Vector operator-based description of evolutional velocity field for water flow between rough fractures in granite under large compression-shear displacements

An accurate field description of fracture flow still presents a huge obstacle in flow mechanics. Unlike some classic flow models，i.e. parallel plate flow，focusing on the velocity distribution along the longitudinal section of the fracture，very little attention is paid to the velocity distribution within the fracture cross-section. The spatial distribution of fracture aperture indicates a geometric field，which significantly impacts the flow velocity distribution within the cross-section，while lacking proper correlation models induces a difficult understanding of statistical analysis of geometric field's effect on fracture flow distribution. To solve the challenge of carrying out a seepage test with relative compression or shear displacement exceeding 5% in lab，the Reynolds equation-based discrete solution of fracture flow considering the large shear-compression displacements for Beishan granite is made，and through the gradient of seepage rate and velocity divergence，the differential characterization of the seepage field's field function was achieved. For the same group of cracks，three fields of flow velocity，gradient and divergence presents a consistent spatial geometric distribution under different shear or compression displacements and nearly all fields conform to the normal distribution. In addition，with the increase in closed aperture and contact area，the full-scale fracture flow turns into local-scale flow and two vector operators of gradient and divergence describing the evolutional distribution of fracture flow are still effective. The results show that in the statistical sense，under low-permeability conditions，a rough fracture flow，characterized by the average gradient and the average divergence of the flow velocity field tend towards 0，can be equivalently treated as uniform flat plate flow with low velocity.