# Simulation of the Infiltration of Fractured Rock in the Unsaturated Zone
## 4 Results
### Hand Calculations of Infiltration Front Velocity  
The parallel plate law (Equation (13)) gives an average wetting front velocity of 0.01 m/s in a fracture with a uniform aperture of 0.1 mm, 0.2 m/s for an aperture of 0.5 mm, and 90 m/s for a 1-cm aperture fracture. All these values are for gravity-driven laminar flow of water displacing air, and ignoring capillary effects. To create an approximate multi-fracture model of the Tiva Canyon Tuff, the fracture aperture-frequency distribution (Figure 4), fitting the powerlaw,  
\[f=37.2824\ a^{-1.5715} \tag{14}\]  
is sampled at the aperture values 0.125, 0.25, 0.5, 1, 2, 4, 8 and 16 mm, yielding a total of 1475 vertical fractures. The fluid supply rate or volume of finite fluid reservoir at the top of the model connecting all the fractures depends on fracture and rainfall intensity. Taken the well-studied Yucca Mountain as an example ([PERSON] et al. (2016)), fracture intensity has been measured in outcrops and underground workings using the cumulative fracture length per area measure (P21, [PERSON] (2017)). The obtained background P21 \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Soil & \\ \hline Porosity (-) & 0.28 \\ Permeability (D) & 100 \\ Relative permeability mode (-) & Mixed model \\ Brooks-Corey parameter (-) & 1.1 \\ van Genuchten parameter (-) & 0.8 \\ Entry pressure (Pa) & 100 \\ \hline Matrix & \\ \hline Porosity (-) & 0.25 \\ Permeability (D) & 0.3 \\ Relative permeability model (-) & Mixed model \\ Brooks-Corey parameter (-) & 1.1 \\ van Genuchten parameter (-) & 0.8 \\ Entry pressure (Pa) & 24,400 \\ \hline Fracture & \\ \hline Porosity (-) & 1.0 \\ Average aperture (mm) & 0.5 \\ Minimun aperture (mm) & 0.091 \\ Maximum aperture (mm) & 0.91 \\ Permeability (D) & cubic law \\ Relative permeability model (-) & van Genuchten \\ van Genuchten parameter (-) & 0.2 \\ Entry pressure (Pa) & 1000 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameterisation of 3D fractured tuff models TUFF3D and TUFF3D-VA.  
value is 0.1 and the maximum intensity lies around 2, translating into model surface areas of 14,749 and 737 m\({}^{2}\), respectively. Corresponding fluid volumes depend on the thickness and porosity of the sandy soil layer. Assuming a 10-cm thickness and 40% porosity, the volumes for the different fracture densities are 590 and 29.5 m\({}^{3}\). Maximum precipitation rates at Yuca Mountain determined for 10-min rainstorm intervals range up to 73 mm/h ([PERSON] et al. [78]). Integrated over the top surface of this model these translate into peak rates of 0.3 (P21 = 0.1) and 0.015 m\({}^{3}\)/s (P21 = 2). In the aperture-statistics based multi-fracture model, wider, \(\geq\)3-mm-aperture fractures determine the transport capacity in spite of their relatively rare occurrence. The maximum rate at which water can infiltrate is 0.0016 m\({}^{3}\)/s. This means that the amount of water needed to saturate the fracture network was available at the historic peak precipitation rate irrespective of fracture intensity. An excess volume of fluid would have been available where surface runoff collects into depressions, canyons or washes. These back-of-the-envelope calculations further suggest that due to the very small fracture porosity of the modelled system (\(\leq\)10\({}^{-6}\)) and amplified by preferential flow in the larger fractures, drainage of the fully water saturated soil layer downward into the fractures would support the \(\geq\)100-m-deep infiltration of \(\geq\)1-cm aperture fractures. For these calculations to be applicable, flowing fractures would need to become fully saturated, flow would have to remain laminar, and imbibition of the rock matrix should not occur. Inducing peak fracture flow velocities of metres per second, a multi-hour rainfall event might even provoke penetration down to the base of the vadose zone. Yet this is just a simplistic back-of-the-envelope calculation for idealised vertical fractures.