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Determining the abutment angle in longwall coal mining using NLMR, GEP and GEO techniques

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Abstract

Abutment angle is a key parameter to correctly determine the weight of overlying strata of destressed zone above the longwall panel roof that is transmitted to the adjacent barrier pillars and the corresponding face access tunnels. Thus, estimation of the abutment angle is crucial to safely design the corresponding barrier pillars’ widths. This paper, at first, presents a new quadratic model based on non-linear multivariate regression (NLMR) analysis to estimate the abutment angle. Then, the paper continues to present two new powerful mathematical models by utilizing gene expression programming (GEP) and golden eagle optimizer (GEO) algorithms. To do so, depth of cover (H), panel width (P), and barrier pillar width (W) were used as input parameters to result abutment angle (β) as output. The accuracy and efficiency of the NLMR, GEP, and GEO models were evaluated by using performance indices including coefficient of determination (R2), variance accounted for (VAF), a20-index, root mean square error (RMSE), and mean absolute error (MAE) and compared with three existing empirical equations. Furthermore, the capability of all models, based on Taylor diagram and regression error characteristic (REC) curve, have been comparatively examined. Residual analysis confirmed the normal distribution and randomness of errors, indicating no systematic bias and confirming the models' reliability. The results revealed that the present developed GEO and GEP models perform with much higher accuracy than the NLMR model and the existing empirical equations. Additionally, the analysis of input parameters’ importance using the Shapley Additive Explanation (SHAP) method indicated that the depth of cover (H) has the greatest influence on the abutment angle (β). Finally, a case study was used to validate the practical applicability of the proposed models, demonstrating their accuracy and reliability in real-world scenarios.

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Acknowledgements

The views expressed in this paper are merely those of the authors. The authors received no financial support for the research, authorship, and publication of this article.

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Authors and Affiliations

  1. School of Mining Engineering, College of Engineering, University of Tehran, Tehran, 1439957131, Iran

    Fariborz Matinpour & Abbas Majdi

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  1. Fariborz Matinpour
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Contributions

F.M. Performed the literature review, prepared the required data, performed the codes and mathematical formulations, provided three formulas based on which provided the corresponding primary interpretation along with the required tables and figures. A.M. proposed the research subject and the methodology, supervised, reviewed and edited the manuscript.

Corresponding author

Correspondence to Abbas Majdi.

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Communicated by: Hassan Babaie

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Matinpour, F., Majdi, A. Determining the abutment angle in longwall coal mining using NLMR, GEP and GEO techniques. Earth Sci Inform 18, 358 (2025). https://doi.org/10.1007/s12145-025-01872-3

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