This method utilizes a ratio between two key parameters: the cyclic resistance ratio (CRR), which reflects the soil’s ability to resist liquefaction, and the cyclic stress ratio (CSR), which represents the level of stress imposed by earthquake shaking and is expressed as C S R = 0.65 σ v o a max σ v 0 ′ r d M S F 1 K σ (1)

Youd and Perkins, 1978 introduced a factor of 0.65 to convert the irregular earthquake load into a comparable uniform stress cycle shown in Equation 1. The reduction coefficient (rd) is not constant and varies depending on the depth z Equations 2–4 by Idriss (1999). r d = exp α z + β z M (2) α z = − 1.012 − 1.126 ⁡ sin z 11.73 + 5.133 (3) β z = 0.106 + 118 ⁡ sin z 11.28 + 5.142 (4) where σ _vo represents the total effective overburden pressure, σ′ _vo represents the effective vertical overburden stress at depth z, a _max represents the peak ground acceleration in the horizontal direction, MSF represents the magnitude scaling factor that provides the combinational effect of relative amplitude and the number of load cycles Equations 5 and 6 for sand and clay, respectively. Kσ represents the correction factor for the effective overburden, as shown in Equations 7, 8. M S F = 6.9 ⁡ exp − M 4 − 0.058 ≤ 1.8 ; (5) M S F = 1.12 ⁡ exp − M 4 + 0.828 ≤ 1.13 ; (6) K σ = 1 − C σ σ ′ P a ≤ 1.1 (7) C σ = 1 18.9 − 2.55 N 1 60 c s ≤ 0.3 (8)

The mathematical Expression to evaluate CRR in Equation 9 generated from the corrected blow count (N₁)₆₀ is as follows: C R R = N 1 60 C S 14.1 1 + N 1 60 C S 126 2 − N 1 60 C S 23.6 3 + N 1 60 C S 25.4 4 − 2.8 (9)

SPT-N values are tuned to an equivalent clean sand value using Equation 10 comprised of N 1 60 along with corrections mentioned in Equation 11, and variation Δ N 1 60 with FC (%) is estimated using Equation 12. N 1 60 C s = N 1 60 + Δ N 1 60 (10) N 1 60 = N M C N C E C B C R C S (11) where N M = Measured standard penetration resistance, C N = Overburden correction factor, C E = Correction of hammer energy ratio, C B = Correction of borehole diameter, C R = Correction of rod length, C S = Correction of samplers with or without liner. Δ N 1 60 = exp 1.63 + 9.7 F . C + 0.1 − 15.7 F . C + 0.1 2 (12)

Finally, in Equation 13, the expression used to evaluate the safety factor of safety (FOS) against liquefaction is described as follows: if the safety factor is less than 1, there is a liquefaction potential. If the safety factor is greater than one, there is no liquefaction potential. F O S = C R R C S R (13)

The current study distinguishes itself by focusing on DCPT, a method that is less commonly used in liquefaction studies but offers significant advantages over traditional tests. DCPT is more time-efficient, cost-effective, and adaptable to various soil types (Benz Navarrete et al., 2022; Park G. et al., 2023). Its dynamic nature and real-time data-collection capabilities make it particularly suitable for rapid and accurate liquefaction assessments (Duan et al., 2023a). The adaption of susceptibility studies based on DCPT is mainly due to its dynamic and adaptable characteristics, as it stands out as a valuable tool in the geotechnical engineer’s toolkit. Notably, one of its primary advantages over traditional SPT is its superior time and cost efficiency. DCPT offers a remarkable reduction in testing time owing to its rapid deployment capabilities (Benz Navarrete et al., 2022). Unlike the SPT, which involves a slower and more labor-intensive process, the dynamic penetration of DCPT into the soil allows for a quicker assessment of soil strength. This time efficiency is particularly advantageous in conditions where swift decision making is crucial, such as liquefaction estimation.

Moreover, DCPT requires minimal drilling and presents a significant cost-saving advantage. The direct dynamic penetration of the cone into the soil eliminates the need for extensive borehole preparation, reduces associated costs, and minimizes the environmental impact. This makes the DCPT a more economical alternative for liquefaction assessment, contributing to the overall project cost-effectiveness (Park I. et al., 2023).

The real-time data-collection capability of the DCPT further enhances its appeal. This feature allows for on-site analysis, enabling immediate decision making based on accurate and up-to-date information. In scenarios where time-sensitive projects demand rapid liquefaction assessments, DCPT proves to be an invaluable asset (Duan et al., 2023b). The simplified equipment setup and ease of operation of the DCPT also translate into reduced equipment and personnel costs. With a smaller team and more economical equipment requirements compared with the SPT, the DCPT offers an attractive cost-effective solution for geotechnical investigations. Additionally, the DCPT demonstrated enhanced accuracy and consistency in data collection (Park G. et al., 2023). Its dynamic nature generates more reliable and repeatable results compared to the SPT and CPT, contributing to a more precise characterization of soil behavior. Moreover, the adaptability of the DCPT to various soil types further underscores its versatility and applicability in diverse geological settings. This heightened accuracy and wide range of soil adaptability improve the reliability of the results, making the DCPT a preferred choice for liquefaction assessments. In essence, by capitalizing on the advantages presented above by the DCPT, this study aims to revolutionize the methodology for estimating liquefaction potential in soils.

The DCPT was designed to penetrate soils up to a depth of 1 m, utilizing a 20 mm diameter and a 60-degree cone, along with an 8 kg hammer, as depicted in Figure 2. The soil dynamic resistance ( q d ) at each test point was determined using the DCPT data (BS EN ISO 22476-2) as follows: q d = m m + m ′ * m g h A * e (14)

Where A cone tip area, e is the rate of penetration at each drop, and m and m' are the masses of the anvil, rods, and drop hammer, respectively. From Equation 14, by dividing one/e, Equation 15 can be obtained. The rearranged equation, From Equation 14, we can calculate e/ q d as e q d = 1 m m + m ′ * m g h A (15)

Consequently, the fine-grained soil equation is as follows (Gholami et al., 2022): N S P T = 5.76 * q d 0.74 (16)

ML has transformed the landscape of civil engineering and has presented innovative solutions to intricate challenges. Applied extensively in civil engineering tasks, ML techniques span predictive modelling to decision support systems (Thapa and Ghani 2024a; Ghani and Chhetri Sapkota, 2024; Mustafa et al., 2024). ML algorithms meticulously scrutinize extensive datasets, uncovering patterns and trends that yield valuable insights into structural behavior, material performance, and project management. In the realm of structural engineering, ML is instrumental in forecasting the structural health and lifespan of bridges and buildings using real-time monitoring data (Ghani et al., 2023; Gupta et al., 2024; Shrestha et al., 2023; Thapa et al., 2024a). Geotechnical engineering reaps the benefits of ML in soil classification, slope stability analysis, ground settlement prediction, and liquefaction assessment (Ghani et al., 2024b; Ghani and Kumari, 2022a; 2022b; 2023b; 2023a; N; Kumar and Kumari, 2024; Mahmoodzadeh et al., 2022; Thapa and Ghani, 2023; Thapa and Ghani, 2024). Several researchers have promoted the application and adaptability of ML for liquefaction assessment (Hanandeh et al., 2022; Sui et al., 2023). Moreover, optimizing ML models with metaheuristic optimization algorithms has shown promising results in enhancing the accuracy and reliability of liquefaction prediction results (Duan et al., 2023a; Ghani et al., 2022). The ML model’s hyperparameters are fine-tuned by the optimization algorithm, resulting in more accurate predictive results. A concise summary of the optimized ML models utilized is provided below. For a comprehensive background on these ML and optimization methods, readers can consult the pertinent literature (Asteris et al., 2021; Davoodi et al., 2023; D. R; Kumar et al., 2022; Nagaraju et al., 2023).

In the present investigation, the focus was on the capabilities of the DCPT method in evaluating the liquefaction susceptibility. A pivotal aspect highlights the significance of the e/qd ratio in gauging the likelihood of liquefaction-induced failures. Termed the safety ratio, this ratio outlines the relationship between the rate of penetration (e) and cone resistance (q _d), thereby emerging as a pivotal factor in evaluating the potential for soil liquefaction. The DCPT method employs Equation 14 to calculate the soil dynamic resistance (q _d). This equation incorporates key factors such as the equipment mass, gravitational force, and cone tip dimensions. By rearranging this formula, Equation 15 expresses the ratio of the penetration rate to the dynamic resistance (e/q _d), which is often referred to as the safety ratio. This parameter offers valuable insights into the soil behavior under dynamic stress conditions. Generally, a higher e/q _d value suggests an increased susceptibility to liquefaction, as it indicates the tendency of the soil to yield more readily under applied forces. To bridge the gap between the DCPT results and more conventional soil-testing methods, Equation 16 establishes a correlation between q _d and the Standard Penetration Test (SPT) N-value for cohesionless fine-grained soils. This relationship enhances the applicability of the DCPT by allowing comparisons with widely used SPT data, thereby facilitating a more comprehensive assessment of the liquefaction potential across various soil types and conditions.

The establishment of a threshold criterion, illustrated in Figure 8, proved instrumental in determining the soil liquefaction susceptibility based on the e/q _d ratio. The sample index was plotted along the y-axis, representing the different soil samples analyzed. The Safety Factor is plotted on the x-axis, indicating the ratio between the rate of penetration and dynamic resistance for each sample. The red vertical line at e/q _d = 4 represents the critical threshold separating the liquefied and nonliquefied zones. Samples with e/q _d ≥ 4 were classified as liquefied (LQ) and are represented by orange bars. Samples with e/q _d < 4 were classified as non-liquefied (NLQ) and are shown as blue bars. The Liquefied Zone on the right side of the red line indicates that the soil samples falling within this region are more likely to experience liquefaction. The graph visually demonstrates the separation between the liquefied and non-liquefied cases based on their e/q _d values, providing insight into the safety margins for various soil samples under dynamic loading conditions. This classification is based on the understanding that soils with higher e/qd ratios generally exhibit lower resistance to liquefaction, which increases the risk of failure under seismic loading conditions.

This differentiation is briefly summarized using the tabular liquefaction susceptibility criterion, as shown in Table 5. Figure 8 serves as a visual aid to elucidate the relationship between the e/q _d ratio and the liquefaction prediction. Figure 9 provides a quantitative assessment of the accuracy of liquefaction predictions derived from the e/q _d ratio obtained using the DCPT method. Notably, the accuracy rates for the liquefied and non-liquefied scenarios were 82.7% and 86.5%, respectively, as shown in Figures 9A, B. The overall accuracy of the prediction rate for liquefied and non-liquefied conditions highlighted the precision of the proposed method.

The results of this study underscore the pivotal role of the e/q _d ratio in fortifying our understanding of soil liquefaction. The e/q _d ratio is a key component that provides crucial information for projects involving engineering and construction, particularly in areas with high seismic activity. Through meticulous analysis and empirical validation, the present findings underscore the efficacy of employing this safety ratio within the DCPT framework, offering a robust and novel tool for evaluating liquefaction susceptibility at different locations.

Figure 10 illustrates the connection between the input variables and the e/qd ratio through four subfigures: FC (%), PGA, rd, and e. The amount of finer particles in the soil, known as FC (%), affects its vulnerability to liquefaction. An increased FC usually results in a higher e/qd ratio, indicating a higher likelihood of liquefaction. PGA is the seismic factor acting on the soil, which directly affects the e/qd ratio. With an increase in PGA, the e/qd ratio increased, indicating a greater likelihood of liquefaction. rd accounts for the depth-related weakening of seismic energy; smaller rd values are linked to greater e/qd ratios, suggesting that deeper layers are at an increased risk of liquefaction. The penetration rate (e) in the DCPT test is an important factor. A higher e/qd ratio indicates a weaker soil strength when the penetration rate is increased. Figure 10 shows how variations in FC, PGA, rd, and e affect the e/qd ratio, thereby impacting the soil liquefaction potential. Comprehending these relationships assists in evaluating the engineering characteristics of soil and its response to seismic forces.

The present study employed grid search as the primary hyperparameter tuning method to optimize the performance of our ML models. The grid search performs an exhaustive search over a predefined parameter space, allowing us to systematically evaluate different combinations of hyperparameters. For the SVM model, the regularization parameter (C), which controls the trade-off between maximizing the margin and minimizing classification errors, and the kernel coefficient (gamma) for the Radial Basis Function (RBF) kernel, which determines the influence of a single training example were tuned (Ghani et al., 2021; Ghani et al., 2024a; Guan et al., 2022; Jamal et al., 2021; Ghani et al., 2024b; Talamkhani et al., 2023; Wang et al., 2023). The grid search process was performed in combination with the k-fold cross-validation to ensure robustness (Man et al., 2023; Roy et al., 2023). This cross-validation technique divides the dataset into k subsets, where the model is trained on k-1 subsets and tested on the remaining subset. The process is repeated k times, and the results are averaged to minimize overfitting and ensure that the model generalizes well to the unseen data (Ghani and Kumari 2022; Thapa et al., 2024b; Ghani and Kumari 2021b; Shrestha et al., 2024; Mustafa and Ahmad 2024). The grid search explored a range of values for C (0.1–100) and gamma (0.001–1). After tuning, we observed a significant improvement in the model performance. The optimized SVM model, for instance, demonstrated a reduction in the root mean square error (RMSE) and an increase in the coefficient of determination (R²). These enhancements were crucial for achieving higher accuracy in predicting liquefaction susceptibility, as the tuned parameters allowed the model to better capture the complex nonlinear relationships between the input variables and liquefaction outcomes. In addition to the grid search, we also experimented with a random search for other models, such as decision trees and neural networks, where we randomly sampled the hyperparameter space. Although random search is less computationally expensive, a grid search was chosen for the SVM model to ensure a more precise optimization of the hyperparameters. The results from hyperparameter tuning clearly demonstrate that model performance is highly sensitive to the choice of parameters. The fine-tuned SVM model outperformed the default settings, confirming the effectiveness of the proposed grid search strategy.

Furthermore, this study focuses on developing a data-driven ML model for utilizing DCPT test data utilizing four key variables: fine content (FC), peak ground acceleration (PGA), reduction factor (r_d), and rate of penetration (e). Table 6 presents a statistical summary of the input and output variables for the entire dataset. To gain a deeper understanding of the relationship between key parameters influencing safety, Figure 11 presents the frequency distribution of the normalized values for FC, PGA, r _d, e, and e/q _d. Figure 12 illustrates the relative frequency distribution of the five key variables affecting the soil liquefaction susceptibility. The distributions were mostly right-skewed, indicating that most data points fell within the lower ranges for each parameter. For instance, fine content predominantly lies between 10% and 30%, whereas PGA values are mainly low, with a significant portion of samples having low seismic activity. The reduction factor values cluster around 0.8 to 0.9, suggesting a moderate energy reduction with depth. The penetration rate (e) showed a concentration of approximately 5–15, indicating moderate resistance in the soil. Finally, the safety ratio (e/qd) values were low for most samples, indicating that the majority of the soils tested had lower liquefaction potential. These distributions highlight the critical role of these variables in assessing the liquefaction risk.

Hybridized ML models were used to evaluate e/qd. Both the model construction and validation phases were specifically addressed to provide a comprehensive understanding of the effectiveness of the ML model. The primary focus of the discussion was model performance during the training and testing phases. Table 7 presents the statistical performance of the model during the training and testing phases. Table 8 presents a thorough examination of the various models using multiple indices to determine the scores. The performance of each model was assessed during both training and testing stages. The scores represent the extent to which each model predicts the e/qd ratio. In the testing phase, the SVM-FF model demonstrated superior predictive ability by achieving the highest total score of 36, surpassing all other indices. In contrast, the SVM-GA model had the lowest score of nine in testing, indicating less accurate predictions. The SVM-PSO model consistently achieved high scores in both the training and testing stages. This in-depth score analysis helps to pinpoint the strongest and most dependable models for predicting soil behavior in different situations, guaranteeing precise evaluations of soil liquefaction potential. The SVM-FF model showed high accuracy in predicting e/qd with R² values of 0.999 and 0.998 and low RMSE values of 0.332 and 0.452 in the training and testing stages, respectively, achieving the highest score of 66. This was followed by the SVM-PSO model, which also showed high accuracy in predicting e/qd with R² values of 0.999 and 0.989 and low RMSE values of 0.220 and 1.082 in the training and testing stages, respectively, achieving a score of 63. The SVM-GA model, being the poorest performer, still had an R² value above 0.83 in both the training and testing phases with a score of 21, whereas the SVM-GWO model showed good predicting capability, obtaining R2 above 0.98 in both the training and testing phases, obtaining a score of 39.

Figure 13 shows the actual and predicted scatter plots, where the orange dot represents the actual value, and the green dot represents the predicted e/qd values. Figure 14 illustrates the error graph of the prediction models, where the green triangle represents the training dataset and the orange square represents the testing dataset. From Figures 13, 14, the SVM-FA and SVM-PSO models have the best accuracy because of the presence of 95% of the dataset in the ideal line and an error of less than 30%.

Figure 15 presents a detailed evaluation of the general performance of the model using the Pearson correlation coefficient (R), standard deviation (SD), and root mean square error (RMSE) measurements. The Taylor diagram included information from the training and testing datasets. Evaluating the effectiveness of the model is simpler compared to the benchmarks of R = 1 and RMSE = 0. During both the training and testing stages, the proposed models accurately predicted the actual value (e/qd), as shown in Figure 15. Throughout both stages, the SVM-PSO model excels significantly, approaching the reference point near the red square. To validate the performance improvements of the hybrid models, we conducted a paired t-test. This test evaluates whether the observed differences in key performance metrics, such as R², RMSE, and MAE, are statistically significant. The paired t-test was used to determine whether the mean difference between the performances of the two models was significantly different from zero. The relationship for the paired t-test is shown in Equation 21 t = d ¯ s d n (21)

Where:

d ¯ is the mean of the differences between paired observations (e.g., the RMSE values of the two models), s d is the standard deviation of the differences, and n is the number of paired observations.

We applied the test to the performance metrics of each model across the same datasets with a significance level of 0.05. If the resulting p-value is less than 0.05, we reject the null hypothesis and conclude that the performance improvement of the hybrid models over the standalone models is statistically significant. The results show that for key metrics, such as RMSE and R², the improvements in the hybrid models (e.g., SVM-PSO and SVM-FF) are statistically significant compared to the standalone models, confirming the superiority of the hybrid models in liquefaction risk prediction.

This statistical analysis reinforces the validity of the enhanced performance of the hybrid models.

This demonstrates how the model’s forecasting accuracy validates its potential for accurately predicting e/qd in real-world applications. However, the study’s dataset, while comprehensive for the specific region and soil type analyzed, may not adequately represent soil variability across diverse locations, potentially limiting the model’s applicability in substantially different conditions. The generalizability of the model across regions and soil profiles necessitates further validation with more heterogeneous datasets. Uncertainties in the DCPT data, the primary input, may introduce variability that affects the predictive accuracy. Despite measures to mitigate overfitting, the relatively limited dataset size presents a potential risk, necessitating additional validation on larger and more diverse datasets to ensure robustness and scalability.

In conclusion, this study not only contributes to the evolving landscape of liquefaction potential assessment, but also bridges the gap between field testing and advanced computational techniques. The integration of these advanced computational models with DCPT data, specifically the e/qd ratio (rate of penetration to cone resistance), represents a significant advancement. The DCPT, known for its rapidity, cost-effectiveness, and versatility across soil types (Rollins et al., 2021), provides a practical and efficient field-testing method. The e/qd ratio, when exceeding a threshold of 4, signifies a high likelihood of liquefaction and offers a quick and reliable assessment tool.

The computational efficiency of the models was evaluated by assessing the mean training duration and resource utilization across multiple trials. Table 9 presents the average training time (in min) and memory consumption (in GB) for each ML model.

As shown in Table 1, the SVM-PSO model demonstrated low memory and CPU usage, proving its efficiency in real-time applications. While models such as SVM-GA and SVM-FA require marginally more training time, their resource consumption remains within acceptable bounds and is suitable for deployment in resource-limited environments such as in-field devices or real-time monitoring systems.

In addition to resource utilization, we evaluated the temporal requirements of each model to process the novel data inputs after training. Figure 16 shows the prediction duration (in seconds) for each model when processing the new DCPT data points. This demonstrates that the prediction time for all models was less than 15 s, which underscores their capacity for real-time analysis. This capability is particularly significant for applications, such as post-earthquake site assessments, where rapid and accurate predictions of liquefaction susceptibility are essential.

The integration of these ML models with DCPT data presents a streamlined approach for liquefaction assessment. In contrast to traditional methods, which may require labor-intensive and time-consuming data collection and processing, DCPT provides real-time data inputs that can be immediately analyzed by ML models. This renders the proposed methodology particularly valuable in field scenarios in which real-time risk assessment is crucial. The combination of efficient processing times and low resource consumption renders these machine-learning models suitable for deployment in both real-time and near-real-time geotechnical applications. Their capacity for integration with lightweight hardware systems further enhances their applicability to real-world engineering projects.