Establishing a Fractal Theory‐Based Fluid Permeability Model for Fractured Loess and Its Engineering Applications

The fractures developed in earth‐rock dams in the loess hilly area of southern Ningxia, China, are one of the significant channels for reservoir leakage. However, the evolution rules of the occurrence and development of soil seepage erosion under the conditions of multiple complex porous networks have not been fully understood. Based on the extended fractal theory, an equivalent permeability model of the intermingled fractal units (IFU) for the dual‐porosity and bi‐dispersed porous media (DBPM) is methodically established under saturated state. Then, taking the Nanping Reservoir in the loess hilly area of southern Ningxia, China, as an engineering case study, the discrepancies between the permeability model proposed in the present work and the existing literature models are comparatively analyzed and discussed, further validating the rationality of the proposed calculation model. The obtained results reveal that in the absence of fractures, the pore matrix is modeled as bi‐dispersed porous media instead of mono‐dispersed porous media in this model, which makes the model's predicted value closer to the actual permeability value of engineering soil. According to the existing literature models, due to the presence of fractures, the predicted value of this model is 3–4 orders of magnitude lower than the existing fractal permeability model in dual‐porous media. Actually, in the other two models, the relationship between the fracture length and the aperture is almost linear, leading to excessive flow rate in their calculations. However, the present model takes into account the “small‐scale yielding of fractures and the state with large stress concentration at the tip” and believes that the relationship between the fracture length and the aperture almost corresponds to a power‐law scaling index of 0.5, which makes the prediction result more objective and reasonable.