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## User Function Weertman Friction Law

### General Informations

• USF Fortran File: `USF_Sliding.f90`
• USF Name: `Sliding_Weertman`
• Required Input Variable(s): A `Flow Solution` in `Flow Solution Name`, `Normal Vector`

### General Description

The file `USF_Sliding.f90` contains user functions to apply non-linear friction at the base of glacier.

The first user function (`Sliding_Weertman`) is a non-linear Weertman-type friction law and is described in this page. The second user function (`Friction_Coulomb`) is a non-linear water pressure dependant friction law, as proposed by Schoof (2005) and Gagliardini et al. (2007), and is presented here. The third user function (`Sliding_Budd`) is described here and is from Budd et al 1984 (Annals of Glaciology 5, page 29-36).

The friction law in `Weertman_Sliding` is of the form:

The Slip Coefficient in Elmer is then given as

When , in the previous equation is replaced by (linearisation for small velocity).

The parameters to be given are:

• `Weertman Friction Coefficient`
• `Weertman Exponent`
• `Weertman Linear Velocity`

### SIF contents

The required keywords in the SIF file for this user function are:

```!!! Bedrock Boundary Condition
Boundary Condition 1
Target Boundaries = 1

Normal-Tangential Velocity = Logical True
Flow Force BC = Logical True

Velocity 1 = Real 0.0

Slip Coefficient 2 =  Variable Coordinate 1
Real Procedure "ElmerIceUSF" "Sliding_Weertman"
Slip Coefficient 3 =  Variable Coordinate 1
Real Procedure "ElmerIceUSF" "Sliding_Weertman"

Weertman Friction Coefficient = Real 2.412579e-2
Weertman Exponent = Real \$1.0/3.0
Weertman Linear Velocity = Real 0.00001

End
```

### Examples

The Weertman friction law is used in the tests `[ELMER_TRUNK]/elmerice/Tests/GL_MISMIP` and `[ELMER_TRUNK]/elmerice/Tests/Contact` and especially tested in `[ELMER_TRUNK]/elmerice/Tests/Friction_Weertman`.