# Simulation of the Infiltration of Fractured Rock in the Unsaturated Zone
## 4 Results
### Infiltration Simulations  
For a fully water-saturated rock matrix, the velocity in stand-alone vertical fractures only depends on aperture and fluid availability. The maximum velocity observed in the simulations conducted with model TUFF2D in its 1.1 and 0.5-mm aperture fractures at the low rainfall intensity are 0.006 and 0.0029 m/s, respectively. At the high intensity, these velocities rise to 0.041 m/s and 0.020 m/s, but are still almost an order of magnitude lower than those predicted by the back-of-the-envelope calculations. Apart from the consideration of FMT, this difference arises because the numeric model also considers the multiphase fluid flow in the soil layer at its top while the back-of-the-envelope model assumes an unlimited fluid supply rate to each fracture.  
The velocity field of the fully water-saturated model is shown in Figure 15. The 1.1-mm aperture fractures become the preferential flow paths regardless of rainfall rate.  
Snapshots of an initially dry version of model TUFF2D, after three hours of low-intensity rainfall are shown in Figure 16a. This saturation map shows saturation jump discontinuities at the interface between the soil and the bedrock as well as between the fractures and the rock matrix. Water absorbs into 76% of the domain area. While the single-phase velocity analysis suggests that the wetting front might advance very quickly, at least in the cm-aperture fractures, the results for the initially dry system and the moderate rainfall intensity show a much reduced wetting front velocity. This is the effect of spontaneous imbibition of water into the rock matrix that dominates the behaviour of the system. The infiltrating water imbibes creating a large and smooth halo surrounding each fracture and there are hardly any aperture-related differences. While fracture water imbibes the matrix, matrix air drains out in a counter-current flow, rises upward, and discharges into the soil layer where the fracture terminates. Due to the limited rainwater supply, water saturation is higher in the 0.5-mm-wide fractures than in the mm-wide ones, which remain essentially air saturated. This difference is due also to the lower capillary pressure within the mm-wide fractures. Within each fracture, water and air move by counter-current flow, while the dry rock matrix rapidly absorbs most of the water expelling its air into the fracture. This composite behaviour explains the relative slowdown of the wetting front in the mm-wide fractures.  
Figure 15: Fracture flow velocity (m/s) in an initially fully water-saturated version of model TUFF2D. (**a**) low precipitation rate, and (**b**) high precipitation rate.  
For the high rainfall intensity (Case B), the front moves much faster through the initially dry model TUFF2D, reaching the same infiltration depth as in the low-intensity Case A in just 10 min Figure 17a. Now, the water penetrates the mm-wide fractures multiple times faster than the narrower ones. The wetted fracture matrix halos are correspondingly narrower spanning only about 35% of the total model area. At this early time in the evolution, less air has a chance to leak out into the soil layer through the fracture system.  
Figure 18 displays co- and counter-current flows in detail, revealing that the flow pattern is essentially the same for the 1.1 and 0.5-mm wide fractures: air and water move in the same direction ahead of the wetting front. Behind the wetting front counter-current flow of water and air occurs.  
Figure 16: Air distribution in model TUFF2D after three hours corresponding to a low precipitation rate scenario (case A). (**a**) low initial water saturation, (**b**) high initial water saturation.  
Figure 17: Air distribution in model TUFF2D after ten minutes corresponding to a high precipitation rate scenario (case B). (**a**) low initial water saturation, (**b**) high initial water saturation.