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

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 , in the previous equation 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 →

The effective pressure where is the normal Cauchy stress and the water pressure. Here, at time t+dt, the normal Cauchy stress is estimated from the stress computed at time t. The water pressure is prescribed as an *External Pressure* (Positive - Compressive convention).

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 !! Water pressure given through this parameter (Positive = Compressive) External Pressure = Equals Water Pressure 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 End

An example of the usage of the user function *Friction_Weertman* TODO

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.