtain the corrected hardened soil model parameters.

[0038] The correction process employs an iterative optimization strategy: after each correction, the finite element simulation is rerun to recalculate the first difference and energy difference, and to determine whether convergence (or the optimal solution) has been achieved. This embodiment's two-dimensional correction (trend and energy) effectively avoids the problem of parameters getting trapped in local optima, because multiple parameter combinations may produce the same global trend, but the energy difference further distinguishes the merits of these combinations, causing the hardened soil model parameters to converge towards the real soil.

[0039] More importantly, the correction of the internal energy increment of the unit using the spectral distribution of the wave component in the above steps further enhances the directionality of parameter optimization: since the corrected internal energy increment carries real local details of the soil, the correction process corresponding to the energy difference can make the hardened soil model after parameter correction take into account the real local details of the soil, providing a clearer gradient direction for the correction of the global parameters of the hardened soil model, thereby further reducing the risk of getting trapped in a local optimum.

[0040] Step S105: Perform finite element analysis on the pull-out process of the helical anchor using the modified hardened soil model parameters.

[0041] Based on the modified hardened soil model parameters, the pull-out process of the helical anchor is analyzed by finite element method under the initial stress-strain state of the simulation results during the screw-in stage. The bearing capacity of the helical anchor under different pull-out displacements is calculated, and the pull-out performance evaluation results of the helical anchor (such as ultimate pull-out bearing capacity, load-displacement curve, etc.) are finally obtained.

[0042] Preferably, the method for obtaining the trend component of the measured torque curve is as follows: First, the measured torque curve is sampled. In this embodiment, it starts from the rotation angle of 0 (radians) (that is, 0 is the first sampled radian), and samples one radian every preset radian. The torque corresponding to that radian is obtained from the measured torque curve. All sampled radians and their corresponding torques are used as all sampling points.

[0043] In this embodiment, the preset radian value is set to (0.5~2)×π / 180 (radians). In other embodiments, the preset radian value can be set to other values ​​outside this range, but this will result in too many or too few sampling points, leading to excessive computation or low computational accuracy. In this embodiment, π / 180 (radians) is preferred. Specifically, if the torque corresponding to the sampled radian value cannot be directly read from the measured torque curve, a linear interpolation algorithm can be used to interpolate the corresponding torque based on the coordinate point with the smallest difference (absolute value of the difference) between the measured torque curve and the sampled radian value.

[0044] The sampling curve formed by all sampling points is denoted as the initial curve. Its spectrum is obtained using the Fast Fourier Transform (FFT) algorithm. For the sake of distinction, this spectrum is denoted as the first spectrum, which is the amplitude spectrum, representing the amplitude of each frequency.

[0045] A cutoff frequency is preset, and the amplitude of frequencies greater than or equal to the cutoff frequency in the first spectrum is set to 0, while the amplitude of frequencies less than the cutoff frequency remains unchanged, thereby achieving low-pass filtering of the first spectrum. The first spectrum of the low-pass filter is subjected to inverse Fourier transform, and the resulting filtered curve is denoted as the trend component of the measured torque curve.

[0046] The difference curve between the initial curve and the filtered curve (that is, the curve obtained by finding the difference between the ordinates corresponding to the same abscissa) is denoted as the fluctuation component of the measured torque curve.

[0047] Preferred methods for setting the cutoff frequency include: A minimum resolvable soil layer thickness is preset, denoted as λ (i.e., the spatial period of the spiral direction is set to λ). The angular domain frequency F1 = P / (2π×λ) is used as the cutoff frequency. Where P represents the pitch of the helical anchor. In this embodiment, P = 300mm, which means that the helical anchor theoretically advances 300mm for each complete rotation (i.e., 2π radians) (in actual practice, it may not be 300mm due to soil compression).

[0048] The methods for obtaining the trend components of the simulated torque curve and the measured torque curve are similar, and will not be described in detail in this embodiment. The length of the trend component of the simulated torque curve is the same as the length of the trend component of the measured torque curve (that is, the number of sampling points of the simulated torque curve is the same as the number of sampling points of the measured torque curve).

[0049] λ is set to 1 / 3 to 2 times the pitch of the helical anchor. If λ is set too large, for example, greater than 2 times the pitch, only a very macroscopic trend will be retained. If λ is set too small, for example, less than 1 / 3 of the pitch, finer trend changes will be retained, and only extremely local fluctuations will be filtered out. In this embodiment, λ can be set to 1 times the pitch.

[0050] Preferably, the difference in trend components between the simulated torque curve and the measured torque curve is denoted as the first difference. This difference is achieved by dividing the trend components of the measured torque curve into several first segments. Similarly, the trend components of the simulated torque curve are divided into several second segments using the same method. The sequence of ordinates (i.e., torques) of all sampling points in the first and second segments is treated as a vector. The cosine similarity of the corresponding vectors of the first and second segments with the same number is denoted as the similarity of each pair of segments. The mean of the similarities of all pairs of segments is denoted as the comprehensive similarity of the trend components between the simulated torque curve and the measured torque curve.

[0051] The first difference is negatively correlated with the overall similarity.

[0052] As an example, the first difference is y = 1 - x, where x represents the overall similarity.

[0053] As an example, the trend component of the measured torque curve is divided into several first segments, including the following methods: In this example, a first segment is divided every 2π radians. That is, the curve formed by the sampling points in the corner interval [0, 2π) is the first segment numbered 1, the curve formed by the sampling points in the corner interval [2π, 4π) is the first segment numbered 2, and so on, to obtain all the first segments. At this time, each first segment represents the curve of torque change with the corner angle when screwing in one revolution (that is, 1 pitch).

[0054] Specifically, if the last first segment contains fewer than 50 sampling points, then that first segment is not retained.

[0055] The method for dividing the second segment is the same as that for the first segment, and will not be described in detail in this embodiment.

[0056] Preferably, the method for evaluating soil quality differences at different depths in a hardened soil model using the spectral distribution of the fluctuation component of the measured torque curve includes: Following the method described in the first segment division above, the fluctuation component is also divided into several third segments. For any third segment, the spectrum of the third segment is obtained using FFT and denoted as the second spectrum. It should be noted that in this embodiment, the third segment needs to be windowed before obtaining the second spectrum (this embodiment uses a Hamming window).

[0057] Obtain the mean θ of the abscissas of all sampling points in the third segment, which represents the rotation angle when the helical anchor screws into the third segment. Convert this rotation angle into a screw-in depth D = θ × P / 2π. Thus, for any third segment, a second spectrum and a screw-in depth are obtained. For all third segments and their corresponding second spectra, calculate the spectral difference between the two second spectra corresponding to any pair of screw-in depths. The spectral difference corresponding to each pair of screw-in depths is denoted as the soil quality difference at any two soil depths. The spectral differences corresponding to all pairs of screw-in depths describe the soil quality differences at different depths.

[0058] It should be noted that the insertion depth may not accurately describe the actual depth to which the helical anchor penetrates the soil. This is because soil is not a rigid body and can be compressed and deformed, resulting in the insertion depth not being equal to the depth of penetration. However, this does not affect the implementation of this embodiment. The reason is that the fact that the depth is not equal to the actual depth of penetration is precisely a reflection of the physical properties of the soil. When subsequently correcting the parameters of the hardened soil model based on the insertion depth, the hardened soil model can still approximate the real soil properties.

[0059] The method for obtaining the spectral difference between the two second spectra in this embodiment is as follows: For each second spectrum, all frequency components (excluding those below the cutoff frequency) are divided into several sub-intervals. The mean amplitude of all frequency components within each sub-interval is denoted as the mean amplitude of that sub-interval. The absolute value of the difference between the mean amplitudes of the same sub-intervals in two second spectra is denoted as the local difference of that sub-interval. The mean of the local differences across all sub-intervals is taken as the spectral difference.

[0060] Preferably, the sub-interval division method is as follows: the interval containing all frequency components greater than or equal to the cutoff frequency in each second spectrum is equally divided into n0 sub-intervals, where n0 is equal to the square root (rounded down) of the number of all frequency components greater than or equal to the cutoff frequency. This value can take into account both the resolution and statistical stability of the sub-intervals. In other embodiments, n0 can also be set to other values, but this embodiment does not impose specific limitations.

[0061] Preferably, the internal energy increment of each unit is corrected by utilizing the soil quality differences at different depths. The method includes arranging all the ingress depths obtained above in ascending order to obtain a depth sequence.

[0062] Starting from the first spiral depth D(1) in the depth sequence, a spiral depth is sampled every k elements, denoted as the sampling depth, for a total of n sampling depths, where k represents the soil layer depth scale; these n sampling depths are D(1), D(1+k), D(1+2k), ..., D(1+(n-1)k). D(1+(n-1)k) represents the 1+(n-1)kth element in the depth sequence.

[0063] Obtain the mean values ​​d(1) of D(1) and D(1+k), d(2) of D(1+k) and D(1+2k), ..., d(n-1) of D(1+(n-2)k) and D(1+(n-1)k), and divide the hardened soil model into layers using these mean values ​​as dividing lines. That is, the depth intervals [0, d(1)], (d(1), d(2)], ..., (d(n-2), d(n-1)], and (d(n-1), dm] are each considered as a soil layer, resulting in a total of n soil layers.

[0064] Where dm represents the maximum penetration depth of the soil mass. In this embodiment, dm = θmax × P / 2π + P, where θmax represents the maximum penetration angle in the physical penetration test, θmax × P / 2π represents the maximum penetration depth, and +P is to add an extra margin on the basis of the actual maximum penetration depth to ensure that dm covers the soil area directly and indirectly affected by the helical anchor as much as possible. Soil areas with a depth greater than dm are less affected by the direct and indirect effects of the helical anchor or can be ignored. In this embodiment, soil areas with a depth greater than dm are not considered.

[0065] It is easy to see that each sampling depth corresponds to a soil layer, and this sampling depth is used to represent the location of the soil layer in the soil mass.

[0066] In the hardened soil model, the sum of the internal energy increments of all elements within each soil layer is denoted as the first energy index of each soil layer, which is also the first energy index of each sampling depth. Following the ascending order of all sampling depths, the absolute values ​​of the differences between the first energy indices of adjacent sampling depths are calculated and denoted as the energy difference between adjacent sampling depths. The energy differences corresponding to all adjacent sampling depths constitute an energy difference sequence. Similarly, for the spectral differences between adjacent sampling depths, the spectral differences corresponding to all adjacent sampling depths constitute a spectral difference sequence.

[0067] Both energy difference sequences and spectral difference sequences can describe the differences in soil properties at different soil depths. This embodiment normalizes both the energy difference sequence (i.e., all elements are normalized using the softmax formula) and the spectral difference sequence (i.e., all elements are normalized using the softmax formula). The purpose is to eliminate the influence of dimensions and focus only on the relative variation patterns of the energy difference sequence and the spectral difference sequence. The difference between the normalized energy difference sequence and the normalized spectral difference sequence is denoted as the soil characteristic error at the soil depth scale k.

[0068] In this embodiment, the difference between the normalized energy difference sequence and the normalized spectral difference sequence is equal to the cosine distance between them.

[0069] Thus, for any soil depth scale k, a corresponding soil characteristic error is calculated. The soil depth scale k is used to quantify the size of local regions of the soil. The larger k is, the larger each local region (i.e., the longer the depth interval corresponding to the soil layer) is after dividing the soil into multiple local regions (multiple soil layers), allowing us to focus on relatively macroscopic local regions of the soil. The smaller k is, the smaller each local region (i.e., the shorter the depth interval corresponding to the soil layer) is after dividing the soil into multiple local regions (multiple soil layers), allowing us to focus on relatively microscopic local regions of the soil. The soil characteristic error represents the difference between the actual physical properties of the soil and the simulated physical properties within a local region after the soil has been layered at a specific depth scale (i.e., k).

[0070] For all values ​​of soil depth scale k, the mean of the soil characteristic error obtained for each value is denoted as the multi-scale error of soil characteristics.

[0071] In this embodiment, a fine-tuning amount is randomly initialized for the internal energy increment of each element in the hardened soil model (ignoring elements with a depth greater than dm). The internal energy increment of each element is then summed with this fine-tuning amount to obtain the adjusted internal energy increment of each element. In this embodiment, random initialization within the range of -10% to 10% of the internal energy increment of each element is sufficient.

[0072] The fine-tuning of all elements in the hardened soil model is continuously optimized (ignoring elements with a depth greater than dm). After each optimization of the fine-tuning of all elements, the multi-scale error of soil properties is recalculated until the multi-scale error of soil properties reaches its minimum value. At this point, the correction of the internal energy increment of each element is completed, and the corrected internal energy increment of each element is obtained.

[0073] It should be noted that this embodiment, by performing multi-scale depth division on the hardened soil model (i.e., obtaining multi-scale errors of soil properties based on multiple values ​​of the soil depth scale k), has at least the following effects: On the one hand, since the complex nonlinear relationship between the spectrum of the fluctuation component of the measured torque curve and the internal energy increment of each unit cannot be determined in advance, the multi-scale error of soil properties obtained under a single scale (i.e., when k only takes one value) cannot be effectively used as a guiding target for internal energy increment correction, resulting in an unreliable internal energy increment correction process. This embodiment calculates the multi-scale error of soil properties using multiple scales (i.e., multiple values ​​of k), giving the multi-scale error of soil properties a strong nonlinear capability, making it an effective guiding target for internal energy increment correction. On the other hand, since the specific stratification of the soil during the physical indentation test may be complex and unpredictable, different stratification methods (i.e., different values ​​of k) are considered simultaneously to adapt to complex soil conditions.

[0074] Preferably, the method for obtaining all values ​​of the soil depth scale k is as follows: Starting from 1, iterate through all positive integers. When you reach integer j, set k = j. If the total number of sampling depths n is less than 3, then 1, 2, ..., j-1 are all possible values ​​for k. If the total number of sampling depths n is greater than or equal to 3, then continue iterating through the next positive integer.

[0075] In other words, the maximum value of k must ensure that two sampling depths can be sampled.

[0076] Preferably, the method for continuously optimizing the fine-tuning of all elements in the hardened soil model includes: It should be noted that in this embodiment, the soil layer division process is determined by k and is independent of the internal energy increment of all elements in the hardened soil model. The multi-scale error of soil layer properties is obtained through operations such as summing, normalizing, and differentiating from the spectral difference sequence based on the internal energy increment (or adjusted internal energy increment). This process is a differentiable nonlinear model. Therefore, in this embodiment, the Adam optimizer is used to optimize the fine-tuning of all elements, with a learning rate set to 0.001. In this embodiment, the multi-scale error of soil layer properties is considered to have reached its minimum value if the standard deviation of the multi-scale error obtained in the most recent 5 iterations is less than 0.16, where the maximum number of iterations is set to 500.

[0077] In other embodiments, to avoid over-correction of the internal energy increment, a regularization term needs to be added after the multi-scale error of soil properties. Specifically, the ratio of each fine-tuning amount to the initial internal energy increment of each element (i.e., the internal energy increment output by the finite element simulation in step S102) is calculated and denoted as the fine-tuning ratio of each fine-tuning amount. The average of the squares of the fine-tuning ratios of all elements is denoted as L, and γL is used as the regularization term. When the Adam optimizer is used to optimize the fine-tuning amounts of all elements, the sum of the multi-scale error of soil properties and the regularization term is minimized, thus obtaining the corrected internal energy increment of each element. Here, γ is the regularization coefficient, which can be set to 0.1.

[0078] Other methods, such as simulated annealing or particle swarm optimization, can be used in other embodiments to optimize the fine-tuning of all elements in the hardened soil model. However, these optimization methods tend to be less efficient due to the large number of elements.

[0079] Preferably, the method for determining the error of the hardened soil model parameters based on the difference between the total work done by rotation determined by the measured torque curve and the increase in comprehensive internal energy, as well as the first difference, includes: The ratio of the difference between the total work of rotation and the increase in comprehensive internal energy to the total work of rotation is denoted as the second difference. The sum of the squares of the second difference and the squares of the first difference is denoted as the error of the hardened soil model parameters.

[0080] The purpose of comparing the ratio to the total work done is to remove the dimensions and order of magnitude of the second difference, thus avoiding an excessive difference in order of magnitude between the second and first differences. The total work done is equal to the integral of the measured torque curve (i.e., the area enclosed by the measured torque curve and the horizontal axis).

[0081] It should be noted that in some embodiments, considering that the total internal energy increment may not represent all the energy absorbed by the hardened soil model, the total work input and the total internal energy increment may not be the same or close. Therefore, this embodiment allows a certain difference between the total work input and the total internal energy increment, for example, a difference of 10%. That is, when the square of the second difference is less than 0.01, the second difference is directly set to 0 (that is, the square of the second difference is directly set to the minimum value). The purpose is that when the total work input and the total internal energy increment are allowed to be relatively close (for example, when the square of the second difference is less than 0.01), even if a certain difference between the total work input and the total internal energy increment is allowed, the second difference is determined to be the minimum value. This provides a margin for the unpredictable dissipated energy in the finite element simulation process and avoids overfitting in the subsequent optimization process in order to ensure that the total work input and the total internal energy increment are equal.

[0082] In other embodiments, the weighted sum of the squares of the second difference and the squares of the first difference can be recorded as the error of the hardened soil model parameters; wherein, in the weighted summation, the weight of the first difference is greater than the weight of the second difference. The purpose is that, in other embodiments, when the accuracy of the corrected internal energy increment of all elements is sacrificed to improve optimization efficiency (i.e., when the second difference is unreliable), more attention is paid to the first difference; as an example, the weight of the first difference is set to 0.67 and the weight of the second difference is set to 0.33.

[0083] Furthermore, the hardened soil model parameters are considered as a vector to be optimized. In this embodiment, only the first 6 parameters in Table 2 need to be optimized (other parameters are not optimized). Therefore, the hardened soil model parameters are considered as a 6-dimensional vector to be optimized. The next step in this embodiment is to optimize the hardened soil model parameters to minimize their error.

[0084] Since the functional relationship between the error of the hardened soil model parameters and the hardened soil model parameters is complex and unclear, the Adam optimizer is no longer used. In this embodiment, the particle swarm optimization algorithm is used for optimization. The reason is that, on the one hand, the hardened soil model parameters have fewer dimensions (only 6), and on the other hand, the particle swarm optimization algorithm has strong parallelism and global search capabilities.

[0085] The parameter settings for the particle swarm optimization algorithm in this embodiment are shown in Table 3 below: In other embodiments, the relevant parameters of the particle swarm algorithm can be set to other values. This embodiment does not limit this. In addition, since the particle swarm algorithm is a well-known technology, this embodiment will not elaborate on it.

[0086] It should be noted that during the initialization phase of the particle swarm optimization (PSO) algorithm, a finite element analysis (FEM) operation is required for each particle (i.e., each 6-dimensional hardened soil model parameter). Based on this embodiment, the error of the hardened soil model parameters is evaluated (the calculation formula for the error of the hardened soil model parameters is the fitness function of the PSO algorithm). In this embodiment, the 10 particles need to perform 10 FEM operations in parallel, each taking 2-3 hours. After the first round of updates for the 10 particles, the PSO algorithm performs 10 more FEM operations in parallel for each of the 10 particles, taking 2-3 hours in parallel. After each subsequent round of updates, 10 more FEM operations are performed in parallel for each of the 10 particles, each taking 2-3 hours in parallel. The PSO algorithm performs a total of 10 rounds of updates to obtain the corrected hardened soil model parameters, involving a total of 100 FEM operations, taking approximately 26 hours in total.

[0087] In other embodiments, to speed up the time required for a single finite element analysis, the mesh size of the blades of the helical anchor model can be set to 10 mm and the mesh size of the hardened soil model can be set to 15 mm; the maximum screw-in angle of the helical anchor in the physical screw-in test (and finite element simulation) can be halved; at this time, the process of correcting the parameters of the hardened soil model using the particle swarm optimization algorithm only takes about 8 hours; this embodiment improves the optimization efficiency by sacrificing the accuracy of the corrected hardened soil model parameters.

[0088] In other embodiments, the particle swarm optimization algorithm described above can be replaced with an optimized algorithm such as simulated annealing. This embodiment does not impose specific limitations.

[0089] Preferably, the finite element analysis of the helical anchor pull-out process is performed using the modified hardened soil model parameters, including the following methods: For the corrected hardened soil model parameters, a finite element simulation of the helical anchor insertion process is performed using the hardened soil model with these parameters. After the insertion process simulation is completed, a finite element simulation of the helical anchor pull-out process is performed, and the load-displacement curve is obtained, as shown below. Figure 2 As shown, the curve represents the change in displacement of the helical anchor as a function of the load along the direction of the helical anchor bolt.

[0090] The maximum value of the load-displacement curve is denoted as the ultimate tensile strength. Figure 2 The ultimate pull-out bearing capacity shown is 138.7 kN, and the corresponding displacement is 47 mm. The ultimate pull-out bearing capacity, its corresponding displacement, and the load-displacement curve are used as the results of the pull-out performance analysis of the helical anchor.

[0091] Finite element simulation and analysis of the pull-out process of a spiral anchor is a conventional technique, and will not be described in detail in this embodiment.

[0092] Another embodiment of the present invention provides a finite element-based helical anchor pull-out performance analysis system, the system comprising: a physical testing module.

[0093] In the physical testing module, the hydraulic power head is fixed to a reaction frame. The reaction frame is used to withstand the counter-torque and counter-force during the screwing-in process, ensuring that the power head remains vertically stable during screwing-in. Within the hydraulic power head, the helical anchor is connected to the power head via a connecting assembly. This connecting assembly transmits torque and axial force. The connecting assembly includes: a reducing coupling (used to connect the power head output shaft to the top of the helical anchor rod), an anti-loosening pin (inserted at the connection between the reducing coupling and the helical anchor rod to prevent loosening of the joint due to counter-torque during screwing-in), and a centering guide sleeve (installed at the bottom of the reaction frame to ensure the helical anchor remains vertical during screwing-in).

[0094] The physical testing module includes a strain gauge torque sensor, installed between the power head output shaft and the reducer joint, to directly measure the screwing torque applied to the helical anchor. Specifically, the upper and lower flanges of the strain gauge torque sensor are rigidly connected to the power head output shaft and the reducer joint respectively via bolts. The strain gauge torque sensor used has a measuring range of 0~20000 N·m.

[0095] The physical testing module also includes an incremental rotary encoder. It is coaxially connected to the output shaft of the power head or the flange side of the torque sensor via a coupling. Its resolution is 2000 pulses per revolution (P / R), which is quadrupled to 8000 P / R, corresponding to an angular resolution of 0.045°. Starting from the initial screw-in moment, the encoder pulses are accumulated to obtain the cumulative rotation angle: Cumulative rotation angle (radians) = Cumulative pulse count × 2π / 8000.

[0096] It should be noted that, since the reverse rotation of the helical anchor in this embodiment would increase the difficulty of finite element simulation, the helical anchor is not reversed in this embodiment. If, during the physical screw-in test, hard rock prevents the helical anchor from screwing in, the physical screw-in test is stopped, a new location is sampled in the target construction area (such as the construction area of ​​the transmission line tower foundation), and the physical screw-in test is repeated.

[0097] The system also includes a finite element simulation module, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor runs the computer program, it first reads the measured torque curve obtained by the physical testing module and then implements all the steps of the above embodiments.

[0098] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analyzing the pull-out performance of a helical anchor based on the finite element method, characterized in that, The method includes the following steps: The curve of the screwing torque as the rotation angle when the helical anchor is screwed into the soil was measured by physical screwing test and recorded as the measured torque curve. The parameters of the hardened soil model are initialized, and a finite element simulation is performed on the process of the spiral anchor being screwed into the hardened soil model to obtain simulation results. The simulation results include the internal energy increment of each element in the hardened soil model and the simulated torque curve. The difference between the trend component of the simulated torque curve and the measured torque curve is denoted as the first difference. The spectral distribution of the fluctuation component of the measured torque curve is used to evaluate the soil quality differences of the hardened soil model at different depths. The soil quality differences at different depths are used to correct the internal energy increment of each element, and the sum of the corrected internal energy increments of all elements is denoted as the comprehensive internal energy increment. The error of the hardened soil model parameters is determined based on the difference between the total screwing work determined by the measured torque curve and the comprehensive internal energy increment, as well as the first difference. The hardened soil model parameters are then corrected based on the error. Finite element analysis was performed on the pull-out process of the helical anchor using the modified hardened soil model parameters.

2. The method for analyzing the pull-out performance of a spiral anchor based on the finite element method according to claim 1, characterized in that, The specific steps for obtaining the trend component and the fluctuation component of the measured torque curve are as follows: Several sampling points are sampled from the measured torque curve; the sampling curve formed by all sampling points is called the initial curve; the initial curve is subjected to Fourier transform to obtain the first spectrum; the first spectrum is low-pass filtered using a preset cutoff frequency; the low-pass filtered first spectrum is subjected to inverse Fourier transform to obtain the trend component of the measured torque curve. The difference between the initial curve and the trend component is denoted as the fluctuation component of the measured torque curve.

3. The method for analyzing the pull-out performance of a helical anchor based on the finite element method according to claim 1, characterized in that, The difference in the trend component between the simulated torque curve and the measured torque curve is denoted as the first difference, and the specific steps involved are as follows: The trend component of the measured torque curve is divided into several first segments, and the trend component of the simulated torque curve is divided into several second segments. The first and second segments with the same number are considered as each pair of segments, and the cosine similarity of each pair of segments is recorded as the similarity of each pair of segments. The mean of the similarities of all pairs of segments is recorded as the comprehensive similarity of the trend components between the simulated torque curve and the measured torque curve. The first difference is negatively correlated with the comprehensive similarity.

4. The method for analyzing the pull-out performance of a helical anchor based on the finite element method according to claim 1, characterized in that, The specific steps for evaluating the soil quality differences of a hardened soil model at different depths using the spectral distribution of the fluctuation component of the measured torque curve are as follows: The fluctuation component is divided into several third segments; the second spectrum of each third segment is obtained; the ingress depth corresponding to the mean of the abscissa of each third segment is obtained; for all third segments, the ingress depth and their second spectra are calculated, and the spectral difference between the two second spectra corresponding to any pair of ingress depths is calculated; the spectral difference corresponding to each pair of ingress depths is taken as the soil quality difference of the hardened soil model at any two soil layer depths.

5. The method for analyzing the pull-out performance of a helical anchor based on the finite element method according to claim 4, characterized in that, The specific steps involved in correcting the internal energy increment of each unit by utilizing soil quality differences at different depths are as follows: All the spiral depths constitute a depth sequence; a sampling depth is sampled every k elements from the depth sequence, where k represents the soil layer depth scale; the hardened soil model is divided into layers by using the mean of adjacent sampling depths as the soil layer dividing line, thus obtaining the soil layer represented by each sampling depth; For any two soil layers represented by any adjacent sampling depths, the difference in the internal energy increment of all units within the two soil layers is denoted as the energy difference between adjacent sampling depths. The difference between the energy difference corresponding to all adjacent sampling depths and the spectral difference corresponding to all adjacent sampling depths is used to obtain the soil layer characteristic error at the soil layer depth scale k. For several values ​​of soil depth scale k, the mean of the soil characteristic error obtained under all values ​​is denoted as the multi-scale error of soil characteristics. The internal energy increment of each element in the hardened soil model is optimized. When the multi-scale error of soil properties reaches its minimum value, the corrected internal energy increment of each element is obtained.

6. The method for analyzing the pull-out performance of a spiral anchor based on the finite element method according to claim 1, characterized in that, The specific steps for determining the hardened soil model parameters based on the difference between the total work done and the incremental internal energy determined by the measured torque curve, and the error in determining the hardened soil model parameters based on the first difference, and correcting the hardened soil model parameters based on the error are as follows: The ratio of the difference between the total work of rotation and the increase in comprehensive internal energy to the total work of rotation is denoted as the second difference. The sum of the squares of the second difference and the squares of the first difference is denoted as the error of the hardened soil model parameters. The parameters of the hardened soil model are optimized using an optimization algorithm. The optimized hardened soil model parameters, which are obtained when the error of the hardened soil model parameters is minimized, are denoted as the corrected hardened soil model parameters.

7. The method for analyzing the pull-out performance of a helical anchor based on the finite element method according to claim 1, characterized in that, The specific steps involved in performing finite element analysis on the pull-out process of the helical anchor using the modified hardened soil model parameters are as follows: Finite element simulations of the screw anchor insertion and pull-out processes were performed using the modified hardened soil model parameters to obtain the load-displacement curves of the pull-out process. The maximum value of the load-displacement curve was recorded as the ultimate pull-out bearing capacity, and the ultimate pull-out bearing capacity and the load-displacement curves were used as the results of the screw anchor pull-out performance analysis.

8. The method for analyzing the pull-out performance of a spiral anchor based on the finite element method according to claim 4, characterized in that, The specific steps for calculating the spectral difference between the two second spectra corresponding to any pair of insertion depths are as follows: Each second spectrum is divided into several sub-intervals, and the mean of the amplitudes of all frequency components in each sub-interval is recorded as the mean amplitude of each sub-interval. The absolute value of the difference between the two mean amplitudes of the same sub-intervals in the two second spectra is recorded as the local difference of each sub-interval. The mean of the local differences of all sub-intervals is recorded as the spectrum difference.

9. The method for analyzing the pull-out performance of a spiral anchor based on the finite element method according to claim 5, characterized in that, The specific steps for obtaining the soil layer characteristic error at the soil layer depth scale k are as follows: In the hardened soil model, the summation of the internal energy increments of all elements within each soil layer is denoted as the first energy index at each sampling depth; the absolute value of the difference between the first energy indices of adjacent sampling depths is denoted as the energy difference between adjacent sampling depths; the energy differences corresponding to all adjacent sampling depths constitute an energy difference sequence; for the spectral differences between adjacent sampling depths, the spectral differences corresponding to all adjacent sampling depths constitute a spectral difference sequence. The energy difference sequence is normalized, and the spectral difference sequence is also normalized; the difference between the normalized energy difference sequence and the normalized spectral difference sequence is denoted as the soil characteristic error at the soil depth scale k.

10. A finite element method-based helical anchor pull-out performance analysis system, comprising a physical testing module; the physical testing module utilizes a hydraulic power head to drive the helical anchor into the soil layer; the physical testing module also includes a torque sensor and a rotary encoder for acquiring measured torque curves; the system further includes a finite element simulation module, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor runs the computer program, it first reads the measured torque curve obtained by the physical testing module, and then implements all the steps of the finite element-based helical anchor pull-out performance analysis method according to any one of claims 1 to 9.

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