Examination of Determinants and Predictive Modeling of Artificially Frozen Soil Strength Utilizing the XGBoost Algorithm

Abstract

A freezing method is usually employed in the construction of metro links. Unconfined compressive strength (UCS) is a pivotal mechanical parameter in freezing design. Due to the limitations of indoor experiments and the complexity of influencing factors, the applicability of empirical strength formulas is poor. This study predicts the strength of frozen soil with different particle size distributions based on the highly integrated XGBoost algorithm. Compared with other empirical formula methods, the accuracy is high. Through the analysis of Pearson’s correlation coefficient results, further analysis is needed on the nonlinear correlation between the temperature, the strain rate, and the unconfined compressive strength of frozen soil. The results indicated a strong negative correlation between temperature and unconfined compressive strength; the strength initially increased at a faster rate, slowed down during the intermediate phase, and again increased at a faster rate toward the end. There was a positive correlation between the strain rate and the unconfined compressive strength, with the strength exhibiting varying sensitivities to different sizes of strain rates. When the strain rate was relatively small, the strength increased slightly; as the strain rate increased, the strength increased more significantly. Different soils showed similar trends, but differences in the particle size distribution resulted in variations in the final strength. This study can provide a scientific basis for predicting the strength of soil bodies in the freeze–thaw construction of subway connection tunnels.

1. Introduction

Saturated permafrost is primarily composed of a solid soil matrix, unfrozen water, and ice, resulting in significant differences in physical properties compared with conventional soils. The artificial freezing method utilizes refrigeration technology to transform regular soil into permafrost, effectively isolating groundwater from underground structures. This technique has found wide application in the construction of underground passages and tunnels [1,2,3]. Simultaneously, numerous infrastructure projects are underway in permanently frozen soil regions [4,5,6]. Accidents resulting from insufficient freezing strength have occurred frequently during engineering construction, drawing considerable attention from scholars [7]. Unconfined compressive strength (UCS), as a vital indicator reflecting the physical-mechanical properties of soil in engineering, finds extensive application across various fields [8,9,10]. It commonly serves as a basis for studying the reinforcement level of soil after freezing.

Numerous scholars have conducted indoor experiments on the unconfined compressive strength of frozen soil. Jiang Zihua [11] and others studied the variation in the uniaxial compressive strength of remodeled frozen soil under different sand contents and moisture levels, but they overlooked the influence of temperature on strength. Wang et al. [12] conducted experiments on the unconfined compressive strength of different types of in situ frozen soil, considering various soils. Yang et al. [13] investigated the impact of high moisture content on the mechanical properties of frozen silty soil. Bai et al. [14] conducted a series of repetitive unilateral freezing tests on an unsaturated silty clay soil under uniform initial and boundary conditions to reveal changes in temperature, moisture content, and freezing expansion. More researchers have focused on studying the influence of external factors on the unconfined compressive strength of frozen soil. Among these factors, temperature is the most crucial determinant of the unfrozen water content, significantly affecting the degree of soil freezing [15,16]. Ma Qinyong [17], based on the experimental results of uniaxial compressive strength of remodeled frozen soil, concluded that the unconfined compressive strength of frozen soil increases with decreasing temperature. However, limited by experimental conditions, more results under different temperatures were not provided. Li Haipeng et al. [18] studied the trend of strength changes with different temperatures for saturated frozen clay at different dry densities and constant strain rates, deriving empirical formulas. However, the complexity of the formulas arises from the consideration of different parameters for different soil categories. Du et al. [19] investigated the strength characteristics of frozen sandy silt under different strain loading rates. Chen Xin et al. [20] further explored the influence of loading rate on the strength of frozen improved soil, taking into account variations in particle size. The strain loading rate also has a significant impact on strength [21,22], with varying loading rates used in experimental studies by different researchers [23,24], resulting in noticeable differences in test results. Therefore, it is essential to involve strain rates and other factors collectively in the data analysis process across different studies.

In previous studies, numerous empirical formulas for permafrost strength have been derived; however, these formulas are limited to specific experimental soils, and the extrapolation capability of empirical formulas has not been thoroughly investigated. There is a lack of universality in the study of permafrost strength characteristics. The extreme gradient boosting (XGB) algorithm [25], based on gradient boosting trees, is renowned for its high predictive accuracy and strong generalization capabilities. It has been widely applied in various domains, including land subsidence [26,27], soil strength [28,29], and slope stability [30,31]. This study, by collecting a substantial amount of existing research data, employed the XGB algorithm to establish a predictive model for the unconfined compressive strength of frozen soil. The application of this model in data analysis explored the relationship between the unconfined compressive strength of frozen soil under different particle size distributions and temperature and strain rates, yielding insights into strength properties applicable to common permafrost.

2. Data Preprocessing

2.1. Data Preprocessing

In this investigation, a comprehensive database was constructed by compiling soil physical properties and unconfined compressive strength test data from the relevant literature sources [12,17,23,32,33,34,35]. These data are not randomly generated but rather obtained from rigorous experimental processes, ensuring the accuracy and reliability of the information. During the data collection process, with the unconfined compressive strength of frozen soil as the core physical indicator, the literature related to temperature variations and strain rates was gathered, and the raw data along with environmental information were documented. Utilizing these data for further analysis can lead to more reliable results. The collected data were utilized to develop a strength prediction model using the XGB algorithm.

If the extraction of data from images using Origin software (2018C SR1 Version) is required, it is crucial to select clearly discernible data points to minimize potential errors during the data extraction process. The key factors taken into account for the strength prediction model development based on the XGB algorithm included the grain size distribution, dry density, initial moisture content, temperature, and strain loading rate.

To ensure a high prediction accuracy and generalization ability of the XGB prediction model, preprocessing of the parameters was necessary. A total of 487 datasets were compiled from the results of unconfined compressive strength tests reported in the literature [12,17,18,23,32,33,34,35,36,37,38,39]. Since the XGB algorithm utilizes gradient descent to search for the optimal solution, it can face difficulties in convergence when there is a significant difference in magnitude among different input variables. To address this issue, the data were standardized. Normalization helps eliminate scale differences between features, ensuring that the model’s impact on each feature is relatively balanced and facilitating faster convergence of the algorithm [40]. Standardization transformed the data into a normal distribution with a mean of 0 and a standard deviation of 1, as represented by Equation (1).

The purpose of dividing the dataset into training and testing sets was to assess the model’s performance on unseen data. The training set was utilized for training the model parameters, while the testing set was employed to evaluate the model’s ability to generalize to new data, i.e., whether the model could effectively adapt to unseen samples. The choice of the partition ratio involved a trade-off. If the training set was too small, the model may not learn sufficiently complex patterns, leading to underfitting. Conversely, if the testing set was too small, the evaluation results may lack reliability. In common practice, a widely accepted and used partition ratio for machine learning is 70% for training and 30% for testing. Therefore, this widely agreed-upon ratio was adopted in this paper as well. A random selection of 70% of the samples (341 groups) was used for training, while 30% (146 groups) were used for testing. The overall distribution of the data is illustrated in

Table 1. Data distribution for the XGB model.

Input Variable	Minimum Value	Maximum Value	Average Value
Moisture content (%)	10.48	51.2	29.98
Dry density (g·cm−3)	1.02	2.08	1.49
Temperature (°C)	−0.5	−25	−7.15
Strain rate (s−1)	1.05 × 10−7	0.07	-
Sand content (%)	0	90	-
Powder content (%)	5	94.66	-
Sticky grain content (%)	3.43	89.5	-

.

$$x\prime =\frac{x-\mu }{\sigma }$$

(1)

where x is the sample value, µ is the sample mean, and σ is the sample standard deviation.

2.2. The XGB Algorithm

2.2.1. Principle of XGB

The gradient boosted decision tree (GBDT) algorithm employs gradient descent to iteratively create new trees, aiming to minimize the objective function [41]. The XGB algorithm is derived from GBDT and is widely applied to classification and regression tasks. It is a potent machine learning algorithm, characterized by notable advantages such as high predictive performance, robust modeling capabilities for complex relationships, and excellent performance on large-scale datasets [42,43,44].

XGB possesses an inherent advantage over models like neural networks in terms of mitigating overfitting. This advantage stems from the algorithm’s built-in regularization terms and pruning mechanisms, allowing for effective control of model complexity. This characteristic makes XGB particularly adept at handling relatively small datasets or situations with high data noise, contributing to its widespread adoption in various practical applications. By incorporating regression trees, the model continuously learns feature partitions for the data at each internal node. It generates a new classification and regression tree (CART) based on the residuals of the previous model, keeps track of the total number of trees in the training model, and assigns weights to the predictions from each tree to obtain the final prediction value. In this study, Python 3.9 was utilized to construct the XGB model for data training.

As an integrated algorithm, XGB combines multiple weak learners to produce the final learning outcome. During the processing of the objective function, a regularization term is introduced to decrease the model’s variance and prevent overfitting. Additionally, XGB employs a second-order Taylor expansion to enhance the convergence speed and improve the prediction accuracy. The predicted value for the i-th sample at the t-th iteration is given by the following equation:

$${\widehat{y}}_i^{(t)}={\widehat{y}}_i^{(t-1)}+f_t(x_i)$$

(2)

where ${\widehat{y}}_i^{(t)}$ is the predicted value of sample i after the t-th iteration, ${\widehat{y}}_i^{(t-1)}$ is the predicted value of the t−1st tree, $f_t(x_i)$ is the model of the t-th tree, and x_i is the input value.

The XGB objective function form is shown in Equation (3):

$$O\mathrm{b}{j}^{(t)}={\displaystyle \sum _{i=1}^{\mathrm{n}}l(y_i,{\widehat{y}}_i^{(t)})+\mathsf{\Omega }(f_t)+c}$$

(3)

where $l(y_i,{\widehat{y}}_i^{(t)})$ is the loss function of the model, y_i is the true value of the i-th sample, n is the total number of samples, $\mathsf{\Omega }\left(f_t\right)$ is the regularization term, and c is a constant term. The specific form of the regularization term is

$$\mathsf{\Omega }(f_t)=\gamma T+\frac{1}{2}\lambda ||\omega |{|}^2$$

(4)

where γ and λ are penalty coefficients, T is the number of leaves, and ω is the weight of the leaf node.

The second-order Taylor approximation is expanded for the objective function, omitting higher-order infinitesimal and constant terms:

$$O\mathrm{b}{j}^{(t)}={\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}[l(y_i,{\widehat{y}}_i^{(t)})+g_i{f}_t(x_i)+\frac{1}{2}{h}_i{f}_t^2(x_i\left)\right]}+\mathsf{\Omega }(f_t)+c$$

(5)

where g_i and h_i are Taylor expansion constant terms.

The simplified objective function is obtained by removing the constant term for the t-th round of iterations:

$$O\mathrm{b}{j}^{(t)}={\displaystyle \sum _{i=1}^{\mathrm{n}}[g_i{f}_t(x_i)+\frac{1}{2}{h}_i{f}_t^2(x_i\left)\right]}+\gamma T+\frac{1}{2}\lambda {\displaystyle \sum _{j=1}^T{\omega }_j^2}$$

(6)

Simplify the objective function by making $H_j={\displaystyle {\sum }_{i\in I_j}{h}_i}$ and $G_j={\displaystyle {\sum }_{i\in I_j}{g}_i}$:

$$O\mathrm{b}{j}^{(t)}={\displaystyle \sum _{i=1}^{\mathrm{n}}[G_i{f}_t(x_i)+\frac{1}{2}(H_i+\lambda ){\omega }_j^2]}+\gamma T$$

(7)

The optimal objective function is obtained as shown in Equation (8):

$$O\mathrm{b}j=-\frac{1}{2}{\displaystyle \sum _{j=1}^T\frac{G_j^2}{H_j+\lambda }}+\gamma T$$

(8)

2.2.2. Ten-Fold Cross-Validation Parameter Tuning

The XGB algorithm does not rely on predefined relationships between input and output variables The specificity of hyperparameters lies in the fact that they are not learned from data but require experience and experimentation to determine the optimal values. Their importance is evident in the fact that selecting appropriate hyperparameters can significantly enhance model performance, influencing both the model’s generalization ability and training effectiveness. Hyperparameter tuning is a crucial task in machine learning and is essential for constructing effective models. Therefore, it is essential to tune these hyperparameters [45,46,47]. The hyperparameters associated with the XGB algorithm are presented in

Table 2. Hyperparameters of XGB algorithm.

Hyperparameterization	Meaning of Parameter	Parameter Tuning Range
learning_rate	Learning rate	0.01, 0.05, 0.07, 0.1, 0.2
n_estimators	Optimal number of iterations	[100,1000]
max_depth	Maximum depth of the tree	3, 4, 5, 6, 7, 8, 9, 10
min_child_weight	The minimum sum of weights of the child nodes generated from the sample	1, 2, 3, 4, 5, 6
subsample	Sample proportion for each tree	0.5, 0.6, 0.7, 0.8, 0.9, 1
colsample_bytree	The ratio of features randomly selected for each tree	0.5, 0.6, 0.7, 0.8, 0.9, 1
gamma	The reduction ratio of the loss function	0.1, 0.2, 0.3, 0.4, 0.5, 0.6
reg_alpha	Weights for L1 regularization	0.05, 0.1, 1, 2, 3
reg_lambda	Weights for L2 regularization	0.05, 0.1, 1, 2, 3

.

For hyperparameter tuning, 10-fold cross-validation is commonly employed as a statistical method to assess the model’s generalization ability [48,49]. According to the theory of 10-fold cross-validation, the training set is divided into ten parts, with nine parts used as the test data and one part as the validation data in each iteration. The results of 10-fold cross-validation are more robust compared with the randomness of data partitioning. Since each data point appears in different rounds of model selection, the final performance evaluation is more statistically meaningful. By adjusting hyperparameters in each iteration of cross-validation and selecting the best-performing ones, it is more efficient to find the parameter configuration that optimizes the model’s performance. To evaluate the XGB algorithm’s performance in predicting the unconfined compressive strength of the training set under different parameter combinations, various hyperparameters were introduced, and the 10-fold cross-validation method was applied. The optimal parameter was selected based on the performance observed during cross-validation. Figure 1 illustrates the 10-fold cross-validation method, and

Table 3. Hyperparameter tuning results.

Hyperparameterization	Optimal Results
learning_rate	0.1
n_estimators	225
max_depth	10
min_child_weight	4
Subsample	0.5
colsample_bytree	0.9
Gamma	0.3
reg_alpha	0.02
reg_lambda	0.9

presents the results of hyperparameter tuning.

3. Results of Model Predictions

3.1. Evaluation Indicators

Using the optimal hyperparameters identified through the 10-fold cross-validation, the model was applied to the test set to assess its accuracy and generalization ability. The process of predicting the unconfined compressive strength using the XGB algorithm is illustrated in Figure 2. The evaluation of the model’s prediction accuracy was based on the mean square error (MSE) and coefficient of determination (R²). MSE measures the average squared error between the model’s predicted values and the actual observed values, serving as an indicator of the model’s prediction accuracy. On the other hand, R² quantifies the extent to which the model explains the variance of the target variable, representing the model’s ability to fit the data’s variability.

3.2. Projected Results

Figure 3a displays the results of predicting the unconfined compressive strength of permafrost. The test set exhibited a mean square error (MSE) of 0.39 and a coefficient of determination (R²) of 0.962. These results indicated that the model demonstrated high prediction accuracy and could be effectively utilized for predicting the unconfined compressive strength of permafrost. The scatter plot in Figure 3b illustrates the relationship between the experimental and predicted values. It can be observed that a significant number of experimental results fell within the range of 0~8 MPa, and the model exhibited high prediction accuracy within this range. However, the number of samples exceeding 8 MPa was noticeably limited, resulting in reduced prediction accuracy for values beyond this range. The empirical formulas used for strength prediction under various working conditions often involve significant parameter variations and high complexity. In contrast, the strength model based on the XGB algorithm offered high prediction accuracy. By inputting the relevant parameters, it enabled the estimation of the unconfined compressive strength of permafrost. Moreover, this model exhibited strong generalization capabilities and offered a simplified approach.

4. Discussion

The Pearson correlation coefficient is employed to measure the linear relationship between two variables. Numerically, a correlation coefficient closer to 1 or −1 indicates a stronger linear correlation, while proximity to 0 suggests a weaker correlation. This holds significant implications for under-standing the interdependence, trends, and mutual influences among variables.

The Pearson correlation coefficient was applied to measure the variable correlation. The principle of calculation is shown in Equation (9), and the results are shown in Figure 4. The Pearson correlation coefficient between the temperature and unconfined compressive strength of permafrost was −0.590, while the Pearson correlation coefficient between the strain rate and unconfined compressive strength was 0.370. According to the Pearson correlation coefficient correlation standards, the temperature and strength exhibited a moderately linear correlation, potentially indicating a negative linear relationship due to the negative coefficient. The strain rate and strength showed a weak correlation, suggesting a relatively weak positive correlation between the strain rate and strength, necessitating further assessment of their relationship based on predictions from the XGB model.

$$Pearson=\frac{{\displaystyle {\sum }_{i=1}^n(x_i-\overline{x})}(y_i-\overline{y})}{\sqrt{{{\displaystyle {\sum }_{i=1}^n(x_i-\overline{x})}}^2}\sqrt{{{\displaystyle {\sum }_{i=1}^n(y_i-\overline{y})}}^2}}$$

(9)

where x_i and y_i are the input and output values of the i-th sample, $\overline{x}$ and $\overline{y}$ are the input and output averages of the overall sample, respectively.

To explore the impact of temperature and strain rate on the variation in unconfined compressive strength in clay, pulverized soil, and sandy soil, a dataset was created due to the limited availability of experimental data. This dataset was based on common soil physical properties and experimental conditions that resembled actual working conditions. Additionally, the study aimed to analyze the strength differences among clay, silt, and sand after freezing. The soil particle size distribution was represented as the relative content percentage of particles, as outlined in

Table 4. Values of different variables in the new dataset.

Input Variable	Minimum Value	Maximum Value	Value Range
Moisture content (%)	10.48	51.2	10, 20, 30, 40, 50
Dry density (g·cm−3)	1.02	2.08	1.1, 1.3, 1.5, 1.7, 1.9
Temperature (°C)	−0.5	−25	−2, −4, −8, 12, −16, −20
Strain rate (s−1)	1.05 × 10−7	0.07	10−5, 10−4, 10−3, 10−2
Sand (%)	-	-	Sand particles: 90%, silt particles: 5%, clay particles: 5%
Silt (%)	-	-	Sand particles: 5%, silt particles: 87%, clay particles: 8%
Clay (%)	-	-	Sand particles: 5%, silt particles: 5%, clay particles: 90%

.

A new dataset (2160 sets) was finally obtained. The XGB model was used to predict the magnitude of the unconfined compressive strength. The trends of strength with temperature and strain rate were analyzed for different permafrosts; the results for strength with temperature are shown in Figure 5, and the results for strength with strain rate are shown in Figure 6.

From Figure 5, it can be observed that the unconfined compressive strength of the three types of frozen soil exhibited a similar trend, increasing with decreasing temperature and increasing strain rate. The most rapid increase in unconfined compressive strength occurred within the S1 and S3 ranges, while the strength increase was relatively gradual during the S2 stage. In the temperature range of −2 to −4 °C (S1), the soil reached the freezing point of free water, leading to rapid freezing of the free water and consequently a significant increase in strength. In the temperature range of −4 to −16 °C (S2), the linear relationship between strength and temperature weakened. However, in the range of −16 to −20 °C (S3), the strength experienced a substantial increase due to the complete freezing of weakly bound water within the pores. When considering strain rates between 10⁻⁵ s⁻¹ and 10⁻⁴ s⁻¹, as well as between 10⁻³ s⁻¹ and 10⁻² s⁻¹, the strength values exhibited similar levels with only minor increments. During this stage, the dominant factor influencing the strength was the strain rate, where higher strain rates led to increased soil density and higher unconfined compressive strength. When the temperature dropped below −20 °C, it further affected the freezing process of strongly bound water within the soil body. However, due to the limited range of experimental data, the influence of strongly bound water on the strength of frozen soil was not taken into consideration. Consequently, the unconfined compressive strength exhibited a substantial growth rate in the initial period, a moderate growth rate in the intermediate period, and a significant growth rate in the later period as the temperature decreased. This finding aligned with the research conducted by Du et al. [19] and Zhang et al. [50], confirming the generalizability of the model. Comparing the three different permafrost soils, pulverized soils exhibited the highest overall strength, followed by clays and sands. Fine-grained soils, such as clay and silt, contained a higher proportion of weakly bound water. As the temperature decreased, more weakly bound water froze, leading to increased soil cohesion and higher strength. However, the strongly bound water remained unfrozen but enveloped the soil particles, maintaining its ice cementation capacity. On the other hand, coarse-grained soils, represented by sandy soils, possessed a monogranular structure characterized by low densities and large interparticle pores. This weakened the ice cementation ability after the freezing of unfrozen water. Additionally, a significant amount of pore water remained unfrozen in these soils, resulting in an overall lower strength. The bonding pattern is illustrated in Figure 7.

As depicted in Figure 6, the unconfined compressive strength of three permafrost types increased with an increase in the strain rate. The strength exhibited varying degrees of sensitivity to different strain rates, demonstrating stronger sensitivity within the S2 strain rate range, while exhibiting relatively minor variations within the S1 and S3 rate intervals. At a small strain rate (S1), although there was an increase in compressive strength, the overall increment was modest, indicating low sensitivity. Conversely, when the strain rate increased from 10⁻⁴ s⁻¹ to 10⁻³ s⁻¹ (S2), the rise in the compressive strength became significant. Moreover, the lower the temperature was, the more pronounced the increase and the higher the sensitivity. Consequently, the unconfined compressive strength of permafrost was higher at elevated strain rates and lower temperatures. It is important to note that at a temperature of −20 °C, there was a tendency for the rate of strength increase to diminish when the strain rate increased from 10⁻³ s⁻¹ to 10⁻² s⁻¹ (S3). This change could likely be attributed to the freezing of all free and weakly bonded water within the soil, resulting in a decrease in unfrozen water within the pore space of the densely compacted soil. As a result, the magnitude of the strength increase diminished.

Earlier studies mostly focused on the physical properties of some single permafrost, this study was conducted by collecting a wide range of different data and analyzing them using XGB. A broader understanding of the strength properties of permafrost can be obtained through big data analysis. However, due to the prevalent lack of interpretability in machine learning, it fails to intuitively illustrate underlying physical mechanisms. Future research endeavors could overcome the limitations of purely data-driven methods by integrating physical information into computational models, such as employing physical information as constraints in data processing. This integration would aid in bridging the gap between data-driven methodologies and physical insights, enhancing the interpretability of the models used in permafrost analysis.

5. Conclusions

With the increasing prevalence of frozen soil engineering, there is a growing need for a more profound understanding of the key factor of unfrozen compressive strength in frozen soils. Previous research on frozen soil strength has largely been confined to individual soil types, characterized by limited sample sizes and a lack of generalized studies on the strength properties of frozen soil. This study focused on remodeled permafrost as the research subject and employed a machine learning approach to develop a prediction model for unconfined compressive strength using the XGB algorithm. By incorporating the Pearson correlation coefficient, the most influential factors affecting the strength were identified. Additionally, a new dataset was created to investigate the relationship between strength, temperature, and strain rate.

In comparison with previous unconfined compressive strength characteristic tests on individual soil samples, this study, leveraging a large dataset, obtained results that were more representative and comprehensive. The following conclusions can be drawn from this study:

• The XGB-based prediction model for unconfined compressive strength demonstrated a high level of accuracy in the test set, with a mean squared error (MSE) of 0.39 and a coefficient of determination (R²) of 0.962. This predictive model contributes to assessing the strength characteristics crucial for engineering design, infrastructure development, and mitigating potential hazards in permafrost regions, thereby aiding in informed decision-making and ensuring the safety and sustainability of various constructions and activities in these environments.
• The Pearson correlation coefficient was employed to quantify the strength and direction of the relationship between variables. The Pearson correlation coefficient between the temperature and unconfined compressive strength of permafrost was −0.590. For the strain rate and unconfined compressive strength, the Pearson correlation coefficient was 0.370. The analysis indicated a moderate negative relationship between the temperature and permafrost strength and a weak positive relationship between the strain rate and permafrost strength. Utilizing the XGB model provides a more precise representation of such correlations.
• The unconfined compressive strength of frozen silt is the highest, followed by frozen clay and frozen sand. The reason may be that the content of weak bound water in the fine-grained soil represented by clay and silt was higher, and the weak bound water froze, increasing the cohesion of the soil and obtaining higher strength. Coarse-grained soil, represented by sandy soil, presented a single-grain structure, which weakened the ice cementation ability after freezing by unfrozen water, resulting in a low overall strength.
• Temperature exerted a substantial influence on the unconfined compressive strength of permafrost. As the temperature decreased, the strength of permafrost exhibited a noticeable upward trend. In the early stages of freezing (−2 to −4 °C), the strength of the soil experienced a rapid increase due to the freezing of free water within the soil. Subsequently, the growth tendency became relatively stable. In engineering, the adequate strength of frozen soil can be ensured by controlling temperature, thereby mitigating the risk of accidents caused by insufficient strength.
• The loading rate applied during testing significantly impacted the unconfined compressive strength of frozen soil. A clear increasing trend was observed as the strain rate rose. The sensitivity of the compressive strength to the strain rate was relatively low within the range of 10⁻⁵~10⁻⁴ s⁻¹, while it became more pronounced within the range of 10⁻⁴~10⁻² s⁻¹. Therefore, in the design and implementation of engineering projects, the consideration of strain rate has become one of the crucial factors in ensuring the stability of frozen soil structures. When formulating engineering plans, it is essential to control the strain rate to meet the requirements of diverse environmental and loading conditions.

Utilizing a large volume of data for permafrost property prediction and analysis allows for the identification of more generalized features. However, the data collected in this experiment remain limited. While the results of this study demonstrate good performance in common soils, they are still subject to limitations, particularly in the case of diverse soil types where the effectiveness may be suboptimal. Furthermore, this entirely data-dependent analytical approach has room for optimization. XGB, as a black-box model, exhibits relatively weak interpretability, a common challenge in machine learning. Despite the outstanding predictive performance of the XGB algorithm, enhancing model interpretability is crucial for understanding the underlying mechanisms of predicted outcomes in practical applications. Therefore, future research could focus on improving the interpretability of the XGB model, considering the incorporation of physical information into the computational model to overcome the limitations of purely data-driven methods.