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Original Research

Frontiers in Earth Science ·

Volume 14 - 2026 | https://doi.org/10.3389/feart.2026.1839550

Feature attention model for soil-geocomposite interface strength

  • Peng Tang1
  • Zhilin Wu1
  • Siyu Gu2
  • Jiaming Zhao1*corresponding author
  • Peng Cui3,4*corresponding author
  1. 1College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai, China
  2. 2College of Textiles, Donghua University, Shanghai, China
  3. 3School of Civil Engineering, Nanjing Forestry University, Nanjing, China
  4. 4Department of Applied Physics and Electronics, Umea University, Umea, Sweden
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Abstract

In geotechnical engineering, excess pore water pressure is one of the main reasons that cause structural instability. It greatly reduces the effective stress of soil and may lead to problems such as piping. At present, geocomposite drainage layers (GDL) are commonly used as effective drainage materials. However, it remains difficult to accurately predict the peak shear strength at the interface between soil and geocomposite drainage layers. The main reason is that many factors interact with each other, making the whole problem very complicated. This paper puts forward a deep learning model based on feature attention to predict the peak shear strength of the interface. The model uses residual connections to make deep features transfer better, and uses feature attention to automatically select and focus on important information. We verified the model with 209 sets of large scale direct shear test data. The results show that the Attention-DNN model has better prediction effect when dealing with geotechnical data that has a small sample size and large dispersion. On the test set, the model has an R 2 of 0.958 and an RMSE of 3.38 kPa, which is obviously better than the traditional DNN model. In order to make the research more useful in engineering, we also used Ridge regression and a dual threshold screening method to get an empirical formula. We tested this formula with 25 typical large scale direct shear test examples. The formula has a MAPE of 17.18% and shows good stability. It is more convenient for engineering technicians to apply. This study builds a complete and reliable technical system, which can provide scientific support for the interface design and safety evaluation of composite drainage systems in geotechnical engineering.

Keywords

1 Introduction

In geotechnical engineering, excessive pore water pressure is a major factor that causes structural instability (Wang X. et al., 2025; Zhao et al., 2025). It seriously weakens the effective stress and overall strength of the soil matrix (Xiao et al., 2024; Yao et al., 2025). For engineering projects using granular materials such as sand and sandy mixtures, this problem is more likely to trigger pathologies like piping and sand boiling, which in turn threaten the stability of infrastructure and lead to structural deformation (Cui et al., 2024; Shi et al., 2025a). Therefore, effectively reducing pore water pressure and controlling seepage effects are key to keeping geotechnical structures stable (Chao et al., 2024d). Geotechnical instability remains a critical concern in engineering systems, where material behavior and interface conditions significantly influence structural performance (Alsabhan et al., 2021).

To tackle the core geotechnical problem of high pore water pressure, physical drainage reinforcement methods have become widely accepted because they perform stably and work for many different engineering projects (Ding et al., 2024; Xiao and Xu, 2024). Among these methods, the Geocomposite Drainage Layer (GDL) is a key technical approach that has great practical value (Peng et al., 2026). The material has excellent drainage performance and can directly replace the traditional graded sand gravel to meet the soil drainage requirements (Wang Z. et al., 2025). In addition, it also has a variety of engineering characteristics such as soil isolation and structural reinforcement, which can quickly reduce the source pore water pressure and effectively solve various engineering hazards (Chao et al., 2025b; Shi et al., 2023). In actual geotechnical arrangements, GDL is usually installed under the cover soil, and the interface shear strength between GDL and the soil is vital for keeping the engineering system stable in the long run (Chao et al., 2024a; Chao et al., 2024g). In practical geotechnical engineering, soil-GDL interfaces are widely involved in slope drainage systems, landfill cover and liner systems, reinforced backfills, and drainage layers beneath cover soils. Overestimating the interface shear strength may lead to insufficient anti-sliding resistance, resulting in slope instability, excessive cover-soil deformation, or degradation of landfill liner system performance.

However, the wide adoption of GDL has also brought many challenges to be solved (Yue et al., 2026; Zhang et al., 2025). It is difficult to accurately predict the interface mechanical response during long-term use through a single test or short-term measurement, thus affecting the long-term engineering safety (Zhao et al., 2026a; Zhao et al., 2026b). Previous studies have highlighted the complex coupled response of soil systems under varying loading conditions, where multiple interacting factors govern system behavior and performance (Ahmad et al., 2021). In addition, the traditional test methods are expensive and time-consuming, which are difficult to adapt to the needs of large scale applications (Chen et al., 2026a; Chen et al., 2026b). In response, an interdisciplinary approach combining machine learning (ML) and geotechnical engineering has emerged to predict key parameters for GDL applications (Chao et al., 2025a; Chao et al., 2024e). In addition, fluid-structure interaction effects have been investigated in related engineering systems, highlighting the complexity of coupled response mechanisms (Haroon et al., 2017). The increasing availability of high-resolution experimental datasets has enabled more reliable data-driven modeling of subsurface behavior, improving prediction accuracy in complex engineering systems (Ahmad et al., 2026). These studies not only ensure long-term engineering safety by accurately predicting mechanical properties, but also help cut down on experimental costs and labor. Recent studies have further demonstrated the efficacy of machine learning in addressing complex interface and material challenges across various geotechnical and maritime environments (Chao et al., 2024c; Shi et al., 2025b). These advancements highlight the growing reliance on robust data-driven frameworks to predict mechanical responses in large-scale infrastructure and soil-structure interactions (Chao et al., 2021).

With the deepening of the intersection of geotechnical engineering and artificial intelligence, the limitations of traditional prediction models in analyzing sand body coupling GDL system are becoming more and more obvious (Chao et al., 2024b; Chao et al., 2024c). Data-driven approaches, including machine learning techniques, have shown strong potential in predicting complex material behavior in geotechnical systems (Ahmad et al., 2025a). Recent investigations have further revealed the complexity of soil behavior under coupled field conditions, where conventional approaches often fail to capture nonlinear and multi-physics interactions (Ahmad et al., 2025b). Advanced numerical modeling approaches have attempted to capture the complex behavior of geomaterials; however, challenges remain in representing multi-scale interactions and nonlinear responses (Rizvi et al., 2020). These models usually rely on linear or simple nonlinear structures, which is not enough to capture the complex coupling relationships in multivariable and multi conditional scenarios (Chao et al., 2023a; Dong et al., 2022). Fixed feature weights and their vulnerability to redundant information make it difficult to accurately distinguish the differential effects of core factors such as soil type and normal stress (Chao et al., 2023c; Song et al., 2024). This means that the prediction accuracy and generalization ability are limited in practical engineering applications. Therefore, key feature extraction has become a core research hotspot. Scholars have tried to introduce attention mechanism to highlight the core influence of soil type, or designed feature enhancement module for parameters such as water content, but the systematic feature extraction method for the synergistic effect of multiple factors in soil GDL interface still needs to be improved. Furthermore, the integration of nature-inspired meta-heuristic algorithms with neural networks has significantly enhanced the optimization of predictive paradigms, demonstrating high precision in modeling complex structural responses and soil parameters (Bardhan and Asteris, 2023; Zhao et al., 2022).

Existing machine-learning studies in geotechnical engineering mainly apply conventional neural networks or ensemble algorithms to prediction tasks, while the specific combination of residual connectivity and feature attention for small-sample, highly dispersed soil–GDL interface data remains insufficiently explored. To address this gap, this study develops an Attention-DNN that adaptively weights the expanded geotechnical features while improving the transmission of deep features through residual connections. The novelty of the proposed framework is not limited to the use of an attention mechanism. First, its model structure is specifically designed to capture the nonlinear and multi-factor coupling characteristics of soil–GDL interface shear strength. Second, the derived interaction coefficients provide an engineering interpretation of the coupled effects among variables such as drainage core thickness, consolidation conditions, and soil density. Third, ridge regression and dual-threshold screening are used to convert the complex Attention-DNN into a transparent empirical formula that directly uses raw engineering measurements without normalization. The framework is established using 209 large-scale direct-shear test samples and further evaluated using 25 representative test conditions, thereby linking model development, physical interpretation, and practical engineering application.

2 Deep learning models

This study uses an optimized deep neural network called Attention-DNN, which integrates residual connection and feature attention mechanism, and uses a K-fold strategy to predict the peak shear strength (Chao et al., 2024f; Li et al., 2025). Although the dataset contains only 209 samples, the peak shear strength of the soil-GDL interface is governed by nonlinear interactions among multiple engineering variables. The deep architecture was therefore selected to capture hierarchical and high-order feature relationships that simpler models may underfit. To reduce the risk of overfitting, five-fold cross-validation, dropout, AdamW weight decay, and early stopping were employed (Chao et al., 2023b; Cheng et al., 2024).

  • The architecture is optimized to accurately model complex nonlinear relationships and focus on key hierarchical features (Kardani et al., 2020).
  • The model is especially suitable for small sample data sets of rock and soil, showing significant generalization and over fitting prevention (Chen et al., 2023).
  • The model training and validation procedures are standardized to ensure the stability and reliability of the prediction (Shi et al., 2025a).

The following briefly introduces the basic specifications of the deep learning model, core modules and verification strategies adopted.

2.1 DNN

As a classic fully connected feedforward network, deep neural network (DNN) is the basic architecture of the optimization model developed in this study (Zhang et al., 2021). The DNN architecture constructed follows a hierarchical configuration composed of input layer, hidden layer and output layer, and all layers adopt a fully connected design. The input layer contains 9 nodes, corresponding to 9 core input parameters. The optimized hidden layer adopts a hierarchical structure with 96, 192 and 96 nodes respectively, and the output layer contains only one node to output the predicted value of peak shear strength.

The ReLU activation function is used in the hidden layer, and the batch normalization layer is added to reduce the internal covariate transfer (Fu et al., 2025). In order to suppress over fitting and enhance the generalization of the model, a Dropout layer is introduced. Kaiming normal distribution is used to initialize the network weights and deviations to improve the convergence efficiency in the training process. The structure of the baseline DNN model is shown in Figure 1.

DNN model.
Figure 1. DNN model.

2.2 Residual connections

Residual connections can effectively reduce the problems of gradient vanishing and network degradation by adding residual blocks into the hidden layers of deep neural networks. These residual blocks adopt the mechanism of feature transformation and shortcut connection, so that the network can prioritize the residual mapping and reduce the training complexity. Each residual block performs linear transformation, batch normalization, ReLU activation, and attention weighting in turn (Jastrzębski et al., 2017).

In order to ensure the feasibility of residual addition, linear projection layer is used for dimension matching. The architecture effectively supports deep feature extraction and enhances the ability of the model to express the GDL interface features of complex soil. The structure of the remaining connection model is shown in Figure 2.

Residual connection model.
Figure 2. Residual connection model.

2.3 Feature attention mechanism

The feature attention mechanism is a core module for adaptive feature weight allocation, embedded within residual blocks to optimize the process alongside residual connections (Xu et al., 2021). In data-driven predictive models, input features typically exhibit varying degrees of importance with respect to the target variable. To accurately capture such discrepancies and enhance feature representation, the attention mechanism dynamically assigns optimal weights to different features during network training. When integrated with residual architectures, this module not only maintains the stability of deep network training but also strengthens the extraction of critical information (Hu et al., 2024).

2.4 K-fold strategy

The k-fold strategy is used to reduce the randomness of small sample data sets (Inan and Uzer, 2021). First, the dataset is stratified according to the quantiles of peak shear strength to ensure the consistency of target variables in the five mutually exclusive subsets. In the training phase, four subsets are used for training in turn, and one subset is used as the validation set to complete five independent iterations.

At the same time, the early stop strategy is integrated to prevent the model from over fitting in the limited data scene. The generalization ability of the model is evaluated according to the average of these validation results. After completion, use the complete data set for the last training to maximize the use of data and optimize the overall performance. This system framework ensures the robustness of strength prediction in geotechnical engineering applications.

3 Model optimization

DNNs are prone to the problem of key features being obscured by redundant information when processing high-dimensional features, leading to the limited ability of the model to capture the core influence laws of peak shear strength at the soil-GDL interface. Therefore, this study employs a feature attention mechanism as the core means of model optimization. Through adaptive feature weight allocation, it strengthens the contribution of key features and suppresses redundant information interference to achieve an improvement in model prediction performance. Existing studies have confirmed that the attention mechanism can effectively improve the focusing ability of deep models on core features in complex tasks, and its optimization logic is highly adaptable to the multi factor coupling characteristics of the soil-GDL interface.

The core of the feature attention mechanism optimization is to dynamically learn feature weights, allowing the model to prioritize input features strongly related to peak shear strength, such as confining pressure, geocomposite drainage layer type, and soil moisture content. It’s optimization principle can be described as follows: for the output features after feature transformation by residual blocks, the importance weights of each feature are calculated through parametric mapping. Then, the weights are multiplied element wise with the original features to complete the reinforcement of key features and the suppression of redundant features. Finally, the optimized features are output for subsequent network layer learning. This process can be simplified by Equation 1:

X o p t = X ⊙ σ W 2 · R e L U W 1 · X + b 1 + b 2 (1)

Specifically, X represents the input feature matrix following feature transformation within the residual block, while W1 and W2 denote the weight matrices for the feature compression and restoration processes, respectively. b1 and b2 are the corresponding bias terms, ReLU serves as the nonlinear activation function, and σ represents the Sigmoid function. Furthermore, Xopt is the optimized feature matrix.

The specific optimization workflow of the feature attention mechanism is as follows: (1) features from the residual block after linear transformation, Batch Normalization, and ReLU activation are utilized as inputs; (2) the feature dimension is compressed to 1/4 of the original magnitude through the W1, and nonlinear feature transformation is implemented through ReLU activation; (3) the feature dimension is restored to the original dimension through the W2, and attention weights corresponding to each feature are generated in conjunction with the Sigmoid function; (4) the attention weights and input features are multiplied element wise to obtain the optimized feature Xopt; (5) after the optimized features undergo Dropout regularization, they are added to the identity mapping features of the residual connection and input to the next layer of the network.

In this study, the key optimization parameters of the feature attention mechanism are configured as follows: the feature compression ratio is 1:4, and the activation function is the middle layer and the weight output layer, respectively. This mechanism is embedded after the activation of the internal ReLU of the residual block and before the Dropout layer. This configuration effectively ensures the flexibility of weight learning, while avoiding the excessive increase of additional computational complexity.

4 Methodology

4.1 Model building and hyperparameter tuning

Hyperparameters are very important to the performance of deep neural networks, and its optimization is very important to achieve accurate model prediction. Due to the large number of hyperparameters involved in DNN, grid search is computationally expensive and inefficient. In order to solve this problem, this study uses random search combined with theoretical reasoning to adjust the hyperparameters, which allows flexible exploration of the hyperparameter space in limited computing resources. The key hyperparameters were not manually fixed based only on theoretical considerations, but were selected through random-search-based tuning and validation performance monitoring to reduce overfitting on the small-sample dataset. Specifically, the dropout rate was set to 0.20 to balance feature learning and regularization, the AdamW weight decay was set to 5e-5 to stabilize weight updates, and the initial learning rate was set to 0.0003 to ensure smooth convergence. The Attention-DNN model was trained for 350 epochs and adopted three residual blocks with 96, 192, and 96 nodes, respectively. These settings were further evaluated using K-fold cross-validation to ensure robust generalization. To improve reproducibility, all experiments were implemented in Python using PyTorch, NumPy, scikit-learn, and imbalanced-learn. A fixed random seed of 42 was used for parameter initialization, data partitioning, and SMOTE processing. According to the architecture described above, the proposed Attention-DNN and the baseline DNN contain 105,217 and 38,977 trainable parameters, respectively.

In order to evaluate the optimization effect and feature attention mechanism of residual connections, the control variable method was used to model. After a large number of experiments, the core hyperparameters of the basic DNN model were determined, and the remaining connection modules and feature attention mechanism were embedded into its architecture, and the optimized DNN model was developed, so as to ensure the performance comparison between the two model types.

Given the small sample size and high dispersion of geotechnical test data, the original dataset underwent standardized preprocessing. Winsorization was applied to the target variable using the standard IQR criterion, with the lower and upper limits defined as Q1 - 1.5IQR and Q3 + 1.5IQR, respectively, to reduce the influence of extreme strength values while retaining valid samples. For sample balancing, the continuous peak shear strength was first divided into five quantile-based intervals, and SMOTE was then applied to reduce imbalance among these intervals. Thus, SMOTE was used as an adapted target-distribution balancing strategy for regression rather than as a direct classification procedure. Feature engineering was then conducted to construct an extended feature set, and all features were normalized to remove dimensional differences.

Both the base DNN and optimized DNN models utilize a fully connected architecture consisting of an input layer, hidden layers, and an output layer. The hyperparameters for both models were finalized using the aforementioned methods, and the detailed hyperparameter configurations for all models are summarized in Table 1.

TABLE 1. Hyperparameters of machine learning and deep learning models.

AlgorithmHyperparameterRange of values
DNNLearning rate0.0001
Weight decay1e-6
Dropout rate0.01
Batch size16
OptimizerAdamW
Loss functionCombinedLoss
Attention-DNNLearning rate0.0003
Weight decay5e-5
Dropout rate0.20
Batch size16
OptimizerAdamW

4.2 Database establishment and data processing

The database used in this study for the prediction of peak shear strength at the soil-GDL interface consists of 209 valid samples. These were derived from 316 large scale direct shear tests conducted by the Chao (Chao et al., 2021) and Othman (Othman, 2016; Othman et al., 2018). Before merging, only common variables were retained, categorical parameters were uniformly recoded, continuous variables were converted to consistent units, and protocol-related conditions were preserved as model inputs. A total of 107 tests were excluded because of incomplete input parameters.

The database incorporates nine critical input parameters and one output parameter. The input parameters include soil type (T), soil density (D), soil moisture saturation (W), normal stress, shear surface (F), drainage core thickness (TH), geocomposite drainage layer type (TY), geotextile specification (GE), and consolidation condition (C). The output parameter is the peak shear strength (τ) of the soil-GDL interface. The degree-of-saturation values were obtained directly from the source datasets, and no additional drying or constant-mass procedure was performed in this study.

To improve modeling efficiency and ensure data consistency, the dataset was first divided into training, validation, and test sets using a quantile-based hierarchical strategy. All preprocessing was performed using custom-designed Python programs. Winsorization was applied to the target variable using the IQR criterion to reduce the influence of extreme values without deleting valid samples. For regression-oriented SMOTE, the continuous peak shear strength values in the training set were divided into five quantile-based intervals, and synthetic samples were generated to reduce distributional imbalance. The nine core features were expanded to 30 dimensions through physically meaningful combinations, nonlinear transformations, and selected interaction terms. Manual feature elimination was avoided, while redundancy was controlled using the Feature Attention module and AdamW weight decay. Finally, StandardScaler was fitted to the training set and then applied to the validation and test sets.

K-fold was implemented for model development and validation. The training, validation, and test sets accounted for 64%, 16%, and 20% of the dataset, respectively. The training set was used for model fitting and SMOTE processing, the validation set was used for hyperparameter tuning and early stopping, and the test set was reserved for independent evaluation. The validation and test sets retained their original distributions and were processed using parameters obtained from the training set. This procedure reduced the risk of information leakage and ensured an objective assessment of model generalization. Table 2 summarizes the statistics of the input and output variables.

TABLE 2. The statistics.

Data categoryParametersSymbolVariable typeUnitMinimumMaximum
InputSoil typeTCategorical-1 = Clay, 2 = Sand, 3 = Gravel
Soil densityDNumericalg/cm31.362.03
Moisture saturationW%0100
Thickness of drainage coreTHCategoricalmm49
Shearing surfaceF-1 = Flat side, 2 = Dimple side
Type of drainage coreTY-1 = Continuous, 2 = With cut-outs
Geotextile specificationGE-0 = Only dimple side bonded, 1 = Both sides bonded
Consolidation conditionC-0 = Non-consolidation1 = 24 h consolidation
Normal stressNormal stressNumericalkPa0400
OutputPeak shear strengthτNumericalkPa5.5078.14

Furthermore, the potential correlation between input features was examined using a correlation matrix. As shown in Figure 3, soil density and moisture saturation show a strong positive correlation of 0.72, while shearing surface and normal stress show a moderate negative correlation of −0.43. Normal stress also positively correlates with peak shear strength at 0.40, which is consistent with the Mohr-Coulomb failure criterion. Although these correlations indicate potential multicollinearity, the correlated variables were retained because they represent physically meaningful soil-GDL interaction factors. Instead of manual feature deletion, the Feature Attention module and AdamW weight decay were used to reduce the adverse influence of redundant information during model training. Compared with the conventional DNN, the Attention-DNN improved the test-set R2 from 0.9309 to 0.9481 and reduced RMSE from 3.8977 kPa to 3.3781 kPa under the same input-variable system.

Correlation matrix map of the input and output features.
Figure 3. Correlation matrix map of the input and output features.

4.3 Model evaluation metrics

In this study, a multi-dimensional evaluation system was established to assess the peak shear strength model’s performance. Key metrics included the coefficient of determination R2, root mean square error RMSE, mean absolute error MAE, and a20. The a20 index represents the percentage of predictions whose relative deviation from the measured value is within ±20%. It is commonly used as a supplementary accuracy indicator in machine-learning-based engineering regression because it directly reflects the proportion of predictions within an acceptable error band. Considering the inherent variability of soil materials and testing uncertainty, the ±20% threshold was adopted as a practical tolerance rather than an independent design standard. The definitions of R2, RMSE, MAE, and TotalLoss are given in Equations 2–5, respectively. where n is the number of samples, y i and y i ^ are the measured and predicted peak shear strength, respectively. ρ denotes the Pearson correlation coefficient between predicted and measured values, used to quantify the degree of linear correlation between them.

R 2 = 1 − ∑ i = 1 n y i − y i ^ 2 ∑ i = 1 n y i − y i ¯ 2 (2)

R M S E = 1 n ∑ i = 1 n y i − y i ^ 2 (3)

M A E = 1 n ∑ i = 1 n y i − y i ^ (4)

T o t a l L o s s = 0.5 × M S E + 0.3 × M A E + 0.2 × 1 − ρ (5)

4.4 Verification of overfitting prevention

Overfitting is a major challenge in engineering deep learning, particularly in small sample regression tasks. A systematic framework of prevention, detection, and validation is adopted. Prevention involves weight decay, Dropout, and early stopping; detection utilizes training/validation and learning curve analysis; and validation employs cross-validation to evaluate stability. The rigorous application of these regularization and validation techniques is essential for ensuring that the high dimensional features captured by the attention mechanism translate into robust generalization on unseen data (Armaghani and Asteris, 2021; Asteris et al., 2021b). Tailored control schemes for attention-enhanced and baseline models are summarized in Table 3.

TABLE 3. Overfitting prevention steps.

Control dimensionDNNAttention-DNN
Regularization configurationDropout0.003Dropout0.20
AdamW1e-6AdamW5e-5
Max_norm0.5Max_norm0.5
Learning process regulationLearning rate0.001Learning rate0.001
Initial learning rate0.0003Initial learning rate0.0003
Validation strategyk-fold cross validation89.11% ± 5.02%k-fold cross validation95.19% ± 3.86%

Both models effectively mitigated overfitting and demonstrated robust generalization capabilities in predicting peak shear strength. The Attention-DNN model achieved R2 values of 0.9865, 0.9770, and 0.9745 on the training, validation, and test sets, respectively, with performance stabilizing once training data exceeded 70%. The DNN model exhibited high efficiency, maintaining a small R2 gap of 18.26% between the training and validation sets, while an optimal Dropout rate of 0.003 ensured model stability. For the Attention-DNN, the optimal Dropout rate was 0.20, the K-fold strategy yielded a standard deviation of merely 0.0636, and the test RMSE was reduced to 2.37 kPa. These fold-specific validation results provide repeated assessments of predictive performance across different data partitions and support the consistency of the model. Overall, these models provide a reusable framework for overfitting control in geotechnical engineering applications, confirming the effectiveness of the proposed schemes.

5 Results and analysis

5.1 Model training and testing

Table 1 summarizes the training parameters of the two deep learning models, DNN and attention-DNN, proposed in this study. In the process of model training, the optimizer plays an important role in minimizing the loss function, which directly affects the convergence speed of the model and the final prediction accuracy. Considering the small sample nature of the geotechnical data used here, 209 samples remain after preprocessing. And stable parameter update is required. We choose to use adamw optimizer for the two models. In essence, adamw combines the adaptive learning rate advantage of Adam optimizer and weight attenuation regularization, which can not only dynamically adjust the learning rate according to the training process, but also suppress excessive parameter amplitude. This feature makes it particularly effective in reducing over fitting, which is a common challenge in small sample regression tasks like ours.

To further reduce overfitting and enhance the generalization ability of the model, we applied dropout layers after each hidden layer of the two models. For Attention-DNN, the initial learning rate is set to 0.0003. This choice is consistent with its three-tiered symmetric architecture, which is inherently capable of powerful feature representation. An excessively high dropout rate may weaken the model’s ability to capture key input features such as normal stress, soil density, and peak shear strength. In contrast, the dropout rate of Attention-DNN is set to 0.20. The introduction of residual connections and feature attention mechanisms significantly increases model complexity and requires such a dropout rate to randomly deactivate 20% of hidden neurons during training. This design forces the model to depend on more diverse feature combinations instead of relying on a small number of specific features.

Both models were trained for a maximum of 1,200 epochs and adopted EarlyStopping to monitor the validation CombinedLoss, with patience set to 200 epochs and min_delta set to zero. Training was terminated after 200 consecutive epochs without a decrease in validation loss, and the parameters corresponding to the minimum validation loss were retained.

Figure 4 compares the predictive performance of the DNN and Attention-DNN models for the peak shear strength of the soil-GDL interface. As shown in (Figures 4a–d), the Attention-DNN predictions are more concentrated around the ideal fitting line and exhibit a narrower error distribution. The loss curves in (Figures 4e,f) show no sustained divergence between the training and validation losses. The DNN reached its minimum validation loss at epoch 913 and stopped at epoch 1,113, whereas the Attention-DNN reached its minimum validation loss at epoch 407 and stopped at epoch 607. Together with the five-fold R2 standard deviation of 0.0636, these results support the stable and consistent convergence of both models.

Predictive performance between DNN and Attention-DNN models. **(a)** DNN train. **(b)** Attention-DNN train. **(c)** DNN test. **(d)** Attention-DNN test. **(e)** Loss function curves of DNN. **(f)** Loss function curves of Attention-DNN. **(g)** Residual plot of DNN. **(h)** Residual plot of Attention-DNN.
Figure 4. Predictive performance between DNN and Attention-DNN models. (a) DNN train. (b) Attention-DNN train. (c) DNN test. (d) Attention-DNN test. (e) Loss function curves of DNN. (f) Loss function curves of Attention-DNN. (g) Residual plot of DNN. (h) Residual plot of Attention-DNN.

The residual analysis results plotted in (Figures 4g,h) provide further evidence for this conclusion. The residual error generated by Attention-DNN model is closer to zero, the significant outliers are less, and the system deviation is not obvious, indicating that the prediction performance is more stable and reliable. In contrast, the residual distribution of the standard DNN model is relatively scattered, and the error of individual samples is relatively large. By introducing feature attention mechanism and residual connection, Attention-DNN model not only improves the overall prediction accuracy, but also realizes the adaptive weighting of input features. This can better characterize the mechanical behavior of the interface under the coupling effect of various influencing factors. The model provides a reliable technical basis for structural design, stability evaluation and shear performance optimization of composite drainage interface.

5.2 Prediction performance comparison

Figure 4 compares the prediction performance of the DNN and Attention-DNN models on both the training and test sets. The results show that the Attention-DNN model, which combines residual connections and feature attention mechanisms, has obvious advantages in describing the complex nonlinear relationship between input features such as soil density and normal stress and the peak shear strength. On the training set, the Attention-DNN achieves an R2 value of 0.976, higher than the 0.9472 obtained by the DNN. Meanwhile, its RMSE and MAE are reduced to 2.78 kPa and 1.96 kPa, while those of the DNN are 3.60 kPa and 2.55 kPa respectively. On the test set, the Attention-DNN still shows better generalization ability. It delivers an R2 of 0.958, an RMSE of 3.38 kPa and an MAE of 2.48 kPa, while the corresponding values for the DNN are 0.931, 3.90 kPa and 2.95 kPa.

Attention-DNN shows higher accuracy and stability by efficiently capturing complex nonlinear relationships and adaptively enhancing the contribution of key features through the attention mechanism. In geotechnical engineering, these results highlight the potential of mechanism enhanced deep learning in predicting the peak shear strength of soil-GDL interface, and provide reliable technical support for interface design, stability evaluation and shear performance optimization of composite drainage system.

By combining the visualization results of R2 and the a20 index in Figure 5 with the model performance metrics in Table 4. The a20 index intuitively evaluates the reliability and predictive stability of the model in engineering practice by quantifying the proportion of samples within a 20% deviation range (Asteris et al., 2025; Asteris et al., 2024; Bendriss et al., 2026). it can be clearly observed that the Attention-DNN model is better than other methods to predict the peak shear strength of the soil-GDL interface. This benefit is in line with the performance, and the model retains favorable performance on the training set and the test set, further verifying its prediction reliability.

The R<sup>2</sup> value for the DNN and Attention-DNN on train and test datasets. **(a)** Training set of DNN. **(b)** Testing set of DNN. **(c)** Training set of Attention-DNN. **(d)** Testing set of Attention-DNN.
Figure 5. The R2 value for the DNN and Attention-DNN on train and test datasets. (a) Training set of DNN. (b) Testing set of DNN. (c) Training set of Attention-DNN. (d) Testing set of Attention-DNN.

TABLE 4. The model performance metrics.

ModelDatasetR2RMSEMAE
DNNTraining0.94723.602.55
Validation0.9383.752.67
Testing0.9313.902.95
Attention-DNNTraining0.9762.781.96
Validation0.9663.392.08
Testing0.9583.382.48

The Attention-DNN model combines residual connections and feature attention mechanisms, retaining the advantages of deep neural networks in high order feature learning. Its core mechanism can further enhance the model’s performance. Specifically, the residual connections effectively solve the common problem of gradient vanishing in deep networks through feature transformation to make sure that the efficient transmission of complex features. From the perspective of data features, the correlation coefficients of soil density and normal stress are 0.50 and 0.40. In the small-sample scenarios of geotechnical engineering, this model can more accurately identify the coupling effect of soil properties and test conditions on peak shear strength by adaptively filtering redundant information. This is accurately the key reason why the mechanism design of Attention-DNN is suitable for this task. Its strong regularization ability, combined with a dropout rate of 0.20, can effectively alleviate the problem of model overfitting; the interpretability brought by the attention weights also provides us with a new approach to exploring the laws of interface mechanics. To further clarify this interpretability, the learned attention weights can be regarded as an internal measure of the model’s adaptive emphasis on different feature representations. The greater importance of variables such as soil density, normal stress, moisture saturation, drainage core thickness, and consolidation conditions is consistent with their physical roles in soil compaction, interfacial friction, particle interlocking, and coupled interface behavior. However, these attention weights represent model-based feature emphasis rather than direct causal importance. More systematic explainability analyses, such as SHAP evaluation and global feature-importance ranking, will be considered in future work.

In geotechnical engineering, the peak shear strength of the GDL interface actually plays a decisive role in the stability of the structure. Different from traditional models, the Attention-DNN model can provide more reliable predictions under small sample conditions, owing to its excellent capacity to model intricate nonlinear associations and favorable generalization capability. This approach thus shows greater practical value in engineering applications. The results also verify the effectiveness of residual connections and attention mechanisms in geotechnical deep learning research. This further underscores the value of mechanism enhanced model in addressing nonlinear and multi factor coupling problem, while establishing a reusable technical framework that can be applied to similar prediction tasks.

6 Empirical formula

Previous studies have shown that the Attention-DNN model can effectively describe the multi factor coupling characteristics and nonlinear evolution laws involved in the peak shear strength of the soil GDL interface, and then achieve high precision prediction. However, the inherent complexity of the deep learning model often makes it difficult to be directly applied by those engineering and technical personnel who lack sufficient professional background. In order to improve the practicability of the proposed model and make it more widely used in engineering scenarios, an empirical formula is constructed in this section to approximate the prediction behavior of the trained Attention-DNN model. This provides a simple and efficient tool for rapid evaluation of key parameters in geotechnical engineering practice.

The Attention-DNN model follows an optimized structure, in which the basic features are extracted from the fully connected layers, the remaining connections ensure the transmission of deep features, and the feature attention mechanism focuses on the key information. The output can be characterized by the weight parameters, bias terms, and feature interaction rules, as detailed below: where τ represents the peak shear strength of the soil-GDL interface; the input feature vector V = [V1, V2, V3, V4, V5, V6, V7, V8, V9]T corresponds to key engineering parameters, including soil type (T), soil density (D), moisture saturation (W), drainage core thickness (TH), shear surface (F), geocomposite drainage layer type (TY), geotextile specification (GE), consolidation condition (C), and normal stress.

τ = d 0 + F 1 V + F 2 V + F 3 V (6)

F 1 V = ∑ i = 1 9 a i V i (6a)

F 2 V = ∑ i = 1 9 b i V i 2 (6b)

F 3 V = ∑ i = 1 9 ∑ j = i + 1 9 c i j V i V j + γ 0 (6c)

This empirical formula is constructed to approximate the trained Attention-DNN model. Specifically, we generated polynomial features, including linear, quadratic, and two way interactions, from raw inputs and used ridge regression to fit them to the Attention-DNN’s outputs. Ridge regression’s L2 penalty effectively handles multicollinearity among these terms. To simplify the structure, a dual-threshold screening was then applied: the first threshold filtered out primary linear and quadratic terms with negligible ridge coefficients, while a second, stricter threshold removed weak high-order interactions. These thresholds were chosen and validated by iteratively monitoring predictive performance, ensuring redundant terms were eliminated only if the formula’s overall R2 remained above an acceptable baseline. This derivation inherently involves a trade-off between accuracy and simplicity. While the empirical formula sacrifices some predictive precision compared to the highly non-linear deep learning model, yielding an R2 of 0.8349 versus 0.958, it successfully translates a complex “black box” algorithm into a mathematically transparent tool. Crucially, the formula directly utilizes raw, unstandardized measurements, significantly reducing operational difficulty and enabling rapid, on-site manual calculations for field engineers. The corresponding parameters are summarized in Table 5.

TABLE 5. Weights and parameters for the constructed Attention-DNN algorithm.

Feature nameAverage weightWeight stdMax weightMin weightWeight rangea ib iOutput bias
T−0.544.84+7.65−8.5916.24+1.50−8.5921.7950
D+0.034.16+8.14−6.0514.19−1.27−3.54
W−0.320.81+0.58−2.082.66−2.08+0.01
TH+3.936.44+19.20−3.4422.64+7.50−3.44
F−0.452.76+4.64−4.419.05−1.47−4.41
TY+0.784.08+8.80−4.9713.76+2.93+8.80
GE+1.082.62+6.03−2.918.940+0.04
C+4.565.45+19.20−1.6920.89+3.37+3.37
Normal stress+0.020.15+0.24−0.240.4800

In the process of constructing the empirical formula, we introduce the interaction coefficient Cij to capture the coupling effect between different input characteristics, which is a key step to improve the accuracy of the formula’s prediction. Specifically, from the data results, C48 = 19.2000 and C24 = 8.1435 show the interaction between drainage core thickness and consolidation conditions, and between soil density and drainage core thickness, which plays a significant positive contribution to the peak shear strength of the soil-GDL interface. The synergistic effect of these two sets of features will significantly enhance the interfacial shear properties. On the contrary, C12 = −6.0498 and C16 = −4.9659 respectively reflect the negative interaction effects between soil type and soil density, and between soil type and geocomposite drainage layer, since the combination of these characteristics will weaken the peak shear strength of the interface to a certain extent. In general, it is the joint action of these positive and negative interaction coefficients that determines the direction and amplitude of nonlinear correction in the prediction process. In addition, the constant term d0 = 21.7950 plays the role of a baseline offset. Even if the characteristic parameters are at a medium level, this constant term can also provide a reasonable reference for the initial strength of the interface, avoiding the problem of distortion in the prediction of initial strength caused by the parameters being at an intermediate level.

This empirical expression integrates physical interpretability with engineering utility. While capturing complex non linear relationships, it facilitates rapid estimation of the soil-GDL interface peak shear strength without requiring additional normalization preprocessing, providing directly applicable technical guidance for interface design, construction parameter optimization, and prolonged structural safety assessment of composite drainage layers.

7 Experimental verifications

To evaluate the applicability and predictive accuracy of the Attention-DNN model and the empirical formula proposed in this study under various working conditions, we predicted the peak shear strength of the soil-GDL interface. Toward this objective, 25 typical test cases were selected and summarized in Table 6. Predictions were conducted using detailed test parameters through Equation 6. The predicted values were then compared with the measured data from the original large-scale direct shear tests, as shown in Figure 6. This comparison helps to fully evaluate the prediction ability of the formula and further proves its practical value in geotechnical engineering.

TABLE 6. 25 sets of data selected for the experiment.

TD (g/cm3)W (%)TH (mm)FTYGECNormal stress (kPa)
Clay1.3625.04210010.0
1.3615.04210010.0
1.36100.04210010.0
1.9070.06220011.4
1.3625.04210020.0
1.3620.04210020.0
1.7670.09120120.0
1.9070.06210024.4
1.7562.04211140.0
2.00100.06210140.0
1.93100.06210150.0
1.76100.06211050.0
Sand1.5523.04220010.0
2.0193.36211010.0
2.0192.77210010.0
1.7570.06210020.0
1.7570.06211020.0
2.0193.36211020.0
1.7570.07210020.0
1.7570.07211020.0
1.72100.07211020.0
1.5520.04120030.0
Gravel1.93100.04210010.0
1.82100.04210030.0
2.03100.04210040.0
Performance evaluation of empirical formulas. **(a)** The predicted value and experiment data. **(b)** The R<sup>2</sup> value.
Figure 6. Performance evaluation of empirical formulas. (a) The predicted value and experiment data. (b) The R2 value.

As shown in Figure 6, the developed empirical formula exhibits reliable performance in predicting the peak shear strength of the soil-GDL interface across 25 representative test cases. The formula achieved an R2 of 0.8349, RMSE of 5.80 kPa, MAE of 4.12 kPa, and MAPE of 17.18%, demonstrating satisfactory prediction accuracy. To further evaluate its statistical stability, a nonparametric Bootstrap analysis was conducted using all 209 observations while keeping the formula terms and coefficients fixed. Based on 2,000 paired resamples, the R2, RMSE, MAE, and MAPE were 0.861, 6.289 kPa, 4.610 kPa, and 22.582%, respectively. The Bootstrap distributions and corresponding 95% confidence intervals presented in Figure 7 demonstrate that the formula maintains stable predictive performance within the available parameter space.

Bootstrap stability assessment of the empirical formula. **(a)** Measured versus predicted shear strength. **(b)** Bootstrap distribution of R<sup>2</sup>. **(c)** Bootstrap distribution of RMSE. **(d)** Bootstrap distribution of MAE. **(e)** Bootstrap distribution of MAPE.
Figure 7. Bootstrap stability assessment of the empirical formula. (a) Measured versus predicted shear strength. (b) Bootstrap distribution of R2. (c) Bootstrap distribution of RMSE. (d) Bootstrap distribution of MAE. (e) Bootstrap distribution of MAPE.

Compared with complex deep learning models, the empirical formula in this study is easier to use for geotechnical engineering technicians who lack knowledge of algorithms. This formula has a clear polynomial structure, reasonable parameters, and simple inputs. It is easy to calculate by hand and estimate on site. This method lowers the difficulty of using advanced models, offers a useful tool for engineering design and stability analysis, and shows that it can be widely used in geotechnical engineering.

8 Limitations

The use of data driven models in geotechnical engineering has many clear advantages. However, we must carefully check the limits and practical use. The Attention-DNN model and its simple formula in this study work well in predicting the peak shear strength of the soil-GDL interface. Even so, there are still some problems that need to be studied in future work. Firstly, the prediction accuracy and reliability of the deep learning model are essentially limited by the size of the data set. Although the existing geosynthetics test database is large in scale, the data are often incomplete and inconsistent, which makes the direct application of machine learning face challenges. Therefore, it is still urgent to build a more comprehensive and standardized data set. Furthermore, expand the dataset to adequately cover the full range of parameter values is vital to ensure the model’s reliability across the entire multi-dimensional parameter space (Asteris et al., 2021a; Sarir et al., 2021). Secondly, the current modeling framework only relies on nine core input parameters, and may omit other key microstructure variables that affect interface shear behavior. In particular, full grain size distribution curves were not consistently available in the compiled database, although previous research on hybrid soil strength prediction using convolutional neural networks and ensemble learning has shown that detailed gradation information can improve the characterization of soil behavior (Zhang et al., 2024). Future studies should incorporate full grain size distributions, D10, D30, D50, Cu, Cc, particle morphology, and interface-specific roughness. Thirdly, the ranges of normal stress and degree of saturation remain limited. Although degree of saturation was included, the model does not explicitly account for matric suction or unsaturated hydraulic behavior. Pore-based modelling has highlighted the importance of pore structure in predicting unsaturated hydraulic conductivity (Wang H. et al., 2025), supporting the future inclusion of suction-related descriptors. Moreover, partially drained conditions can significantly affect the cyclic behavior of reinforced soils (Tai et al., 2024). Since drainage conditions were not consistently reported in the compiled database, future models should incorporate drainage state and cyclic loading parameters. Finally, the present study mainly compares the proposed Attention-DNN with its baseline DNN to isolate the effects of residual connections and feature attention. Therefore, the reported improvement should be interpreted as an enhancement over the controlled DNN baseline rather than as universal superiority over all machine-learning methods. Future work will include systematic comparisons with ensemble, kernel-based, and other state-of-the-art regression models under unified tuning and validation protocols. Moreover, although early stopping reduces unnecessary training and the empirical formula enables low-cost engineering calculations, the training time, inference time, model size, and hardware-dependent efficiency were not systematically evaluated in this study. Future work will benchmark these computational indicators under unified hardware and software conditions.

9 Conclusion

This study systematically explored the prediction method for the peak shear strength of the soil-GDL interface, including the data processing of large scale direct shear tests, the construction and optimization of deep learning models, the derivation of empirical formulas, and test verification. By constructing an Attention-DNN model that integrates residual connections and a feature attention mechanism, and combining the K-fold strategy and a multidimensional evaluation system, the evolution law of the strength under the coupling effect of multiple factors was revealed, forming a complete and feasible engineering application system.

  • The Attention-DNN model alleviates the gradient disappearance problem through residual connections, and focuses on key features adaptively using feature attention mechanism. The model shows stable and consistently improved prediction performance on the small-sample and highly dispersed geotechnical dataset compared with the conventional DNN model. It provides an efficient tool for high precision prediction of interface strength.
  • The peak shear strength of the soil-GDL interface is governed by the synergistic effects of multiple factors. Based on the correlation matrix analysis, the optimal moisture content improve the compaction effect, and has a significant positive correlation with soil density; in addition, an increase of normal stress will improve the interfacial friction resistance and shear capacity, which is positively correlated with the peak shear strength.
  • The model accurately captures the complex nonlinear interactions among input features. The Cij index derived during the development of the empirical formula reflects a significant coupling effect.
  • The empirical formula is derived using ridge regression and a dual threshold screening strategy. It can well reproduce the prediction pattern of the Attention-DNN model. The formula does not need to be normalized, which has good results, effectively reduces the application barrier for engineering, and promotes the engineering application of complex models.
  • Based on the test verification of typical working conditions, the empirical formula maintains reliable stability under different construction conditions. The formula can be directly applied to interface design, construction parameter optimization and safety evaluation of composite drainage layers.

This study enriches the deep learning prediction theory of mechanical properties of rock soil interface, and develops models. Through the derivation and verification of empirical formulas, the research provides scientific and convenient technical support for the engineering practice of soil-GDL composite drainage systems, and has important reference value for improving the rationality and safety of similar geotechnical interface designs.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/feart.2026.1839550/full#supplementary-material

Supplementary material Supplementary material at the source

Footnotes

Edited by: Srđan Kostić, Jaroslav Černi Water Institute, Serbia

Reviewed by: Panagiotis G. Asteris, School of Pedagogical and Technological Education, Greece

Tengfei Nian, Lanzhou University of Technology, China

Zhaofeng Li, Harbin Institute of Technology, China

Vinh Le, Posts and Telecommunications Institute of Technology (PTIT), Vietnam

Statements

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Funding

The author(s) declared that financial support was received for this work and/or its publication. The authors would like to acknowledge the consistent support of National Natural Science Foundation of China: No 52471290, No 52301327; Project funded by China Postdoctoral Science Foundation: No 2024T170217, No 2023M730929; Failure Mechanics and Engineering Disaster Prevention, Key Lab of Sichuan Province: No FMEDP202209; Shanghai Sailing Program: No 22YF1415800, No 23YF1416100; Shanghai Natural Science Foundation: No 23ZR1426200, No 24ZR1427900; The Shanghai Soft Science Key Project: No 23692119700; Funded by Key Laboratory of Ministry of Education for Coastal Disaster and Protection, Hohai University, No 202302; Funded by Key Laboratory of Estuarine & Coastal Engineering, Ministry of Transport, No KLECE202302.

Data availability

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

PT: Writing – original draft, Writing – review and editing, Data curation, Methodology, Supervision, Conceptualization, Formal Analysis, Project administration, Validation, Investigation, Funding acquisition, Resources, Visualization, Software. ZW: Writing – original draft, Writing – review and editing, Data curation, Methodology, Supervision, Conceptualization, Formal Analysis, Validation, Investigation, Funding acquisition, Resources, Visualization, Software. SG: Conceptualization, Data curation, Formal Analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review and editing. JZ: Conceptualization, Data curation, Formal Analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review and editing. PC: Conceptualization, Formal Analysis, Funding acquisition, Investigation, Project administration, Resources, Supervision, Validation, Writing – original draft, Writing – review and editing.

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Citation

Tang, P., et al. (2026). Feature attention model for soil-geocomposite interface strength. Frontiers in Earth Science, Volume 14. https://doi.org/
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14 - 2026

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Copyright © 2026 Tang, Wu, Gu, Zhao and Cui.

License: https://creativecommons.org/licenses/by/4.0/

*Correspondence: Jiaming Zhao; Peng Cui

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