A fuzzy mathematical model for evaluation of rock-fracture and structural complexity: application for Southern Atlas in Tunisia

In the present paper, a fuzzy model of assessment is proposed according the framework of fuzzy mathematical theory to estimate the complexity of rock fractures and geological structures. We established the fuzzy evaluation model and decided a trapezoidal membership function using the fuzzy mathematics. Dataset acquisition is integrated with an advanced technique of coupling multiscale fracture data obtained from both high-resolution satellite imagery and field data. Five parameters were selected, including qualitative and quantitative data from different scales, namely fractal dimension, fracture length, fracture intensity, the intersection angle between fractures and beddings and the fracture density. The weight of each factor is obtained with the principle that the relative value of the complexity index is larger and the weight is significant. This model was applied to the complexity assessment of the southwestern Tunisia. The rank of complexity of each sub-area in the study region is from strong to weak. The result shows that Jebal Orbata and Jebal Chamsi have the strongest complexity due to their position beside the 140 dextral strike-slip Gafsa fault. The east and central zone of the region of investigation has the weakest complexity.