Mechanism of inclined fracture slurry transport based on non⁃stable Bingham fluid

The determination of the penetration length of cement⁃based Bingham fluid slurry in inclined fractures influ⁃ ences directly the selection of grouting parameters. To calculate the penetration length of Bingham fluid grout，an im⁃ proved physical model of slurry layered filling is established based on the unstable characteristic of “slurry⁃water” separation during slurry transport，and the reliability of the layered filling assumption is verified by using the physical sim⁃ ulation method. Based on this model，the concepts of “effective spread radius” and “ineffective spread radius” are de⁃ veloped. The concept of “effective spread radius” and “ineffective spread radius” is proposed with the improved phys⁃ ical model of layered filling. A theoretical formula for the effective spread radius of Bingham fluid grout in roughly in⁃ clined fractures is derived using the improved physical model and the N-S equation，which considers the effects of four main control factors on the spread radius of the grout，the fracture dip，the fracture gap width，and the fracture roughness. The analytic solution of the “maximum effective spread radius” for the azimuth angle θ=90° of Bingham fluid grout was further derived，given that the values are usually used as the basis for design in grouting projects. To validate the reliability of the improved physical model of layered filling and the analytical solution of the “maximum ef⁃ fective spread radius ” at an azimuth angle of θ = 90°， it is compared with the conventional theoretical model and the calculated value of the “effective spread radius” is verified by using numerical simulations. To validate the re⁃ liability of the improved physical model of layered filling and the analytical solution of the “effective spread radius” at an azimuth angle of θ=90°，it is compared with the conventional theoretical model and numerical simulation models. Indoor grout spread test shows that the cement⁃based Bingham slurry transport does have the phenomenon of layered zoning transport，and the grout distribution on the plane can be divided into three zones:slurry mixing zone，layered spread zone，and layered grout front surface zone. This phenomenon is consistent with the numerical simulation in which the slurry has obvious density zoning phenomenon. The maximum effective spread radius in the fissure depends on the parameters of fissure width，grouting pressure difference，and fissure roughness at the time of last filling， rather than the initial values. Compared with the existing common models，the theoretical calculation of the “effective spread radius” of Bingham’ s fluid grout along the fracture direction is more consistent with the empirical values in grouting projects.