Effective Diffusion Range of Exponential Fluids Based on Navier-Stokes Equation in Collapse Area

In order to study the diffusion range and pressure distribution of cement paste during grouting in the fractured rock mass, based on the deduced Navier-Stokes equation, a single fracture model is established on the COMSOL platform to simulate the flow characteristics of slurry on irregular single fracture surface. In this regard, a plane fracture model with different penetration coefficients is established to simulate the diffusion law of the slurry in the broken rock mass. The results show that when the crack penetration coefficient is low in the model (0.1−0.5), the effective diffusion range of the slurry is small, about 1.5−4.1 m, and the diffusion distance increases slowly and nonlinearly with the increase of pressure difference, and the increase rate decreases to near 0 quickly. When the fracture penetration coefficient in the model is larger (0.5−1.0), the effective diffusion range of the slurry increases significantly, about 4.1−6.2 m; and it increases nonlinearly with the increase of pressure difference, and the rate of increase decreases gradually. When the fracture penetration coefficient of the model is 1.0, the fractured surface of broken rock is all connected. The diffusion distance of slurry increases approximately linearly with the increase of pressure difference, and the maximum diffusion distance is about 6.2 m. Meanwhile, the results of coring at 6 m around the grouting hole show that the fractured rock mass consolidated by the slurry can be clearly observed, which is consistent with the calculation results of the model.