The experimental materials comprised marine coral sand and kaolin clay. The coral sand was sourced from a reef island in the South China Sea. To ensure consistency and reliability of the test results, the collected sand was subjected to a series of preparatory procedures including oven drying and mechanical sieving. The particle size fraction retained between 0.074 mm and 2 mm was selected for use in the experiments. The kaolin clay employed in this study consisted of particles with a uniform diameter of 10 μm, ensuring its suitability for mixing and compaction with the sand matrix. Photographs of the marine coral sand and kaolin clay are provided in Figure 1, while their corresponding physical properties are summarized in Table 1. According to the particle size distribution analysis, the marine coral sand demonstrated a coefficient of uniformity (Cu) of 3.1 and a coefficient of curvature (Cc) of 1.2. These values indicate that the sand has a well-graded distribution.

A triaxial geogrid was manufactured using stereolithography (SLA)-based 3D printing, as illustrated in Figure 2. The geogrid features ribs with a width of 1.5 mm and a thickness of 2 mm. The apertures are designed as equilateral triangles, each with a side length of 2 mm. To minimize boundary effects during specimen preparation, the overall diameter of the triaxial geogrid was set at 39.1 mm. A comprehensive summary of the geometric and structural properties of the printed geogrid is presented in Table 2.

In the natural conditions of islands and reefs in the South China Sea (Gao and Ye, 2024), surface and near-surface marine coral sand typically remains in an unsaturated state for extended periods, leading to significantly low shear strength (Chao et al., 2025; Ye and Gao, 2024). These regions are considered potential target zones for geogrid-based reinforcement (Gao and Ye, 2024). A thorough understanding of their mechanical behavior and the establishment of an effective reinforcement mechanism are essential to ensure the structural safety and stability of island infrastructure. To explore the fundamental mechanical response, deformation behavior, and particle crushing characteristics of marine coral sand–clay mixtures (MCCM) reinforced with triaxial geogrids, a series of unconsolidated undrained (UU) triaxial tests were performed. These tests, summarized in Table 3, examined the influence of several key factors, including clay content, number of geogrid layers, water content, and confining pressure.

All tests were carried out using a static-dynamic triaxial testing apparatus (VJ Tech, UK), as illustrated in Figure 3. For each specimen, the mass of individual layers was pre-calculated based on the target water content, followed by accurate weighing and water adjustment. The MCCM material was thoroughly mixed, placed into the mold in layers, and compacted to the specified height. During specimen preparation, the geogrid volume was accounted for and subtracted to ensure consistent sample density. After specimen preparation, triaxial compression tests were performed, with loading continued until an axial strain of 15% was reached. Upon completion, the specimens were disassembled, washed, oven-dried, and subjected to sieve analysis to determine the post-shear particle size distribution of the marine coral sand.

Based on the experimental results, deviator stress–strain curves corresponding to the test groups listed in Table 3 were obtained. Figures 4a–d illustrate the stress–strain responses of dried MCCM specimens with varying confining pressure. The results indicate that increasing the confining pressure and the number of geogrid layers, as well as reducing the clay content, leads to a noticeable rise in peak deviator stress and a more evident hardening behavior. Notably, the specimen containing 30% clay, tested under a confining pressure of 200 kPa with two reinforcement layers, exhibited a maximum deviator stress of 5300.15 kPa at 15% axial strain.

Figure 5 presents the deviator stress–strain curves of MCCM specimens containing 70% clay and reinforced with a single geogrid layer under varying moisture conditions. The results show that specimens with higher water content exhibit lower strength compared to their dried counterparts. However, it can also be observed that the strength of MCCM does not decrease monotonically with increasing water content; instead, it first declines, then rises, and eventually drops again. This trend indicates a nonlinear and highly complex relationship between water content and the strength behavior of MCCM.

The observed variation in strength can be attributed to several factors. Initially, the increase in water content leads to the softening of the clay particles, causing a decrease in the material’s overall strength. As the water content continues to increase, the water may act as a lubricating agent, temporarily improving the internal structure of the material and enhancing its shear strength. However, beyond a certain point, excessive water content can result in the weakening of the cemented bonds between the particles, leading to a reduction in strength. This non-monotonic behavior suggests that there may be an optimal water content for MCCM, where the balance between lubrication and cementation is most favorable for strength development.

In this study, a machine learning approach based on the Back Propagation Neural Network (BPNN) is adopted. To enhance the model’s performance, optimization techniques including Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Logical Development Algorithm (LDA) are incorporated. These methods offer several advantages, among which three primary benefits are particularly noteworthy:

Hyperparameter optimization plays a crucial role in enhancing the performance of machine learning models, as different configurations can significantly affect training efficiency and predictive accuracy. In this study, GA, PSO, and LDA were used to optimize the hyperparameters of a BPNN to improve overall model performance.

To ensure efficient convergence and improved accuracy, key parameters in each optimization algorithm were carefully selected, as summarized in Table 4. In GA, the population size(pop_num) was set to 5 to reduce computational overhead while maintaining sufficient search diversity. The number of generations (gen) was fixed at 100 to ensure comprehensive exploration. The selection function parameter (normGeomSelect) was set to 0.05 to increase the probability of selecting high-fitness individuals. The crossover function (arithXover) was assigned a value of 3 to enhance diversity, while the mutation function (nonUnifMutation) was configured as [0.5, 50, 3] to strengthen global search capabilities and prevent premature convergence. The optimal solution tolerance (maxGenTerm) was set to 1e-6, allowing continued search near the optimum and improving solution stability. In PSO, the learning factors (c1, c2) were set to 1.5 to balance individual and collective influence on particle velocity. The position limits were set between -1.0 and 1.0 to constrain the search space. A population size (sizepop) of 30 was used to maintain a trade-off between computational cost and global search ability. The number of population update times (maxgen) was set to 100, and the training epochs (epochs) for the BPNN were set to 150 to ensure adequate learning. For LDA, the population size (pop_num) was set to 30 and the maximum number of iterations (max_iter) to 50. The mutation factor (F) was set to 0.5 to improve global exploration, and the crossover probability (CR) was set to 0.9 to enhance diversity within the solution space. These settings enabled the model to more effectively capture class separability, thereby improving classification accuracy after dimensionality reduction. Overall, the well-tuned hyperparameters allowed GA, PSO, and LDA to significantly enhance BPNN performance. These optimizations accelerated convergence, reduced overfitting, and ultimately improved prediction accuracy, demonstrating strong potential in applications such as reinforced MCCM strength prediction.

Figure 8 illustrates the RMSE-based performance comparison of GA, PSO, and LDA during the optimization process. The horizontal axis represents the number of iterations (0–50), while the vertical axis denotes the RMSE values, reflecting model prediction error. As shown, the RMSE values for all three algorithms decrease progressively with the increase in iterations, indicating their effectiveness in reducing prediction error. Notably, PSO demonstrates the fastest convergence rate, reaching lower RMSE values within fewer iterations. This suggests higher search efficiency in exploring the solution space. Although PSO achieves a rapid initial drop in RMSE, the rate of decline slows in later iterations, eventually stabilizing around 5.6. In contrast, GA also shows a sharp early decrease in RMSE but with a more gradual decline, stabilizing near 4 after approximately 20 iterations. LDA, on the other hand, exhibits a slower initial reduction, followed by an accelerated decrease, ultimately converging to an RMSE close to 1. Overall, the comparison indicates that while PSO offers faster early convergence, LDA achieves superior final accuracy and convergence stability, outperforming both GA and PSO in the optimization process.

To investigate the strength of MCCM under various conditions, a dataset consisting of 900 samples was established. This dataset includes five variables: clay content, number of reinforcement layers, confining pressure, water content, and strain. All input and output variables were normalized to ensure effective modeling:

As shown in Equation 1, where x is the original data value, x′ is the normalized data value, x_min is the smallest value in the data, and x_max is the largest value in the data set.

The summary statistics of the variables in the dataset are presented in Table 5. The clay content ranges from 30% to 70%, the number of reinforcement layers includes three levels: 0, 1, and 2, the confining pressure varies from 50 kPa to 200 kPa, and the water content includes six levels ranging from 9% to 36%. Strain values range from 0% to 15%. Data preprocessing steps, including cleaning, normalization, and dataset splitting, were conducted to ensure data quality and suitability for machine learning modeling.

In the process of model construction and optimization, it is essential to select appropriate assessment metrics to evaluate the predictive performance of the model. In this study, two key assessment indicators are utilized:

1、Root Mean Square Error (RMSE): RMSE represents the standard deviation of the difference between predicted values and actual values. A smaller RMSE indicates a lower prediction error, reflecting a more accurate and reliable model as shown in Equation 2.

Where n is the number of samples, y_i is the observed value, and f_i is the predicted value.

2、Mean Absolute Percentage Error (MAPE): MAPE calculates the average of the absolute errors between predicted and actual values, expressed as a percentage of the actual values. A smaller MAPE indicates a lower prediction error, demonstrating better model accuracy and performance as shown in Equation 3.

Where n is the number of samples, y_i is the observed value, and y^i  is the predicted value.

In this study, the dataset creation serves as the foundation for training the machine learning algorithms. A dataset with 5 input parameters and 1 output parameter was developed to train and validate the performance of BPNN, GA-BPNN, PSO-BPNN, and LDA-BPNN, as illustrated in Figure 9.

A database with 900 datasets was created, containing four key input parameters: clay content, number of reinforcement layers, confining pressure, water content, and strain. To assess the model’s generalization capability, the dataset was split into two subsets: the training set and the test set. The training set was used to train the model, while the test set provided the basis for final performance evaluation. The dataset was divided into 80% for training and 20% for testing, ensuring a more accurate assessment of the model’s generalization ability and practical performance. The correlation analysis of different inputs is shown in Figure 10.

The prediction results obtained from the machine learning model, based on 900 training and testing samples, are shown in Figures 11 , 12.

Overall, the predicted values (red hollow circles) produced by each model generally align with the actual values (purple hollow diamonds), indicating that all models are capable of effectively fitting the training data and capturing the nonlinear relationships between the input features and the target output. However, noticeable differences are observed in prediction accuracy across the models. The LDA model (Figure 11h) exhibits the smallest deviation from the actual values, reflecting its superior fitting performance. In contrast, the BPNN model (Figure 11b) shows relatively large prediction errors, particularly for high-peak samples, suggesting that its shallow architecture is insufficient to model the complex patterns inherent in the data. Both GA-BPNN (Figure 11d) and PSO-BPNN (Figure 11f) enhance the baseline BPNN through the integration of optimization algorithms, resulting in predictions that better match the actual values, though slight overfitting is still evident in certain samples. Overall, the LDA model outperforms the other models on both the training and testing sets, demonstrating more robust learning capability and better generalization performance.

As shown in Figure 12, when evaluated using the testing dataset, the LDA model consistently outperforms the other three machine learning models. Specifically, the LDA model achieves the highest prediction accuracy, with the lowest RMSE values of 1.24356 and 3.34974 for the testing and training sets, respectively. It also records the lowest MAPE values—7.15134% for the testing set and 9.10231% for the training set. In terms of correlation, the LDA model attains an R value of 0.99651 on the testing set, indicating an extremely strong linear relationship between the predicted and measured values.

By contrast, although the GA-BPNN model benefits from genetic algorithm optimization and shows improved performance, it still falls short of the LDA model. GA-BPNN yields RMSE values of 4.0397 and 8.1878, and MAPE values of 5.5479% and 10.1739% for the testing and training sets, respectively. The R value of 0.98509 suggests limited ability to capture the underlying data patterns.

The PSO-BPNN model performs relatively poorly, with larger prediction errors and more scattered residuals, indicating that particle swarm optimization fails to significantly enhance the predictive capability of BPNN. For PSO-BPNN, the RMSE values are 5.60674 and 8.65794, and MAPE values are 9.51099% and 16.014% for the testing and training sets, respectively, with an R value of 0.99411.

The original BPNN model exhibits the lowest prediction accuracy among all models. It produces RMSE values of 5.81524 and 13.0744, and MAPE values of 15.2679% and 21.7309% for the testing and training sets, respectively. The R value of 0.97887, along with a significant deviation of data points from the fitted line, suggests that the simple architecture of BPNN lacks the capacity to represent complex data features effectively.

In summary, the LDA-BPNN model demonstrates superior performance over GA-BPNN, PSO-BPNN, and BPNN in both the training and testing phases. It offers higher predictive accuracy and robustness, particularly on unseen test data. Notably, even under identical optimization strategies, the predictive capability of the LDA model is markedly better than that of the other models.

Understanding machine learning models is crucial for ensuring transparency and encouraging broader adoption (Yang et al., 2025). Feature importance analysis plays a key role in uncovering the internal logic of these models, offering insights into their decision-making processes. Among various interpretability approaches, the SHAP (Shapley Additive Explanations) method has gained significant traction (Lundberg and Lee, 2017). Based on game theory, SHAP evaluates all possible feature combinations to assess their interactions and calculates a SHAP value for each prediction. This value reflects the individual contribution of each feature to the model’s output, with positive values indicating an increase and negative values a decrease in the predicted result.

Figure 13 presents the five most influential features affecting the output of the LDA model, along with a brief analysis of their respective impacts. The pie chart illustrates the mean SHAP values for each feature, where a larger SHAP value denotes a stronger contribution to the model’s prediction. On the left, the beeswarm plot offers a more detailed visualization of feature effects. In this plot, the horizontal axis corresponds to the SHAP value, while the vertical axis represents the feature value. A high SHAP value combined with a high feature value suggests a positive correlation—larger feature values lead to higher predicted outputs. Conversely, negative SHAP values indicate a negative influence on the model output. As shown, water content exerts the most significant impact on strain prediction, with a relative importance of 35.9%, followed by clay content at 29.5%. In contrast, strain itself contributes the least, accounting for only 7.8%. The SHAP-based analysis identifies water content as the dominant factor influencing the model’s predictive performance. This can be attributed to its critical role in governing interparticle contact behavior and pore water pressure distribution, both of which are key determinants of soil strength and deformation. Clay content, ranking second in importance, significantly affects soil fabric and moisture retention. A higher clay fraction generally implies stronger cohesion and more pronounced plasticity, which are essential to stress accumulation and dissipation during the shearing process of MCCM.

These findings highlight the necessity of implementing targeted optimization strategies that consider the varying influence of different parameters to ensure the stability and reliability of marine infrastructure constructed with MCCM as the principal material.