Intelligent cemented paste backfill-strength design framework: Interpretable machine learning and mix-proportion optimization

Abstract

The rapid advancement of artificial intelligence has introduced new vitality into cemented paste backfill (CPB) technology. However, current machine learning models for CPB-strength prediction are generally forward-only and single-output, and lack clarity on multi-feature interactions and an integrated full-process design framework. To this end, this study proposes a light gradient boosting machine (LightGBM) model, optimized by Optuna, for predicting the CPB strength at multiple curing ages (3, 7, and 28 d). The model dataset comprised the unconfined compressive strength (UCS) results of 738 CPB specimens prepared with various types of tailings and mix proportions. SHapley Additive exPlanations (SHAP) were employed to elucidate the influence patterns and relative importance of input features while inherently considering their complex, multi-feature interaction effects on the output of the model. Additionally, a simulated annealing (SA) algorithm was integrated with the predictive model to enable the inverse process from the target UCS value to the optimal material-mix proportions. The results demonstrated the effectiveness of Optuna in hyperparameter tuning, leading to an optimized LightGBM model that accurately predicted the multi-age CPB UCS (R² > 0.98). SHAP analysis identified key features, notably the high correlation of the water–cement ratio and CaO content in the tailings with the CPB strength. The SA algorithm effectively provided optimal CPB mix proportions that met the target 28-d UCS value, balancing multiple conflicting objectives such as the solid content and cement dosage. Finally, a user-friendly graphical user interface was developed to integrate these models and provide an accessible, visual, machine-learning-based CPB-strength design tool for mining engineers.

Keywords

Cemented paste backfill / Light gradient boosting machine / Unconfined compressive strength / SHapley Additive exPlanations / Simulated annealing

References

[1] M.F. Cai, D.L. Xue, F.H. Ren, Current status and development strategy of metal mines, Chin. J. Eng. 41 (4) (2019).

[2] A.X. Wu, Y. Wang, Z.E. Ruan, B.L. Xiao, J.D. Wang, L.Q. Wang, Key theory and technology of cemented paste backfill for green mining of metal mines, Green Smart Min. Eng. 1 (1) (2024) 27-39.

[3] A.X. Wu, H. Li, H.Y. Cheng, Y.M. Wang, C.P. Li, Z.E. Ruan, Status and prospects of research on the rheology of paste backfill using unclassified tailings (Part 2): rheological measurement and prospects, Chin. J. Eng. 43 (4) (2021).

[4] W.T. Xia, K. Yang, Y.Q. Hou, X. Yu, X. He, H.H. Du, Experimental study on the early compressive strength, fluidity, and microstructure of multisource coal-based solid waste cemented backfill, Green Smart Min. Eng. 1 (4) (2024) 405-420.

[5] A.X. Wu, Y. Yang, H.Y. Cheng, S.M. Chen, Y. Han, Status and prospects of paste technology in China, Chin. J. Eng. 40 (5) (2018) 517-525.

[6] X.J. Deng, B. Klein, L.B. Tong, B. de Wit, Experimental study on the rheological behavior of ultra-fine cemented backfill, Constr. Build. Mater. 158 (2018) 985-994.

[7] Z.L. Xue, D.Q. Gan, Y.Z. Zhang, Z.Y. Liu, Rheological behavior of ultrafine-tailings cemented paste backfill in high-temperature mining conditions, Constr. Build. Mater. 253 (2020) 119212.

[8] Q.S. Chen, Q.L. Zhang, A. Fourie, X. Chen, C.C. Qi, Experimental investigation on the strength characteristics of cement paste backfill in a similar stope model and its mechanism, Constr. Build. Mater. 154 (2017) 34-43.

[9] H.Q. Jiang, M. Fall, Yield stress and strength of saline cemented tailings in sub-zero environments: portland cement paste backfill, Int. J. Miner. Process. 160 (2017) 68-75.

[10] K. Klein, D. Simon, Effect of specimen composition on the strength development in cemented paste backfill, Can. Geotech. J. 43 (3) (2006) 310-324.

[11] B. Ercikdi, T. Yılmaz, G. Külekci, Strength and ultrasonic properties of cemented paste backfill, Ultrasonics 54 (1) (2014) 195-204.

[12] M. Fall, M. Pokharel, Coupled effects of sulphate and temperature on the strength development of cemented tailings backfills: portland cement-paste backfill, Cem. Concr. Compos. 32 (10) (2010) 819-828.

[13] C.C. Qi, X.Y. Yang, G.C. Li, Q.S. Chen, Y.T. Sun, Research status and perspectives of the application of artificial intelligence in mine backfilling, J. China Coal Soc. 46 (2) (2021) 688-700.

[14] H. Mashhadban, S.S. Kutanaei, M.Ali Sayarinejad, Prediction and modeling of mechanical properties in fiber reinforced self-compacting concrete using particle swarm optimization algorithm and artificial neural network, Constr. Build. Mater. 119 (2016) 277-287.

[15] C.C. Qi, H.B. Ly, L. Minh Le, X.Y. Yang, L. Guo, B.Thai Pham, Improved strength prediction of cemented paste backfill using a novel model based on adaptive neuro fuzzy inference system and artificial bee colony, Constr. Build. Mater. 284 (2021) 122857.

[16] J.L. Yao, T.Y. Yang, D.P. Qiao, H.Y. Cheng, H. Chen, Intelligent design framework for predicting thixotropic rheological parameters of ultra-fine tailings cemented paste backfill: a stacking machine learning model, Min. Metall. Explor. 42 (2025) 837-854.

[17] L. Lang, K. Song, D. Lao, T. Kwon, Rheological properties of cemented tailing backfill and the construction of a prediction model, Material 8 (5) (2015) 2076-2092.

[18] C.C. Qi, Q.S. Chen, X.J. Dong, Q.L. Zhang, Z.M. Yaseen, Pressure drops of fresh cemented paste backfills through coupled test loop experiments and machine learning techniques, Powder Technol. 361 (2020) 748-758.

[19] C.C. Qi, L. Guo, H.B. Ly, H. Van Le, B.T. Pham, Improving pressure drops estimation of fresh cemented paste backfill slurry using a hybrid machine learning method, Miner. Eng. 163 (2021) 106790.

[20] Y.H. Niu, H.Y. Cheng, S.C. Wu, J.L. Sun, J.X. Wang, Rheological properties of cemented paste backfill and the construction of a prediction model, Case Stud. Constr. Mater. 16 (2022) e01140.

[21] C.C. Qi, A. Fourie, Q.S. Chen, Neural network and particle swarm optimization for predicting the unconfined compressive strength of cemented paste backfill, Constr. Build. Mater. 159 (2018) 473-478.

[22] C.C. Qi, Q.S. Chen, S.S. Kim, Integrated and intelligent design framework for cemented paste backfill: a combination of robust machine learning modelling and multi-objective optimization, Miner. Eng. 155 (2020) 106422.

[23] M.A. Helsel, C.F. Ferraris, D. Bentz, Comparative study of methods to measure the density of cementious powders, J. Test. Eval. 44 (6) (2016) 2147-2154.

[24] F. Wu, Q. Gao, Z.Q. Yang, Orthogonal experiment on ratio of whole tailings cementitious materials and strength model of filling body, Chin. J. Nonferrous Met. 31 (8) (2021) 2269-2278.

[25] T.Y. Yang, J. Wang, D.P. Qiao, G.T. Li, H.Y. Cheng, X. Zhang, R.Z. Shi, The thixotropic characteristics of rheological parameters of waste stone-tailings cemented paste backfill and the time effect of pipeline resistance, Constr. Build. Mater. 423 (2024) 135858.

[26] H.Y. Cheng, S.C. Wu, H. Li, X.Q. Zhang, Influence of time and temperature on rheology and flow performance of cemented paste backfill, Constr. Build. Mater. 231 (2020) 117117.

[27] L. Liu, Z.Y. Fang, C.C. Qi, B. Zhang, L.J. Guo, K.I.I.L. Song, Numerical study on the pipe flow characteristics of the cemented paste backfill slurry considering hydration effects, Powder Technol. 343 (2019) 454-464.

[28] H.M. Ahmed, B. Bharathan, M. Kermani, F. Hassani, M.A. Hefni, H.A.M. Ahmed, G.S.A. Hassan, E.B. Moustafa, H.A. Saleem, A.P. Sasmito, Evaluation of rheology measurements techniques for pressure loss in mine paste backfill transportation, Minerals 12 (6) (2022) 678.

[29] N. Niroshan, N. Sivakugan, R.L. Veenstra, Flow characteristics of cemented paste backfill, Geotech. Geol. Eng. 36 (4) (2018) 2261-2272.

[30] G.L. Ke, Q. Meng, T. Finley, T.F. Wang, W. Chen, W.D. Ma, Q.W. Ye, T.Y. Liu, LightGBM: a highly efficient gradient boosting decision tree, Adv. Neural Inf. Process. Syst. 30 (2017) 3146-3154.

[31] L. Li, Z.B. Liu, J.M. Shen, F. Wang, W.B. Qi, S. Jeon, A LightGBM-based strategy to predict tunnel rockmass class from TBM construction data for building control, Adv. Eng. Inf. 58 (2023) 102130.

[32] W.Z. Liang, S.Z. Luo, G.Y. Zhao, H. Wu, Predicting hard rock pillar stability using GBDT, XGBoost, and LightGBM algorithms, Mathematics 8 (5) (2020) 765.

[33] T. Akiba, S. Sano, T. Yanase, T. Ohta, M. Koyama, Optuna: A next-generation hyperparameter optimization framework, in: Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Anchorage, AK, USA, 2019, pp. 2623-2631.

[34] J.P. Lai, Y.L. Lin, H.C. Lin, C.Y. Shih, Y.P. Wang, P.F. Pai, Tree-based machine learning models with optuna in predicting impedance values for circuit analysis, Micromachines 14 (2) (2023) 265.

[35] T. Fushiki, Estimation of prediction error by using K-fold cross-validation, Stat. Comput. 21 (2) (2011) 137-146.

[36] T.T. Wong, P.Y. Yeh, Reliable accuracy estimates from k-fold cross validation, IEEE Trans. Knowl. Data Eng. 32 (8) (2019) 1586-1594.

[37] Y. Jung, Multiple predicting k-fold cross-validation for model selection , J. Nonparam Stat. 30 (1) (2018) 197-215.

[38] G. Van den Broeck, A. Lykov, M. Schleich, D. Suciu, On the tractability of SHAP explanations, J. Artif. Intell. Res. 74 (2022) 851-886.

[39] Y. Meng, N.H. Yang, Z.L. Qian, G.Y. Zhang, What makes an online review more helpful: an interpretation framework using XGBoost and SHAP values, J. Theor. Appl. Electron. Commer. Res. 16 (3) (2021) 466-490.

[40] Z.Q. Li, Extracting spatial effects from machine learning model using local interpretation method: an example of SHAP and XGBoost, Comput. Environ. Urban Syst. 96 (2022) 101845.

[41] D.C. Feng, W.J. Wang, S. Mangalathu, E. Taciroglu, Interpretable XGBoost-SHAP machine-learning model for shear strength prediction of squat RC walls, J. Struct. Eng. 147 (11) (2021) 04021173.

[42] J. Moosbauer, J. Herbinger, G. Casalicchio, M. Lindauer, B. Bischl, Explaining hyperparameter optimization via partial dependence plots, Adv. Neural Inf. Process. Syst. 34 (2021) 2280-2291.

[43] C. Molnar, T. Freiesleben, G. König, J. Herbinger, T. Reisinger, G. Casalicchio, M.N. Wright, B. Bischl, Relating the partial dependence plot and permutation feature importance to the data generating process, in: L. Longo (Ed.), Explainable Artificial Intelligence. xAI 2023. Communications in Computer and Information Science, Springer, Cham, 2023, pp. 456-479.

[44] R.A. Rutenbar, Simulated annealing algorithms: an overview, IEEE Circuits Devices Mag. 5 (1) (1989) 19-26.

[45] U. Aickelin, D. Dasgupta, F. Gu, Artificial immune systems, in: E.K. Burke, G. Kendall (Eds.), Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, Springer, Boston, 2013, pp. 187-211.