## 5 Discussion and Validation  
Using a numerical approach, which can consider the fracture-induced weakening, we investigated the fracture-weakening effect on the mining-induced stress redistribution through a parametric study with respect to the indicator of fracture intensity in tension, \(GSI_{t}\). According to the analysis in Section 4, the tensile fracture intensity in the FZ strongly affected the mining-induced stress distribution and strata movement. Thus, this factor should not be ignored in studies related to the behaviors of the FZ, mining-induced stress redistribution and overlying strata movement.  
The numerical results of the parametric study showed an interesting and rational changing law, which was consistent with the behaviors of the overlying strata. The changes in fracture intensity led to different abutment stress distributions and roof caving, which contributed to the design of the shield support in the working face.  
The in situ stress measurement in longwall mining is generally difficult; there is only a small amount of measured data in this regard [35; 36; 37]. The extreme difficulties in stress measurement in the non-backfill goat area [1] is due to the inaccessibility of the goat. Even though the stress monitoring cells can be put in the goat, but are easily damaged by the fallen rocks. Therefore, few attempts have successfully acquired the field stress data in the goat and have used it to validate the numerical results.  
Consequently, the studies on the mining-induced stress and its indicated overlying strata movement often rely on empirical or analytical methods, but only few analytical models are suitable for jointed strata. [PERSON] and [PERSON] [38] proposed an expression to estimate the caving span of the jointed roof beam structure \(L\) as follows:  
\[L=F\sqrt{\frac{2 KRtT_{r}}{\lambda}} \tag{6}\]  
where \(F\) is the orientation factor, \(t\) is the thickness of the bed, \(T_{r}\) is the rock tensile strength, and \(K\) and \(R\) are the jointing factor and stratification factor, respectively, which are determined by the core study. It was noted that \(K\) and \(R\) had a positive correlation with \(L\). According to [PERSON] and [PERSON]'s study, a roof with more fractures would have a lower \(K\) and \(R\). Therefore, highly jointed and fractured roof strata would have a small caving span, which is consistent with the numerical results presented in Section 4. Unfortunately, the study of [PERSON] and [PERSON] [38] did not describe how to quantify these parameters. Hence, at this stage, Equation (6) could not be directly used to quantitatively validate this numerical study. However, this equation and its indicated relationship is consistent with the trend obtained from the numerical analysis (presented in Section 4) and hereby served to validate the present study.  
According to the aforementioned analysis, the further studies on the quantitative analysis, by means of analytical or numerical analysis, in this regard is surely need to investigate the behaviors of mining-induced roof strata. In addition, the following instructions for applying the Tension weakening model can be drawn: The fracture intensity of the FZ should be case-dependent in light of geological and geotechnical conditions; differences in geological (strata lithology, thickness, properties, etc.) and geotechnical (mining height, length of each mining cycle) conditions will lead to different extents and intensities of the FZ. Hence, it should be estimated based on the core loggings with long roof boreholes or back-analyzed according to field measurements.  
This study focused on investigating the mining-induced roof behaviors with a newly proposed simulation technique, and the study was carried out based on a case study with typical geological conditions of underground coal mines. The results of this study may vary with the geological structures and mechanical properties of strata, the sensitivity analysis of different structures and hence these properties will be investigated in future studies.