Flow Characteristics in a 3D-Printed Rough Fracture

Based on the 3D-printing technique, totally 44 transparent specimens each containing a single fracture with 4 types of aperture and 11 types of roughness are designed and printed in this study. To perform the seepage test for these printed single fractures, an apparatus is designed and successfully manufactured to measure the water flux and the hydraulic gradient of seepage. Using the designed equipment, a series of seepage tests are conducted for the 44 3D-printed specimens. It is confirmed by the test results that the flow speed of seepage and the hydraulic gradient can always be mathematically described by the Forchheimer equation (I = Au + Bu2), regardless of the aperture and the roughness of fractures; and that the linear drag coefficient A and the nonlinear drag coefficient B in the Forchheimer equation are significantly affected by the aperture and roughness of fractures. As for the smooth fracture, the traditional cubic law is merely applicable to the situation in which the hydraulic gradient I < 0.01. Based on these experimental results, a new set of formulations illustrating the relationship between the linear drag coefficient A, the nonlinear drag coefficient B and the aperture e, the roughness JRC of fractures is firstly established in this study. Finally, adopting the method of solving the Navier–Stokes equation, the seepage process in single rough fractures is numerically investigated. The comparative analysis shows that the numerical result agrees quite well with the experimental results. Most importantly, the numerical results can clearly reveal that there are typical boundary layers close to the two walls of fractures in the process of seeping; and the velocity and pressure fields in fractures also can be observed intuitively from the numerical results. Summarily, it is recognized that the numerical method is a reliable and feasible method to study the seepage in fractures, and is a beneficial complement to the laboratory tests.