## 7 Parametric Study  
Cost and time restrictions, as well as limited access to applicable equipment, are typically the main problems in laboratory studies. In most cases, examining the effects of each input variable on the output variables requires preparing several samples, which is costly and time consuming. One merit of modelling is that developed models can be used for parametric studies and evaluation of the impact of each input variable on the model output.  
As was already noted, in this study, the input parameters were SC, \(\sigma_{n}\), Dr, and SL. This study made use of the optimal EPR model to examine the interation impact of SC and Dr, Dr and \(\sigma_{n}\), Dr and SL, and SL and \(\sigma_{n}\) on the collapse settlement and coefficient of stress release. To this end, the desired variable altered between its minimum and maximum values and other variables were considered equal to the mean value. Then, the collapse settlement and coefficient of stress release were determined via EPR. The pertinent results are shown in Figures 16 and 17.  
Figure 16: _Cont._  
Figure 15: Importance of the variables based on CAM method for coefficient of stress release.  
Figure 16: Effect of input parameters on collapse settlement. (**a**) interactive effect of \(\sigma_{n}\) and SL, (**b**) interactive effect of Dr and SC, (**c**) interactive effect of \(\sigma_{n}\) and Dr\({}_{r}\) (**d**) interactive effect of SL and Dr.  
Figure 17: Effect of input parameters on coefficient of stress release. (**a**) interactive effect of \(\sigma_{n}\) and SL, (**b**) interactive effect of [PERSON] and SC, (**c**) interactive effect of \(\sigma_{n}\) and Dr, (**d**) interactive effect of SL and Dr.  
The interaction of \(\sigma_{n}\) and SL indicates that increasing SL led to an increase in the collapse settlement and a reduction in the coefficient of stress release. Additionally, an increase in \(\sigma_{n}\) led to an increase in both the collapse settlement and coefficient of stress release. Furthermore, the interaction of SC and Dr indicated the high impact of SC in increasing the collapse settlement and decreasing the coefficient of stress release. The trivial effect of Dr in increasing the coefficient of stress release and decreasing the collapse settlement is obvious. The interaction of Dr and \(\sigma_{n}\) also revealed that an increase in \(\sigma_{n}\) resulted in increases in both the collapse settlement and the coefficient of stress release. Increases in Dr also increased the coefficient of stress release and decreased collapse settlement. The interaction of SL and Dr implied a remarkable effect of SL on increasing the collapse settlement and coefficient of stress release. Finally, the changes related to Dr implied that an increase in Dr resulted in increasing the coefficient of stress release and decreasing the collapse settlement. Table 12 presents a comparison of the parametric study results for the present study model and the models by [PERSON] et al. [46] and [PERSON] et al. [47].  
Table 12 reveals that the effects of the input variables on the collapse settlement and coefficient of stress release in the EPR model had a similar trend to those of [PERSON] et al. [46] and [PERSON] et al. [47]. This, in fact, indicates the precision of the developed model.