Fractures caused by mining are the main form of water inrush disaster. However, the temporal and spatial development characteristics of fractures of the rock mass due to mining are not clearly understood at present. In this paper, two geometric parameters, namely, fractal dimension and fracture entropy, are proposed to determine the spatial and temporal states of rock mass fractures caused by mining. The spatial and temporal structure characteristics of fractures in the rock mass due to mining are simulated with physical scale model testing based on digital image processing technology. A spatiotemporal model is created to examine the spatial and temporal patterns of hot and cold spots of the fractures based on a Geographic Information System (GIS). Results indicate that the fractal dimensions and entropy of the fractures network in the rock mass increase and decrease with the progression of mining, respectively, which can be examined in three stages. When the fractal dimension of the fractures in rock mass rapidly increases, the conductive fracture zone has a saddle shape. The fracture entropy of fracture has periodic characteristics in the advancing direction of the panel, which reflects the characteristics of periodic weighting. The fractal dimension and fracture entropy of fractures of the rock mass increase with time, and the rock mass system undergoes a process of increasing entropy. When the fractal dimension and fracture entropy of the fractures increase, the spatiotemporal state of fractures in rock mass caused by mining is initiated. When the fractal dimension and fracture entropy of the fractures decrease, the spatiotemporal state of fractures in rock mass is closed.

Over time and across space, the hydraulic conductivity, fractal dimension, and porosity of embankment soil have strong randomness, which makes analyzing seepage fields difficult, affecting embankment risk analysis and early disaster warning. This strong randomness limits the application of fractal theory in embankment engineering and sometimes keeps it in the laboratory stage. Based on the capillary model of porous soil, an analytical formula of the fractal relationship between hydraulic conductivity and fractal dimension is derived herein. It is proposed that the influencing factors of hydraulic conductivity of embankment soil mainly include the capillary aperture, fractal dimension, and fluid viscosity coefficient. Based on random field theory and combined with the embankment parameters of Shijiu Lake, hydraulic conductivity is discretized, and then the soil fractal dimension is approximately solved to reveal the internal relationship between hydraulic gradient, fractal dimension, and hydraulic conductivity. The results show that an increased fractal dimension will reduce the connectivity of soil pores in a single direction, increase the hydraulic gradient, and reduce the hydraulic conductivity. A decreased fractal dimension will lead to consistency of seepage channels in the soil, increased hydraulic conductivity, and decreased hydraulic gradient.

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