A method, equipment, and medium for calculating internal forces and displacements in the cantilever section of an anti-slide pile.

Abstract

This invention discloses a method, equipment, and medium for calculating the internal forces and displacements of cantilever sections of anti-slide piles, relating to the field of engineering design technology. The method includes: solving structural mechanics equations by applying time-varying support reaction field parameter sets and cantilever section depth calculation domains to generate predicted displacement and internal force curves; reconstructing the predicted displacement and internal force curves into a high-order tensor field; extracting local response correlation features using depth-separable convolution kernels to generate a coupled response feature field; and based on the coupled response feature field, applying reverse constraints to the time-varying support reaction field parameter sets and performing joint solving in conjunction with the cantilever section depth calculation domain to generate corrected displacement and internal force curves. This invention, by constructing a spatiotemporal Gaussian process prior model, improves the accuracy of internal force and displacement prediction in computer-aided engineering, enhancing the reliability and applicability of cantilever section structural analysis under complex geological conditions.

Description

Technical Field

[0001] This invention relates to the field of engineering design technology, and in particular to a method, equipment and medium for calculating the internal forces and displacements of the cantilever section of an anti-slide pile. Background Technology

[0002] With the continuous development of mountain transportation engineering, slope protection engineering, and geological disaster prevention engineering, anti-slide piles, as a key support structure for controlling landslide deformation and improving the overall stability of slopes, have been widely used in highway, railway, water conservancy, and urban infrastructure construction. In recent years, with the deepening research on geological disaster mechanisms in computer-aided engineering, the academic community has gradually realized that the working conditions of the strata are not static constants. Especially under the influence of environmental factors such as freeze-thaw cycles, rainfall infiltration, and groundwater level fluctuations, the stiffness, strength, and support characteristics of the soil exhibit time-varying evolution characteristics, making the stress state of the cantilever section of the anti-slide pile time-varying and nonlinear.

[0003] However, existing methods for calculating the internal forces and displacements of the cantilever section of anti-slide piles still have certain limitations. On the one hand, simplified ground reaction assumptions are usually used in the calculation process, treating the ground support reaction force as a parameter that is distributed with depth but approximately constant in the time dimension. This makes it difficult to truly reflect the continuous influence of the evolution of the ground conditions over time on the stress response of the cantilever section. On the other hand, they often focus on single forward calculations, that is, solving for the displacement and internal forces of the cantilever section under given ground parameters. It is difficult to make reverse corrections to the ground support reaction force parameters based on the structural response characteristics, thus limiting the stability and reliability of the calculation results under complex working conditions. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides a method for calculating the internal forces and displacements of the cantilever section of an anti-slide pile to solve the problems of insufficient time-varying characterization of ground support reaction and insufficient reliability of the calculation results of internal forces and displacements in the cantilever section.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: In a first aspect, the present invention provides a method for calculating the internal forces and displacements of the cantilever segment of an anti-slide pile. The method includes: collecting geometric material information and ground condition time series of the cantilever segment, establishing a depth calculation domain for the cantilever segment, and discretizing it to obtain a basic dataset for cantilever segment calculation; constructing a spatiotemporal Gaussian process prior model based on the basic dataset, a depth prior characterization layer, a time condition mapping layer, and a spatiotemporal fusion layer, and performing latent spatial mapping on the ground condition time series to generate a time-varying support reaction field parameter set; solving the structural mechanics equations using the time-varying support reaction field parameter set and the cantilever segment depth calculation domain to generate predicted displacement curves and predicted internal force curves; reconstructing the predicted displacement curves and predicted internal force curves into a high-order tensor field, extracting local response correlation features through a depth-separable convolution kernel to generate a coupled response feature field; and performing reverse constraint correction on the time-varying support reaction field parameter set based on the coupled response feature field, and performing joint solving in conjunction with the cantilever segment depth calculation domain to generate corrected displacement curves and corrected internal force curves.

[0007] As a preferred embodiment of the method for calculating the internal forces and displacements of the cantilever section of the anti-slide pile described in this invention, the geometric material information includes the length of the anti-slide pile, the location of key nodes, the depth of the cantilever section, and the mechanical parameters of the material. The time series of geological conditions includes soil stiffness, soil density, water content, and timestamps.

[0008] As a preferred embodiment of the method for calculating the internal forces and displacements of the cantilever segment of the anti-slide pile according to the present invention, the specific steps for acquiring the geometric material information and ground condition time series of the cantilever segment of the anti-slide pile, establishing a depth calculation domain for the cantilever segment, and discretizing it to obtain the basic dataset for cantilever segment calculation are as follows. A continuous depth coordinate system is established based on the anti-slide pile length and key node locations. The soil parameter change rate is calculated by combining the time series of stratum conditions and the coordinate mapping is used to generate the cantilever segment depth calculation domain. Based on the depth calculation domain of the cantilever segment, the depth of the cantilever segment is divided into discrete grids and nodes are bound to obtain the basic dataset for cantilever segment calculation.

[0009] As a preferred embodiment of the method for calculating the internal forces and displacements of the cantilever segment of the anti-slide pile described in this invention, the specific steps for constructing a spatiotemporal Gaussian process prior model based on the cantilever segment calculation dataset, a deep prior representation layer, a time condition mapping layer, and a spatiotemporal fusion layer are as follows. The depth prior characterization layer uses the depth statistical analysis method to map the soil parameters of the depth nodes in the cantilever segment calculation basis dataset into depth-related response characterizations to obtain the depth prior distribution field. The time condition mapping layer maps the depth prior distribution field with the formation working condition time series and statistically analyzes the time evolution conditions of depth nodes to obtain the time condition distribution. The spatiotemporal fusion layer employs a tensor fusion algorithm to couple the depth prior distribution with the temporal condition distribution, generating a joint depth-time prior field for the cantilever segment. The deep prior representation layer provides spatial depth constraints, the temporal condition mapping layer obtains temporal evolution constraints, and through the spatiotemporal fusion layer, a spatiotemporal Gaussian process prior model is constructed.

[0010] As a preferred embodiment of the method for calculating the internal forces and displacements of the cantilever segment of the anti-slide pile described in this invention, the specific steps for generating the time-varying support reaction field parameter set are as follows: Based on the joint depth-time prior field of the cantilever segment, tensor encoding is performed on the computational basis dataset of the cantilever segment, and depth-time coupling features are extracted to generate a latent space. Based on the potential space, a nonlinear mapping algorithm is used to mine the potential structures with deep temporal coupling relationships and obtain the characteristics of potential support reaction forces. The potential support reaction force characteristics are transformed into time-varying support reaction force parameters through potential space mapping, thereby generating a time-varying support reaction force field parameter set.

[0011] As a preferred embodiment of the method for calculating the internal forces and displacements of the cantilever segment of the anti-slide pile described in this invention, the specific steps for solving the structural mechanics equations by applying the time-varying support reaction field parameter set and the cantilever segment depth calculation domain to generate predicted displacement curves and predicted internal force curves are as follows. Based on the depth calculation domain of the cantilever section, the time-varying support reaction force field parameter set is mapped point by point according to the continuous depth coordinate system to obtain the time-varying load input sequence; By using the time-varying load input sequence as an external constraint and combining it with geometric and material information, structural mechanics equations are constructed. Based on the time-varying support reaction field parameter set, the displacement response value is calculated by a high-precision time integration algorithm and continuously spliced ​​together to generate a predicted displacement curve by combining the structural mechanics equations. Based on the predicted displacement curve, the displacement gradient calculation is performed to calculate the internal force response value and continuously organize it to generate the predicted internal force curve.

[0012] As a preferred embodiment of the method for calculating the internal force and displacement of the cantilever segment of the anti-slide pile described in this invention, the steps of reconstructing the predicted displacement curve and the predicted internal force curve into a high-order tensor field, and extracting local response correlation features through depthwise separable convolution kernels to generate a coupled response feature field are as follows. Based on the predicted displacement curve and the predicted internal force curve, the data is aligned and reconstructed according to the continuous depth coordinate system to obtain joint multidimensional data. The joint multidimensional data is reconstructed into a high-order tensor field through dimensional expansion and axis rearrangement operations, and local window aggregation operations are performed to extract local response correlation features. The local response-related features are reorganized into channels and aggregated, and then normalized to generate a coupled response feature field.

[0013] As a preferred embodiment of the method for calculating the internal forces and displacements of the cantilever segment of the anti-slide pile described in this invention, the following steps are taken: Based on the coupled response characteristic field, the time-varying support reaction field parameter set is corrected by reverse constraint, and a joint solution is performed in conjunction with the cantilever segment depth calculation domain to generate corrected displacement curves and corrected internal force curves. Based on the coupled response feature field, feature decoupling operation is performed along the continuous depth coordinate system of the cantilever segment, and the non-consistent components of the local response associated features are extracted to generate the response deviation feature field. Tensor alignment is performed between the response deviation feature field and the time-varying support reaction force field parameter set to construct the correspondence between the support reaction force response deviation; Based on the correspondence between the support reaction force response deviation, the reverse constraint propagation algorithm is used to superimpose the time-varying support reaction force field parameter set point by point to generate the corrected time-varying support reaction force field parameter set. Based on the modified time-varying support reaction field parameter set, a joint solution is performed using the cantilever segment depth calculation domain to generate the corrected displacement curve and the corrected internal force curve.

[0014] In a second aspect, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, wherein when the computer program is executed by the processor, it implements any step of the method for calculating the internal force and displacement of the cantilever segment of the anti-slide pile as described in the first aspect of the present invention.

[0015] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program is executed by a processor, it implements any step of the method for calculating the internal force and displacement of the cantilever segment of the anti-slide pile as described in the first aspect of the present invention.

[0016] The beneficial effects of this invention are as follows: by constructing a spatiotemporal Gaussian process prior model and generating a time-varying support reaction field parameter set, the coupled characterization of soil parameters at depth nodes and time-evolved conditions is realized; in computer-aided engineering, the time-varying load and response of the cantilever segment of anti-slide pile can be simulated, improving the accuracy of internal force and displacement prediction, and realizing the reliability and applicability of cantilever segment structural analysis under complex geological conditions. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the calculation method for internal forces and displacements in the cantilever section of an anti-slide pile.

[0019] Figure 2 A flowchart for generating the time-varying support reaction field parameter set.

[0020] Figure 3 A flowchart for executing structural mechanics equations.

[0021] Figure 4 This is a flowchart for generating the calibration curve.

[0022] Figure 5 This is a comparative data graph showing the time variation of relative displacement error.

[0023] Figure 6 This is a statistical comparison chart of the relative error of internal forces over a time window. Detailed Implementation

[0024] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0025] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0026] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0027] Reference Figures 1-6 As one embodiment of the present invention, this embodiment provides a method for calculating the internal forces and displacements of the cantilever segment of an anti-slide pile, including the following steps: S1: Collect the geometric material information and geological condition time series of the cantilever section of the anti-slide pile, and establish a depth calculation domain for the cantilever section for discrete division to obtain the basic dataset for cantilever section calculation.

[0028] S1.1: Geometric material information includes the length of the anti-slide pile, the location of key nodes, the depth of the cantilever section, and the mechanical parameters of the material.

[0029] Specifically, after the anti-slide piles are completed, a rangefinder is used to measure the position of the pile top and the position of the pile bottom, collect the corresponding spatial position and elevation data, and obtain the length of the anti-slide pile by reading the measured record from the pile top to the pile bottom.

[0030] During the construction phase of the anti-slide piles, node markings were performed on the anti-slide piles, and a total station was used to measure the pile top, the starting position of the cantilever section, and the ending position of the cantilever section point by point to collect the spatial position of each node in the pile body and obtain the position of key nodes.

[0031] The key node positions of the start and end nodes of the cantilever segment are read and collected, and the depth of the cantilever segment is obtained by directly reading the depth identifier record corresponding to the cantilever segment.

[0032] During the construction or material delivery phase of anti-slide piles, mechanical property tests are conducted on concrete or steel reinforcement samples to collect the bending stiffness and deformation parameters of the materials as material mechanical parameters.

[0033] S1.2: The time series of geological conditions includes soil stiffness, soil density, water content and timestamp.

[0034] Specifically, controlled loads are applied and soil stress and displacement response signals are collected simultaneously using in-situ mechanical sensors around the anti-slide piles as stiffness parameters.

[0035] Soil samples were obtained at different depths, and the mass and volume of the soil samples were measured using on-site density sensors. The test results were used as the soil density at the corresponding spatial location.

[0036] Moisture sensors within the influence range of anti-slide piles are used to collect real-time soil moisture change signals, generating moisture content data that varies over time.

[0037] The clock built into the sensor node timestamps each collection of soil stiffness, soil density, and moisture content data, ensuring the consistency and traceability of various geological conditions data in the time dimension, and obtaining timestamps.

[0038] S1.3: Establish a continuous depth coordinate system based on the anti-slide pile length and key node positions, and calculate the soil parameter change rate by combining the time series of stratum conditions, and generate the cantilever segment depth calculation domain through coordinate mapping.

[0039] Specifically, based on the spatial location and elevation data of the pile top and bottom positions collected, a continuous depth coordinate axis with the anti-sliding pile length as the scale is constructed according to the measured records from the pile top to the pile bottom, and the key node positions are mapped to the continuous depth coordinate axis to generate a continuous depth coordinate system.

[0040] Under the constraint of continuous depth coordinate axis, soil stiffness, soil density and water content are aligned time-by-time. The difference between soil stiffness, soil density and water content corresponding to adjacent time stamps is used as the time series stratum working condition deviation (including soil stiffness deviation, soil density deviation and water content deviation). The ratio of soil stiffness, soil density and water content corresponding to the preceding time stamp in the adjacent time stamp to the time series stratum working condition deviation is used as the soil parameter change rate (including soil stiffness change rate, soil density change rate and water content change rate).

[0041] The rate of change of soil parameters is mapped to the corresponding depth of the key node in the continuous depth coordinate system, and finally the depth calculation domain of the cantilever segment is generated within the depth range defined by the starting node and the ending node of the cantilever segment.

[0042] S1.4: Based on the depth calculation domain of the cantilever segment, the depth of the cantilever segment is divided into discrete grids and nodes are bound to obtain the basic dataset for cantilever segment calculation.

[0043] Specifically, based on the cantilever segment's starting node and ending node, the cantilever segment's depth calculation domain is divided into multiple continuously arranged discrete depth grids according to the continuous depth coordinate system in the depth direction. The boundary position of each discrete depth grid is used as the depth node position.

[0044] Under the constraint of a continuous depth coordinate system, the soil stiffness change rate, soil density change rate, and water content change rate are bound to the corresponding discrete depth grid one by one according to the correspondence between the depth node positions in the cantilever segment depth calculation domain; the anti-slide pile length, key node positions, cantilever segment depth, and material mechanical parameters are bound according to the depth node positions to form a set of node parameter entries that correspond one-to-one in the depth direction.

[0045] By compiling the set of node parameter entries from all discrete depth grids, a basic dataset for cantilever segment calculation is obtained, which includes the location of discrete depth grids and corresponding geometric material information (including anti-slide pile length, key node location, cantilever segment depth and material mechanical parameters) as well as soil parameters of depth nodes.

[0046] S2: Based on the cantilever segment computational basic dataset, deep prior characterization layer, time condition mapping layer and spatiotemporal fusion layer, a spatiotemporal Gaussian process prior model is constructed, and potential spatial mapping is performed on the formation working condition time series to generate a time-varying support reaction force field parameter set.

[0047] S2.1: The depth prior characterization layer adopts the depth statistical analysis method to map the soil parameters of the depth nodes in the cantilever segment calculation basis dataset into depth-related response characterizations, and obtains the depth prior distribution field.

[0048] Specifically, based on the discrete depth grid locations and corresponding depth node soil parameters in the cantilever segment calculation dataset, the mean, variance, and rate of change of soil parameters of each depth node and adjacent depth nodes are statistically analyzed using the depth statistical analysis method according to the depth direction.

[0049] Under the constraint of a continuous depth coordinate system, the mean, variance of each depth node and the rate of change of soil parameters of adjacent depth nodes are integrated into a depth-related response characterization. The depth-related response characterizations of all depth nodes are arranged in depth order to obtain a complete depth prior distribution field, providing a depth direction constraint basis for subsequent time condition mapping and spatiotemporal fusion.

[0050] It should be noted that the depth statistical analysis method is a method for statistically processing soil parameters at discrete depth nodes in a continuous depth coordinate system. By calculating the mean, variance, and parameter change rate between adjacent nodes for each depth node, statistical features in the depth direction are extracted to reflect the distribution law and trend of soil parameters in depth, providing basic data for subsequent depth-related response characterization and spatiotemporal coupling analysis.

[0051] S2.2: The time condition mapping layer maps the depth prior distribution field with the formation working condition time series and statistically analyzes the time evolution conditions of depth nodes to obtain the time condition distribution.

[0052] Specifically, based on the depth-related response characterization of each depth node in the depth prior distribution field, the time series of stratum working conditions, which show the changes of soil stiffness, soil density, and water content over time, are mapped to the corresponding depth node positions, and the depth-time correspondence is established node by node according to the continuous depth coordinate system.

[0053] For each depth node, the difference between the soil parameters at each time point and the depth-related response is taken as the deviation, and the trend of the deviation over time is statistically analyzed to obtain the temporal evolution conditions of the depth node (such as the mean, variance, and slope of the linear trend of the deviation within the sliding window). The temporal evolution conditions of all depth nodes are summarized in depth order to obtain the complete temporal condition distribution, providing a temporal evolution constraint basis for the spatiotemporal fusion layer.

[0054] S2.3: The spatiotemporal fusion layer uses a tensor fusion algorithm to couple the depth prior distribution with the temporal condition distribution to generate a joint depth-time prior field for the cantilever segment.

[0055] Specifically, based on the depth-related response representation of each depth node in the depth prior distribution field, the corresponding temporal conditional distribution is mapped node by node according to the continuous depth coordinate system to form a joint tensor representation of each depth node as it changes over time.

[0056] Based on the tensor representation of each depth node, the soil parameters of each depth node are expanded into a multidimensional array, so that different types of parameters occupy different dimensions and are arranged continuously on the time axis. For example, the original one-dimensional parameter vector is expanded into a two-dimensional matrix or a three-dimensional tensor, where one dimension represents the parameter type and another dimension represents the time step.

[0057] After expansion, the tensor representations of each depth node are rearranged so that the depth dimension, time dimension, and parameter dimension correspond to different axes. For example, the tensor originally arranged as [node, parameter type, time] is rearranged as [node, time, parameter type], so that the depth dimension and time dimension are coupled in a unified tensor space, and the coupled tensor of the depth node is obtained. The coupling tensors of all depth nodes are aggregated in depth order to generate a joint temporal prior field of cantilever segment depth covering the depth range from the starting node to the ending node of the cantilever segment. This provides a complete spatiotemporal constraint basis for subsequent potential spatial mapping and generation of time-varying support reaction force field parameter sets.

[0058] It should be noted that the tensor fusion algorithm is a method for structurally representing multidimensional features or multi-source data according to depth, time, and parameter dimensions. By expanding, rearranging, and coupling the data in each dimension, a unified high-order tensor is formed, which fuses the depth prior distribution and the temporal conditional distribution, thereby preserving spatial and temporal constraints and realizing the joint representation and continuous mapping of multidimensional features.

[0059] The deep prior representation layer provides spatial depth constraints, the temporal condition mapping layer obtains temporal evolution constraints, and through the spatiotemporal fusion layer, a spatiotemporal Gaussian process prior model is constructed.

[0060] S2.4: Based on the joint depth-time prior field of the cantilever segment, tensor quantization encoding is performed on the basic dataset for cantilever segment computation, and depth-time coupling features are extracted to generate the latent space.

[0061] Specifically, based on the joint depth-time prior field of the cantilever segment, the geometric material information of each depth node in the cantilever segment computational basis dataset is mapped to the formation condition time series as a multidimensional tensor representation, forming the encoding structure of each node in the depth and time dimensions.

[0062] Extract feature channels from the coding structure, such as soil stiffness channel, density channel, water content channel, and material parameter channel; integrate the soil stiffness change rate, soil density change rate, water content change rate, and material mechanical parameters in each feature channel to obtain deep time-coupled features.

[0063] By summarizing the deep temporal coupling features in depth order, a latent space is generated, providing a complete high-dimensional feature foundation for the mining of potential support reaction force features and the generation of time-varying support reaction force field parameter sets.

[0064] S2.5: Based on the latent space, the latent structures with deep temporal coupling relationships are mined through nonlinear mapping algorithms to obtain the characteristics of potential support reaction forces.

[0065] Specifically, based on the latent space, the latent feature vectors of each depth node are arranged in chronological order to form a latent feature sequence with depth as the primary axis and time as the secondary axis. For each latent feature sequence, a nonlinear mapping algorithm (such as radial basis function kernel mapping and multilayer perceptron mapping) is applied to map the nonlinear relationship between the depth nodes and time nodes contained in the latent feature sequence element by element into the latent support reaction force response.

[0066] The potential support reaction force response obtained by mapping is used to extract the potential support reaction force feature value corresponding to each depth node at each time point in the depth and time directions. The potential support reaction force feature values ​​of all depth nodes at different time points are integrated to form a potential support reaction force feature that fully covers the depth range of the cantilever segment and reflects the time evolution, providing basic data for the subsequent generation of time-varying support reaction force field parameter set through potential spatial mapping.

[0067] It should be noted that the nonlinear mapping algorithm is a method of mapping the input feature space to the target feature space. It is used to capture the complex nonlinear relationship between input features in different dimensions or time nodes, thereby transforming the latent feature sequence into output features that reflect the depth and time coupling relationship, and realizing the accurate representation of hidden patterns and response laws.

[0068] S2.6: Transform the potential support reaction force characteristics into time-varying support reaction force parameters through potential space mapping, and generate a time-varying support reaction force field parameter set.

[0069] Specifically, based on the potential support reaction force characteristics, according to the correspondence between the node position and depth time in the potential space, the potential support reaction force characteristics of each node are mapped to the dimension of the actual support reaction force parameters to obtain the support reaction force values ​​of each node under different time states, and arranged in the order of continuous depth coordinate axis and time series.

[0070] The mapping results of all nodes are aggregated to form a set of support reaction force parameters that cover the entire depth range of the cantilever segment and evolve over time, thus generating a time-varying support reaction force field parameter set.

[0071] S3: Solve the structural mechanics equations by applying the time-varying support reaction field parameter set and the cantilever segment depth calculation domain to generate predicted displacement curves and predicted internal force curves.

[0072] S3.1: Based on the depth calculation domain of the cantilever segment, the time-varying support reaction force field parameter set is mapped point by point according to the continuous depth coordinate system to obtain the time-varying load input sequence.

[0073] Specifically, based on the depth calculation domain of the cantilever segment, the positions of each depth node are obtained according to the continuous depth coordinate system, and the support reaction force parameters of each depth node at different time points in the time-varying support reaction force field parameter set are matched with the node positions in the continuous depth coordinate system according to the depth order.

[0074] For each depth node, the corresponding support reaction force parameters are read in time sequence and mapped to the corresponding positions on the continuous depth coordinate axis to form the support reaction force of each depth node as time changes; the support reaction forces of all depth nodes are collected point by point in depth order and time order to generate the support reaction force input matrix.

[0075] All support reaction force input matrices are collected and organized into a time-varying load input sequence in a continuous depth coordinate system.

[0076] S3.2: Using the time-varying load input sequence as an external constraint, and combining it with geometric and material information, construct the structural mechanics equations.

[0077] Specifically, based on the time-varying load input sequence, the positions of each depth node in the cantilever segment are determined according to the continuous depth coordinate system. The support reaction force of each node in the time-varying load input sequence that changes with time is mapped to the corresponding depth node position. Combining the geometric and material information of each depth node in the cantilever segment calculation basis dataset (including anti-slide pile length, key node position, cantilever segment depth and material mechanical parameters), the material mechanical parameters and support reaction force are correlated at the node level.

[0078] The node parameter entries for each depth node and the time-varying load input sequence at the corresponding time point are summarized to form a set of node constraint information and establish structural mechanics equations, providing a complete mechanical description framework for subsequent internal force and displacement calculations.

[0079] It should be noted that the structural mechanics equations describe the relationship between the displacement and internal force of the cantilever segment under external loads. By combining the geometric material information and support reaction force constraints of each depth node, a node-level mechanical equilibrium equation is formed, providing a complete mechanical description basis for subsequent high-precision time integration algorithms to calculate displacement response values ​​and internal force response values.

[0080] S3.3: Based on the time-varying support reaction field parameter set, the displacement response value is calculated by a high-precision time integration algorithm and continuously spliced ​​together to generate a predicted displacement curve by combining the structural mechanics equations.

[0081] Specifically, based on the time-varying support reaction field parameter set, the support reaction force of each depth node at different time points is mapped to the node constraint position in the structural mechanics equation; the geometric material information of each node in the cantilever segment calculation basis dataset is combined with the mapped support reaction force to form a complete mechanical constraint condition for each node.

[0082] The structural mechanics equations are solved using a high-precision time integration algorithm over continuous time steps to obtain the displacement response values ​​of each depth node. The continuous displacement response values ​​of all nodes are then integrated to generate a complete predicted displacement curve, providing accurate time-depth response data for displacement evolution analysis of the cantilever segment.

[0083] The expression for calculating the displacement response value is: ; in, This is the displacement response value. The step size for a continuous time series. For time-varying support reaction field parameter lumens At time step The supporting reaction force, For local deep neighborhood nodes The corresponding material mechanical parameters include bending stiffness. It is the set of local depth neighbor nodes of a depth node.

[0084] It should be noted that the combined calculation of time series step size, support reaction force and bending stiffness results in a dimension consistent with the displacement response value, and the output displacement response value is consistent with the length dimension of the depth node displacement.

[0085] High-precision time integration algorithms are methods for solving structural mechanics equations over continuous time steps. Through precise discretization, they enable accurate prediction of the displacement evolution of a structure over the entire time series. Within each time step, the displacement state and support reaction force inputs from previous time steps are comprehensively considered to ensure continuous and smooth displacement response values ​​at depth nodes, providing reliable time-depth response data for internal force calculation and subsequent feature extraction.

[0086] like Figure 5 The results show the comparison of relative displacement errors obtained when calculating the displacement of the cantilever section of the antislide pile. Figure 5 The upper sub-graph in the image reflects the overall distribution of the relative displacement error of the cantilever section of the anti-slide pile over time throughout the entire testing period. Figure 5 The lower subgraph in the middle corresponds to Figure 5 The time interval marked by the red dashed box in the upper subplot is used to show the detailed changes in the relative displacement error within a local time range. Figure 5The results show that the relative error of the displacement of the cantilever segment of the anti-slide pile exhibits a shift, accompanied by an increase in the degree of error dispersion. By adopting a spatiotemporal Gaussian process prior model combined with a reverse constraint correction mechanism, the overall distribution of the relative error of the displacement of the cantilever segment of the anti-slide pile becomes more concentrated, and the trend of error evolution over time becomes more stable. Within a local time interval, it can effectively suppress the accumulation of displacement error caused by the change of support reaction force over time, ensuring that the calculated displacement of the cantilever segment of the anti-slide pile maintains good consistency with the reference true value even under high deviation conditions. This verifies the prediction accuracy and calculation stability of the displacement of the cantilever segment of the anti-slide pile in this invention.

[0087] S3.4: Based on the predicted displacement curve, perform displacement gradient calculation to calculate the internal force response value and continuously organize it to generate the predicted internal force curve.

[0088] Specifically, based on the predicted displacement curve, gradient calculations are performed on the discrete depth grid positions and corresponding displacements in the cantilever segment's computational dataset. By reading the displacement difference between adjacent depth nodes and the discrete depth grid position difference, the ratio of the displacement difference between adjacent depth nodes to the discrete depth grid position difference is used as the local displacement gradient.

[0089] The internal force response values ​​are calculated by combining the structural mechanics equations with the continuous depth coordinate system and time series order, and then organized node by node. The internal force response values ​​of all depth nodes are summarized in depth order and time order to generate a predicted internal force curve that covers the complete depth range of the cantilever segment and reflects the time evolution.

[0090] The expression for calculating the internal force response value is: ; in, This is the internal force response value. For depth nodes The corresponding material mechanical parameters include bending stiffness. For depth nodes The depth distance between adjacent nodes in a continuous depth coordinate system For depth nodes At time step The displacement response value.

[0091] It should be noted that the internal force response value is calculated by comparing the length dimension of the displacement with the length dimension of the depth spacing, so that the dimension of the internal force response value is consistent with the bending stiffness, thus achieving dimensional unification.

[0092] Figure 6 The results show the statistical comparison of the relative errors of internal forces obtained when calculating the internal forces of the cantilever section of the antislide pile. Figure 6The upper subplot shows the distribution of the mean relative error of the internal force of the cantilever section of the anti-slide pile and the error fluctuation range for different time windows throughout the entire calculation time range. Figure 6 The lower subgraph in the middle corresponds to Figure 6 The time window interval marked by the red dashed box in the upper subplot is used to illustrate the statistical characteristics of the relative error of internal forces within a local time range. Figure 6 The results show that the comparative calculation method exhibits fluctuations in the relative error of the internal force in the cantilever section of the anti-slide pile within certain time windows, reflecting its limited responsiveness to the time-varying characteristics of the ground support reaction force. By constructing a time-varying support reaction field parameter set, effective coupling of the time-varying ground parameters with the internal force calculation process in the cantilever section of the anti-slide pile is achieved, reducing the mean level and dispersion of the relative error of the internal force in the cantilever section of the anti-slide pile. Figure 6 Within the local time window shown in the lower sub-figure, the method of the present invention can compress the fluctuation range of the relative error of internal forces and improve the reliability of the internal force calculation results of the cantilever section of the anti-slide pile.

[0093] S4: Reconstruct the predicted displacement curve and predicted internal force curve into a high-order tensor field, extract local response correlation features through depthwise separable convolution kernels, and generate a coupled response feature field.

[0094] S4.1: Based on the predicted displacement curve and the predicted internal force curve, the data is aligned and reconstructed according to the continuous depth coordinate system to obtain joint multidimensional data.

[0095] Specifically, all depth nodes in the predicted displacement curve and predicted internal force curve are arranged sequentially according to the continuous depth coordinate system. The displacement response value and internal force response value of each depth node at different times are matched one by one to form a two-dimensional matrix of node-time-response type.

[0096] Extract the depth dimension, time dimension, and response type dimension from the two-dimensional matrix, so that the depth dimension corresponds to the node order on the continuous depth coordinate system, the time dimension corresponds to the time series of the predicted displacement curve and the predicted internal force curve, and the response type dimension contains the displacement channel and the internal force channel, thus generating a joint multidimensional data structure.

[0097] Based on the joint multidimensional data structure, the displacement response value and internal force response value of each depth node at each time point are integrated element by element to obtain joint multidimensional data.

[0098] S4.2: Reconstruct the joint multidimensional data into a high-order tensor field through dimensional expansion and axis rearrangement operations, and perform local window aggregation operations to extract local response correlation features.

[0099] Specifically, based on joint multidimensional data, the predicted displacement curve and the predicted internal force curve are aligned node by node in the continuous depth coordinate system and time series sequence to generate a two-dimensional vector; the displacement response value and internal force response value of each depth node over time are combined into a unified vector representation.

[0100] The vector representation of each depth node is expanded into a multidimensional array along the depth and time dimensions, and different types of curves occupy different dimensions. For example, the predicted displacement and predicted internal force values ​​contained in the vector representation of each depth node are expanded into a two-dimensional array, where one dimension represents the curve type (displacement or internal force) and the other dimension represents the time step. The curve type dimension is obtained and formed into a continuous arrangement on the continuous depth coordinate system.

[0101] Under the constraint of a continuous depth coordinate system, with each depth node as the center, multiple adjacent depth nodes are selected to form a local range in the depth direction. The sum of the feature values ​​of each node in the local range at the same time state is taken as the local depth response.

[0102] Select consecutive time points along the time series direction to form a local range in the time direction. Take the sum of the local depth response values ​​in the corresponding time range as the local time response. Bind the local depth response and the local time response to the same timestamp to obtain the local response association features.

[0103] S4.3: Perform channel recombination and feature aggregation on the local response correlation features, and normalize the structure to generate a coupled response feature field.

[0104] Specifically, based on the local response correlation features, the local response correlation features are reorganized according to the response type (such as displacement response features, internal force response features, and displacement-internal force coupled response features). For each depth node and each time point, the local response value from the predicted displacement curve is assigned to the displacement channel, and the local response value from the predicted internal force curve is assigned to the internal force channel, while maintaining a consistent correspondence between the displacement channel and the internal force channel in terms of depth node position and time series position.

[0105] For the same depth node and time point, the values ​​of corresponding positions in the displacement channel and internal force channel are merged item by item according to the channel order to obtain local response features; the local response features are scaled to a uniform dimension to make the response features of each depth node and time point comparable in amplitude and to ensure the consistency of subsequent feature analysis, thereby generating a coupled response feature field.

[0106] S5: Based on the coupled response characteristic field, the time-varying support reaction force field parameter set is corrected by reverse constraint, and combined with the cantilever segment depth calculation domain, a joint solution is performed to generate the corrected displacement curve and the corrected internal force curve.

[0107] S5.1: Based on the coupled response feature field, feature decoupling operation is performed along the continuous depth coordinate system of the cantilever segment, and the non-consistent components of the local response associated features are extracted to generate the response deviation feature field.

[0108] Specifically, based on the coupled response feature field, the coupled response feature values ​​of all depth nodes of the cantilever segment are arranged sequentially according to the continuous depth coordinate system, and the coupled response feature values ​​of different depth nodes at the same time point are used to form a depth response sequence.

[0109] In the depth response sequence, the coupling response feature values ​​between adjacent depth nodes are used as the analysis object, and the difference between the coupling response feature values ​​of adjacent depth nodes is used as the depth response difference sequence. When the depth response difference sequence shows discontinuous changes on the continuous depth coordinate system, it can be determined that there are abnormal fluctuations in the local depth response.

[0110] The depth response difference sequence, which exhibits discontinuous changes in the depth direction, is identified as an inconsistent component of local response correlation features. The inconsistent components corresponding to all depth nodes at each time point are summarized according to the continuous depth coordinate system and time series order to generate a response deviation feature field.

[0111] S5.2: Tensor-align the response deviation characteristic field with the time-varying support reaction force field parameter set to construct the correspondence between the support reaction force response deviation and the time-varying support reaction force field parameter set.

[0112] Specifically, the response deviation feature field is expanded sequentially according to the continuous depth coordinate system and time series order, and the response deviation feature values ​​corresponding to each depth node at each time point in the response deviation feature field are expanded sequentially to generate the deviation feature tensor.

[0113] Based on the time-varying support reaction field parameter set, the support reaction parameters of each depth node at each time point are uniformly arranged according to the continuous depth coordinate system and time series order, and the support reaction parameter tensor is generated.

[0114] The response deviation feature field tensor and the time-varying support reaction force field parameter set tensor are aligned element-wise at the depth node index and time index, so that each response deviation feature value has a unique correspondence with the support reaction force parameter corresponding to the same depth node and the same time point.

[0115] The response deviation characteristic value and the support reaction force parameter are paired and associated according to depth location and time state to establish a support reaction force response deviation correspondence to describe the correspondence between the support reaction force change and the response deviation.

[0116] S5.3: Based on the correspondence between the support reaction force response deviation, the reverse constraint propagation algorithm is used to superimpose the time-varying support reaction force field parameter set point by point to generate the corrected time-varying support reaction force field parameter set.

[0117] Specifically, based on the correspondence between the support reaction force and the response deviation, the response deviation characteristic value and the support reaction force parameter are read in pairs at each time point for each depth node according to the continuous depth coordinate system and time series order. The response deviation characteristic value is then used as a constraint correction amount and applied to the corresponding support reaction force parameter.

[0118] Along the time series direction, the response deviation characteristics of subsequent time states are continuously constrained and transmitted to the support reaction force parameters of previous time points, and expanded node by node along the continuous depth coordinate system at the same time point, so that the response deviation characteristics of adjacent depth nodes are continuously corrected in the depth direction, and the propagation correction amount is obtained.

[0119] The support reaction force parameters and propagation corrections corresponding to each depth node and each time point are superimposed point by point to obtain the updated support reaction force parameter values. These updated values ​​are then collected according to the continuous depth coordinate system and time series order to generate the corrected time-varying support reaction force field parameter set.

[0120] It should be noted that the reverse constraint propagation algorithm is a method that feeds back response deviation information to the input constraints point by point. By mapping the response deviations of each depth node and time point in reverse along the continuous depth coordinate system to the time-varying support reaction force field parameter set, the original support reaction force parameters are corrected node by node, thereby realizing the distribution adjustment of local deviations and the consistency of overall mechanical constraints, and thus generating the corrected time-varying support reaction force field parameter set.

[0121] S5.4: Based on the modified time-varying support reaction field parameter set, a joint solution is performed in conjunction with the cantilever segment depth calculation domain to generate the corrected displacement curve and the corrected internal force curve.

[0122] Specifically, based on the corrected time-varying support reaction field parameter set, according to the continuous depth coordinate system established in the depth calculation domain of the cantilever segment, the corrected support reaction parameters corresponding to each depth node at each time point are read sequentially, and the corrected support reaction parameters are mapped point by point to the corresponding depth node positions in the depth calculation domain of the cantilever segment, forming a corrected time-varying load input sequence that changes with time.

[0123] Under the constraints of the continuous depth coordinate system, the corrected time-varying load input sequence is integrated node by node with the geometric material information already bound in the cantilever segment calculation basis dataset to construct a set of node constraint information. A high-precision time integration algorithm is used on the set of node constraint information in the time series direction to obtain the displacement response value of each depth node at each time point, and the values ​​are continuously spliced ​​according to the continuous depth coordinate system and time series order to generate the corrected displacement curve.

[0124] After obtaining the corrected displacement curve, the displacement gradient is calculated along the discrete depth grid position in the depth calculation domain of the cantilever segment, and the corresponding internal force response value is calculated node by node in combination with the structural mechanics equations. The results are collected and organized in the order of continuous depth coordinate system and time series to generate the corrected internal force curve.

[0125] This embodiment also provides a computer device applicable to the calculation method of internal force and displacement of the cantilever segment of anti-slide piles, including: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to realize the calculation method of internal force and displacement of the cantilever segment of anti-slide piles as proposed in the above embodiment.

[0126] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0127] This embodiment also provides a storage medium storing a computer program. When executed by a processor, the program implements the method for calculating the internal forces and displacements of the cantilever segment of the anti-slide pile as proposed in the above embodiment. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Red-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0128] In summary, this invention achieves coupled characterization of soil parameters at depth nodes and time-evolved conditions by constructing a spatiotemporal Gaussian process prior model and generating a time-varying support reaction field parameter set. In computer-aided engineering, it can simulate the time-varying load and response of the cantilever segment of anti-slide piles, improving the accuracy of internal force and displacement prediction and realizing the reliability and applicability of cantilever segment structural analysis under complex geological conditions.

[0129] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for calculating internal forces and displacements of a cantilevered segment of a anti-slide pile, characterized in that: include, Collect geometric material information and geological condition time series of the cantilever section of the anti-slide pile, and establish a depth calculation domain for the cantilever section for discrete division to obtain the basic dataset for cantilever section calculation; Based on the cantilever segment computational basic dataset, deep prior characterization layer, time condition mapping layer and spatiotemporal fusion layer, a spatiotemporal Gaussian process prior model is constructed, and potential spatial mapping is performed on the formation working condition time series to generate a time-varying support reaction force field parameter set. The time-varying support reaction field parameter set and the cantilever segment depth calculation domain are used to solve the structural mechanics equations to generate predicted displacement curves and predicted internal force curves. The predicted displacement curve and the predicted internal force curve are reconstructed into a high-order tensor field. Local response correlation features are extracted by depthwise separable convolution kernels to generate a coupled response feature field. Based on the coupled response characteristic field, the time-varying support reaction force field parameter set is corrected by reverse constraint, and combined with the cantilever segment depth calculation domain, a joint solution is performed to generate the corrected displacement curve and the corrected internal force curve.

2. The method for calculating internal forces and displacements of a cantilevered pile segment according to claim 1, wherein: The geometric material information includes the length of the anti-slide pile, the location of key nodes, the depth of the cantilever section, and the material mechanical parameters; The time series of geological conditions includes soil stiffness, soil density, water content, and timestamps.

3. The method for calculating internal forces and displacements of a cantilevered pile segment according to claim 2, wherein: The process involves collecting geometric and material information and time series data of the cantilever segment of the anti-slide pile, establishing a depth calculation domain for the cantilever segment, and discretizing it to obtain the basic dataset for cantilever segment calculation. The specific steps are as follows: A continuous depth coordinate system is established based on the anti-slide pile length and key node locations. The soil parameter change rate is calculated by combining the time series of stratum conditions and the coordinate mapping is used to generate the cantilever segment depth calculation domain. Based on the depth calculation domain of the cantilever segment, the depth of the cantilever segment is divided into discrete grids and nodes are bound to obtain the basic dataset for cantilever segment calculation.

4. The method for calculating internal forces and displacements of a cantilevered pile segment according to claim 3, wherein: The specific steps for constructing a spatiotemporal Gaussian process prior model based on the cantilever segment computational dataset, deep prior representation layer, temporal condition mapping layer, and spatiotemporal fusion layer are as follows. The depth prior characterization layer uses the depth statistical analysis method to map the soil parameters of the depth nodes in the cantilever segment calculation basis dataset into depth-related response characterizations to obtain the depth prior distribution field. The time condition mapping layer maps the depth prior distribution field with the formation working condition time series and statistically analyzes the time evolution conditions of depth nodes to obtain the time condition distribution. The spatiotemporal fusion layer employs a tensor fusion algorithm to couple the depth prior distribution with the temporal condition distribution, generating a joint depth-time prior field for the cantilever segment. The deep prior representation layer provides spatial depth constraints, the temporal condition mapping layer obtains temporal evolution constraints, and through the spatiotemporal fusion layer, a spatiotemporal Gaussian process prior model is constructed.

5. The method for calculating the internal forces and displacements of the cantilever section of an anti-slide pile as described in claim 4, characterized in that: The specific steps for generating the time-varying support reaction field parameter set are as follows: Based on the joint depth-time prior field of the cantilever segment, tensor encoding is performed on the computational basis dataset of the cantilever segment, and depth-time coupling features are extracted to generate a latent space. Based on the potential space, a nonlinear mapping algorithm is used to mine the potential structures with deep temporal coupling relationships and obtain the characteristics of potential support reaction forces. The potential support reaction force characteristics are transformed into time-varying support reaction force parameters through potential space mapping, thereby generating a time-varying support reaction force field parameter set.

6. The method for calculating the internal forces and displacements of the cantilever section of an anti-slide pile as described in claim 5, characterized in that: The steps for solving the structural mechanics equations using the time-varying support reaction field parameter set and the cantilever segment depth calculation domain to generate predicted displacement and internal force curves are as follows. Based on the depth calculation domain of the cantilever section, the time-varying support reaction force field parameter set is mapped point by point according to the continuous depth coordinate system to obtain the time-varying load input sequence; By using the time-varying load input sequence as an external constraint and combining it with geometric and material information, structural mechanics equations are constructed. Based on the time-varying support reaction field parameter set, the displacement response value is calculated by a high-precision time integration algorithm and continuously spliced ​​together to generate a predicted displacement curve by combining the structural mechanics equations. Based on the predicted displacement curve, the displacement gradient calculation is performed to calculate the internal force response value and continuously organize it to generate the predicted internal force curve.

7. The method for calculating the internal forces and displacements of the cantilever section of an anti-slide pile as described in claim 6, characterized in that: The process of reconstructing the predicted displacement curve and predicted internal force curve into a high-order tensor field, and extracting local response correlation features using depthwise separable convolution kernels to generate a coupled response feature field, is detailed below. Based on the predicted displacement curve and the predicted internal force curve, the data is aligned and reconstructed according to the continuous depth coordinate system to obtain joint multidimensional data. The joint multidimensional data is reconstructed into a high-order tensor field through dimensional expansion and axis rearrangement operations, and local window aggregation operations are performed to extract local response correlation features. The local response-related features are reorganized into channels and aggregated, and then normalized to generate a coupled response feature field.

8. The method for calculating the internal forces and displacements of the cantilever section of an anti-slide pile as described in claim 7, characterized in that: The method involves applying reverse constraints to the time-varying support reaction force field parameter set based on the coupled response characteristic field, and performing a joint solution in conjunction with the cantilever segment depth calculation domain to generate corrected displacement curves and corrected internal force curves. The specific steps are as follows. Based on the coupled response feature field, feature decoupling operation is performed along the continuous depth coordinate system of the cantilever segment, and the non-consistent components of the local response associated features are extracted to generate the response deviation feature field. Tensor alignment is performed between the response deviation feature field and the time-varying support reaction force field parameter set to construct the correspondence between the support reaction force response deviation; Based on the correspondence between the support reaction force response deviation, the reverse constraint propagation algorithm is used to superimpose the time-varying support reaction force field parameter set point by point to generate the corrected time-varying support reaction force field parameter set. Based on the modified time-varying support reaction field parameter set, a joint solution is performed using the cantilever segment depth calculation domain to generate the corrected displacement curve and the corrected internal force curve.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the method for calculating the internal force and displacement of the cantilever segment of the anti-slide pile as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the method for calculating the internal force and displacement of the cantilever segment of the anti-slide pile as described in any one of claims 1 to 8.

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