Determination of the Degree of Sodic Modification of Bentonite Using Response Surface Analysis

Abstract

Sodium modification is an effective approach for enhancing the properties of bentonite and reducing its usage in pellets. However, due to limited research, the relationship between the physicochemical properties of bentonite and its green ball properties remains unclear, and the optimal degree of modification for bentonite has rarely been discussed. Therefore, this paper proposes a novel research idea: to exploring the correlation between the five most commonly used indexes for evaluating the physicochemical properties of bentonite (water absorption, methylene blue index, swell capacity, colloid index, and cation exchange capacity) and the most frequently used evaluation indexes for assessing green ball performance (drop strength), in order to determine the optimal degree of sodium modification of bentonite for pellets. The response surface methodology was employed in this paper to investigate the quantitative relationship between the five indexes and the green ball drop strength. The results demonstrate that when the drop strength of the green ball reaches its optimal level, the five commonly used indicators of bentonite are as follows: water absorption is 545.27%, methylene blue index is 22.94 g/100 g, swell capacity is 72.36 ml/g, colloid index is 35.95 ml/g, and cation exchange capacity is 68.93 mmol/100 g. Under these conditions, it has been the predicted value for green ball drop strength is determined to be 12.88, which exceeds the maximum value in the experimental conditions by 48.05%. The study determined the optimal degree of sodium modification for bentonite in pelletizing, providing valuable guidance for optimizing the properties of bentonite.

1. Introduction

The pellet method is a crucial technique in the smelting of iron and steel. In comparison to the sintering method, it offers advantages such as uniform particle size, high smelting grade, and reduced environmental pollution.¹⁾ In the context of environmental concerns regarding energy conservation and emission reduction, the utilization of pelletizing method in iron and steel smelting is progressively increasing.^2,3) In the process of pelletizing, the addition of a binder is essential to agglomerate the fine iron ore particles. Bentonite, an abundant and cost-effective material, is widely used as the standard binder for iron ore pellets. The weight ratio of bentonite as a binder typically ranges from 0.5% to 1.5%. However, it should be noted that China’s bentonite resources mainly consist of calcium bentonite which generally exhibits lower properties compared to sodium bentonite. To ensure that the raw balls meet production requirements in terms of strength, it is common practice to increase this proportion to approximately 2–3%.⁴⁾ However, the use of bentonite as a binder has its drawbacks, as it introduces silica into the pellets, thereby reducing both the combustion efficiency of blast furnaces and the quality of smelting products.⁵⁾ Studies have shown that for every 1.0% reduction in bentonite usage, there is a corresponding increase in pellet grade by 0.6% and a decrease in fuel ratio by 1.2%.^6,7) Therefore, minimizing the amount of bentonite used in pellets is crucial.

Currently, research on reducing the amount of bentonite in pellets is primarily focused on developing new binders and enhancing the performance of bentonite. Numerous studies have demonstrated that replacing or partially replacing bentonite with organic binders is feasible. However, due to their high cost and thermal instability, they are not widely utilized.^8,9,10,11) The use of low-cost solid waste as binder raw materials is also a research hotspot. Nevertheless, it can introduce new impurities and exhibit low bonding performance, making it far from industrial applications.^12,13,14) It is foreseeable that bentonite will continue to be the dominant binder for a prolonged period of time.^15,16) Sodium modification, as a widely used, simple, effective and cost-efficient method, can improve the properties of bentonite and reduce its consumption. Most of the properties such as water absorption, methylene blue index, swell capacity, colloid index and cation exchange capacity of bentonite have shown varying degrees of improvement after sodium modification. Therefore, in the practice of pellet production in China, almost all calcium bentonite clay needs to undergo sodium modification.¹⁷⁾ However, achieving efficient sodium modification of bentonite has long been a challenging issue for researchers in this field. In addition to exploring various methods and processes for sodium modification, scholars have also sought new insights by investigating the correlation between the physicochemical properties of bentonite and pellet characteristic.

For instance, several Chinese scholars have employed the least square method in conjunction with computational software to examine the correlation between various bentonite indices and green ball performance.^18,19,20,21) However, this analysis primarily remains qualitative, limiting the model’s and conclusions’ applicability for guiding bentonite modification and optimization. Therefore, it is crucial to conduct further investigations into the correlation between the physicochemical properties of bentonite and pellet characteristics in order to facilitate a prompt determination of the direction and extent of optimizing the physicochemical properties of bentonite.

In accordance with the common practice of metallurgical pellet companies to quickly assess pellet performance by analyzing the drop strength of green balls,²²⁾ this study incorporates response surface analysis method to investigate the complex relationship between key physicochemical properties of sodium-modified bentonite and the drop strength of green balls. This will clarify the optimization direction and extent for crucial performance indicators of bentonite used in pellet production. Such an approach represents a new research perspective. The research process is as follows: five commonly utilized indicators of pellet bentonite, including the methylene blue index, water absorption, swell capacity, colloid index, and cation exchange capacity were selected to investigate their relationship with green ball drop strength (GBDS). The Box-Benhnken (BBD) design was employed in the Design Expert software to optimize the parameters of sodium-modified bentonite, determine the optimal value range for the index parameters of bentonite, and provide guidance for optimizing pellet bentonite.

2. Materials and Methods

2.1. Raw Materials

The iron concentrate utilized in the pelletizing process is sourced from the actual production materials of an iron and steel enterprise located in Guangxi, China. Its chemical element composition and primary physical properties are presented in Tables 1 and 2, respectively. This particular type of iron concentrate powder exhibits a TFe content of 65.87%, possesses fine overall particle size characteristics, and demonstrates a pelletizing index¹⁷⁾ K value of 0.62, thereby establishing it as a highly suitable material for pelletization.

Table 1. Chemical element composition of experimental iron concentrate powder (%).

place of origin	TFe	FeO	SiO2	Al2O3	CaO	Na2O	K2O	TiO2	V2O5	S	P
Chile	65.87	29.18	4.72	1.66	0.51	0.07	042	0.26	0.10	0.38	0.01

Table 2. Performance indexes of experimental iron concentrate powder.

−0.037 mm (%)	+0.037 ~ 0.074 mm (%)	−0.074 mm (%)	+0.074 mm (%)	Specific surface area (cm2/g)	Sphericity index K
62.87	32.96	95.83	4.17	1289	0.62

The bentonite samples utilized for pelletizing were obtained from Tiandong, Chenling, and Huoshiling in Guangxi, Jianping in Liaoning, and Chifeng in Inner Mongolia. All of these locations represent typical calcium bentonite soils found in China. In order to obtain more controlled experimental samples, the bentonite from these five producing areas was purified in four stages using hydrocyclones (DX-5, China Haiwang) with column diameters of 100 mm, 75 mm, 50 mm, and 25 mm. Finally, we obtained twenty-five bentonite samples with different mineral compositions (i.e., the original bentonite from each producing area and its four-grade purified sample composition). The samples were abbreviated as CL, HSL, TD, JP, and CF, with subscript character nP indicating purification separation stage. For example, CL3P indicates that Chenling bentonite has undergone tertiary purification treatment. According to the production requirements of the pelletizing enterprises, sodium modification was applied to modify the bentonite before pelletization. The method used for sodium modification was semi-dry sodium modification with a concentration of 2.5% sodium carbonate as the modifier. Additionally, during the process, 30% water was added and aged for 3 days.

2.2. Experimental Methods

2.2.1. Method of Making Balls

The iron concentrate powder is mixed with sodium modification bentonite and appropriate water, and then formed into balls using the disk ball making machine (ZL10, Zhengzhou Chunchang). The ball-making method follows the procedures described in the relevant literature.²³⁾ The equipment specifications, operational details, and material parameters are as follows: the disc ball making machine has a diameter of 1 m, rotates at a speed of 28 r/min with a tilt angle of 49°. The amount of iron concentrate powder added is 1.5 kg, while the amount of bentonite added is 2%.

2.2.2. Index Test Method

In this experiment, five commonly used indicators of pellet bentonite were tested, including methylene blue index (MBI), water absorption (WA), swelling capacity (SC), colloid index (CI) and cation exchange capacity (CEC). These indicators were determined in accordance with the national standard GB/T 20973-2020.²⁴⁾ The bentonite indicators test method has been included in the supplementary information, which is available on the journal’s website.

The green ball drop strength is an index that characterizes the mechanical strength of green pellets, specifically the number of impacts that can be withstood when falling freely at a certain height. It is also the most used indicator of pellet quality evaluation in the production process of pellet enterprises. Its test method has been mentioned in many papers in the same field,²¹⁾ specifically: take 20 qualified raw balls with diameters of 10–12 mm, drop them freely on a 10 mm thick steel plate at a height of 0.5 m, and repeat the operation several times until cracks appear in the raw balls, and if rupture occurs after dropping the raw balls for n times, the dropping strength of the balls will be (n−1) times/each. The test data of the samples are shown in Table 3.

Table 3. Summary of test data of pellet bentonite.

Samples	Methylene blue index (g/100 g)	Water absorption (%)	Swelling capacity (ml/g)	Colloid index (ml/g)	Cation exchange capacity (mmol/100 g)	Green ball drop strength Times/(each)
CLraw	21.68	411.26	19.95	29.55	24.1	2.9
CL1P	23.69	475.75	24.95	32.50	29.1	3.4
CL2P	29.34	492.34	33.45	35.50	34.9	3.9
CL3P	30.15	524.55	35.00	38.25	45.5	4.5
CL4P	28.11	566.58	34.11	35.80	39.1	7.2
HSLraw	32.21	324.86	11.55	19.35	50.9	3.6
HSL1P	32.49	312.01	11.10	16.25	41.1	4.6
HSL2P	33.42	335.28	11.05	14.55	58.9	5.5
HSL3P	34.20	374.48	12.75	16.80	59.9	6.7
HSL4P	34.61	430.45	15.65	20.95	60.2	7.9
TDraw	24.94	422.69	11.90	24.40	38.7	3.3
TD1P	20.35	382.13	10.90	17.95	35.9	2.5
TD2P	21.46	401.80	11.45	19.65	36.9	2.8
TD3P	22.64	441.62	15.00	25.95	44.3	3.1
TD4P	23.98	453.74	13.30	19.80	43.4	4.4
JPraw	26.76	444.91	33.25	93.75	45.2	3.7
JP1P	31.71	539.34	43.60	95.95	52.1	7.7
JP2P	33.73	565.35	44.25	96.15	58.0	6.8
JP3P	34.38	578.99	48.05	97.65	70.2	6.6
JP4P	34.11	569.36	37.45	41.21	61.6	8.7
CFraw	27.80	387.60	18.85	25.55	39.1	3.5
CF1P	32.71	536.42	22.70	26.45	44.5	4.7
CF2P	32.52	484.53	19.40	19.50	43.6	5.9
CF3P	34.18	625.95	26.20	29.00	56.7	6.1
CF4P	33.91	559.84	23.90	25.20	52.8	6.0

2.3. Response Surface Optimization Methods

The Response Surface Method (RSM) is an optimization technique that integrates experimental design and mathematical modeling, enabling the reduction of experiments and examination of interaction between influencing factors effectively. RSM is commonly employed in scientific research to determine experimental conditions during pre-experimental design and optimize parameters in industrial processes.^25,26) Design Expert software is typically used for designing and analyzing response surface methods. Among these methods, Box-Behnken Design (BBD) stands out as the most frequently utilized model in Design Expert. BBD is a test design approach capable of evaluating nonlinear relationships between exponents and factors. Compared to other designs, it requires fewer consecutive experiments while allowing control over variable parameters within the desired range, making it more cost-effective.²⁷⁾

In contrast to the linear model of least square method employed by previous researchers,^19,20,21,22) this study utilizes a quadratic polynomial model from the response surface method to establish the association between the response and variables. The formulated model is represented as follows:

  

$$R={\beta }_0+{\sum }_{i=1}^n{\beta }_i{x}_i+{\sum }_{i=1}^n{\beta }_i{x}_i{}^2+{\sum }_{i=1}^{n-1}{\sum }_{j=i+1}^n{\beta }_{ij}{x}_i{x}_j+\epsilon$$(1)

Where R is the dependent variable, x_i is the i th independent variable, n is the number of independent variables, β₀ is the constant term, β_i is the coefficient of the linear term, β_ii is the coefficient of the quadratic term, β_ij is the coefficient of the interaction term, ε is the error term.

3. Results and Discussion

3.1. Modeling and Statistical Analysis

The Analysis of Variance (ANOVA) is a statistical method used to compare whether the means of three or more groups are significantly different from each other. It is based on decomposing the overall variance of the data into two components: within-group variance (SSE) and between-group variance (SSB). These variances, along with their derived correlation parameters (e.g., R², F, p), are used to determine the significance of factors affecting a variable. The quadratic model ANOVA of green ball drop strength influenced by the bentonite index is presented in Table 4. In regression analysis, F-values and P-values are commonly used to determine both how well the model fits and whether the independent variable as a whole has a significant effect on the dependent variable. The F-value is the ratio of the between-group variance (SSB) to the within-group variance (SSE). Whether the corresponding independent variable has a significant effect on the dependent variable is determined by comparing if the F-value is greater than the critical value. Additionally, it is possible to determine whether the overall model is significant based on the F-value. If the model is significant, it indicates that at least one of the independent variables has an effect on the dependent variable. The P-value represents the probability that the coefficient of the corresponding variable is zero. If the P-value of an independent variable is less than the significance level (usually set at 0.05), it can be assumed that the coefficient of that independent variable is non-zero and influencing the model. If the P-value of the entire model is less than the significance level, then it indicates that there is a significant fit for the entire model and at least one independent variable has an effect on the dependent variable. Based on the results from the contrast analysis table, it is evident that the overall fitting effect of the model is highly satisfactory. The F value (50.02>3.84) and P value (0.0009) both indicate a significant relationship, with the latter being much lower than 0.05, thereby demonstrating that the model effectively explains variations in the dependent variable. In the model, the interaction variables AC (0.0125), AD (0.0021), AE (0.0152), BE (0.0243), and CE (0.0187) exhibit statistical significance, indicating that bentonite parameters primarily influence falling strength through diverse interactions. Furthermore, significant quadratic variables A^2 (0.0009) and E^2 (0.01142) suggest a non-linear relationship between A and E with GBDS, thereby highlighting the intricate nature of pellet bentonite mechanisms.

Table 4. Analysis of variance table.

Sources	Sum of squares	df	Mean square error	F-value	P value
Model	78.37	20	3.92	50.02	0.0009
A-WA	0.2406	1	0.2406	3.07	0.1546
B-MBI	0.2256	1	0.2256	2.88	0.1649
C-CI	0.3362	1	0.3362	4.29	0.107
D-SC	0.0001	1	0.0001	0.0008	0.9791
E-CEC	0.2311	1	0.2311	2.95	0.161
AB	0.2081	1	0.2081	2.66	0.1785
AC	1.46	1	1.46	18.6	0.0125
AD	3.89	1	3.89	49.67	0.0021
AE	1.3	1	1.3	16.59	0.0152
BC	0.5159	1	0.5159	6.59	0.0622
BD	0.3453	1	0.3453	4.41	0.1037
BE	0.9737	1	0.9737	12.43	0.0243
CD	0.2401	1	0.2401	3.06	0.1549
CE	1.15	1	1.15	14.62	0.0187
DE	0.0101	1	0.0101	0.1287	0.7379
A2	6.19	1	6.19	79.03	0.0009
B2	0.0321	1	0.0321	0.4093	0.5571
C2	0.0627	1	0.0627	0.7998	0.4217
D2	0.4487	1	0.4487	5.73	0.0749
E2	1.54	1	1.54	19.66	0.0114
Residual	0.3133	4	0.0783
Total	78.68	24

The results are fitted to a second-order polynomial model, and the regression quadratic equation is derived. The polynomial regression model demonstrates the relationship between the process variables in terms of coding factors as follows:

  

$$\begin{array}{l}\text{GBDS}=1.67-4.15\text{A}+2.48\text{B}-2.76\text{C}+0.0576\text{D}-1.49\text{E}\\ +4.14\text{AB}-18.02\text{AC}+33.25\text{AD}+7.76\text{AE}+13.85\text{BC}\\ -12.12\text{BD}-11.29\text{BE}+11.46\text{CD}-15.24\text{CE}+1.56\text{DE}\\ -13.07{\text{A}}^2-0.5824{\text{B}}^2+2.67{\text{C}}^2-11.16{\text{D}}^2+11.82{\text{E}}^2\end{array}$$(2)

Where A, B, C, D and E represents WA, MBI, CI, SC, and CEC, respectively. According to the results presented in Table 5, the model exhibits a remarkable fitting effect with both the coefficient of determination and adjusted coefficient of determination approaching unity, indicating that the model explains approximately 99.6% of the variance in the dependent variable. Moreover, the data demonstrates minimal dispersion and volatility as evidenced by a standard deviation of only 0.28 and a coefficient of variation at 5.55%. The graphical representation of the predicted and actual values for all parameters is depicted in Fig. 1. The model exhibits a significant accuracy level of 24.07, surpassing the signal-to-noise ratio measure of 4, thereby indicating its suitability for identifying the optimal combination of variables.²⁸⁾

Table 5. Descriptive statistical table.

Anova indicators	value	Anova indicators	value
Std. Dev.	0.2799	R2	0.9960
Mean	5.04	Adjusted R2	0.9761
C.V.%	5.55	Adeq Precision	24.0696

Fig. 1(a). Fitting values compared to actual values. (Online version in color.)

Fig. 1(b). Model residuals versus predicted values. (Online version in color.)

3.2. Influence of Indicator Parameters on GBDS

The disturbance diagram in Fig. 2 illustrates the impact of analysis factors on the response variable. The black dots represent the intersections of the five perturbation lines, which correspond to the five sets of data. By determining the positional relationship between the perturbation lines and the black dots, we can determine the effect of each set of data on the response variable GBDS. The lines labeled A, B, C, D and E represent water absorption, blue absorption, expansion capacity, gum price, and cation exchange capacity of bentonite respectively. It can be observed that A, C, D and E are all arcs in the figure, indicating a significant nonlinear trend between these four index variables and the response variable with values close to their optimal levels. The downward opening direction of AD suggests a negative correlation between their curve effect and the response variable, while the upward opening direction of CE indicates a positive correlation between their curve effect and the response variable. On the other hand, B’s disturbance line is linear, implying that the influence variable increases in a linear fashion under its influence. This observation aligns with field experience, as it is commonly believed that higher levels of Methylene blue absorption index are associated with improved performance.²⁹⁾

Fig. 2. Parametric perturbation diagram. (Online version in color.)

The 3D Surface diagram in Design expert provides an intuitive representation of the influence of the interaction between two parameters on the response value. Based on the P-value data (P<0.5) presented in Table 4, significant interactions include AD (0.0021), while relatively significant interactions include AC (0.0125), AE (0.0152), BE (0.0243), and CE (0.0187). The corresponding 3D Surface diagrams are depicted in Fig. 3. The steepness of these plots indicates the sensitivity of the response value to independent variables, while their bending shape reflects the strength of interaction between these variables. Taking (b) AD as an example, which exhibits the most significant interaction, its overall shape can be characterized as ridge-shaped. By analyzing the curve on the XY axis, it is evident that both response variables decrease with increasing A and D values, indicating a negative correlation curve response. However, examining the middle region reveals an upward trend in response variables with increasing interaction between A and D. Similar analysis methods apply to other 3D Surface plots. It is observed that interactive images of (a) AC and (b) AD also exhibit a ridge-shaped pattern, where increased interaction leads to enhanced response. The interactive images of (d) BE and (e) CE exhibit a concave valley shape, with an increasing level of interaction while the response remains relatively stable or even slightly decreases. The image of AE displays a saddle-shaped pattern, indicating a complex interaction where the direction of the maximum point cannot be determined from the image. In summary, the interaction between bentonite WA and other indicators exerts a positive influence on GBCS, whereas the interaction between CEC and other indicators has a detrimental effect on it.

Fig. 3(a). 3D Surface diagram of parameter interaction of AC.

Fig. 3(b). 3D Surface diagram of parameter interaction of AD.

Fig. 3(c). 3D Surface diagram of parameter interaction of AE.

Fig. 3(d). 3D Surface diagram of parameter interaction of BE.

Fig. 3(e). 3D Surface diagram of parameter interaction of CE.

3.3. Optimal Parameter Value Prediction

The analysis in Section 3.1 reveals that the established quadratic fitting model demonstrates significant influence from interaction terms AC, AD, AE, BE and CE. However, as discussed in Section 3.2, it is evident that these interactions exhibit variations. Moreover, intricate and convoluted interactions pose challenges for practical applications. The numerical optimization part of the Design-Expert software can be used with some common mathematical optimization algorithms, such as Gradient Descent, Newton’s Fitting, Genetic Algorithms, and so on. These algorithms adjust and iterate the parameters according to the specific optimization objectives and constraints to find the optimal solution.

Calculation of optimal values within the range of metrics tested in this experiment, with specific data presented in Table 6, and the final optimization result displayed in Fig. 4. Figure 4 is a schematic diagram of the optimal parameter values in design expert. The left and right values in the figure are the value ranges of the corresponding indicators, with red dots indicating the locations of optimal values within each visualization diagram (ABCDE). For instance, in the A-WA diagram, the value range is from 312.01 to 625.95, and the optimal parameter is 545.271; thus, the red dot represents its location within this value range. Under the experimental conditions, the following parameters of bentonite are found to yield pellets with enhanced strength: a WA of 545.27%, MBI of 22.94 g, SC of 72.36 ml, CI of 35.95 ml, and CEC of 68.93 mmol. The predicted GBDS value at these parameter values is determined to be 12.88, representing a significant improvement by 48.05% compared to the original maximum value achieved previously. Based on the predicted optimal value range and interrelationships among discussed indices, guidance regarding modification direction and target range for bentonite was provided.

Table 6. Optimization target and variable range of response.

Name	Goals	Minimum	Maximum
Water absorption	Being in range	312.01	625.95
Methylene blue index	In range	20.35	34.61
Colloid index	In range	14.55	97.65
Swelling capacity	In range	10.9	48.05
Cation exchange capacity	In range	24.1	70.2
Green ball drop strength	Maximum	2.5	8.7

Fig. 4. Parameter values and predicted response values after optimization. (Online version in color.)

3.4. Model Validation

In general, articles involving modeling also require validation of the model. However, it is difficult to simultaneously satisfy the parametric conditions of bentonite clay, making it challenging to accomplish validation of the optimal conditions in reality. Nevertheless, for experiments that cannot be measured, it does not imply that their effects cannot be predicted. Machine learning is commonly used in the civil engineering field to simulate unmeasurable data with remarkable results. With reference to this idea, this study employs machine learning to validate the model.³⁰⁾

Machine learning is a branch of artificial intelligence. Regression analysis is a common task in machine learning. However, regression analysis with machine learning, unlike traditional regression analysis software, ensures that the model’s have a good fit by iteratively replacing the optimal feature values. It is in fact a ‘black box’ that can build a good predictive model, but there is no way to know what the exact parameters of that model are. It is worth noting that machine learning prediction fits well with the prediction task of this study because if traditional regression analysis software such as R and spss are used, the source data are the same and the models built are almost the same. And the prediction model built by machine learning is more convincing.

In this study, machine learning is used to build regression model in python. The code used and its remarks can be seen in the supplementary information, which is available on the journal’s website. In this study, Polynomial Features of Scikit-learn was used to generate the quadratic term features,³¹⁾ the dataset was divided into a training set and a test set, a linear regression model was created and trained, and finally the optimal parameters of bentonite clay from 3.3 were brought in and the corresponding predicted y-values were calculated. The final result machine learning predicted GBDS of 14.68 which is close to the result of 12.88 predicted in 3.3.

4. Conclusion

A quadratic model is established to describe the relationship between the bentonite index and green ball drop strength. The model exhibits significant and stable characteristics, effectively explaining a majority of the data. Through data analysis, it is observed that apart from MBI which has a linear effect on GBDS, all other indices exhibit non-linear relationships. Specifically, WA and SC have negative influences, while MBI, CI, and CEC have positive influences.

According to the 3D surface image analysis of significant interactions in Design Expert, it was observed that the positive impact of WA on GBDS is influenced by other indicators of bentonite, whereas the negative impact of CEC on GBDS is influenced by other indicators.

The optimal values of bentonite parameters for the pellets were determined as follows: a WA of 545.27%, a MBI of 22.94 g/100 g, an SC of 72.36 ml/g, a CI of 35.95 ml/g, and a CEC of 68.93 mmol/100 g. The predicted GBDS value at this parameter setting was found to be 12.88, representing an increase of 48.05% compared to the original maximum value.

The study determined the optimal degree of sodium modification for bentonite in pelletizing, providing valuable guidance for optimizing the properties of bentonite.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data Availability

Data will be made available on request.

Supporting Information

Due to the large number of bentonite indexes and the different test standard methods in various countries, the detailed test methods and index descriptions of the bentonite performance indicators used in this paper have been written in the supplementary materials.

This material is available on the journal website at https://doi.org/10.2355/isijinternational.ISIJINT-2024-006.

Acknowledgments

This work was supported by National Natural Science Foundation of China (No. 51964005).

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