# HydroGeoSphere/Discrete Fractures (Variably-Saturated)

By default, all discrete fracture zones (and elements) in the domain will use a constitutive relationship based on the pseudo-soil relation, as developed by Huyakorn et al. [1994]. Essentially, in the pseudo soil relation, the medium is assigned a nodal saturation of 1 above the water table and 0 (zero) below it. Also by default, the effective area available for flow across the fracture-matrix interface is maintained at its maximum value, regardless of the state of fracture saturation.

## Default functional relationships

If you wish to use Van Genuchten or Brooks-Corey functions to describe the constitutive relationships you can do so using the instructions given in Section 5.8.3.4. Unless you modify them, the default values given in Table 5.13 will be used to define the functional relationships:
Table 5.13: Default Values for Functions Defining the Discrete Fracture Constitutive Relationships, for the Van Genuchten and Brooks-Corey models :
| Parameter | Value | Unit |
| Residual water saturation, $S_{wr}$ | 0.053 | - |
| Power index (alpha), ${\alpha }$ | 3.5237 | m$^{−1}$ |
| Power index (beta), ${\beta }$ | 3.1768 | - |
| Power index (gamma, computed), ${\gamma }$ | 1 - 1/${\beta }$ | - |
| Pore-connectivity, $l_{p}$ | 0.5 | - |
| Brooks-Corey exponent | 2/${\beta }$ + $l_{p}$ + 2 | - |

## Default tabular relationships

If you wish to use tables to describe the constitutive relationships you can do so using the instructions given in Section 5.8.3.5. Unless you modify them, the default values of water saturation versus pressure head and saturation versus relative permeability listed in Table 5.14 will be used to define the tabular relationships:
Table 5.14: Default Pressure-saturation and Saturation-relative permeability Tables for Variably-saturated Discrete Fractures :
| Pressure(m) ${\psi }$ | Saturation $S_{w}$ |
| -10.0 | 0.053 |
| 0.0 | 1.0 |
| Saturation $S_{w}$ | Relative permeability $k_{rw}$ |
| 0.053 | 0.053 |
| 1.0 | 1.0 |

## Modifying default relationships

If you wish to modify the default relationship between pressure, saturation and effective area you can do so using the instructions given below. For each instruction we will again indicate its scope (i.e. .grok, .fprops). Note that the functional relationships are always applied in a similar way to all fracture zones in the domain, while tabular relationships can vary from fracture zone to fracture zone if so desired.
The following instructions should be applied to discrete fractures, as discussed in Section 5.8.1:

## Effective area tables...end

Scope:.grok .fprops
Causes grok to use tables to describe the pressure-effective area relationship for the fracture and to begin reading a group of effective area table instructions until it encounters an End instruction.
By default values of contact area versus pressure head listed in Table 5.15 will be used:
Table 5.15: Default Pressure-Effective Area Table for Variably-saturated Discrete Fractured Media :
| Pressure(m) | Effective Area |
| 0.0 | 1.0 |
These instructions are available for modifying the default pressure-effective area relationship:

## Pressure-effective area

Scope: .grok .fprops
* pressure(1), effective area(1) First entry.
* pressure(2), effective area(2) Second entry.
       ...etc.
    n. pressure(n), effective area(n) nth entry.
    n+1. end The string 'end'
Causes HydroGeoSphere to begin reading instructions which describe the pressure-contact area table which will define the relationship for the fracture.
Paired values of pressure ${\psi }$ and effective area, which varies between 0 (full reduction) and 1 (no reduction), should be entered from lowest pressure (i.e. most negative) to highest pressure, usually zero. The last line of the table must be an end card, and the number of entries in the list are counted automatically to determine the table size.

## Effective area Wang-Narasimhan functions

Scope:.grok
Causes HydroGeoSphere to use the approach of Wang and Narasimhan [1985], as discussed in Section 4.1.4, for computing the pressure-effective area relationship for the fractures. These functions will automatically be applied to all fracture zones.