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## User Function Coulomb Friction Law

### General Informations

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

### 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 here. 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 in this page.

The friction law in Friction_Coulomb is of the form: where and The Slip Coefficient in Elmer is then given as When , \$u_b\$ in the previous is replaced by .

The parameters to be given are:

• Friction Law Sliding Coefficient → • Friction Law Post-Peak Exponent → • Friction Law Maximum Value → ~ max bed slope
• Friction Law Exponent → m = (n Glen's law)
• Friction Law 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 "./USF_Sliding" "Friction_Coulomb"
Slip Coefficient 3 =  Variable Coordinate 1
Real Procedure "./USF_Sliding" "Friction_Coulomb"

!! Parameters needed for the Coulomb Friction Law
Friction Law Sliding Coefficient = Real 4.1613e5
Friction Law Post-Peak Exponent  = Real 1.0      !(q=1)
Friction Law Maximum Value = Real 1.0            !(C=1)
Friction Law PowerLaw Exponent = Real 3.0        !(m = n = 3 Glen's law)
Friction Law Linear Velocity = Real 0.01         !(=1m/a dans un premier temps)
End```

### Examples

An example of the usage of the user function Friction_Weertman TODO

### Reference

When this friction law is used, it can be cited using the following reference:
Gagliardini O., D. Cohen, P. Råback and T. Zwinger, 2007. Finite-Element Modeling of Subglacial Cavities and Related Friction Law. J. of Geophys. Res., Earth Surface, 112, F02027. 