Finite-difference based response surface methodology to optimize tailgate support systems in longwall coal mining

Designing a suitable support system is of great importance in longwall mining to ensure the safe and stable working conditions over the entire life of the mine. In high-speed mechanized longwall mining, the most vulnerable zones to failure are roof strata in the vicinity of the tailgate roadway and T-junctions. Severe roof displacements are occurred in the tailgate roadway due to the high-stress concentrations around the exposed roof span. In this respect, Response Surface Methodology (RSM) was utilized to optimize tailgate support systems in the Tabas longwall coal mine, northeast of Iran. The nine geomechanical parameters were obtained through the field and laboratory studies including density, uniaxial compressive strength, angle of internal friction, cohesion, shear strength, tensile strength, Young's modulus, slake durability index, and rock mass rating. A design of experiment was developed through considering a Central Composite Design (CCD) on the independent variables. The 149 experiments are resulted based on the output of CCD, and were introduced to a software package of finite difference numerical method to calculate the maximum roof displacements (d_max) in each experiment as the response of design. Therefore, the geomechanical variables are merged and consolidated into a modified quadratic equation for prediction of the d_max. The proposed model was executed in four approaches of linear, two-factor interaction, quadratic, and cubic. The best squared correlation coefficient was obtained as 0.96. The prediction capability of the model was examined by testing on some unseen real data that were monitored at the mine. The proposed model appears to give a high goodness of fit with the accuracy of 0.90. These results indicate the accuracy and reliability of the developed model, which may be considered as a reliable tool for optimizing or redesigning the support systems in longwall tailgates. Analysis of variance (ANOVA) was performed to identify the key variables affecting the d_max, and to recognize their pairwise interaction effects. The key parameters influencing the d_max are respectively found to be slake durability index, Young's modulus, uniaxial compressive strength, and rock mass rating.