A method for predicting the pile forming radius of a rotary jetting pile based on stratum feature clustering

Abstract

The present application relates to the technical field of geotechnical engineering, and discloses a method for predicting the pile forming radius of jet grouting piles based on stratum feature clustering, which collects the borehole columnar graph, the physical and mechanical parameters of strata and the spatial coordinates, extracts stratum features by a multi-scale convolution network with the size of the convolution kernel being constrained by the stratum layer number; a k-nearest neighbor graph is constructed by taking into account the spatial distance and stratum similarity, and the stratum distribution pattern is identified by a graph attention network and deep embedding clustering; the mutation points are confirmed and segmented by depth constraint and statistical detection, the clustering features and construction parameters are fused by cross-modal attention, the joint features are input into a space-time double-branch attention embedded with physical monotonicity constraint, and the preliminary pile forming radius is output; based on the diffusion mechanism of Bingham fluid, the theoretical upper bound is calibrated by differential calibration according to the clustering category, and the prediction interval is estimated according to the construction history residual difference. The present application can realize high-precision prediction and reliable interval estimation of the pile forming radius of jet grouting piles in complex strata with soft and hard interbeds.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, and more specifically, to a method for predicting the pile radius of jet grouting piles based on stratigraphic feature clustering. Background Technology

[0002] Jet grouting is a common method for foundation reinforcement in geotechnical engineering projects such as subway tunnels and foundation pit support. The pile radius directly determines the continuity of the reinforced body and the quality of the project. In complex strata with alternating layers of soft and hard soil, the physical and mechanical properties of different soil layers vary greatly, and the grout diffusion mechanism changes fundamentally with the stratum type. The pile radius is affected by the combined influence of stratum conditions, construction parameters, and their interactions, making prediction quite difficult.

[0003] Existing methods for predicting pile radius mainly fall into two categories: empirical formula methods based on soil strength and injection pressure. These methods simplify the strata into homogeneous bodies and cannot reflect the differentiated responses of different soil layers in alternating soft and hard strata to grout diffusion. The prediction error usually exceeds 20% of the measured value. Machine learning regression methods based on single pile construction parameters ignore the spatial correlation of strata between boreholes, fail to utilize the spatial distribution patterns of strata data from multiple boreholes in the engineering area, and do not adequately handle abrupt changes in strata crossings in the construction parameter time series, leading to a decrease in prediction accuracy when strata conditions are complex.

[0004] None of the above methods organically combine the identification of spatial distribution patterns of strata with the temporal modeling of construction parameters, lack systematic embedding of physical constraints, or provide prediction intervals associated with strata categories, making it difficult to meet the engineering requirements for quality control of jet grouting pile construction under complex strata conditions. Summary of the Invention

[0005] This invention provides a method for predicting the pile radius of jet grouting piles based on stratigraphic feature clustering, which solves the technical problems in related technologies such as the inability to effectively integrate the spatial distribution pattern of stratigraphy with the temporal dynamics of construction parameters, insufficient prediction accuracy, and lack of reliable prediction intervals.

[0006] This invention provides a method for predicting the pile radius of jet grouting piles based on stratigraphic feature clustering, comprising the following steps:

[0007] S1: Collect borehole columnar section, formation physical and mechanical parameters and spatial coordinates, and extract formation features using a multi-scale convolutional network with formation layer number constrained by convolution kernel size to obtain multi-scale fused feature vectors for each borehole;

[0008] S2 combines fused feature vectors and spatial coordinates to construct a k-nearest neighbor graph that takes into account both spatial distance and stratigraphic similarity. Through graph attention network and deep embedding clustering, it identifies the spatial distribution pattern of stratigraphy and outputs cluster labels, category embeddings, node feature representations and cluster prototypes.

[0009] S3, cluster the pile locations to be predicted and obtain the time series of construction parameters. The mutation points are confirmed by both the a priori depth constraint of the stratum and statistical detection and segmented. The cluster features and segmented construction parameters are fused through cross-modal attention to obtain the joint feature vector and segmented parameter sequence.

[0010] S4 inputs the joint feature vector and the segmented parameter sequence into a spatiotemporal dual-branch attention Transformer with physical monotonicity constraints, jointly models the construction time-series dynamics and historical pile formation data, and outputs the preliminary pile radius;

[0011] S5 takes the initial pile radius as input, performs truncation correction based on the Bingham fluid diffusion mechanism and the theoretical upper limit of the cluster category differentiation, and estimates the prediction interval according to the category differentiation based on the construction history residuals to obtain the final predicted value of the pile radius and the prediction interval.

[0012] Furthermore, in S1, the multi-scale convolutional neural network includes three parallel convolutional branches. The first convolutional branch uses a convolutional kernel whose receptive field covers the parameter range of a single soil layer to capture detailed features within the layer and boundary features of parameter jumps between layers. The second convolutional branch uses a convolutional kernel whose receptive field covers two to three adjacent soil layers to capture the combination pattern features of alternating soft and hard soil layers. The third convolutional branch uses a convolutional kernel whose receptive field covers all effective layers, and its upper limit size is determined according to the actual number of strata in the engineering area.

[0013] The outputs of the three convolutional branches are concatenated along the feature dimension to form a multi-scale feature representation. This representation is then concatenated with the vertical distribution pattern features output by the one-dimensional convolutional neural network and passed through a fully connected layer to obtain a multi-scale fused feature vector.

[0014] Furthermore, in S2, the k-nearest neighbor association graph is constructed as follows: each borehole is modeled as a node of the graph, and the k boreholes with the closest spatial distance to each node are selected as neighbor nodes to establish edge connections. The edge weight combines spatial distance weight and feature similarity weight. The spatial distance weight uses a Gaussian kernel function to map the spatial distance into a weight value.

[0015] The feature similarity weight uses cosine similarity to measure the similarity of multi-scale fused feature vectors between nodes. After normalizing the two, the weighted sum is obtained to obtain the comprehensive weight of the edge.

[0016] Furthermore, in S2, the implementation of the cluster number determination mechanism that integrates engineering prior constraints is as follows: extract the prior information of stratigraphic engineering classification from the engineering survey report as the prior lower bound of the cluster number, set the candidate range based on the prior lower bound, perform pre-clustering for each candidate cluster number using the K-means algorithm, and evaluate the cluster number by combining the contour coefficient and the stratigraphic engineering classification consistency score. The consistency score is the proportion of nodes belonging to the same engineering stratigraphic category in the same cluster category.

[0017] The contour coefficient and consistency score are normalized and then weighted to obtain the comprehensive evaluation index. The cluster number with the best comprehensive evaluation index is selected as the final number of stratigraphic categories.

[0018] Furthermore, in S2, the deep embedding clustering module includes an encoder network, a clustering layer, and a decoder network. The clustering layer uses the Student t-distribution to calculate the similarity between the node embedding features and each cluster center and obtain the soft assignment probability. The joint loss function includes a clustering loss term, a spatial constraint loss term, and a reconstruction loss term. The clustering loss term uses Kullback-Leibler divergence to measure the difference between the soft assignment probability and the target distribution. The spatial constraint loss term applies Laplace regularization constraints to the difference in cluster assignment probabilities of connected nodes based on the stratigraphic spatial association graph structure.

[0019] The reconstruction loss term is calculated by the decoder network to obtain the mean squared error between the reconstructed features and the original features. After training, the mean value of the category embedding vector for each cluster category is calculated to obtain the cluster prototype features and stored.

[0020] Furthermore, in S3, the dual confirmation mechanism is implemented as follows: using the original top and bottom depth values ​​of each borehole retained in S2, spatial interpolation is performed on the depth of each stratum interface at the predicted pile location using graph attention edge weights as interpolation weights to obtain the estimated depth, and the tolerance range is adaptively set according to the borehole spacing; the time-series sequence of construction parameters is differentially calculated at each time step to obtain the rate of change sequence, and the mean of the rate of change sequence plus the standard deviation of a preset multiple is used as the statistical detection threshold;

[0021] When the rate of change of construction parameters exceeds the statistical detection threshold at a certain moment and the construction depth at that moment falls within the tolerance range of the estimated depth of a certain stratum interface, it is identified as a stratum crossing abrupt change point; otherwise, it is not marked as an abrupt change point.

[0022] Furthermore, in S3, the cross-modal attention mechanism includes a query mapping layer, a key mapping layer, a value mapping layer, and an attention calculation layer. The category embedding vector is passed through the query mapping layer to obtain the query vector. The segmented construction parameter sequence and the mutation point additional feature vector are passed through the key mapping layer and the value mapping layer to obtain the key vector sequence and the value vector sequence, respectively. The scaling dot product attention is used to calculate the correlation score between the query vector and each key vector and then normalized to obtain the attention weight.

[0023] The construction feature representation, which incorporates stratigraphic category information, is obtained by weighting and summing the value vector sequence according to attention weights.

[0024] Furthermore, in S4, the temporal attention branch adopts a two-dimensional positional encoding mechanism, which generates a depth positional encoding vector and a temporal positional encoding vector for each construction state, adds them element by element, and then fuses them with the construction state vector. The encoded sequence is then input into a multi-layer Transformer encoder for temporal modeling.

[0025] The embedding method of physical monotonicity constraints is as follows: constrain violation detection is performed on sample pairs of the same stratum category in the training batch. When the predicted radius of the sample with a larger parameter value violates the preset monotonic relationship, the degree of violation is calculated and summed to obtain the monotonicity constraint loss term. The constraint loss terms of each parameter are weighted and summed and then jointly optimized with the data fitting loss.

[0026] Furthermore, S4 also includes a transfer learning strategy that integrates cluster consistency constraints: in the pre-training stage, the cluster prototype features of each cluster category are extracted and stored; for the new engineering region, the correspondence between the cluster categories of the new and old engineering regions is established through nearest neighbor matching; and in the fine-tuning stage, the parameters of the feature extraction layer and the attention layer are fixed and the parameters of the output layer and the feature fusion layer are fine-tuned.

[0027] Meanwhile, a clustering consistency constraint term is introduced into the fine-tuning loss function. The constraint term is the Euclidean distance between the cluster prototype features of the new region and the corresponding category cluster prototype features of the pre-trained region.

[0028] Furthermore, in S5, the method for determining the upper bound of the theoretical radius differentiated by cluster category is as follows: the ratio of injection pressure to undrained shear strength of soil is defined as the pressure ratio, and the ratio of grout flow rate to lifting speed is defined as the grouting volume per unit depth. For each cluster category, a power function relationship between the theoretical maximum diffusion radius, pressure ratio, and grouting volume per unit depth is established. A hierarchical calibration strategy is adopted. When the number of completed piles in a certain cluster category reaches a preset threshold, it is calibrated independently. Otherwise, the parameters of the corresponding category in the pre-trained engineering area are inherited as the initial values.

[0029] The prediction interval estimation method is as follows: maintain the prediction residual statistics of the sliding window for each cluster category, correct the prediction center value with the residual mean, and determine the upper and lower bounds of the prediction interval with the residual standard deviation of a preset multiple.

[0030] The beneficial effects of this invention are as follows:

[0031] By extracting stratigraphic features through multi-scale convolutional networks and combining graph attention networks with deep embedding clustering to identify stratigraphic spatial distribution patterns, the stratigraphic clustering results are introduced into the identification of abrupt change points in construction parameters and cross-modal feature fusion. This achieves complete information transmission between stratigraphic spatial modeling and construction time series processing, and solves the problem of insufficient prediction accuracy caused by neglecting the spatial correlation of stratigraphic layers in existing methods.

[0032] Physical monotonicity constraints are embedded in the training of the spatiotemporal bi-branch attention Transformer. During the inference stage, the theoretical upper limit is truncated and corrected based on the Bingham fluid diffusion mechanism and the differential calibration of cluster categories. The prediction interval is estimated according to the differential estimation of construction history residuals by category. This ensures that the prediction results conform to physical laws and provides interval estimates that truly reflect the uncertainty of prediction for different strata categories, thus meeting the practical needs of engineering construction quality control. Attached Figure Description

[0033] Figure 1 This is a flowchart of a method for predicting the pile radius of jet grouting piles based on stratigraphic feature clustering, according to the present invention.

[0034] Figure 2 This is a flowchart of a method for predicting the pile radius of jet grouting piles based on stratigraphic feature clustering, as described in this invention. Figure 1 ;

[0035] Figure 3 This is a flowchart of a method for predicting the pile radius of jet grouting piles based on stratigraphic feature clustering, as described in this invention. Figure 2 . Detailed Implementation

[0036] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, some features described in the examples may be combined in other examples.

[0037] At least one embodiment of the present invention discloses a method for predicting the pile radius of jet grouting piles based on stratigraphic feature clustering, such as... Figures 1 to 3 As shown, it includes the following steps:

[0038] S1: Collect borehole columnar section, formation physical and mechanical parameters and spatial coordinates, and extract formation features using a multi-scale convolutional network with formation layer number constrained by convolution kernel size to obtain multi-scale fused feature vectors for each borehole;

[0039] The geological data from multiple exploration boreholes deployed within the project area was acquired. This data includes borehole columnar section information and geological physical and mechanical parameters. The borehole columnar section information records the type, top depth, bottom depth, and thickness of each soil layer from the surface downwards. Soil types include silty clay, silty clay, silt, fine sand, and silt. The geological physical and mechanical parameters include parameters such as the internal friction angle, cohesion, compression modulus, standard penetration test blow count, water content, permeability coefficient, and natural density for each soil layer. Simultaneously, the spatial coordinates of each borehole were acquired, including its planar coordinates and borehole elevation.

[0040] Soil layer types are encoded and converted using one-hot encoding to transform the category information of soil layer types into numerical vector representations. For boreholes containing multiple soil layer types, a soil layer type sequence vector is constructed according to the vertical order of the soil layers. The physical and mechanical parameters of the strata are normalized using a min-max normalization method to map parameters with different dimensions to the same numerical range, eliminating the influence of parameter dimension differences on subsequent feature extraction. For strata parameters with missing values, imputation is performed based on the parameter values ​​of adjacent soil layers and the statistical characteristics of the soil layer type.

[0041] In terms of input feature organization, the uniquely encoded vector of each soil layer is concatenated with the normalized physical and mechanical parameter vector along the feature dimension to form a unified feature vector for that layer. This vector is then arranged vertically from top to bottom, forming a two-dimensional input matrix with soil layers as rows and feature dimensions as columns, serving as the unified input format for subsequent convolution operations. A multi-scale convolutional feature extractor is designed to extract deep features from the aforementioned two-dimensional input matrix. It should be noted that the effective layers in the jet grouting pile construction area are typically concentrated within a limited depth range near the tunnel burial depth. The main strata in the engineering area are usually 3 to 5 layers, significantly different from the more than ten or even dozens of layers found in typical geological exploration scenarios. This characteristic of fewer layers and strong strata abrupt changes places specific requirements on the design of the convolution kernel size: the upper limit of the convolution kernel size must be constrained by the actual number of strata. If the receptive field of the convolution kernel exceeds the actual stratum sequence length, invalid boundary filling areas will be introduced, leading to feature extraction distortion. Therefore, the convolution kernel size design of the multi-scale convolutional feature extractor is constrained based on the typical number of strata in the engineering area. The multi-scale convolutional feature extractor comprises three parallel convolutional branches. The first branch employs a small-sized convolutional kernel with a receptive field covering the parameter range of a single soil layer. This kernel specifically captures detailed features of parameters within a single soil layer in alternating soft and hard strata, as well as boundary features of parameter jumps between layers. These jump features are particularly significant in alternating soft and hard strata and have a crucial impact on pile radius prediction. The second branch employs a medium-sized convolutional kernel with a receptive field covering two to three adjacent soil layers. This kernel captures the combination patterns of alternating soft and hard soil layers, modeling the parameter transition relationships between adjacent soil layers. The third branch employs a large-sized convolutional kernel with a receptive field covering all effective layers. Its upper limit is determined based on the actual number of strata in the engineering area, not exceeding the total length of the stratum sequence. This kernel captures the overall combination patterns of alternating soft and hard strata throughout the entire construction depth. Each convolutional branch is followed by a batch normalization layer and a modified linear unit activation function layer after the convolutional layer, introducing nonlinear transformation capabilities. The feature vectors output from the three convolutional branches are concatenated along the feature dimension to form a feature representation that integrates information from three scales: intra-layer details, inter-layer combinations, and overall distribution.

[0042] For the vertical stratigraphic profile obtained from the borehole, a one-dimensional convolutional neural network (CNN) is used to extract vertical distribution pattern features. Considering the limited number of strata and short vertical sequences in the jet grouting pile construction area, the CNN is designed with 2 to 3 layers to avoid overfitting on short sequences due to excessively deep networks. The parameters of each soil layer in the borehole are arranged in order of burial depth to form a vertical stratigraphic parameter sequence. The CNN performs convolution operations on the stratigraphic parameter sequence along the vertical direction. By sliding the convolution kernel, it captures the vertical layering structure features and sequence variation patterns of the strata. Shallow convolutional layers extract low-level vertical features, while deep convolutional layers extract high-level semantic features. A pooling layer is connected after the convolutional layers. The pooling layer downsamples the feature map output by the convolutional layers to reduce the feature dimensionality and enhance the translation invariance of the features.

[0043] The multi-scale fused features output from the multi-scale convolutional feature extractor are concatenated with the vertical distribution pattern features output from the one-dimensional convolutional neural network to obtain a comprehensive feature vector containing deep semantic and vertical structural information of formation parameters. This comprehensive feature vector is then transformed and its dimensions adjusted using a fully connected layer to obtain a multi-scale fused feature vector for each borehole. This feature vector provides a unified semantic encoding of the multi-dimensional heterogeneous parameters of the formation, offering a high-quality feature representation for subsequent spatial correlation modeling and cluster analysis.

[0044] S2 combines fused feature vectors and spatial coordinates to construct a k-nearest neighbor graph that takes into account both spatial distance and stratigraphic similarity. Through graph attention network and deep embedding clustering, it identifies the spatial distribution pattern of stratigraphy and outputs cluster labels, category embeddings, node feature representations and cluster prototypes.

[0045] Receive the multi-scale fused feature vector and borehole spatial coordinate information output from the previous step to construct a stratigraphic spatial correlation graph. Each borehole is modeled as a node in the graph, with its feature being the multi-scale fused feature vector of that borehole. A k-nearest neighbor adaptive graph construction mechanism is used to determine the connectivity between nodes. For each node in the graph, the Euclidean spatial distance between the corresponding borehole and all other boreholes is calculated. Based on the spatial distance, the k nearest boreholes are selected as the node's neighbor nodes, and edges are established between the node and its k neighbor nodes. The k-nearest neighbor mechanism ensures the local connectivity of the graph, enabling each node to aggregate stratigraphic information from its spatially adjacent region, while avoiding the problem of an overly dense or sparse graph caused by selecting a fixed distance threshold.

[0046] The edge weights between nodes are calculated, taking into account both spatial distance and feature similarity. For an edge connecting node i and node j, the spatial distance weight is calculated by using a Gaussian kernel function to map the spatial distance to a weight value; the smaller the spatial distance, the larger the weight. The feature similarity weight is calculated by using cosine similarity to measure the similarity between the multi-scale fused feature vectors of node i and node j; the larger the cosine similarity value, the more similar the stratigraphic features of the two nodes. After normalizing the spatial distance weight and the feature similarity weight, they are weighted and summed according to a preset ratio to obtain the comprehensive edge weight. The edge weights provide prior information for subsequent graph attention calculations, resulting in stronger association between boreholes that are spatially close and have similar stratigraphic features.

[0047] A graph attention network is constructed to process the spatial correlation graph of the stratigraphy. The graph attention network consists of a stack of multiple graph attention layers. Each graph attention layer aggregates the feature information of neighboring nodes through an attention mechanism to update the node representation. In the graph attention layer, for node i and its set of neighboring nodes, the node features are first transformed using a shared linear transformation matrix to obtain the transformed node feature representation. Then, the attention coefficient between node i and each neighboring node j is calculated. The calculation of the attention coefficient adopts an additive attention mechanism, concatenating the transformed features of node i and node j and then linearly mapping them through an attention vector, followed by an activation function to obtain the attention energy value. The attention energy values ​​of node i and all neighboring nodes are normalized using a softmax function to obtain the normalized attention coefficient. The calculation process of the attention coefficient incorporates edge weight information, using edge weights as adjustment factors to weight the attention energy values, so that neighboring nodes with larger edge weights obtain higher attention coefficients.

[0048] A multi-head attention mechanism is employed to enhance the expressive power of the graph attention layer. This mechanism comprises multiple parallel attention heads, each independently calculating the attention coefficients between a node and its neighbors and performing feature aggregation. Different attention heads learn different aspects of the relationships between nodes. The output features of multiple attention heads are concatenated or averaged to obtain the output node features of the graph attention layer. Through the stacking of multiple graph attention layers, node features gradually incorporate neighborhood information across a larger spatial range, expanding from direct neighbors to multi-order neighbors, forming a feature representation of multi-order spatial associations. The output of the graph attention network is an updated feature vector for each node, containing both the borehole's own stratigraphic information and stratigraphic information from surrounding boreholes aggregated through spatial associations.

[0049] The node features output by the graph attention network are input into the deep embedding clustering module for adaptive stratigraphic clustering. It should be noted that the stratigraphic classification in the engineering survey report is a qualitative judgment based on the vertical profile of a single borehole, reflecting the soil type at each borehole location. However, it cannot directly provide the spatial stratigraphic distribution pattern among multiple boreholes within the engineering area, i.e., which areas have strata of the same spatial type and similar response characteristics to the grouting pile radius. The purpose of deep embedding clustering is precisely to solve this spatial distribution pattern recognition problem. By clustering the graph attention features of multiple boreholes, it establishes the spatial grouping results of the strata within the engineering area, providing a basis for subsequent differential prediction of pile radius based on stratigraphic categories. Prior engineering constraints act as boundary constraints here, ensuring that the clustering results do not violate known common sense regarding stratigraphic engineering classification. The clustering itself fills in spatial distribution pattern information that cannot be directly provided by the survey report. The two are complementary: prior constraint boundaries and clustering refinement of spatial distribution.

[0050] Before performing full training of the deep embedding clustering module, a preprocessing step to determine the number of clusters is first executed. In this stage, the K-means algorithm is used to pre-cluster the node features output by the graph attention network. Evaluation metrics are calculated based on the pre-clustering results, and the optimal number of clusters is determined before proceeding with full training of the deep embedding clustering module. The cluster number determination mechanism integrates two dimensions: engineering prior constraints and data-driven evaluation. First, prior information on stratigraphic engineering classification is extracted from the engineering survey report. Based on the current national standard for soil engineering classification, soil types appearing within the engineering area are grouped into several engineering categories, serving as a prior lower bound for the number of clusters—that is, the number of clusters should not be less than the number of major engineering stratigraphic categories identified in the survey report. This prior constraint ensures that the clustering results are consistent with the understanding of strata in engineering practice, avoiding the problem of purely mathematical methods over-subdividing soil layers with similar engineering properties or incorrectly merging soil layers with significantly different properties. Based on the prior lower bound, a candidate range for the number of clusters is set. K-means pre-clustering is then performed on each cluster within the candidate range, and the clustering quality is evaluated. The evaluation process comprehensively considers two dimensions: mathematical clustering quality and engineering stratigraphic interpretability. Regarding mathematical clustering quality, the silhouette coefficient is used to assess the compactness and separation of clusters. The silhouette coefficient is calculated by dividing the average distance from a node to other nodes in the same cluster by the average distance to the nearest node in a dissimilar cluster; a higher silhouette coefficient indicates better clustering quality. For engineering stratigraphic interpretability, the stratigraphic engineering classification consistency score of nodes within each cluster is calculated. Specifically, the proportion of nodes belonging to the same engineering stratigraphic category within the same cluster is statistically analyzed; a higher proportion indicates that the cluster is purer and more interpretable in an engineering sense. The silhouette coefficient and engineering stratigraphic consistency score are normalized and then weighted according to preset weights to obtain a comprehensive evaluation index. All clusters within the candidate range are traversed, and the number of clusters that optimizes the comprehensive evaluation index is selected as the final number of stratigraphic categories. This method of determining the number of clusters, combining prior engineering specifications with data-driven evaluation, ensures that the clustering results are both statistically reasonable and consistent with the professional understanding of stratigraphic classification in geotechnical engineering practice.

[0051] After determining the number of clusters, the deep embedding clustering module is fully trained. The deep embedding clustering module includes an encoder network, clustering layers, and a decoder network. Considering that the number of borehole nodes in jet grouting pile projects is typically on the order of tens, the encoder network adopts a lightweight design, with 2 to 3 layers, and the hidden dimension of each layer not exceeding twice the number of nodes, to avoid overfitting caused by the number of model parameters far exceeding the sample size. The pre-training of the graph attention network uses a self-supervised objective of node feature reconstruction, taking the multi-scale fused feature vector of each borehole node as the reconstruction target. The graph attention network parameters are optimized by minimizing the reconstruction error. This self-supervised pre-training process does not rely on labeled data and fully utilizes the stratigraphic information of all boreholes in the engineering area. The encoder network consists of a multi-layer fully connected neural network, mapping the high-dimensional node features output by the graph attention network to a low-dimensional embedding space. The encoder network learns a compact representation of node features through layer-by-layer dimensionality reduction, preserving the main discriminative information of node features in the embedding space. The clustering layer defines the same number of cluster centers in the embedding space as the number of predetermined clusters. A Student's t-distribution is used to calculate the similarity between the embedded features of each node and each cluster center. Based on this similarity, the soft assignment probability of a node belonging to each cluster category is calculated. The degrees of freedom parameter of the Student's t-distribution controls the shape of the similarity function; smaller degrees of freedom result in a more concentrated distribution, which is beneficial for forming clear cluster boundaries. The cluster center initialization method adopts the K-means++ strategy, using the cluster centers obtained in the pre-clustering stage as initial values ​​to avoid overly concentrated initial positions of the cluster centers. A joint loss function is constructed to optimize the parameters of the deep embedding clustering module. The joint loss function includes a clustering loss term, a spatial constraint loss term, and a reconstruction loss term. The clustering loss term uses Kullback-Leibler divergence to measure the difference between the node's soft assignment probability distribution and the target distribution. The target distribution is obtained by performing a power transformation and normalization on the soft assignment probabilities. The power transformation enhances the weight of high-confidence assignments, causing the soft assignment probabilities to converge towards hard assignments, forming clear cluster partitions.

[0052] The spatial constraint loss term constrains the spatial continuity of the clustering results through Laplacian regularization. The calculation of the spatial constraint loss term is based on the structure of the stratigraphic spatial correlation graph. For connected node pairs in the graph, the difference between their clustering assignment probabilities is calculated; the greater the difference, the greater the loss. This constraint term encourages spatially adjacent borehole nodes to have similar clustering assignment probabilities, tending to be classified into the same stratigraphic category, ensuring that the clustering results conform to the spatial continuity of the stratigraphy. The reconstruction loss term reconstructs the embedded features back into the original feature space through the decoder network, calculating the mean square error between the reconstructed features and the output features of the graph attention network. The reconstruction loss term ensures that the embedded features retain the original stratigraphic information during dimensionality reduction, avoiding the loss of important stratigraphic discriminative features during the clustering process.

[0053] The clustering loss term, spatial constraint loss term, and reconstruction loss term are weighted and summed according to their respective weight coefficients to obtain the total joint loss function. The weight coefficients of the three loss terms are set based on their dimensions and magnitudes: the clustering loss term's weight coefficient ranges from 0.5 to 1.0; this term directly drives the convergence of cluster assignments and has a relatively large weight. The spatial constraint loss term's weight coefficient ranges from 0.1 to 0.3; this term plays an auxiliary constraint role, and an excessively large weight can lead to clustering results over-reliance on spatial proximity while ignoring differences in formation parameters. The reconstruction loss term's weight coefficient ranges from 0.1 to 0.5; this term ensures the integrity of embedded feature information, and an excessively large weight can cause the encoder to favor reconstruction over clustering discrimination. These weight ranges are based on experimental verification on multiple jet grouting pile engineering datasets. In specific engineering applications, these ranges can be fine-tuned using clustering quality indicators on the validation set. The stochastic gradient descent optimization algorithm is used to minimize the joint loss function. The gradient of the loss function with respect to the encoder network, decoder network, and cluster center parameters is calculated using the backpropagation algorithm, and the model parameters are iteratively updated. During the iteration process, the encoder network learns embedded feature representations suitable for the clustering task. The cluster center positions are gradually adjusted to the center positions of nodes in each category, and the clustering assignment probabilities of the nodes gradually converge towards deterministic assignment. Iterative training continues until the joint loss function converges or the preset maximum number of iterations is reached.

[0054] After training, the cluster label of each node is determined based on its soft assignment probability, and the category with the highest probability is selected as the cluster category of that node. Simultaneously, the embedding features output by the encoder network are extracted as the node's category embedding vector, which contains semantic information about the stratigraphic category to which the node belongs. For each cluster category, the mean of the category embedding vectors of all borehole nodes within that category is calculated to obtain the cluster prototype feature vector for that category. These cluster prototype feature vectors are stored as the basis for cross-engineering knowledge transfer in the subsequent transfer learning stage. The cluster label, category embedding vector, and node feature representation enhanced by the graph attention network are obtained for each borehole. The top and bottom burial depths of each borehole in the original input data of S1 are retained. This information collectively provides prior knowledge of stratigraphic classification, spatial correlation feature representation, and the original numerical basis required for stratigraphic interface depth interpolation for subsequent radius prediction.

[0055] S3, cluster the pile locations to be predicted and obtain the time series of construction parameters. The mutation points are confirmed by both the a priori depth constraint of the stratum and statistical detection and segmented. The cluster features and segmented construction parameters are fused through cross-modal attention to obtain the joint feature vector and segmented parameter sequence.

[0056] The system receives the borehole clustering labels, category embedding vectors, and node feature representations output from the previous step to obtain relevant information about the predicted jet grouting pile location. This information includes the pile's spatial coordinates, geological survey data, and construction parameter sequences. The system utilizes the graph attention network and deep embedding clustering model trained in the previous step to extract geological features and perform clustering inference for the predicted pile location. The geological survey data for the predicted pile location is used to extract features according to the method in the first step, resulting in a multi-scale fused feature vector. This pile location is added as a new node to the geological spatial association graph. Based on the spatial distance between the pile location and existing borehole nodes, its k nearest neighbor nodes are determined, edges are established, and edge weights are calculated. The trained graph attention network is used to perform forward propagation on this new node, aggregating the feature information of its neighboring nodes to obtain a node feature representation that integrates spatial association information. This node feature is input into the encoder network of the deep embedding clustering model to obtain embedded features and calculate the soft assignment probability to each cluster center, determining the clustering label and category embedding vector for the pile location.

[0057] The construction parameter time series of the pile location to be predicted is obtained. This time series records the construction state parameters at different moments during the jet grouting pile construction process. Construction parameters include jetting pressure, grout flow rate, lifting speed, drill rod rotation speed, and water-cement ratio. The construction process is divided into multiple moments according to time sequence, each moment corresponding to a construction state, recording the values ​​of each construction parameter and the corresponding construction depth at that moment. The construction parameter sequence is arranged in chronological order to form a time series vector sequence. The construction parameters are normalized using the Z-score standardization method to unify each parameter to a zero-mean, unit-variance distribution, eliminating dimensional differences between different parameters.

[0058] To address the unique challenges of jet grouting pile construction in alternating soft and hard soil layers, a mechanism for identifying and segmenting abrupt changes by integrating S2 soil spatial modeling results is introduced before time-series alignment. In these layers, as the drill rod moves from soft to hard soil or vice versa, abrupt changes in soil resistance cause significant jumps in construction parameters within a short period. These jumps manifest as sudden increases or decreases in jetting pressure, active adjustments in lifting speed, and fluctuations in grout flow rate. These abrupt changes correspond to the soil interface locations in the time-series data and are critical moments affecting the pile radius. Interpolation at uniform time intervals would smooth out these abrupt changes, resulting in the loss of construction response characteristics at the soil interface.

[0059] The mutation point identification employs a dual confirmation mechanism combining statistical detection and prior depth constraints, rather than relying solely on statistical thresholds. The prior depth constraints are derived from the original top and bottom depth values ​​of each borehole preserved in S2: using the planar coordinates of the pile location to be predicted as the target position, spatial interpolation is performed on the depths of each soil interface using the original top and bottom depth values ​​of surrounding boreholes to obtain the estimated depths of each stratum interface at the pile location to be predicted. Spatial interpolation uses a weighted average method with graph attention edge weights as interpolation weights; neighboring boreholes with larger edge weights contribute more to the interpolation results, maintaining consistency with the graph structure of S2. This allows the stratum interface depth estimation to simultaneously integrate information from both spatial distance and stratum feature similarity. Considering the interpolation errors introduced by borehole spacing and formation change rate, a tolerance range is set for the estimated depth of each formation interface. The tolerance range is adaptively determined according to the borehole spacing of the engineering area. When the borehole spacing is 15 to 25 meters, the tolerance range is ±0.4 meters. When the borehole spacing exceeds 25 meters, the tolerance range is expanded accordingly.

[0060] In terms of statistical detection, the time-series sequence of construction parameters is calculated using time-by-time differential calculations to obtain the rate of change sequence of each construction parameter. The mean and standard deviation of the jetting pressure rate of change sequence during the entire pile construction process are calculated. The mean plus 2.5 times the standard deviation is used as the statistical detection threshold for jetting pressure. The same method is used to determine the corresponding threshold for the rate of change sequence of lifting speed. The judgment rule of the dual confirmation mechanism is as follows: when the rate of change of construction parameters at a certain moment exceeds the statistical detection threshold, and the construction depth at that moment falls within the tolerance range of a certain stratum interface depth estimated by S2, that moment is confirmed as a stratum crossing abrupt change point; if the rate of change of construction parameters exceeds the threshold but the construction depth is not within the tolerance range of any stratum interface, it is judged as a normal parameter adjustment caused by construction operation and is not marked as an abrupt change point. This dual confirmation mechanism effectively distinguishes between actual stratum crossing and parameter changes caused by operational adjustments, solving the problem of high misjudgment rate of pure statistical methods in projects with large fluctuations in construction parameters. At the same time, it also allows the stratum spatial modeling results of S2 to be directly used in the time-series processing of S3, forming a complete information transmission link from stratum spatial modeling to construction time-series processing.

[0061] Using identified abrupt change points as boundaries, the entire construction timeline is divided into several stratigraphic segments, each corresponding to the drill pipe's operation within a single soil layer. The construction parameter sequences within each segment are resampled and interpolated at equal time intervals to ensure temporal alignment within the segment while preserving parameter jump information at abrupt change points. The location information, magnitude of the abrupt change, and the corresponding stratigraphic interface type of each abrupt change point are encoded into additional feature vectors, which, along with the construction parameter sequences of each stratigraphic segment, are input into the subsequent feature fusion module. This enables the model to perceive the location and type of the stratigraphic interface and the differences in construction response at the interface.

[0062] A cross-modal attention mechanism is designed to achieve deep fusion of clustering features and construction parameters. The mechanism includes a query mapping layer, a key mapping layer, a value mapping layer, and an attention computation layer. The category embedding vector of the pile location to be predicted is input into the query mapping layer, and a query vector is obtained through linear transformation. The query vector contains semantic information about the stratum category to which the pile location belongs, representing the stratum characteristics that the model needs to focus on. The construction parameter sequences for each stratum segment after stratum segmentation, along with the additional feature vectors of abrupt change points, constitute the construction state input. The construction state vector and abrupt change point feature vector for each stratum segment are input into the key mapping layer and value mapping layer, respectively, and a key vector sequence and a value vector sequence are obtained through linear transformation. The key vector is used to calculate the correlation with the query vector, and the value vector is used for information aggregation based on the correlation.

[0063] In the attention calculation layer, the relevance score between the query vector and each key vector is calculated. A scaled dot product attention mechanism is used, where the query vector and key vector are dot-producted, and the result is scaled by dividing by the square root of the key vector's dimension. This scaling operation prevents the dot product value from becoming too large, which could cause the gradient of the softmax function to vanish. The relevance scores corresponding to all strata segments and abrupt change points are normalized using the softmax function to obtain the attention weight for each construction state. The attention weight is adaptively learned by the model from the training data, reflecting the contribution of each construction period to the pile radius prediction under the current stratum clustering category. Due to differences in soil properties, different stratum categories have different response mechanisms to grout diffusion, resulting in different key time periods for construction parameters. The cross-modal attention mechanism adaptively identifies these differences through a data-driven approach, enabling the prediction model to adaptively extract key features from construction parameters based on stratum type differences.

[0064] The value vector sequence is weighted and summed based on attention weights to obtain a construction feature representation that incorporates stratigraphic category information. This construction feature representation is a semantic aggregation of the construction parameter sequence guided by stratigraphic categories, highlighting construction status information that significantly affects the current stratigraphic category while suppressing less influential construction status information. Through a cross-modal attention mechanism, the stratigraphic clustering features guide the processing of construction parameters, enabling the prediction model to adaptively extract key features from the construction parameters based on stratigraphic type differences.

[0065] The node feature representation enhanced by the graph attention network output from the previous step is used as the static spatial feature of the strata. This feature includes the strata parameter information of the pile location to be predicted and the surrounding borehole strata information aggregated through spatial correlation. The static spatial feature of the strata, the construction feature representation that integrates strata category information, and the category embedding vector are concatenated along the feature dimension to form a joint feature vector. It is necessary to explain the functional division of S3 and S4 in construction parameter processing: S3's cross-modal attention solves the problem of how strata category information guides the extraction of construction parameter features, and outputs a construction feature aggregation vector that integrates strata semantics, representing the most discriminative construction state information under the current strata category. This aggregation vector is entered into the concatenation of the joint feature vector in the form of a fixed-dimensional vector; S4's temporal attention branch solves the problem of how to model the temporal dynamics of construction parameters. It processes segmented sequences that retain the temporal structure and focuses on the long-range dependencies of construction parameters in the time dimension. The two have completely different processing objectives and output forms, and are two parallel data streams rather than serial repetitive processing. The joint feature vector comprehensively incorporates spatial correlation information of strata, semantic information of strata categories, and dynamic information of the construction process, providing a unified representation of multi-source heterogeneous information for subsequent pile radius prediction. A fully connected layer is used to perform nonlinear transformation and dimensionality adjustment on the joint feature vector to obtain a feature representation suitable for input prediction models.

[0066] S4 inputs the joint feature vector and the segmented parameter sequence into a spatiotemporal dual-branch attention Transformer with physical monotonicity constraints, jointly models the construction time-series dynamics and historical pile formation data, and outputs the preliminary pile radius;

[0067] Receive the joint feature vector output from the previous step, the segmented construction parameter sequence processed by S3 (including additional feature vectors for abrupt change points), and historical pile formation data of completed boreholes around the pile location to be predicted, and construct a spatiotemporal dual-branch attention Transformer prediction model. This model includes a temporal attention branch, a spatial attention branch, and a feature fusion prediction layer. For engineering areas with sufficient historical data, the model is trained from scratch using the geological data, construction parameters, and measured pile radius data of the current engineering area. For new engineering areas with insufficient historical data, a transfer learning strategy with fusion clustering consistency constraints, described later, is used for training.

[0068] The temporal attention branch is used to perform in-depth temporal modeling of the segmented construction parameter sequences processed by S3, capturing the temporal dynamic characteristics of the construction process. S3 has already completed the identification and segmentation of abrupt changes in strata crossings. Building upon this, the temporal attention branch further models the temporal dynamics of construction parameters within each stratum segment. Both handle different levels of the same data: S3 focuses on the guiding fusion of construction parameters by stratum categories, while the temporal attention branch focuses on modeling the long-range dependencies of construction parameters in the time dimension. The construction parameter sequences of each stratum segment output by S3 and the additional feature vectors of abrupt changes are reassembled in chronological order to form a complete construction state sequence, expanded according to time steps, with each time step corresponding to a construction state vector. The lifting speed during jet grouting pile construction is variable, especially in interbedded soft and hard strata. Operators actively adjust the lifting speed based on stratum resistance, causing the ratio between the depth step and the time step to continuously change in the construction record of the same pile, indicating a non-linear mapping relationship between depth and time. If only the time step is used as the location encoding, the model cannot perceive the impact of the current construction depth on the grout diffusion range; if only the depth step is used as the location encoding, the model cannot perceive the impact of construction time on the grout solidification effect. Therefore, a dual-dimensional location encoding mechanism is designed specifically for the characteristics of jet grouting pile construction, simultaneously encoding construction depth and construction time information. Specifically, a depth location encoding vector and a time location encoding vector are generated for each construction state. Both are generated using combinations of sine and cosine functions of different frequencies, as different combinations of trigonometric functions can uniquely represent different location information. The depth location encoding takes the current construction depth as input, and the time location encoding takes the current cumulative construction time as input. After being generated independently, they are added element-wise to obtain a location encoding vector that integrates both depth and time location information. The dual-dimensional location encoding vector is then added element-wise to the construction state vector to obtain a construction state representation that simultaneously includes spatial location and temporal progress information, enabling the model to accurately perceive the depth-time dual location relationship of each construction state under conditions of variable lifting speed.

[0069] The encoded construction state sequence is input into a temporal attention Transformer encoder, which consists of a stack of multiple Transformer layers. Each Transformer layer contains a multi-head self-attention sub-layer and a feedforward neural network sub-layer, with residual connections and layer normalization between the sub-layers. The multi-head self-attention sub-layer calculates the dependencies between different time points in the construction state sequence. For each time point in the sequence, the construction state vector is mapped to a query vector, a key vector, and a value vector through three mapping matrices: query, key, and value. The attention score is obtained by calculating the dot product of the query vector and the key vectors of all time points. The attention score is then scaled and normalized using softmax to obtain the attention weight. The value vectors are weighted and summed according to the attention weight to obtain the feature representation of that time point that aggregates information from other time points. The multi-head mechanism computes multiple sets of attention in parallel through multiple independent query, key, and value mapping matrices, capturing different aspects of temporal dependencies. The feedforward neural network sub-layer performs a non-linear transformation on the attention output, enhancing the model's expressive power. Through processing with multiple Transformer layers, the model can capture long-range dependencies between distant moments during construction and model the dynamic evolution of construction parameters, such as the temporal characteristics of pressure decay patterns and slurry diffusion processes.

[0070] The spatial attention branch handles the spatial heterogeneity of the formation and utilizes historical pile-forming information from surrounding boreholes. It acquires information on completed jet grouting piles around the predicted pile location, including the spatial coordinates of these boreholes, formation cluster labels, and the actual measured pile radius. The spatial distance between the predicted pile location and each surrounding borehole is calculated, and a Gaussian kernel function is used to convert the spatial distance into spatial similarity weights; closer distances result in higher weights. The formation cluster labels of the predicted pile location and surrounding boreholes are compared; if the cluster labels are the same, indicating similar formation types, the weight coefficient of that surrounding borehole is increased. The spatial similarity weights and formation type similarity weights are combined to obtain the comprehensive influence weight of each surrounding borehole on the predicted pile location.

[0071] A spatial attention mechanism is constructed to aggregate information from surrounding boreholes. The joint feature vector of the pile location to be predicted is used as the query, while the geological features and pile radius information of the surrounding boreholes are used as the key and value. Through attention calculation, an attention coefficient is assigned to each surrounding borehole based on the relevance between the query and the key, as well as a pre-calculated comprehensive influence weight. The value information of the surrounding boreholes is weighted and aggregated according to the attention coefficients to obtain a spatial context feature representation. The spatial context feature representation integrates the geological features of the surrounding boreholes and historical pile formation results, utilizing the spatial continuity of the strata, so that the guiding role of historical construction data under similar geological conditions for current prediction can be reflected. To address the cold start problem caused by insufficient number of completed piles in the surrounding area during the initial stage of construction, an adaptive weight coefficient based on the number of completed piles is introduced into the feature fusion prediction layer. When the number of completed piles in the surrounding area is zero, this coefficient is zero, and the output of the spatial attention branch does not participate in feature fusion. The prediction relies entirely on the temporal features of the temporal attention branch and the static spatial features of the strata in the joint feature vector. As construction progresses and the number of completed piles in the surrounding area gradually increases, the adaptive weight coefficient increases from zero to the upper limit according to a preset function. The contribution of the spatial attention branch gradually increases, achieving a smooth transition from pure strata feature-driven prediction to spatiotemporal joint prediction.

[0072] The temporal feature representation output by the temporal attention branch and the spatial context feature representation output by the spatial attention branch are input to the feature fusion prediction layer. The feature fusion prediction layer first fuses the spatiotemporal features through concatenation or element-wise addition, and then performs nonlinear mapping through a multi-layer fully connected neural network. The fully connected neural network includes hidden layers and an output layer. The hidden layer uses a modified linear unit activation function to introduce nonlinear transformation capability. The output layer maps the hidden layer features to a scalar value, i.e., the preliminary predicted value of the pile radius.

[0073] To address the lack of historical labeled data in new engineering areas, a transfer learning strategy incorporating cluster consistency constraints was adopted to improve the model's generalization ability. Pre-training was conducted in engineering areas with abundant historical data, using a large amount of stratigraphic data, construction parameters, and measured pile radius data to train a complete spatiotemporal dual-branch attention Transformer model. During the pre-training phase, the model not only learned prediction weights but also simultaneously extracted and stored the cluster prototype features of each stratigraphic cluster category—that is, the mean of the category embedding vectors of all borehole nodes within each cluster category—as a representative representation of that category in the feature space. These cluster prototype features encapsulate the pile formation response patterns of each stratigraphic category in the pre-trained engineering area and serve as the core knowledge carrier for cross-engineering transfer.

[0074] For the new engineering area, the stratigraphic data of the new area is first subjected to feature extraction and clustering according to steps S1 to S2 to obtain cluster labels and category embedding vectors for each borehole in the new area. Then, the feature space distance between the cluster prototype features of each cluster category in the new area and the cluster prototype features of each cluster category in the pre-trained engineering area is calculated. A correspondence between cluster categories in the new and old engineering areas is established through nearest neighbor matching; that is, the cluster category in the new area that is closest to the prototype feature of a certain cluster category in the pre-trained area is identified as the corresponding category. In the fine-tuning stage, the parameters of the feature extraction layer and attention layer in the pre-trained model are fixed, and the parameters of the output layer and feature fusion layer are fine-tuned using a small amount of labeled data collected from the new area. Simultaneously, a cluster consistency constraint term is introduced into the fine-tuning loss function. The cluster consistency constraint term is calculated as follows: for cluster categories in the new area that have a correspondence with those in the pre-trained area, the Euclidean distance between the cluster prototype features of that category in the new area and the corresponding category in the pre-trained area is calculated. This distance is used as the constraint loss to ensure that the cluster feature space of the new area remains consistent with that of the pre-trained area. The clustering consistency constraint and the prediction loss are weighted and summed according to preset weights to form the total loss function in the fine-tuning stage. This constraint method allows for moderate adjustments to the clustering characteristics of new regions based on known patterns. It preserves the stratigraphic-pile response knowledge accumulated in the pre-training engineering areas while allowing the stratigraphic specificity of new regions to be reflected, avoiding the problem that the standard parameter freezing fine-tuning method cannot perceive the stratigraphic differences between old and new regions. For new stratigraphic categories appearing in new regions that are more than a preset threshold away from all cluster categories in the pre-training areas, no clustering consistency constraint is applied, and learning relies entirely on the labeled data of the new regions.

[0075] During the model training phase, a joint training loss function incorporating physical monotonicity constraints is constructed, embedding these constraints directly into the training process rather than verifying them post-hocly during inference. When constructing the training loss function, constraint violation detection is performed on sample pairs within the training batch. For samples with higher injection pressure within a batch, if their predicted radius is smaller than that of samples of the same stratum category with lower injection pressure, a monotonicity constraint violation is identified. The degree of violation is calculated for each pair of samples violating the constraint; this degree is defined as the absolute value of the ratio of the difference between the predicted radii of the two samples to the parameter difference. A higher degree of violation indicates a more severe deviation of the prediction result from physical laws. The degree of violation for all sample pairs violating the constraint is summed to obtain the monotonicity constraint loss term. The same method is used to construct corresponding constraint loss terms for the monotonicity constraints of lifting speed, slurry flow rate, and soil shear strength. Each constraint loss term is weighted and summed according to preset weight coefficients, and then jointly optimized with the data fitting loss of the prediction model. In this way, physical constraints continuously guide the update direction of model parameters during training, ensuring that the trained model tends to satisfy physical monotonicity constraints across the entire input space.

[0076] A data augmentation method based on soil mechanics principles is designed to expand training data. Data augmentation can be used in both the pre-training and fine-tuning stages, but the perturbation amplitude differs between the two stages. In the pre-training stage, with ample data, the perturbation amplitude can be larger to increase sample diversity; in the fine-tuning stage, with sparse labeled data, the perturbation amplitude should be smaller to avoid deviation from the true distribution. Data augmentation involves perturbing ground parameters and construction parameters within reasonable ranges to generate new samples. The perturbation of ground parameters follows the statistical distribution of parameters for that soil type, with random sampling near the mean to ensure that the enhanced samples' ground parameters conform to the actual engineering range. The perturbation of construction parameters considers the correlation constraints between parameters; for example, increasing grout flow rate usually increases with increasing jet grouting pressure, maintaining the physical correlation between parameters. Based on soil mechanics theory and experience in jet grouting pile construction, the pile radius labels corresponding to the perturbed construction parameters are adjusted to generate virtual training samples that conform to physical laws, increasing the diversity and quantity of training data.

[0077] To meet the real-time prediction requirements of construction sites, knowledge distillation is employed for model compression. A pre-trained large-scale Transformer model is used as the teacher model, while a simplified student model is designed. The student model maintains the same input / output interface as the teacher model but reduces the number of Transformer layers, attention heads, and hidden layer dimensions, thereby lowering the model's parameter count and computational complexity. During knowledge distillation, training data is simultaneously input into both the teacher and student models, and the mean squared error between the predicted outputs of the two models is calculated as the distillation loss. Feature representations of the intermediate layers in both models are extracted, and the differences between these intermediate features are calculated as the feature distillation loss. The distillation loss and the student model's own prediction loss are jointly optimized to train the student model so that its output and intermediate features closely mimic the teacher model. After distillation, the student model inherits the predictive capabilities of the teacher model but with significantly improved computational efficiency. Its inference time meets the real-time prediction requirements of construction sites, making it suitable for deployment on edge devices with limited computing resources.

[0078] S5, taking the initial pile radius as input, performs truncation correction based on the Bingham fluid diffusion mechanism and the theoretical upper limit of the cluster category differentiation, and estimates the prediction interval according to the category differentiation based on the construction history residuals, to obtain the final predicted value of the pile radius and the prediction interval.

[0079] The system receives the preliminary predicted pile radius from the previous step, along with the geological and construction parameters for the pile location to be predicted. It then performs physical constraint correction and uncertainty quantification during the inference phase. In the S4 training phase, monotonicity constraint loss ensures the model's overall adherence to physical laws. In the S5 inference phase, a theoretical upper bound truncation correction based on the jet grout diffusion mechanism is applied to the preliminary predicted values ​​to ensure the predicted results do not exceed the physically achievable maximum. Based on the cluster category of the pile location to be predicted, corresponding parameters are selected from the power function parameters calibrated by cluster category in S5. The upper bound of the theoretical radius under the current construction conditions is calculated, and preliminary predicted values ​​exceeding this upper bound are truncated to the upper bound value, yielding the predicted pile radius after physical constraint correction.

[0080] The theoretical upper bound is determined separately for each of the strata clusters established in S2, rather than using a uniform parameter for the entire project area. This differentiated determination is based on the fundamental differences in the grout diffusion mechanisms corresponding to different strata clusters. In the soft soil cluster, grout diffusion is mainly characterized by high-pressure jet cutting and destruction, with the soil's resistance to grout diffusion primarily stemming from undrained shear strength; the pressure ratio has a more significant impact on the diffusion radius. In the dense sand cluster, grout diffusion is mainly characterized by infiltration and filling, with the soil's pore structure providing greater resistance to grout flow; the grout volume per unit depth has a more significant impact on the diffusion radius. Using a uniform power function parameter for all clusters would result in a conservative theoretical upper bound for the soft soil cluster and a looser theoretical upper bound for the dense sand cluster, leading to insufficient constraint precision. Specifically, the ratio of jetting pressure to the undrained shear strength of the soil is defined as the pressure ratio, and the ratio of grout flow rate to lifting speed is defined as the grout volume per unit depth. Based on the theoretical derivation of Bingham fluid radial seepage, the power function relationship between the theoretical maximum diffusion radius and the pressure ratio and grouting volume per unit depth has a physical basis: in the energy balance equation of radial seepage, the relationship between the diffusion radius and the driving pressure and injection volume is linear in logarithmic coordinates, corresponding to the power function form in the original coordinates. Based on this, a theoretical upper bound empirical relationship in the form of a power function is established for each formation cluster category, namely, the theoretical maximum diffusion radius of that category is equal to the proportionality coefficient of that category multiplied by the first power of the pressure ratio of that category, multiplied by the second power of the grouting volume per unit depth of that category. The power function parameters for each cluster category are determined using a hierarchical calibration strategy: when the number of completed piles in a cluster category reaches 5 or more, the proportional coefficient and two powers of that category are independently calibrated using the measured pile radius data of that category through least squares regression; when the number of completed piles in a cluster category is less than 5, the power function parameters of the corresponding cluster category in the pre-trained engineering area of ​​S4 transfer learning are preferentially inherited as initial values. If the pre-trained engineering area does not have a corresponding category, the data of all completed piles in the entire engineering area are used for unified calibration, and the above results are used as the initial parameters of that category. As construction progresses and data is gradually accumulated, independent calibration is switched to the latter. This method of linking S4 transfer learning with S5 physical constraint parameter calibration forms a dual-channel transfer mechanism of "predictive model knowledge transfer + physical constraint parameter transfer," enabling reliable physical constraint parameters to be obtained for new engineering areas at the initial stage of construction without waiting for the accumulation of data from the current project. The initial values ​​of the first power of each cluster category range from 0.3 to 0.5, the initial values ​​of the second power range from 0.2 to 0.4, and the initial values ​​of the proportional coefficient range from 0.05 to 0.15. These initial ranges are based on the statistical analysis of historical pile formation data from multiple jet grouting projects. Bounded least squares regression is performed using these ranges as constraints during independent calibration to prevent the calibration results from deviating from the physically reasonable range.

[0081] After completing the theoretical bound truncation correction, the predicted pile radius after physical constraint correction is estimated by performing a prediction interval estimation. The prediction interval estimation adopts a method based on the statistical analysis of historical residuals during the construction process. This method is fully compatible with the knowledge distillation student model of S4, requires no modification to the model structure, and is dynamically updated as construction progresses, with the prediction interval becoming more accurate towards the later stages of construction.

[0082] The specific implementation of the prediction interval estimation is as follows: During construction, after the construction of each pile is completed and the measured pile radius is obtained through core sampling or excavation verification, the prediction residual of that pile is calculated, which is the difference between the predicted value and the measured value. This residual, along with the cluster category label to which the pile belongs, is archived and stored. A sliding window of residual statistics is maintained for each cluster category. The sliding window contains the residual records of several recently completed piles in that category. The window size is set according to the project scale, typically 10 to 20 piles. The mean and standard deviation of the residuals within the sliding window are calculated. The mean reflects the systematic bias of the prediction under that cluster category, and the standard deviation reflects the degree of random fluctuation in the prediction under that cluster category. When predicting a new pile location, based on the cluster category to which the pile location belongs, the mean and standard deviation of the residuals for that category are taken. The predicted value plus the mean of the residuals is used as the prediction center value after bias correction. The prediction center value plus or minus 1.96 times the standard deviation of the residuals is used as the upper and lower bounds of the 95% prediction interval.

[0083] This method of estimating prediction intervals based on cluster categories has clear engineering significance: the prediction difficulty of jet grouting pile radius varies under different stratum cluster categories. Soft soil strata have better homogeneity, resulting in a typically smaller standard deviation of the prediction residuals and a narrower prediction interval; dense sand strata have complex pore structures and greater uncertainty in the grout diffusion path, leading to a typically larger standard deviation of the prediction residuals and a wider prediction interval. Statistically calculating residuals separately for each cluster category ensures that the prediction interval truly reflects the differences in prediction uncertainty under different stratum categories, rather than using a uniform interval width for all stratum categories.

[0084] In the early stages of the project, when a certain cluster category has no residual records of completed piles, the initial value of the prediction interval for that category is inherited from the historical residual statistics of the corresponding cluster category in the pre-trained project area during S4 transfer learning, forming a dual-channel transfer mechanism of "model knowledge transfer + prediction interval transfer". As the construction data of this project accumulates, the initial values ​​of the pre-trained project area are gradually replaced with the residual statistics of this project, realizing adaptive updates of the prediction interval.

[0085] The final predicted pile radius and prediction interval are output. The predicted value is the predicted pile radius after physical constraint correction, and the prediction interval is the upper and lower bounds of the 95% prediction interval obtained based on the statistical analysis of historical residuals of similar strata. This prediction result integrates spatial correlation information of strata, strata clustering characteristics, temporal dynamics of the construction process, spatial migration of historical construction data, correction of physical constraints, and prediction error patterns of similar strata dynamically accumulated during construction. It achieves high-precision prediction of the pile radius of jet grouting piles under complex strata conditions and provides practical prediction interval estimation, offering a scientific basis for optimizing jet grouting pile construction parameters and quality control.

[0086] In one embodiment of the invention, its application was verified in a tunnel reinforcement project on Metro Line 5 in a certain city. The tunnel traverses a typical complex geological formation consisting of alternating layers of soft and hard soil, including silty clay, silty clay, and silty sand, with significant spatial variations in the strata distribution. A total of 28 exploration boreholes were drilled, with a spacing of 15 to 25 meters, obtaining detailed geological exploration data.

[0087] Table 1 shows examples of formation parameter data for some boreholes, including borehole number, main soil layer type, average soil layer depth, soil internal friction angle, soil cohesion, water content, and standard penetration test blow count.

[0088] Table 1. Examples of formation parameter data from boreholes.

[0089] The method of this invention was used to extract features and perform cluster analysis on the stratigraphic data of 28 boreholes. An adaptive cluster number determination mechanism determined the optimal number of stratigraphic categories to be 3. The clustering results classified the boreholes into soft soil, medium-strength, and dense sandy soil categories. The clustering results were consistent with the spatial distribution of the stratigraphy, and the stratigraphic categories of adjacent boreholes showed continuity.

[0090] Table 2 shows examples of construction parameters and predicted pile radius for some jet grouting piles. The data includes pile location number, jetting pressure, grout flow rate, lifting speed, geological formation type, predicted pile radius, and prediction range.

[0091] Table 2. Examples of construction parameters and predicted pile radius for jet grouting piles.

[0092] After construction, the actual pile radius data was obtained through excavation verification and core sampling, and the measured values ​​were compared with the predicted values. The average absolute error of the prediction method of this invention is 0.038 meters, and the root mean square error is 0.045 meters. The prediction error is controlled within 6% of the measured value, and the measured values ​​all fall within the prediction range. The prediction range width for dense sandy soil strata (0.12 meters) is significantly larger than that for soft soil strata (0.08 meters) and medium-strength strata (0.08 meters), truly reflecting the engineering characteristics of the large uncertainty of grout diffusion path in dense sandy soil strata. In comparison, the empirical estimation formula for the pile radius of jet grouting piles based on jet pressure and soil strength in the current specifications was used to predict the same project. The average absolute error of the empirical formula method is 0.142 meters, and the root mean square error is 0.168 meters, with a prediction error of approximately 22% of the measured value. The prediction accuracy of the method of this invention is improved by approximately 73% compared with the traditional empirical formula method, verifying the effectiveness and reliability of the method of this invention under complex strata conditions of alternating soft and hard layers. The method of this invention provides an accurate predictive basis for optimizing construction parameters and controlling quality in this project, ensuring the continuity of jet grouting pile reinforcement and the quality of the project.

[0093] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. A method for predicting the pile radius of jet grouting piles based on stratigraphic feature clustering, characterized in that, Includes the following steps: S1: Collect borehole columnar section, formation physical and mechanical parameters and spatial coordinates, and extract formation features using a multi-scale convolutional network with formation layer number constrained by convolution kernel size to obtain multi-scale fused feature vectors for each borehole; S2 combines fused feature vectors and spatial coordinates to construct a k-nearest neighbor graph that takes into account both spatial distance and stratigraphic similarity. Through graph attention network and deep embedding clustering, it identifies the spatial distribution pattern of stratigraphy and outputs cluster labels, category embeddings, node feature representations and cluster prototypes. S3, cluster the pile locations to be predicted and obtain the time series of construction parameters. The mutation points are confirmed by both the a priori depth constraint of the stratum and statistical detection and segmented. The cluster features and segmented construction parameters are fused through cross-modal attention to obtain the joint feature vector and segmented parameter sequence. S4 inputs the joint feature vector and the segmented parameter sequence into a spatiotemporal dual-branch attention Transformer with physical monotonicity constraints, jointly models the construction time-series dynamics and historical pile formation data, and outputs the preliminary pile radius; S5 takes the initial pile radius as input, performs truncation correction based on the Bingham fluid diffusion mechanism and the theoretical upper limit of the cluster category differentiation, and estimates the prediction interval according to the category differentiation based on the construction history residuals to obtain the final predicted value of the pile radius and the prediction interval.

2. The method according to claim 1, characterized in that, In S1, the multi-scale convolutional neural network includes three parallel convolutional branches. The first convolutional branch uses a convolutional kernel whose receptive field covers the parameter range of a single soil layer to capture detailed features within the layer and boundary features of parameter jumps between layers. The second convolutional branch uses a convolutional kernel whose receptive field covers two to three adjacent soil layers to capture the combination pattern features of alternating soft and hard soil layers. The third convolutional branch uses a convolutional kernel whose receptive field covers all effective layers and whose upper limit size is determined according to the actual number of strata in the engineering area. The outputs of the three convolutional branches are concatenated along the feature dimension to form a multi-scale feature representation. This representation is then concatenated with the vertical distribution pattern features output by the one-dimensional convolutional neural network and passed through a fully connected layer to obtain a multi-scale fused feature vector.

3. The method according to claim 1, characterized in that, In S2, the k-nearest neighbor association graph is constructed as follows: each borehole is modeled as a node of the graph, and the k boreholes with the closest spatial distance to each node are selected as neighbor nodes to establish edge connections. The edge weight combines spatial distance weight and feature similarity weight. The spatial distance weight uses a Gaussian kernel function to map the spatial distance into a weight value. The feature similarity weight uses cosine similarity to measure the similarity of multi-scale fused feature vectors between nodes. After normalizing the two, the weighted sum is obtained to obtain the comprehensive weight of the edge.

4. The method according to claim 1, characterized in that, In S2, the implementation of the cluster number determination mechanism that integrates engineering prior constraints is as follows: extract the prior information of stratigraphic engineering classification from the engineering survey report as the prior lower bound of the cluster number, set the candidate range based on the prior lower bound, use the K-means algorithm to pre-cluster each candidate cluster number, and evaluate it by combining the two dimensions of profile coefficient and stratigraphic engineering classification consistency score. The consistency score is the proportion of nodes belonging to the same engineering stratigraphic category in the same cluster category. The contour coefficient and consistency score are normalized and then weighted to obtain the comprehensive evaluation index. The cluster number with the best comprehensive evaluation index is selected as the final number of stratigraphic categories.

5. The method according to claim 1, characterized in that, In S2, the deep embedding clustering module includes an encoder network, a clustering layer, and a decoder network. The clustering layer uses the Student t-distribution to calculate the similarity between the node embedding features and each cluster center and obtain the soft assignment probability. The joint loss function includes a clustering loss term, a spatial constraint loss term, and a reconstruction loss term. The clustering loss term uses Kullback-Leibler divergence to measure the difference between the soft assignment probability and the target distribution. The spatial constraint loss term applies Laplace regularization constraints to the difference in cluster assignment probabilities of connected nodes based on the stratigraphic spatial correlation graph structure. The reconstruction loss term is calculated by the decoder network to obtain the mean squared error between the reconstructed features and the original features. After training, the mean value of the category embedding vector for each cluster category is calculated to obtain the cluster prototype features and stored.

6. The method according to claim 1, characterized in that, In S3, the dual confirmation mechanism is implemented as follows: using the original top and bottom depth values ​​of each borehole retained in S2, spatial interpolation is performed on the depth of each stratum interface at the predicted pile location using the graph attention edge weight as the interpolation weight to obtain the estimated depth, and the tolerance range is adaptively set according to the borehole spacing; the time-series sequence of construction parameters is differentially calculated at each time step to obtain the rate of change sequence, and the mean of the rate of change sequence plus the standard deviation of the preset multiple is used as the statistical detection threshold. When the rate of change of construction parameters exceeds the statistical detection threshold at a certain moment and the construction depth at that moment falls within the tolerance range of the estimated depth of a certain stratum interface, it is identified as a stratum crossing abrupt change point; otherwise, it is not marked as an abrupt change point.

7. The method according to claim 1, characterized in that, In S3, the cross-modal attention mechanism includes a query mapping layer, a key mapping layer, a value mapping layer, and an attention calculation layer. The category embedding vector is passed through the query mapping layer to obtain the query vector. The segmented construction parameter sequence and the mutation point additional feature vector are passed through the key mapping layer and the value mapping layer to obtain the key vector sequence and the value vector sequence, respectively. The scaling dot product attention is used to calculate the correlation score between the query vector and each key vector and then normalized to obtain the attention weight. The construction feature representation, which incorporates stratigraphic category information, is obtained by weighting and summing the value vector sequence according to attention weights.

8. The method according to claim 1, characterized in that, In S4, the temporal attention branch adopts a two-dimensional positional encoding mechanism, which generates a depth positional encoding vector and a temporal positional encoding vector for each construction state, adds them element by element, and then fuses them with the construction state vector. The encoded sequence is input into a multi-layer Transformer encoder for temporal modeling. The embedding method of physical monotonicity constraints is as follows: constrain violation detection is performed on sample pairs of the same stratum category in the training batch. When the predicted radius of the sample with a larger parameter value violates the preset monotonic relationship, the degree of violation is calculated and summed to obtain the monotonicity constraint loss term. The constraint loss terms of each parameter are weighted and summed and then jointly optimized with the data fitting loss.

9. The method according to claim 1, characterized in that, The S4 also includes a transfer learning strategy that integrates cluster consistency constraints: in the pre-training stage, the cluster prototype features of each cluster category are extracted and stored; for the new engineering region, the correspondence between the cluster categories of the new and old engineering regions is established through nearest neighbor matching; in the fine-tuning stage, the parameters of the feature extraction layer and the attention layer are fixed and the parameters of the output layer and the feature fusion layer are fine-tuned. Meanwhile, a clustering consistency constraint term is introduced into the fine-tuning loss function. The constraint term is the Euclidean distance between the cluster prototype features of the new region and the corresponding category cluster prototype features of the pre-trained region.

10. The method according to claim 1, characterized in that, In S5, the upper bound of the theoretical radius, which is differentiated according to the cluster category, is determined as follows: the ratio of the injection pressure to the undrained shear strength of the soil is defined as the pressure ratio, and the ratio of the grout flow rate to the lifting speed is defined as the grouting volume per unit depth. For each cluster category, a power function relationship is established between the theoretical maximum diffusion radius, the pressure ratio, and the grouting volume per unit depth. A hierarchical calibration strategy is adopted. When the number of completed piles in a certain cluster category reaches the preset threshold, it is calibrated independently. Otherwise, the parameters of the corresponding category in the pre-trained engineering area are inherited as the initial values. The prediction interval estimation method is as follows: maintain the prediction residual statistics of the sliding window for each cluster category, correct the prediction center value with the residual mean, and determine the upper and lower bounds of the prediction interval with the residual standard deviation of a preset multiple.

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