## User Function Weertman Friction Law

**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 two 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 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`

.