Yield Stress Prediction of Filling Slurry Based on Rheological Experiments and Machine Learning

Abstract

Cemented filling technology is an effective approach to solving tailings accumulation and goaf, with rheological properties serving as key indicators of slurry fluidity. Since slurry rheology is influenced by multiple factors, accurate prediction of its parameters is essential for optimizing filling design. In this study, we developed a model to predict static and dynamic yield stress using the extreme gradient boosting (XGBoost) algorithm, trained on 140 experimental samples (105 for training and 35 for validation, split 75:25). For comparison, adaptive boosting tree (ADBT), gradient boosting decision tree (GBDT), and random forest (RF) algorithms were also applied. Model performance was evaluated using four metrics: coefficient of determination (R²), mean absolute error (MAE), root mean square error (RMSE), and explained variance score (EVS). The Shapley additive explanation (SHAP) method was employed to interpret model outputs. The results show that XGBoost achieved superior predictive accuracy for slurry yield stress compared with other models. Analysis of importance revealed that underflow concentration had the strongest influence on predictions, followed by the binder-to-tailings ratio, while the fine-to-coarse tailings ratio contributed least. These findings highlight the potential of machine learning as a powerful tool for modeling the rheological parameters of filling slurry, offering valuable guidance for engineering applications.

1. Introduction

With the advancement of science and technology and the growing demand for mineral resources, global iron ore consumption has continued to increase [1]. As ore grades decline, enhanced recovery processes generate large volumes of fine tailings, whose long-term accumulation poses serious environmental and safety risks. These risks include geological hazards such as mudslides, groundwater contamination from heavy metals, and ecological degradation [2,3,4]. For example, the 2019 Brumadinho dam failure in Brazil resulted in 270 fatalities and severe river pollution [5]. In China, remediation of a vast number of tailings ponds has been identified as an urgent priority, as highlighted in the 2022 MIIT guidelines [6]. Such documented impacts underscore the need for innovative tailings management strategies.

Cemented filling technology provides an effective means of reusing tailings by transporting them underground to fill mined-out voids, thereby achieving the dual goal of waste disposal and ground support [7,8,9,10]. The process typically involves three steps: (1) thickening low-concentration tailings slurry to produce a high-concentration slurry, (2) preparing the filling slurry by mixing this concentrate with coarse aggregates, binders, and additives, and (3) transporting the slurry to the stope either by gravity or pumping [11,12]. Among these, the mixing stage is critical. A well-prepared slurry not only ensures good flowability but also produces a filling body with high compressive strength. Rheological parameters serve as macroscopic indicators of the slurry’s microstructural behavior and thus provide an essential basis for optimizing the mixing process [13,14,15].

Dynamic and static yield stress are two fundamental parameters that characterize the rheological behavior of filling slurries [16,17]. However, slurry rheology is influenced by many factors, and experimental observations are often case-specific, limiting their applicability across different tailings sources. Moreover, direct measurement of rheological parameters is both costly and time-consuming, making it difficult to integrate rheological testing into large-scale mining operations. Consequently, predictive approaches are vital for enabling practical applications of slurry rheology in cemented filling technology.

In recent years, predictive models have been increasingly applied to estimate the rheological and mechanical properties of filling slurries [18,19,20,21]. Since slurry properties are strongly dependent on material composition, conventional mathematical models are often restricted to specific material systems. Given the limited availability of experimental datasets, machine learning offers a promising alternative, capable of improving predictive accuracy and generalization. Previous studies have successfully linked unconfined compressive strength to mix composition [22,23,24] and established models mapping slurry composition to slump and compressive strength [25]. Various machine learning methods—including artificial neural networks, support vector machines, and random forests—have proven effective for such predictions [26,27,28,29]. For instance, Gomaa et al. [30] used random forests to predict the slump and compressive strength of fly ash-based concrete, while Nehdi and Al Martini [31] applied genetic algorithms to model the relationship between shear strain and shear stress in cement paste under different temperatures and shear conditions. Ensemble learning approaches, which integrate multiple models to leverage their complementary strengths, have further enhanced predictive accuracy. For example, Nguyen et al. [32] developed a hybrid model based on least squares support vector machines and particle swarm optimization to predict interface yield stress and plastic viscosity in concrete.

Among ensemble methods, extreme gradient boosting (XGBoost), proposed by Chen, has emerged as a particularly powerful tool [33]. XGBoost combines high computational efficiency with improved predictive accuracy [34,35].

This study develops an XGBoost-based predictive model for static and dynamic yield stress, trained on experimental data from 140 samples. The selected input features include underflow concentration, binder-to-tailings ratio, and fine-to-coarse tailings ratio, while the outputs are static and dynamic yield stresses. This study first describes the rheological experiments, then presents the machine learning methodology, compares XGBoost to alternative algorithms, and finally interprets the results using the Shapley additive explanation (SHAP) method. The framework of the XGBoost model is shown in Figure 1.

2. Experiments and Results

2.1. Materials and Experimental Procedures

The tailings used in this study were collected from an iron mine in China, and the binder was a specially formulated anhydrous gypsum cement. The filling slurry was prepared from fine tailings, coarse tailings, binder, and water. Prior to testing, the tailings were dried, cleaned, and crushed. The fine tailings were generated by a ball mill in a concentrator, while the coarse tailings were collected as the underflow from spiral classification.

The particle size distributions of the fine tailings and binder were analyzed using a laser particle size analyzer (Malvern Panalytical, Mastersizer 3000, Malvern Panalytical Ltd., Malvern, UK), as shown in Figure 2. The median particle size was 13.52 μm for the fine tailings and 11.2 μm for the binder. The particle size distribution of the coarse tailings is presented in

Table 1. Particle size distribution of the coarse tailings.

Particle Size	150–220 μm	220–400 μm	400–500 μm	500–630 μm	630–800 μm	800–1000 μm
Percentage	20.61%	20.52%	8.89%	13.86%	28.18%	7.85%

. The densities were measured using a pycnometer: 2.898 g/cm³ for the tailings and 2.363 g/cm³ for the binder. Distilled water was used in all experiments.

The oxide compositions of the tailings and binder were determined by X-ray fluorescence spectroscopy (Thermo Fisher ARL Perform X4200W, Thermo Fisher Scientific Inc., Waltham, MA, USA) (

Table 2. Chemical composition of the tailings and binder.

Material	Oxide (wt%)
	SiO2	MgO	Fe2O3	Al2O3	CaO	P2O5	K2O	SO3	Others
Tailing	41.25	15.00	12.60	12.03	10.02	3.18	3.11	0.82	1.99
Binders	29.76	5.36	1.43	15.97	37.95	-	0.50	7.2	1.20

). The tailings were rich in SiO₂, followed by MgO, Fe₂O₃, and Al₂O₃, while the binder was primarily composed of CaO, SiO₂, SO₃, and Al₂O₃.

2.2. Experimental Setup

To evaluate the effects of key parameters on slurry rheology, experiments were conducted under varying fine-to-coarse tailings ratios, binder-to-tailings ratios, and underflow concentrations. Based on actual production conditions, the fine-to-coarse tailings ratio was set at four levels (9:1, 10:1, 11:1, and 12:1), and the binders–tailings ratio was set at seven levels (1:4, 1:6, 1:8, 1:10, 1:12, 1:14, and 0). Five levels of underflow concentration (measured in mass fraction) obtained in the thickening stage were set based on different fine-to-coarse tailings ratios. The fine–coarse tailings ratio was calculated as the mass ratio of fine tailings (ball mill output) to coarse tailings (spiral classifier underflow). The experimental conditions were shown in

Table 3. Experimental influencing factors and level settings.

Influence Factors	Experimental Level
Fine–coarse tailings ratio	9:1, 10:1, 11:1, 12:1
Binders–tailings ratio	0, 1:14, 1:12, 1:10, 1:8, 1:6, 1:4
Underflow concentration	Fine–coarse tailings ratio 9:1	49.24%, 51.42%, 53.6%, 55.78%, 57.96%
	Fine–coarse tailings ratio 10:1	48.43%, 49.89%, 51.35%, 52.81%, 54.27%
	Fine–coarse tailings ratio 11:1	45.72%, 48.74%, 51.76%, 54.78%, 57.8%
	Fine–coarse tailings ratio 12:1	46.04%, 48.59%, 51.14%, 53.69%, 56.24%

, and a total of 140 test sets were conducted.

Slurry samples were first mixed manually for 120 s, then transferred to a mechanical mixer and stirred at 65 r/min for an additional 120 s. Homogeneity was defined by the absence of visible agglomerates and variation of less than 5% across three replicate tests. All experiments were conducted at a controlled temperature of 25 ± 1 °C.

Rheological measurements were performed using a Brookfield RST rotary rheometer with a VT80-40 cross-paddle rotor (40 mm diameter, 80 mm height) in a stainless steel cylindrical container (inner diameter 130 mm, height 170 mm). The test program included both static yield stress and dynamic yield stress measurements (Figure 3). Research from Li et al. shows that setting the shear rate at around 0.3 s⁻¹ can ensure that the slurry is not excessively damaged, and the static yield stress of the slurry can be obtained [36]. Therefore, the static yield stress experiment is carried out at a constant shear rate of 0.3 s⁻¹ for 60 s to obtain a shear stress–time curve for the sample, with the static yield stress of the slurry as the peak point of the curve. At the same time, relevant studies have shown that steady-state shear stress under certain shear rate conditions can only be obtained when the slurry is sheared for more than 10 s [37,38]. The dynamic yield stress experiment is performed by decreasing from 80 s⁻¹ to 10 s⁻¹ in steps of 10 s⁻¹, then shearing the slurry at shear rates of 5 s⁻¹ and 1 s⁻¹ for 10 s at each shear rate level to obtain a shear stress–shear rate curve for the sample. The shear rate is not set below 1 s⁻¹, to reduce the influence of unsteady flow on the rheological parameters of filling slurry [39].

2.3. Experimental Results

Figure 4 shows the flow curves of the slurry at a fine-to-coarse tailings ratio of 12:1. Shear stress increased with shear rate, confirming that the slurry behaved as a typical Herschel–Bulkley fluid. The dynamic yield stress was obtained by fitting the descending portion of the shear rate curve. Flow curves for other ratios (9:1, 10:1, 11:1) are provided in the Supplementary Materials.

Three key input features—fine-to-coarse ratio, underflow concentration, and binder-to-tailings ratio—were selected for subsequent modeling. Figure 5 presents the distributions of experimental features and outputs. Both static and dynamic yield stresses exhibited strong correlations with the independent variables. Static yield stress consistently exceeded dynamic yield stress, consistent with theoretical expectations of slurry behavior.

3. Construction and Implementation of the Model

3.1. XGBoost Methodology

The predictive model was developed in Python (Anaconda, version 3.9.7) using the XGBoost algorithm to estimate static and dynamic yield stress. Unlike traditional decision trees, which follow a simple binary structure to arrive at terminal nodes, XGBoost is an ensemble method that integrates a sequence of decision trees. Each tree builds on the errors of the previous ones, progressively improving model accuracy [40].

Assume a dataset with independent variables x_i each with b eigenvalues, where x_i ∈ R^m. Each independent variable corresponds to a dependent variable y_i, where y_i ∈ R. The prediction function of XGBoost can be expressed as

$${\widehat{y}}_i=\gamma (x_i)={\displaystyle \sum _{k=1}^K{f}_k(x_i)}, f_k\in F$$

(1)

where ${\widehat{y}}_i$ is the predicted value, f_k represents the function corresponding to a decision tree, and F is the set of all possible regression trees.

Similar to other machine learning models, the prediction function of the XGBoost model includes a loss function and a canonical term, and the canonical term is respon-sible for measuring the complexity of the model. Equation (2) shows the objective func-tion to predict yield stress:

$$G={\displaystyle \sum _{i}E\left(y_i,{\widehat{y}}_i\right)+}{\displaystyle \sum _{k}H\left(f_k\right)}$$

(2)

The training error of E sample x_i in Equation (2) is the loss function, and the regu-larization term H, the canonical term, is calculated as

$$H\left(f\right)=\gamma T+{\displaystyle \frac{1}{2}}\lambda {{\displaystyle {\sum }_j\omega }}_j^2$$

(3)

where γ is the regular term coefficient for the complexity of each leaf, and T and ω_i represent the number of leaves and the weight of the jth leaf, respectively.

The canonical term avoids overfitting, and the objective function prefers a simple model with predictive power. ${\widehat{y}}_i^t$ in the tth iteration is calculated as

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

(4)

It can be seen that the tth iteration model consists of the t − 1st iteration model and a new sub-model $f_t(x_i)$. Therefore, in order to minimize the objective function G, an approximation method is used to optimize the objective function, and a Taylor second-order expansion of the objective function is obtained as

$$G^{(t)}\cong {\displaystyle \sum _{i=1}^n\left[E(y_i,{\widehat{y}}_i^{(t-1)})+g_i{f}_t(x_i)+\frac{1}{2}{h}_i{f}_t^2(x_i)\right]}+H(f_t)$$

(5)

where $g_i$ is the first-order derivative of $E(y_i,{\widehat{y}}_i^{(t-1)})$ concerning ${\widehat{y}}_i^{(t-1)}$, and $h_i$ is the second-order derivative of $E(y_i,{\widehat{y}}_i^{(t-1)})$ for ${\widehat{y}}_i^{(t-1)}$.

$I_j$ is defined as the set of samples at leaf node j, in which all samples fall on leaf node j. $f_t(x_i)$ divides the sample into leaf nodes and calculates the score ω for that leaf node. When $i\in I_j$, $f_t(x_i)$ can be replaced by ${\omega }_j$. Equation (5) is simplified, and the partial derivative of ${\omega }_j$ is taken, such that the partial derivative is zero. The minimum value of the preferred weight and objective function is

$${\omega }_j^{*}=-{\displaystyle \frac{{\displaystyle \sum _{i\in I_j}{g}_i}}{{\displaystyle \sum _{i\in I_j}{h}_i}+\lambda }}$$

(6)

$$M^{(t)}=-{\displaystyle \frac{1}{2}}{\displaystyle \sum _{j=1}^T\frac{{\left({\displaystyle \sum _{i\in I_j}{g}_i}\right)}^2}{{\displaystyle \sum _{i\in I_j}{h}_i}+\lambda }}+\gamma T$$

(7)

It is impossible to solve the above equations for all possible trees. XGBoost uses a greedy algorithm to obtain a more straightforward formulation. Assuming that I_L and I_R are the sample sets of the left and right child nodes after the split, I denotes the sample set of the node before splitting, where I = I_L ∪ I_R. The formula for the change of the objective function before and after the node split is shown in Equation (8):

$$M_{split}={\displaystyle \frac{1}{2}}\left[{\displaystyle \frac{{\left({\displaystyle \sum _{i\in I_L}{g}_i}\right)}^2}{{\displaystyle \sum _{i\in I_L}{h}_i}+\lambda }}+{\displaystyle \frac{{\left({\displaystyle \sum _{i\in I_R}{g}_i}\right)}^2}{{\displaystyle \sum _{i\in I_R}{h}_i}+\lambda }}-{\displaystyle \frac{{\left({\displaystyle \sum _{i\in I}{g}_i}\right)}^2}{{\displaystyle \sum _{i\in I}{h}_i}+\lambda }}\right]-\gamma$$

(8)

When M_split reaches the maximum, the splitting point is the most excellent splitting point, and the optimal integration model is eventually established after many repetitions.

3.2. Model Evaluation

In supervised learning, the entire dataset needs to be split into two subsets: a training set and a test set. The training set is used for model training and hyperparameter tuning, while the test set is used for performance evaluation. Drawing on relevant research [41], this paper analyzes and optimizes the split dataset. In this paper, 75% (105 samples) of the entire dataset was used as the training set, and the remaining 25% (35 samples) was used as the test set. Four evaluation metrics are selected to assess the adequacy and validity of the XGBoost model, including coefficient of determination (R²), mean absolute error (MAE), root mean square error (RMSE), and explained variance score (EVS), and the definition of each metric is shown in

Table 4. Model performance evaluation indicators.

Indicator	Description	Equation
R2	Describes regression model variance score, with a range of from (0, 1], with larger values indicating higher accuracy of the prediction model	$R^2=1-{\displaystyle \frac{SSE}{SST}}$
MAE	Evaluates how close the predictions are to the true dataset; the smaller the value, the better the fit	$MAE={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n\left|Y{S}_{pi}-Y{S}_{ti}\right|}}{n}}$
RMSE	Explains distribution of forecast errors, with smaller values of RMSE indicating less variation in forecast distribution	$RMSE=\sqrt{{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n{\left(Y{S}_{pi}-Y{S}_{ti}\right)}^2}}{n}}}$
EVS	Defines a model variance score in the range of (0, 1], with larger values being more effective	$EVS=1-{\displaystyle \frac{n\ast SSE-ME}{n\ast SST}}$

Notes: YS_pi is the predicted yield stress value, YS_ti is the true yield stress value, SSE is the sum of squared errors, SST is the sum of total squares, and ME is the mean residual.

. The coefficient of determination (R²) quantifies the proportion of variance explained by the model, with values >0.9 indicating excellent fit. Mean absolute error (MAE) reflects the average magnitude of prediction errors, directly indicating engineering relevance. Root mean square error (RMSE) emphasizes larger errors due to its quadratic weighting, making it a key safety indicator in engineering contexts. Explained variance score (EVS) assesses robustness against input variations, where values > 0.9 confirm model stability under diverse mix designs.

3.3. Hyperparameter Tuning

The predictive accuracy of XGBoost is highly sensitive to hyperparameter settings. To avoid overfitting and maximize performance, systematic parameter optimization was performed. The learning rate “Eta” is an important parameter that can effectively prevent model overfitting and improve model robustness by reducing the weight of each step. The model usually divides nodes when the loss function is greater than 0. The parameter “gamma” gives the loss function required by the model, with larger values of “gamma” making the model more conservative. The parameter “subsample” describes the fraction of training model subsamples in collecting samples. “Colsample_bytree” characterizes the proportion of features that are randomly sampled when building the tree and takes a value between 0 and 1. “Min_child_weight” represents the minimum number of samples needed to construct each model. The parameters “lambda” and “alpha” are the L2 and L1 regularization terms, respectively, which are added to make the model more robust. “Max_depth” is the maximum depth of the tree, indicating the maximum number of splits. Increasing the maximum depth is more likely to lead to overfitting.

Parameter tuning entails giving initial values to some of the parameters and then adjusting the tuning parameters one by one until the model is optimal. The criterion for parameter tuning is based on RMSE minimization. The learning rate is determined at first, which generally fluctuates in the range of 0.05–0.3; for a given learning rate, tuning for specific parameters of the decision tree (e.g., max_depth, min_weight, gamma, subsample, and colsample_bytree) requires large-scale adjustment followed by a small-scale fine-tuning. Based on the above two types of parameters, the regularization parameters are then adjusted to improve the model performance; finally, the learning rate is reduced to complete the tuning of the model parameters.

This study sets the fitness function as RMSE to prevent overfitting, and evolution takes place for 500 generations [42,43]. It can be seen in Figure 6 that RMSE shows a tendency to first decrease faster and then slow down as the number of iterations increases. After repeated iterations, the algorithm converged to the optimal solution after about 300 generations for the dynamic yield test set, and the algorithm converged to the optimal solution after about 400 generations for the static yield stress test set. The training set also converged, indicating that the prediction models are not overfitting. The initial settings and the results from the parameter tuning are listed in

Table 5. Optimized hyperparameter settings.

Parameter Classification	Parameter	Initial Setting	Static Yield Stress Model Results	Dynamic Yield Stress Model Results
Tree booster	Eta	0.05–0.3	0.15	0.16
	Min_child_weight	1	1	1
	Max_depth	[3, 10]	4	5
	Gamma	[0, 0.2]	0.1	0.1
	Subsample	[0.5, 0.9]	0.8	0.72
	Colsample_bytree	[0, 1]	0.76	0.78
	Alpha	1	0	0
	Lambda	1	2	2
Learning Task	Objective	LinearRegression	LinearRegression	LinearRegression
	Eval_metric	RMSE	RMSE	RMSE
Command line	Num_round	500	400	300

.

3.4. Comparison Analysis of Models

To benchmark the performance of XGBoost, its results were compared against adaptive boosting tree (ADBT), gradient boosting decision tree (GBDT), and random forest (RF) models. Among them, ADBT and GBDT are boosting algorithms, while RF represents a bagging-based ensemble approach.

The validation diagrams for the static yield stress and dynamic yield stress prediction models are shown in Figure 7 and Figure 8. The XGBoost model performs better in predicting static and dynamic yield stress. By combining the performance of algorithms in predicting static yield stress with that of dynamic yield stress, the XGBoost model achieves the best prediction performance.

Figure 9 evaluates four machine learning models (XGBoost, ADBT, GBDT, RF) using four metrics for static (a) and dynamic (b) yield stress prediction. R² shows that XGBoost achieves the highest values for both static (0.938) and dynamic (0.935) predictions, explaining >93% of data variability. It can be seen in MAE that ADBT shows the lowest MAE in static prediction (4.239), while XGBoost outperforms ADBT in dynamic prediction (3.115 > 2.962). RMSE shows that XGBoost attains the minimal RMSE in dynamic prediction (4.334) and static prediction (5.623). EVS shows that XGBoost peaks in both categories (static 0.94, dynamic 0.939), confirming robust interpretability for mixed design variations.

To further compare the performance of the four models mentioned above, each is scored based on the results of four indicators. Figure 10 summarizes the scores of models in a stacked graph format. It is shown that XGBoost has the highest score ranking and best performance for both the static and dynamic yield stress prediction models.

4. Results and Discussions

4.1. Effect of a Single Feature on the Yield Stress

The effect of a single feature on the yield stress of the filling slurry is shown in Figure 11. It can be seen that there is a positive correlation between underflow concentration and slurry yield stress, which means that, the higher the underflow concentration, the greater the slurry static yield stress and dynamic yield stress. Notably, as the underflow concentration increased from 55.78% to 57.96%, the static yield stress increased by 80%, and the dynamic yield stress increased by 72%, indicating that the underflow concentration has a significant effect on the slurry yield stress.

Similarly, the binder-to-tailings ratio exhibited a positive correlation with yield stress (Figure 11b). Both static and dynamic yield stress increased with higher binder content, highlighting its strong contribution to rheological behavior.

In contrast, the fine-to-coarse ratio exerted only a minor influence (Figure 11c). Variations in this parameter resulted in yield stress differences of less than 4 Pa, indicating that its effect was comparatively negligible.

4.2. Effect of Feature Coupling on the Yield Stress

The underflow concentration and binders–tailings ratio significantly impact the rheological properties of the filling slurry. The interaction of these characteristics is shown in Figure 12. Under low underflow concentration, the contour curvature is higher for the filling slurry with a fine–coarse tailings ratio of 9:1, and the interaction between the tailings and the binders has a substantial effect on the static yield stress. At a high underflow concentration, the contour line of static yield stress is close to a straight line, suggesting that there is no strong interaction between the two parameters of binders–tailings ratio and underflow concentration. The interplay between underflow concentration and binders–tailings ratio significantly affects the static yield stress with a fine–coarse tailings ratio of 10:1; as the underflow concentration falls below 53%, the curvature of the static yield stress contour changes significantly. The interaction between the two factors of underflow concentration and binders–tailings ratio has a considerable influence on the static yield stress with a fine–coarse tailings ratio of 11:1. In the case of a fine–coarse tailings ratio of 12:1, the curvature of the static yield stress contour drastically alters as the underflow concentration exceeds 51%, and the interaction between the underflow concentration and the binders–tailings ratio has a considerable effect on the static yield stress.

Figure 13 shows the impact of the fine–coarse tailings ratio and binders–tailings ratio on the dynamic yield stress of filling slurry. It can be seen that the binders–tailings ratio has a more significant influence on the dynamic yield stress value at a low underflow concentration, and the binders–tailings ratio has less effect at a high underflow concentration, revealing that the interaction with the two features is weak. With a fine–coarse tailings ratio of 10:1, the influence of the binders–tailings ratio on the dynamic yield stress is minor for slurry at a low underflow concentration. The effect of the binders–tailings ratio on the dynamic yield stress is greater at a high underflow concentration, suggesting that the interaction between the binders–tailings ratio and the underflow concentration is stronger. As the fine–coarse tailings ratio is 11:1, the effect of the binders–tailings ratio on the dynamic yield stress is negligible at a low underflow concentration, and there exists a strong interaction between the underflow concentration and the binders–tailings ratio at a high underflow concentration. With a fine–coarse tailings ratio of 12:1, the effect of the binders–tailings ratio on the dynamic yield stress is negligible at a low underflow concentration, and the impact of the binders–tailings ratio on the dynamic yield stress is greater at a high underflow concentration. It can be seen that the underflow concentration and the binders–tailings ratio significantly impact the rheological properties of the filling slurry.

4.3. Feature Importance Analysis

The analysis in Section 3.4 demonstrates that the XGBoost algorithm predicts the static yield stress and dynamic yield stress of slurry more accurately than other algorithms. Still, it cannot directly interpret the output in detail. SHAP (Shapley additive explanation), proposed by Lundberg and Lee, is capable of quantitatively evaluating the output of a machine learning model and analyzing the role of any single feature in any sample, with the SHAP value indicating the contribution of each feature to the predicted value [44,45,46]. Assuming that the ith sample is x_i, the sample has j eigenvalues, the jth feature of that sample is x_ij, and the SHAP value y_i is calculated as

$$y_i=y_{base}+f\left(x_{i1}\right)+f\left(x_{i2}\right)+\dots +f\left(x_{ij}\right)$$

(9)

where y_base is the model baseline, typically the mean value of the target variable for the sample. f(x_ij) is the SHAP value of x_ij, which represents the contribution of the jth feature to the predicted value yi. As f(x_ij) > 0 indicates that the feature plays a positive role, f(x_ij) < 0 means that the feature plays a negative role (meaning that the feature lowers the predicted value).

Figure 14 shows the SHAP analysis of the static yield stress prediction model, with each row representing a feature. Figure 14a shows a SHAP plot of the importance of the features. The features in the plot are ranked in order of absolute value of their influence on the model, with the features in descending order of importance being underflow concentration, binders–tailings ratio, and fine–coarse tailings ratio, with the underflow concentration being much more important than the other two features. Figure 14b is a scatter plot of the feature density of the static yield stress prediction model; the horizontal coordinates represent the corresponding SHAP values of the features, any point in the plot is a sample in the dataset, red samples represent larger feature values, and blue samples represent smaller feature values. A feature that plays a positive role in static yield stress prediction with SHAP values greater than zero with a high red point is underflow concentration; compared to the two features of binders–tailings ratio and fine–coarse tailings ratio, the underflow concentration slurry sample is more dispersed, and the underflow concentration has a more significant effect. The binders–tailings ratio is more critical for static yield stress prediction than the fine–coarse particle ratio, which contributes less to static yield stress prediction. Figure 14c is the SHAP decision plot for the static yield stress prediction model, with the x-axis showing the model output and the y-axis showing SHAP values. Each fold represents a sample resulting from a cumulative eigenvalue process. Figure 14c shows the same performance as Figure 14a,b, with the underflow concentration of the samples being more critical than the binders–tailings ratio and fine–coarse tailings ratio. The SHAP values increase significantly with underflow concentration, indicating that underflow concentration makes the most significant contribution to predicted values.

The SHAP method can also interpret the output of the dynamic yield stress prediction model. Figure 15 depicts the SHAP analysis of the dynamic yield stress model. Figure 15a shows the feature importance of dynamic yield stress, similar to the static yield stress prediction model, with the underflow concentration being most important, with an absolute value of average SHAP greater than 12, followed by the binders–tailings ratio and fine–coarse tailings ratio. Figure 15b illustrates the scatter plot for the feature density of the dynamic yield stress prediction model. The underflow concentration is critical to the model, and the SHAP values of the high underflow concentration score red points are greater than 0, indicating that underflow concentration positively affects the predicted values. In contrast, the sample distributions of the binders–tailings ratio and fine–coarse tailings ratio are mainly distributed at SHAP = 0, indicating that these two features have a minor effect on most samples. Figure 15c depicts the SHAP decision diagram for the dynamic yield stress prediction model, which yields the same results as Figure 15a,b, with the fold line significantly increased in this part of the underflow concentration. The above indicates that, for both the static and dynamic yield stress prediction models, the underflow concentration contributes most significantly to the predicted values, followed by the binders–tailings ratio and fine–coarse tailings ratio.

5. Conclusions

Cemented filling technology provides an effective approach to managing tailings and stabilizing goafs, with slurry rheology serving as a key determinant of flowability and filling body strength. In this study, static and dynamic yield stress were identified as critical parameters for evaluating slurry performance, and a predictive framework was developed using the extreme gradient boosting (XGBoost) algorithm.

A total of 140 experimental samples were used to train and validate the model (105 training, 35 testing). Three input features—underflow concentration, binder-to-tailings ratio, and fine-to-coarse ratio—were selected as predictors. Model performance was benchmarked against ADBT, GBDT, and RF algorithms using four evaluation metrics (R², MAE, RMSE, EVS). The results demonstrated that XGBoost consistently outperformed the other models in accuracy and robustness.

The SHAP method was further applied to interpret the model predictions. Feature importance analysis revealed that the underflow concentration contributed most to yield stress predictions, followed by the binder-to-tailings ratio, with the fine-to-coarse ratio exerting the least influence.

Limitations and future work:

This study considered only three influencing factors. Additional material properties, such as particle size distribution and gradation, are known to affect slurry rheology and should be incorporated to further improve prediction accuracy. Future research will also explore hybrid machine learning models (e.g., WOA-XGBoost, GWO-XGBoost, BO-XGBoost) to leverage their complementary strengths and enhance generalization across different tailings types.

Practical implications:

By integrating machine learning into slurry design, the proposed framework simplifies the prediction of rheological parameters, reduces experimental costs, and offers a powerful tool for optimizing cemented filling technology in engineering practice.